Finite Group Databasebeta

← #11675178

Subgroups — #11675178

Order 768.

1738 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#87046C211yesmaximal, characteristic, complemented
2#87033C211yesmaximal, characteristic
3C3×#3363C211yesmaximal, characteristic, complemented
4#83708C211yesmaximal, characteristic, complemented
5#83699C211yesmaximal, characteristic, complemented
6#81625C212yesmaximal, complemented
7#81624C211yesmaximal, characteristic, complemented
8#81599C212yesmaximal, complemented
9#81598C211yesmaximal, characteristic
10#81139C211yesmaximal, characteristic, complemented
11#81111C212yesmaximal, complemented
12#81108C211yesmaximal, characteristic, complemented
13#81101C212yesmaximal, complemented
14#80478C212yesmaximal, complemented
15#80476C211yesmaximal, characteristic
16#80467C212yesmaximal, complemented
17#80465C211yesmaximal, characteristic, complemented
18#79935C211yesmaximal, characteristic, complemented
19#79917C211yesmaximal, characteristic, complemented
20#79719C212yesmaximal, complemented
21C4×D3×Q16C211yesmaximal, characteristic, complemented
22#79701C211yesmaximal, characteristic, complemented
23#79700C212yesmaximal, complemented
24#61328—31nomaximal, Sylow
25C3×Q82C2211yescharacteristic
26C3×#557C2211yescharacteristic
27C2×#918C2212yes—
28C2×D3×Q16C2211yescharacteristic
29#5732C2212yes—
30#5729—22no—
31#5729C2212yes—
32#5728—21no—
33#5728C2211yescharacteristic
34#5725C2211yescharacteristic
35#5724C2212yes—
36#5722—21no—
37#5722C2211yescharacteristic
38#5721—22no—
39#5721C2211yescharacteristic
40#5721C2212yes—
41#5693—22no—
42#5692—22no—
43#5691—21no—
44#5690—21no—
45#5585C2211yescharacteristic
46#5585C2211yescharacteristic
47#5580—21no—
48#5578—21no—
49#5578C2211yescharacteristic
50#5574C2212yes—
51#5572C2212yes—
52C4×D3×Q8C2211yescharacteristic
53C4×D3×Q8C2211yescharacteristic
54#5570C2211yescharacteristic
55#5569C2212yes—
56#5568—21no—
57#5568C2212yes—
58#5567—21no—
59#5567C2211yescharacteristic
60C3×#487C2211yescharacteristic
61C3×#487C2212yes—
62C3×#477C2212yes—
63C3×#477C2211yescharacteristic
64C3×#462C2211yescharacteristic
65C3×#462C2212yes—
66C3×C8×Q8C2211yescharacteristic
67C3×C4×Q16C2212yes—
68C3×C4×Q16C2211yescharacteristic
69#5185C2212yes—
70#5185C2212yes—
71#5184C2212yes—
72#5182C2212yes—
73Dic3×Q16C2211yescharacteristic
74#5091C2211yescharacteristic
75#5090C2211yescharacteristic
76#5090C2212yes—
77#5089C2212yes—
78#5088C2211yescharacteristic
79#5087C2212yes—
80#5082C2212yes—
81#5079C2211yescharacteristic
82#5030C2212yes—
83C4×#216C2211yescharacteristic
84C4×#216C2211yescharacteristic
85#5028C2212yes—
86#5027C2211yescharacteristic
87#5026C2212yes—
