Finite Group Databasebeta

← #11675504

Subgroups — #11675504

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87033C211yesmaximal, characteristic, complemented
2#87018C211yesmaximal, characteristic, complemented
3C3×#3374C211yesmaximal, characteristic, complemented
4#83697C211yesmaximal, characteristic, complemented
5#83688C211yesmaximal, characteristic, complemented
6#81738C212yesmaximal, complemented
7#81734C212yesmaximal, complemented
8#81620C211yesmaximal, characteristic, complemented
9#81601C211yesmaximal, characteristic, complemented
10#81265C212yesmaximal, complemented
11#81235C212yesmaximal, complemented
12#81038C211yesmaximal, characteristic, complemented
13D3×#475C211yesmaximal, characteristic, complemented
14#80479C212yesmaximal, complemented
15#80475C211yesmaximal, characteristic
16#80465C211yesmaximal, characteristic, complemented
17#80464C212yesmaximal, complemented
18#79973C211yesmaximal, characteristic, complemented
19#79960C211yesmaximal, characteristic, complemented
20#79832C212yesmaximal, complemented
21#79815C212yesmaximal, complemented
22C4×#918C211yesmaximal, characteristic, complemented
23#79701C211yesmaximal, characteristic, complemented
24#61346—31nomaximal, Sylow
25C3×#557C2211yescharacteristic
26C3×#557C2211yescharacteristic
27C2×#919C2212yes—
28C2×#918C2211yescharacteristic
29#5732C2212yes—
30#5727—21no—
31#5727C2211yescharacteristic
32#5725C2211yescharacteristic
33#5724C2212yes—
34D3×C4⋊Q8—21no—
35D3×C4⋊Q8C2211yescharacteristic
36#5721C2211yescharacteristic
37#5693—22no—
38#5692—22no—
39#5691—21no—
40#5690—22no—
41#5690—21no—
42#5690C2212yes—
43#5689—22no—
44#5689C2212yes—
45#5585C2211yescharacteristic
46#5585C2211yescharacteristic
47#5580—21no—
48#5578—21no—
49#5578C2211yescharacteristic
50Q8×D12—21no—
51Q8×D12C2211yescharacteristic
52#5574C2212yes—
53#5574C2212yes—
54C4×#239C2211yescharacteristic
55C4×D3×Q8C2211yescharacteristic
56#5570C2211yescharacteristic
57#5568—21no—
58#5568C2212yes—
59Q8×Dic6C2212yes—
60C3×#491C2212yes—
61C3×#487C2211yescharacteristic
62C3×#479C2212yes—
63C3×#475C2211yescharacteristic
64C3×#462C2212yes—
65C3×#462C2211yescharacteristic
66C3×#446C2211yescharacteristic
67C3×#441C2212yes—
68C3×C4×Q16C2211yescharacteristic
69#5185C2212yes—
70#5185C2212yes—
71#5184C2211yescharacteristic
72#5184C2212yes—
73#5182C2212yes—
74#5094C2211yescharacteristic
75#5088C2211yescharacteristic
76#5083C2212yes—
77#5083C2211yescharacteristic
78#5079C2212yes—
79#5079C2211yescharacteristic
80#5068C2212yes—
81#5066C2212yes—
82C4×#216C2211yescharacteristic
83#5028C2212yes—
84#5027C2211yescharacteristic
85C4×#215C2212yes—
86C4×#215C2211yescharacteristic
87C4×#215C2212yes—
88Q8×C3⋊C8C2211yescharacteristic
89#5020C2212yes—
90#5020C2211yescharacteristic
91#4891C2212yes—
92#4889C2211yescharacteristic
