Finite Group Databasebeta

← #31764122

Subgroups — #31764122

Order 17152.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574314C214yesmaximal, complemented
2#22574308C214yesmaximal, complemented
3#22574224C212yesmaximal, complemented
4#22574218C212yesmaximal, complemented
5#22574213C212yesmaximal, complemented
6#22574207C212yesmaximal, complemented
7#22574063C211yesmaximal, characteristic, complemented
8#22574058C211yesmaximal, characteristic, complemented
9#22574052C214yesmaximal, complemented
10#22574014C211yesmaximal, characteristic, complemented
11#22573975C211yesmaximal, characteristic, complemented
12#22573926C212yesmaximal, complemented
13#22573921C214yesmaximal, complemented
14#22573863C212yesmaximal, complemented
15#22573835C212yesmaximal, complemented
16#22573833C212yesmaximal, complemented
17#22573827C212yesmaximal, complemented
18#22573824C212yesmaximal, complemented
19#22573802C214yesmaximal, complemented
20#22573800C214yesmaximal, complemented
21#22573627C214yesmaximal, complemented
22#22573625C212yesmaximal, complemented
23#22573505C211yesmaximal, characteristic, complemented
24#22573503C214yesmaximal, complemented
25C4×#14524090C212yesmaximal, complemented
26C2×C4×#11761628C211yesmaximal, characteristic, complemented
27C67×#3444C211yesmaximal, characteristic, complemented
28C2×#14524090C2212yes—
29C22×#11761628C2211yescharacteristic
30#16864131C2214yescomplemented
31#16864130C2218yescomplemented
32#16864129C2218yescomplemented
33#16864128C2214yescomplemented
34Q8×Dic134C2212yescomplemented
35#16864126C2212yescomplemented
36#16864124C2212yescomplemented
37#16864124C2214yescomplemented
38#16864123C2214yescomplemented
39#16864121C2212yescomplemented
40#16864120C2212yescomplemented
41#16864119C2212yescomplemented
42#16864118C2218yescomplemented
43#16864117C2214yescomplemented
44#16864117C2214yescomplemented
45#16864116C2214yescomplemented
46#16864114C2214yescomplemented
47#16864113C2218yescomplemented
48#16864112C2212yescomplemented
49#16864111C2214yescomplemented
50#16864111C2212yescomplemented
51#16864110C2214yescomplemented
52#16864110C2214yescomplemented
53#16864109C2218yescomplemented
54#16864109C2214yescomplemented
55#16864108C2218yescomplemented
56#16864099C2214yescomplemented
57#16864097C2218yescomplemented
58#16864095C2218yescomplemented
59#16864095C2218yescomplemented
60#16864093C2214yescomplemented
61#16864092C2214yescomplemented
62#16864092C2214yescomplemented
63#16864091C2218yescomplemented
64#16864086C2214yescomplemented
65#16864080C2214yescomplemented
66#16864079C2218yescomplemented
67#16864078C2218yescomplemented
68#16864068C2212yescomplemented
69#16864067C2214yes—
70#16864067C2214yes—
71#16864067C2212yescomplemented
72#16864066C2212yescomplemented
73#16864066C2212yescomplemented
74#16864065C2214yescomplemented
75#16864064C2214yes—
76#16864064C2214yes—
77#16864064C2214yescomplemented
78D4×Dic134C2212yescomplemented
79#16864061C2212yescomplemented
80#16864056C2214yes—
81#16864056C2214yes—
82#16864055C2214yes—
83#16864055C2214yes—
84#16864055C2214yescomplemented
85#16864054C2214yescomplemented
86#16864050C2212yescomplemented
87#16864049C2212yescomplemented
88#16864048C2214yescomplemented
89#16864045C2214yescomplemented
90#16864025C2214yes—
91#16864024C2212yes—
92#16864018C2214yescomplemented
93#16864017C2214yescomplemented
94#16864016C2218yescomplemented
95#16864014C2218yescomplemented
96#16864001C2214yescomplemented
97#16863998C2218yescomplemented
98#16863997C2214yescomplemented
99#16863996C2218yescomplemented
100#16863986C2214yes—
101#16863983C2214yes—
102#16863981C2218yes—
103#16863979C2218yes—
104#16863974C2212yes—
105#16863973C2214yes—
106#16863965C2212yes—
107#16863961C2218yes—
108#16863960C2212yes—
109#16863953C2211yescharacteristic
110#16863953C2211yescharacteristic, complemented
111#16863953C2211yescharacteristic, complemented
112#16863952C2214yescomplemented
113#16863950C2214yescomplemented
114#16863948C2214yes—
115#16863946C2211yescharacteristic
116#16863946C2211yescharacteristic, complemented
117#16863946C2214yescomplemented
118#16863946C2211yescharacteristic, complemented
119#16863945C2214yescomplemented
120#16863943C2214yescomplemented
121#16863943C2214yescomplemented
122#16863943C2218yescomplemented
123#16863942C2218yescomplemented
124#16863941C2214yes—
125#16863933C2214yescomplemented
126#16863931C2214yescomplemented
127#16863930C2212yes—
128#16863930C2212yes—
129#16863930C2214yescomplemented
130#16863930C2212yescomplemented
131#16863930C2212yescomplemented
132#16863930C2212yescomplemented
133#16863930C2212yescomplemented
134#16863929C2218yescomplemented
135#16863929C2218yescomplemented
136#16863926C2218yescomplemented
137#16863925C2214yescomplemented
138#16863924C2218yescomplemented
139#16863924C2218yescomplemented
140#16863923C2218yes—
141#16863909C2214yes—
142#16863907C2212yes—
143#16863907C2212yes—
144#16863907C2212yes—
145#16863906C2214yes—
146#16863905C2218yes—
147#16863904C2218yes—
148#16863879C2212yes—
149#16863876C2212yes—
150#16863876C2214yescomplemented
151#16863875C2218yes—
152#16863875C2214yescomplemented
153#16863873C2212yes—
154#16863873C2214yescomplemented
155#16863872C2214yescomplemented
156C4×#11761629C2214yescomplemented
157C4×#11761628C2212yes—
158C4×#11761628C2212yes—
159C4×#11761628C2212yes—
160C4×#11761628C2212yes—
161C4×#11761628C2212yes—
162C4×#11761628C2212yes—
163C4×#11761628C2212yes—
164C4×#11761628C2212yes—
165C4×#11761628C2212yes—
166C4×#11761628C2212yescomplemented
