Finite Group Databasebeta

← #31764119

Subgroups — #31764119

Order 17152.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574319C214yesmaximal, complemented
2#22574307C214yesmaximal, complemented
3#22574217C214yesmaximal, complemented
4#22574206C214yesmaximal, complemented
5#22574060C216yesmaximal, complemented
6#22574015C211yesmaximal, characteristic, complemented
7#22573976C211yesmaximal, characteristic, complemented
8#22573926C216yesmaximal, complemented
9#22573867C211yesmaximal, characteristic, complemented
10#22573832C214yesmaximal, complemented
11#22573825C214yesmaximal, complemented
12#22573808C214yesmaximal, complemented
13#22573799C214yesmaximal, complemented
14#22573622C216yesmaximal, complemented
15#22573501C216yesmaximal, complemented
162−1+4×Dic67C211yesmaximal, characteristic, complemented
17#22573418C211yesmaximal, characteristic, complemented
18C2×#41×Dic67C211yesmaximal, characteristic, complemented
19C67×#3487C211yesmaximal, characteristic, complemented
20C2×#14524091C2211yescharacteristic
21#16864132C22112yescomplemented
22#16864128C22112yescomplemented
23Q8×Dic134C2214yescomplemented
24#16864125C2214yescomplemented
25#16864122C2214yescomplemented
26#16864122C2214yescomplemented
27#16864117C22112yescomplemented
28#16864116C22112yescomplemented
29#16864115C22112yescomplemented
30#16864111C22112yescomplemented
31#16864110C22112yescomplemented
32#16864110C22112yescomplemented
33#16864098C22112yescomplemented
34#16864093C22112yescomplemented
35#16864093C22112yescomplemented
36#16864092C22112yescomplemented
37#16864086C22112yescomplemented
38#16864080C22112yescomplemented
39#16864066C22112yescomplemented
40#16864065C2214yes—
41#16864065C2214yes—
42#16864065C2214yescomplemented
43Q8×C22⋊D67C2214yescomplemented
44#16864057C2214yescomplemented
45#16864053C2214yes—
46#16864053C2214yes—
47#16864053C2214yescomplemented
48#16864046C22112yescomplemented
49#16864024C2216yes—
50#16864015C22112yescomplemented
51#16864013C22112yescomplemented
52#16864000C22112yescomplemented
53#16863999C22112yescomplemented
54#16863981C22124yes—
55#16863974C2216yes—
56#16863963C2216yes—
57#16863949C2216yes—
58#16863948C2216yescomplemented
59#16863948C2216yescomplemented
60#16863944C22112yescomplemented
61#16863942C2216yes—
62#16863941C2216yescomplemented
63#16863941C22112yescomplemented
64#16863941C2216yescomplemented
65#16863932C2216yescomplemented
66#16863932C2216yescomplemented
67#16863927C22112yescomplemented
68#16863927C2216yescomplemented
69#16863927C2216yescomplemented
70#16863926C22112yescomplemented
71#16863926C22112yescomplemented
72#16863925C22112yescomplemented
73#16863923C22112yes—
74#16863923C2214yes—
75#16863907C2216yes—
76#16863902C22112yes—
77#16863902C22112yes—
78#16863879C2216yes—
79#16863879C2214yescomplemented
