Finite Group Databasebeta

← #11675954

Subgroups — #11675954

Order 768.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86282C211yesmaximal, characteristic, complemented
2#86281C211yesmaximal, characteristic, complemented
3C3×#2961C211yesmaximal, characteristic, complemented
4#79987C212yesmaximal, complemented
5#79986C212yesmaximal, complemented
6#79979C212yesmaximal, complemented
7#79978C212yesmaximal, complemented
8#79978C212yesmaximal, complemented
9#79977C212yesmaximal, complemented
10#79976C212yesmaximal, complemented
11#79975C212yesmaximal, complemented
12#79092C211yesmaximal, characteristic, complemented
13#79092C211yesmaximal, characteristic, complemented
14#79091C211yesmaximal, characteristic, complemented
15#79091C211yesmaximal, characteristic, complemented
16#79061C211yesmaximal, characteristic, complemented
17#79060C211yesmaximal, characteristic, complemented
18#78574C211yesmaximal, characteristic
19#78562C211yesmaximal, characteristic
20#78546C211yesmaximal, characteristic, complemented
21#78545C211yesmaximal, characteristic, complemented
22#78494C211yesmaximal, characteristic
23C2×#4702C211yesmaximal, characteristic, complemented
24#61380—31nomaximal, Sylow
25C3×#533C2211yescharacteristic
26C2×#904C2211yescharacteristic
27#5729—21no—
28#5729—21no—
29#5728—21no—
30D3×C4⋊Q8—21no—
31#5689—21no—
32#5689—21no—
33#5688—21no—
34D3×#125—21no—
35#5636—22no—
36#5636—22no—
37#5635—22no—
38#5632—22no—
39#5579C2212yes—
40#5579C2212yes—
41#5579C2212yes—
42Q8×D12C2212yes—
43#5567C2212yes—
44#5567C2212yes—
45#5567C2212yes—
46Q8×Dic6C2212yes—
47#5523C2211yescharacteristic
48#5523C2211yescharacteristic
49#5523C2211yescharacteristic
50#5523C2211yescharacteristic
51#5519C2211yescharacteristic
52#5519C2211yescharacteristic
53#5519C2211yescharacteristic
54#5519C2211yescharacteristic
55C4×#235C2211yescharacteristic
56C4×#235C2211yescharacteristic
57C2×#870C2211yescharacteristic
58C2×#869C2211yescharacteristic
59C3×#446C2212yes—
60C3×#446C2212yes—
61C3×#446C2212yes—
62C3×#446C2212yes—
63C3×#424C2211yescharacteristic
64C3×#424C2211yescharacteristic
65C3×#423C2211yescharacteristic
66C3×#405C2211yescharacteristic
67C3×#405C2211yescharacteristic
68C2×C3×#97C2211yescharacteristic
69#5133C2211yescharacteristic
70#5133C2211yescharacteristic
71#5133C2211yescharacteristic
72#5133C2211yescharacteristic
73#5121C2211yescharacteristic
74#5121C2211yescharacteristic
75#5121C2211yescharacteristic
76#5121C2211yescharacteristic
77#5113C2211yescharacteristic
78#5113C2211yescharacteristic
79#5106C2211yescharacteristic
80C2×#818C2211yescharacteristic
81C2×#818C2211yescharacteristic
82C2×#817C2211yescharacteristic
83C2×#817C2211yescharacteristic
84#4851C2212yes—
85#4851C2212yes—
86#4851C2212yes—