167C4×#11761628C2214yescomplemented
168C4×#11761628C2212yescomplemented
169#16863864C2218yescomplemented
170C4×#11761627C2218yes—
171C4×#11761627C2214yescomplemented
172C4×#11761627C2214yescomplemented
173C2×C4×Dic134C2211yescharacteristic
174C2×C4×Dic134C2211yescharacteristic
175C2×C4×Dic134C2214yescomplemented
176C4×Q8×D67C2214yescomplemented
177C2×C4×D268C2211yescharacteristic
178C2×C4×D268C2211yescharacteristic
179C2×C4×C22⋊D67C2212yes—
180C2×C4×C22⋊D67C2212yes—
181C2×#14524002C2211yescharacteristic
182C2×#14524000C2212yes—
183C2×C42×D67C2212yes—
184#533×C67C2211yescharacteristic
185#533×C67C2211yescharacteristic, complemented
186#533×C67C2211yescharacteristic, complemented
187#532×C67C2211yescharacteristic
188#532×C67C2211yescharacteristic, complemented
189#532×C67C2211yescharacteristic, complemented
190#529×C67C2212yes—
191#529×C67C2212yes—
192#529×C67C2212yescomplemented
193#529×C67C2212yescomplemented
194#529×C67C2212yescomplemented
195#529×C67C2212yescomplemented
196#525×C67C2212yes—
197#525×C67C2212yes—
198#525×C67C2212yes—
199C4×#41×C67C2212yes—
200C4×#41×C67C2212yescomplemented
201C4×#41×C67C2212yescomplemented
202C22×C42×C67C2211yescharacteristic
203#14524090—216no—
204C2×#11761629C2314yes—
205C2×#11761628—28no—
206C2×#11761628C2312yes—
207C2×#11761628C2312yes—
208C2×#11761628C2314yes—
209C2×#11761628C2312yes—
210C2×#11761628C2312yes—
211C2×#11761628C2312yes—
212C2×#11761628C2312yes—
213C2×#11761628C2318yes—
214C2×#11761628C2312yes—
215C2×#11761627C2314yes—
216C2×#11761627C2318yes—
217C2×#11761627C2314yes—
218C22×Dic134C2314yes—
219C22×Dic134C2311yescharacteristic
220C2×Q8×D67C2314yes—
221C22×D268C2311yescharacteristic
222C22×C22⋊D67C2312yes—
223C22×C4×D67C2312yes—
224C22×C4×D67C2312yes—
225C22×C4×D67C2312yes—
226#14524043C2314yes—
227#14524043C2311yescharacteristic
228#14524043C2311yescharacteristic
229#14524043C2311yescharacteristic
230#14524042C2318yes—
231#14524042C2314yes—
232#14524042C2314yes—
233#14524042C2314yes—
234#14524041C2318yes—
235#14524041C2314yes—
236#14524040C2314yes—
237#14524040C2311yescharacteristic
238#14524039C2314yes—
239#14524039C2318yes—
240#14524039C2318yes—
241#14524039C2314yes—
242#14524038C2318yes—
243#14524038C2318yes—
244#14524038C2318yes—
245#14524038C2318yes—
246#14524037C2318yes—
247#14524037C2314yes—
248#14524037C2314yes—
249#14524036C2318yes—
250#14524036C2318yes—
251#14524036C2318yes—
252#14524035C2314yes—
253#14524035C2312yes—
254#14524035C2312yes—
255#14524035C2312yes—
256#14524034C2314yes—
257#14524033C2318yes—
258#14524033C2318yes—
259#14524033C2318yes—
260#14524033C2318yes—
261#14524032C2318yes—
262#14524032C2314yes—
263#14524031C2314yes—
264#14524031C2318yes—
265#14524031C2312yes—
266#14524031C2312yes—
267#14524031C2312yes—
268#14524030C2318yes—
269#14524029C2318yes—
270#14524029C2318yes—
271#14524029C2318yes—
272#14524029C2318yes—
273#14524029C2318yes—
274#14524029C2318yes—
275#14524029C2318yes—
276#14524028C2318yes—
277#14524028C2318yes—
278#14524028C2318yes—
279#14524028C2318yes—
280#14524027C2318yes—
281#14524026C2314yes—
282#14524026C2318yes—
283#14524026C2314yes—
284#14524026C2314yes—
285#14524025C2318yes—
286#14524025C2318yes—
287#14524025C2318yes—
288#14524024C2318yes—
289#14524023C2314yes—
290#14524022C2312yes—
291#14524022C2314yes—
292#14524022C2312yes—
293#14524022C2312yes—
294#14524022C2312yes—
295#14524022C2312yes—
296#14524022C2312yes—
297#14524021C2318yes—
298#14524021C2318yes—
299#14524021C2318yes—
300#14524021C2318yes—
301#14524020C2318yes—
302#14524020C2318yes—
303#14524019C2314yes—
304#14524019C2314yes—
305#14524018C2314yes—
306#14524018C2314yes—
307#14524018C2314yes—
308#14524018C2318yes—
309#14524017C2314yes—
310#14524017C2314yes—
311#14524017C2314yes—
312#14524017C2312yes—
313#14524017C2318yes—
314#14524017C2312yes—
315#14524017C2312yes—
316#14524017C2312yes—
317#14524017C2312yes—
318#14524017C2312yes—
319#14524016C2318yes—
320#14524016C2318yes—
321#14524016C2318yes—
322#14524016C2318yes—
323#14524016C2318yes—
324#14524016C2318yes—
325#14524016C2318yes—
326#14524015C2318yes—
327#14524015C2318yes—
328#14524015C2318yes—
329#14524015C2318yes—
330#14524015C2318yes—
331#14524015C2318yes—
332#14524014C2314yes—
333#14524014C2314yes—
334#14524014C2318yes—
335#14524013C2318yes—
336#14524012C2314yes—
337#14524011C2318yes—
338Q8×Dic67C2314yes—
339Q8×Dic67C2314yes—
340C4×Dic134C2312yes—
341C4×Dic134C2312yes—
342C4×Dic134C2314yes—
343C4×Dic134C2314yes—
344C4×Dic134C2312yes—
345C4×Dic134C2312yes—
346C4×Dic134C2312yes—
347C4×Dic134C2312yes—
348C4×Dic134C2318yes—
349C4×Dic134C2314yes—
350C4×Dic134C2312yes—
351C4×Dic134C2312yes—
352C4×Dic134C2318yes—
353C4×Dic134C2312yes—
354C4×Dic134C2312yes—
355C4×Dic134C2312yes—
356C4×Dic134C2312yes—
357C4×Dic134C2312yes—
358C4×Dic134C2312yes—
359#14524008C2318yes—
360#14524008C2314yes—
361#14524008C2314yes—
362#14524008C2314yes—
363#14524008C2318yes—
364#14524008C2318yes—
365#14524008C2318yes—
366C4×D268C2312yes—
367C4×D268C2312yes—
368C4×D268C2312yes—
369C4×D268C2312yes—
370C4×D268C2312yes—
371C4×D268C2312yes—
372C4×D268C2312yes—
373C4×D268C2314yes—
374C4×D268C2312yes—
375C4×D268C2312yes—
376C4×D268C2312yes—
377C4×D268C2312yes—
378C4×D268C2312yes—
379C4×D268C2312yes—
380C4×D268C2312yes—
381C4×D268C2318yes—
382D4×Dic67C2314yes—
383D4×Dic67C2314yes—
384D4×Dic67C2318yes—
385#14524005C2314yes—
386#14524005C2318yes—
387#14524005C2318yes—
388#14524005C2318yes—
389C4×C22⋊D67C2314yes—
390C4×C22⋊D67C2314yes—
391C4×C22⋊D67C2314yes—