80#16863878C2214yescomplemented
81#16863876C2216yes—
82#16863874C2211yescharacteristic
83#16863874C2214yescomplemented
84#16863872C2214yescomplemented
85#41×Dic67C2214yes—
86#41×Dic67C2216yes—
87#41×Dic67C2214yes—
88#41×Dic67C2214yes—
89#41×Dic67C2214yes—
90#41×Dic67C2214yescomplemented
91C4×#11761629C2214yescomplemented
92#16863864C2216yes—
93C4×#11761627C22112yescomplemented
94C4×#11761627C22112yescomplemented
95C2×Q8×Dic67C2211yescharacteristic
96C2×Q8×Dic67C2211yescharacteristic
97C2×Q8×Dic67C2214yescomplemented
98C4×Q8×D67C2214yescomplemented
99C2×D4×Dic67C2213yes—
100C2×D4×Dic67C2213yes—
101C2×#14524002C2213yes—
102C22×C4×Dic67C2213yes—
103C2×2−1+4×C67C2211yescharacteristic
104C22×#41×C67C2211yescharacteristic
105#550×C67C2214yes—
106#550×C67C2214yes—
107#548×C67C2214yes—
108#548×C67C2214yes—
109#535×C67C2216yes—
110#525×C67C2216yes—
111#519×C67C2211yescharacteristic
112#14524091—28no—
113C2×#11761629C2314yes—
114C2×#11761628C2316yes—
115C2×#11761627C23112yes—
116C2×#11761627C23112yes—
117C2×Q8×D67C2314yes—
118C23×Dic67C2313yes—
119C23×Dic67C2313yes—
120#14524043C23112yes—
121#14524042C23112yes—
122#14524042C2316yes—
123#14524042C2316yes—
124#14524041C2316yes—
125#14524039C23112yes—
126#14524039C2316yes—
127#14524038C23112yes—
128#14524038C2314yes—
129#14524036C23124yes—
130#14524036C23124yes—
131#14524036C23112yes—
132#14524036C2314yes—
133#14524035C23112yes—
134#14524034C23112yes—
135#14524034C2316yes—
136#14524034C2316yes—
137#14524033C23112yes—
138#14524033C2314yes—
139#14524032C2316yes—
140#14524030C23112yes—
141#14524030C23124yes—
142#14524030C2316yes—
143#14524029C23124yes—
144#14524029C23112yes—
145#14524029C2314yes—
146#14524027C23112yes—
147#14524027C23112yes—
148#14524026C2314yes—
149#14524025C23124yes—
150#14524024C23112yes—
151#14524024C23124yes—
152#14524024C23112yes—
153#14524022C23112yes—
154#14524022C2316yes—
155#14524022C2316yes—
156#14524020C23112yes—
157#14524020C23112yes—
158#14524020C23112yes—
159#14524020C2314yes—
160#14524019C23112yes—
161#14524017C23112yes—
162#14524017C2316yes—
163#14524017C2316yes—
164#14524015C23112yes—
165#14524015C23124yes—
166#14524015C23112yes—
167#14524015C2314yes—
168#14524015C23112yes—
169#14524014C23112yes—
170#14524014C23112yes—
171#14524014C23112yes—
172#14524014C23124yes—
173#14524012C23112yes—
174Q8×Dic67C2316yes—
175Q8×Dic67C2314yes—
176Q8×Dic67C2314yes—
177Q8×Dic67C2314yes—
178Q8×Dic67C2314yes—
179Q8×Dic67C23112yes—
180Q8×Dic67C2314yes—
181Q8×Dic67C2314yes—
182Q8×Dic67C2316yes—
183C4×Dic134C23112yes—
184C4×Dic134C23112yes—
185C4×Dic134C23112yes—
186#14524008C2316yes—
187#14524008C2316yes—
188#14524008C23112yes—
189#14524008C2314yes—
190C4×D268C23112yes—
191D4×Dic67C2316yes—
192D4×Dic67C23112yes—
193D4×Dic67C23112yes—
194D4×Dic67C23112yes—
