Finite Group Databasebeta

← #11675228

Subgroups — #11675228

Order 768.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87018C211yesmaximal, characteristic, complemented
2#86983C211yesmaximal, characteristic, complemented
3C3×#3364C211yesmaximal, characteristic, complemented
4#83698C211yesmaximal, characteristic, complemented
5#83668C211yesmaximal, characteristic, complemented
6#81639C212yesmaximal, complemented
7#81632C212yesmaximal, complemented
8#81620C211yesmaximal, characteristic, complemented
9D3×#487C211yesmaximal, characteristic, complemented
10#81233C212yesmaximal, complemented
11#81219C212yesmaximal, complemented
12#80993C211yesmaximal, characteristic, complemented
13#80966C211yesmaximal, characteristic, complemented
14#80603C212yesmaximal
15#80582C212yesmaximal, complemented
16#80477C211yesmaximal, characteristic, complemented
17#80465C211yesmaximal, characteristic, complemented
18#79925C211yesmaximal, characteristic, complemented
19#79917C211yesmaximal, characteristic, complemented
20#79719C212yesmaximal, complemented
21#79699C212yesmaximal, complemented
22C4×#916C211yesmaximal, characteristic
23#79623C211yesmaximal, characteristic, complemented
24#61330—31nomaximal, Sylow
25C3×#557C2211yescharacteristic
26C3×#556C2211yescharacteristic
27C2×#918C2212yes—
28C2×#916C2211yescharacteristic
29#5727—21no—
30#5727C2211yescharacteristic
31D3×C4⋊Q8—21no—
32D3×C4⋊Q8C2211yescharacteristic
33D3×C4⋊Q8C2211yescharacteristic
34#5721C2211yescharacteristic
35#5708—22no—
36#5701—22no—
37#5690—22no—
38#5690C2212yes—
39#5689—22no—
40#5689C2212yes—
41#5675C2212yes—
42#5671C2212yes—
43#5639—21no—
44#5622—21no—
45#5578—21no—
46#5578C2211yescharacteristic
47Q8×D12—21no—
48Q8×D12C2211yescharacteristic
49#5574C2212yes—
50C4×#239C2211yescharacteristic
51#5572C2212yes—
52#5570C2211yescharacteristic
53#5570C2211yescharacteristic
54#5567C2212yes—
55Q8×Dic6C2212yes—
56#5542C2211yescharacteristic
57C4×#237C2211yescharacteristic
58#5529—21no—
59#5517—21no—
60C3×#488C2212yes—
61C3×#487C2211yescharacteristic
62C3×#479C2212yes—
63C3×#474C2211yescharacteristic
64C3×#464C2212yes—
65C3×#462C2211yescharacteristic
66C3×C8×Q8C2211yescharacteristic
67C3×C4×Q16C2212yes—
68C3×C4×SD16C2211yescharacteristic
69#5184C2212yes—
70#5182C2212yes—
71#5182C2212yes—
72#5166C2212yes—
73Dic3×SD16C2211yescharacteristic
74#5094C2211yescharacteristic
75#5093C2211yescharacteristic
76#5083C2211yescharacteristic
77#5079C2211yescharacteristic
78#5069C2212yes—
79#5063C2212yes—
80#5057C2212yes—
81#5055C2212yes—
82#5031C2211yescharacteristic
83#5031C2212yes—
84#5030C2212yes—
85C4×#216C2211yescharacteristic
86#5026C2212yes—
87#5024C2211yescharacteristic
88#5021C2212yes—
89C4×#213C2211yescharacteristic
90#5007C2211yescharacteristic