87#4850C2212yes—
88#4850C2212yes—
89#4850C2212yes—
90#4847C2212yes—
91#4847C2212yes—
92#4847C2212yes—
93#4847C2212yes—
94#4847C2212yes—
95#4847C2212yes—
96#4846C2212yes—
97#4846C2212yes—
98#4846C2212yes—
99#4842C2212yes—
100#4842C2212yes—
101#4842C2212yes—
102#4829C2212yes—
103#4829C2212yes—
104#4829C2212yes—
105#4829C2212yes—
106#4829C2212yes—
107#4829C2212yes—
108#4716C2211yescharacteristic
109#4716C2212yes—
110#4716C2211yescharacteristic
111#4711C2211yescharacteristic
112#4711C2212yes—
113#4711C2211yescharacteristic
114#4710C2211yescharacteristic
115#4710C2212yes—
116#4710C2211yescharacteristic
117#4710C2212yes—
118#4710C2211yescharacteristic
119#4710C2211yescharacteristic
120#4702C2212yes—
121#4702C2212yes—
122#4702C2212yes—
123#4702C2212yes—
124#4702C2212yes—
125#4702C2212yes—
126#4702C2212yes—
127#4702C2212yes—
128C4×Dic12C2212yes—
129C4×D24C2212yes—
130C4×#204C2212yes—
131C4×#204C2212yes—
132#4683C2212yes—
133#4683C2212yes—
134#4682C2212yes—
135#4680C2212yes—
136#3504—31no—
137#3503—31no—
138#3390—32no—
139#3389—32no—
140#3388—32no—
141#3388—32no—
142#3387—32no—
143#3386—32no—
144#3385—32no—
145#3384—32no—
146#3164—31no—
147#3163—31no—
148C2×#501—31no—
149#3084—31no—
150#3084—31no—
151#3083—31no—
152#3083—31no—
153#3080—31no—
154#3079—31no—
155#2961D311yescharacteristic, complemented
156#2952—31no—
157#2951—31no—
158#2943—31no—
159C2×D3×Q8—22no—
160C2×#235C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6—21no—
163C2×C3×M16C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C22×C3×C8C2311yescharacteristic
166C22×C3×C8C2311yescharacteristic
167C3×C4⋊Q8D411yescharacteristic
168C3×C4⋊Q8D411yescharacteristic
169C3×#125D411yescharacteristic
170C3×#125D411yescharacteristic
171C3×C22⋊Q8D412yes—
172C3×C22⋊Q8D412yes—
173C3×C4×Q8C2312yes—
174C3×C4×Q8C2312yes—
175C3×#117C2311yescharacteristic
176C3×#117C2311yescharacteristic
177C2×C3×C42C2311yescharacteristic
178#946—22no—
179#946—22no—
180#946—22no—
181Q8×Dic3—22no—
182#944—22no—
183#944—22no—
184#944—22no—
185C4×#67—21no—
186C4×#67—21no—
187C4×#67—21no—
188C4×#67—21no—
189#926C2311yescharacteristic
190#926C2311yescharacteristic
191C2×C4⋊Dic3—21no—
192C2×C4⋊Dic3C2311yescharacteristic
193C2×C4⋊Dic3C2311yescharacteristic
194C2×C4⋊Dic3C2311yescharacteristic
195C2×C4⋊Dic3C2311yescharacteristic
196C2×Dic3⋊C4—21no—
197C2×Dic3⋊C4—21no—
198C2×Dic12C2311yescharacteristic
199#904Q818yescomplemented
200C2×D24C2311yescharacteristic
201C2×#204C2311yescharacteristic
202C2×#204C2311yescharacteristic
203#897—22no—
204#897—22no—
205#897—22no—
206#896—22no—
207#896—22no—
208#896—22no—
209#896—22no—
210#896—22no—
211#896—22no—
212#892—21no—
213#892—21no—
214#892—21no—
215#892—21no—
216D3×C4⋊C4—22no—
217D3×C4⋊C4—22no—