195D4×Dic67C23112yes—
196D4×Dic67C23112yes—
197D4×Dic67C23112yes—
198D4×Dic67C23112yes—
199D4×Dic67C2314yes—
200D4×Dic67C2316yes—
201D4×Dic67C23112yes—
202#14524005C2316yes—
203#14524005C2316yes—
204C4×C22⋊D67C23112yes—
205C4×C22⋊D67C23112yes—
206C4×C22⋊D67C23112yes—
207C4×C22⋊D67C23112yes—
208(C22⋊D67)⋊C4C23112yes—
209(C22⋊D67)⋊C4C23112yes—
210(C22⋊D67)⋊C4C2314yes—
211(C22⋊D67)⋊C4C23112yes—
212(C22⋊D67)⋊C4C2314yes—
213(C22⋊D67)⋊C4C23112yes—
214#14524002C23112yes—
215#14524002C2316yes—
216#14524002C23112yes—
217#14524002C23112yes—
218#14524002C23112yes—
219#14524001C23112yes—
220#14524001C23112yes—
221#14524001C2314yes—
222#14524000C23112yes—
223#14523999C23112yes—
224#14523999C23112yes—
225#14523999C2314yes—
226#14523999C23112yes—
227C2×C4⋊Dic67C2313yes—
228C2×C4⋊Dic67C23112yes—
229C2×C4⋊Dic67C2313yes—
230C4⋊C4×D67C23112yes—
231C2×C22⋊Dic67C2316yes—
232C2×C4×Dic67C2311yescharacteristic
233C2×C4×Dic67C2313yes—
234C2×C4×Dic67C2313yes—
235C2×C4×Dic67C2313yes—
236C2×C4×Dic67C2316yes—
237C2×C4×Dic67C2316yes—
238C2×C4×Dic67C2316yes—
239C2×C4×Dic67C2316yes—
240C2×C4×Dic67C23112yes—
241C42×D67C23112yes—
2422−1+4×C67—28no—
243C2×#41×C67—28no—
244C2×#41×C67C2314yes—
245C2×#41×C67C2314yes—
246C2×#41×C67C2314yes—
247C2×#41×C67C2316yes—
248C22×Q8×C67C2314yes—
249C22×Q8×C67C2311yescharacteristic
250C22×D4×C67C2313yes—
251C23×C4×C67C2313yes—
252#127×C67C23112yes—
253#124×C67C23112yes—
254#123×C67C2314yes—
255C22⋊Q8×C67C2316yes—
256C22⋊Q8×C67C2316yes—
257#121×C67C23112yes—
258#121×C67C23112yes—
259#121×C67C2316yes—
260#121×C67C2316yes—
261#120×C67C23112yes—
262C4×Q8×C67C2314yes—
263C4×Q8×C67C2314yes—
264C4×D4×C67C23112yes—
265C4×D4×C67C23112yes—
266#117×C67C2316yes—
267#11761629—216no—
268#11761628—224no—
269#11761627—424no—
270#11761627—424no—
271C2×Dic134C2416yes—
272C2×Dic134C2414yes—
273C2×Dic134C24112yes—
274Q8×D67—216no—
275C2×D268C2416yes—
276C2×C22⋊D67C2414yes—
277C2×C22⋊D67C2414yes—
278C2×C22⋊D67C24112yes—
279C2×C22⋊D67C24112yes—
280C2×C22⋊D67C24112yes—
281C22×Dic67—46no—
282C22×Dic67—46no—
283C22×Dic67C2411yescharacteristic
284C22×Dic67C2411yescharacteristic
285C22×Dic67C2414yes—
286C22×Dic67C2416yes—
287C22×Dic67C2416yes—
288C22×Dic67C2413yes—
289C22×Dic67C2413yes—
290C22×Dic67C2416yes—
291C22×Dic67C2416yes—
292C22×Dic67C24112yes—
293C2×C4×D67C2414yes—
294C2×C4×D67C24112yes—
295C2×C4×D67C24112yes—
296C4⋊Dic67C24112yes—
297C4⋊Dic67C2416yes—
298C4⋊Dic67C24112yes—
299C4⋊Dic67C24112yes—
300C4⋊Dic67C2414yes—
301C4⋊Dic67C24112yes—
302C4⋊Dic67C2416yes—
303C4⋊Dic67C2414yes—
304Dic67⋊C4C24112yes—
305Dic67⋊C4C2414yes—
306Dic67⋊C4C2414yes—
307Dic67⋊C4C2414yes—
308Dic67⋊C4C2414yes—
309Dic67⋊C4C24112yes—
310Dic67⋊C4C24112yes—
311Dic67⋊C4C2414yes—
312Dic67⋊C4C24112yes—
313Dic67⋊C4C2414yes—
314C22⋊Dic67C24124yes—
315C22⋊Dic67C2414yes—
