Finite Group Databasebeta

← #11675546

Subgroups — #11675546

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85892C211yesmaximal, characteristic, complemented
2#85889C211yesmaximal, characteristic, complemented
3C3×#2951C211yesmaximal, characteristic, complemented
4#83902C211yesmaximal, characteristic, complemented
5#83900C211yesmaximal, characteristic
6#82572C211yesmaximal, characteristic, complemented
7#82559C211yesmaximal, characteristic, complemented
8#79758C212yesmaximal, complemented
9#79756C212yesmaximal, complemented
10#79755C212yesmaximal, complemented
11#79751C212yesmaximal, complemented
12#79704C212yesmaximal, complemented
13#79699C212yesmaximal, complemented
14#79571C212yesmaximal, complemented
15#79569C212yesmaximal, complemented
16C2×#4875C211yesmaximal, characteristic, complemented
17#79162C211yesmaximal, characteristic, complemented
18#78878C211yesmaximal, characteristic, complemented
19#78877C211yesmaximal, characteristic, complemented
20#78868C211yesmaximal, characteristic, complemented
21#78867C211yesmaximal, characteristic, complemented
22#78575C211yesmaximal, characteristic, complemented
23#78544C211yesmaximal, characteristic, complemented
24#61348—31nomaximal, Sylow
25C2×C3×#135C2211yescharacteristic
26C3×#520C2211yescharacteristic
27C3×#520C2211yescharacteristic
28#5832C2211yescharacteristic
29#5827C2211yescharacteristic
30Dic3×#41C2211yescharacteristic
31#5825C2211yescharacteristic
32C2×#951C2211yescharacteristic
33C2×#950C2211yescharacteristic
34#5569C2212yes—
35#5568C2212yes—
36#5567C2212yes—
37Q8×Dic6C2212yes—
38#5564—22no—
39#5559C2212yes—
40#5542C2212yes—
41#5539—22no—
42#5539C2212yes—
43#5538—22no—
44D4×Dic6—22no—
45D4×Dic6C2212yes—
46#5533—21no—
47#5529—21no—
48#5526C2211yescharacteristic
49#5519—21no—
50#5519C2211yescharacteristic
51#5517—21no—
52#5517C2211yescharacteristic
53#5513—21no—
54#5511—21no—
55#5504C2211yescharacteristic
56#5500—21no—
57#5500C2211yescharacteristic
58C2×#888—21no—
59C2×#888C2211yescharacteristic
60C2×#887C2211yescharacteristic
61C3×#440C2212yes—
62C3×#440C2212yes—
63C3×C4×Q16C2212yes—
64C3×C4×D8C2212yes—
65C2×C3×#107C2211yescharacteristic
66C3×#417C2211yescharacteristic
67C3×#417C2211yescharacteristic
68C3×#405C2211yescharacteristic
69#5233C2211yescharacteristic
70#5232C2211yescharacteristic
71#5185C2211yescharacteristic
72#5182C2211yescharacteristic
73#5182C2212yes—
74#5166C2212yes—
75#5166C2211yescharacteristic
76#5165C2211yescharacteristic
77#5163C2211yescharacteristic
78#5162C2212yes—
79#5162C2211yescharacteristic
80#5153C2211yescharacteristic
81#5153C2212yes—
82#5150C2211yescharacteristic
83#5133C2211yescharacteristic
84#5122C2211yescharacteristic
85#5120C2211yescharacteristic
86Dic3×M16C2211yescharacteristic
87#5113C2211yescharacteristic
88C2×#816C2211yescharacteristic
