Finite Group Databasebeta

← #11675084

Subgroups — #11675084

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#557C211yesmaximal, characteristic, complemented
2#86923C211yesmaximal, characteristic
3C3×#3372C211yesmaximal, characteristic, complemented
4#83699C211yesmaximal, characteristic, complemented
5#83644C211yesmaximal, characteristic, complemented
6#81739C212yesmaximal, complemented
7#81733C212yesmaximal, complemented
8#81624C211yesmaximal, characteristic, complemented
9#81600C211yesmaximal, characteristic, complemented
10#81230C212yesmaximal, complemented
11#81220C212yesmaximal, complemented
12#81138C211yesmaximal, characteristic, complemented
13#81108C211yesmaximal, characteristic, complemented
14#80429C212yesmaximal
15#80429C211yesmaximal, characteristic
16#80418C212yesmaximal, complemented
17#80414C211yesmaximal, characteristic, complemented
18#79983C211yesmaximal, characteristic, complemented
19#79962C211yesmaximal, characteristic, complemented
20#79774C212yesmaximal
21#79755C212yesmaximal, complemented
22C4×#915C211yesmaximal, characteristic
23#79619C211yesmaximal, characteristic, complemented
24#61322—31nomaximal, Sylow
25C3×#557C2211yescharacteristic
26C3×#554C2211yescharacteristic
27C2×#915C2211yescharacteristic
28C2×#915C2212yes—
29#5728C2211yescharacteristic
30D3×C4⋊Q8C2212yes—
31D3×C4⋊Q8C2211yescharacteristic
32#5722C2211yescharacteristic
33#5721C2211yescharacteristic
34#5721C2212yes—
35#5688C2212yes—
36D3×#125—22no—
37D3×#125—21no—
38#5685—21no—
39#5685—22no—
40#5685C2212yes—
41#5636—22no—
42#5632—21no—
43#5622—21no—
44#5622—22no—
45C4×D3×Q8—21no—
46C4×D3×Q8C2211yescharacteristic
47C4×D3×Q8C2212yes—
48C4×D3×Q8C2211yescharacteristic
49#5570C2211yescharacteristic
50#5569—21no—
51#5567C2211yescharacteristic
52#5567C2212yes—
53#5567C2211yescharacteristic
54#5539C2212yes—
55D4×Dic6C2211yescharacteristic
56C4×#237C2211yescharacteristic
57C4×#237C2212yes—
58#5511—21no—
59C2×#887—21no—
60C3×#491C2212yes—
61C3×#487C2211yescharacteristic
62C3×#479C2212yes—
63C3×#477C2211yescharacteristic
64C3×#461C2211yescharacteristic
65C3×#461C2212yes—
66C3×#446C2211yescharacteristic
67C3×#440C2212yes—
68C3×C4×SD16C2211yescharacteristic
69#5164C2211yescharacteristic
70#5162C2212yes—
71#5162C2212yes—
72#5162C2212yes—
73Dic3×SD16C2212yes—
74#5093C2211yescharacteristic
75#5091C2211yescharacteristic
76#5090C2212yes—
77#5090C2211yescharacteristic
78#5082C2212yes—
79#5079C2211yescharacteristic
80#5069C2212yes—
81#5063C2212yes—
82#5030C2212yes—
83C4×#216C2211yescharacteristic
84#5024C2211yescharacteristic
85#5022C2212yes—
86#5020C2211yescharacteristic
87#5019C2211yescharacteristic
88#5019C2212yes—
89#5018C2212yes—
90C4×#214C2211yescharacteristic
91#4881C2212yes—
92#4877C2212yes—