218D3×C4⋊C4—22no—
219D3×C4⋊C4—21no—
220D3×C4⋊C4—21no—
221D3×C4⋊C4—21no—
222D3×C4⋊C4—21no—
223#890—21no—
224#890—21no—
225#890—21no—
226#890—21no—
227#889—22no—
228#889—22no—
229#889—22no—
230#889—22no—
231#889—22no—
232#889—22no—
233#888—22no—
234#888—22no—
235#888—22no—
236#888—21no—
237#888—21no—
238#888—21no—
239#888—21no—
240#887—22no—
241#887—22no—
242#887—22no—
243#67⋊C4—22no—
244#67⋊C4—22no—
245#67⋊C4—22no—
246#67⋊C4—22no—
247#878—22no—
248#878—22no—
249#878—22no—
250#878—22no—
251C4×D12C2312yes—
252C4×D12C2312yes—
253C4×D12C2312yes—
254C4×D12C2312yes—
255C4×D12C2311yescharacteristic
256C4×D12C2311yescharacteristic
257C4×D12C2311yescharacteristic
258C4×D12C2311yescharacteristic
259#872—21no—
260#872—21no—
261C42×D3—21no—
262C42×D3—21no—
263#870—21no—
264#870—21no—
265#870C2312yes—
266#870C2312yes—
267#870C2312yes—
268#870C2312yes—
269#870C2312yes—
270#870C2312yes—
271#869—21no—
272#869—21no—
273#869C2312yes—
274#869C2312yes—
275#869C2312yes—
276#869C2312yes—
277#869C2312yes—
278#869C2312yes—
279C4×Dic6C2312yes—
280C4×Dic6C2312yes—
281C4×Dic6C2312yes—
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C4×Dic6C2311yescharacteristic
285C4×Dic6C2311yescharacteristic
286C4×Dic6C2311yescharacteristic
287C3×C4⋊C8C2312yes—
288C3×C4⋊C8C2312yes—
289C3×C4⋊C8C2312yes—
290C3×C4⋊C8C2312yes—
291C3×C4⋊C8C2312yes—
292C3×C4⋊C8C2312yes—
293C3×#97C2311yescharacteristic
294C3×#97C2311yescharacteristic
295C3×#97C2312yes—
296C3×#97C2311yescharacteristic
297C3×#97C2311yescharacteristic
298C3×#97C2312yes—
299C3×C4×C8C2312yes—
300C3×C4×C8C2312yes—
301#821C2312yes—
302#821C2312yes—
303#821C2312yes—
304#821C2312yes—
305#821C2311yescharacteristic
306#821C2311yescharacteristic
307#821C2311yescharacteristic
308#821C2311yescharacteristic
309#818C2312yes—
310#818C2312yes—
311#818C2312yes—
312#818C2312yes—
313#818C2311yescharacteristic
314#818C2312yes—
315#818C2311yescharacteristic
316#818C2312yes—
317#818C2312yes—
318#818C2312yes—
319#817C2312yes—
320#817C2312yes—
321#817C2312yes—
322#817C2312yes—
323#817C2311yescharacteristic
324#817C2312yes—
325#817C2311yescharacteristic
326#817C2312yes—
327#817C2312yes—
328#817C2312yes—
329#816C2312yes—
330#816C2312yes—
331#816C2312yes—
332#816C2312yes—
333#816C2311yescharacteristic
334#816C2311yescharacteristic
335#816C2311yescharacteristic
336#816C2311yescharacteristic
337C2×#135—31no—
338Q82—32no—
339#557—32no—
340#557—32no—
341#557—32no—
342#554—32no—
343#554—32no—
344#554—32no—
345#554—62no—
346#554—62no—
347#554—62no—
348D4×Q8—32no—
349D4×Q8—62no—
350#544—31no—
351#544—31no—
352#544—31no—
353#544—31no—
354#544—61no—
355#544—61no—
356#544—61no—
357#544—61no—
358#533—61no—
359#533—61no—
360#533C2×D311yescharacteristic
361C2×C4⋊Q8—31no—
362C2×C4⋊Q8—61no—