91#4889C2212yes—
92#4881C2212yes—
93#4875C2212yes—
94#4875C2212yes—
95#4860C2211yescharacteristic
96#4857C2212yes—
97#4852C2211yescharacteristic
98#4851C2211yescharacteristic
99#4851C2212yes—
100#4841C2212yes—
101#4841C2211yescharacteristic
102#4839C2212yes—
103#4837C2211yescharacteristic
104#4831C2211yescharacteristic
105#4828C2212yes—
106#4818C2212yes—
107#4818C2212yes—
108#4804C2211yescharacteristic
109#4802C2212yes—
110D3×#103C2212yes—
111D3×#103C2212yes—
112#4799C2212yes—
113#4797C2212yes—
114#4792C2212yes—
115#4792C2212yes—
116#4792C2212yes—
117#4791C2212yes—
118#4790C2212yes—
119#4790C2211yescharacteristic
120#4788C2212yes—
121#4787C2212yes—
122#4772C2211yescharacteristic
123#4771C2212yes—
124#4768C2212yes—
125#4765C2212yes—
126#4761C2212yes—
127#4756C2211yescharacteristic
128C4×#204C2211yescharacteristic
129C4×#204C2212yes—
130#4689C2212yes—
131C4×D3×C8C2211yescharacteristic
132#4681C2211yescharacteristic
133#4681C2212yes—
134C8×Dic6C2211yescharacteristic
135C8×Dic6C2212yes—
136#3509—31no—
137#3503—31no—
138#3374—31no—
139#3374—31no—
140#3372—32no—
141#3369—32no—
142#3367—31no—
143#3367—31no—
144#3364—31no—
145#3364D311yescharacteristic, complemented
146#3363—32no—
147#3360—32no—
148#3359—31no—
149#3359—31no—
150#3137—32no—
151C2×#487—31no—
152#3082—32no—
153#3079—31no—
154#3046—32no—
155#3039—31no—
156#2960—31no—
157#2947—32no—
158C4×#135—31no—
159C2×#239C2311yescharacteristic
160C2×D3×Q8—21no—
161C2×D3×Q8—21no—
162C2×D3×Q8—21no—
163C2×D3×Q8C2312yes—
164C2×#237C2311yescharacteristic
165C2×C3×Q16C2312yes—
166C2×C3×SD16C2311yescharacteristic
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8C2311yescharacteristic
169C3×C4⋊Q8C2311yescharacteristic
170C3×#126—22no—
171C3×#125—22no—
172C3×#125C2312yes—
173C3×#124C2312yes—
174C3×C22⋊Q8—21no—
175C3×C4×Q8—21no—
176C3×C4×Q8C2312yes—
177C3×C4×Q8C2311yescharacteristic
178C3×C4×Q8C2312yes—
179C3×C4×Q8C2311yescharacteristic
180C3×C4×D4C2311yescharacteristic
181C3×#117—21no—
182#946—21no—
183#946D411yescharacteristic
184Q8×Dic3—21no—
185Q8×Dic3C2312yes—
186Q8×Dic3C2311yescharacteristic
187Q8×Dic3C2312yes—
188#944—21no—
189#944D411yescharacteristic
190#944C2312yes—
191#944C2312yes—
192C2×#216C2312yes—
193C2×#216C2311yescharacteristic
194C2×#215C2312yes—
195#936C2312yes—
196D4×Dic3C2311yescharacteristic
197C2×#213C2311yescharacteristic
198C4×#67—21no—
199#926—21no—
200#924—21no—
201C2×C4×Dic3—21no—
202#918—28no—
203#916—24no—
204C2×#204C2312yes—
205C2×#204C2311yescharacteristic
206C2×ΓL(1,𝔽25)C2312yes—
207C2×D3×C8C2311yescharacteristic
208C2×D3×C8C2311yescharacteristic
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#896D412yes—
219#893—21no—
220#893—22no—
221#893C2312yes—
222#893C2311yescharacteristic