93#4875C2212yes—
94#4873C2212yes—
95#4861C2211yescharacteristic
96#4854C2212yes—
97#4853C2211yescharacteristic
98#4851C2211yescharacteristic
99#4849C2212yes—
100#4849C2211yescharacteristic
101#4837C2212yes—
102#4837C2211yescharacteristic
103#4830C2211yescharacteristic
104#4829C2212yes—
105#4828C2212yes—
106#4802C2211yescharacteristic
107#4802C2212yes—
108#4802C2212yes—
109#4802C2212yes—
110#4802C2212yes—
111#4799C2212yes—
112#4797C2212yes—
113#4797C2212yes—
114#4795C2212yes—
115#4795C2212yes—
116#4795C2212yes—
117#4793C2212yes—
118#4792C2212yes—
119#4792C2212yes—
120#4792C2212yes—
121#4792C2212yes—
122#4791C2212yes—
123#4790C2212yes—
124#4789C2211yescharacteristic
125#4771C2211yescharacteristic
126#4758C2212yes—
127#4757C2211yescharacteristic
128#4716C2212yes—
129#4707C2212yes—
130#4703C2212yes—
131#4701C2212yes—
132C4×Dic12C2211yescharacteristic
133C4×ΓL(1,𝔽25)C2211yescharacteristic
134#4681C2211yescharacteristic
135C8×Dic6C2211yescharacteristic
136Q8×#41—31no—
137C2×#557—31no—
138#3374—32no—
139#3374—32no—
140#3374—31no—
141#3374—31no—
142#3372—32no—
143#3372—32no—
144#3372—31no—
145#3372D311yescharacteristic, complemented
146#3363—31no—
147#3363—31no—
148#3359—31no—
149#3359—31no—
150#3139—32no—
151#3139—31no—
152#3078—32no—
153#3078—31no—
154#3039—32no—
155#3039—31no—
156Q8×M16—31no—
157C4×#137—32no—
158C4×#137—31no—
159C2×D3×Q8D411yescharacteristic
160C2×D3×Q8C2311yescharacteristic
161C2×D3×Q8C2312yes—
162C2×#237C2311yescharacteristic
163C22×Dic6—21no—
164C2×C3×SD16C2312yes—
165C2×C3×SD16C2311yescharacteristic
166C3×C4⋊Q8C2311yescharacteristic
167C3×C4⋊Q8C2312yes—
168C3×C4⋊Q8C2311yescharacteristic
169C3×#125—21no—
170C3×#125—22no—
171C3×#125C2312yes—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—22no—
174C3×C4×Q8—21no—
175C3×C4×Q8C2311yescharacteristic
176C3×C4×Q8C2312yes—
177C3×C4×Q8C2311yescharacteristic
178C3×C4×D4C2311yescharacteristic
179C3×C4×D4C2312yes—
180C2×C3×C4⋊C4—21no—
181#946—21no—
182Q8×Dic3—21no—
183Q8×Dic3—21no—
184Q8×Dic3D411yescharacteristic
185Q8×Dic3C2312yes—
186Q8×Dic3C2311yescharacteristic
187#944—21no—
188#944—22no—
189#944C2312yes—
190#944C2312yes—
191#944C2312yes—
192C2×#216C2311yescharacteristic
193C2×#216C2312yes—
194D4×Dic3C2312yes—
195D4×Dic3C2311yescharacteristic
196C2×#214C2311yescharacteristic
197C2×#214C2312yes—
198C4×#67—21no—
199C4×#67—22no—
200#924—21no—
201#924—22no—
202C2×Dic3⋊C4—22no—
203C2×C4×Dic3—21no—
204C2×C4×Dic3—22no—
205#915—24no—
206#915—28no—
207C2×Dic12C2312yes—
208C2×Dic12C2311yescharacteristic
209C2×ΓL(1,𝔽25)C2312yes—
210C2×ΓL(1,𝔽25)C2311yescharacteristic
211C2×ΓL(1,𝔽25)C2311yescharacteristic
212#897—21no—
213#896—22no—
214#896—22no—
215#892C2312yes—
216#892C2311yescharacteristic
217D3×C4⋊C4—21no—