363C2×#125—31no—
364C2×#125—61no—
365#520—31no—
366#520—31no—
367#520—31no—
368#520—31no—
369C4×#41—31no—
370C4×#41—31no—
371#501—32no—
372#501—32no—
373#501—32no—
374#501—32no—
375#501—32no—
376#501—32no—
377#501—32no—
378#501—32no—
379#500—32no—
380#499—32no—
381#499—32no—
382#498—32no—
383#479—32no—
384#479—32no—
385#479—32no—
386#479—32no—
387#479—32no—
388#479—32no—
389#478—32no—
390#478—32no—
391#478—32no—
392#478—32no—
393#478—32no—
394#478—32no—
395#477—32no—
396#477—32no—
397#477—32no—
398#476—32no—
399#476—32no—
400#476—32no—
401#475—32no—
402#475—32no—
403#475—32no—
404#474—32no—
405#474—32no—
406#474—32no—
407#446C2×D312yes—
408#446C2×D312yes—
409#446C2×D312yes—
410#446C2×D312yes—
411#442—31no—
412#442—32no—
413#442—31no—
414#441—31no—
415#441—32no—
416#441—31no—
417#440—31no—
418#440—32no—
419#440—31no—
420#440—32no—
421#440—31no—
422#440—31no—
423C4×Q16—32no—
424C4×SD16—32no—
425C4×SD16—32no—
426C4×D8—32no—
427#428—31no—
428#428—31no—
429#428—31no—
430#428—31no—
431#427—31no—
432C2×#107—31no—
433C2×#107—31no—
434C2×#106—31no—
435C2×#106—31no—
436#424C2×D311yescharacteristic
437#424C2×D311yescharacteristic
438#423C2×D311yescharacteristic
439#417—31no—
440#417—31no—
441#417—31no—
442#417—31no—
443#416—31no—
444#416—31no—
445#405C2×D311yescharacteristic
446#405C2×D311yescharacteristic
447C2×#97C2×D311yescharacteristic
448C2×C3×Q8C2×D412yes—
449C2×C3×Q8C2×D412yes—
450C22×C3×C4C2×D411yescharacteristic
451C22×C3×C4C2×D411yescharacteristic
452C22×C3×C4C2411yescharacteristic
453C2×#67—21no—
454C2×#67—21no—
455C22×Dic3—21no—
456C22×Dic3—21no—
457C22×Dic3—21no—
458C22×Dic3—21no—
459D3×Q8—84no—
460#235—22no—
461#235—22no—
462#235C2×Q814yes—
463#235C2×Q814yescomplemented
464C2×D12C2411yescharacteristic
465C2×D12C2411yescharacteristic
466C2×C4×D3—21no—
467C2×C4×D3—21no—
468C2×C4×D3—21no—
469C2×C4×D3—21no—
470C2×C4×D3—21no—
471C2×C4×D3—21no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×Dic6—22no—
477C2×Dic6—22no—
478C2×Dic6—22no—
479C2×Dic6—22no—
480C2×Dic6—22no—
481C2×Dic6—22no—
482C2×Dic6—82no—
483C2×Dic6C2411yescharacteristic
484C2×Dic6C2411yescharacteristic
485C3×M16—22no—
486C3×M16—22no—
487C2×C3×C8—22no—
488C2×C3×C8C2×Q814yescomplemented
489C2×C3×C8C2412yes—
490C2×C3×C8C2412yes—
491C2×C3×C8C2411yescharacteristic
492C2×C3×C8C2411yescharacteristic
493C2×C3×C8C2411yescharacteristic
494C2×C3×C8C2411yescharacteristic
495C3×C4⋊C4C2×D412yes—
496C3×C4⋊C4C2×D412yes—
497C3×C4⋊C4C2×D412yes—
498C3×C4⋊C4C2×D411yescharacteristic
499C3×C4⋊C4C2×D412yes—
500C3×C4⋊C4C2×D412yes—
501C3×C4⋊C4C2×D411yescharacteristic
502C3×C4⋊C4C2×D411yescharacteristic
503C3×C4⋊C4C2×D412yes—
504C3×C4⋊C4C2×D411yescharacteristic
505C3×C22⋊C4C2×D412yes—
506C3×C22⋊C4C2×D412yes—
507C3×C42C2×D411yescharacteristic
