Finite Group Databasebeta

← #11675594

Subgroups — #11675594

Order 768.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85892C211yesmaximal, characteristic, complemented
2#85890C211yesmaximal, characteristic, complemented
3C3×#2952C211yesmaximal, characteristic, complemented
4#83902C211yesmaximal, characteristic, complemented
5#83900C211yesmaximal, characteristic
6#82572C211yesmaximal, characteristic, complemented
7#82559C211yesmaximal, characteristic, complemented
8#79854C212yesmaximal, complemented
9#79852C212yesmaximal, complemented
10#79818C212yesmaximal, complemented
11#79817C212yesmaximal, complemented
12#79628C212yesmaximal, complemented
13#79627C212yesmaximal, complemented
14#79623C212yesmaximal, complemented
15#79620C212yesmaximal, complemented
16C2×#4857C211yesmaximal, characteristic, complemented
17#79130C211yesmaximal, characteristic, complemented
18#78879C211yesmaximal, characteristic, complemented
19#78877C211yesmaximal, characteristic, complemented
20#78868C211yesmaximal, characteristic, complemented
21#78867C211yesmaximal, characteristic, complemented
22#78575C211yesmaximal, characteristic, complemented
23#78544C211yesmaximal, characteristic, complemented
24#61350—31nomaximal, Sylow
25C2×C3×#135C2211yescharacteristic
26C3×#520C2211yescharacteristic
27C3×#520C2211yescharacteristic
28#5832C2211yescharacteristic
29#5827C2211yescharacteristic
30Dic3×#41C2211yescharacteristic
31#5825C2211yescharacteristic
32C2×#951C2211yescharacteristic
33C2×#950C2211yescharacteristic
34#5570C2212yes—
35#5569C2212yes—
36#5568C2212yes—
37#5567C2212yes—
38#5564—22no—
39#5559C2212yes—
40#5543—22no—
41#5543C2212yes—
42#5542C2212yes—
43#5539—22no—
44#5539C2212yes—
45#5538—22no—
46#5533—21no—
47#5529—21no—
48#5526C2211yescharacteristic
49#5519—21no—
50#5519C2211yescharacteristic
51#5517—21no—
52#5517C2211yescharacteristic
53#5513—21no—
54#5511—21no—
55#5504C2211yescharacteristic
56#5500—21no—
57#5500C2211yescharacteristic
58C2×#890—21no—
59C2×#890C2211yescharacteristic
60C2×#887C2211yescharacteristic
61C3×#442C2212yes—
62C3×#441C2212yes—
63C3×C4×SD16C2212yes—
64C3×C4×SD16C2212yes—
65C2×C3×#106C2211yescharacteristic
66C3×#417C2211yescharacteristic
67C3×#417C2211yescharacteristic
68C3×#405C2211yescharacteristic
69#5233C2211yescharacteristic
70#5232C2211yescharacteristic
71#5185C2211yescharacteristic
72#5182C2211yescharacteristic
73#5182C2212yes—
74#5166C2211yescharacteristic
75#5166C2212yes—
76#5165C2211yescharacteristic
77#5163C2211yescharacteristic
78#5162C2212yes—
79#5162C2211yescharacteristic
80#5153C2211yescharacteristic
81#5153C2212yes—
82#5150C2211yescharacteristic
83#5133C2211yescharacteristic
84#5122C2211yescharacteristic
85#5120C2211yescharacteristic
86Dic3×M16C2211yescharacteristic
87#5113C2211yescharacteristic
88C2×#816C2211yescharacteristic
89#5102C2211yescharacteristic
90C2×Dic3⋊C8C2211yescharacteristic
91#5031C2212yes—
92#5028C2212yes—
93#5022C2212yes—
94#5021C2212yes—
95#5019C2212yes—
96#5016C2212yes—
97#5009C2212yes—
98#5007C2212yes—
99#4999C2211yescharacteristic
100C2×#810C2211yescharacteristic
101#4966C2211yescharacteristic
102#4964C2211yescharacteristic
103C2×#807C2211yescharacteristic
104#4871C2212yes—
105#4870C2212yes—
106#4857C2212yes—
107#4857C2212yes—