89#5102C2211yescharacteristic
90C2×Dic3⋊C8C2211yescharacteristic
91#5031C2212yes—
92#5028C2212yes—
93#5022C2212yes—
94#5021C2212yes—
95#5019C2212yes—
96#5016C2212yes—
97#5009C2212yes—
98#5007C2212yes—
99#4999C2211yescharacteristic
100C2×#810C2211yescharacteristic
101#4966C2211yescharacteristic
102#4964C2211yescharacteristic
103C2×#807C2211yescharacteristic
104#4891C2212yes—
105#4890C2212yes—
106#4877C2212yes—
107#4875C2212yes—
108#4875C2212yes—
109#4875C2212yes—
110#4875C2212yes—
111#4875C2212yes—
112#4817C2212yes—
113#4797C2212yes—
114#4794C2212yes—
115#4792C2212yes—
116#4792C2212yes—
117#4790C2212yes—
118#4790C2212yes—
119#4789C2212yes—
120#4768C2212yes—
121#4765C2212yes—
122#4765C2212yes—
123#4760C2212yes—
124#4758C2212yes—
125#4757C2212yes—
126#4757C2212yes—
127#4756C2212yes—
128#4714C2212yes—
129#4703C2212yes—
130#4701C2212yes—
131#4701C2212yes—
132#4697C2212yes—
133#4681C2212yes—
134#4679C2212yes—
135C8×Dic6C2212yes—
136#3507—31no—
137#3503—31no—
138#3377—32no—
139#3377—32no—
140#3375—32no—
141#3372—32no—
142#3367—32no—
143#3367—32no—
144#3363—32no—
145#3361—32no—
146#3141—31no—
147#3137—31no—
148#3137—31no—
149#3083—31no—
150#3083—31no—
151C2×#477—31no—
152#3046—31no—
153#3046—31no—
154#3035—31no—
155#2962—31no—
156#2951—31no—
157#2951D311yescharacteristic, complemented
158C4×#137—31no—
159C2×C3×#41C2311yescharacteristic
160C2×C3×#41C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6—21no—
163C22×Dic6—22no—
164C22×Dic6C2311yescharacteristic
165C3×#135—24no—
166C2×C3×Q16C2311yescharacteristic
167C2×C3×SD16C2311yescharacteristic
168C2×C3×SD16C2311yescharacteristic
169C2×C3×D8C2311yescharacteristic
170C2×C3×M16C2311yescharacteristic
171C22×C3×C8C2311yescharacteristic
172C3×C4×Q8C2312yes—
173C3×C4×Q8C2312yes—
174C3×C4×D4—22no—
175C3×C4×D4—22no—
176C3×C4×D4C2312yes—
177C3×C4×D4C2312yes—
178C3×#117—21no—
179C3×#117—21no—
180C3×#117C2311yescharacteristic
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C4⋊C4C2311yescharacteristic
185#951—24no—
186#950—24no—
187#947C2311yescharacteristic
188Q8×Dic3C2311yescharacteristic
189Q8×Dic3C2312yes—
190Q8×Dic3C2311yescharacteristic
191#944C2311yescharacteristic
192#944C2312yes—
193C2×#216C2312yes—
194C2×#216C2311yescharacteristic
195C2×#215C2311yescharacteristic
196#940C2311yescharacteristic
197#939—21no—
198#939—21no—
199#936C2311yescharacteristic
200#936C2312yes—
201#935—22no—
202D4×Dic3—21no—
203D4×Dic3—21no—
204D4×Dic3—22no—
205D4×Dic3C2311yescharacteristic
206D4×Dic3C2312yes—
207D4×Dic3C2311yescharacteristic
208C2×#214C2311yescharacteristic
209C2×#214C2312yes—
210C2×#213C2311yescharacteristic
211#929—22no—
212C4×#67—22no—
213C4×#67—22no—
214C4×#67—21no—
215C4×#67—21no—
216#926—21no—
217#926—22no—
218#926—21no—
219#926C2311yescharacteristic
220#926C2311yescharacteristic
221C2×C4⋊Dic3—21no—
222C2×C4⋊Dic3C2311yescharacteristic