508C3×C42C2×D411yescharacteristic
509C3×C42C2412yes—
510C3×C42C2412yes—
511C3×C42C2411yescharacteristic
512C3×C42C2411yescharacteristic
513#217—21no—
514#217—21no—
515(C2×D3)⋊C4—21no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—21no—
518(C2×D3)⋊C4—21no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523C4⋊Dic3—21no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—22no—
529C4⋊Dic3—22no—
530C4⋊Dic3—22no—
531C4⋊Dic3—21no—
532C4⋊Dic3—21no—
533C4⋊Dic3C2411yescharacteristic
534C4⋊Dic3C2412yes—
535C4⋊Dic3C2411yescharacteristic
536C4⋊Dic3C2412yes—
537C4⋊Dic3C2412yes—
538C4⋊Dic3C2411yescharacteristic
539C4⋊Dic3C2411yescharacteristic
540C4⋊Dic3C2412yes—
541Dic3⋊C4—21no—
542Dic3⋊C4—21no—
543Dic3⋊C4—21no—
544Dic3⋊C4—21no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561C4×Dic3—21no—
562C4×Dic3—21no—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3—22no—
566C4×Dic3—22no—
567C4×Dic3—22no—
568C4×Dic3—22no—
569C4×Dic3—21no—
570C4×Dic3—21no—
571Dic12C2×Q814yescomplemented
572D24C2×Q814yescomplemented
573#204C2×Q814yescomplemented
574#204C2×Q814yescomplemented
575C2×#41—31no—
576C2×#41—31no—
577C22×Q8—62no—
578C22×Q8—61no—
579#135—38no—
580C2×Q16—31no—
581C2×SD16—31no—
582C2×SD16—31no—
583C2×D8—31no—
584C2×M16C22×D311yescharacteristic
585C2×M16C22×D311yescharacteristic
586C22×C8C22×D311yescharacteristic
587C22×C8C22×D311yescharacteristic
588C4⋊Q8—32no—
589C4⋊Q8—32no—
590C4⋊Q8—32no—
591C4⋊Q8—32no—
592C4⋊Q8—32no—
593C4⋊Q8—32no—
594C4⋊Q8—62no—
595C4⋊Q8—62no—
596C4⋊Q8—62no—
597C4⋊Q8—61no—
598C4⋊Q8—61no—
599C4⋊Q8—62no—
600C4⋊Q8—61no—
601C4⋊Q8—61no—
602C4⋊Q8—62no—
603C4⋊Q8—62no—
604C4⋊Q8—61no—
605C4⋊Q8—61no—
606C4⋊Q8D1211yescharacteristic
607C4⋊Q8D1211yescharacteristic
608#125—32no—
609#125—32no—
610#125—32no—
611#125—32no—
612#125—32no—
613#125—32no—
614#125—61no—
615#125—61no—
616#125—62no—
617#125—62no—
618#125—61no—
619#125—61no—
620#125—62no—
621#125—62no—
622#125—62no—
623#125—62no—
624#125—61no—
625#125—61no—
626#125D1211yescharacteristic
627#125D1211yescharacteristic
628C22⋊Q8—62no—
629C22⋊Q8—62no—
630C22⋊Q8—62no—
631C22⋊Q8—62no—
632C22⋊Q8—62no—
633C22⋊Q8—62no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8D1212yes—
645C22⋊Q8D1212yes—
646C4×Q8—31no—
647C4×Q8—31no—
648C4×Q8—31no—
649C4×Q8—31no—
650C4×Q8—32no—
651C4×Q8—32no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—62no—
655C4×Q8—62no—
656C4×Q8—62no—
657C4×Q8—62no—
658C4×Q8C22×D312yes—
659C4×Q8C22×D312yes—
660C4×D4—31no—
661C4×D4—31no—
662C4×D4—31no—
663C4×D4—31no—
664C4×D4—32no—
665C4×D4—32no—
666C4×D4—32no—
667C4×D4—32no—
668C4×D4—61no—
669C4×D4—61no—
670C4×D4—61no—
671C4×D4—61no—
672C4×D4—62no—
673C4×D4—62no—
674C4×D4—62no—
675C4×D4—62no—
676#117—31no—
677#117—31no—