218D3×C4⋊C4—22no—
219D3×C4⋊C4—21no—
220D3×C4⋊C4—22no—
221D3×C4⋊C4—22no—
222D3×C4⋊C4—21no—
223D3×C4⋊C4D412yes—
224D3×C4⋊C4D411yescharacteristic
225D3×C4⋊C4C2311yescharacteristic
226#890—21no—
227#890—22no—
228#890—22no—
229#890—21no—
230#890C2312yes—
231#889—22no—
232#889—22no—
233#889—22no—
234#889—22no—
235#889—22no—
236#889—22no—
237#889—22no—
238#889—22no—
239#889—22no—
240#888—22no—
241#888—21no—
242#888—21no—
243#888—22no—
244#888—22no—
245#888—21no—
246#888C2312yes—
247#888C2312yes—
248#887—21no—
249#887—22no—
250#887—21no—
251#887—21no—
252#887—22no—
253#887—21no—
254#887—22no—
255#887—22no—
256#887—22no—
257#887—21no—
258#887D411yescharacteristic
259#887D412yes—
260#887C2312yes—
261#887C2312yes—
262#887C2311yescharacteristic
263#887C2311yescharacteristic
264#67⋊C4—22no—
265#67⋊C4—21no—
266#878—22no—
267#878—22no—
268#878—22no—
269#877—21no—
270#877—22no—
271C42×D3—22no—
272C42×D3—21no—
273C42×D3C2312yes—
274C42×D3C2311yescharacteristic
275#870—22no—
276#870—21no—
277#870C2312yes—
278#869C2311yescharacteristic
279#869C2312yes—
280#869C2311yescharacteristic
281C4×Dic6—22no—
282C4×Dic6—21no—
283C4×Dic6—22no—
284C4×Dic6—21no—
285C4×Dic6C2312yes—
286C4×Dic6C2311yescharacteristic
287C4×Dic6C2312yes—
288C4×Dic6C2311yescharacteristic
289C4×Dic6C2312yes—
290C4×Dic6C2311yescharacteristic
291C3×#107C2312yes—
292C3×#106C2311yescharacteristic
293C3×C4⋊C8C2312yes—
294C3×C4⋊C8C2311yescharacteristic
295C3×#103C2311yescharacteristic
296C3×#103C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#103C2312yes—
300C3×#102C2311yescharacteristic
301C3×#97C2312yes—
302C3×C4×C8C2311yescharacteristic
303#835C2312yes—
304#835C2312yes—
305#835C2312yes—
306#835C2312yes—
307#835C2311yescharacteristic
308#832C2311yescharacteristic
309#818C2311yescharacteristic
310#817C2312yes—
311#816C2312yes—
312#816C2312yes—
313#816C2312yes—
314#816C2312yes—
315#816C2311yescharacteristic
316#816C2311yescharacteristic
317#815C2311yescharacteristic
318#815C2311yescharacteristic
319Dic3⋊C8C2312yes—
320Dic3⋊C8C2312yes—
321Dic3⋊C8C2312yes—
322C8×Dic3C2312yes—
323C8×Dic3C2312yes—
324#810C2311yescharacteristic
325#810C2312yes—
326#810C2312yes—
327#810C2312yes—
328#810C2311yescharacteristic
329#810C2312yes—
330#808C2312yes—
331#808C2311yescharacteristic
332#807C2311yescharacteristic
333#807C2312yes—
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4⋊(C3⋊C8)C2312yes—
336#803C2312yes—
337C4×C3⋊C8C2311yescharacteristic
338C2×#137—32no—
339C2×#137—31no—
340Q82—31no—
341#557—32no—
342#557—31no—
343#557—32no—
344#557—31no—
345#557—32no—
346#557—31no—
347#557—31no—
348#557—61no—
349#557—61no—
350#557—62no—
351#557C2×D311yescharacteristic
352#554—32no—
353#554—61no—
354#554—62no—
355#554C2×D311yescharacteristic
356D4×Q8—31no—