88#5024C2211yescharacteristic
89#5022C2212yes—
90#5020C2211yescharacteristic
91#4891C2212yes—
92#4890C2212yes—
93#4889C2212yes—
94#4881C2212yes—
95D3×#107C2211yescharacteristic
96#4877C2212yes—
97#4873C2211yescharacteristic
98#4851C2211yescharacteristic
99#4848C2211yescharacteristic
100#4847C2212yes—
101#4845C2212yes—
102#4839C2212yes—
103#4837C2211yescharacteristic
104#4831C2211yescharacteristic
105#4828C2212yes—
106#4804C2212yes—
107#4804C2212yes—
108#4803C2212yes—
109#4802C2212yes—
110D3×#103C2211yescharacteristic
111D3×#103C2211yescharacteristic
112#4800C2212yes—
113#4800C2212yes—
114#4800C2212yes—
115#4799C2212yes—
116#4799C2212yes—
117#4798C2212yes—
118#4798C2212yes—
119#4797C2212yes—
120#4795C2212yes—
121#4794C2212yes—
122#4793C2212yes—
123#4792C2212yes—
124#4790C2211yescharacteristic
125#4790C2211yescharacteristic
126#4790C2212yes—
127#4788C2212yes—
128C4×Dic12C2211yescharacteristic
129#4697C2212yes—
130#4694C2211yescharacteristic
131C4×#204C2212yes—
132#4689C2212yes—
133C4×D3×C8C2211yescharacteristic
134C8×Dic6C2212yes—
135C8×Dic6C2211yescharacteristic
136#3507—31no—
137#3502—31no—
138#3377—32no—
139#3377—32no—
140#3375—31no—
141#3375—31no—
142#3374—31no—
143#3374—31no—
144#3365—31no—
145#3365—31no—
146#3364—32no—
147#3364—32no—
148#3363—31no—
149#3363D311yescharacteristic, complemented
150#3137—32no—
151#3131—31no—
152#3083—32no—
153#3078—31no—
154#3044—32no—
155#3037—31no—
156#2960—31no—
157#2947—32no—
158C2×C4×Q16—31no—
159C2×#239C2312yes—
160C2×D3×Q8C2311yescharacteristic
161C2×D3×Q8C2311yescharacteristic
162C2×C3×Q16C2311yescharacteristic
163C2×C3×Q16C2312yes—
164C3×C4⋊Q8—22no—
165C3×C4⋊Q8—21no—
166C3×C4⋊Q8C2311yescharacteristic
167C3×C4⋊Q8C2312yes—
168C3×C4⋊Q8C2312yes—
169C3×C4⋊Q8C2311yescharacteristic
170C3×#125—21no—
171C3×#125—22no—
172C3×C4×Q8—21no—
173C3×C4×Q8—21no—
174C3×C4×Q8C2312yes—
175C3×C4×Q8C2311yescharacteristic
176C3×C4×Q8C2311yescharacteristic
177C3×C4×Q8C2312yes—
178C3×C4×Q8C2311yescharacteristic
179#947—21no—
180#947C2312yes—
181#947C2312yes—
182#946—21no—
183#946—22no—
184#946D411yescharacteristic
185Q8×Dic3—22no—
186Q8×Dic3—21no—
187Q8×Dic3C2311yescharacteristic
188Q8×Dic3C2311yescharacteristic
189Q8×Dic3C2312yes—
190Q8×Dic3C2312yes—
191#944—21no—
192#944—22no—
193#944—22no—
194#944—22no—
195#944D411yescharacteristic
196#944C2312yes—
197C2×#216C2311yescharacteristic
198C2×#216C2311yescharacteristic
199C2×#216C2312yes—
200C2×#215C2312yes—
201#918—28no—
202D3×Q16—24no—
203C2×Dic12C2311yescharacteristic
204C2×#204C2312yes—
205C2×ΓL(1,𝔽25)C2312yes—
206C2×D3×C8C2311yescharacteristic
207C2×D3×C8C2311yescharacteristic
208#898—22no—
209#898—22no—
210#898—22no—
211#897—21no—
212#897—22no—
