Finite Group Databasebeta

← #31763671

Subgroups — #31763671

Order 17152.

6518 conjugacy classes of subgroups.

The subgroup lattice has 2068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574715C211yesmaximal, characteristic, complemented
2#22574711C212yesmaximal, complemented
3#22574702C211yesmaximal, characteristic, complemented
4#22574696C212yesmaximal, complemented
5#22574689C212yesmaximal, complemented
6#22574679C212yesmaximal, complemented
7#22574672C212yesmaximal, complemented
8#22574656C214yesmaximal, complemented
9#22574643C214yesmaximal, complemented
10#22574617C212yesmaximal, complemented
11#22574603C211yesmaximal, characteristic, complemented
12#22574501C214yesmaximal, complemented
13#22574493C214yesmaximal, complemented
14#22574355C214yesmaximal, complemented
15#22573823C214yesmaximal, complemented
16#22573805C212yesmaximal, complemented
17#22573801C212yesmaximal, complemented
18#22573791C212yesmaximal, complemented
19#22573788C212yesmaximal, complemented
20#22573639C214yesmaximal, complemented
21#22573635C214yesmaximal, complemented
22#22573600C211yesmaximal, characteristic, complemented
23#22573596C212yesmaximal, complemented
24#22573593C211yesmaximal, characteristic, complemented
25#22573503C212yesmaximal, complemented
26#533×D67C211yesmaximal, characteristic, complemented
27C67×#3557C211yesmaximal, characteristic, complemented
28C67⋊#564C2214yescomplemented
29#16864150C2214yes—
30#16864148C2214yes—
31#16864148C2214yescomplemented
32#16864148C2214yescomplemented
33#16864148C2214yescomplemented
34#16864147C2214yes—
35#16864147C2214yescomplemented
36#16864145C2214yes—
37#16864145C2214yescomplemented
38#16864143C2214yes—
39#16864143C2214yescomplemented
40#16864142C2214yes—
41#16864142C2214yes—
42#16864140C2214yes—
43#16864131C2212yescomplemented
44#16864129C2212yescomplemented
45#16864129C2212yescomplemented
46#16864128C2212yescomplemented
47#16864128C2212yescomplemented
48Q8×Dic134C2212yescomplemented
49#16864126C2212yescomplemented
50#16864124C2212yescomplemented
51#16864124C2212yescomplemented
52#16864123C2214yescomplemented
53#16864123C2212yescomplemented
54#16864123C2212yescomplemented
55#16864122C2212yescomplemented
56#16864122C2212yescomplemented
57#16864121C2212yescomplemented
58#16864119C2212yescomplemented
59#16864118C2214yes—
60#16864118C2212yescomplemented
61#16864118C2212yescomplemented
62#16864115C2212yescomplemented
63#16864115C2212yescomplemented
64#16864113C2214yes—
65#16864113C2214yescomplemented
66#16864106C2214yes—
67#16864106C2212yescomplemented
68#16864105C2212yescomplemented
69#16864105C2212yescomplemented
70#16864102C2214yes—
71#16864102C2214yes—
72#16864102C2212yescomplemented
73#16864102C2212yescomplemented
74#16864101C2214yes—
75#16864100C2214yes—
76#16864100C2214yes—
77#16864097C2214yes—
78#16864097C2214yes—
79#16864096C2214yes—
80#16864091C2214yes—
81#16864091C2214yes—
82#16864090C2214yes—
83#16864085C2214yescomplemented
84#16864079C2214yes—
85#16864079C2214yescomplemented
86#16864078C2214yes—
87#16864078C2214yescomplemented
88#16864067C2212yescomplemented
89#16864066C2212yescomplemented
90D4×Dic134C2212yescomplemented
91#16864061C2214yes—
92#16864061C2212yescomplemented
93#16864059C2214yes—
94#16864059C2214yescomplemented
95#16864056C2214yes—
96#16864056C2214yes—
97#16864055C2214yes—
98#16864054C2214yes—
99#16864047C2214yes—
100#16864044C2214yes—
101#16864044C2214yescomplemented
102#16864025C2214yescomplemented
103#16864023C2214yescomplemented
104#16864020C2212yes—
105#16864019C2212yes—
106#16864018C2212yes—
107#16864017C2212yes—
108#16864016C2214yes—
109#16864016C2214yescomplemented
110#16864015C2212yes—
111#16864014C2214yes—
112#16864014C2214yes—
113#16864013C2212yes—
114#16864011C2212yes—
115#16864011C2214yes—
116#16864010C2214yes—
117#16864010C2214yescomplemented
118#16864009C2211yescharacteristic
119#16864008C2211yescharacteristic
120#16864008C2214yescomplemented
121#16864007C2211yescharacteristic
122#16864006C2212yes—
123#16864005C2214yescomplemented
124#16864005C2214yescomplemented
125#16864004C2212yes—
126#16864004C2214yescomplemented
127#16864003C2214yes—
128#16864003C2214yes—
129#16864003C2214yescomplemented
130#16864003C2214yescomplemented
131#16864002C2211yescharacteristic
132#16864001C2211yescharacteristic
133#16864000C2211yescharacteristic
134#16863999C2212yes—
135#16863997C2212yes—
136#16863994C2214yes—
137#16863993C2214yescomplemented
138#16863992C2214yes—
139#16863992C2214yes—
140#16863992C2214yescomplemented
141#16863989C2214yes—
142#16863989C2214yes—
143#16863989C2214yescomplemented
144#16863988C2214yes—
145#16863988C2214yescomplemented
146#16863987C2214yes—
147#16863985C2214yes—
148#16863982C2214yes—
149#16863980C2214yes—
150#16863978C2214yes—
151#16863975C2214yes—
152#16863973C2214yes—
153#16863969C2214yescomplemented
154#16863968C2214yes—
155#16863968C2214yescomplemented
156#16863966C2214yes—
157#16863953C2211yescharacteristic
158#16863952C2211yescharacteristic
159#16863952C2211yescharacteristic
160#16863952C2212yes—
161#16863952C2212yes—
162#16863952C2214yescomplemented
163#16863952C2214yescomplemented
164#16863951C2212yes—
165#16863951C2212yes—
166#16863951C2214yescomplemented
167#16863950C2212yes—
168#16863950C2212yes—
169#16863950C2212yes—
170#16863949C2211yescharacteristic
171#16863949C2211yescharacteristic
172#16863948C2212yes—
173#16863948C2212yes—
174#16863948C2212yes—
175#16863948C2214yescomplemented
176#16863948C2214yescomplemented
177#16863948C2214yescomplemented
178#16863947C2211yescharacteristic
179#16863945C2212yes—
180#16863945C2212yes—
181#16863944C2211yescharacteristic
182#16863943C2212yes—
183#16863941C2212yes—
184C4⋊Q8×D67C2212yes—
185#16863932C2214yes—
186#16863932C2214yescomplemented
187#16863931C2214yes—
188#16863931C2212yes—
189#16863930C2212yes—
190#16863929C2214yes—
191#16863929C2214yes—
192#16863929C2214yes—
193#16863929C2214yes—