392C4×C22⋊D67C2314yes—
393C4×C22⋊D67C2314yes—
394C4×C22⋊D67C2314yes—
395C4×C22⋊D67C2318yes—
396C4×C22⋊D67C2314yes—
397C4×C22⋊D67C2314yes—
398C4×C22⋊D67C2314yes—
399C4×C22⋊D67C2314yes—
400C4×C22⋊D67C2314yes—
401C4×C22⋊D67C2314yes—
402C4×C22⋊D67C2318yes—
403C4×C22⋊D67C2318yes—
404C4×C22⋊D67C2314yes—
405C4×C22⋊D67C2314yes—
406(C22⋊D67)⋊C4C2318yes—
407(C22⋊D67)⋊C4C2318yes—
408(C22⋊D67)⋊C4C2318yes—
409(C22⋊D67)⋊C4C2318yes—
410(C22⋊D67)⋊C4C2318yes—
411(C22⋊D67)⋊C4C2318yes—
412(C22⋊D67)⋊C4C2318yes—
413(C22⋊D67)⋊C4C2318yes—
414#14524002C2312yes—
415#14524002C2312yes—
416#14524002C2312yes—
417#14524002C2312yes—
418#14524002C2314yes—
419#14524002C2312yes—
420#14524002C2312yes—
421#14524002C2312yes—
422#14524001C2318yes—
423#14524001C2318yes—
424#14524001C2314yes—
425#14524001C2314yes—
426#14524001C2314yes—
427#14524000C2314yes—
428#14524000C2314yes—
429#14524000C2314yes—
430#14524000C2314yes—
431#14524000C2314yes—
432#14524000C2318yes—
433#14524000C2314yes—
434#14524000C2314yes—
435#14524000C2318yes—
436#14523999C2318yes—
437#14523999C2318yes—
438#14523999C2318yes—
439#14523999C2318yes—
440C2×C4⋊Dic67C2311yescharacteristic
441C2×C4⋊Dic67C2314yes—
442C2×C4⋊Dic67C2311yescharacteristic
443C2×Dic67⋊C4C2312yes—
444C2×Dic67⋊C4C2318yes—
445C2×Dic67⋊C4C2312yes—
446C4⋊C4×D67C2318yes—
447C4⋊C4×D67C2314yes—
448C2×C22⋊Dic67C2312yes—
449C2×(C2×D67)⋊C4C2312yes—
450C2×(C2×D67)⋊C4C2312yes—
451C2×C4×Dic67C2312yes—
452C2×C4×Dic67C2312yes—
453C2×C4×Dic67C2312yes—
454C2×C4×Dic67C2318yes—
455C42×D67C2314yes—
456C42×D67C2314yes—
457C42×D67C2314yes—
458C42×D67C2314yes—
459C42×D67C2318yes—
460C42×D67C2314yes—
461C2×#41×C67C2312yes—
462C2×#41×C67C2312yes—
463C2×#41×C67C2312yes—
464C23×C4×C67C2311yescharacteristic
465C23×C4×C67C2311yescharacteristic
466C23×C4×C67C2311yescharacteristic
467C4⋊Q8×C67C2311yescharacteristic
468C4⋊Q8×C67C2311yescharacteristic
469C4⋊Q8×C67C2311yescharacteristic
470#127×C67C2311yescharacteristic
471#126×C67C2314yes—
472#126×C67C2314yes—
473#125×C67C2312yes—
474#125×C67C2312yes—
475#125×C67C2312yes—
476#124×C67C2312yes—
477#124×C67C2312yes—
478#124×C67C2312yes—
479#123×C67C2314yes—
480#123×C67C2314yes—
481#123×C67C2314yes—
482C22⋊Q8×C67C2312yes—
483C22⋊Q8×C67C2312yes—
484C22⋊Q8×C67C2312yes—
485C22⋊Q8×C67C2312yes—
486C22⋊Q8×C67C2312yes—
487C22⋊Q8×C67C2312yes—
488#121×C67C2312yes—
489#121×C67C2312yes—
490#121×C67C2312yes—
491#121×C67C2312yes—
492#121×C67C2312yes—
493#121×C67C2312yes—
494#120×C67C2314yes—
495C4×Q8×C67C2312yes—
496C4×Q8×C67C2312yes—
497C4×Q8×C67C2312yes—
498C4×Q8×C67C2312yes—
499C4×Q8×C67C2312yes—
500C4×Q8×C67C2312yes—
501C4×D4×C67C2312yes—
502C4×D4×C67C2314yes—
503C4×D4×C67C2314yes—
504C4×D4×C67C2312yes—
505C4×D4×C67C2314yes—
506C4×D4×C67C2314yes—
507C4×D4×C67C2312yes—
508C4×D4×C67C2312yes—
509C4×D4×C67C2314yes—
510C4×D4×C67C2314yes—
511C4×D4×C67C2312yes—
512C4×D4×C67C2312yes—
513#117×C67C2314yes—
514#117×C67C2312yes—
515#117×C67C2312yes—
516#117×C67C2312yes—
517#117×C67C2314yes—
518#117×C67C2314yes—
519C2×C42×C67C2311yescharacteristic
520C2×C42×C67C2311yescharacteristic
521C2×C42×C67C2311yescharacteristic
522C2×C42×C67C2311yescharacteristic
523C2×C42×C67C2311yescharacteristic
524C2×C42×C67C2311yescharacteristic
525C2×C42×C67C2311yescharacteristic
526C2×C42×C67C2311yescharacteristic
527C2×C42×C67C2311yescharacteristic
528C2×C42×C67C2311yescharacteristic
529C2×C42×C67C2311yescharacteristic
530C2×C42×C67C2311yescharacteristic
531C2×C42×C67C2314yes—
532C23×D67C2412yes—
533#11761629—48no—
534#11761628—28no—
535#11761628—28no—
536#11761628—28no—
537#11761628—28no—
538#11761628—28no—
539#11761628—216no—
540#11761628—44no—
541#11761628—416no—
542#11761628—44no—
543#11761627—232no—
544#11761627—216no—
545#11761627—48no—
546C2×Dic134—216no—
547C2×Dic134#4118yescomplemented
548C2×Dic134C2418yes—
549C2×Dic134C2412yes—
550C2×Dic134C2412yes—
551C2×Dic134C2418yes—
552C2×Dic134C2412yes—
553C2×Dic134C2412yes—
554C2×Dic134C2412yes—
555Q8×D67—216no—
556C2×D268—24no—
557C2×D268C2412yes—
558C2×D268C2412yes—
559C2×D268C2412yes—
560C2×D268C2412yes—
561C2×D268C2418yes—
562C2×D268C2418yes—
563C2×D268C2412yes—
564C2×C22⋊D67—28no—
565C2×C22⋊D67C2414yes—
566C2×C22⋊D67C2418yes—
567C2×C22⋊D67C2414yes—
568C2×C22⋊D67C2414yes—
569C2×C22⋊D67C2418yes—
570C2×C22⋊D67C2418yes—
571C2×C22⋊D67C2418yes—
572C2×C22⋊D67C2414yes—
573C2×C22⋊D67C2414yes—
574C22×Dic67C2418yes—
575C22×Dic67C2412yes—
576C22×Dic67C2412yes—
577C22×Dic67C2418yes—
578C22×Dic67C2412yes—
579C2×C4×D67—28no—
580C2×C4×D67—44no—
581C2×C4×D67—44no—
582C2×C4×D67C2414yes—
583C2×C4×D67C2414yes—
584C2×C4×D67C2414yes—
585C2×C4×D67C2414yes—
586C2×C4×D67C2414yes—
587C2×C4×D67C2418yes—
588C2×C4×D67C2414yes—
589C2×C4×D67C2414yes—
590C2×C4×D67C2414yes—
591C2×C4×D67C2414yes—
592C2×C4×D67C2418yes—
593C4⋊Dic67C2412yes—
594C4⋊Dic67C2418yes—
595C4⋊Dic67C2412yes—
596C4⋊Dic67C2412yes—
597C4⋊Dic67C2412yes—
598C4⋊Dic67C2412yes—
599C4⋊Dic67C2412yes—
600C4⋊Dic67C2412yes—
601C4⋊Dic67C2418yes—
602C4⋊Dic67C2412yes—
603C4⋊Dic67C2412yes—
604C4⋊Dic67C2412yes—
605Dic67⋊C4C2414yes—
606Dic67⋊C4C2418yes—
607Dic67⋊C4C2418yes—
608Dic67⋊C4C2414yes—
609Dic67⋊C4C2414yes—
610Dic67⋊C4C2414yes—
611Dic67⋊C4C2414yes—
612Dic67⋊C4C2414yes—
613Dic67⋊C4C2418yes—
614Dic67⋊C4C2414yes—
615Dic67⋊C4C2418yes—
616Dic67⋊C4C2414yes—
617Dic67⋊C4C2414yes—
618Dic67⋊C4C2418yes—
619Dic67⋊C4C2418yes—
620Dic67⋊C4C2414yes—
621C22⋊Dic67C2414yes—
622C22⋊Dic67C2414yes—
623C22⋊Dic67C2414yes—
624C22⋊Dic67C2418yes—
625C22⋊Dic67C2418yes—
626C22⋊Dic67C2414yes—
627C22⋊Dic67C2414yes—