213#897D411yescharacteristic
214#896—22no—
215#896—22no—
216#896—22no—
217#896—22no—
218#896D412yes—
219#895—21no—
220#895—21no—
221#894—22no—
222#894—22no—
223#894—22no—
224#894—22no—
225#893—21no—
226#893—22no—
227#893—21no—
228#893—21no—
229#893C2312yes—
230#892—22no—
231#892—22no—
232#892C2312yes—
233D3×C4⋊C4—21no—
234D3×C4⋊C4—21no—
235D3×C4⋊C4—22no—
236D3×C4⋊C4C2311yescharacteristic
237D3×C4⋊C4C2311yescharacteristic
238#890—21no—
239#890—22no—
240#890—22no—
241#890C2312yes—
242#890C2312yes—
243#889—22no—
244#889—22no—
245#889—22no—
246#889—22no—
247#889—22no—
248#889D412yes—
249#888—22no—
250#888—21no—
251#888D411yescharacteristic
252#888C2312yes—
253#887—21no—
254#887—21no—
255#887—21no—
256#887—22no—
257#887—21no—
258#887—21no—
259#887—21no—
260#887C2311yescharacteristic
261#887C2311yescharacteristic
262#887C2312yes—
263#876—22no—
264#875—21no—
265#875C2312yes—
266#874C2311yescharacteristic
267C4×D12—22no—
268C4×D12—21no—
269C4×D12C2312yes—
270#872—22no—
271#872—22no—
272#872—22no—
273#872C2312yes—
274C42×D3—21no—
275C42×D3—21no—
276C42×D3C2311yescharacteristic
277#870—22no—
278#870C2312yes—
279#869—21no—
280#869C2311yescharacteristic
281C4×Dic6—21no—
282C4×Dic6—22no—
283C4×Dic6—22no—
284C4×Dic6—21no—
285C4×Dic6—21no—
286C4×Dic6C2312yes—
287C4×Dic6C2311yescharacteristic
288C4×Dic6C2311yescharacteristic
289C4×Dic6C2311yescharacteristic
290C4×Dic6C2312yes—
291C3×#107C2311yescharacteristic
292C3×#107C2312yes—
293C3×C4⋊C8C2312yes—
294C3×C4⋊C8C2311yescharacteristic
295C3×#103C2311yescharacteristic
296C3×#103C2312yes—
297C3×#103C2311yescharacteristic
298C3×#103C2312yes—
299C3×#103C2312yes—
300C3×#103C2312yes—
301C3×C4×C8C2311yescharacteristic
302C3×C4×C8C2312yes—
303#835C2311yescharacteristic
304#835C2311yescharacteristic
305#835C2312yes—
306#835C2312yes—
307#835C2312yes—
308#835C2312yes—
309#821C2312yes—
310#821C2312yes—
311#821C2312yes—
312#818C2311yescharacteristic
313#817C2312yes—
314#816C2312yes—
315#816C2311yescharacteristic
316#816C2311yescharacteristic
317#815C2312yes—
318Dic3⋊C8C2312yes—
319Dic3⋊C8C2312yes—
320Dic3⋊C8C2312yes—
321C8×Dic3C2311yescharacteristic
322C8×Dic3C2311yescharacteristic
323C8×Dic3C2312yes—
324#810C2311yescharacteristic
325#810C2311yescharacteristic
326#810C2312yes—
327#809C2312yes—
328#809C2312yes—
329#809C2312yes—
330#808C2312yes—
331#807C2311yescharacteristic
332#807C2311yescharacteristic
333#807C2312yes—
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4⋊(C3⋊C8)C2312yes—
336#803C2312yes—
337C4×C3⋊C8C2311yescharacteristic
338C2×#137—32no—
339C22×Q16—31no—
340#559—31no—
341#559—31no—
342Q82—31no—
343Q82—61no—
344Q82C2×D311yescharacteristic
345#557—32no—
346#557—31no—