678#117—61no—
679#117—61no—
680#117—61no—
681#117—61no—
682#117—61no—
683#117—61no—
684#117C22×D311yescharacteristic
685#117C22×D311yescharacteristic
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—61no—
691C2×C4⋊C4—61no—
692C2×C4⋊C4—61no—
693C2×C4⋊C4—61no—
694C2×C4⋊C4—61no—
695C2×C4⋊C4—61no—
696C2×C4⋊C4—61no—
697C2×C4⋊C4—62no—
698C2×C4⋊C4—62no—
699C2×C4⋊C4—62no—
700C2×C42—61no—
701C2×C42—61no—
702C2×C42C22×D311yescharacteristic
703#107—32no—
704#107—32no—
705#107—32no—
706#107—32no—
707#107—31no—
708#107—31no—
709#107—32no—
710#107—32no—
711#107—32no—
712#107—32no—
713#106—32no—
714#106—32no—
715#106—32no—
716#106—32no—
717#106—31no—
718#106—31no—
719#106—32no—
720#106—32no—
721#106—32no—
722#106—32no—
723C4⋊C8C22×D312yes—
724C4⋊C8C22×D312yes—
725C4⋊C8C22×D312yes—
726C4⋊C8C22×D312yes—
727C4⋊C8C22×D312yes—
728C4⋊C8C22×D312yes—
729#103—31no—
730#103—31no—
731#103—31no—
732#103—31no—
733#103—32no—
734#103—32no—
735#103—32no—
736#103—32no—
737#102—31no—
738#102—31no—
739#102—31no—
740#102—31no—
741#102—32no—
742#102—32no—
743#102—32no—
744#102—32no—
745#97C22×D311yescharacteristic
746#97C22×D311yescharacteristic
747#97C22×D311yescharacteristic
748#97C22×D311yescharacteristic
749#97C22×D312yes—
750#97C22×D312yes—
751C4×C8C22×D312yes—
752C4×C8C22×D312yes—
753C23×C3C22×D411yescharacteristic
754C22×D3—21no—
755C22×D3—21no—
756C3×Q8—42no—
757C3×Q8—42no—
758C2×C3×C4—41no—
759C2×C3×C4—41no—
760C2×C3×C4C22×D412yes—
761C2×C3×C4C22×D411yescharacteristic
762C2×C3×C4C22×D411yescharacteristic
763C2×C3×C4C22×D412yes—
764C2×C3×C4C22×D411yescharacteristic
765C2×C3×C4C22×D411yescharacteristic
766C2×C3×C4C22×D412yes—
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D411yescharacteristic
769C2×C3×C4C22×Q812yes—
770C2×C3×C42−1+412yes—
771C2×C3×C4C2511yescharacteristic
772#67—24no—
773#67—24no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—22no—
783C2×Dic3—22no—
784C2×Dic3—81no—
785C2×Dic3—81no—
786C2×Dic3—81no—
787C2×Dic3—81no—
788D12—21no—
789D12—21no—
790D12C22×Q812yes—
791D12C22×Q812yes—
792C4×D3—24no—
793C4×D3—24no—
794C4×D3—42no—
795C4×D3—42no—
796C4×D3—81no—
797C4×D3—82no—
798C4×D3—81no—
799C4×D3—82no—
800C4×D3—82no—
801C4×D3—82no—
802Dic6—21no—
803Dic6—21no—
804Dic6—44no—
805Dic6—82no—
806Dic6—82no—
807Dic6—82no—
808Dic6—82no—
809Dic6—82no—
810Dic6C22×Q812yes—
811Dic6C22×Q812yes—
812C3×C8—21no—
813C3×C8—21no—
814C3×C8—22no—
815C3×C8—22no—
816C3×C8C22×Q812yes—
817C3×C8C22×Q812yes—
818#41—34no—
819#41—34no—
820#41—62no—
821#41—62no—
822C2×Q8—31no—
823C2×Q8—31no—
824C2×Q8—62no—
825C2×Q8—62no—
826C2×Q8—62no—
827C2×Q8—62no—
828C2×Q8—62no—
829C2×Q8—62no—
830C2×Q8—242no—
831C2×Q8—244no—
832C2×Q8C2×D1212yes—
833C2×Q8C2×D1212yes—
834C2×D4—31no—
835C2×D4—31no—
836C2×D4—61no—