357D4×Q8—61no—
358#533—31no—
359#533—32no—
360#533—61no—
361#533—62no—
362C2×C4⋊Q8—32no—
363C2×C4⋊Q8—31no—
364C2×#125—62no—
365C2×#125—61no—
366C4×#41—32no—
367C4×#41—31no—
368C2×C4×Q8—31no—
369C2×C4×Q8—32no—
370C2×C4×Q8—31no—
371C2×C4×Q8—61no—
372C2×C4×Q8—61no—
373#491—32no—
374#491—32no—
375#491—32no—
376#491—32no—
377#491—32no—
378#491C2×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#479—32no—
391#479—32no—
392#479C2×D312yes—
393#477—31no—
394#477—32no—
395#477—32no—
396#477C2×D311yescharacteristic
397#475—31no—
398#475—32no—
399#475—31no—
400#475—32no—
401#462—31no—
402#462—32no—
403#462—31no—
404#462—32no—
405#462—32no—
406#462—32no—
407#462—32no—
408#461—32no—
409#461—32no—
410#461—32no—
411#461—31no—
412#461—32no—
413#461C2×D311yescharacteristic
414#461C2×D312yes—
415#446—31no—
416#446—32no—
417#446—32no—
418#446C2×D311yescharacteristic
419C8×Q8—31no—
420C8×Q8—31no—
421#441—32no—
422#441—31no—
423#441—31no—
424#441—32no—
425#440—31no—
426#440—32no—
427#440—31no—
428#440C2×D312yes—
429C4×Q16—31no—
430C4×Q16—32no—
431C4×Q16—32no—
432C4×Q16—31no—
433C4×SD16—32no—
434C4×SD16—31no—
435C4×SD16—32no—
436C4×SD16C2×D311yescharacteristic
437#428—32no—
438#428—31no—
439#423—32no—
440#423—31no—
441#419—32no—
442#419—32no—
443#419—32no—
444#419—32no—
445#419—31no—
446#417—31no—
447C4×M16—32no—
448C4×M16—31no—
449C2×C3×Q8—21no—
450C2×C3×Q8C2×D411yescharacteristic
451C2×C3×Q8C2412yes—
452C2×C3×Q8C2411yescharacteristic
453C2×C3×D4C2411yescharacteristic
454C22×C3×C4—21no—
455C22×C3×C4—22no—
456C2×#67—21no—
457C22×Dic3—21no—
458C22×Dic3—22no—
459C22×Dic3—21no—
460D3×Q8—24no—
461D3×Q8—22no—
462D3×Q8—24no—
463D3×Q8—22no—
464D3×Q8—24no—
465#237—22no—
466#237#4114yes—
467C2×C4×D3—21no—
468C2×C4×D3—22no—
469C2×C4×D3—21no—
470C2×C4×D3C2×D412yes—
471C2×C4×D3C2×D411yescharacteristic
472C2×C4×D3C2×D411yescharacteristic
473C2×C4×D3C2×D412yes—
474C2×C4×D3C2411yescharacteristic
475C2×Dic6—21no—
476C2×Dic6—22no—
477C2×Dic6—21no—
478C2×Dic6—22no—
479C2×Dic6—22no—
480C2×Dic6—44no—
481C2×Dic6C2×D412yes—
482C2×Dic6C2×D411yescharacteristic
483C2×Dic6C2412yes—
484C2×Dic6C2411yescharacteristic
485C2×Dic6C2411yescharacteristic
486C3×SD16—24no—
487C3×SD16—22no—
488C2×C3×C8C2411yescharacteristic
489C2×C3×C8C2412yes—
490C2×C3×C8C2411yescharacteristic
491C3×C4⋊C4—21no—
492C3×C4⋊C4—22no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4—21no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—21no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—21no—
500C3×C4⋊C4C2×D411yescharacteristic
501C3×C4⋊C4C2×D412yes—
502C3×C4⋊C4C2411yescharacteristic
503C3×C4⋊C4C2412yes—
504C3×C4⋊C4C2411yescharacteristic
505C3×C22⋊C4—22no—
506C3×C22⋊C4—21no—
507C3×C42—22no—
508C3×C42—21no—
509C3×C42C2411yescharacteristic