223#924—22no—
224#924—22no—
225#924—22no—
226#924—21no—
227#924—21no—
228#924—22no—
229C2×Dic3⋊C4—21no—
230C2×Dic3⋊C4—21no—
231C2×Dic3⋊C4—22no—
232C2×C4×Dic3—21no—
233C2×C4×Dic3—21no—
234C2×C4×Dic3C2311yescharacteristic
235C2×#208C2311yescharacteristic
236C22×C3⋊C8C2311yescharacteristic
237#898—22no—
238#897—21no—
239#897—21no—
240#896—22no—
241#893C2312yes—
242#892—21no—
243D3×C4⋊C4—21no—
244#890—21no—
245#890—21no—
246#890—22no—
247#890D411yescharacteristic
248#890D411yescharacteristic
249#890C2312yes—
250#889—22no—
251#889—22no—
252#888—22no—
253#888—21no—
254#888—21no—
255#888—22no—
256#888—22no—
257#888—21no—
258#888—21no—
259#888D411yescharacteristic
260#888D411yescharacteristic
261#888C2312yes—
262#888C2312yes—
263#888C2312yes—
264#887—21no—
265#887—21no—
266#887C2312yes—
267#887C2312yes—
268#887C2312yes—
269#886—22no—
270#885—22no—
271#883—22no—
272#879—22no—
273#879—22no—
274#878—22no—
275#878—22no—
276#878—22no—
277#878—22no—
278#878—22no—
279#878D412yes—
280#878D412yes—
281#876—22no—
282#875C2312yes—
283#872—22no—
284#870—22no—
285#870—22no—
286#870C2312yes—
287#869—22no—
288#869C2312yes—
289#869C2312yes—
290C4×Dic6—22no—
291C4×Dic6—22no—
292C4×Dic6—22no—
293C4×Dic6C2312yes—
294C4×Dic6C2312yes—
295C3×#107C2312yes—
296C3×#107C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#102C2312yes—
300C3×#102C2312yes—
301C3×#97C2312yes—
302C3×C4×C8C2312yes—
303#835C2312yes—
304#835C2311yescharacteristic
305#835C2311yescharacteristic
306#832C2311yescharacteristic
307#832C2311yescharacteristic
308#832C2312yes—
309#821C2312yes—
310#821C2311yescharacteristic
311#821C2311yescharacteristic
312#816C2312yes—
313#816C2312yes—
314#816C2311yescharacteristic
315#816C2312yes—
316#816C2312yes—
317#816C2311yescharacteristic
318#816C2312yes—
319#815C2312yes—
320#815C2312yes—
321Dic3⋊C8C2311yescharacteristic
322Dic3⋊C8C2311yescharacteristic
323Dic3⋊C8C2311yescharacteristic
324Dic3⋊C8C2311yescharacteristic
325Dic3⋊C8C2312yes—
326Dic3⋊C8C2312yes—
327C8×Dic3C2312yes—
328C8×Dic3C2312yes—
329#810C2312yes—
330#810C2312yes—
331#810C2312yes—
332#809C2312yes—
333#808C2312yes—
334#807C2312yes—
335#807C2312yes—
336#807C2312yes—
337C4⋊(C3⋊C8)C2312yes—
338C4⋊(C3⋊C8)C2312yes—
339C2×#137—31no—
340C2×#135—31no—
341C2×#135C2×D311yescharacteristic
342#559—32no—
343Q82—32no—
344#557—32no—
345#557—32no—
346#556—32no—
347#556—32no—
348#556—61no—
349#554—32no—
350#554—61no—
351#554—62no—
352#552—61no—
353#552—61no—
354D4×Q8—32no—
355D4×Q8—62no—
356#544—31no—
357#544—31no—
358#544—61no—
359#544—61no—
360#539—62no—
361#536—31no—
362#536—31no—
363#533—31no—
364#533—61no—
365#532—31no—
366C2×C4⋊Q8—31no—
367C2×C4⋊Q8—61no—
368#529—62no—
369#520—31no—
370#520—31no—
371#520C2×D311yescharacteristic
372#520C2×D311yescharacteristic
373C4×#41—31no—
374C2×C4×Q8—31no—
375#491—32no—
376#491—32no—