93#4881C2211yescharacteristic
94#4870C2212yes—
95#4869C2212yes—
96D3×#106C2212yes—
97#4854C2212yes—
98#4851C2211yescharacteristic
99#4844C2212yes—
100#4843C2211yescharacteristic
101#4842C2212yes—
102#4839C2212yes—
103D3×C4⋊C8C2211yescharacteristic
104#4831C2212yes—
105#4831C2211yescharacteristic
106#4819C2212yes—
107#4819C2212yes—
108#4818C2212yes—
109#4817C2211yescharacteristic
110#4804C2212yes—
111#4803C2212yes—
112#4803C2212yes—
113#4803C2211yescharacteristic
114#4802C2211yescharacteristic
115D3×#103C2212yes—
116#4800C2212yes—
117#4799C2212yes—
118#4797C2212yes—
119#4794C2212yes—
120#4794C2212yes—
121#4794C2212yes—
122#4792C2212yes—
123#4791C2212yes—
124#4791C2212yes—
125#4789C2211yescharacteristic
126#4788C2212yes—
127#4788C2212yes—
128#4714C2212yes—
129#4711C2212yes—
130#4708C2212yes—
131#4701C2212yes—
132#4694C2211yescharacteristic
133C4×#204C2211yescharacteristic
134C4×ΓL(1,𝔽25)C2211yescharacteristic
135C8×Dic6C2211yescharacteristic
136#3507—31no—
137#3503—31no—
138#3376—32no—
139#3376—32no—
140#3374—31no—
141#3374D311yescharacteristic, complemented
142#3373—31no—
143#3373—31no—
144#3369—32no—
145#3369—32no—
146#3365—31no—
147#3365—31no—
148#3359—31no—
149#3359—31no—
150#3141—31no—
151#3137—32no—
152#3084—32no—
153C2×#475—31no—
154#3046—32no—
155#3035—31no—
156#2962—31no—
157#2952—32no—
158C4×#137—31no—
159C2×#239C2312yes—
160C2×#239C2311yescharacteristic
161C2×D3×Q8—21no—
162C2×D3×Q8—21no—
163C2×D3×Q8—21no—
164C2×D3×Q8C2311yescharacteristic
165C2×C3×Q16C2312yes—
166C2×C3×Q16C2311yescharacteristic
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8C2311yescharacteristic
169C3×C4⋊Q8C2312yes—
170C3×C4⋊Q8C2311yescharacteristic
171C3×#125—22no—
172C3×#125—21no—
173C3×#125—22no—
174C3×#125C2312yes—
175C3×C4×Q8—21no—
176C3×C4×Q8—21no—
177C3×C4×Q8C2312yes—
178C3×C4×Q8C2311yescharacteristic
179C3×C4×Q8C2312yes—
180C3×C4×Q8C2311yescharacteristic
181C3×C4×Q8C2311yescharacteristic
182#947—21no—
183#947C2312yes—
184#947C2312yes—
185#946—21no—
186#946D411yescharacteristic
187Q8×Dic3C2312yes—
188Q8×Dic3C2311yescharacteristic
189Q8×Dic3C2312yes—
190Q8×Dic3C2311yescharacteristic
191#944—21no—
192#944D411yescharacteristic
193#944C2312yes—
194C2×#216C2311yescharacteristic
195C2×#215C2312yes—
196C2×#215C2311yescharacteristic
197C2×#215C2312yes—
198#919—28no—
199#918—24no—
200C2×D24C2312yes—
201C2×#204C2311yescharacteristic
202C2×ΓL(1,𝔽25)C2311yescharacteristic
203C2×ΓL(1,𝔽25)C2311yescharacteristic
204C2×D3×C8C2312yes—
205#898—22no—
206#898—22no—
207#898—22no—
208#897—22no—
209#897—22no—
210#897—21no—
211#897—22no—
212#897—22no—
213#897D411yescharacteristic
214#896—22no—
215#896—22no—
216#896—22no—
217#896—22no—
218#896—22no—
219#896—22no—
220#896—22no—
221#896D412yes—
222#895—21no—
223#895—21no—
224#894—22no—
225#894—22no—