223#892—22no—
224#892—21no—
225#892C2311yescharacteristic
226#892C2311yescharacteristic
227D3×C4⋊C4—21no—
228D3×C4⋊C4—21no—
229D3×C4⋊C4—21no—
230D3×C4⋊C4—22no—
231D3×C4⋊C4—22no—
232D3×C4⋊C4C2312yes—
233#890—22no—
234#890—21no—
235#890—21no—
236#890—22no—
237#890C2312yes—
238#889—22no—
239#889—22no—
240#889—22no—
241#889—22no—
242#889D412yes—
243#888—22no—
244#888—22no—
245#888—22no—
246#888—21no—
247#888—21no—
248#888—21no—
249#888D411yescharacteristic
250#888C2312yes—
251#888C2312yes—
252#887—21no—
253#887—22no—
254#887C2311yescharacteristic
255#887C2312yes—
256#883—22no—
257#883—22no—
258#67⋊C4—21no—
259#879—22no—
260#879—22no—
261#879—22no—
262#878—22no—
263#878—22no—
264#878—22no—
265#877—22no—
266#877—21no—
267C4×D12—21no—
268C4×D12—22no—
269C4×D12C2312yes—
270C4×D12C2311yescharacteristic
271#872—22no—
272#872—22no—
273#872C2312yes—
274C42×D3—21no—
275C42×D3C2311yescharacteristic
276#870—22no—
277#869—21no—
278#869—22no—
279#869C2312yes—
280#869C2311yescharacteristic
281#869C2312yes—
282#869C2311yescharacteristic
283C4×Dic6—22no—
284C4×Dic6—22no—
285C4×Dic6—21no—
286C4×Dic6—22no—
287C4×Dic6C2312yes—
288C4×Dic6C2311yescharacteristic
289C4×Dic6C2312yes—
290C4×Dic6C2311yescharacteristic
291C3×#107C2312yes—
292C3×#106C2311yescharacteristic
293C3×C4⋊C8C2311yescharacteristic
294C3×C4⋊C8C2312yes—
295C3×#103C2312yes—
296C3×#103C2311yescharacteristic
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#102C2311yescharacteristic
300C3×#102C2312yes—
301C3×C4×C8C2311yescharacteristic
302C3×C4×C8C2312yes—
303#835C2311yescharacteristic
304#835C2312yes—
305#835C2312yes—
306#835C2312yes—
307#832C2311yescharacteristic
308#832C2312yes—
309#821C2311yescharacteristic
310#817C2312yes—
311#817C2311yescharacteristic
312#816C2312yes—
313#816C2312yes—
314#816C2312yes—
315#816C2312yes—
316#816C2311yescharacteristic
317#815C2312yes—
318Dic3⋊C8C2312yes—
319Dic3⋊C8C2312yes—
320Dic3⋊C8C2312yes—
321C8×Dic3C2311yescharacteristic
322C8×Dic3C2311yescharacteristic
323C8×Dic3C2312yes—
324#810C2312yes—
325#810C2312yes—
326#810C2312yes—
327#810C2312yes—
328#810C2311yescharacteristic
329#809C2311yescharacteristic
330#808C2312yes—
331#807C2311yescharacteristic
332#807C2312yes—
333#807C2311yescharacteristic
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4⋊(C3⋊C8)C2312yes—
336#803C2312yes—
337C4×C3⋊C8C2311yescharacteristic
338C2×#137—32no—
339C2×#135—31no—
340Q82—32no—
341#557—31no—
342#557—31no—
343#557—32no—
344#557—31no—
345#557C2×D311yescharacteristic
346#556—32no—
347#556—31no—
348#556C2×D311yescharacteristic
349#554—32no—
350#554—62no—
351#552—61no—
352#552—61no—
353#552—62no—
354D4×Q8—31no—
355D4×Q8—31no—
356D4×Q8—61no—
357D4×Q8—61no—
358#544—32no—
359#544—62no—
360#541—62no—
361#536—32no—