628(C2×D67)⋊C4C2414yes—
629(C2×D67)⋊C4C2414yes—
630(C2×D67)⋊C4C2414yes—
631(C2×D67)⋊C4C2414yes—
632(C2×D67)⋊C4C2414yes—
633(C2×D67)⋊C4C2418yes—
634(C2×D67)⋊C4C2414yes—
635(C2×D67)⋊C4C2414yes—
636(C2×D67)⋊C4C2414yes—
637(C2×D67)⋊C4C2414yes—
638(C2×D67)⋊C4C2418yes—
639(C2×D67)⋊C4C2418yes—
640(C2×D67)⋊C4C2414yes—
641(C2×D67)⋊C4C2418yes—
642(C2×D67)⋊C4C2418yes—
643(C2×D67)⋊C4C2418yes—
644C4×Dic67C2414yes—
645C4×Dic67C2414yes—
646C4×Dic67C2414yes—
647C4×Dic67C2414yes—
648C4×Dic67C2414yes—
649C4×Dic67C2414yes—
650C4×Dic67C2414yes—
651C4×Dic67C2414yes—
652C4×Dic67C2418yes—
653C4×Dic67C2418yes—
654C4×Dic67C2414yes—
655C4×Dic67C2418yes—
656C4×Dic67C2418yes—
657C24×C67C2411yescharacteristic
658#41×C67—28no—
659#41×C67—44no—
660#41×C67—44no—
661C2×Q8×C67C2412yes—
662C2×Q8×C67C2412yes—
663C2×Q8×C67C2412yes—
664C2×D4×C67C2414yes—
665C2×D4×C67C2412yes—
666C2×D4×C67C2412yes—
667C2×D4×C67C2414yes—
668C2×D4×C67C2414yes—
669C2×D4×C67C2412yes—
670C22×C4×C67—24no—
671C22×C4×C67—42no—
672C22×C4×C67—42no—
673C22×C4×C67C2411yescharacteristic
674C22×C4×C67C2411yescharacteristic
675C22×C4×C67C2411yescharacteristic
676C22×C4×C67C2411yescharacteristic
677C22×C4×C67C2411yescharacteristic
678C22×C4×C67C2411yescharacteristic
679C22×C4×C67C2411yescharacteristic
680C22×C4×C67C2411yescharacteristic
681C22×C4×C67C2411yescharacteristic
682C22×C4×C67C2411yescharacteristic
683C22×C4×C67C2411yescharacteristic
684C22×C4×C67C2414yes—
685C22×C4×C67C2414yes—
686C22×C4×C67C2411yescharacteristic
687C22×C4×C67C2411yescharacteristic
688C22×C4×C67C2411yescharacteristic
689C22×C4×C67C2411yescharacteristic
690C22×C4×C67C2411yescharacteristic
691C22×C4×C67C2411yescharacteristic
692C22×C4×C67C2414yes—
693C22×C4×C67C2411yescharacteristic
694C4⋊C4×C67C2412yes—
695C4⋊C4×C67C2412yes—
696C4⋊C4×C67C2412yes—
697C4⋊C4×C67C2412yes—
698C4⋊C4×C67C2412yes—
699C4⋊C4×C67C2412yes—
700C4⋊C4×C67C2414yes—
701C4⋊C4×C67C2414yes—
702C4⋊C4×C67C2414yes—
703C4⋊C4×C67C2414yes—
704C4⋊C4×C67C2414yes—
705C4⋊C4×C67C2414yes—
706C22⋊C4×C67C2414yes—
707C22⋊C4×C67C2414yes—
708C22⋊C4×C67C2414yes—
709C22⋊C4×C67C2414yes—
710C22⋊C4×C67C2414yes—
711C22⋊C4×C67C2414yes—
712C22⋊C4×C67C2414yes—
713C22⋊C4×C67C2414yes—
714C22⋊C4×C67C2414yes—
715C42×C67C2411yescharacteristic
716C42×C67C2411yescharacteristic
717C42×C67C2411yescharacteristic
718C42×C67C2411yescharacteristic
719C42×C67C2411yescharacteristic
720C42×C67C2411yescharacteristic
721C42×C67C2411yescharacteristic
722C42×C67C2411yescharacteristic
723C42×C67C2411yescharacteristic
724C42×C67C2411yescharacteristic
725C42×C67C2411yescharacteristic
726C42×C67C2411yescharacteristic
727C42×C67C2411yescharacteristic
728C42×C67C2411yescharacteristic
729C42×C67C2411yescharacteristic
730C42×C67C2411yescharacteristic
731C42×C67C2414yes—
732C42×C67C2414yes—
733C42×C67C2414yes—
734C23×C67—22no—
735C23×C67—41no—
736C23×C67—41no—
737C23×C67C2514yes—
738C23×C67C2511yescharacteristic
739C23×C67C2511yescharacteristic
740C23×C67C2511yescharacteristic
741C22×D67—24no—
742C22×D67—42no—
743C22×D67—42no—
744C22×D67C2514yes—
745C22×D67C2514yes—
746Q8×C67—24no—
747Q8×C67—24no—
748Q8×C67—42no—
749D4×C67—28no—
750D4×C67—24no—
751D4×C67—24no—
752D4×C67—44no—
753D4×C67—44no—
754D4×C67—42no—
755C2×C4×C67—22no—
756C2×C4×C67—22no—
757C2×C4×C67—22no—
758C2×C4×C67—22no—
759C2×C4×C67—22no—
760C2×C4×C67—28no—
761C2×C4×C67—22no—
762C2×C4×C67—22no—
763C2×C4×C67—22no—
764C2×C4×C67—22no—
765C2×C4×C67—22no—
766C2×C4×C67—22no—
767C2×C4×C67—28no—
768C2×C4×C67—41no—
769C2×C4×C67—41no—
770C2×C4×C67—41no—
771C2×C4×C67—41no—
772C2×C4×C67—41no—
773C2×C4×C67—41no—
774C2×C4×C67—44no—
775C2×C4×C67C2×#4114yes—
776C2×C4×C67C2511yescharacteristic
777C2×C4×C67C2511yescharacteristic
778C2×C4×C67C2511yescharacteristic
779C2×C4×C67C2511yescharacteristic
780C2×C4×C67C2511yescharacteristic
781C2×C4×C67C2511yescharacteristic
782C2×C4×C67C2511yescharacteristic
783C2×C4×C67C2511yescharacteristic
784C2×C4×C67C2514yes—
785C2×C4×C67C2514yes—
786C2×C4×C67C2514yes—
787C2×C4×C67C2511yescharacteristic
788C2×C4×C67C2511yescharacteristic
789C2×C4×C67C2511yescharacteristic
790C2×C4×C67C2511yescharacteristic
791C22⋊D67—28no—
792C22⋊D67—28no—
793C22⋊D67—28no—
794C22⋊D67—216no—
795C22⋊D67—48no—
796C22⋊D67—44no—
797C22⋊D67—48no—
798C22⋊D67—44no—
799C22⋊D67—48no—
800C2×Dic67—216no—
801C2×Dic67—42no—
802C2×Dic67—42no—
803C2×Dic67—48no—
804C2×Dic67C2×#4118yes—
805C2×Dic67C2514yes—
806C2×Dic67C2514yes—
807C2×Dic67C2514yes—
808C2×Dic67C2514yes—
809C2×Dic67C2514yes—
810C2×Dic67C2514yes—
811D268—24no—
812D268—24no—
813D268—24no—
814D268—24no—
815D268—42no—
816D268—48no—
817D268—48no—
818C4×D67—28no—
819C4×D67—28no—
820C4×D67—28no—
821C4×D67—28no—
822C4×D67—28no—
823C4×D67—28no—
824C4×D67—216no—
825C4×D67—44no—
826C4×D67—44no—
827C4×D67—44no—
828C4×D67—48no—
829Dic134—24no—
830Dic134—24no—
831Dic134—216no—
832Dic134—42no—
833Dic134—48no—
834Dic134C2×#4118yes—
835Dic134C2×#4118yes—
836C22×C67—21no—
837C22×C67—21no—
838C22×C67—24no—
839C22×C67—21no—
840C22×C67—21no—
841C22×C67—24no—
842C22×C67—21no—
843C22×C67—21no—
844C22×C67—24no—
845C22×C67—21no—
846C22×C67—21no—
847C22×C67—44no—
848C22×C67C22×#4112yes—
849C22×C67C2611yescharacteristic
850C2×D67—24no—
851C2×D67—24no—
852C2×D67—24no—
853C2×D67—24no—
854C2×D67—24no—
855C2×D67—24no—
856C2×D67—48no—
857C4×C67—24no—
858C4×C67—21no—
859C4×C67—21no—
860C4×C67—21no—
861C4×C67—24no—
862C4×C67—21no—
863C4×C67—21no—
864C4×C67—21no—
865C4×C67—24no—
866C4×C67—21no—
867C4×C67—21no—
868C4×C67C22×#4112yes—
869C4×C67C22×#4112yes—