226#894—22no—
227#894—22no—
228#893—21no—
229#893—21no—
230#893—22no—
231#893—22no—
232#893—21no—
233#893—21no—
234#893C2312yes—
235#893C2312yes—
236#893C2311yescharacteristic
237#892—22no—
238#892—21no—
239#892C2311yescharacteristic
240D3×C4⋊C4—21no—
241D3×C4⋊C4—21no—
242D3×C4⋊C4—22no—
243D3×C4⋊C4—22no—
244D3×C4⋊C4—22no—
245D3×C4⋊C4C2311yescharacteristic
246D3×C4⋊C4C2312yes—
247#890—21no—
248#890—22no—
249#890C2312yes—
250#889—22no—
251#889—22no—
252#889D412yes—
253#888—22no—
254#888—22no—
255#888—22no—
256#888—21no—
257#888D411yescharacteristic
258#888C2312yes—
259#888C2312yes—
260#887—21no—
261#887—21no—
262#887C2311yescharacteristic
263#876—22no—
264#875—21no—
265#875C2312yes—
266#874C2311yescharacteristic
267C4×D12—21no—
268C4×D12—22no—
269C4×D12—22no—
270C4×D12—21no—
271C4×D12C2312yes—
272C4×D12C2311yescharacteristic
273C4×D12C2312yes—
274#872—22no—
275#872—22no—
276#872—22no—
277#872C2312yes—
278C42×D3—21no—
279C42×D3—21no—
280C42×D3C2311yescharacteristic
281#869—21no—
282#869—22no—
283#869C2312yes—
284#869C2311yescharacteristic
285C4×Dic6—22no—
286C4×Dic6—21no—
287C4×Dic6—21no—
288C4×Dic6C2311yescharacteristic
289C4×Dic6C2312yes—
290C4×Dic6C2311yescharacteristic
291C3×#107C2311yescharacteristic
292C3×#106C2312yes—
293C3×C4⋊C8C2311yescharacteristic
294C3×C4⋊C8C2312yes—
295C3×#103C2311yescharacteristic
296C3×#103C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#103C2312yes—
300C3×#103C2311yescharacteristic
301C3×#97C2312yes—
302C3×C4×C8C2311yescharacteristic
303#835C2312yes—
304#835C2311yescharacteristic
305#835C2311yescharacteristic
306#835C2312yes—
307#835C2312yes—
308#835C2312yes—
309#821C2312yes—
310#821C2312yes—
311#821C2311yescharacteristic
312#821C2312yes—
313#817C2311yescharacteristic
314#817C2312yes—
315#816C2312yes—
316#816C2311yescharacteristic
317#815C2312yes—
318#815C2311yescharacteristic
319#815C2311yescharacteristic
320Dic3⋊C8C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323C8×Dic3C2312yes—
324#810C2311yescharacteristic
325#810C2312yes—
326#809C2311yescharacteristic
327#809C2312yes—
328#809C2312yes—
329#809C2312yes—
330#808C2311yescharacteristic
331#808C2312yes—
332#808C2312yes—
333#807C2311yescharacteristic
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4⋊(C3⋊C8)C2312yes—
336C4×C3⋊C8C2311yescharacteristic
337C4×C3⋊C8C2312yes—
338C2×#137—31no—
339C2×#135—32no—
340#559—31no—
341#559—31no—
342Q82—32no—
343#557—31no—
344#557—31no—
345#557C2×D311yescharacteristic
346#557C2×D311yescharacteristic
347#556—32no—
348#556—32no—
349#556—61no—
350#554—32no—
351#554—62no—
352#554—61no—
353#552—62no—
354D4×Q8—31no—
355D4×Q8—31no—
356D4×Q8—61no—
357D4×Q8—61no—
358#544—32no—
359#544—62no—
360#539—62no—
361#536—32no—
362#533—31no—
363#533—61no—
364#532—31no—
365C2×C4⋊Q8—31no—
366C2×C4⋊Q8—61no—