194#16863929C2214yescomplemented
195#16863929C2214yescomplemented
196#16863927C2214yes—
197#16863925C2214yes—
198#16863925C2212yes—
199#16863925C2214yescomplemented
200#16863924C2214yes—
201#16863923C2214yes—
202#16863923C2214yes—
203#16863923C2214yes—
204#16863923C2214yescomplemented
205#16863923C2214yescomplemented
206#125×D67C2212yes—
207#16863909C2212yes—
208#16863906C2212yes—
209#16863905C2214yes—
210#16863904C2214yes—
211C22⋊Q8×D67C2212yes—
212C22⋊Q8×D67C2212yes—
213C4×#11761629C2212yes—
214C4×#11761629C2212yes—
215C4×#11761629C2212yes—
216#16863864C2214yes—
217#16863864C2214yescomplemented
218C4×#11761627C2212yes—
219C4×#11761627C2212yes—
220C4×#11761627C2214yes—
221C4×#11761627C2212yes—
222C4×#11761627C2214yescomplemented
223C2×#14524008C2214yescomplemented
224C4×Q8×D67C2212yes—
225C4×Q8×D67C2212yes—
226C4×Q8×D67C2214yescomplemented
227#117×D67C2211yescharacteristic
228#117×D67C2211yescharacteristic
229C2×C42×D67C2211yescharacteristic
230#563×C67C2214yescomplemented
231#559×C67C2212yescomplemented
232#557×C67C2212yescomplemented
233#556×C67C2212yescomplemented
234#554×C67C2212yescomplemented
235#552×C67C2214yescomplemented
236#542×C67C2212yes—
237#542×C67C2214yes—
238#541×C67C2211yescharacteristic
239#540×C67C2211yescharacteristic
240#539×C67C2214yes—
241#533×C67C2211yescharacteristic
242#529×C67C2212yes—
243C2×#11761629C2312yes—
244C2×#11761628C2314yes—
245C2×#11761628C2314yes—
246C2×#11761627C2312yes—
247C2×#11761627C2314yes—
248C2×#11761627C2314yes—
249C22×Dic134C2314yes—
250C2×Q8×D67C2312yes—
251C2×Q8×D67C2312yes—
252C2×Q8×D67C2314yes—
253C22×C4×D67C2311yescharacteristic
254C22×C4×D67C2312yes—
255#14524043C2311yescharacteristic
256#14524043C2314yes—
257#14524043C2312yes—
258#14524043C2312yes—
259#14524042C2314yes—
260#14524042C2314yes—
261#14524042C2312yes—
262#14524042C2314yes—
263#14524042C2312yes—
264#14524042C2314yes—
265#14524042C2312yes—
266#14524042C2314yes—
267#14524042C2314yes—
268#14524042C2314yes—
269#14524042C2312yes—
270#14524042C2312yes—
271#14524042C2312yes—
272#14524042C2312yes—
273#14524042C2312yes—
274#14524041C2312yes—
275#14524041C2314yes—
276#14524041C2314yes—
277#14524041C2312yes—
278#14524041C2314yes—
279#14524041C2312yes—
280#14524041C2312yes—
281#14524040C2311yescharacteristic
282#14524039C2312yes—
283#14524039C2312yes—
284#14524038C2314yes—
285#14524038C2314yes—
286#14524038C2314yes—
287#14524038C2314yes—
288#14524038C2314yes—
289#14524038C2314yes—
290#14524038C2314yes—
291#14524038C2314yes—
292#14524038C2314yes—
293#14524038C2314yes—
294#14524038C2314yes—
295#14524037C2314yes—
296#14524037C2314yes—
297#14524037C2314yes—
298#14524037C2314yes—
299#14524037C2314yes—
300#14524036C2314yes—
301#14524036C2314yes—
302#14524036C2314yes—
303#14524036C2314yes—
304#14524036C2314yes—
305#14524036C2314yes—
306#14524036C2314yes—
307#14524036C2314yes—
308#14524036C2314yes—
309#14524036C2314yes—
310#14524036C2314yes—
311#14524035C2311yescharacteristic
312#14524035C2311yescharacteristic
313#14524035C2314yes—
314#14524035C2314yes—
315#14524035C2314yes—
316#14524035C2314yes—
317#14524035C2312yes—
318#14524035C2312yes—
319#14524034C2314yes—
320#14524034C2314yes—
321#14524034C2314yes—
322#14524034C2312yes—
323#14524034C2314yes—
324#14524034C2314yes—
325#14524034C2312yes—
326#14524034C2312yes—
327#14524034C2312yes—
328#14524033C2314yes—
329#14524033C2314yes—
330#14524033C2314yes—
331#14524033C2314yes—
332#14524033C2314yes—
333#14524033C2314yes—
334#14524033C2314yes—
335#14524033C2312yes—
336#14524033C2314yes—
337#14524033C2314yes—
338#14524033C2314yes—
339#14524033C2312yes—
340#14524033C2314yes—
341#14524033C2312yes—
342#14524033C2314yes—
343#14524033C2314yes—
344#14524033C2314yes—
345#14524033C2312yes—
346#14524033C2314yes—
347#14524033C2314yes—
348#14524032C2314yes—
349#14524032C2312yes—
350#14524032C2314yes—
351#14524031C2312yes—
352#14524031C2314yes—
353#14524031C2312yes—
354#14524030C2314yes—
355#14524030C2312yes—
356#14524029C2314yes—
357#14524029C2314yes—
358#14524029C2314yes—
359#14524029C2314yes—
360#14524029C2314yes—
361#14524029C2314yes—
362#14524029C2314yes—
363#14524029C2314yes—
364#14524029C2314yes—
365#14524029C2314yes—
366#14524028C2314yes—
367#14524028C2314yes—
368#14524028C2314yes—
369#14524028C2314yes—
370#14524028C2314yes—
371#14524028C2314yes—
372#14524028C2314yes—
373#14524028C2314yes—
374#14524027C2314yes—
375#14524027C2314yes—
376#14524027C2314yes—
377#14524027C2314yes—
378#14524026C2314yes—
379#14524026C2314yes—
380#14524026C2314yes—
381#14524026C2314yes—
382#14524026C2314yes—
383#14524025C2314yes—
384#14524025C2314yes—
385#14524025C2314yes—
386#14524025C2314yes—
387#14524025C2314yes—
388#14524025C2314yes—
389#14524025C2314yes—
390#14524025C2314yes—
391#14524025C2314yes—
392#14524025C2314yes—
393#14524024C2314yes—
394#14524024C2314yes—
395#14524023C2312yes—
396#14524023C2314yes—
397#14524023C2314yes—
398#14524023C2314yes—
399#14524023C2314yes—
400#14524023C2312yes—
401#14524023C2312yes—
402#14524022C2312yes—
403#14524022C2314yes—
404#14524022C2314yes—
405#14524022C2312yes—
406#14524022C2314yes—
407#14524022C2312yes—
408#14524022C2314yes—
409#14524021C2314yes—
410#14524021C2314yes—
411#14524021C2314yes—
412#14524021C2314yes—
413#14524021C2314yes—
414#14524021C2314yes—
415#14524021C2314yes—
416#14524021C2314yes—
417#14524021C2314yes—
418#14524021C2314yes—
419#14524021C2314yes—
420#14524021C2314yes—
421#14524021C2312yes—
422#14524021C2312yes—
423#14524021C2312yes—
424#14524021C2312yes—
425#14524021C2314yes—
426#14524021C2314yes—
427#14524021C2314yes—
428#14524021C2314yes—
429#14524021C2314yes—
430#14524020C2312yes—
431#14524020C2312yes—
432#14524020C2314yes—
433#14524020C2314yes—
434#14524020C2314yes—
435#14524020C2314yes—
436#14524020C2314yes—
437#14524020C2312yes—
438#14524020C2314yes—
439#14524020C2314yes—
440#14524020C2314yes—
441#14524020C2314yes—
442#14524020C2312yes—
443#14524020C2314yes—