362#533—31no—
363#533—61no—
364#533—61no—
365#533—61no—
366C2×C4⋊Q8—31no—
367C2×C4⋊Q8—31no—
368C2×C4⋊Q8—61no—
369#520—32no—
370#519—32no—
371C4×#41—31no—
372C4×#41—31no—
373#491—32no—
374#491—32no—
375#489—32no—
376#489—32no—
377#488—32no—
378#488C2×D312yes—
379#487—31no—
380#487—31no—
381#487—32no—
382#487—32no—
383#487—32no—
384#487—32no—
385#487—31no—
386#487C2×D311yescharacteristic
387#479—32no—
388#479—32no—
389#479—32no—
390#479C2×D312yes—
391#477—32no—
392#477—32no—
393#477—32no—
394#476—32no—
395#475—31no—
396#475—31no—
397#475—32no—
398#475—32no—
399#474—31no—
400#474C2×D311yescharacteristic
401#464—32no—
402#464C2×D312yes—
403#463—32no—
404#463—32no—
405#462—32no—
406#462—32no—
407#462—32no—
408#462—31no—
409#462C2×D311yescharacteristic
410#461—31no—
411#461—31no—
412#461—32no—
413#461—32no—
414#461—32no—
415#446—31no—
416#446—31no—
417#446—32no—
418C8×Q8—31no—
419C8×Q8—32no—
420C8×Q8C2×D311yescharacteristic
421#441—32no—
422#441—32no—
423#440—32no—
424#440—32no—
425C4×Q16—31no—
426C4×Q16—31no—
427C4×Q16—32no—
428C4×Q16C2×D312yes—
429C4×SD16—31no—
430C4×SD16—31no—
431C4×SD16—32no—
432C4×SD16—31no—
433C4×SD16—32no—
434C4×SD16C2×D311yescharacteristic
435C4×D8—31no—
436C4×D8—31no—
437#428—32no—
438#427—31no—
439#424—32no—
440#423—31no—
441#419—32no—
442#417—32no—
443#416—31no—
444#416—31no—
445C2×#103—32no—
446C2×#103—32no—
447#405—32no—
448C2×C4×C8—31no—
449C2×C3×Q8—21no—
450C2×C3×Q8C2×D411yescharacteristic
451C2×C3×Q8C2412yes—
452C2×C3×Q8C2411yescharacteristic
453C2×C3×D4C2411yescharacteristic
454C22×C3×C4—21no—
455C2×#67—21no—
456C22×Dic3—21no—
457C22×Dic3—21no—
458#239—22no—
459#239#4114yes—
460D3×Q8—24no—
461D3×Q8—24no—
462D3×Q8—82no—
463D3×Q8—82no—
464D3×Q8—82no—
465#237—22no—
466#237—22no—
467C2×D12—21no—
468C2×D12C2411yescharacteristic
469C2×C4×D3—21no—
470C2×C4×D3—22no—
471C2×C4×D3—21no—
472C2×C4×D3—21no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3C2×D411yescharacteristic
477C2×C4×D3C2×D411yescharacteristic
478C2×C4×D3C2411yescharacteristic
479C2×Dic6—21no—
480C2×Dic6—22no—
481C2×Dic6—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6C2×D412yes—
485C2×Dic6C2×D411yescharacteristic
486C2×Dic6C2412yes—
487C2×Dic6C2411yescharacteristic
488C3×Q16—24no—
489C3×SD16—22no—
490C2×C3×C8C2411yescharacteristic
491C2×C3×C8C2411yescharacteristic
492C2×C3×C8C2412yes—
493C3×C4⋊C4—21no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—21no—
497C3×C4⋊C4—21no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—21no—
501C3×C4⋊C4C2×D411yescharacteristic
502C3×C4⋊C4C2×D412yes—
503C3×C4⋊C4C2411yescharacteristic
504C3×C4⋊C4C2411yescharacteristic
505C3×C4⋊C4C2412yes—
506C3×C22⋊C4—22no—
507C3×C22⋊C4—21no—
508C3×C22⋊C4—22no—
509C3×C42—22no—
510C3×C42—21no—