837C2×D4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—62no—
849C22×C4—62no—
850C22×C4—62no—
851C22×C4—62no—
852C22×C4C2×D1211yescharacteristic
853C22×C4C2×D1211yescharacteristic
854C22×C4C23×D311yescharacteristic
855Q16—34no—
856SD16—34no—
857SD16—34no—
858D8—34no—
859M16—22no—
860M16—22no—
861C2×C8—22no—
862C2×C8D3×Q814yescomplemented
863C2×C8C23×D312yes—
864C2×C8C23×D312yes—
865C2×C8C23×D311yescharacteristic
866C2×C8C23×D311yescharacteristic
867C2×C8C23×D311yescharacteristic
868C2×C8C23×D311yescharacteristic
869C4⋊C4—32no—
870C4⋊C4—31no—
871C4⋊C4—32no—
872C4⋊C4—32no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—32no—
876C4⋊C4—31no—
877C4⋊C4—61no—
878C4⋊C4—61no—
879C4⋊C4—61no—
880C4⋊C4—61no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—62no—
890C4⋊C4—62no—
891C4⋊C4—62no—
892C4⋊C4—62no—
893C4⋊C4—62no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—61no—
898C4⋊C4—61no—
899C4⋊C4—61no—
900C4⋊C4—61no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4C2×D1211yescharacteristic
908C4⋊C4C2×D1211yescharacteristic
909C4⋊C4C2×D1211yescharacteristic
910C4⋊C4C2×D1212yes—
911C4⋊C4C2×D1212yes—
912C4⋊C4C2×D1212yes—
913C4⋊C4C2×D1211yescharacteristic
914C4⋊C4C2×D1212yes—
915C4⋊C4C2×D1212yes—
916C4⋊C4C2×D1212yes—
917C22⋊C4—61no—
918C22⋊C4—61no—
919C22⋊C4—61no—
920C22⋊C4—61no—
921C22⋊C4—61no—
922C22⋊C4—61no—
923C22⋊C4—62no—
924C22⋊C4—62no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C22⋊C4C2×D1212yes—
928C22⋊C4C2×D1212yes—
929C42—61no—
930C42—61no—
931C42—61no—
932C42—61no—
933C42—61no—
934C42—61no—
935C42—62no—
936C42—62no—
937C42—62no—
938C42—62no—
939C42C2×D1211yescharacteristic
940C42C2×D1211yescharacteristic
941C42C23×D312yes—
942C42C23×D312yes—
943C42C23×D311yescharacteristic
944C42C23×D311yescharacteristic
945C22×C3—21no—
946C22×C3—21no—
947C22×C3D4×Q812yes—
948C22×C3C23×D411yescharacteristic
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—41no—
952C2×D3—41no—
953C2×D3—41no—
954C2×D3—41no—
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—22no—
958C3×C4—22no—
959C3×C4—22no—
960C3×C4—21no—
961C3×C4—21no—
962C3×C4—22no—
963C3×C4D4×Q812yes—
964C3×C4C23×Q811yescharacteristic
965C3×C4C2×2−1+411yescharacteristic
966Dic3—22no—
967Dic3—22no—
968Dic3—42no—
969Dic3—42no—
970Dic3—41no—
971Dic3—41no—
972Dic3—42no—
973Dic3—41no—
974Dic3—42no—
975Dic3—41no—
976C23—61no—
977C23—61no—
978C23C22×D1211yescharacteristic
979Q8—32no—
980Q8—32no—
981Q8—42no—
982Q8—42no—
983Q8—61no—
984Q8—61no—
985Q8—124no—
986Q8—242no—
987Q8—242no—
988Q8—242no—
989Q8—242no—
990Q8—242no—
991D4—32no—
992D4—32no—
993D4—64no—
994D4—64no—
995D4—61no—
996D4—61no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—64no—
1002C2×C4—64no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—122no—