367#529—61no—
368#529—61no—
369#520—32no—
370#520—32no—
371C4×#41—31no—
372C2×C4×Q8—31no—
373#491—32no—
374#491C2×D312yes—
375#489—32no—
376#489—32no—
377#489—32no—
378#489—32no—
379#488—32no—
380#488—32no—
381#487—32no—
382#487—31no—
383#487—32no—
384#487C2×D311yescharacteristic
385#486—31no—
386#486—31no—
387#479—32no—
388#479C2×D312yes—
389#478—32no—
390#478—32no—
391#476—32no—
392#476—32no—
393#475—31no—
394#475—31no—
395#475—32no—
396#475—32no—
397#475—31no—
398#475—32no—
399#475—32no—
400#475C2×D311yescharacteristic
401#464—32no—
402#464—32no—
403#464—32no—
404#463—32no—
405#463—32no—
406#463—32no—
407#462—32no—
408#462C2×D312yes—
409#462C2×D311yescharacteristic
410#461—31no—
411#461—32no—
412#461—32no—
413#460—31no—
414#459—31no—
415#446—32no—
416#446—31no—
417#446—32no—
418#446C2×D311yescharacteristic
419C8×Q8—31no—
420C8×Q8—31no—
421#442—32no—
422#442—32no—
423#441—31no—
424#441—32no—
425#441—31no—
426#441C2×D312yes—
427#440—31no—
428#440—31no—
429C4×Q16—31no—
430C4×Q16C2×D311yescharacteristic
431C4×SD16—31no—
432C4×SD16—32no—
433C4×SD16—32no—
434C4×SD16—32no—
435C4×SD16—32no—
436C4×SD16—31no—
437#428—31no—
438C2×#106—32no—
439#424—32no—
440C2×C4⋊C8—31no—
441#419—31no—
442#417—32no—
443#417—32no—
444#417—31no—
445#416—32no—
446C2×#103—32no—
447#405—32no—
448C4×M16—31no—
449C2×C3×Q8—21no—
450C2×C3×Q8C2×D411yescharacteristic
451C2×C3×Q8C2412yes—
452C2×C3×Q8C2411yescharacteristic
453C2×C3×Q8C2411yescharacteristic
454#239—22no—
455#239—24no—
456#239—24no—
457#239#4114yes—
458D3×Q8—22no—
459D3×Q8—22no—
460D3×Q8—82no—
461D3×Q8—82no—
462D3×Q8—82no—
463C2×D12—21no—
464C2×D12—22no—
465C2×D12—21no—
466C2×D12—21no—
467C2×D12C2412yes—
468C2×D12C2411yescharacteristic
469C2×C4×D3—21no—
470C2×C4×D3—21no—
471C2×C4×D3—21no—
472C2×C4×D3—21no—
473C2×C4×D3—22no—
474C2×C4×D3—21no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3C2×D411yescharacteristic
481C2×C4×D3C2×D411yescharacteristic
482C2×C4×D3C2411yescharacteristic
483C2×Dic6—21no—
484C2×Dic6—21no—
485C2×Dic6—22no—
486C2×Dic6—22no—
487C2×Dic6—22no—
488C2×Dic6C2×D411yescharacteristic
489C2×Dic6C2×D412yes—
490C2×Dic6C2411yescharacteristic
491C3×Q16—22no—
492C3×Q16—24no—
493C2×C3×C8C2411yescharacteristic
494C2×C3×C8C2412yes—
495C2×C3×C8C2411yescharacteristic
496C3×C4⋊C4—21no—
497C3×C4⋊C4—21no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—21no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—21no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—21no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—22no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4C2×D411yescharacteristic
508C3×C4⋊C4C2×D412yes—
509C3×C4⋊C4C2411yescharacteristic
510C3×C4⋊C4C2411yescharacteristic
511C3×C4⋊C4C2412yes—
512C3×C42—21no—
513C3×C42—22no—
514C3×C42—21no—
515C3×C42—22no—