510C3×C42C2412yes—
511#217—21no—
512#217—22no—
513#216—22no—
514#216—24no—
515#214—22no—
516#214—24no—
517(C2×D3)⋊C4—21no—
518(C2×D3)⋊C4—22no—
519C4⋊Dic3—22no—
520C4⋊Dic3—21no—
521C4⋊Dic3—21no—
522C4⋊Dic3—22no—
523C4⋊Dic3—21no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3C2×D412yes—
528C4⋊Dic3C2×D411yescharacteristic
529C4⋊Dic3C2411yescharacteristic
530C4⋊Dic3C2411yescharacteristic
531C4⋊Dic3C2412yes—
532Dic3⋊C4—22no—
533Dic3⋊C4—21no—
534Dic3⋊C4—22no—
535Dic3⋊C4—21no—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—21no—
539Dic3⋊C4—21no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—21no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554Dic3⋊C4C2×D412yes—
555C4×Dic3—22no—
556C4×Dic3—21no—
557C4×Dic3—21no—
558C4×Dic3—22no—
559C4×Dic3—21no—
560C4×Dic3—22no—
561C4×Dic3—21no—
562C4×Dic3—22no—
563C4×Dic3—21no—
564C4×Dic3—22no—
565C4×Dic3—22no—
566C4×Dic3—21no—
567C4×Dic3C2×D412yes—
568C4×Dic3C2×D411yescharacteristic
569C4×Dic3C2×D411yescharacteristic
570C4×Dic3C2×D412yes—
571C4×Dic3C2412yes—
572C4×Dic3C2411yescharacteristic
573C2×C3⋊C8C2411yescharacteristic
574C2×C3⋊C8C2411yescharacteristic
575C2×C3⋊C8C2412yes—
576Dic12—24no—
577Dic12—22no—
578ΓL(1,𝔽25)—24no—
579ΓL(1,𝔽25)—22no—
580ΓL(1,𝔽25)—22no—
581C2×#41—31no—
582C22×Q8—31no—
583C22×Q8—32no—
584C22×Q8—31no—
585C22×Q8—61no—
586#137—68no—
587#137—64no—
588C2×Q16—31no—
589C2×Q16—32no—
590C2×Q16—32no—
591C2×Q16—31no—
592C2×SD16—31no—
593C2×SD16—32no—
594C2×SD16C22×D312yes—
595C2×SD16C22×D311yescharacteristic
596C2×M16—32no—
597C2×M16—31no—
598C2×M16—31no—
599C4⋊Q8—32no—
600C4⋊Q8—32no—
601C4⋊Q8—32no—
602C4⋊Q8—32no—
603C4⋊Q8—32no—
604C4⋊Q8—31no—
605C4⋊Q8—31no—
606C4⋊Q8—32no—
607C4⋊Q8—61no—
608C4⋊Q8—62no—
609C4⋊Q8—62no—
610C4⋊Q8—61no—
611C4⋊Q8—61no—
612C4⋊Q8—62no—
613C4⋊Q8—62no—
614C4⋊Q8—61no—
615C4⋊Q8C22×D311yescharacteristic
616C4⋊Q8C22×D312yes—
617C4⋊Q8C22×D311yescharacteristic
618#125—21no—
619#125—22no—
620#125—32no—
621#125—32no—
622#125—62no—
623#125—61no—
624#125—62no—
625#125—62no—
626#125—62no—
627#125—62no—
628#125—62no—
629#125—62no—
630#125—62no—
631#125—61no—
632#125—62no—
633#125—62no—
634#125—61no—
635#125—62no—
636#125—62no—
637#125C22×D312yes—
638C22⋊Q8—21no—
639C22⋊Q8—22no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—61no—
645C22⋊Q8—62no—
646C22⋊Q8—61no—
647C22⋊Q8—62no—
648C22⋊Q8—61no—
649C4×Q8—21no—
650C4×Q8—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—31no—
654C4×Q8—32no—
655C4×Q8—32no—
656C4×Q8—31no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—31no—
660C4×Q8—32no—
661C4×Q8—31no—
662C4×Q8—32no—
663C4×Q8—32no—
664C4×Q8—31no—
665C4×Q8—61no—
666C4×Q8—62no—
667C4×Q8—61no—
668C4×Q8—62no—
669C4×Q8—62no—
670C4×Q8—61no—
671C4×Q8—62no—
672C4×Q8—61no—