108#4857C2212yes—
109#4857C2212yes—
110#4857C2212yes—
111#4854C2212yes—
112#4817C2212yes—
113#4800C2212yes—
114#4797C2212yes—
115#4797C2212yes—
116#4792C2212yes—
117#4790C2212yes—
118#4790C2212yes—
119#4789C2212yes—
120#4768C2212yes—
121#4768C2212yes—
122#4765C2212yes—
123#4764C2212yes—
124#4758C2212yes—
125#4757C2212yes—
126#4757C2212yes—
127#4756C2212yes—
128#4714C2212yes—
129#4703C2212yes—
130#4701C2212yes—
131#4701C2212yes—
132#4697C2212yes—
133#4681C2212yes—
134#4679C2212yes—
135C8×Dic6C2212yes—
136#3507—31no—
137#3504—31no—
138#3377—32no—
139#3376—32no—
140#3374—32no—
141#3372—32no—
142#3371—32no—
143#3370—32no—
144#3364—32no—
145#3360—32no—
146#3142—31no—
147#3137—31no—
148#3137—31no—
149#3084—31no—
150#3083—31no—
151C2×#479—31no—
152#3046—31no—
153#3046—31no—
154#3035—31no—
155#2962—31no—
156#2952D311yescharacteristic, complemented
157#2951—31no—
158C4×#137—31no—
159C2×C3×#41C2311yescharacteristic
160C2×C3×#41C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6C2311yescharacteristic
163C3×#135—24no—
164C2×C3×Q16C2311yescharacteristic
165C2×C3×SD16C2311yescharacteristic
166C2×C3×SD16C2311yescharacteristic
167C2×C3×D8C2311yescharacteristic
168C2×C3×M16C2311yescharacteristic
169C22×C3×C8C2311yescharacteristic
170C3×C4×Q8C2312yes—
171C3×C4×Q8C2312yes—
172C3×C4×D4—22no—
173C3×C4×D4—22no—
174C3×C4×D4C2312yes—
175C3×C4×D4C2312yes—
176C3×#117—21no—
177C3×#117—21no—
178C3×#117C2311yescharacteristic
179C2×C3×C4⋊C4—21no—
180C2×C3×C4⋊C4—21no—
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C4⋊C4C2311yescharacteristic
183#951—24no—
184#950—24no—
185#947C2311yescharacteristic
186Q8×Dic3C2311yescharacteristic
187Q8×Dic3C2312yes—
188Q8×Dic3C2311yescharacteristic
189#944C2312yes—
190#944C2311yescharacteristic
191C2×#216C2312yes—
192C2×#216C2311yescharacteristic
193C2×#215C2311yescharacteristic
194#940C2311yescharacteristic
195#939—21no—
196#939—21no—
197#936C2312yes—
198#936C2311yescharacteristic
199#935—22no—
200D4×Dic3—21no—
201D4×Dic3—21no—
202D4×Dic3—22no—
203D4×Dic3C2311yescharacteristic
204D4×Dic3C2312yes—
205D4×Dic3C2311yescharacteristic
206C2×#214C2311yescharacteristic
207C2×#214C2312yes—
208C2×#213C2311yescharacteristic
209#929—22no—
210C4×#67—22no—
211C4×#67—22no—
212C4×#67—21no—
213C4×#67—21no—
214#926—21no—
215#926—22no—
216#926—21no—
217#926C2311yescharacteristic
218#926C2311yescharacteristic
219C2×C4⋊Dic3—21no—
220C2×C4⋊Dic3—21no—
221C2×C4⋊Dic3—22no—
222C2×C4⋊Dic3C2311yescharacteristic
223#924—22no—
224#924—22no—
225#924—22no—
226#924—21no—
227#924—21no—
228#924—22no—
229C2×Dic3⋊C4—21no—
230C2×Dic3⋊C4—21no—
231C2×Dic3⋊C4—22no—
232C2×C4×Dic3—21no—
233C2×C4×Dic3—21no—
234C2×C4×Dic3C2311yescharacteristic
235C2×#208C2311yescharacteristic
236C22×C3⋊C8C2311yescharacteristic
237#898—22no—
238#897—21no—
239#897—21no—
240#896—22no—
241#893C2312yes—
242#892—21no—
243D3×C4⋊C4—21no—
244#890—21no—
245#890—21no—
246#890—22no—
247#890—22no—
248#890—22no—
249#890—21no—
250#890—21no—
251#890D411yescharacteristic
252#890D411yescharacteristic
253#890C2312yes—
254#890C2312yes—
255#890C2312yes—
256#889—22no—
257#889—22no—
258#888—22no—
259#888—21no—
260#888—21no—
261#888D411yescharacteristic
262#888D411yescharacteristic
263#888C2312yes—
264#887—21no—
265#887—21no—
266#887C2312yes—