516C3×C42C2411yescharacteristic
517C3×C42C2412yes—
518#216—22no—
519#215—24no—
520#215—22no—
521#215—24no—
522(C2×D3)⋊C4—21no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—21no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—21no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4C2×D412yes—
536(C2×D3)⋊C4C2×D412yes—
537C4⋊Dic3—22no—
538C4⋊Dic3—21no—
539C4⋊Dic3—21no—
540C4⋊Dic3—21no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3—22no—
544C4⋊Dic3C2×D411yescharacteristic
545C4⋊Dic3C2×D412yes—
546C4⋊Dic3C2411yescharacteristic
547C4⋊Dic3C2411yescharacteristic
548C4⋊Dic3C2412yes—
549Dic3⋊C4—21no—
550Dic3⋊C4—21no—
551Dic3⋊C4—21no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4C2×D412yes—
559Dic3⋊C4C2×D412yes—
560Dic3⋊C4C2×D412yes—
561Dic3⋊C4C2×D412yes—
562Dic3⋊C4C2×D412yes—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3—22no—
566C4×Dic3—21no—
567C4×Dic3—21no—
568C4×Dic3—21no—
569C4×Dic3—22no—
570C4×Dic3C2×D411yescharacteristic
571C4×Dic3C2×D411yescharacteristic
572C4×Dic3C2412yes—
573C4×Dic3C2411yescharacteristic
574C2×C3⋊C8C2411yescharacteristic
575C2×C3⋊C8C2411yescharacteristic
576C2×C3⋊C8C2412yes—
577D24—24no—
578#204—22no—
579ΓL(1,𝔽25)—22no—
580ΓL(1,𝔽25)—22no—
581D3×C8—24no—
582C2×#41—31no—
583C2×#41—32no—
584C22×Q8—31no—
585C22×Q8—61no—
586C22×Q8—61no—
587C22×Q8—61no—
588#137—64no—
589#135—68no—
590C2×Q16—31no—
591C2×Q16C22×D312yes—
592C2×Q16C22×D311yescharacteristic
593C2×SD16—32no—
594C2×SD16—32no—
595C2×SD16—31no—
596C2×SD16—31no—
597C2×D8—32no—
598C2×M16—31no—
599C2×M16—31no—
600C22×C8—32no—
601C4⋊Q8—21no—
602C4⋊Q8—31no—
603C4⋊Q8—31no—
604C4⋊Q8—32no—
605C4⋊Q8—32no—
606C4⋊Q8—32no—
607C4⋊Q8—31no—
608C4⋊Q8—32no—
609C4⋊Q8—62no—
610C4⋊Q8—61no—
611C4⋊Q8—61no—
612C4⋊Q8—61no—
613C4⋊Q8—62no—
614C4⋊Q8—62no—
615C4⋊Q8—62no—
616C4⋊Q8C22×D311yescharacteristic
617C4⋊Q8C22×D312yes—
618C4⋊Q8C22×D311yescharacteristic
619#127—31no—
620#126—62no—
621#126—62no—
622#126—62no—
623#126—62no—
624#125—21no—
625#125—22no—
626#125—22no—
627#125—32no—
628#125—32no—
629#125—61no—
630#125—62no—
631#125—62no—
632#125—62no—
633#125C22×D312yes—
634#124—32no—
635#124—32no—
636#124—32no—
637#124—61no—
638#124—61no—
639#123—62no—
640#123—62no—
641#123—62no—
642#123—62no—
643C22⋊Q8—31no—
644C22⋊Q8—31no—
645C22⋊Q8—32no—
646C22⋊Q8—62no—
647C22⋊Q8—62no—
648C22⋊Q8—62no—
649C22⋊Q8—62no—
650C22⋊Q8—62no—
651C22⋊Q8—62no—
652C22⋊Q8—62no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—61no—
657C22⋊Q8—61no—
658C22⋊Q8—62no—
659#121—61no—
660#121—61no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—31no—
664C4×Q8—32no—
665C4×Q8—31no—
666C4×Q8—31no—
667C4×Q8—32no—
668C4×Q8—32no—
669C4×Q8—31no—
670C4×Q8—31no—
671C4×Q8—61no—
672C4×Q8—61no—
673C4×Q8—62no—
674C4×Q8—61no—
675C4×Q8—61no—
676C4×Q8C22×D311yescharacteristic
677C4×Q8C22×D311yescharacteristic