511C3×C42—22no—
512C3×C42C2411yescharacteristic
513C3×C42C2412yes—
514#217—22no—
515#217—21no—
516#217—22no—
517#216—22no—
518#216—24no—
519#215—24no—
520#213—22no—
521(C2×D3)⋊C4—21no—
522(C2×D3)⋊C4—21no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—21no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—21no—
527(C2×D3)⋊C4C2×D412yes—
528(C2×D3)⋊C4C2×D412yes—
529C4⋊Dic3—22no—
530C4⋊Dic3—22no—
531C4⋊Dic3—22no—
532C4⋊Dic3—21no—
533C4⋊Dic3—21no—
534C4⋊Dic3—21no—
535C4⋊Dic3—22no—
536C4⋊Dic3—21no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3C2×D411yescharacteristic
540C4⋊Dic3C2×D412yes—
541C4⋊Dic3C2411yescharacteristic
542C4⋊Dic3C2411yescharacteristic
543C4⋊Dic3C2412yes—
544Dic3⋊C4—22no—
545Dic3⋊C4—21no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—21no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4C2×D412yes—
557Dic3⋊C4C2×D412yes—
558Dic3⋊C4C2×D412yes—
559Dic3⋊C4C2×D412yes—
560Dic3⋊C4C2×D412yes—
561C4×Dic3—22no—
562C4×Dic3—21no—
563C4×Dic3—21no—
564C4×Dic3—22no—
565C4×Dic3—21no—
566C4×Dic3—22no—
567C4×Dic3—21no—
568C4×Dic3—21no—
569C4×Dic3—22no—
570C4×Dic3C2×D411yescharacteristic
571C4×Dic3C2×D411yescharacteristic
572C4×Dic3C2411yescharacteristic
573C4×Dic3C2412yes—
574C2×C3⋊C8C2411yescharacteristic
575C2×C3⋊C8C2411yescharacteristic
576C2×C3⋊C8C2412yes—
577#204—22no—
578#204—24no—
579ΓL(1,𝔽25)—24no—
580D3×C8—22no—
581D3×C8—22no—
582C2×#41—31no—
583C2×#41—31no—
584C22×Q8—32no—
585C22×Q8—61no—
586C22×Q8—61no—
587C22×Q8—61no—
588#137—68no—
589#135—64no—
590C2×Q16—31no—
591C2×Q16—32no—
592C2×Q16C22×D312yes—
593C2×SD16—32no—
594C2×SD16—31no—
595C2×SD16—32no—
596C2×SD16C22×D311yescharacteristic
597C2×D8—31no—
598C2×M16—32no—
599C22×C8—31no—
600C22×C8—31no—
601C4⋊Q8—21no—
602C4⋊Q8—31no—
603C4⋊Q8—31no—
604C4⋊Q8—32no—
605C4⋊Q8—32no—
606C4⋊Q8—32no—
607C4⋊Q8—32no—
608C4⋊Q8—31no—
609C4⋊Q8—32no—
610C4⋊Q8—31no—
611C4⋊Q8—32no—
612C4⋊Q8—62no—
613C4⋊Q8—61no—
614C4⋊Q8—61no—
615C4⋊Q8—61no—
616C4⋊Q8—61no—
617C4⋊Q8—61no—
618C4⋊Q8—62no—
619C4⋊Q8—62no—
620C4⋊Q8—62no—
621C4⋊Q8C22×D311yescharacteristic
622C4⋊Q8C22×D311yescharacteristic
623#126—22no—
624#126—62no—
625#126—62no—
626#126—62no—
627#125—22no—
628#125—32no—
629#125—32no—
630#125—62no—
631#125—62no—
632#125—62no—
633#125—61no—
634#125—62no—
635#125—62no—
636#125—62no—
637#125—61no—
638#125—62no—
639#125C22×D312yes—
640#124—32no—
641#124C22×D312yes—
642#123—62no—
643#123—62no—
644C22⋊Q8—21no—
645C22⋊Q8—31no—
646C22⋊Q8—31no—
647C22⋊Q8—32no—
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—62no—
657C22⋊Q8—61no—
658C22⋊Q8—61no—
659C22⋊Q8—61no—
660C22⋊Q8—62no—
661C4×Q8—21no—
662C4×Q8—31no—
663C4×Q8—32no—
664C4×Q8—31no—
665C4×Q8—32no—
666C4×Q8—32no—
667C4×Q8—31no—
668C4×Q8—32no—
669C4×Q8—31no—
670C4×Q8—32no—