673C4×Q8—62no—
674C4×Q8—61no—
675C4×Q8—62no—
676C4×Q8—61no—
677C4×Q8—61no—
678C4×Q8—62no—
679C4×Q8—61no—
680C4×Q8—61no—
681C4×Q8C22×D311yescharacteristic
682C4×Q8C22×D312yes—
683C4×Q8C22×D311yescharacteristic
684C4×D4—32no—
685C4×D4—31no—
686C4×D4—62no—
687C4×D4—61no—
688C4×D4—61no—
689C4×D4—62no—
690C4×D4C22×D311yescharacteristic
691C4×D4C22×D312yes—
692#117—32no—
693#117—31no—
694#117—61no—
695#117—62no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—32no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—62no—
701C2×C4⋊C4—61no—
702C2×C4⋊C4—62no—
703C2×C4⋊C4—61no—
704C2×C4⋊C4—62no—
705C2×C4⋊C4—61no—
706C2×C4⋊C4—62no—
707C2×C42—32no—
708C2×C42—31no—
709C2×C42—62no—
710C2×C42—61no—
711C2×C42—61no—
712C2×C42—62no—
713#107—31no—
714#107—32no—
715#107—31no—
716#107C22×D312yes—
717#106—32no—
718#106—31no—
719#106—32no—
720#106C22×D311yescharacteristic
721C4⋊C8—32no—
722C4⋊C8—32no—
723C4⋊C8—32no—
724C4⋊C8—31no—
725C4⋊C8—32no—
726C4⋊C8C22×D311yescharacteristic
727C4⋊C8C22×D312yes—
728#103—32no—
729#103—31no—
730#103—32no—
731#103—32no—
732#103—32no—
733#103—31no—
734#103—32no—
735#103—31no—
736#103—32no—
737#103—32no—
738#103—32no—
739#103—31no—
740#103—31no—
741#103—32no—
742#103—32no—
743#103—32no—
744#103—32no—
745#103C22×D311yescharacteristic
746#103C22×D312yes—
747#103C22×D312yes—
748#103C22×D312yes—
749#103C22×D312yes—
750#102—31no—
751#102C22×D311yescharacteristic
752#97—31no—
753#97—31no—
754#97—32no—
755#97C22×D312yes—
756C4×C8—32no—
757C4×C8—32no—
758C4×C8—31no—
759C4×C8C22×D311yescharacteristic
760C23×C3—21no—
761C22×D3C22×D411yescharacteristic
762C3×Q8—22no—
763C3×Q8—21no—
764C3×Q8—22no—
765C3×Q8—22no—
766C3×Q8—21no—
767C3×Q8—81no—
768C3×D4—21no—
769C3×D4C2×#4112yes—
770C2×C3×C4—21no—
771C2×C3×C4—22no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4—42no—
776C2×C3×C4—82no—
777C2×C3×C4C22×D412yes—
778C2×C3×C4C22×D412yes—
779C2×C3×C4C22×D411yescharacteristic
780C2×C3×C4C22×D411yescharacteristic
781C2×C3×C4C2511yescharacteristic
782#67—24no—
783C2×Dic3—21no—
784C2×Dic3—24no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—22no—
788C2×Dic3—21no—
789C2×Dic3—22no—
790C2×Dic3—44no—
791C2×Dic3—81no—
792C2×Dic3C22×D411yescharacteristic
793C2×Dic3C22×D411yescharacteristic
794C2×Dic3C22×D412yes—
795C2×Dic3C22×D411yescharacteristic
796C2×Dic3C22×D412yes—
797C4×D3—22no—
798C4×D3—24no—
799C4×D3—42no—
800C4×D3—41no—
801C4×D3—42no—
802C4×D3—44no—
803C4×D3—42no—
804C4×D3C2×#4112yes—
805C4×D32−1+412yes—
806Dic6—21no—
807Dic6—24no—
808Dic6—22no—
809Dic6—21no—
810Dic6—22no—
811Dic6—21no—
812Dic6—42no—
813Dic6—44no—
814Dic6—42no—
815Dic6—44no—
816Dic6—82no—
817Dic6#13714yescomplemented
818Dic6C2×#4112yes—
819C3×C8—22no—
820C3×C8—21no—
821C3×C8—21no—
822C3⋊C8—21no—