444#14524020C2314yes—
445#14524019C2312yes—
446#14524019C2314yes—
447#14524019C2314yes—
448#14524019C2314yes—
449#14524019C2314yes—
450#14524019C2314yes—
451#14524019C2312yes—
452#14524019C2312yes—
453#14524018C2312yes—
454#14524018C2314yes—
455#14524018C2314yes—
456#14524017C2312yes—
457#14524017C2314yes—
458#14524017C2314yes—
459#14524016C2314yes—
460#14524016C2314yes—
461#14524016C2314yes—
462#14524016C2314yes—
463#14524016C2314yes—
464#14524016C2314yes—
465#14524016C2314yes—
466#14524016C2314yes—
467#14524016C2314yes—
468#14524015C2314yes—
469#14524015C2314yes—
470#14524015C2314yes—
471#14524015C2314yes—
472#14524015C2314yes—
473#14524014C2312yes—
474#14524014C2314yes—
475#14524014C2314yes—
476#14524014C2314yes—
477#14524013C2314yes—
478#14524011C2314yes—
479Q8×Dic67C2312yes—
480Q8×Dic67C2312yes—
481Q8×Dic67C2312yes—
482Q8×Dic67C2312yes—
483Q8×Dic67C2314yes—
484Q8×Dic67C2312yes—
485C4×Dic134C2314yes—
486C4×Dic134C2314yes—
487C4×Dic134C2314yes—
488C4×Dic134C2314yes—
489C4×Dic134C2312yes—
490C4×Dic134C2312yes—
491C4×Dic134C2314yes—
492C4×Dic134C2312yes—
493C4×Dic134C2312yes—
494C4×Dic134C2312yes—
495C4×Dic134C2312yes—
496C4×Dic134C2312yes—
497C4×Dic134C2312yes—
498C4×Dic134C2312yes—
499#14524008C2314yes—
500#14524008C2314yes—
501#14524008C2314yes—
502#14524008C2314yes—
503#14524008C2314yes—
504#14524008C2312yes—
505#14524008C2312yes—
506#14524008C2314yes—
507#14524008C2312yes—
508#14524008C2312yes—
509#14524008C2312yes—
510#14524008C2312yes—
511#14524008C2312yes—
512#14524008C2312yes—
513#14524008C2314yes—
514#14524008C2314yes—
515#14524008C2314yes—
516#14524008C2314yes—
517#14524008C2312yes—
518#14524008C2314yes—
519C4×D268C2312yes—
520C4×D268C2312yes—
521C4×D268C2314yes—
522C4×D268C2314yes—
523C4×D268C2314yes—
524C4×D268C2312yes—
525D4×Dic67C2312yes—
526D4×Dic67C2312yes—
527D4×Dic67C2312yes—
528D4×Dic67C2314yes—
529D4×Dic67C2314yes—
530#14524005C2312yes—
531#14524005C2312yes—
532#14524005C2314yes—
533#14524005C2314yes—
534#14524005C2314yes—
535#14524005C2314yes—
536#14524005C2314yes—
537#14524005C2312yes—
538#14524005C2314yes—
539#14524005C2314yes—
540C4×C22⋊D67C2314yes—
541C4×C22⋊D67C2314yes—
542C4×C22⋊D67C2314yes—
543C4×C22⋊D67C2314yes—
544C4×C22⋊D67C2314yes—
545C4×C22⋊D67C2314yes—
546C4×C22⋊D67C2314yes—
547(C22⋊D67)⋊C4C2314yes—
548(C22⋊D67)⋊C4C2314yes—
549(C22⋊D67)⋊C4C2314yes—
550(C22⋊D67)⋊C4C2314yes—
551(C22⋊D67)⋊C4C2314yes—
552(C22⋊D67)⋊C4C2314yes—
553(C22⋊D67)⋊C4C2314yes—
554(C22⋊D67)⋊C4C2314yes—
555(C22⋊D67)⋊C4C2314yes—
556(C22⋊D67)⋊C4C2314yes—
557(C22⋊D67)⋊C4C2314yes—
558(C22⋊D67)⋊C4C2314yes—
559(C22⋊D67)⋊C4C2314yes—
560#14524002C2311yescharacteristic
561#14524002C2311yescharacteristic
562#14524001C2314yes—
563#14524001C2314yes—
564#14524001C2312yes—
565#14524001C2312yes—
566#14524001C2312yes—
567#14524001C2312yes—
568#14524001C2314yes—
569#14524001C2314yes—
570#14524001C2314yes—
571#14524000C2311yescharacteristic
572#14524000C2311yescharacteristic
573#14524000C2312yes—
574#14524000C2314yes—
575#14524000C2314yes—
576#14524000C2314yes—
577#14524000C2314yes—
578#14523999C2314yes—
579#14523999C2314yes—
580#14523999C2314yes—
581#14523999C2314yes—
582#14523999C2311yescharacteristic
583#14523999C2311yescharacteristic
584#14523999C2312yes—
585#14523999C2314yes—
586#14523999C2314yes—
587#14523999C2314yes—
588C2×Dic67⋊C4C2314yes—
589C2×Dic67⋊C4C2314yes—
590C4⋊C4×D67C2314yes—
591C4⋊C4×D67C2314yes—
592C4⋊C4×D67C2314yes—
593C4⋊C4×D67C2312yes—
594C4⋊C4×D67C2312yes—
595C4⋊C4×D67C2312yes—
596C4⋊C4×D67C2312yes—
597C4⋊C4×D67C2312yes—
598C4⋊C4×D67C2312yes—
599C4⋊C4×D67C2312yes—
600C4⋊C4×D67C2312yes—
601C22⋊C4×D67C2312yes—
602C22⋊C4×D67C2311yescharacteristic
603C22⋊C4×D67C2311yescharacteristic
604C2×C4×Dic67C2312yes—
605C2×C4×Dic67C2311yescharacteristic
606C2×C4×Dic67C2314yes—
607C2×C4×Dic67C2314yes—
608C2×C4×Dic67C2314yes—
609C42×D67C2312yes—
610C42×D67C2311yescharacteristic
611C42×D67C2311yescharacteristic
612C42×D67C2312yes—
613C42×D67C2311yescharacteristic
614C42×D67C2311yescharacteristic
615C42×D67C2311yescharacteristic
616C42×D67C2312yes—
617C42×D67C2311yescharacteristic
618C42×D67C2314yes—
619C42×D67C2314yes—
620C42×D67C2314yes—
621C4⋊Q8×C67C2311yescharacteristic
622C4⋊Q8×C67C2312yes—
623C4⋊Q8×C67C2314yes—
624C4⋊Q8×C67C2312yes—
625#127×C67C2311yescharacteristic
626#126×C67C2314yes—
627#126×C67C2314yes—
628#126×C67C2314yes—
629#126×C67C2314yes—
630#126×C67C2314yes—
631#125×C67C2311yescharacteristic
632#125×C67C2314yes—
633#125×C67C2314yes—
634#125×C67C2311yescharacteristic
635#125×C67C2312yes—
636#125×C67C2312yes—
637#125×C67C2314yes—
638#124×C67C2314yes—
639#124×C67C2314yes—
640#124×C67C2312yes—
641#124×C67C2312yes—
642#123×C67C2314yes—
643#123×C67C2314yes—
644#123×C67C2314yes—
645#123×C67C2314yes—
646#123×C67C2314yes—
647C22⋊Q8×C67C2312yes—
648C22⋊Q8×C67C2312yes—
649C22⋊Q8×C67C2314yes—
650C22⋊Q8×C67C2314yes—
651C22⋊Q8×C67C2314yes—
652C22⋊Q8×C67C2314yes—
653C22⋊Q8×C67C2312yes—
654C22⋊Q8×C67C2314yes—
655#121×C67C2312yes—
656#121×C67C2314yes—
657C4×Q8×C67C2312yes—
658C4×Q8×C67C2314yes—
659C4×Q8×C67C2312yes—
660C4×Q8×C67C2312yes—
661C4×Q8×C67C2312yes—
662C4×Q8×C67C2312yes—
663C4×D4×C67C2312yes—
664C4×D4×C67C2314yes—
665C4×D4×C67C2314yes—
666C4×D4×C67C2312yes—
667C4×D4×C67C2312yes—
668#117×C67C2311yescharacteristic
669#117×C67C2314yes—
670#117×C67C2311yescharacteristic
671#117×C67C2314yes—
672C2×C4⋊C4×C67C2314yes—
673C2×C42×C67C2311yescharacteristic
674C23×D67C2411yescharacteristic
675#11761629—28no—
676#11761628—48no—
677#11761628—48no—
678#11761627—28no—
679#11761627—48no—
680#11761627—48no—
681C2×Dic134—48no—
682C2×Dic134C2412yes—
683C2×Dic134C2412yes—
684C2×Dic134C2414yes—
685C2×Dic134C2412yes—
686C2×Dic134C2412yes—
687C2×Dic134C2412yes—
688C2×Dic134C2414yes—
689C2×Dic134C2414yes—
690C2×Dic134C2412yes—
691C2×Dic134C2412yes—
692C2×Dic134C2414yes—
693C2×Dic134C2414yes—
694Q8×D67—48no—
695Q8×D67—44no—
696Q8×D67—44no—
697C2×D268C2414yes—