678C4×Q8C22×D312yes—
679C4×Q8C22×D312yes—
680C4×Q8C22×D311yescharacteristic
681C4×D4—31no—
682C4×D4—32no—
683C4×D4—32no—
684C4×D4—31no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—62no—
688C4×D4—62no—
689C4×D4—61no—
690C4×D4—61no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4—62no—
694C4×D4—62no—
695C4×D4—61no—
696C4×D4—61no—
697#117—32no—
698#117—31no—
699#117—62no—
700#117—62no—
701#117—62no—
702#117—61no—
703#117—62no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—32no—
706C2×C4⋊C4—62no—
707C2×C4⋊C4—62no—
708C2×C4⋊C4—62no—
709C2×C4⋊C4—61no—
710C2×C4⋊C4—61no—
711C2×C42—31no—
712C2×C42—61no—
713C2×C42—61no—
714#107—31no—
715#107C22×D311yescharacteristic
716#106—32no—
717#106—31no—
718#106—32no—
719#106—32no—
720#106—31no—
721#106C22×D312yes—
722C4⋊C8—32no—
723C4⋊C8—32no—
724C4⋊C8—32no—
725C4⋊C8—31no—
726C4⋊C8—32no—
727C4⋊C8C22×D311yescharacteristic
728C4⋊C8C22×D312yes—
729#103—32no—
730#103—32no—
731#103—31no—
732#103—32no—
733#103—32no—
734#103—31no—
735#103—32no—
736#103—31no—
737#103—32no—
738#103—31no—
739#103C22×D312yes—
740#103C22×D312yes—
741#103C22×D311yescharacteristic
742#103C22×D312yes—
743#103C22×D312yes—
744#103C22×D311yescharacteristic
745#102—32no—
746#102—31no—
747#102—32no—
748#102—32no—
749#102—32no—
750#102—31no—
751#102—32no—
752#102—32no—
753#97—31no—
754#97—31no—
755#97—32no—
756#97C22×D312yes—
757C4×C8—32no—
758C4×C8—31no—
759C4×C8—32no—
760C4×C8C22×D311yescharacteristic
761C22×D3—21no—
762C22×D3—22no—
763C22×D3C22×D411yescharacteristic
764C3×Q8—22no—
765C3×Q8—21no—
766C3×Q8—21no—
767C3×Q8—22no—
768C3×Q8—21no—
769C3×Q8—22no—
770C3×Q8—42no—
771C3×Q8C2×#4112yes—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—22no—
778C2×C3×C4C22×D411yescharacteristic
779C2×C3×C4C22×D412yes—
780C2×C3×C4C22×D412yes—
781C2×C3×C4C22×D411yescharacteristic
782C2×C3×C4C2511yescharacteristic
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3C22×D411yescharacteristic
788C2×Dic3C22×D411yescharacteristic
789C2×Dic3C22×D412yes—
790C2×Dic3C22×D412yes—
791C2×Dic3C22×D411yescharacteristic
792D12—24no—
793D12—22no—
794D12—21no—
795D12—22no—
796D12—44no—
797D12—42no—
798D12—81no—
799D12C2×#4112yes—
800C4×D3—22no—
801C4×D3—24no—
802C4×D3—41no—
803C4×D3—42no—
804C4×D3—42no—
805C4×D3—42no—
806C4×D3—44no—
807C4×D3—82no—
808C4×D3—82no—
809C4×D3—82no—
810C4×D3—82no—
811C4×D3—81no—
812C4×D3—82no—
813C4×D3C2×#4112yes—
814C4×D32−1+412yes—
815Dic6—22no—
816Dic6—21no—
817Dic6—21no—
818Dic6—42no—
819Dic6—42no—
820Dic6—42no—
821Dic6—82no—
822Dic6—82no—
823Dic6—82no—
824C3×C8—22no—
825C3×C8—21no—
826C3×C8—21no—
827C3⋊C8—22no—
828C3⋊C8—21no—
829C3⋊C8—21no—
830#41—34no—
831#41—62no—
832#41—64no—
833#41—64no—
834C2×Q8—21no—
835C2×Q8—31no—
836C2×Q8—32no—
837C2×Q8—31no—
838C2×Q8—61no—
839C2×Q8—62no—
840C2×Q8—62no—