823C3⋊C8—22no—
824C3⋊C8—21no—
825#41—34no—
826#41—62no—
827C2×Q8—21no—
828C2×Q8—31no—
829C2×Q8—32no—
830C2×Q8—31no—
831C2×Q8—32no—
832C2×Q8—31no—
833C2×Q8—62no—
834C2×Q8—61no—
835C2×Q8—62no—
836C2×Q8—62no—
837C2×Q8—64no—
838C2×Q8—62no—
839C2×Q8—64no—
840C2×Q8—62no—
841C2×Q8—64no—
842C2×Q8—61no—
843C2×Q8—124no—
844C2×Q8D3×D411yescharacteristic
845C2×Q8C23×D312yes—
846C2×Q8C23×D311yescharacteristic
847C2×D4—61no—
848C2×D4C23×D311yescharacteristic
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—31no—
852C22×C4—32no—
853C22×C4—31no—
854C22×C4—31no—
855C22×C4—32no—
856C22×C4—61no—
857C22×C4—62no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—62no—
861C22×C4—61no—
862Q16—64no—
863Q16—62no—
864Q16—62no—
865Q16—64no—
866SD16—24no—
867SD16—22no—
868SD16—62no—
869SD16—64no—
870M16—64no—
871M16—62no—
872M16—62no—
873C2×C8—31no—
874C2×C8—32no—
875C2×C8—31no—
876C2×C8C23×D311yescharacteristic
877C2×C8C23×D312yes—
878C2×C8C23×D311yescharacteristic
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—22no—
882C4⋊C4—21no—
883C4⋊C4—22no—
884C4⋊C4—21no—
885C4⋊C4—22no—
886C4⋊C4—21no—
887C4⋊C4—22no—
888C4⋊C4—32no—
889C4⋊C4—32no—
890C4⋊C4—32no—
891C4⋊C4—32no—
892C4⋊C4—31no—
893C4⋊C4—31no—
894C4⋊C4—32no—
895C4⋊C4—31no—
896C4⋊C4—61no—
897C4⋊C4—61no—
898C4⋊C4—62no—
899C4⋊C4—61no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—61no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—61no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—61no—
918C4⋊C4—62no—
919C4⋊C4—61no—
920C4⋊C4—62no—
921C4⋊C4—61no—
922C4⋊C4—62no—
923C4⋊C4—61no—
924C4⋊C4D3×D411yescharacteristic
925C4⋊C4D3×D412yes—
926C4⋊C4C23×D311yescharacteristic
927C4⋊C4C23×D311yescharacteristic
928C4⋊C4C23×D312yes—
929C22⋊C4—21no—
930C22⋊C4—22no—
931C22⋊C4—61no—
932C22⋊C4—62no—
933C22⋊C4—61no—
934C22⋊C4—62no—
935C42—22no—
936C42—21no—
937C42—32no—
938C42—31no—
939C42—31no—
940C42—32no—
941C42—32no—
942C42—31no—
943C42—61no—
944C42—62no—
945C42—61no—
946C42—62no—
947C42—62no—
948C42—61no—
949C42—62no—
950C42—61no—
951C42—62no—
952C42—61no—
953C42—62no—
954C42—61no—
955C42C23×D311yescharacteristic
956C42C23×D312yes—
957C22×C3—22no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3C23×D411yescharacteristic
961C2×D3—21no—
962C2×D3—21no—
963C2×D3#54812yes—
964C3×C4—22no—
965C3×C4—21no—
966C3×C4—22no—
967C3×C4—42no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—42no—
971C3×C4—41no—
972C3×C4C2×#13712yes—
973C3×C4C22×#4111yescharacteristic
974C3×C4C2×2−1+411yescharacteristic
975Dic3—22no—
976Dic3—21no—
977Dic3—22no—
978Dic3—21no—
979Dic3—41no—
980Dic3—41no—
981Dic3—42no—
982Dic3—41no—
983Dic3—42no—
984Dic3#54812yes—
985Dic3C2×#13714yes—
986C23—21no—
987C23—31no—
988Q8—22no—
989Q8—22no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—34no—