698C2×D268C2412yes—
699C2×D268C2414yes—
700C2×D268C2414yes—
701C2×C22⋊D67C2414yes—
702C2×C22⋊D67C2414yes—
703C2×C22⋊D67C2414yes—
704C2×C22⋊D67C2414yes—
705C2×C22⋊D67C2414yes—
706C2×C22⋊D67C2414yes—
707C2×C22⋊D67C2414yes—
708C22×Dic67C2414yes—
709C22×Dic67C2411yescharacteristic
710C22×Dic67C2412yes—
711C22×Dic67C2414yes—
712C22×Dic67C2414yes—
713C22×Dic67C2414yes—
714C2×C4×D67—24no—
715C2×C4×D67—44no—
716C2×C4×D67C2414yes—
717C2×C4×D67C2411yescharacteristic
718C2×C4×D67C2412yes—
719C2×C4×D67C2411yescharacteristic
720C2×C4×D67C2412yes—
721C2×C4×D67C2411yescharacteristic
722C2×C4×D67C2414yes—
723C2×C4×D67C2412yes—
724C2×C4×D67C2412yes—
725C2×C4×D67C2412yes—
726C2×C4×D67C2412yes—
727C2×C4×D67C2412yes—
728C2×C4×D67C2412yes—
729C2×C4×D67C2414yes—
730C2×C4×D67C2414yes—
731C2×C4×D67C2414yes—
732C2×C4×D67C2414yes—
733C2×C4×D67C2414yes—
734C2×C4×D67C2411yescharacteristic
735C4⋊Dic67C2412yes—
736C4⋊Dic67C2412yes—
737C4⋊Dic67C2412yes—
738C4⋊Dic67C2414yes—
739C4⋊Dic67C2412yes—
740C4⋊Dic67C2414yes—
741C4⋊Dic67C2414yes—
742C4⋊Dic67C2412yes—
743C4⋊Dic67C2412yes—
744C4⋊Dic67C2412yes—
745C4⋊Dic67C2412yes—
746C4⋊Dic67C2412yes—
747C4⋊Dic67C2412yes—
748C4⋊Dic67C2414yes—
749C4⋊Dic67C2414yes—
750C4⋊Dic67C2414yes—
751C4⋊Dic67C2414yes—
752C4⋊Dic67C2414yes—
753Dic67⋊C4C2412yes—
754Dic67⋊C4C2412yes—
755Dic67⋊C4C2412yes—
756Dic67⋊C4C2412yes—
757Dic67⋊C4C2414yes—
758Dic67⋊C4C2414yes—
759Dic67⋊C4C2412yes—
760Dic67⋊C4C2412yes—
761Dic67⋊C4C2412yes—
762Dic67⋊C4C2412yes—
763Dic67⋊C4C2412yes—
764Dic67⋊C4C2412yes—
765Dic67⋊C4C2412yes—
766Dic67⋊C4C2412yes—
767Dic67⋊C4C2412yes—
768Dic67⋊C4C2414yes—
769Dic67⋊C4C2412yes—
770Dic67⋊C4C2412yes—
771Dic67⋊C4C2412yes—
772Dic67⋊C4C2414yes—
773Dic67⋊C4C2414yes—
774Dic67⋊C4C2414yes—
775Dic67⋊C4C2414yes—
776Dic67⋊C4C2414yes—
777Dic67⋊C4C2414yes—
778Dic67⋊C4C2414yes—
779Dic67⋊C4C2414yes—
780Dic67⋊C4C2414yes—
781Dic67⋊C4C2414yes—
782Dic67⋊C4C2414yes—
783Dic67⋊C4C2414yes—
784Dic67⋊C4C2414yes—
785Dic67⋊C4C2414yes—
786Dic67⋊C4C2414yes—
787Dic67⋊C4C2414yes—
788Dic67⋊C4C2414yes—
789Dic67⋊C4C2414yes—
790Dic67⋊C4C2414yes—
791C22⋊Dic67C2411yescharacteristic
792C22⋊Dic67C2411yescharacteristic
793C22⋊Dic67C2412yes—
794C22⋊Dic67C2414yes—
795C22⋊Dic67C2414yes—
796C22⋊Dic67C2414yes—
797C22⋊Dic67C2414yes—
798C22⋊Dic67C2414yes—
799C22⋊Dic67C2414yes—
800C22⋊Dic67C2414yes—
801(C2×D67)⋊C4C2412yes—
802(C2×D67)⋊C4C2412yes—
803(C2×D67)⋊C4C2412yes—
804(C2×D67)⋊C4C2412yes—
805(C2×D67)⋊C4C2414yes—
806(C2×D67)⋊C4C2414yes—
807(C2×D67)⋊C4C2414yes—
808(C2×D67)⋊C4C2414yes—
809(C2×D67)⋊C4C2414yes—
810(C2×D67)⋊C4C2414yes—
811(C2×D67)⋊C4C2414yes—
812(C2×D67)⋊C4C2414yes—
813(C2×D67)⋊C4C2414yes—
814(C2×D67)⋊C4C2414yes—
815(C2×D67)⋊C4C2414yes—
816(C2×D67)⋊C4C2414yes—
817(C2×D67)⋊C4C2414yes—
818(C2×D67)⋊C4C2414yes—
819(C2×D67)⋊C4C2414yes—
820(C2×D67)⋊C4C2414yes—
821(C2×D67)⋊C4C2414yes—
822(C2×D67)⋊C4C2414yes—
823C4×Dic67C2412yes—
824C4×Dic67C2412yes—
825C4×Dic67C2412yes—
826C4×Dic67C2412yes—
827C4×Dic67C2412yes—
828C4×Dic67C2414yes—
829C4×Dic67C2411yescharacteristic
830C4×Dic67C2412yes—
831C4×Dic67C2412yes—
832C4×Dic67C2411yescharacteristic
833C4×Dic67C2412yes—
834C4×Dic67C2414yes—
835C4×Dic67C2412yes—
836C4×Dic67C2414yes—
837C4×Dic67C2414yes—
838C4×Dic67C2411yescharacteristic
839C4×Dic67C2412yes—
840C4×Dic67C2411yescharacteristic
841C4×Dic67C2414yes—
842C4×Dic67C2414yes—
843C4×Dic67C2414yes—
844C4×Dic67C2414yes—
845C4×Dic67C2414yes—
846C4×Dic67C2414yes—
847C4×Dic67C2414yes—
848C2×Q8×C67C2412yes—
849C2×Q8×C67C2412yes—
850C2×Q8×C67C2414yes—
851C2×Q8×C67C2412yes—
852C2×D4×C67C2412yes—
853C2×D4×C67C2414yes—
854C2×D4×C67C2414yes—
855C22×C4×C67C2411yescharacteristic
856C22×C4×C67C2412yes—
857C22×C4×C67C2414yes—
858C22×C4×C67C2414yes—
859C22×C4×C67C2414yes—
860C4⋊C4×C67C2412yes—
861C4⋊C4×C67C2414yes—
862C4⋊C4×C67C2414yes—
863C4⋊C4×C67C2414yes—
864C4⋊C4×C67C2412yes—
865C4⋊C4×C67C2414yes—
866C4⋊C4×C67C2412yes—
867C4⋊C4×C67C2414yes—
868C4⋊C4×C67C2412yes—
869C4⋊C4×C67C2412yes—
870C4⋊C4×C67C2412yes—
871C4⋊C4×C67C2412yes—
872C4⋊C4×C67C2414yes—
873C4⋊C4×C67C2412yes—
874C4⋊C4×C67C2414yes—
875C4⋊C4×C67C2412yes—
876C4⋊C4×C67C2414yes—
877C4⋊C4×C67C2412yes—
878C4⋊C4×C67C2414yes—
879C4⋊C4×C67C2414yes—
880C22⋊C4×C67C2414yes—
881C22⋊C4×C67C2412yes—
882C22⋊C4×C67C2414yes—
883C22⋊C4×C67C2411yescharacteristic
884C22⋊C4×C67C2411yescharacteristic
885C22⋊C4×C67C2414yes—
886C22⋊C4×C67C2414yes—
887C22⋊C4×C67C2414yes—
888C22⋊C4×C67C2414yes—
889C22⋊C4×C67C2414yes—
890C22⋊C4×C67C2414yes—
891C22⋊C4×C67C2414yes—
892C42×C67C2411yescharacteristic
893C42×C67C2412yes—
894C42×C67C2411yescharacteristic
895C42×C67C2414yes—
896C42×C67C2411yescharacteristic
897C42×C67C2412yes—
898C42×C67C2411yescharacteristic
899C42×C67C2414yes—
900C42×C67C2414yes—
901C23×C67C2511yescharacteristic
902C23×C67C2514yes—
903C22×D67—22no—
904C22×D67—42no—
905C22×D67C2511yescharacteristic
906C22×D67C2514yes—
907C22×D67C2511yescharacteristic
908Q8×C67—24no—
909Q8×C67—42no—
910Q8×C67—44no—
911Q8×C67—42no—
912D4×C67—24no—
913D4×C67—44no—
914D4×C67—44no—
915C2×C4×C67—22no—
916C2×C4×C67—42no—
917C2×C4×C67—44no—
918C2×C4×C67—44no—
919C2×C4×C67—44no—
920C2×C4×C67C2512yes—
921C2×C4×C67C2514yes—
922C2×C4×C67C2512yes—
923C2×C4×C67C2512yes—
924C2×C4×C67C2511yescharacteristic
925C2×C4×C67C2512yes—
926C2×C4×C67C2514yes—
927C2×C4×C67C2512yes—
928C2×C4×C67C2514yes—
929C2×C4×C67C2512yes—
930C2×C4×C67C2511yescharacteristic
931C22⋊D67—28no—
932C22⋊D67—28no—
933C22⋊D67—44no—
934C22⋊D67—44no—
935C22⋊D67—44no—
936C22⋊D67—44no—
937C22⋊D67—44no—
938C2×Dic67—22no—
939C2×Dic67—28no—
940C2×Dic67—24no—
941C2×Dic67—28no—
942C2×Dic67—44no—
943C2×Dic67—44no—
944C2×Dic67C2514yes—
945C2×Dic67C2512yes—
946C2×Dic67C2511yescharacteristic
947C2×Dic67C2514yes—
948C2×Dic67C2512yes—
949C2×Dic67C2514yes—
950C2×Dic67C2512yes—
951C2×Dic67C2512yes—
952C2×Dic67C2512yes—
953C2×Dic67C2511yescharacteristic
954C2×Dic67C2512yes—
955D268—28no—
956D268—24no—
957D268—44no—
958D268—44no—
959C4×D67—22no—