347#557—32no—
348#557—31no—
349#557—31no—
350#557—61no—
351#557—62no—
352#557C2×D311yescharacteristic
353#556—32no—
354#556—32no—
355#556—61no—
356#554—61no—
357#552—62no—
358#544—32no—
359#544—62no—
360#539—62no—
361#536—32no—
362#533—31no—
363#533—31no—
364#533—61no—
365#533—61no—
366#532—31no—
367#529—61no—
368#529—61no—
369#520—32no—
370#519—32no—
371C2×C4×Q8—31no—
372C2×C4×Q8—31no—
373#491—32no—
374#491—32no—
375#489—32no—
376#489—32no—
377#488—32no—
378#488—32no—
379#488—32no—
380#488—32no—
381#487—31no—
382#487—32no—
383#487C2×D311yescharacteristic
384#487C2×D312yes—
385#486—31no—
386#486—31no—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#478—32no—
392#478—32no—
393#477—31no—
394#477—32no—
395#477C2×D311yescharacteristic
396#477C2×D312yes—
397#475—31no—
398#475—31no—
399#474—32no—
400#474—32no—
401#464—32no—
402#464—32no—
403#464—32no—
404#464—32no—
405#464—32no—
406#464—32no—
407#462—32no—
408#462—31no—
409#462—32no—
410#462—32no—
411#462C2×D311yescharacteristic
412#462C2×D312yes—
413#460—31no—
414#460—31no—
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—31no—
428C4×Q16—31no—
429C4×Q16—32no—
430C4×Q16—31no—
431C4×Q16—31no—
432C4×Q16—31no—
433C4×Q16C2×D312yes—
434C4×Q16C2×D311yescharacteristic
435C4×SD16—32no—
436C4×SD16—32no—
437#428—32no—
438C2×#107—31no—
439#424—32no—
440#423—31no—
441#419—32no—
442#417—32no—
443#416—32no—
444#416—32no—
445C2×#103—31no—
446C2×#103—31no—
447#405—32no—
448C2×C4×C8—31no—
449C2×C3×Q8—21no—
450C2×C3×Q8—22no—
451C2×C3×Q8C2×D411yescharacteristic
452C2×C3×Q8C2412yes—
453C2×C3×Q8C2411yescharacteristic
454C2×C3×Q8C2411yescharacteristic
455#239—24no—
456#239—24no—
457D3×Q8—22no—
458D3×Q8—22no—
459D3×Q8—22no—
460D3×Q8#4114yes—
461C2×D12—22no—
462C2×D12—21no—
463C2×D12—21no—
464C2×D12C2412yes—
465C2×C4×D3—21no—
466C2×C4×D3—21no—
467C2×C4×D3—22no—
468C2×C4×D3—21no—
469C2×C4×D3—21no—
470C2×C4×D3—22no—
471C2×C4×D3—22no—
472C2×C4×D3C2×D411yescharacteristic
473C2×C4×D3C2×D411yescharacteristic
474C2×C4×D3C2411yescharacteristic
475C2×Dic6—21no—
476C2×Dic6—21no—
477C2×Dic6—21no—
478C2×Dic6—22no—
479C2×Dic6C2×D411yescharacteristic
480C2×Dic6C2×D412yes—
481C2×Dic6C2411yescharacteristic
482C2×Dic6C2411yescharacteristic
483C3×Q16—22no—
484C3×Q16—24no—
485C2×C3×C8C2411yescharacteristic
486C2×C3×C8C2411yescharacteristic
487C2×C3×C8C2412yes—
488C3×C4⋊C4—21no—
489C3×C4⋊C4—22no—
490C3×C4⋊C4—21no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4—21no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—21no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—22no—
498C3×C4⋊C4C2×D411yescharacteristic
499C3×C4⋊C4C2×D412yes—
500C3×C4⋊C4C2411yescharacteristic
501C3×C4⋊C4C2412yes—