870C4×C67#58512yes—
871C4×C67#58512yes—
872Dic67—24no—
873Dic67—24no—
874Dic67—24no—
875Dic67—24no—
876Dic67—24no—
877Dic67C22×#4118yes—
878#62793—671nomaximal, Sylow
879C2×C67—22no—
880C2×C67—44no—
881C2×C67—41no—
882C2×C67—41no—
883C2×C67C23×#4111yescharacteristic
884C2×C67C2×#58511yescharacteristic
885C2×C67C2×#58511yescharacteristic
886D67—44no—
887D67—44no—
888#3524—674no—
889#3524—674no—
890#3518—672no—
891#3518—672no—
892#3517—672no—
893#3517—672no—
894#3506—671no—
895#3506—671no—
896#3506—674no—
897#3502—671no—
898#3497—671no—
899#3493—674no—
900#3493—672no—
901#3487—672no—
902#3483—672no—
903#3483—672no—
904#3482—672no—
905#3482—672no—
906#3480—674no—
907#3480—674no—
908#3460—674no—
909#3460—672no—
910#3444—671no—
911#3444—674no—
912#3444D6711yescharacteristic, complemented
913C4×2−1+4—672no—
914C2×C4×#41—671no—
915C67#6279311yescharacteristic, complemented, Sylow
916C2×2−1+4—672no—
917C22×#41—671no—
918#559—674no—
919#559—678no—
920#559—674no—
921#559—678no—
922Q82—672no—
923Q82—672no—
924#557—672no—
925#557—674no—
926#557—674no—
927#557—672no—
928#556—672no—
929#556—678no—
930#556—674no—
931#556—674no—
932#556—678no—
933#556—672no—
934#556—674no—
935#556—674no—
936#555—672no—
937#555—678no—
938#555—674no—
939#555—674no—
940#555—674no—
941#555—672no—
942#555—678no—
943#555—674no—
944#553—678no—
945#553—674no—
946#553—678no—
947#553—674no—
948#553—674no—
949#553—674no—
950#553—678no—
951#553—678no—
952#552—678no—
953#552—674no—
954#552—674no—
955#552—678no—
956#550—674no—
957#550—672no—
958#550—672no—
959#550—674no—
960#550—674no—
961#550—674no—
962#550—672no—
963#550—674no—
964#550—674no—
965#550—672no—
966D4×Q8—672no—
967D4×Q8—672no—
968#548—674no—
969#548—674no—
970#548—674no—
971#548—674no—
972#548—674no—
973#548—674no—
974#547—674no—
975#547—672no—
976#547—674no—
977#547—672no—
978#544—674no—
979#544—672no—
980#542—678no—
981#542—678no—
982#542—674no—
983#542—674no—
984#540—678no—
985#540—678no—
986#540—674no—
987#540—674no—
988#538—674no—
989#538—674no—
990#538—678no—
991#538—678no—
992#537—672no—
993#537—674no—
994#535—672no—
995#535—678no—
996#535—672no—
997#533—674no—
998#533—674no—
999#533—674no—
1000#533—671no—
1001#533—671no—
1002#533—671no—
1003#533C2×D6711yescharacteristic
1004#533C2×D6711yescharacteristic, complemented
1005#533C2×D6711yescharacteristic, complemented
1006#532—678no—
1007#532—674no—
1008#532—674no—
1009#532—674no—
1010#532—678no—
1011#532—674no—
1012#532—671no—
1013#532—671no—
1014#532—671no—
1015#532—674no—
1016#532C2×D6711yescharacteristic
1017#532C2×D6711yescharacteristic, complemented
1018#532C2×D6711yescharacteristic, complemented
1019#529—678no—
1020#529—678no—
1021#529—674no—
1022#529—674no—
1023#529—678no—
1024#529—674no—
1025#529—678no—
1026#529—678no—
1027#529—678no—
1028#529—672no—
1029#529—672no—
1030#529—672no—
1031#529—672no—
1032#529—672no—
1033#529—672no—
1034#529—674no—
1035#529C2×D6712yes—
1036#529C2×D6712yes—
1037#529C2×D6712yescomplemented
1038#529C2×D6712yescomplemented
1039#529C2×D6712yescomplemented
1040#529C2×D6712yescomplemented
1041#525—672no—
1042#525—672no—
1043#525—672no—
1044#525—678no—
1045#525—674no—
1046#525—674no—
1047#525—678no—
1048#525C2×D6712yes—
1049#525C2×D6712yes—
1050#525C2×D6712yes—
1051#520—672no—
1052#520—678no—
1053#520—674no—
1054#520—672no—
1055#520—674no—
1056#519—674no—
1057#519—672no—
1058#519—674no—
1059C4×#41—674no—
1060C4×#41—678no—
1061C4×#41—674no—
1062C4×#41—674no—
1063C4×#41—678no—
1064C4×#41—672no—
1065C4×#41—672no—
1066C4×#41—672no—
1067C4×#41—672no—
1068C4×#41—672no—
1069C4×#41—672no—
1070C4×#41—672no—
1071C4×#41—672no—
1072C4×#41—672no—
1073C4×#41—674no—
1074C4×#41—672no—
1075C4×#41—672no—
1076C4×#41C2×D6712yes—
1077C4×#41C2×D6712yescomplemented
1078C4×#41C2×D6712yescomplemented
1079C2×C4×Q8—674no—
1080C2×C4×Q8—671no—
1081C2×C4×Q8—671no—
1082C2×C4×Q8—674no—
1083C2×C4×D4—672no—
1084C2×C4×D4—672no—
1085C2×C4×D4—671no—
1086C2×C4×D4—671no—
1087C2×#117—671no—
1088C2×#117—672no—
1089C22×C42—672no—
1090C22×C42C2×D6711yescharacteristic
10912−1+4—13416no—
1092C2×#41—674no—
1093C2×#41—674no—
1094C2×#41—678no—
1095C2×#41—674no—
1096C2×#41—672no—
1097C2×#41—678no—
1098C2×#41—672no—
1099C2×#41—672no—
1100C2×#41—672no—
1101C2×#41—672no—
1102C2×#41—672no—
1103C2×#41—672no—
1104C2×#41—674no—
1105C2×#41—1348no—
1106C2×#41C22×D6712yes—
1107C2×#41C22×D6712yes—
1108C2×#41C22×D6712yes—
1109C22×Q8—674no—
1110C22×Q8—671no—
1111C22×Q8—674no—
1112C22×D4—672no—
1113C22×D4—671no—
1114C23×C4—672no—
1115C23×C4—672no—
1116C23×C4—672no—
1117C23×C4C22×D6711yescharacteristic
1118C23×C4C22×D6711yescharacteristic
1119C23×C4C22×D6711yescharacteristic
1120C4⋊Q8—674no—
1121C4⋊Q8—678no—
1122C4⋊Q8—674no—
1123C4⋊Q8—674no—
1124C4⋊Q8—678no—
1125C4⋊Q8—674no—
1126C4⋊Q8—671no—
1127C4⋊Q8—671no—
1128C4⋊Q8—671no—
1129C4⋊Q8—674no—
1130C4⋊Q8C22×D6711yescharacteristic
1131C4⋊Q8C22×D6711yescharacteristic
1132C4⋊Q8C22×D6711yescharacteristic
1133#127—674no—
1134#127—674no—
1135#127—678no—
1136#127—678no—
1137#127—671no—
1138#127—674no—
1139#127C22×D6711yescharacteristic
1140#126—678no—
1141#126—678no—
1142#126—678no—
1143#126—678no—
1144#126—678no—
1145#126—678no—
1146#126—678no—
1147#126—674no—
1148#126—674no—
1149#126—678no—
1150#126C22×D6714yes—
1151#126C22×D6714yes—
1152#125—678no—
1153#125—678no—
1154#125—678no—
1155#125—678no—
1156#125—674no—
1157#125—672no—
1158#125—672no—
1159#125—672no—
1160#125—674no—
1161#125C22×D6712yes—
1162#125C22×D6712yes—
1163#125C22×D6712yes—
1164#124—674no—