267#887C2312yes—
268#887C2312yes—
269#886—22no—
270#885—22no—
271#883—22no—
272#879—22no—
273#879—22no—
274#878—22no—
275#878—22no—
276#878—22no—
277#878—22no—
278#878—22no—
279#878D412yes—
280#878D412yes—
281#876—22no—
282#875C2312yes—
283#872—22no—
284#870—22no—
285#870—22no—
286#870C2312yes—
287#869—22no—
288#869C2312yes—
289#869C2312yes—
290C4×Dic6—22no—
291C4×Dic6—22no—
292C4×Dic6—22no—
293C4×Dic6C2312yes—
294C4×Dic6C2312yes—
295C3×#106C2312yes—
296C3×#106C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#102C2312yes—
300C3×#102C2312yes—
301C3×#97C2312yes—
302C3×C4×C8C2312yes—
303#835C2312yes—
304#835C2311yescharacteristic
305#835C2311yescharacteristic
306#832C2311yescharacteristic
307#832C2311yescharacteristic
308#832C2312yes—
309#821C2311yescharacteristic
310#821C2311yescharacteristic
311#821C2312yes—
312#816C2312yes—
313#816C2312yes—
314#816C2312yes—
315#816C2311yescharacteristic
316#816C2312yes—
317#816C2311yescharacteristic
318#816C2312yes—
319#815C2312yes—
320#815C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2311yescharacteristic
324Dic3⋊C8C2311yescharacteristic
325Dic3⋊C8C2311yescharacteristic
326Dic3⋊C8C2311yescharacteristic
327C8×Dic3C2312yes—
328C8×Dic3C2312yes—
329#810C2312yes—
330#810C2312yes—
331#810C2312yes—
332#809C2312yes—
333#808C2312yes—
334#807C2312yes—
335#807C2312yes—
336#807C2312yes—
337C4⋊(C3⋊C8)C2312yes—
338C4⋊(C3⋊C8)C2312yes—
339C2×#137—31no—
340C2×#135—31no—
341C2×#135C2×D311yescharacteristic
342#559—32no—
343#557—32no—
344#557—32no—
345#557—32no—
346#556—32no—
347#556—32no—
348#556—61no—
349#554—32no—
350#554—32no—
351#554—61no—
352#554—62no—
353#554—62no—
354#552—61no—
355#552—61no—
356#544—31no—
357#544—31no—
358#544—61no—
359#544—61no—
360#539—62no—
361#536—31no—
362#536—31no—
363#533—31no—
364#533—61no—
365#532—31no—
366#529—62no—
367C2×#125—31no—
368C2×#125—61no—
369#520—31no—
370#520—31no—
371#520C2×D311yescharacteristic
372#520C2×D311yescharacteristic
373C4×#41—31no—
374C2×C4×Q8—31no—
375#491—32no—
376#491—32no—
377#491—32no—
378#490—32no—
379#489—32no—
380#489—32no—
381#488—32no—
382#488—32no—
383#488—32no—
384#488—32no—
385#487—32no—
386#487—32no—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479—32no—
392#479—32no—
393#478—32no—
394#478—32no—
395#477—32no—
396#476—32no—
397#475—32no—
398#474—32no—
399#464—31no—
400#464—31no—
401#464—32no—
402#464—32no—
403#463—31no—
404#463—32no—
405#463—31no—
406#463—32no—
407#462—31no—
408#462—32no—
409#462—32no—
410#461—32no—
411#461—31no—
412#461—32no—
413#460—31no—
414#459—31no—
415#446—32no—
416#446—32no—
417#446—32no—
418C8×Q8—32no—
419#442C2×D312yes—
420#441—32no—
421#441C2×D312yes—
422#440—32no—
423#440—32no—
424#440—32no—
425C4×Q16—32no—
426C4×Q16—32no—
427C4×SD16—32no—
428C4×SD16C2×D312yes—
429C4×SD16C2×D312yes—
430C4×D8—32no—
431#428—31no—
432C2×#107—31no—
433C2×#106C2×D311yescharacteristic
434#424—31no—
435#424—31no—
436C2×C4⋊C8—31no—
437#419—31no—
438#417—31no—
439#417—31no—
440#417—31no—
441#417C2×D311yescharacteristic
442#417C2×D311yescharacteristic
443#416—31no—
444#416—31no—
445C2×#103—31no—
446C2×#103—31no—
447#405—31no—
448#405C2×D311yescharacteristic
449C4×M16—31no—
450C3×#41—22no—
451C3×#41—22no—
452C3×#41—22no—
453C3×#41#4114yes—
454C2×C3×Q8C2411yescharacteristic