671C4×Q8—62no—
672C4×Q8—61no—
673C4×Q8—62no—
674C4×Q8—62no—
675C4×Q8—62no—
676C4×Q8—61no—
677C4×Q8—61no—
678C4×Q8C22×D311yescharacteristic
679C4×Q8C22×D312yes—
680C4×Q8C22×D312yes—
681C4×Q8C22×D311yescharacteristic
682C4×D4—31no—
683C4×D4—31no—
684C4×D4—32no—
685C4×D4—31no—
686C4×D4—32no—
687C4×D4—62no—
688C4×D4—61no—
689C4×D4—61no—
690C4×D4—62no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4C22×D311yescharacteristic
694#117—21no—
695#117—32no—
696#117—31no—
697#117—31no—
698#117—62no—
699#117—62no—
700#117—61no—
701#117—61no—
702#117—62no—
703#117—62no—
704#117—61no—
705C2×C4⋊C4—32no—
706C2×C4⋊C4—62no—
707C2×C4⋊C4—62no—
708C2×C4⋊C4—61no—
709C2×C4⋊C4—61no—
710C2×C4⋊C4—61no—
711C2×C42—31no—
712C2×C42—61no—
713C2×C42—61no—
714#107—31no—
715#107—31no—
716#107—32no—
717#107C22×D312yes—
718#106—31no—
719#106—32no—
720#106—32no—
721#106C22×D311yescharacteristic
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—32no—
735#103—31no—
736#103—32no—
737#103—32no—
738#103—32no—
739#103—32no—
740#103—31no—
741#103—32no—
742#103—32no—
743#103C22×D312yes—
744#103C22×D312yes—
745#103C22×D311yescharacteristic
746#103C22×D312yes—
747#102—31no—
748#102—32no—
749#102—31no—
750#102—31no—
751#102C22×D311yescharacteristic
752#102C22×D312yes—
753#97—32no—
754#97—32no—
755C4×C8—31no—
756C4×C8—31no—
757C4×C8—32no—
758C4×C8—31no—
759C4×C8C22×D311yescharacteristic
760C4×C8C22×D312yes—
761C23×C3—21no—
762C22×D3—21no—
763C22×D3C22×D411yescharacteristic
764C3×Q8—22no—
765C3×Q8—21no—
766C3×Q8—22no—
767C3×Q8—22no—
768C3×Q8—42no—
769C3×Q8C2×#4112yes—
770C3×D4—21no—
771C3×D4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4—21no—
776C2×C3×C4—22no—
777C2×C3×C4—42no—
778C2×C3×C4C22×D412yes—
779C2×C3×C4C22×D411yescharacteristic
780C2×C3×C4C22×D412yes—
781C2×C3×C4C22×D411yescharacteristic
782C2×C3×C4C2511yescharacteristic
783#67—42no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—21no—
788C2×Dic3—22no—
789C2×Dic3—42no—
790C2×Dic3—42no—
791C2×Dic3C22×D412yes—
792C2×Dic3C22×D412yes—
793C2×Dic3C22×D411yescharacteristic
794C2×Dic3C22×D411yescharacteristic
795C2×Dic3C22×D411yescharacteristic
796D12—24no—
797D12—21no—
798D12C2×#4112yes—
799C4×D3—22no—
800C4×D3—24no—
801C4×D3—22no—
802C4×D3—44no—
803C4×D3—42no—
804C4×D3—42no—
805C4×D3—82no—
806C4×D3—82no—
807C4×D3—82no—
808C4×D3C2×#4112yes—
809C4×D32−1+412yes—
810Dic6—22no—
811Dic6—24no—
812Dic6—21no—
813Dic6—22no—
814Dic6—21no—
815Dic6—22no—
816Dic6—42no—
817Dic6—44no—
818Dic6—82no—
819Dic6—82no—
820Dic6—82no—
821C3×C8—21no—
822C3×C8—22no—
823C3×C8—21no—
824C3⋊C8—21no—
825C3⋊C8—22no—
826C3⋊C8—21no—
827#41—34no—
828#41—62no—
829#41—62no—
830#41—62no—
831C2×Q8—21no—
832C2×Q8—32no—
833C2×Q8—31no—
834C2×Q8—32no—
835C2×Q8—31no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—62no—