1165#124—678no—
1166#124—678no—
1167#124—678no—
1168#124—678no—
1169#124—678no—
1170#124—678no—
1171#124—678no—
1172#124—678no—
1173#124—678no—
1174#124—672no—
1175#124—672no—
1176#124—672no—
1177#124—674no—
1178#124—678no—
1179#124C22×D6712yes—
1180#124C22×D6712yes—
1181#124C22×D6712yes—
1182#123—678no—
1183#123—674no—
1184#123—674no—
1185#123—674no—
1186#123—678no—
1187#123—678no—
1188#123—678no—
1189#123—678no—
1190#123—678no—
1191#123—678no—
1192#123—678no—
1193#123—678no—
1194#123—678no—
1195#123C22×D6714yes—
1196#123C22×D6714yes—
1197#123C22×D6714yes—
1198C22⋊Q8—674no—
1199C22⋊Q8—674no—
1200C22⋊Q8—672no—
1201C22⋊Q8—672no—
1202C22⋊Q8—672no—
1203C22⋊Q8—672no—
1204C22⋊Q8—672no—
1205C22⋊Q8—672no—
1206C22⋊Q8—674no—
1207C22⋊Q8—678no—
1208C22⋊Q8—674no—
1209C22⋊Q8—678no—
1210C22⋊Q8—678no—
1211C22⋊Q8—678no—
1212C22⋊Q8—678no—
1213C22⋊Q8—678no—
1214C22⋊Q8C22×D6712yes—
1215C22⋊Q8C22×D6712yes—
1216C22⋊Q8C22×D6712yes—
1217C22⋊Q8C22×D6712yes—
1218C22⋊Q8C22×D6712yes—
1219C22⋊Q8C22×D6712yes—
1220#121—678no—
1221#121—674no—
1222#121—678no—
1223#121—678no—
1224#121—674no—
1225#121—678no—
1226#121—678no—
1227#121—678no—
1228#121—678no—
1229#121—672no—
1230#121—672no—
1231#121—672no—
1232#121—672no—
1233#121—672no—
1234#121—672no—
1235#121—674no—
1236#121—674no—
1237#121—674no—
1238#121—678no—
1239#121—674no—
1240#121—674no—
1241#121—674no—
1242#121—678no—
1243#121—678no—
1244#121—678no—
1245#121—678no—
1246#121—678no—
1247#121—678no—
1248#121—678no—
1249#121—678no—
1250#121C22×D6712yes—
1251#121C22×D6712yes—
1252#121C22×D6712yes—
1253#121C22×D6712yes—
1254#121C22×D6712yes—
1255#121C22×D6712yes—
1256#120—674no—
1257#120—678no—
1258#120—678no—
1259#120C22×D6714yes—
1260C4×Q8—674no—
1261C4×Q8—674no—
1262C4×Q8—674no—
1263C4×Q8—678no—
1264C4×Q8—678no—
1265C4×Q8—674no—
1266C4×Q8—674no—
1267C4×Q8—678no—
1268C4×Q8—678no—
1269C4×Q8—672no—
1270C4×Q8—672no—
1271C4×Q8—678no—
1272C4×Q8—672no—
1273C4×Q8—672no—
1274C4×Q8—672no—
1275C4×Q8—672no—
1276C4×Q8—672no—
1277C4×Q8—672no—
1278C4×Q8—672no—
1279C4×Q8—674no—
1280C4×Q8—674no—
1281C4×Q8—678no—
1282C4×Q8—672no—
1283C4×Q8—672no—
1284C4×Q8—674no—
1285C4×Q8—672no—
1286C4×Q8—672no—
1287C4×Q8—672no—
1288C4×Q8C22×D6712yes—
1289C4×Q8C22×D6712yes—
1290C4×Q8C22×D6712yes—
1291C4×Q8C22×D6712yes—
1292C4×Q8C22×D6712yes—
1293C4×Q8C22×D6712yes—
1294C4×D4—678no—
1295C4×D4—674no—
1296C4×D4—674no—
1297C4×D4—674no—
1298C4×D4—674no—
1299C4×D4—674no—
1300C4×D4—674no—
1301C4×D4—674no—
1302C4×D4—674no—
1303C4×D4—674no—
1304C4×D4—674no—
1305C4×D4—674no—
1306C4×D4—678no—
1307C4×D4—674no—
1308C4×D4—678no—
1309C4×D4—674no—
1310C4×D4—678no—
1311C4×D4—674no—
1312C4×D4—674no—
1313C4×D4—674no—
1314C4×D4—678no—
1315C4×D4—678no—
1316C4×D4—678no—
1317C4×D4—674no—
1318C4×D4—678no—
1319C4×D4—678no—
1320C4×D4—678no—
1321C4×D4—678no—
1322C4×D4—678no—
1323C4×D4—678no—
1324C4×D4—678no—
1325C4×D4—678no—
1326C4×D4—672no—
1327C4×D4—672no—
1328C4×D4—672no—
1329C4×D4—672no—
1330C4×D4—672no—
1331C4×D4—672no—
1332C4×D4—672no—
1333C4×D4—672no—
1334C4×D4—672no—
1335C4×D4—672no—
1336C4×D4—672no—
1337C4×D4—674no—
1338C4×D4—678no—
1339C4×D4—672no—
1340C4×D4—672no—
1341C4×D4—672no—
1342C4×D4C22×D6714yes—
1343C4×D4C22×D6712yes—
1344C4×D4C22×D6712yes—
1345C4×D4C22×D6714yes—
1346C4×D4C22×D6712yes—
1347C4×D4C22×D6714yes—
1348C4×D4C22×D6714yes—
1349C4×D4C22×D6714yes—
1350C4×D4C22×D6714yes—
1351C4×D4C22×D6712yes—
1352C4×D4C22×D6712yes—
1353C4×D4C22×D6712yes—
1354#117—672no—
1355#117—672no—
1356#117—672no—
1357#117—672no—
1358#117—672no—
1359#117—674no—
1360#117—672no—
1361#117—672no—
1362#117—678no—
1363#117—674no—
1364#117—674no—
1365#117—674no—
1366#117—678no—
1367#117—678no—
1368#117—678no—
1369#117—678no—
1370#117—678no—
1371#117—674no—
1372#117—674no—
1373#117—674no—
1374#117—674no—
1375#117—674no—
1376#117—674no—
1377#117—678no—
1378#117—678no—
1379#117—674no—
1380#117C22×D6714yes—
1381#117C22×D6712yes—
1382#117C22×D6714yes—
1383#117C22×D6712yes—
1384#117C22×D6712yes—
1385#117C22×D6714yes—
1386C2×C4⋊C4—672no—
1387C2×C4⋊C4—671no—
1388C2×C4⋊C4—672no—
1389C2×C4⋊C4—671no—
1390C2×C4⋊C4—678no—
1391C2×C4⋊C4—674no—
1392C2×C4⋊C4—678no—
1393C2×C4⋊C4—674no—
1394C2×C22⋊C4—672no—
1395C2×C22⋊C4—672no—
1396C2×C22⋊C4—672no—
1397C2×C42—672no—
1398C2×C42—672no—
1399C2×C42—672no—
1400C2×C42—678no—
1401C2×C42—678no—
1402C2×C42—674no—
1403C2×C42—674no—
1404C2×C42—674no—
1405C2×C42—674no—
1406C2×C42—674no—
1407C2×C42C22×D6711yescharacteristic
1408C2×C42C22×D6711yescharacteristic
1409C2×C42C22×D6711yescharacteristic
1410C2×C42C22×D6714yes—
1411C2×C42C22×D6711yescharacteristic
1412C2×C42C22×D6711yescharacteristic
1413C2×C42C22×D6711yescharacteristic
1414C2×C42C22×D6711yescharacteristic
1415C2×C42C22×D6711yescharacteristic
1416C2×C42C22×D6711yescharacteristic
1417C2×C42C22×D6711yescharacteristic
1418C2×C42C22×D6711yescharacteristic
1419C2×C42C22×D6711yescharacteristic
1420C24—672no—
1421C24C23×D6711yescharacteristic
1422#41—28no—
1423#41—44no—
1424#41—44no—
1425#41—2684no—
1426#41—2684no—
1427#41—26816no—
1428#41—2688no—
1429#41—2688no—
1430#41—1348no—
1431#41—1348no—
1432#41—1348no—
1433#41—1348no—
1434#41—13416no—
1435#41—13432no—
1436#41—13416no—
1437#41—1348no—
1438C2×Q8—678no—
1439C2×Q8—672no—
1440C2×Q8—678no—
1441C2×Q8—672no—
1442C2×Q8—672no—
1443C2×Q8—678no—
1444C2×Q8—672no—
1445C2×Q8—672no—
1446C2×Q8—13416no—
1447C2×Q8—13416no—
1448C2×Q8C23×D6712yes—
1449C2×Q8C23×D6712yes—
1450C2×Q8C23×D6712yes—
1451C2×D4—678no—
1452C2×D4—674no—
1453C2×D4—678no—
1454C2×D4—674no—
1455C2×D4—678no—