502C3×C4⋊C4C2411yescharacteristic
503C3×C42—21no—
504C3×C42—22no—
505C3×C42—21no—
506C3×C42—22no—
507C3×C42C2411yescharacteristic
508C3×C42C2412yes—
509#216—22no—
510#216—22no—
511#216—24no—
512#215—24no—
513(C2×D3)⋊C4—22no—
514(C2×D3)⋊C4—22no—
515(C2×D3)⋊C4—22no—
516(C2×D3)⋊C4—22no—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4C2×D412yes—
523(C2×D3)⋊C4C2×D412yes—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—21no—
527C4⋊Dic3—22no—
528C4⋊Dic3—21no—
529C4⋊Dic3—22no—
530C4⋊Dic3—22no—
531C4⋊Dic3C2×D411yescharacteristic
532C4⋊Dic3C2×D412yes—
533C4⋊Dic3C2411yescharacteristic
534C4⋊Dic3C2411yescharacteristic
535C4⋊Dic3C2412yes—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—21no—
539Dic3⋊C4—21no—
540Dic3⋊C4—22no—
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⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554Dic3⋊C4C2×D412yes—
555Dic3⋊C4C2×D412yes—
556C4×Dic3—21no—
557C4×Dic3—21no—
558C4×Dic3—22no—
559C4×Dic3—21no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3—22no—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3—21no—
566C4×Dic3—22no—
567C4×Dic3C2×D411yescharacteristic
568C4×Dic3C2×D411yescharacteristic
569C4×Dic3C2411yescharacteristic
570C4×Dic3C2412yes—
571C2×C3⋊C8C2411yescharacteristic
572C2×C3⋊C8C2411yescharacteristic
573C2×C3⋊C8C2412yes—
574Dic12—22no—
575#204—24no—
576ΓL(1,𝔽25)—24no—
577D3×C8—22no—
578D3×C8—22no—
579C2×#41—32no—
580C22×Q8—31no—
581C22×Q8—31no—
582#137—68no—
583C2×Q16—31no—
584C2×Q16—31no—
585C2×Q16—32no—
586C2×Q16—31no—
587C2×Q16—64no—
588C2×Q16C22×D311yescharacteristic
589C2×Q16C22×D312yes—
590C2×SD16—32no—
591C2×SD16—32no—
592C2×M16—32no—
593C22×C8—31no—
594C22×C8—31no—
595C4⋊Q8—21no—
596C4⋊Q8—22no—
597C4⋊Q8—31no—
598C4⋊Q8—31no—
599C4⋊Q8—32no—
600C4⋊Q8—32no—
601C4⋊Q8—31no—
602C4⋊Q8—61no—
603C4⋊Q8—61no—
604C4⋊Q8—62no—
605C4⋊Q8—62no—
606C4⋊Q8—62no—
607C4⋊Q8—62no—
608C4⋊Q8—61no—
609C4⋊Q8C22×D311yescharacteristic
610C4⋊Q8C22×D312yes—
611C4⋊Q8C22×D311yescharacteristic
612C4⋊Q8C22×D312yes—
613#127—31no—
614#126—62no—
615#126—62no—
616#126—62no—
617#126—62no—
618#125—21no—
619#125—22no—
620#125—32no—
621#125—32no—
622#125—32no—
623#125—32no—
624#125—62no—
625#125—61no—
626#125—62no—
627#125—62no—
628#125—62no—
629#125—62no—
630#125—62no—
631#125—62no—
632#125—62no—
633#124—32no—
634#124—32no—
635#124—32no—
636#124—61no—
637#124—61no—
638#123—62no—
639#123—62no—
640#123—62no—
641#123—62no—
642C22⋊Q8—31no—
643C22⋊Q8—31no—
644C22⋊Q8—32no—
645C22⋊Q8—62no—
646C22⋊Q8—62no—
647C22⋊Q8—62no—
648C22⋊Q8—62no—
649C22⋊Q8—61no—
650C22⋊Q8—62no—
651C22⋊Q8—62no—
652C22⋊Q8—61no—
653#121—61no—
654#121—61no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—31no—