841C2×Q8—62no—
842C2×Q8—62no—
843C2×Q8—61no—
844C2×Q8—62no—
845C2×Q8—242no—
846C2×Q8—242no—
847C2×Q8—242no—
848C2×Q8D3×D411yescharacteristic
849C2×Q8C23×D311yescharacteristic
850C2×Q8C23×D312yes—
851C2×Q8C23×D311yescharacteristic
852C2×D4—31no—
853C2×D4—32no—
854C2×D4—61no—
855C2×D4—62no—
856C2×D4—61no—
857C2×D4—61no—
858C22×C4—31no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—62no—
864C22×C4—62no—
865C22×C4—62no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—62no—
869C22×C4—61no—
870C22×C4—62no—
871C22×C4—62no—
872Q16—24no—
873Q16—22no—
874Q16—62no—
875SD16—62no—
876SD16—64no—
877SD16—62no—
878SD16—64no—
879D8—64no—
880M16—62no—
881M16—62no—
882C2×C8—31no—
883C2×C8—32no—
884C2×C8—31no—
885C2×C8—64no—
886C2×C8C23×D311yescharacteristic
887C2×C8C23×D311yescharacteristic
888C2×C8C23×D312yes—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—22no—
894C4⋊C4—21no—
895C4⋊C4—22no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—32no—
901C4⋊C4—32no—
902C4⋊C4—32no—
903C4⋊C4—32no—
904C4⋊C4—32no—
905C4⋊C4—31no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—31no—
909C4⋊C4—31no—
910C4⋊C4—61no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—62no—
915C4⋊C4—61no—
916C4⋊C4—61no—
917C4⋊C4—62no—
918C4⋊C4—61no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—61no—
924C4⋊C4—61no—
925C4⋊C4—62no—
926C4⋊C4D3×D411yescharacteristic
927C4⋊C4D3×D412yes—
928C4⋊C4C23×D312yes—
929C4⋊C4C23×D311yescharacteristic
930C4⋊C4C23×D311yescharacteristic
931C22⋊C4—32no—
932C22⋊C4—32no—
933C22⋊C4—62no—
934C22⋊C4—61no—
935C22⋊C4—62no—
936C22⋊C4—62no—
937C22⋊C4—62no—
938C22⋊C4—62no—
939C22⋊C4—62no—
940C22⋊C4—61no—
941C22⋊C4—61no—
942C22⋊C4—62no—
943C22⋊C4—62no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C42—21no—
947C42—21no—
948C42—22no—
949C42—22no—
950C42—31no—
951C42—31no—
952C42—32no—
953C42—31no—
954C42—61no—
955C42—61no—
956C42—61no—
957C42—61no—
958C42—62no—
959C42—62no—
960C42—61no—
961C42C23×D311yescharacteristic
962C42C23×D312yes—
963C22×C3C23×D411yescharacteristic
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—22no—
967C2×D3—41no—
968C2×D3—41no—
969C2×D3—42no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3#54812yes—
973C3×C4—22no—
974C3×C4—21no—
975C3×C4—22no—
976C3×C4—22no—
977C3×C4—41no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—42no—
981C3×C4—42no—
982C3×C4#57712yes—
983C3×C4C22×#4111yescharacteristic
984C3×C4C2×2−1+411yescharacteristic
985Dic3—21no—
986Dic3—22no—
987Dic3—22no—
988Dic3—21no—
989Dic3—41no—
990Dic3—41no—
991Dic3—42no—
992Dic3—41no—
993Dic3#54812yes—
994C23—31no—
995C23—61no—
996C23—62no—
997Q8—21no—
998Q8—22no—
999Q8—21no—
1000Q8—22no—
1001Q8—21no—
1002Q8—22no—
1003Q8—42no—
1004Q8—62no—
1005Q8—61no—
1006Q8—61no—
1007Q8—122no—
1008Q8—122no—
1009Q8—122no—
1010Q8—242no—