377#489—32no—
378#489—32no—
379#489—32no—
380#489—32no—
381#488—32no—
382#488—32no—
383#487—32no—
384#487—32no—
385#487—32no—
386#486—32no—
387#479—32no—
388#479—32no—
389#478—32no—
390#478—32no—
391#477—32no—
392#477—32no—
393#477—32no—
394#477—32no—
395#477—32no—
396#477—32no—
397#474—32no—
398#474—32no—
399#464—31no—
400#464—32no—
401#464—31no—
402#464—32no—
403#463—31no—
404#463—32no—
405#463—31no—
406#463—32no—
407#462—31no—
408#462—32no—
409#462—32no—
410#461—32no—
411#461—31no—
412#461—32no—
413#460—31no—
414#459—31no—
415#446—32no—
416#446—32no—
417#446—32no—
418C8×Q8—32no—
419#441—32no—
420#440—32no—
421#440—32no—
422#440—32no—
423#440C2×D312yes—
424#440C2×D312yes—
425C4×Q16—32no—
426C4×Q16—32no—
427C4×Q16C2×D312yes—
428C4×SD16—32no—
429C4×D8—32no—
430C4×D8C2×D312yes—
431#428—31no—
432C2×#107—31no—
433C2×#107C2×D311yescharacteristic
434#424—31no—
435#424—31no—
436C2×C4⋊C8—31no—
437#419—31no—
438#417—31no—
439#417—31no—
440#417—31no—
441#417C2×D311yescharacteristic
442#417C2×D311yescharacteristic
443#416—31no—
444#416—31no—
445C2×#103—31no—
446C2×#103—31no—
447#405—31no—
448#405C2×D311yescharacteristic
449C4×M16—31no—
450C3×#41—22no—
451C3×#41—22no—
452C3×#41—22no—
453C3×#41#4114yes—
454C2×C3×Q8C2411yescharacteristic
455C2×C3×Q8C2411yescharacteristic
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4C2411yescharacteristic
459C2×C3×D4C2411yescharacteristic
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4—22no—
465C22×C3×C4—22no—
466C22×C3×C4C2411yescharacteristic
467C2×#67—21no—
468C2×#67—21no—
469C2×#67—21no—
470C22×Dic3—21no—
471C22×Dic3—21no—
472C22×Dic3—21no—
473C22×Dic3—21no—
474C22×Dic3—22no—
475C22×Dic3C2×D411yescharacteristic
476C22×Dic3C2×D411yescharacteristic
477#235—22no—
478#235—22no—
479C2×D12C2411yescharacteristic
480C2×C4×D3—21no—
481C2×C4×D3—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6—21no—
485C2×Dic6—22no—
486C2×Dic6—22no—
487C2×Dic6—22no—
488C2×Dic6—22no—
489C2×Dic6—84no—
490C2×Dic6—82no—
491C2×Dic6C2×D412yes—
492C2×Dic6C2×D412yes—
493C2×Dic6C2411yescharacteristic
494C2×Dic6C2412yes—
495C3×Q16—22no—
496C3×SD16—22no—
497C3×SD16—22no—
498C3×D8—22no—
499C3×M16—22no—
500C2×C3×C8—22no—
501C2×C3×C8C2412yes—
502C2×C3×C8C2411yescharacteristic
503C2×C3×C8C2411yescharacteristic
504C3×C4⋊C4—21no—
505C3×C4⋊C4—21no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—22no—
508C3×C4⋊C4C2×D411yescharacteristic
509C3×C4⋊C4C2×D411yescharacteristic
510C3×C4⋊C4C2412yes—
511C3×C4⋊C4C2412yes—
512C3×C22⋊C4—22no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4C2×D412yes—
515C3×C42—22no—
516C3×C42—22no—
517C3×C42C2412yes—
518#217—21no—
519#217—21no—
520#217—21no—
521#217—22no—
522#217—21no—
523#217—21no—
524#217—22no—
525#217—22no—
526#217C2×D412yes—
527#216—22no—
528#216—24no—
529#215—22no—
530#214—22no—
531#214—24no—