1456C2×D4—674no—
1457C2×D4—674no—
1458C2×D4—674no—
1459C2×D4—678no—
1460C2×D4—678no—
1461C2×D4—678no—
1462C2×D4—672no—
1463C2×D4—672no—
1464C2×D4—672no—
1465C2×D4—672no—
1466C2×D4—672no—
1467C2×D4—1348no—
1468C2×D4—1344no—
1469C2×D4C23×D6714yes—
1470C2×D4C23×D6712yes—
1471C2×D4C23×D6712yes—
1472C2×D4C23×D6714yes—
1473C2×D4C23×D6714yes—
1474C2×D4C23×D6712yes—
1475C22×C4—24no—
1476C22×C4—42no—
1477C22×C4—42no—
1478C22×C4—2684no—
1479C22×C4—2684no—
1480C22×C4—672no—
1481C22×C4—672no—
1482C22×C4—678no—
1483C22×C4—674no—
1484C22×C4—674no—
1485C22×C4—678no—
1486C22×C4—674no—
1487C22×C4—672no—
1488C22×C4—678no—
1489C22×C4—674no—
1490C22×C4—674no—
1491C22×C4—674no—
1492C22×C4—678no—
1493C22×C4—674no—
1494C22×C4—674no—
1495C22×C4—674no—
1496C22×C4—1348no—
1497C22×C4C23×D6711yescharacteristic
1498C22×C4C23×D6711yescharacteristic
1499C22×C4C23×D6711yescharacteristic
1500C22×C4C23×D6711yescharacteristic
1501C22×C4C23×D6711yescharacteristic
1502C22×C4C23×D6711yescharacteristic
1503C22×C4C23×D6711yescharacteristic
1504C22×C4C23×D6711yescharacteristic
1505C22×C4C23×D6714yes—
1506C22×C4C23×D6711yescharacteristic
1507C22×C4C23×D6714yes—
1508C22×C4C23×D6711yescharacteristic
1509C22×C4C23×D6711yescharacteristic
1510C22×C4C23×D6711yescharacteristic
1511C22×C4C23×D6711yescharacteristic
1512C22×C4C23×D6711yescharacteristic
1513C22×C4C23×D6711yescharacteristic
1514C22×C4C23×D6711yescharacteristic
1515C22×C4C23×D6711yescharacteristic
1516C22×C4C23×D6714yes—
1517C22×C4C23×D6711yescharacteristic
1518C4⋊C4—674no—
1519C4⋊C4—674no—
1520C4⋊C4—672no—
1521C4⋊C4—672no—
1522C4⋊C4—678no—
1523C4⋊C4—672no—
1524C4⋊C4—678no—
1525C4⋊C4—674no—
1526C4⋊C4—678no—
1527C4⋊C4—674no—
1528C4⋊C4—674no—
1529C4⋊C4—672no—
1530C4⋊C4—672no—
1531C4⋊C4—672no—
1532C4⋊C4—674no—
1533C4⋊C4—678no—
1534C4⋊C4—672no—
1535C4⋊C4—672no—
1536C4⋊C4—674no—
1537C4⋊C4—674no—
1538C4⋊C4—674no—
1539C4⋊C4—674no—
1540C4⋊C4—678no—
1541C4⋊C4—678no—
1542C4⋊C4—678no—
1543C4⋊C4—672no—
1544C4⋊C4—678no—
1545C4⋊C4—672no—
1546C4⋊C4C23×D6712yes—
1547C4⋊C4C23×D6714yes—
1548C4⋊C4C23×D6712yes—
1549C4⋊C4C23×D6714yes—
1550C4⋊C4C23×D6712yes—
1551C4⋊C4C23×D6712yes—
1552C4⋊C4C23×D6714yes—
1553C4⋊C4C23×D6714yes—
1554C4⋊C4C23×D6714yes—
1555C4⋊C4C23×D6714yes—
1556C4⋊C4C23×D6712yes—
1557C4⋊C4C23×D6712yes—
1558C22⋊C4—674no—
1559C22⋊C4—674no—
1560C22⋊C4—674no—
1561C22⋊C4—678no—
1562C22⋊C4—674no—
1563C22⋊C4—674no—
1564C22⋊C4—678no—
1565C22⋊C4—674no—
1566C22⋊C4—674no—
1567C22⋊C4—674no—
1568C22⋊C4—674no—
1569C22⋊C4—674no—
1570C22⋊C4—678no—
1571C22⋊C4—674no—
1572C22⋊C4—674no—
1573C22⋊C4—674no—
1574C22⋊C4—674no—
1575C22⋊C4—678no—
1576C22⋊C4—678no—
1577C22⋊C4—678no—
1578C22⋊C4—678no—
1579C22⋊C4—674no—
1580C22⋊C4—678no—
1581C22⋊C4C23×D6714yes—
1582C22⋊C4C23×D6714yes—
1583C22⋊C4C23×D6714yes—
1584C22⋊C4C23×D6714yes—
1585C22⋊C4C23×D6714yes—
1586C22⋊C4C23×D6714yes—
1587C22⋊C4C23×D6714yes—
1588C22⋊C4C23×D6714yes—
1589C22⋊C4C23×D6714yes—
1590C42—674no—
1591C42—674no—
1592C42—674no—
1593C42—674no—
1594C42—674no—
1595C42—678no—
1596C42—678no—
1597C42—674no—
1598C42—678no—
1599C42—678no—
1600C42—674no—
1601C42—674no—
1602C42—674no—
1603C42C23×D6711yescharacteristic
1604C42C23×D6711yescharacteristic
1605C42C23×D6711yescharacteristic
1606C42C23×D6711yescharacteristic
1607C42C23×D6711yescharacteristic
1608C42C23×D6711yescharacteristic
1609C42C23×D6711yescharacteristic
1610C42C23×D6711yescharacteristic
1611C42C23×D6711yescharacteristic
1612C42C23×D6711yescharacteristic
1613C42C23×D6711yescharacteristic
1614C42C23×D6711yescharacteristic
1615C42C23×D6714yes—
1616C42C23×D6714yes—
1617C42C23×D6711yescharacteristic
1618C42C23×D6711yescharacteristic
1619C42C23×D6711yescharacteristic
1620C42C23×D6714yes—
1621C42C23×D6711yescharacteristic
1622C23—22no—
1623C23—41no—
1624C23—41no—
1625C23—2682no—
1626C23—2682no—
1627C23—674no—
1628C23—674no—
1629C23—1344no—
1630C23C24×D6711yescharacteristic
1631C23C24×D6711yescharacteristic
1632C23C24×D6714yes—
1633C23C24×D6711yescharacteristic
1634Q8—24no—
1635Q8—24no—
1636Q8—42no—
1637Q8—2682no—
1638Q8—2688no—
1639Q8—678no—
1640Q8—678no—
1641Q8—13416no—
1642Q8—1344no—
1643Q8—1344no—
1644D4—28no—
1645D4—24no—
1646D4—24no—
1647D4—42no—
1648D4—44no—
1649D4—44no—
1650D4—2682no—
1651D4—2688no—
1652D4—2688no—
1653D4—2684no—
1654D4—2688no—
1655D4—2688no—
1656D4—2684no—
1657D4—2688no—
1658D4—1348no—
1659D4—1348no—
1660D4—13416no—
1661D4—1348no—
1662D4—1344no—
1663D4—1344no—
1664D4—1344no—
1665D4—1344no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—28no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—28no—
1679C2×C4—41no—
1680C2×C4—41no—
1681C2×C4—41no—
1682C2×C4—41no—
1683C2×C4—41no—
1684C2×C4—41no—
1685C2×C4—44no—
1686C2×C4—2684no—
1687C2×C4—2684no—
1688C2×C4—2684no—
1689C2×C4—2688no—
1690C2×C4—2682no—
1691C2×C4—2682no—
1692C2×C4—2688no—
1693C2×C4—678no—
1694C2×C4—674no—
1695C2×C4—674no—
1696C2×C4—674no—
1697C2×C4—674no—
1698C2×C4—674no—
1699C2×C4—674no—
1700C2×C4—1348no—
1701C2×C4—1348no—
1702C2×C4—13416no—
1703C2×C4—13416no—
1704C2×C4—1348no—
1705C2×C4—1348no—
1706C2×C4—1348no—
1707C2×C4—1348no—
1708C2×C4#41×D6714yes—
1709C2×C4C24×D6711yescharacteristic
1710C2×C4C24×D6711yescharacteristic
1711C2×C4C24×D6711yescharacteristic
1712C2×C4C24×D6711yescharacteristic
1713C2×C4C24×D6711yescharacteristic
1714C2×C4C24×D6714yes—
1715C2×C4C24×D6714yes—
1716C2×C4C24×D6714yes—
1717C2×C4C24×D6711yescharacteristic
1718C2×C4C24×D6711yescharacteristic
1719C2×C4C24×D6711yescharacteristic
1720C2×C4C24×D6711yescharacteristic
1721C2×C4C24×D6711yescharacteristic