994Q8—32no—
995Q8—64no—
996Q8—61no—
997Q8—62no—
998Q8—61no—
999Q8—62no—
1000Q8—61no—
1001Q8—81no—
1002Q8—122no—
1003Q8—124no—
1004Q8—124no—
1005Q8—122no—
1006Q8—242no—
1007D4—21no—
1008D4—64no—
1009D4D3×#4112yes—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—31no—
1016C2×C4—32no—
1017C2×C4—32no—
1018C2×C4—32no—
1019C2×C4—31no—
1020C2×C4—31no—
1021C2×C4—32no—
1022C2×C4—42no—
1023C2×C4—64no—
1024C2×C4—64no—
1025C2×C4—61no—
1026C2×C4—62no—
1027C2×C4—61no—
1028C2×C4—62no—
1029C2×C4—61no—
1030C2×C4—62no—
1031C2×C4—61no—
1032C2×C4—82no—
1033C2×C4—122no—
1034C2×C4—121no—
1035C2×C4—124no—
1036C2×C4—124no—
1037C2×C4—122no—
1038C2×C4—122no—
1039C2×C4—241no—
1040C2×C4C2×D3×D412yes—
1041C2×C4C2×D3×D412yes—
1042C2×C4C2×D3×D411yescharacteristic
1043C2×C4C2×D3×D411yescharacteristic
1044C2×C4C24×D311yescharacteristic
1045C8—22no—
1046C8—21no—
1047C8—21no—
1048C8—62no—
1049C8—61no—
1050C8—61no—
1051C2×C3—42no—
1052C2×C3C2×#54811yescharacteristic
1053C2×C3C22×#13711yescharacteristic
1054C2×C3#358611yescharacteristic
1055D3—22no—
1056C22—22no—
1057C22—32no—
1058C22—41no—
1059C22—41no—
1060C22—61no—
1061C22—61no—
1062C22C22×D3×D411yescharacteristic
1063C4—22no—
1064C4—22no—
1065C4—21no—
1066C4—34no—
1067C4—32no—
1068C4—41no—
1069C4—42no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4—61no—
1074C4—61no—
1075C4—62no—
1076C4—62no—
1077C4—122no—
1078C4—121no—
1079C4—121no—
1080C4—122no—
1081C4—121no—
1082C4D3×#13712yes—
1083C4C2×D3×#4111yescharacteristic
1084C4D3×2−1+411yescharacteristic
1085C3#6132211yescharacteristic, complemented, Sylow
1086C2—42no—
1087C2—62no—
1088C2D3×#54811yescharacteristic
1089C2C2×D3×#13711yescharacteristic
1090C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3372C2
socleC22×C3C23×D4
prime radicalC2×#237C23
hypercenter#3372D3
hypocenterC3#61322
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3372

Complements

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

NH ≅ G/Ntype
1. D3×#557C2semidirect
3. C3×#3372C2semidirect
4. #83699C2semidirect
5. #83644C2semidirect
6. #81739C2semidirect
7. #81733C2semidirect
8. #81624C2semidirect
9. #81600C2semidirect
10. #81230C2semidirect
11. #81220C2semidirect
12. #81138C2semidirect
13. #81108C2semidirect
16. #80418C2semidirect
17. #80414C2semidirect
18. #79983C2semidirect
19. #79962C2semidirect
21. #79755C2semidirect
23. #79619C2semidirect
145. #3372D3semidirect
817. Dic6#137semidirect
1085. C3#61322semidirect

Maximal subgroups

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

subgroupindex
D3×#5572
#869232
C3×#33722
#836992
#836442
#817392
#817332
#816242
#816002
#812302
#812202
#811382
#811082
#804292
#804182
#804142
#799832
#799622
#797742
#797552
C4×#9152
#796192
#613223