960C4×D67—22no—
961C4×D67—22no—
962C4×D67—28no—
963C4×D67—24no—
964C4×D67—24no—
965C4×D67—28no—
966C4×D67—42no—
967C4×D67—42no—
968C4×D67—44no—
969C4×D67—42no—
970C4×D67—42no—
971C4×D67—44no—
972C4×D67—42no—
973C4×D67—42no—
974C4×D67—44no—
975C4×D67—44no—
976C4×D67—44no—
977C4×D672−1+414yes—
978Dic134—24no—
979Dic134—24no—
980Dic134—24no—
981Dic134—28no—
982Dic134—24no—
983Dic134—24no—
984Dic134—44no—
985Dic134—42no—
986Dic134—42no—
987Dic134—44no—
988Dic134—44no—
989Dic134—44no—
990C22×C67—24no—
991C22×C67—21no—
992C22×C67—24no—
993C22×C67—22no—
994C22×C67—24no—
995C22×C67C2611yescharacteristic
996C2×D67—22no—
997C2×D67—21no—
998C2×D67—24no—
999C2×D67—24no—
1000C2×D67—22no—
1001C2×D67—24no—
1002C2×D67—44no—
1003C2×D67C2×2−1+412yes—
1004C4×C67—21no—
1005C4×C67—24no—
1006C4×C67—22no—
1007C4×C67—24no—
1008C4×C67—22no—
1009C4×C67—22no—
1010C4×C67—22no—
1011C4×C67—24no—
1012C4×C67—22no—
1013C4×C67—22no—
1014C4×C67C2×2−1+412yes—
1015Dic67—24no—
1016Dic67—21no—
1017Dic67—22no—
1018Dic67—22no—
1019Dic67—24no—
1020Dic67—22no—
1021Dic67—22no—
1022Dic67—24no—
1023Dic67—22no—
1024Dic67C2×2−1+412yes—
1025Dic67#58514yes—
1026#62761—671nomaximal, Sylow
1027C2×C67—41no—
1028C2×C67—44no—
1029C2×C67C22×2−1+411yescharacteristic
1030C2×C67C2×#58512yes—
1031D67—22no—
1032D67—44no—
1033D67—41no—
1034#3557—671no—
1035#3557—672no—
1036#3557D6711yescharacteristic, complemented
1037#3556—671no—
1038#3555—672no—
1039#3555—672no—
1040#3554—672no—
1041#3554—672no—
1042#3553—674no—
1043#3552—674no—
1044#3550—672no—
1045#3548—671no—
1046#3541—674no—
1047#3541—674no—
1048#3531—674no—
1049#3482—674no—
1050#3480—672no—
1051#3480—672no—
1052Q8×#41—672no—
1053Q8×#41—672no—
1054#3461—674no—
1055#3461—674no—
1056#3455—672no—
1057#3455—671no—
1058#3455—671no—
1059#3444—672no—
1060C2×#533—671no—
1061C67#6276111yescharacteristic, complemented, Sylow
1062#564—674no—
1063#563—674no—
1064#563—674no—
1065#563—674no—
1066#563—674no—
1067#563—674no—
1068#563—674no—
1069#563—674no—
1070#563—674no—
1071#563—674no—
1072#563C2×D6714yescomplemented
1073#562—674no—
1074#562—674no—
1075#562—674no—
1076#562—674no—
1077#562—674no—
1078#559—672no—
1079#559—672no—
1080#559—672no—
1081#559—672no—
1082#559—672no—
1083#559C2×D6712yescomplemented
1084Q82—672no—
1085Q82—672no—
1086#557—672no—
1087#557—672no—
1088#557—672no—
1089#557—674no—
1090#557—672no—
1091#557—672no—
1092#557—672no—
1093#557—672no—
1094#557C2×D6712yescomplemented
1095#556—674no—
1096#556—674no—
1097#556—672no—
1098#556—672no—
1099#556—674no—
1100#556—672no—
1101#556—672no—
1102#556—672no—
1103#556C2×D6712yescomplemented
1104#554—674no—
1105#554—674no—
1106#554—672no—
1107#554—672no—
1108#554—674no—
1109#554—674no—
1110#554—674no—
1111#554—672no—
1112#554—672no—
1113#554—672no—
1114#554—674no—
1115#554C2×D6712yescomplemented
1116#553—674no—
1117#553—674no—
1118#553—674no—
1119#553—674no—
1120#553—674no—
1121#553—674no—
1122#552—674no—
1123#552—674no—
1124#552—674no—
1125#552—674no—
1126#552—674no—
1127#552C2×D6714yescomplemented
1128#550—672no—
1129#550—672no—
1130D4×Q8—674no—
1131D4×Q8—672no—
1132D4×Q8—674no—
1133D4×Q8—674no—
1134D4×Q8—672no—
1135#548—674no—
1136#548—674no—
1137#548—674no—
1138#548—674no—
1139#547—674no—
1140#547—674no—
1141#547—674no—
1142#544—674no—
1143#544—674no—
1144#542—672no—
1145#542—674no—
1146#542—674no—
1147#542—672no—
1148#542—674no—
1149#542—674no—
1150#542—674no—
1151#542—674no—
1152#542—672no—
1153#542—672no—
1154#542—672no—
1155#542—672no—
1156#542—674no—
1157#542—672no—
1158#542C2×D6712yes—
1159#542C2×D6714yes—
1160#541—671no—
1161#541—674no—
1162#541—674no—
1163#541—674no—
1164#541—674no—
1165#541—674no—
1166#541—674no—
1167#541—671no—
1168#541—672no—
1169#541—672no—
1170#541—674no—
1171#541—671no—
1172#541—674no—
1173#541C2×D6711yescharacteristic
1174#540—671no—
1175#540—671no—
1176#540—672no—
1177#540—672no—
1178#540—671no—
1179#540C2×D6711yescharacteristic
1180#539—674no—
1181#539—674no—
1182#539—674no—
1183#539—674no—
1184#539—674no—
1185#539—674no—
1186#539—674no—
1187#539—674no—
1188#539—674no—
1189#539—674no—
1190#539—674no—
1191#539C2×D6714yes—
1192#538—674no—
1193#538—674no—
1194#538—674no—
1195#538—674no—
1196#537—674no—
1197#537—674no—
1198#536—674no—
1199#536—674no—
1200#536—674no—
1201#536—674no—
1202#533—672no—
1203#533—672no—
1204#533—674no—
1205#533—672no—
1206#533—672no—
1207#533—671no—
1208#533—671no—
1209#533—674no—
1210#533—674no—
1211#533—672no—
1212#533—672no—
1213#533—672no—
1214#533—674no—
1215#533—674no—
1216#533—674no—
1217#533—672no—
1218#533—672no—
1219#533—672no—
1220#533—671no—
1221#533—671no—
1222#533—671no—
1223#533C2×D6711yescharacteristic
1224#532—671no—
1225#532—671no—
1226#532—672no—
1227#532—672no—
1228#532—672no—
1229#532—672no—
1230C2×C4⋊Q8—672no—
1231#529—674no—
1232#529—674no—
1233#529—674no—
1234#529—674no—
1235#529—674no—
1236#529—674no—
1237#529—672no—
1238#529—674no—
1239#529—672no—
1240#529—674no—
1241#529—674no—
1242#529—674no—
1243#529—674no—
1244#529—674no—
1245#529—674no—
1246#529—674no—
1247#529—674no—
1248#529—674no—
1249#529—674no—
1250#529—674no—
1251#529—672no—
1252#529C2×D6712yes—
1253C2×#125—672no—
1254#525—674no—
1255#525—672no—
1256#525—672no—
1257#525—674no—
1258C2×C22⋊Q8—672no—
1259C2×C22⋊Q8—672no—
1260C4×#41—672no—
1261C4×#41—672no—
1262C4×#41—672no—
1263C4×#41—674no—
1264C4×#41—672no—
1265C4×#41—672no—
1266C4×#41—672no—
1267C4×#41—674no—
1268C4×#41—674no—
1269C4×#41—674no—
1270C2×C4×Q8—672no—
1271C2×C4×Q8—672no—
1272C2×C4×Q8—674no—
1273C2×C4×Q8—674no—
1274C2×#117—671no—
1275C2×#117—671no—
1276C22×C42—671no—
1277C2×#41—672no—
1278C2×#41—674no—
1279C2×#41—674no—
1280C2×#41—672no—
1281C2×#41—674no—
1282C2×#41—674no—
1283C22×Q8—672no—
1284C22×Q8—672no—
1285C22×Q8—674no—
1286C22×Q8—674no—
1287C23×C4—672no—
1288C23×C4—671no—
1289C4⋊Q8—672no—
1290C4⋊Q8—672no—
1291C4⋊Q8—672no—
1292C4⋊Q8—672no—
1293C4⋊Q8—674no—
1294C4⋊Q8—674no—