316C22⋊Dic67C24112yes—
317C22⋊Dic67C24112yes—
318C22⋊Dic67C24112yes—
319C22⋊Dic67C2414yes—
320C22⋊Dic67C24112yes—
321C22⋊Dic67C2414yes—
322(C2×D67)⋊C4C2414yes—
323(C2×D67)⋊C4C24112yes—
324(C2×D67)⋊C4C2414yes—
325(C2×D67)⋊C4C2414yes—
326(C2×D67)⋊C4C2414yes—
327(C2×D67)⋊C4C24112yes—
328C4×Dic67C2414yes—
329C4×Dic67C2416yes—
330C4×Dic67C24112yes—
331C4×Dic67C2411yescharacteristic
332C4×Dic67C2411yescharacteristic
333C4×Dic67C2411yescharacteristic
334C4×Dic67C2411yescharacteristic
335C4×Dic67C2414yes—
336C4×Dic67C2416yes—
337C4×Dic67C2416yes—
338C4×Dic67C2416yes—
339C4×Dic67C2416yes—
340C4×Dic67C2416yes—
341C4×Dic67C24112yes—
342C4×Dic67C24112yes—
343C24×C67C2413yes—
344#41×C67—216no—
345#41×C67—216no—
346#41×C67—216no—
347#41×C67—224no—
348C2×Q8×C67—216no—
349C2×Q8×C67#4118yescomplemented
350C2×Q8×C67C2416yes—
351C2×Q8×C67C2414yes—
352C2×D4×C67—212no—
353C2×D4×C67C2414yes—
354C2×D4×C67C24112yes—
355C2×D4×C67C2416yes—
356C2×D4×C67C24112yes—
357C2×D4×C67C24112yes—
358C22×C4×C67—212no—
359C22×C4×C67C24112yes—
360C22×C4×C67C2416yes—
361C22×C4×C67C2416yes—
362C22×C4×C67C2411yescharacteristic
363C22×C4×C67C2413yes—
364C4⋊C4×C67C2416yes—
365C4⋊C4×C67C2416yes—
366C4⋊C4×C67C2414yes—
367C4⋊C4×C67C2414yes—
368C22⋊C4×C67C2414yes—
369C22⋊C4×C67C2414yes—
370C22⋊C4×C67C2414yes—
371C22⋊C4×C67C24112yes—
372C22⋊C4×C67C24112yes—
373C42×C67C24112yes—
374C23×C67—26no—
375C23×C67—43no—
376C23×C67—43no—
377C23×C67C2516yes—
378C23×C67C2514yes—
379C23×C67C2511yescharacteristic
380C22×D67C2514yes—
381Q8×C67—212no—
382Q8×C67C2×#41116yes—
383D4×C67—28no—
384D4×C67—224no—
385D4×C67—212no—
386D4×C67—412no—
387D4×C67—412no—
388C2×C4×C67—22no—
389C2×C4×C67—212no—
390C2×C4×C67—212no—
391C2×C4×C67—224no—
392C2×C4×C67C2×#41112yes—
393C2×C4×C67C2514yes—
394C2×C4×C67C2514yes—
395C2×C4×C67C2514yes—
396C2×C4×C67C2511yescharacteristic
397C2×C4×C67C2511yescharacteristic
398C2×C4×C67C2516yes—
399C22⋊D67—28no—
400C22⋊D67—28no—
401C22⋊D67—412no—
402C22⋊D67—412no—
403C22⋊D67—412no—
404C2×Dic67—22no—
405C2×Dic67—22no—
406C2×Dic67—212no—
407C2×Dic67—212no—
408C2×Dic67—28no—
409C2×Dic67—43no—
410C2×Dic67—46no—
411C2×Dic67—43no—
412C2×Dic67—46no—
413C2×Dic67—412no—
414C2×Dic67C2511yescharacteristic
415C2×Dic67C2511yescharacteristic
416C2×Dic67C2516yes—
417C2×Dic67C2514yes—
418C2×Dic67C2516yes—
419C2×Dic67C2514yes—
420C2×Dic67C2514yes—
421C2×Dic67C2511yescharacteristic
422C2×Dic67C2511yescharacteristic
423D268—212no—
424C4×D67—224no—
425C4×D67—28no—
426C4×D67—412no—
427Dic134—212no—
428Dic134—28no—
429Dic134—412no—
430C22×C67—21no—
431C22×C67—21no—
432C22×C67—24no—
433C22×C67—26no—
434C22×C67—26no—
435C22×C67—26no—
436C22×C67—24no—
437C22×C67—24no—
438C22×C67—412no—
439C22×C67C22×#4112yes—
440C22×C67C2611yescharacteristic
441C2×D67—24no—
442C2×D67—24no—
443C2×D67—24no—