1011Q8—242no—
1012Q8—242no—
1013Q8D3×#4112yes—
1014D4—32no—
1015D4—64no—
1016D4—62no—
1017D4—61no—
1018D4—62no—
1019D4—124no—
1020D4—122no—
1021D4—241no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—31no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—31no—
1032C2×C4—31no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—64no—
1036C2×C4—62no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—61no—
1040C2×C4—62no—
1041C2×C4—121no—
1042C2×C4—124no—
1043C2×C4—122no—
1044C2×C4—122no—
1045C2×C4—122no—
1046C2×C4—242no—
1047C2×C4—242no—
1048C2×C4—242no—
1049C2×C4—242no—
1050C2×C4—242no—
1051C2×C4—241no—
1052C2×C4C2×D3×D412yes—
1053C2×C4C2×D3×D412yes—
1054C2×C4C2×D3×D411yescharacteristic
1055C2×C4C2×D3×D411yescharacteristic
1056C2×C4C24×D311yescharacteristic
1057C8—22no—
1058C8—21no—
1059C8—21no—
1060C8—62no—
1061C8—61no—
1062C8—61no—
1063C2×C3C2×#54811yescharacteristic
1064C2×C3C2×#57711yescharacteristic
1065C2×C3#358611yescharacteristic
1066D3—22no—
1067D3—42no—
1068D3—82no—
1069C22—32no—
1070C22—61no—
1071C22—61no—
1072C22—62no—
1073C22—121no—
1074C22—121no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22C22×D3×D411yescharacteristic
1079C4—22no—
1080C4—21no—
1081C4—22no—
1082C4—22no—
1083C4—32no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—42no—
1088C4—41no—
1089C4—61no—
1090C4—62no—
1091C4—61no—
1092C4—62no—
1093C4—121no—
1094C4—122no—
1095C4—121no—
1096C4—121no—
1097C4#577812yes—
1098C4C2×D3×#4111yescharacteristic
1099C4D3×2−1+411yescharacteristic
1100C3#6134611yescharacteristic, complemented, Sylow
1101C2—62no—
1102C2—122no—
1103C2—242no—
1104C2D3×#54811yescharacteristic
1105C2C2×#577811yescharacteristic
1106C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3374C2
socleC22×C3C23×D4
prime radical#80475C2
hypercenter#3374D3
hypocenterC3#61346
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3374

Complements

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

NH ≅ G/Ntype
1. #87033C2semidirect
2. #87018C2semidirect
3. C3×#3374C2semidirect
4. #83697C2semidirect
5. #83688C2semidirect
6. #81738C2semidirect
7. #81734C2semidirect
8. #81620C2semidirect
9. #81601C2semidirect
10. #81265C2semidirect
11. #81235C2semidirect
12. #81038C2semidirect
13. D3×#475C2semidirect
14. #80479C2semidirect
16. #80465C2semidirect
17. #80464C2semidirect
18. #79973C2semidirect
19. #79960C2semidirect
20. #79832C2semidirect
21. #79815C2semidirect
22. C4×#918C2semidirect
23. #79701C2semidirect
141. #3374D3semidirect
1100. C3#61346semidirect

Maximal subgroups

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

subgroupindex
#870332
#870182
C3×#33742
#836972
#836882
#817382
#817342
#816202
#816012
#812652
#812352
#810382
D3×#4752
#804792
#804752
#804652
#804642
#799732
#799602
#798322
#798152
C4×#9182
#797012
#613463