532#213—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—21no—
536(C2×D3)⋊C4—21no—
537(C2×D3)⋊C4—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—21no—
542C4⋊Dic3—22no—
543C4⋊Dic3—21no—
544C4⋊Dic3—22no—
545C4⋊Dic3—21no—
546C4⋊Dic3C2×D412yes—
547C4⋊Dic3C2×D412yes—
548C4⋊Dic3C2×D411yescharacteristic
549C4⋊Dic3C2×D411yescharacteristic
550C4⋊Dic3C2411yescharacteristic
551C4⋊Dic3C2412yes—
552C4⋊Dic3C2411yescharacteristic
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—21no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—21no—
560Dic3⋊C4—22no—
561Dic3⋊C4—22no—
562Dic3⋊C4—22no—
563Dic3⋊C4—22no—
564Dic3⋊C4—22no—
565Dic3⋊C4—22no—
566Dic3⋊C4C2×D412yes—
567Dic3⋊C4C2×D412yes—
568Dic3⋊C4C2×D412yes—
569Dic3⋊C4C2×D412yes—
570C4×Dic3—21no—
571C4×Dic3—21no—
572C4×Dic3—21no—
573C4×Dic3—22no—
574C4×Dic3—22no—
575C4×Dic3—22no—
576C4×Dic3—22no—
577C4×Dic3C2×D411yescharacteristic
578C4×Dic3C2×D411yescharacteristic
579C4×Dic3C2411yescharacteristic
580C4×Dic3C2412yes—
581C4×Dic3C2411yescharacteristic
582#208—22no—
583C2×C3⋊C8—22no—
584C2×C3⋊C8C2411yescharacteristic
585C2×C3⋊C8C2411yescharacteristic
586C2×C3⋊C8C2412yes—
587C2×#41—31no—
588C2×#41C22×D311yescharacteristic
589C2×#41C22×D311yescharacteristic
590C22×Q8—31no—
591C22×Q8—61no—
592C22×Q8—62no—
593#137—64no—
594#135—24no—
595#135—64no—
596C2×Q16—31no—
597C2×Q16—32no—
598C2×Q16C22×D311yescharacteristic
599C2×SD16—31no—
600C2×SD16—31no—
601C2×SD16—32no—
602C2×SD16C22×D311yescharacteristic
603C2×SD16C22×D311yescharacteristic
604C2×D8—31no—
605C2×D8C22×D311yescharacteristic
606C2×M16—31no—
607C2×M16C22×D311yescharacteristic
608C22×C8—31no—
609C22×C8C22×D311yescharacteristic
610C4⋊Q8—31no—
611C4⋊Q8—31no—
612C4⋊Q8—32no—
613C4⋊Q8—32no—
614C4⋊Q8—32no—
615C4⋊Q8—31no—
616C4⋊Q8—32no—
617C4⋊Q8—32no—
618C4⋊Q8—32no—
619C4⋊Q8—62no—
620C4⋊Q8—61no—
621C4⋊Q8—61no—
622C4⋊Q8—61no—
623C4⋊Q8—62no—
624C4⋊Q8—62no—
625C4⋊Q8—62no—
626C4⋊Q8—61no—
627#127—31no—
628#126—62no—
629#126—62no—
630#126—62no—
631#126—62no—
632#125—31no—
633#125—31no—
634#125—32no—
635#125—32no—
636#125—62no—
637#125—62no—
638#125—62no—
639#125—61no—
640#125—62no—
641#125—62no—
642#125—61no—
643#124—31no—
644#124—31no—
645#124—32no—
646#124—32no—
647#124—62no—
648#123—62no—
649#123—62no—
650#123—62no—
651#123—62no—
652C22⋊Q8—32no—
653C22⋊Q8—32no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—62no—
659C22⋊Q8—62no—
660C22⋊Q8—61no—
661C22⋊Q8—61no—
662C22⋊Q8—62no—
663C22⋊Q8—62no—
664C22⋊Q8—62no—
665C22⋊Q8—61no—
666C22⋊Q8—61no—
667C22⋊Q8—62no—
668#121—61no—
669#121—61no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—31no—
673C4×Q8—31no—
674C4×Q8—32no—
675C4×Q8—32no—
676C4×Q8—32no—
677C4×Q8—32no—
678C4×Q8—62no—
679C4×Q8—62no—
680C4×Q8—62no—
681C4×Q8—61no—
682C4×Q8—61no—
683C4×Q8C22×D312yes—
684C4×Q8C22×D312yes—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—31no—