444C4×C67—21no—
445C4×C67—21no—
446C4×C67—24no—
447C4×C67—24no—
448C4×C67—24no—
449C4×C67C22×#41112yes—
450Dic67—24no—
451Dic67—24no—
452Dic67—24no—
453Dic67—26no—
454Dic67—26no—
455Dic67—21no—
456Dic67—21no—
457Dic67#58512yes—
458Dic67#58512yes—
459#62793—671nomaximal, Sylow
460C2×C67—22no—
461C2×C67—44no—
462C2×C67—46no—
463C2×C67C23×#4111yescharacteristic
464C2×C67C2×#58511yescharacteristic
465C2×C67C2×#58511yescharacteristic
466D67—44no—
467#3524—674no—
468#3524—674no—
469#3518—674no—
470#3517—674no—
471#3506—676no—
472#3502—671no—
473#3497—671no—
474#3493—676no—
475#3487—671no—
476#3487D6711yescharacteristic, complemented
477#3483—674no—
478#3482—674no—
479#3480—674no—
480#3480—674no—
481#3460—676no—
482#3444—676no—
483C4×2−1+4—671no—
484C4×2−1+4—671no—
485C2×C4×#41—671no—
486C67#6279311yescharacteristic, complemented, Sylow
487C2×2−1+4—671no—
488C2×2−1+4C2×D6711yescharacteristic
489C22×#41C2×D6711yescharacteristic
490#559—6712no—
491#559—6712no—
492Q82—674no—
493#557—674no—
494#557—674no—
495#557—674no—
496#556—6712no—
497#556—6712no—
498#556—6712no—
499#555—6712no—
500#555—6712no—
501#555—6712no—
502#553—6712no—
503#553—6712no—
504#553—6712no—
505#553—6712no—
506#552—6712no—
507#552—6712no—
508#550—674no—
509#550—674no—
510#550—674no—
511#550—6712no—
512#550C2×D6714yes—
513#550C2×D6714yes—
514D4×Q8—674no—
515#548—674no—
516#548—674no—
517#548—674no—
518#548—674no—
519#548C2×D6714yes—
520#548C2×D6714yes—
521#547—6712no—
522#544—676no—
523#542—6712no—
524#542—6712no—
525#540—6712no—
526#540—6712no—
527#538—6724no—
528#537—676no—
529#535—676no—
530#535C2×D6716yes—
531#533—676no—
532#533—676no—
533#533—676no—
534#532—676no—
535#532—6712no—
536#532—676no—
537#532—676no—
538#532—6712no—
539#529—6712no—
540#529—674no—
541#529—6712no—
542#529—676no—
543#529—676no—
544#529—676no—
545#529—676no—
546#529—6712no—
547#529—6712no—
548#529—6712no—
549#525—676no—
550#525—6712no—
551#525—6712no—
552#525C2×D6716yes—
553#520—676no—
554#520—674no—
555#520—674no—
556#520—676no—
557#519—671no—
558#519—674no—
559#519—674no—
560#519C2×D6711yescharacteristic
561C4×#41—674no—
562C4×#41—674no—
563C4×#41—674no—
564C4×#41—674no—
565C4×#41—676no—
566C4×#41—674no—
567C4×#41—674no—
568C4×#41—6712no—
569C4×#41—6712no—
570C4×#41—676no—
571C2×C4×Q8—671no—
572C2×C4×Q8—671no—
573C2×C4×Q8—674no—
574C2×C4×Q8—674no—
575C2×C4×D4—673no—
576C2×C4×D4—673no—
577C2×#117—673no—
578C22×C42—673no—
5792−1+4—28no—
5802−1+4—1348no—
581C2×#41—28no—
582C2×#41—674no—
583C2×#41—6712no—
584C2×#41—6712no—
585C2×#41—676no—
586C2×#41C22×D6714yes—
587C2×#41C22×D6714yes—
588C2×#41C22×D6716yes—
589C2×#41C22×D6714yes—
590C22×Q8—674no—
591C22×Q8C22×D6714yes—
592C22×Q8C22×D6711yescharacteristic
593C22×D4C22×D6713yes—
594C23×C4—673no—
595C23×C4—673no—
596C23×C4C22×D6713yes—