1295C4⋊Q8—674no—
1296C4⋊Q8—672no—
1297C4⋊Q8—672no—
1298C4⋊Q8—672no—
1299C4⋊Q8—672no—
1300C4⋊Q8—672no—
1301C4⋊Q8—672no—
1302C4⋊Q8—674no—
1303C4⋊Q8—674no—
1304C4⋊Q8—674no—
1305C4⋊Q8—674no—
1306C4⋊Q8—672no—
1307C4⋊Q8—672no—
1308C4⋊Q8—674no—
1309C4⋊Q8—674no—
1310C4⋊Q8—674no—
1311C4⋊Q8—672no—
1312C4⋊Q8—671no—
1313C4⋊Q8—674no—
1314C4⋊Q8—672no—
1315C4⋊Q8C22×D6712yes—
1316C4⋊Q8C22×D6711yescharacteristic
1317C4⋊Q8C22×D6712yes—
1318C4⋊Q8C22×D6714yes—
1319#127—672no—
1320#127—672no—
1321#127—671no—
1322#127C22×D6711yescharacteristic
1323#126—674no—
1324#126—674no—
1325#126—674no—
1326#126—674no—
1327#126—674no—
1328#126—674no—
1329#126—674no—
1330#126—674no—
1331#126—674no—
1332#126—674no—
1333#126—674no—
1334#126—674no—
1335#126—674no—
1336#126—674no—
1337#126—674no—
1338#126—674no—
1339#126—674no—
1340#126—674no—
1341#126—674no—
1342#126—674no—
1343#126—674no—
1344#126—674no—
1345#126—674no—
1346#126—674no—
1347#126—674no—
1348#126—674no—
1349#126—674no—
1350#126C22×D6714yes—
1351#126C22×D6714yes—
1352#126C22×D6714yes—
1353#126C22×D6714yes—
1354#126C22×D6714yes—
1355#125—672no—
1356#125—672no—
1357#125—672no—
1358#125—672no—
1359#125—672no—
1360#125—672no—
1361#125—674no—
1362#125—674no—
1363#125—674no—
1364#125—674no—
1365#125—674no—
1366#125—674no—
1367#125—674no—
1368#125—674no—
1369#125—674no—
1370#125—674no—
1371#125—674no—
1372#125—674no—
1373#125—674no—
1374#125—674no—
1375#125—674no—
1376#125—674no—
1377#125—674no—
1378#125—674no—
1379#125—674no—
1380#125—674no—
1381#125—674no—
1382#125—672no—
1383#125—672no—
1384#125—672no—
1385#125—672no—
1386#125—674no—
1387#125—674no—
1388#125—674no—
1389#125—674no—
1390#125—671no—
1391#125—671no—
1392#125C22×D6712yes—
1393#125C22×D6712yes—
1394#125C22×D6714yes—
1395#125C22×D6714yes—
1396#125C22×D6714yes—
1397#125C22×D6711yescharacteristic
1398#125C22×D6711yescharacteristic
1399#124—674no—
1400#124—674no—
1401#124—672no—
1402#124—674no—
1403#124—672no—
1404#124—674no—
1405#124—674no—
1406#124—674no—
1407#124—674no—
1408#124—674no—
1409#124—674no—
1410#124—674no—
1411#124—674no—
1412#124—674no—
1413#124—674no—
1414#124—672no—
1415#124—674no—
1416#124—672no—
1417#124C22×D6712yes—
1418#124C22×D6714yes—
1419#124C22×D6714yes—
1420#124C22×D6712yes—
1421#123—674no—
1422#123—674no—
1423#123—674no—
1424#123—674no—
1425#123—674no—
1426#123—674no—
1427#123—674no—
1428#123—674no—
1429#123—674no—
1430#123—674no—
1431#123—674no—
1432#123—674no—
1433#123—674no—
1434#123—674no—
1435#123—674no—
1436#123—674no—
1437#123—674no—
1438#123—674no—
1439#123—674no—
1440#123—674no—
1441#123—674no—
1442#123—674no—
1443#123—674no—
1444#123—674no—
1445#123—674no—
1446#123—674no—
1447#123—674no—
1448#123—674no—
1449#123—674no—
1450#123C22×D6714yes—
1451#123C22×D6714yes—
1452#123C22×D6714yes—
1453#123C22×D6714yes—
1454#123C22×D6714yes—
1455C22⋊Q8—672no—
1456C22⋊Q8—672no—
1457C22⋊Q8—672no—
1458C22⋊Q8—674no—
1459C22⋊Q8—674no—
1460C22⋊Q8—674no—
1461C22⋊Q8—674no—
1462C22⋊Q8—674no—
1463C22⋊Q8—672no—
1464C22⋊Q8—672no—
1465C22⋊Q8—672no—
1466C22⋊Q8—674no—
1467C22⋊Q8—674no—
1468C22⋊Q8—674no—
1469C22⋊Q8—674no—
1470C22⋊Q8—672no—
1471C22⋊Q8—672no—
1472C22⋊Q8—672no—
1473C22⋊Q8—672no—
1474C22⋊Q8—672no—
1475C22⋊Q8—672no—
1476C22⋊Q8—672no—
1477C22⋊Q8—674no—
1478C22⋊Q8—674no—
1479C22⋊Q8—674no—
1480C22⋊Q8—674no—
1481C22⋊Q8—674no—
1482C22⋊Q8—674no—
1483C22⋊Q8—674no—
1484C22⋊Q8—674no—
1485C22⋊Q8—674no—
1486C22⋊Q8—674no—
1487C22⋊Q8—674no—
1488C22⋊Q8—674no—
1489C22⋊Q8—674no—
1490C22⋊Q8—674no—
1491C22⋊Q8—674no—
1492C22⋊Q8—674no—
1493C22⋊Q8—674no—
1494C22⋊Q8—674no—
1495C22⋊Q8—674no—
1496C22⋊Q8—674no—
1497C22⋊Q8—674no—
1498C22⋊Q8—672no—
1499C22⋊Q8—672no—
1500C22⋊Q8—672no—
1501C22⋊Q8—672no—
1502C22⋊Q8—674no—
1503C22⋊Q8—674no—
1504C22⋊Q8—674no—
1505C22⋊Q8—674no—
1506C22⋊Q8—674no—
1507C22⋊Q8—674no—
1508C22⋊Q8—674no—
1509C22⋊Q8—674no—
1510C22⋊Q8—674no—
1511C22⋊Q8—674no—
1512C22⋊Q8—674no—
1513C22⋊Q8C22×D6712yes—
1514C22⋊Q8C22×D6712yes—
1515C22⋊Q8C22×D6712yes—
1516C22⋊Q8C22×D6714yes—
1517C22⋊Q8C22×D6714yes—
1518C22⋊Q8C22×D6714yes—
1519C22⋊Q8C22×D6714yes—
1520C22⋊Q8C22×D6714yes—
1521#121—674no—
1522#121—672no—
1523#121—674no—
1524#121—674no—
1525#121—674no—
1526#121—674no—
1527#121—674no—
1528#121—674no—
1529#121—674no—
1530#121—672no—
1531#121—674no—
1532#121—674no—
1533#121—672no—
1534#121—674no—
1535#121—674no—
1536#121—674no—
1537#121—674no—
1538#121—674no—
1539#121—674no—
1540#121—674no—
1541#121—674no—
1542#121—674no—
1543#121—674no—
1544#121—674no—
1545#121C22×D6712yes—
1546#121C22×D6714yes—
1547#120—674no—
1548#120—674no—
1549C4×Q8—672no—
1550C4×Q8—672no—
1551C4×Q8—674no—
1552C4×Q8—672no—
1553C4×Q8—672no—
1554C4×Q8—672no—
1555C4×Q8—672no—
1556C4×Q8—672no—
1557C4×Q8—674no—
1558C4×Q8—672no—
1559C4×Q8—672no—
1560C4×Q8—672no—
1561C4×Q8—672no—
1562C4×Q8—674no—
1563C4×Q8—674no—
1564C4×Q8—674no—
1565C4×Q8—674no—
1566C4×Q8—674no—
1567C4×Q8—674no—
1568C4×Q8—674no—
1569C4×Q8—674no—
1570C4×Q8—674no—
1571C4×Q8—672no—
1572C4×Q8—674no—
1573C4×Q8—672no—
1574C4×Q8—672no—
1575C4×Q8—672no—
1576C4×Q8—672no—
1577C4×Q8—672no—
1578C4×Q8—672no—
1579C4×Q8—672no—
1580C4×Q8—672no—
1581C4×Q8—674no—
1582C4×Q8—674no—
1583C4×Q8—674no—
1584C4×Q8—674no—
1585C4×Q8—672no—
1586C4×Q8—674no—
1587C4×Q8—672no—
1588C4×Q8—672no—
1589C4×Q8C22×D6712yes—
1590C4×Q8C22×D6712yes—
1591C4×Q8C22×D6714yes—
1592C4×Q8C22×D6712yes—
1593C4×Q8C22×D6712yes—
1594C4×Q8C22×D6712yes—
1595C4×D4—674no—
1596C4×D4—674no—
1597C4×D4—672no—
1598C4×D4—672no—
1599C4×D4—672no—
1600C4×D4—674no—
1601C4×D4—674no—
1602C4×D4—674no—
1603C4×D4—674no—
1604C4×D4—674no—
1605C4×D4—674no—
1606C4×D4—674no—
1607C4×D4—674no—
1608C4×D4—674no—
1609C4×D4—674no—
1610C4×D4—674no—
1611C4×D4—672no—
1612C4×D4—674no—
1613C4×D4—674no—
1614C4×D4—674no—
1615C4×D4—672no—
1616C4×D4—672no—
1617C4×D4—674no—
1618C4×D4—674no—
1619C4×D4—674no—
1620C4×D4—674no—
1621C4×D4—674no—
1622C4×D4—674no—
1623C4×D4—674no—
1624C4×D4—674no—
1625C4×D4—674no—
1626C4×D4—674no—