688C4×D4—31no—
689C4×D4—32no—
690C4×D4—32no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4—62no—
694C4×D4—62no—
695C4×D4—62no—
696C4×D4—61no—
697C4×D4—61no—
698C4×D4C22×D312yes—
699C4×D4C22×D312yes—
700#117—21no—
701#117—21no—
702#117—31no—
703#117—31no—
704#117—62no—
705#117—61no—
706#117—61no—
707#117—61no—
708#117—62no—
709#117C22×D311yescharacteristic
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—61no—
714C2×C4⋊C4—61no—
715C2×C4⋊C4—62no—
716C2×C4⋊C4—61no—
717C2×C4⋊C4—61no—
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C42—31no—
721C2×C42—61no—
722C2×C42—61no—
723#107—32no—
724#107—32no—
725#107—32no—
726#107C22×D312yes—
727#107C22×D312yes—
728#106—32no—
729C4⋊C8—31no—
730C4⋊C8—31no—
731C4⋊C8—31no—
732C4⋊C8—31no—
733C4⋊C8—32no—
734C4⋊C8—32no—
735C4⋊C8—32no—
736C4⋊C8—32no—
737#103—31no—
738#103—31no—
739#103—32no—
740#103—32no—
741#103—32no—
742#103—31no—
743#103—31no—
744#103—32no—
745#103—32no—
746#103—32no—
747#103—32no—
748#103—32no—
749#103—32no—
750#103C22×D312yes—
751#103C22×D312yes—
752#102—31no—
753#102—31no—
754#102—32no—
755#102—31no—
756#102—31no—
757#102—32no—
758#102—32no—
759#102C22×D312yes—
760#102C22×D312yes—
761#97—32no—
762#97—32no—
763#97C22×D312yes—
764C4×C8—32no—
765C4×C8—32no—
766C4×C8C22×D312yes—
767C23×C3—21no—
768C23×C3—21no—
769C23×C3C22×D411yescharacteristic
770C22×D3—21no—
771C3×Q8—21no—
772C3×Q8—21no—
773C3×Q8—21no—
774C3×Q8C2×#4112yes—
775C3×D4—24no—
776C3×D4—21no—
777C3×D4—21no—
778C3×D4—21no—
779C3×D4—42no—
780C3×D4C2×#4112yes—
781C2×C3×C4—21no—
782C2×C3×C4—24no—
783C2×C3×C4—22no—
784C2×C3×C4—21no—
785C2×C3×C4—22no—
786C2×C3×C4—42no—
787C2×C3×C4—82no—
788C2×C3×C4—82no—
789C2×C3×C4—81no—
790C2×C3×C4—81no—
791C2×C3×C4C22×D412yes—
792C2×C3×C4C22×D412yes—
793C2×C3×C4C22×D411yescharacteristic
794C2×C3×C4C2×#4112yes—
795C2×C3×C42−1+412yes—
796C2×C3×C4C2511yescharacteristic
797#67—42no—
798#67—42no—
799#67—81no—
800C2×Dic3—22no—
801C2×Dic3—21no—
802C2×Dic3—21no—
803C2×Dic3—22no—
804C2×Dic3—21no—
805C2×Dic3—22no—
806C2×Dic3—41no—
807C2×Dic3—42no—
808C2×Dic3—42no—
809C2×Dic3—42no—
810C2×Dic3—82no—
811C2×Dic3—81no—
812C2×Dic3C22×D411yescharacteristic
813C2×Dic3C22×D412yes—
814C2×Dic3C22×D411yescharacteristic
815C2×Dic3C22×D411yescharacteristic
816C2×Dic3C22×D412yes—
817C2×Dic3C22×D411yescharacteristic
818D12—21no—
819D12—21no—
820C4×D3—42no—
821C4×D3—82no—
822Dic6—24no—
823Dic6—22no—
824Dic6—21no—
825Dic6—22no—
826Dic6—21no—
827Dic6—42no—
828Dic6—44no—
829Dic6—42no—
830Dic6—82no—
831Dic6—82no—
832Dic6—82no—
833C3×C8—21no—
834C3×C8—21no—
835C3×C8—22no—
836C3⋊C8—21no—
837C3⋊C8—21no—
838C3⋊C8—22no—
839#41—22no—
840#41—22no—
841#41—22no—
842#41—62no—
843#41—62no—
844#41#23514yes—
845C2×Q8—32no—
846C2×Q8—32no—
847C2×Q8—32no—
848C2×Q8—31no—
849C2×Q8—62no—
850C2×Q8—62no—
851C2×Q8—62no—
852C2×Q8—61no—