597C4⋊Q8—676no—
598C4⋊Q8—676no—
599C4⋊Q8—676no—
600C4⋊Q8—6712no—
601C4⋊Q8—6712no—
602#127—676no—
603#127—6712no—
604#127C22×D67112yes—
605#126—674no—
606#126—6712no—
607#126—674no—
608#126—6712no—
609#126—6724no—
610#126—6724no—
611#125—674no—
612#125—6712no—
613#125—676no—
614#125—676no—
615#125—6712no—
616#125—6712no—
617#124—676no—
618#124—676no—
619#124—6712no—
620#124—6724no—
621#124—674no—
622#124—6712no—
623#124—6724no—
624#124C22×D67112yes—
625#123—6712no—
626#123—6712no—
627#123—6724no—
628#123—674no—
629#123—6712no—
630#123—6712no—
631#123—6724no—
632#123C22×D6714yes—
633C22⋊Q8—6712no—
634C22⋊Q8—676no—
635C22⋊Q8—676no—
636C22⋊Q8—6712no—
637C22⋊Q8—674no—
638C22⋊Q8—6712no—
639C22⋊Q8—6712no—
640C22⋊Q8—6712no—
641C22⋊Q8C22×D6716yes—
642C22⋊Q8C22×D6716yes—
643#121—674no—
644#121—6712no—
645#121—6712no—
646#121—6712no—
647#121—6712no—
648#121—6712no—
649#121—6712no—
650#121—6724no—
651#121—6724no—
652#121—676no—
653#121—676no—
654#121—6712no—
655#121C22×D6716yes—
656#121C22×D6716yes—
657#121C22×D67112yes—
658#121C22×D67112yes—
659#120—6712no—
660#120C22×D67112yes—
661C4×Q8—674no—
662C4×Q8—676no—
663C4×Q8—674no—
664C4×Q8—674no—
665C4×Q8—674no—
666C4×Q8—674no—
667C4×Q8—6712no—
668C4×Q8—676no—
669C4×Q8—674no—
670C4×Q8—676no—
671C4×Q8—674no—
672C4×Q8—676no—
673C4×Q8—6712no—
674C4×Q8—6712no—
675C4×Q8—6712no—
676C4×Q8—6712no—
677C4×Q8C22×D6714yes—
678C4×Q8C22×D6714yes—
679C4×D4—6712no—
680C4×D4—6712no—
681C4×D4—6712no—
682C4×D4—6712no—
683C4×D4—674no—
684C4×D4—676no—
685C4×D4—6712no—
686C4×D4—676no—
687C4×D4—6712no—
688C4×D4—6712no—
689C4×D4—6712no—
690C4×D4—6712no—
691C4×D4—6712no—
692C4×D4—6712no—
693C4×D4—6712no—
694C4×D4—676no—
695C4×D4—676no—
696C4×D4—674no—
697C4×D4—674no—
698C4×D4—6712no—
699C4×D4—6712no—
700C4×D4—6712no—
701C4×D4—6712no—
702C4×D4—6712no—
703C4×D4C22×D67112yes—
704C4×D4C22×D67112yes—
705#117—6712no—
706#117—6712no—
707#117—676no—
708#117—6712no—
709#117—6712no—
710#117—674no—
711#117—6712no—
712#117—6712no—
713#117—674no—
714#117—6712no—
715#117—6712no—
716#117—6712no—
717#117—6712no—
718#117C22×D6716yes—
719C2×C4⋊C4—673no—
720C2×C4⋊C4—673no—
721C2×C4⋊C4—6712no—
722C2×C4⋊C4—6712no—
723C2×C22⋊C4—676no—
724C2×C42—673no—
725C2×C42—673no—
726C2×C42—673no—
727C2×C42—6712no—
728C2×C42—676no—
729C2×C42—676no—
730C2×C42—676no—
731C2×C42—676no—
732C2×C42—671no—
733C2×C42—6712no—
734C24C23×D6713yes—
735#41—216no—
736#41—216no—
737#41—216no—
738#41—224no—
739#41—26824no—
740#41—26824no—
741#41—13416no—
742#41—13424no—
743C2×Q8—216no—
744C2×Q8—6712no—
745C2×Q8—676no—
746C2×Q8—674no—
747C2×Q8—13416no—
748C2×Q8#1176162718yescomplemented
749C2×Q8C23×D6716yes—
750C2×Q8C23×D6714yes—
751C2×D4—212no—
752C2×D4—6712no—
753C2×D4—6712no—
754C2×D4—6712no—
755C2×D4—674no—
756C2×D4—674no—
757C2×D4—676no—