839C2×Q8—64no—
840C2×Q8—64no—
841C2×Q8—61no—
842C2×Q8—62no—
843C2×Q8—242no—
844C2×Q8—242no—
845C2×Q8—242no—
846C2×Q8D3×D411yescharacteristic
847C2×Q8C23×D312yes—
848C2×Q8C23×D311yescharacteristic
849C2×D4—31no—
850C2×D4—61no—
851C2×D4—61no—
852C2×D4C23×D311yescharacteristic
853C22×C4—21no—
854C22×C4—31no—
855C22×C4—31no—
856C22×C4—31no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—62no—
860C22×C4—62no—
861C22×C4—62no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—62no—
866Q16—24no—
867Q16—62no—
868Q16—64no—
869SD16—22no—
870SD16—62no—
871SD16—64no—
872SD16—64no—
873D8—62no—
874M16—64no—
875C2×C8—31no—
876C2×C8—31no—
877C2×C8—32no—
878C2×C8—62no—
879C2×C8—62no—
880C2×C8C23×D311yescharacteristic
881C2×C8C23×D311yescharacteristic
882C2×C8C23×D312yes—
883C4⋊C4—21no—
884C4⋊C4—22no—
885C4⋊C4—21no—
886C4⋊C4—22no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—32no—
892C4⋊C4—32no—
893C4⋊C4—32no—
894C4⋊C4—31no—
895C4⋊C4—32no—
896C4⋊C4—32no—
897C4⋊C4—32no—
898C4⋊C4—32no—
899C4⋊C4—31no—
900C4⋊C4—31no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4—61no—
908C4⋊C4—61no—
909C4⋊C4—62no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—62no—
915C4⋊C4—61no—
916C4⋊C4—61no—
917C4⋊C4—61no—
918C4⋊C4—61no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4D3×D411yescharacteristic
924C4⋊C4D3×D412yes—
925C4⋊C4C23×D311yescharacteristic
926C4⋊C4C23×D312yes—
927C4⋊C4C23×D311yescharacteristic
928C22⋊C4—22no—
929C22⋊C4—21no—
930C22⋊C4—22no—
931C22⋊C4—32no—
932C22⋊C4—32no—
933C22⋊C4—61no—
934C22⋊C4—62no—
935C22⋊C4—61no—
936C22⋊C4—61no—
937C22⋊C4—61no—
938C22⋊C4—62no—
939C22⋊C4—62no—
940C22⋊C4—61no—
941C22⋊C4—62no—
942C42—21no—
943C42—22no—
944C42—22no—
945C42—31no—
946C42—31no—
947C42—31no—
948C42—32no—
949C42—61no—
950C42—61no—
951C42—61no—
952C42—61no—
953C42—62no—
954C42—62no—
955C42—62no—
956C42—61no—
957C42—62no—
958C42C23×D311yescharacteristic
959C42C23×D312yes—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3C23×D411yescharacteristic
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—22no—
967C2×D3—41no—
968C2×D3—41no—
969C2×D3#54812yes—
970C3×C4—22no—
971C3×C4—22no—
972C3×C4—22no—
973C3×C4—21no—
974C3×C4—42no—
975C3×C4—42no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4#57712yes—
979C3×C4C22×#4111yescharacteristic
980C3×C4C2×2−1+411yescharacteristic
981Dic3—22no—
982Dic3—21no—
983Dic3—22no—
984Dic3—42no—
985Dic3—41no—
986Dic3—42no—
987Dic3—41no—
988Dic3—41no—
989Dic3#54812yes—
990Dic3#57812yes—
991C23—21no—
992C23—31no—
993C23—61no—
994Q8—21no—
995Q8—22no—
996Q8—22no—
997Q8—22no—
998Q8—42no—
999Q8—64no—
1000Q8—62no—
1001Q8—62no—
1002Q8—61no—
1003Q8—62no—
1004Q8—61no—
1005Q8—124no—
1006Q8—122no—
1007Q8—242no—