660C4×Q8—31no—
661C4×Q8—32no—
662C4×Q8—32no—
663C4×Q8—31no—
664C4×Q8—31no—
665C4×Q8—32no—
666C4×Q8—31no—
667C4×Q8—31no—
668C4×Q8—32no—
669C4×Q8—61no—
670C4×Q8—61no—
671C4×Q8—62no—
672C4×Q8—62no—
673C4×Q8—61no—
674C4×Q8—61no—
675C4×Q8—61no—
676C4×Q8—61no—
677C4×Q8—61no—
678C4×Q8—62no—
679C4×Q8—61no—
680C4×Q8—61no—
681C4×Q8—62no—
682C4×Q8—61no—
683C4×Q8C22×D311yescharacteristic
684C4×Q8C22×D311yescharacteristic
685C4×Q8C22×D312yes—
686C4×Q8C22×D312yes—
687C4×Q8C22×D311yescharacteristic
688C4×D4—32no—
689C4×D4—32no—
690C4×D4—62no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4—61no—
694C4×D4—62no—
695C4×D4—61no—
696#117—32no—
697#117—32no—
698#117—62no—
699#117—62no—
700#117—62no—
701#117—62no—
702#117—62no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—62no—
706C2×C4⋊C4—61no—
707C2×C4⋊C4—61no—
708C2×C42—31no—
709C2×C42—61no—
710C2×C42—61no—
711#107—31no—
712#107—31no—
713#107—31no—
714#107—32no—
715#107C22×D311yescharacteristic
716#107C22×D312yes—
717#106—32no—
718#106—32no—
719C4⋊C8—32no—
720C4⋊C8—32no—
721C4⋊C8—32no—
722C4⋊C8—31no—
723C4⋊C8—32no—
724C4⋊C8C22×D311yescharacteristic
725C4⋊C8C22×D312yes—
726#103—31no—
727#103—31no—
728#103—32no—
729#103—32no—
730#103—32no—
731#103—32no—
732#103—31no—
733#103—31no—
734#103—32no—
735#103—31no—
736#103—31no—
737#103—32no—
738#103C22×D311yescharacteristic
739#103C22×D311yescharacteristic
740#103C22×D312yes—
741#103C22×D312yes—
742#103C22×D312yes—
743#103C22×D312yes—
744#102—32no—
745#102—32no—
746#102—32no—
747#102—32no—
748#102—32no—
749#102—32no—
750#97—32no—
751#97—32no—
752C4×C8—31no—
753C4×C8—31no—
754C4×C8—32no—
755C4×C8—31no—
756C4×C8C22×D311yescharacteristic
757C4×C8C22×D312yes—
758C22×D3—22no—
759C22×D3C22×D411yescharacteristic
760C3×Q8—22no—
761C3×Q8—21no—
762C3×Q8—21no—
763C3×Q8—22no—
764C3×Q8—21no—
765C3×Q8—22no—
766C3×Q8—82no—
767C3×Q8—81no—
768C3×Q8C2×#4112yes—
769C2×C3×C4—21no—
770C2×C3×C4—22no—
771C2×C3×C4—21no—
772C2×C3×C4—22no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4C22×D412yes—
776C2×C3×C4C22×D411yescharacteristic
777C2×C3×C4C22×D412yes—
778C2×C3×C4C22×D411yescharacteristic
779C2×C3×C4C2511yescharacteristic
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—22no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3C22×D411yescharacteristic
786C2×Dic3C22×D412yes—
787C2×Dic3C22×D412yes—
788C2×Dic3C22×D411yescharacteristic
789C2×Dic3C22×D411yescharacteristic
790D12—22no—
791D12—22no—
792D12—44no—
793D12—42no—
794D12—81no—
795C4×D3—24no—
796C4×D3—22no—
797C4×D3—41no—
798C4×D3—42no—
799C4×D3—44no—
800C4×D3—82no—
801C4×D3—82no—
802C4×D3—81no—
803C4×D3—81no—
804C4×D3C2×#4112yes—
805C4×D32−1+412yes—
806Dic6—22no—
807Dic6—21no—