758C2×D4C23×D6714yes—
759C2×D4C23×D67112yes—
760C2×D4C23×D6716yes—
761C2×D4C23×D67112yes—
762C2×D4C23×D67112yes—
763C22×C4—212no—
764C22×C4—2686no—
765C22×C4—2686no—
766C22×C4—673no—
767C22×C4—673no—
768C22×C4—676no—
769C22×C4—676no—
770C22×C4—6712no—
771C22×C4—6712no—
772C22×C4—671no—
773C22×C4—671no—
774C22×C4—674no—
775C22×C4—676no—
776C22×C4—676no—
777C22×C4—674no—
778C22×C4—6712no—
779C22×C4C23×D6711yescharacteristic
780C22×C4C23×D6716yes—
781C22×C4C23×D6716yes—
782C22×C4C23×D67112yes—
783C22×C4C23×D6713yes—
784C4⋊C4—6712no—
785C4⋊C4—676no—
786C4⋊C4—6712no—
787C4⋊C4—6712no—
788C4⋊C4—6712no—
789C4⋊C4—674no—
790C4⋊C4—674no—
791C4⋊C4—674no—
792C4⋊C4—676no—
793C4⋊C4—674no—
794C4⋊C4—674no—
795C4⋊C4—674no—
796C4⋊C4—674no—
797C4⋊C4—674no—
798C4⋊C4—6712no—
799C4⋊C4—6712no—
800C4⋊C4—6712no—
801C4⋊C4—6712no—
802C4⋊C4C23×D6716yes—
803C4⋊C4C23×D6714yes—
804C4⋊C4C23×D6716yes—
805C4⋊C4C23×D6714yes—
806C22⋊C4—6724no—
807C22⋊C4—674no—
808C22⋊C4—674no—
809C22⋊C4—6712no—
810C22⋊C4—674no—
811C22⋊C4—6712no—
812C22⋊C4—6712no—
813C22⋊C4—6712no—
814C22⋊C4—674no—
815C22⋊C4—6712no—
816C22⋊C4—674no—
817C22⋊C4—674no—
818C22⋊C4—674no—
819C22⋊C4—6712no—
820C22⋊C4C23×D6714yes—
821C22⋊C4C23×D6714yes—
822C22⋊C4C23×D67112yes—
823C22⋊C4C23×D67112yes—
824C22⋊C4C23×D6714yes—
825C42—671no—
826C42—671no—
827C42—676no—
828C42—671no—
829C42—671no—
830C42—676no—
831C42—674no—
832C42—674no—
833C42—676no—
834C42—676no—
835C42—676no—
836C42—676no—
837C42—6712no—
838C42—6712no—
839C42—6712no—
840C42C23×D67112yes—
841C23—26no—
842C23—43no—
843C23—43no—
844C23—674no—
845C23C24×D6716yes—
846C23C24×D6714yes—
847C23C24×D6711yescharacteristic
848Q8—212no—
849Q8—26812no—
850Q8—1348no—
851Q8—13412no—
852Q8C2×#11761627116yes—
853D4—28no—
854D4—224no—
855D4—212no—
856D4—412no—
857D4—412no—
858D4—26812no—
859D4—26812no—
860D4—26812no—
861D4—1348no—
862D4—1348no—
863D4—13412no—
864C2×C4—22no—
865C2×C4—212no—
866C2×C4—212no—
867C2×C4—224no—
868C2×C4—26812no—
869C2×C4—2683no—
870C2×C4—2686no—
871C2×C4—2686no—
872C2×C4—2683no—
873C2×C4—26812no—
874C2×C4—671no—
875C2×C4—671no—
876C2×C4—671no—
877C2×C4—676no—
878C2×C4—671no—
879C2×C4—674no—
880C2×C4—674no—
881C2×C4—676no—
882C2×C4—674no—
883C2×C4—1348no—
884C2×C4—1342no—
885C2×C4—1342no—
886C2×C4—13412no—
887C2×C4—13412no—
888C2×C4—1348no—
889C2×C4—13424no—
890C2×C4C2×#11761627112yes—
891C2×C4C24×D6711yescharacteristic
892C2×C4C24×D6711yescharacteristic
893C2×C4C24×D6714yes—
894C2×C4C24×D6714yes—
895C2×C4C24×D6714yes—
896C2×C4C24×D6716yes—
897C22—21no—
898C22—21no—
899C22—24no—
900C22—26no—
901C22—24no—
902C22—26no—
903C22—26no—
904C22—24no—
905C22—412no—
906C22—1344no—
907C22—1344no—
908C22—1344no—
909C22C22×#1176162712yes—
910C22C25×D6711yescharacteristic
911C4—21no—
912C4—21no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—672no—