1008Q8—242no—
1009Q8—242no—
1010Q8D3×#4112yes—
1011D4—21no—
1012D4—21no—
1013D4—32no—
1014D4—64no—
1015D4—61no—
1016D4—122no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—31no—
1023C2×C4—31no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—31no—
1027C2×C4—32no—
1028C2×C4—32no—
1029C2×C4—42no—
1030C2×C4—62no—
1031C2×C4—64no—
1032C2×C4—62no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—62no—
1036C2×C4—61no—
1037C2×C4—62no—
1038C2×C4—122no—
1039C2×C4—122no—
1040C2×C4—122no—
1041C2×C4—124no—
1042C2×C4—122no—
1043C2×C4—242no—
1044C2×C4—242no—
1045C2×C4—242no—
1046C2×C4C2×D3×D412yes—
1047C2×C4C2×D3×D411yescharacteristic
1048C2×C4C2×D3×D412yes—
1049C2×C4C2×D3×D411yescharacteristic
1050C2×C4C24×D311yescharacteristic
1051C8—21no—
1052C8—22no—
1053C8—21no—
1054C8—61no—
1055C8—62no—
1056C8—61no—
1057C2×C3—81no—
1058C2×C3C2×#54811yescharacteristic
1059C2×C3C2×#57711yescharacteristic
1060C2×C3C2×#57811yescharacteristic
1061D3—22no—
1062D3—42no—
1063C22—32no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—61no—
1068C22—61no—
1069C22—62no—
1070C22—121no—
1071C22—121no—
1072C22C22×D3×D411yescharacteristic
1073C4—22no—
1074C4—21no—
1075C4—22no—
1076C4—22no—
1077C4—32no—
1078C4—32no—
1079C4—41no—
1080C4—42no—
1081C4—41no—
1082C4—42no—
1083C4—61no—
1084C4—62no—
1085C4—62no—
1086C4—121no—
1087C4—122no—
1088C4—121no—
1089C4—121no—
1090C4—122no—
1091C4#577012yes—
1092C4C2×D3×#4111yescharacteristic
1093C4D3×2−1+411yescharacteristic
1094C3#6133011yescharacteristic, complemented, Sylow
1095C2—62no—
1096C2—81no—
1097C2—122no—
1098C2D3×#54811yescharacteristic
1099C2C2×#577011yescharacteristic
1100C2D3×#57811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3364C2
socleC22×C3C23×D4
prime radicalC2×#916C22
hypercenter#3364D3
hypocenterC3#61330
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3364

Complements

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

NH ≅ G/Ntype
1. #87018C2semidirect
2. #86983C2semidirect
3. C3×#3364C2semidirect
4. #83698C2semidirect
5. #83668C2semidirect
6. #81639C2semidirect
7. #81632C2semidirect
8. #81620C2semidirect
9. D3×#487C2semidirect
10. #81233C2semidirect
11. #81219C2semidirect
12. #80993C2semidirect
13. #80966C2semidirect
15. #80582C2semidirect
16. #80477C2semidirect
17. #80465C2semidirect
18. #79925C2semidirect
19. #79917C2semidirect
20. #79719C2semidirect
21. #79699C2semidirect
23. #79623C2semidirect
145. #3364D3semidirect
1094. C3#61330semidirect

Maximal subgroups

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

subgroupindex
#870182
#869832
C3×#33642
#836982
#836682
#816392
#816322
#816202
D3×#4872
#812332
#812192
#809932
#809662
#806032
#805822
#804772
#804652
#799252
#799172
#797192
#796992
C4×#9162
#796232
#613303