853C2×Q8—62no—
854C2×Q8—62no—
855C2×Q8—62no—
856C2×Q8—244no—
857C2×Q8—242no—
858C2×Q8C23×D311yescharacteristic
859C2×Q8C23×D311yescharacteristic
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—31no—
863C2×D4—61no—
864C2×D4—61no—
865C2×D4—61no—
866C2×D4C23×D311yescharacteristic
867C2×D4C23×D311yescharacteristic
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—31no—
875C22×C4—31no—
876C22×C4—62no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—62no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4C23×D311yescharacteristic
884Q16—22no—
885Q16—62no—
886Q16—64no—
887SD16—22no—
888SD16—22no—
889SD16—62no—
890SD16—62no—
891SD16—64no—
892D8—22no—
893D8—62no—
894M16—22no—
895M16—62no—
896C2×C8—22no—
897C2×C8—31no—
898C2×C8—32no—
899C2×C8—31no—
900C2×C8—62no—
901C2×C8C23×D312yes—
902C2×C8C23×D311yescharacteristic
903C2×C8C23×D311yescharacteristic
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—31no—
909C4⋊C4—32no—
910C4⋊C4—31no—
911C4⋊C4—32no—
912C4⋊C4—32no—
913C4⋊C4—32no—
914C4⋊C4—32no—
915C4⋊C4—32no—
916C4⋊C4—31no—
917C4⋊C4—32no—
918C4⋊C4—31no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—62no—
924C4⋊C4—62no—
925C4⋊C4—62no—
926C4⋊C4—61no—
927C4⋊C4—61no—
928C4⋊C4—62no—
929C4⋊C4—61no—
930C4⋊C4—61no—
931C4⋊C4—62no—
932C4⋊C4—62no—
933C4⋊C4—62no—
934C4⋊C4—61no—
935C4⋊C4—62no—
936C4⋊C4—62no—
937C4⋊C4—62no—
938C4⋊C4—62no—
939C4⋊C4—62no—
940C4⋊C4D3×D411yescharacteristic
941C4⋊C4D3×D411yescharacteristic
942C4⋊C4C23×D312yes—
943C4⋊C4C23×D312yes—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—32no—
947C22⋊C4—61no—
948C22⋊C4—62no—
949C22⋊C4—61no—
950C22⋊C4—61no—
951C22⋊C4—61no—
952C22⋊C4—61no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—61no—
956C22⋊C4—62no—
957C22⋊C4—61no—
958C22⋊C4—62no—
959C22⋊C4—62no—
960C22⋊C4D3×D412yes—
961C42—22no—
962C42—22no—
963C42—31no—
964C42—31no—
965C42—31no—
966C42—32no—
967C42—31no—
968C42—62no—
969C42—62no—
970C42—61no—
971C42—61no—
972C42—62no—
973C42—62no—
974C42—61no—
975C42C23×D312yes—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—22no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3#54812yes—
985C22×C3C23×D411yescharacteristic
986C2×D3—41no—
987C2×D3—41no—
988C2×D3—41no—
989C3×C4—22no—
990C3×C4—22no—
991C3×C4—22no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—41no—
995C3×C4#54812yes—
996C3×C4C22×#4111yescharacteristic
997C3×C4C2×2−1+411yescharacteristic
998Dic3—21no—
999Dic3—22no—
1000Dic3—21no—
1001Dic3—22no—
1002Dic3—21no—
1003Dic3—42no—
1004Dic3—41no—
1005Dic3—42no—
1006Dic3—41no—
1007Dic3—41no—
1008Dic3#57812yes—
1009C23—21no—
1010C23—21no—
1011C23—61no—
1012C23C2×D3×D411yescharacteristic
1013Q8—21no—
1014Q8—21no—
1015Q8—21no—
1016Q8—64no—
1017Q8—62no—
1018Q8—61no—
1019Q8—62no—
1020Q8—61no—
1021Q8—122no—
1022Q8—124no—
1023Q8—122no—
1024Q8—242no—
1025Q8—242no—