1012C2×C4—122no—
1013C2×C4—242no—
1014C2×C4—242no—
1015C2×C4—241no—
1016C2×C4—242no—
1017C2×C4—241no—
1018C2×C4—242no—
1019C2×C4—241no—
1020C2×C4—241no—
1021C2×C4—241no—
1022C2×C4—241no—
1023C2×C4C22×D1212yes—
1024C2×C4C22×D1211yescharacteristic
1025C2×C4C22×D1211yescharacteristic
1026C2×C4C22×D1211yescharacteristic
1027C2×C4C22×D1211yescharacteristic
1028C2×C4C22×D1212yes—
1029C2×C4C22×D1212yes—
1030C2×C4C22×D1212yes—
1031C2×C4C22×D1211yescharacteristic
1032C2×C4C2×D3×Q812yes—
1033C2×C4#101012yes—
1034C2×C4C24×D311yescharacteristic
1035C8—21no—
1036C8—21no—
1037C8—22no—
1038C8—22no—
1039C8C2×D3×Q812yes—
1040C8C2×D3×Q812yes—
1041C2×C3—22no—
1042C2×C3C2×D4×Q811yescharacteristic
1043C2×C3#358511yescharacteristic
1044C2×C3#358611yescharacteristic
1045D3—42no—
1046D3—42no—
1047C22—21no—
1048C22—21no—
1049C22—62no—
1050C22—62no—
1051C22—121no—
1052C22—121no—
1053C22—121no—
1054C22—121no—
1055C22Q8×D1212yes—
1056C22C23×D1211yescharacteristic
1057C4—21no—
1058C4—21no—
1059C4—22no—
1060C4—22no—
1061C4—21no—
1062C4—21no—
1063C4—22no—
1064C4—22no—
1065C4—62no—
1066C4—62no—
1067C4—121no—
1068C4—122no—
1069C4—122no—
1070C4—122no—
1071C4—121no—
1072C4—121no—
1073C4—122no—
1074C4—121no—
1075C4Q8×D1212yes—
1076C4C22×D3×Q811yescharacteristic
1077C4C2×#101011yescharacteristic
1078C3#6138011yescharacteristic, complemented, Sylow
1079C2—22no—
1080C2—122no—
1081C2—122no—
1082C2C2×Q8×D1211yescharacteristic
1083C2#8716711yescharacteristic
1084C2#8716811yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2961C2
socleC22×C3C23×D4
prime radicalC2×#904C22
hypercenter#2961D3
hypocenterC3#61380
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #2961

Complements

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

NH ≅ G/Ntype
1. #86282C2semidirect
2. #86281C2semidirect
3. C3×#2961C2semidirect
4. #79987C2semidirect
5. #79986C2semidirect
6. #79979C2semidirect
7. #79978C2semidirect
8. #79978C2semidirect
9. #79977C2semidirect
10. #79976C2semidirect
11. #79975C2semidirect
12. #79092C2semidirect
13. #79092C2semidirect
14. #79091C2semidirect
15. #79091C2semidirect
16. #79061C2semidirect
17. #79060C2semidirect
20. #78546C2semidirect
21. #78545C2semidirect
23. C2×#4702C2semidirect
155. #2961D3semidirect
199. #904Q8semidirect
463. #235C2×Q8semidirect
488. C2×C3×C8C2×Q8semidirect
571. Dic12C2×Q8semidirect
572. D24C2×Q8semidirect
573. #204C2×Q8semidirect
574. #204C2×Q8semidirect
862. C2×C8D3×Q8semidirect
1078. C3#61380semidirect

Maximal subgroups

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

subgroupindex
#862822
#862812
C3×#29612
#799872
#799862
#799792
#799782
#799772
#799762
#799752
#790922
#790912
#790612
#790602
#785742
#785622
#785462
#785452
#784942
C2×#47022
#613803