808Dic6—24no—
809Dic6—21no—
810Dic6—21no—
811Dic6—42no—
812Dic6—42no—
813Dic6—42no—
814Dic6—82no—
815Dic6C2×#4112yes—
816C3×C8—21no—
817C3×C8—22no—
818C3×C8—21no—
819C3⋊C8—21no—
820C3⋊C8—22no—
821C3⋊C8—21no—
822#41—64no—
823#41—64no—
824C2×Q8—21no—
825C2×Q8—22no—
826C2×Q8—31no—
827C2×Q8—32no—
828C2×Q8—34no—
829C2×Q8—31no—
830C2×Q8—31no—
831C2×Q8—61no—
832C2×Q8—61no—
833C2×Q8—62no—
834C2×Q8—62no—
835C2×Q8—62no—
836C2×Q8—62no—
837C2×Q8—61no—
838C2×Q8D3×D411yescharacteristic
839C2×Q8C23×D311yescharacteristic
840C2×Q8C23×D312yes—
841C2×Q8C23×D311yescharacteristic
842C2×D4—32no—
843C2×D4—62no—
844C2×D4—61no—
845C2×D4—61no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—62no—
850C22×C4—62no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—62no—
856Q16—22no—
857Q16—24no—
858Q16—62no—
859Q16—62no—
860Q16—64no—
861Q16—62no—
862SD16—64no—
863SD16—64no—
864M16—64no—
865C2×C8—31no—
866C2×C8—31no—
867C2×C8—32no—
868C2×C8—62no—
869C2×C8—62no—
870C2×C8C23×D311yescharacteristic
871C2×C8C23×D311yescharacteristic
872C2×C8C23×D312yes—
873C4⋊C4—22no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—31no—
888C4⋊C4—32no—
889C4⋊C4—32no—
890C4⋊C4—32no—
891C4⋊C4—31no—
892C4⋊C4—31no—
893C4⋊C4—61no—
894C4⋊C4—61no—
895C4⋊C4—62no—
896C4⋊C4—61no—
897C4⋊C4—61no—
898C4⋊C4—61no—
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—61no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—61no—
915C4⋊C4D3×D411yescharacteristic
916C4⋊C4D3×D412yes—
917C4⋊C4C23×D311yescharacteristic
918C4⋊C4C23×D312yes—
919C4⋊C4C23×D311yescharacteristic
920C22⋊C4—32no—
921C22⋊C4—32no—
922C22⋊C4—62no—
923C22⋊C4—62no—
924C22⋊C4—62no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C22⋊C4—62no—
928C22⋊C4—62no—
929C22⋊C4—62no—
930C22⋊C4—62no—
931C42—21no—
932C42—21no—
933C42—22no—
934C42—22no—
935C42—31no—
936C42—31no—
937C42—31no—
938C42—32no—
939C42—61no—
940C42—61no—
941C42—61no—
942C42—61no—
943C42—62no—
944C42—62no—
945C42—62no—
946C42—62no—
947C42—61no—
948C42—61no—
949C42—62no—
950C42C23×D311yescharacteristic
951C42C23×D312yes—
952C22×C3C23×D411yescharacteristic
953C2×D3—21no—
954C2×D3—21no—
955C2×D3—42no—
956C2×D3—42no—
957C2×D3—42no—
958C2×D3#54812yes—
959C3×C4—22no—
960C3×C4—21no—
961C3×C4—22no—
962C3×C4—22no—
963C3×C4—42no—
964C3×C4—41no—
965C3×C4—41no—
966C3×C4—41no—
967C3×C4—42no—
968C3×C4#57812yes—
969C3×C4C22×#4111yescharacteristic
970C3×C4C2×2−1+411yescharacteristic
971Dic3—21no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—21no—
976Dic3—41no—
977Dic3—41no—
978Dic3—41no—
979Dic3—42no—
980Dic3#54812yes—
981C23—31no—
982C23—62no—
983Q8—21no—
984Q8—22no—
985Q8—21no—
986Q8—22no—
987Q8—21no—
988Q8—22no—
989Q8—32no—
990Q8—64no—