1026Q8—242no—
1027Q8C2×#23512yes—
1028D4—24no—
1029D4—21no—
1030D4—21no—
1031D4—21no—
1032D4—42no—
1033D4—61no—
1034D4—61no—
1035D4—122no—
1036D4—122no—
1037D4—241no—
1038D4C2×#23512yes—
1039C2×C4—21no—
1040C2×C4—24no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—31no—
1045C2×C4—31no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—32no—
1049C2×C4—32no—
1050C2×C4—42no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—61no—
1054C2×C4—61no—
1055C2×C4—61no—
1056C2×C4—62no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—81no—
1060C2×C4—81no—
1061C2×C4—122no—
1062C2×C4—121no—
1063C2×C4—122no—
1064C2×C4—122no—
1065C2×C4—122no—
1066C2×C4—242no—
1067C2×C4—242no—
1068C2×C4—241no—
1069C2×C4C2×#23512yes—
1070C2×C4C2×D3×D412yes—
1071C2×C4C2×D3×D412yes—
1072C2×C4C2×D3×D411yescharacteristic
1073C2×C4#101012yes—
1074C2×C4C24×D311yescharacteristic
1075C8—21no—
1076C8—21no—
1077C8—22no—
1078C8—61no—
1079C8—61no—
1080C8—62no—
1081C2×C3—22no—
1082C2×C3—42no—
1083C2×C3—81no—
1084C2×C3C2×#54811yescharacteristic
1085C2×C3C2×#57811yescharacteristic
1086C2×C3#358511yescharacteristic
1087D3—81no—
1088C22—21no—
1089C22—21no—
1090C22—22no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—121no—
1097C22—121no—
1098C22—121no—
1099C22#555212yes—
1100C22C22×D3×D411yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—32no—
1105C4—42no—
1106C4—42no—
1107C4—41no—
1108C4—61no—
1109C4—61no—
1110C4—62no—
1111C4—61no—
1112C4—62no—
1113C4—121no—
1114C4—122no—
1115C4—121no—
1116C4—121no—
1117C4—122no—
1118C4#555212yes—
1119C4C22×#23511yescharacteristic
1120C4C2×#101011yescharacteristic
1121C3#6134811yescharacteristic, complemented, Sylow
1122C2—22no—
1123C2—42no—
1124C2—81no—
1125C2—241no—
1126C2C2×#555211yescharacteristic
1127C2#8720411yescharacteristic
1128C2D3×#57811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2951C2
socleC22×C3C23×D4
prime radical#83900C2
hypercenter#2951D3
hypocenterC3#61348
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #85892C2semidirect
2. #85889C2semidirect
3. C3×#2951C2semidirect
4. #83902C2semidirect
6. #82572C2semidirect
7. #82559C2semidirect
8. #79758C2semidirect
9. #79756C2semidirect
10. #79755C2semidirect
11. #79751C2semidirect
12. #79704C2semidirect
13. #79699C2semidirect
14. #79571C2semidirect
15. #79569C2semidirect
16. C2×#4875C2semidirect
17. #79162C2semidirect
18. #78878C2semidirect
19. #78877C2semidirect
20. #78868C2semidirect
21. #78867C2semidirect
22. #78575C2semidirect
23. #78544C2semidirect
157. #2951D3semidirect
1121. C3#61348semidirect

Maximal subgroups

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

subgroupindex
#858922
#858892
C3×#29512
#839022
#839002
#825722
#825592
#797582
#797562
#797552
#797512
#797042
#796992
#795712
#795692
C2×#48752
#791622
#788782
#788772
#788682
#788672
#785752
#785442
#613483