1722C2×C4C24×D6711yescharacteristic
1723C2×C4C24×D6711yescharacteristic
1724C22—21no—
1725C22—21no—
1726C22—21no—
1727C22—21no—
1728C22—24no—
1729C22—21no—
1730C22—21no—
1731C22—21no—
1732C22—21no—
1733C22—24no—
1734C22—24no—
1735C22—44no—
1736C22—2688no—
1737C22—1344no—
1738C22—1344no—
1739C22—1344no—
1740C22—1344no—
1741C22—1344no—
1742C22—1344no—
1743C22C2×#41×D6712yes—
1744C22C25×D6711yescharacteristic
1745C4—21no—
1746C4—21no—
1747C4—24no—
1748C4—21no—
1749C4—21no—
1750C4—21no—
1751C4—21no—
1752C4—21no—
1753C4—21no—
1754C4—24no—
1755C4—24no—
1756C4—678no—
1757C4—1344no—
1758C4—1344no—
1759C4—1344no—
1760C4—1344no—
1761C4—1344no—
1762C4C2×#41×D6712yes—
1763C4C2×#41×D6712yes—
1764C4#1686423212yes—
1765C4#1686423212yes—
1766C2—22no—
1767C2—41no—
1768C2—41no—
1769C2—44no—
1770C2—2684no—
1771C2—2684no—
1772C2C22×#41×D6711yescharacteristic
1773C2C2×#1686423211yescharacteristic
1774C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC67×#3444C2
hypercenter#3444D67
hypocenterC67#62793
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #22574314C2semidirect
2. #22574308C2semidirect
3. #22574224C2semidirect
4. #22574218C2semidirect
5. #22574213C2semidirect
6. #22574207C2semidirect
7. #22574063C2semidirect
8. #22574058C2semidirect
9. #22574052C2semidirect
10. #22574014C2semidirect
11. #22573975C2semidirect
12. #22573926C2semidirect
13. #22573921C2semidirect
14. #22573863C2semidirect
15. #22573835C2semidirect
16. #22573833C2semidirect
17. #22573827C2semidirect
18. #22573824C2semidirect
19. #22573802C2semidirect
20. #22573800C2semidirect
21. #22573627C2semidirect
22. #22573625C2semidirect
23. #22573505C2semidirect
24. #22573503C2semidirect
25. C4×#14524090C2semidirect
26. C2×C4×#11761628C2semidirect
27. C67×#3444C2semidirect
30. #16864131C22semidirect
31. #16864130C22semidirect
32. #16864129C22semidirect
33. #16864128C22semidirect
34. Q8×Dic134C22semidirect
35. #16864126C22semidirect
36. #16864124C22semidirect
37. #16864124C22semidirect
38. #16864123C22semidirect
39. #16864121C22semidirect
40. #16864120C22semidirect
41. #16864119C22semidirect
42. #16864118C22semidirect
43. #16864117C22semidirect
44. #16864117C22semidirect
45. #16864116C22semidirect
46. #16864114C22semidirect
47. #16864113C22semidirect
48. #16864112C22semidirect
49. #16864111C22semidirect
50. #16864111C22semidirect
51. #16864110C22semidirect
52. #16864110C22semidirect
53. #16864109C22semidirect
54. #16864109C22semidirect
55. #16864108C22semidirect
56. #16864099C22semidirect
57. #16864097C22semidirect
58. #16864095C22semidirect
59. #16864095C22semidirect
60. #16864093C22semidirect
61. #16864092C22semidirect
62. #16864092C22semidirect
63. #16864091C22semidirect
64. #16864086C22semidirect
65. #16864080C22semidirect
66. #16864079C22semidirect
67. #16864078C22semidirect
68. #16864068C22semidirect
71. #16864067C22semidirect
72. #16864066C22semidirect
73. #16864066C22semidirect
74. #16864065C22semidirect
77. #16864064C22semidirect
78. D4×Dic134C22semidirect
79. #16864061C22semidirect
84. #16864055C22semidirect
85. #16864054C22semidirect
86. #16864050C22semidirect
87. #16864049C22semidirect
88. #16864048C22semidirect
89. #16864045C22semidirect
92. #16864018C22semidirect
93. #16864017C22semidirect
94. #16864016C22semidirect
95. #16864014C22semidirect
96. #16864001C22semidirect
97. #16863998C22semidirect
98. #16863997C22semidirect
99. #16863996C22semidirect
110. #16863953C22semidirect
111. #16863953C22semidirect
112. #16863952C22semidirect
113. #16863950C22semidirect
116. #16863946C22semidirect
117. #16863946C22semidirect
118. #16863946C22semidirect
119. #16863945C22semidirect
120. #16863943C22semidirect
121. #16863943C22semidirect
122. #16863943C22semidirect
123. #16863942C22semidirect
125. #16863933C22semidirect
126. #16863931C22semidirect
129. #16863930C22semidirect
130. #16863930C22semidirect
131. #16863930C22semidirect
132. #16863930C22semidirect
133. #16863930C22semidirect
134. #16863929C22semidirect
135. #16863929C22semidirect
136. #16863926C22semidirect
137. #16863925C22semidirect
138. #16863924C22semidirect
139. #16863924C22semidirect
150. #16863876C22semidirect
152. #16863875C22semidirect
154. #16863873C22semidirect
155. #16863872C22semidirect
156. C4×#11761629C22semidirect
166. C4×#11761628C22semidirect
167. C4×#11761628C22semidirect
168. C4×#11761628C22semidirect
169. #16863864C22semidirect
171. C4×#11761627C22semidirect
172. C4×#11761627C22semidirect
175. C2×C4×Dic134C22semidirect
176. C4×Q8×D67C22semidirect
185. #533×C67C22semidirect
186. #533×C67C22semidirect
188. #532×C67C22semidirect
189. #532×C67C22semidirect
192. #529×C67C22semidirect
193. #529×C67C22semidirect
194. #529×C67C22semidirect
195. #529×C67C22semidirect
200. C4×#41×C67C22semidirect
201. C4×#41×C67C22semidirect
547. C2×Dic134#41semidirect
912. #3444D67semidirect
915. C67#62793semidirect
1004. #533C2×D67semidirect
1005. #533C2×D67semidirect
1017. #532C2×D67semidirect
1018. #532C2×D67semidirect
1037. #529C2×D67semidirect
1038. #529C2×D67semidirect
1039. #529C2×D67semidirect
1040. #529C2×D67semidirect
1077. C4×#41C2×D67semidirect
1078. C4×#41C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225743142
#225743082
#225742242
#225742182
#225742132
#225742072
#225740632
#225740582
#225740522
#225740142
#225739752
#225739262
#225739212
#225738632
#225738352
#225738332
#225738272
#225738242
#225738022
#225738002
#225736272
#225736252
#225735052
#225735032
C4×#145240902
C2×C4×#117616282
C67×#34442
#6279367