991Q8—61no—
992Q8—62no—
993Q8—61no—
994Q8—61no—
995Q8—81no—
996Q8—82no—
997Q8—122no—
998Q8—122no—
999Q8—122no—
1000Q8—242no—
1001Q8D3×#4112yes—
1002D4—62no—
1003D4—62no—
1004D4—124no—
1005D4—122no—
1006D4—241no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—31no—
1014C2×C4—32no—
1015C2×C4—32no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—64no—
1021C2×C4—61no—
1022C2×C4—62no—
1023C2×C4—61no—
1024C2×C4—62no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—121no—
1028C2×C4—124no—
1029C2×C4—122no—
1030C2×C4—242no—
1031C2×C4—242no—
1032C2×C4—241no—
1033C2×C4—241no—
1034C2×C4C2×D3×D412yes—
1035C2×C4C2×D3×D411yescharacteristic
1036C2×C4C2×D3×D412yes—
1037C2×C4C2×D3×D411yescharacteristic
1038C2×C4C24×D311yescharacteristic
1039C8—21no—
1040C8—22no—
1041C8—21no—
1042C8—61no—
1043C8—62no—
1044C8—61no—
1045C2×C3C2×#54811yescharacteristic
1046C2×C3C2×#57811yescharacteristic
1047C2×C3#358411yescharacteristic
1048D3—22no—
1049D3—82no—
1050C22—32no—
1051C22—61no—
1052C22—61no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22C22×D3×D411yescharacteristic
1057C4—22no—
1058C4—21no—
1059C4—22no—
1060C4—22no—
1061C4—32no—
1062C4—41no—
1063C4—41no—
1064C4—42no—
1065C4—42no—
1066C4—41no—
1067C4—61no—
1068C4—62no—
1069C4—61no—
1070C4—62no—
1071C4—62no—
1072C4—122no—
1073C4—121no—
1074C4—121no—
1075C4—121no—
1076C4#576612yes—
1077C4C2×D3×#4111yescharacteristic
1078C4D3×2−1+411yescharacteristic
1079C3#6132811yescharacteristic, complemented, Sylow
1080C2—62no—
1081C2—242no—
1082C2D3×#54811yescharacteristic
1083C2C2×#576611yescharacteristic
1084C2#8720611yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3363C2
socleC22×C3C23×D4
prime radical#5725C22
hypercenter#3363D3
hypocenterC3#61328
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3363

Complements

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

NH ≅ G/Ntype
1. #87046C2semidirect
3. C3×#3363C2semidirect
4. #83708C2semidirect
5. #83699C2semidirect
6. #81625C2semidirect
7. #81624C2semidirect
8. #81599C2semidirect
10. #81139C2semidirect
11. #81111C2semidirect
12. #81108C2semidirect
13. #81101C2semidirect
14. #80478C2semidirect
16. #80467C2semidirect
17. #80465C2semidirect
18. #79935C2semidirect
19. #79917C2semidirect
20. #79719C2semidirect
21. C4×D3×Q16C2semidirect
22. #79701C2semidirect
23. #79700C2semidirect
149. #3363D3semidirect
1079. C3#61328semidirect

Maximal subgroups

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

subgroupindex
#870462
#870332
C3×#33632
#837082
#836992
#816252
#816242
#815992
#815982
#811392
#811112
#811082
#811012
#804782
#804762
#804672
#804652
#799352
#799172
#797192
C4×D3×Q162
#797012
#797002
#613283