1627C4×D4—674no—
1628C4×D4—674no—
1629C4×D4—674no—
1630C4×D4—674no—
1631C4×D4—672no—
1632C4×D4—674no—
1633C4×D4—674no—
1634C4×D4—672no—
1635C4×D4—672no—
1636C4×D4C22×D6714yes—
1637C4×D4C22×D6712yes—
1638C4×D4C22×D6714yes—
1639C4×D4C22×D6712yes—
1640C4×D4C22×D6712yes—
1641#117—671no—
1642#117—671no—
1643#117—672no—
1644#117—672no—
1645#117—672no—
1646#117—672no—
1647#117—674no—
1648#117—674no—
1649#117—674no—
1650#117—674no—
1651#117—674no—
1652#117—671no—
1653#117—671no—
1654#117—672no—
1655#117—674no—
1656#117—674no—
1657#117—674no—
1658#117—674no—
1659#117—674no—
1660#117—674no—
1661#117—674no—
1662#117—671no—
1663#117—671no—
1664#117—672no—
1665#117—674no—
1666#117—674no—
1667#117—674no—
1668#117—674no—
1669#117C22×D6711yescharacteristic
1670#117C22×D6711yescharacteristic
1671#117C22×D6714yes—
1672#117C22×D6714yes—
1673C2×C4⋊C4—674no—
1674C2×C4⋊C4—674no—
1675C2×C4⋊C4—672no—
1676C2×C4⋊C4—672no—
1677C2×C4⋊C4—672no—
1678C2×C4⋊C4—672no—
1679C2×C4⋊C4—672no—
1680C2×C4⋊C4—672no—
1681C2×C4⋊C4—672no—
1682C2×C4⋊C4—672no—
1683C2×C4⋊C4—674no—
1684C2×C4⋊C4—674no—
1685C2×C4⋊C4—674no—
1686C2×C4⋊C4C22×D6714yes—
1687C2×C22⋊C4—671no—
1688C2×C22⋊C4—671no—
1689C2×C22⋊C4—672no—
1690C2×C42—674no—
1691C2×C42—674no—
1692C2×C42—674no—
1693C2×C42—672no—
1694C2×C42—671no—
1695C2×C42—671no—
1696C2×C42—671no—
1697C2×C42—672no—
1698C2×C42—672no—
1699C2×C42—674no—
1700C2×C42—674no—
1701C2×C42—674no—
1702C2×C42—671no—
1703C2×C42—671no—
1704C2×C42—671no—
1705C2×C42—671no—
1706C2×C42—672no—
1707C2×C42C22×D6711yescharacteristic
1708C24—671no—
1709#41—2688no—
1710#41—2688no—
1711#41—2688no—
1712#41—2688no—
1713#41—1348no—
1714#41—1348no—
1715C2×Q8—2688no—
1716C2×Q8—2684no—
1717C2×Q8—2684no—
1718C2×Q8—2688no—
1719C2×Q8—674no—
1720C2×Q8—674no—
1721C2×Q8—672no—
1722C2×Q8—672no—
1723C2×Q8—674no—
1724C2×Q8—674no—
1725C2×Q8—672no—
1726C2×Q8—672no—
1727C2×Q8—672no—
1728C2×Q8—674no—
1729C2×Q8—672no—
1730C2×Q8—672no—
1731C2×Q8C23×D6712yes—
1732C2×Q8C23×D6712yes—
1733C2×Q8C23×D6714yes—
1734C2×Q8C23×D6712yes—
1735C2×D4—674no—
1736C2×D4—674no—
1737C2×D4—674no—
1738C2×D4—674no—
1739C2×D4—674no—
1740C2×D4—674no—
1741C2×D4—674no—
1742C2×D4—674no—
1743C2×D4—674no—
1744C2×D4—674no—
1745C2×D4—672no—
1746C2×D4C23×D6712yes—
1747C2×D4C23×D6714yes—
1748C2×D4C23×D6714yes—
1749C22×C4—2684no—
1750C22×C4—674no—
1751C22×C4—674no—
1752C22×C4—672no—
1753C22×C4—672no—
1754C22×C4—672no—
1755C22×C4—672no—
1756C22×C4—672no—
1757C22×C4—672no—
1758C22×C4—674no—
1759C22×C4—674no—
1760C22×C4—674no—
1761C22×C4—674no—
1762C22×C4—674no—
1763C22×C4—671no—
1764C22×C4—674no—
1765C22×C4—671no—
1766C22×C4—672no—
1767C22×C4—674no—
1768C22×C4—674no—
1769C22×C4—671no—
1770C22×C4—672no—
1771C22×C4—671no—
1772C22×C4—671no—
1773C22×C4—672no—
1774C22×C4—674no—
1775C22×C4—1344no—
1776C22×C4C23×D6711yescharacteristic
1777C22×C4C23×D6712yes—
1778C22×C4C23×D6714yes—
1779C22×C4C23×D6714yes—
1780C22×C4C23×D6714yes—
1781C4⋊C4—672no—
1782C4⋊C4—672no—
1783C4⋊C4—672no—
1784C4⋊C4—672no—
1785C4⋊C4—674no—
1786C4⋊C4—674no—
1787C4⋊C4—672no—
1788C4⋊C4—672no—
1789C4⋊C4—672no—
1790C4⋊C4—672no—
1791C4⋊C4—672no—
1792C4⋊C4—672no—
1793C4⋊C4—672no—
1794C4⋊C4—672no—
1795C4⋊C4—672no—
1796C4⋊C4—672no—
1797C4⋊C4—672no—
1798C4⋊C4—672no—
1799C4⋊C4—672no—
1800C4⋊C4—672no—
1801C4⋊C4—674no—
1802C4⋊C4—674no—
1803C4⋊C4—674no—
1804C4⋊C4—674no—
1805C4⋊C4—674no—
1806C4⋊C4—674no—
1807C4⋊C4—674no—
1808C4⋊C4—674no—
1809C4⋊C4—672no—
1810C4⋊C4—672no—
1811C4⋊C4—672no—
1812C4⋊C4—672no—
1813C4⋊C4—672no—
1814C4⋊C4—672no—
1815C4⋊C4—674no—
1816C4⋊C4—674no—
1817C4⋊C4—672no—
1818C4⋊C4—672no—
1819C4⋊C4—674no—
1820C4⋊C4—674no—
1821C4⋊C4—674no—
1822C4⋊C4—674no—
1823C4⋊C4—674no—
1824C4⋊C4—674no—
1825C4⋊C4—674no—
1826C4⋊C4—674no—
1827C4⋊C4—674no—
1828C4⋊C4—674no—
1829C4⋊C4—674no—
1830C4⋊C4—674no—
1831C4⋊C4—674no—
1832C4⋊C4—674no—
1833C4⋊C4—674no—
1834C4⋊C4—674no—
1835C4⋊C4—674no—
1836C4⋊C4—674no—
1837C4⋊C4C23×D6712yes—
1838C4⋊C4C23×D6712yes—
1839C4⋊C4C23×D6714yes—
1840C4⋊C4C23×D6712yes—
1841C4⋊C4C23×D6712yes—
1842C4⋊C4C23×D6712yes—
1843C4⋊C4C23×D6712yes—
1844C4⋊C4C23×D6714yes—
1845C4⋊C4C23×D6712yes—
1846C4⋊C4C23×D6712yes—
1847C4⋊C4C23×D6714yes—
1848C4⋊C4C23×D6714yes—
1849C4⋊C4C23×D6712yes—
1850C4⋊C4C23×D6712yes—
1851C4⋊C4C23×D6714yes—
1852C4⋊C4C23×D6714yes—
1853C4⋊C4C23×D6714yes—
1854C4⋊C4C23×D6714yes—
1855C4⋊C4C23×D6714yes—
1856C4⋊C4C23×D6714yes—
1857C22⋊C4—671no—
1858C22⋊C4—671no—
1859C22⋊C4—672no—
1860C22⋊C4—674no—
1861C22⋊C4—674no—
1862C22⋊C4—674no—
1863C22⋊C4—674no—
1864C22⋊C4—674no—
1865C22⋊C4—674no—
1866C22⋊C4—674no—
1867C22⋊C4—672no—
1868C22⋊C4—672no—
1869C22⋊C4—672no—
1870C22⋊C4—672no—
1871C22⋊C4—674no—
1872C22⋊C4—674no—
1873C22⋊C4—674no—
1874C22⋊C4—674no—
1875C22⋊C4—674no—
1876C22⋊C4—674no—
1877C22⋊C4—674no—
1878C22⋊C4—674no—
1879C22⋊C4—674no—
1880C22⋊C4—674no—
1881C22⋊C4—674no—
1882C22⋊C4—674no—
1883C22⋊C4—674no—
1884C22⋊C4—674no—
1885C22⋊C4—674no—
1886C22⋊C4—674no—
1887C22⋊C4—674no—
1888C22⋊C4—674no—
1889C22⋊C4C23×D6712yes—
1890C22⋊C4C23×D6711yescharacteristic
1891C22⋊C4C23×D6711yescharacteristic
1892C22⋊C4C23×D6714yes—
1893C22⋊C4C23×D6714yes—
1894C22⋊C4C23×D6714yes—
1895C22⋊C4C23×D6714yes—
1896C22⋊C4C23×D6714yes—
1897C22⋊C4C23×D6714yes—
1898C22⋊C4C23×D6714yes—
1899C22⋊C4C23×D6714yes—
1900C22⋊C4C23×D6714yes—
1901C42—672no—
1902C42—672no—
1903C42—672no—
1904C42—674no—
1905C42—674no—
1906C42—672no—
1907C42—672no—
1908C42—672no—
1909C42—672no—
1910C42—671no—
1911C42—672no—
1912C42—672no—
1913C42—671no—
1914C42—674no—
1915C42—674no—
1916C42—674no—
1917C42—671no—
1918C42—671no—
1919C42—672no—
1920C42—674no—
1921C42—674no—
1922C42—674no—
1923C42—674no—
1924C42—674no—
1925C42—674no—
1926C42C23×D6711yescharacteristic
1927C42C23×D6712yes—
1928C42C23×D6711yescharacteristic
1929C42C23×D6714yes—
1930C42C23×D6711yescharacteristic
1931C42C23×D6712yes—
1932C42C23×D6714yes—
1933C42C23×D6711yescharacteristic
1934C42C23×D6714yes—
1935C23—2682no—
1936C23—671no—
1937C23—671no—