917C4—672no—
918C4—1344no—
919C4—1346no—
920C4—1341no—
921C4—1341no—
922C4—1344no—
923C4—1346no—
924C4—1344no—
925C4C22×#11761627112yes—
926C2—22no—
927C2—46no—
928C2—44no—
929C2—2684no—
930C2C23×#1176162711yescharacteristic
931C2#585×D6711yescharacteristic
932C2#585×D6711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3487C2
hypercenter#3487D67
hypocenterC67#62793
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #22574319C2semidirect
2. #22574307C2semidirect
3. #22574217C2semidirect
4. #22574206C2semidirect
5. #22574060C2semidirect
6. #22574015C2semidirect
7. #22573976C2semidirect
8. #22573926C2semidirect
9. #22573867C2semidirect
10. #22573832C2semidirect
11. #22573825C2semidirect
12. #22573808C2semidirect
13. #22573799C2semidirect
14. #22573622C2semidirect
15. #22573501C2semidirect
16. 2−1+4×Dic67C2semidirect
17. #22573418C2semidirect
18. C2×#41×Dic67C2semidirect
19. C67×#3487C2semidirect
21. #16864132C22semidirect
22. #16864128C22semidirect
23. Q8×Dic134C22semidirect
24. #16864125C22semidirect
25. #16864122C22semidirect
26. #16864122C22semidirect
27. #16864117C22semidirect
28. #16864116C22semidirect
29. #16864115C22semidirect
30. #16864111C22semidirect
31. #16864110C22semidirect
32. #16864110C22semidirect
33. #16864098C22semidirect
34. #16864093C22semidirect
35. #16864093C22semidirect
36. #16864092C22semidirect
37. #16864086C22semidirect
38. #16864080C22semidirect
39. #16864066C22semidirect
42. #16864065C22semidirect
43. Q8×C22⋊D67C22semidirect
44. #16864057C22semidirect
47. #16864053C22semidirect
48. #16864046C22semidirect
50. #16864015C22semidirect
51. #16864013C22semidirect
52. #16864000C22semidirect
53. #16863999C22semidirect
58. #16863948C22semidirect
59. #16863948C22semidirect
60. #16863944C22semidirect
62. #16863941C22semidirect
63. #16863941C22semidirect
64. #16863941C22semidirect
65. #16863932C22semidirect
66. #16863932C22semidirect
67. #16863927C22semidirect
68. #16863927C22semidirect
69. #16863927C22semidirect
70. #16863926C22semidirect
71. #16863926C22semidirect
72. #16863925C22semidirect
79. #16863879C22semidirect
80. #16863878C22semidirect
83. #16863874C22semidirect
84. #16863872C22semidirect
90. #41×Dic67C22semidirect
91. C4×#11761629C22semidirect
93. C4×#11761627C22semidirect
94. C4×#11761627C22semidirect
97. C2×Q8×Dic67C22semidirect
98. C4×Q8×D67C22semidirect
349. C2×Q8×C67#41semidirect
476. #3487D67semidirect
486. C67#62793semidirect
748. C2×Q8#11761627semidirect

Maximal subgroups

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

subgroupindex
#225743192
#225743072
#225742172
#225742062
#225740602
#225740152
#225739762
#225739262
#225738672
#225738322
#225738252
#225738082
#225737992
#225736222
#225735012
2−1+4×Dic672
#225734182
C2×#41×Dic672
C67×#34872
#6279367