1938C23—674no—
1939C23—1342no—
1940C23C24×D6711yescharacteristic
1941C23C24×D6714yes—
1942Q8—24no—
1943Q8—42no—
1944Q8—44no—
1945Q8—42no—
1946Q8—2684no—
1947Q8—2684no—
1948Q8—2684no—
1949Q8—2682no—
1950Q8—2682no—
1951Q8—2684no—
1952Q8—1344no—
1953Q8—1344no—
1954Q8—1348no—
1955Q8—1344no—
1956Q8—1344no—
1957Q8—1344no—
1958D4—24no—
1959D4—44no—
1960D4—44no—
1961D4—2684no—
1962D4—2684no—
1963D4—2684no—
1964D4—2684no—
1965D4—2684no—
1966D4—2684no—
1967D4—2684no—
1968D4—1348no—
1969D4—1348no—
1970D4—1348no—
1971D4—1344no—
1972C2×C4—22no—
1973C2×C4—42no—
1974C2×C4—44no—
1975C2×C4—44no—
1976C2×C4—44no—
1977C2×C4—2682no—
1978C2×C4—2682no—
1979C2×C4—2682no—
1980C2×C4—2684no—
1981C2×C4—2682no—
1982C2×C4—2682no—
1983C2×C4—2682no—
1984C2×C4—2684no—
1985C2×C4—2684no—
1986C2×C4—2684no—
1987C2×C4—2684no—
1988C2×C4—2684no—
1989C2×C4—2684no—
1990C2×C4—671no—
1991C2×C4—672no—
1992C2×C4—674no—
1993C2×C4—674no—
1994C2×C4—671no—
1995C2×C4—672no—
1996C2×C4—672no—
1997C2×C4—674no—
1998C2×C4—674no—
1999C2×C4—672no—
2000C2×C4—672no—
2001C2×C4—672no—
2002C2×C4—1344no—
2003C2×C4—1344no—
2004C2×C4—1342no—
2005C2×C4—1348no—
2006C2×C4—1348no—
2007C2×C4—1342no—
2008C2×C4—1344no—
2009C2×C4—1342no—
2010C2×C4—1348no—
2011C2×C4—1348no—
2012C2×C4—1342no—
2013C2×C4C24×D6712yes—
2014C2×C4C24×D6714yes—
2015C2×C4C24×D6712yes—
2016C2×C4C24×D6714yes—
2017C2×C4C24×D6712yes—
2018C2×C4C24×D6711yescharacteristic
2019C2×C4C24×D6712yes—
2020C2×C4C24×D6714yes—
2021C2×C4C24×D6712yes—
2022C2×C4C24×D6712yes—
2023C2×C4C24×D6711yescharacteristic
2024C22—21no—
2025C22—24no—
2026C22—24no—
2027C22—24no—
2028C22—22no—
2029C22—2684no—
2030C22—672no—
2031C22—1341no—
2032C22—1344no—
2033C22—1344no—
2034C22—1344no—
2035C22—1342no—
2036C22—1342no—
2037C22C25×D6711yescharacteristic
2038C4—21no—
2039C4—24no—
2040C4—22no—
2041C4—22no—
2042C4—24no—
2043C4—22no—
2044C4—24no—
2045C4—22no—
2046C4—22no—
2047C4—22no—
2048C4—672no—
2049C4—674no—
2050C4—1341no—
2051C4—1344no—
2052C4—1342no—
2053C4—1342no—
2054C4—1344no—
2055C4—1342no—
2056C4—1342no—
2057C4—1342no—
2058C4—1344no—
2059C42−1+4×D6712yes—
2060C2—41no—
2061C2—44no—
2062C2—2681no—
2063C2—2684no—
2064C2—1342no—
2065C2C2×2−1+4×D6711yescharacteristic
2066C2#585×D6712yes—
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3557C2
hypercenter#3557D67
hypocenterC67#62761
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3557

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22574715C2semidirect
2. #22574711C2semidirect
3. #22574702C2semidirect
4. #22574696C2semidirect
5. #22574689C2semidirect
6. #22574679C2semidirect
7. #22574672C2semidirect
8. #22574656C2semidirect
9. #22574643C2semidirect
10. #22574617C2semidirect
11. #22574603C2semidirect
12. #22574501C2semidirect
13. #22574493C2semidirect
14. #22574355C2semidirect
15. #22573823C2semidirect
16. #22573805C2semidirect
17. #22573801C2semidirect
18. #22573791C2semidirect
19. #22573788C2semidirect
20. #22573639C2semidirect
21. #22573635C2semidirect
22. #22573600C2semidirect
23. #22573596C2semidirect
24. #22573593C2semidirect
25. #22573503C2semidirect
26. #533×D67C2semidirect
27. C67×#3557C2semidirect
28. C67⋊#564C22semidirect
31. #16864148C22semidirect
32. #16864148C22semidirect
33. #16864148C22semidirect
35. #16864147C22semidirect
37. #16864145C22semidirect
39. #16864143C22semidirect
43. #16864131C22semidirect
44. #16864129C22semidirect
45. #16864129C22semidirect
46. #16864128C22semidirect
47. #16864128C22semidirect
48. Q8×Dic134C22semidirect
49. #16864126C22semidirect
50. #16864124C22semidirect
51. #16864124C22semidirect
52. #16864123C22semidirect
53. #16864123C22semidirect
54. #16864123C22semidirect
55. #16864122C22semidirect
56. #16864122C22semidirect
57. #16864121C22semidirect
58. #16864119C22semidirect
60. #16864118C22semidirect
61. #16864118C22semidirect
62. #16864115C22semidirect
63. #16864115C22semidirect
65. #16864113C22semidirect
67. #16864106C22semidirect
68. #16864105C22semidirect
69. #16864105C22semidirect
72. #16864102C22semidirect
73. #16864102C22semidirect
83. #16864085C22semidirect
85. #16864079C22semidirect
87. #16864078C22semidirect
88. #16864067C22semidirect
89. #16864066C22semidirect
90. D4×Dic134C22semidirect
92. #16864061C22semidirect
94. #16864059C22semidirect
101. #16864044C22semidirect
102. #16864025C22semidirect
103. #16864023C22semidirect
109. #16864016C22semidirect
117. #16864010C22semidirect
120. #16864008C22semidirect
123. #16864005C22semidirect
124. #16864005C22semidirect
126. #16864004C22semidirect
129. #16864003C22semidirect
130. #16864003C22semidirect
137. #16863993C22semidirect
140. #16863992C22semidirect
143. #16863989C22semidirect
145. #16863988C22semidirect
153. #16863969C22semidirect
155. #16863968C22semidirect
162. #16863952C22semidirect
163. #16863952C22semidirect
166. #16863951C22semidirect
175. #16863948C22semidirect
176. #16863948C22semidirect
177. #16863948C22semidirect
186. #16863932C22semidirect
194. #16863929C22semidirect
195. #16863929C22semidirect
199. #16863925C22semidirect
204. #16863923C22semidirect
205. #16863923C22semidirect
217. #16863864C22semidirect
222. C4×#11761627C22semidirect
223. C2×#14524008C22semidirect
226. C4×Q8×D67C22semidirect
230. #563×C67C22semidirect
231. #559×C67C22semidirect
232. #557×C67C22semidirect
233. #556×C67C22semidirect
234. #554×C67C22semidirect
235. #552×C67C22semidirect
1036. #3557D67semidirect
1061. C67#62761semidirect
1072. #563C2×D67semidirect
1083. #559C2×D67semidirect
1094. #557C2×D67semidirect
1103. #556C2×D67semidirect
1115. #554C2×D67semidirect
1127. #552C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225747152
#225747112
#225747022
#225746962
#225746892
#225746792
#225746722
#225746562
#225746432
#225746172
#225746032
#225745012
#225744932
#225743552
#225738232
#225738052
#225738012
#225737912
#225737882
#225736392
#225736352
#225736002
#225735962
#225735932
#225735032
#533×D672
C67×#35572
#6276167