455C2×C3×Q8C2411yescharacteristic
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4C2411yescharacteristic
459C2×C3×D4C2411yescharacteristic
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4—22no—
465C22×C3×C4—22no—
466C22×C3×C4C2411yescharacteristic
467C2×#67—21no—
468C2×#67—21no—
469C2×#67—21no—
470C22×Dic3—21no—
471C22×Dic3—21no—
472C22×Dic3—21no—
473C22×Dic3—21no—
474C22×Dic3—22no—
475C22×Dic3C2×D411yescharacteristic
476C22×Dic3C2×D411yescharacteristic
477#235—22no—
478#235—22no—
479C2×D12C2411yescharacteristic
480C2×C4×D3—21no—
481C2×C4×D3—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6—21no—
485C2×Dic6—22no—
486C2×Dic6—22no—
487C2×Dic6C2×D412yes—
488C2×Dic6C2×D412yes—
489C2×Dic6C2411yescharacteristic
490C2×Dic6C2412yes—
491C3×Q16—22no—
492C3×SD16—22no—
493C3×SD16—22no—
494C3×D8—22no—
495C3×M16—22no—
496C2×C3×C8—22no—
497C2×C3×C8C2412yes—
498C2×C3×C8C2411yescharacteristic
499C2×C3×C8C2411yescharacteristic
500C3×C4⋊C4—21no—
501C3×C4⋊C4—21no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—22no—
504C3×C4⋊C4C2×D411yescharacteristic
505C3×C4⋊C4C2×D411yescharacteristic
506C3×C4⋊C4C2412yes—
507C3×C4⋊C4C2412yes—
508C3×C22⋊C4—22no—
509C3×C22⋊C4—22no—
510C3×C22⋊C4C2×D412yes—
511C3×C42—22no—
512C3×C42—22no—
513C3×C42C2412yes—
514#217—21no—
515#217—21no—
516#217—21no—
517#217—22no—
518#217—21no—
519#217—21no—
520#217—22no—
521#217—22no—
522#217C2×D412yes—
523#216—22no—
524#216—24no—
525#215—22no—
526#214—22no—
527#214—24no—
528#213—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—21no—
532(C2×D3)⋊C4—21no—
533(C2×D3)⋊C4—22no—
534C4⋊Dic3—22no—
535C4⋊Dic3—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—21no—
538C4⋊Dic3—22no—
539C4⋊Dic3—21no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3—21no—
544C4⋊Dic3C2×D412yes—
545C4⋊Dic3C2×D412yes—
546C4⋊Dic3C2×D411yescharacteristic
547C4⋊Dic3C2×D411yescharacteristic
548C4⋊Dic3C2411yescharacteristic
549C4⋊Dic3C2412yes—
550C4⋊Dic3C2411yescharacteristic
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4—21no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—21no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561Dic3⋊C4—22no—
562Dic3⋊C4—22no—
563Dic3⋊C4—22no—
564Dic3⋊C4C2×D412yes—
565Dic3⋊C4C2×D412yes—
566Dic3⋊C4C2×D412yes—
567Dic3⋊C4C2×D412yes—
568C4×Dic3—21no—
569C4×Dic3—22no—
570C4×Dic3—21no—
571C4×Dic3—21no—
572C4×Dic3—22no—
573C4×Dic3—22no—
574C4×Dic3—22no—
575C4×Dic3C2×D411yescharacteristic
576C4×Dic3C2×D411yescharacteristic
577C4×Dic3C2411yescharacteristic
578C4×Dic3C2412yes—
579C4×Dic3C2411yescharacteristic
580#208—22no—
581C2×C3⋊C8—22no—
582C2×C3⋊C8C2411yescharacteristic
583C2×C3⋊C8C2411yescharacteristic
584C2×C3⋊C8C2412yes—
585C2×#41—31no—
586C2×#41C22×D311yescharacteristic
587C2×#41C22×D311yescharacteristic
588C22×Q8—31no—
589#137—64no—
590#135—24no—
591#135—64no—
592C2×Q16—31no—
593C2×Q16—32no—
594C2×Q16C22×D311yescharacteristic
595C2×SD16—31no—
596C2×SD16—31no—
597C2×SD16—32no—
598C2×SD16C22×D311yescharacteristic
599C2×SD16C22×D311yescharacteristic
600C2×D8—31no—
601C2×D8C22×D311yescharacteristic
602C2×M16—31no—
603C2×M16C22×D311yescharacteristic
604C22×C8—31no—
605C22×C8C22×D311yescharacteristic
606C4⋊Q8—31no—
607C4⋊Q8—31no—
608C4⋊Q8—32no—
609C4⋊Q8—31no—
610C4⋊Q8—32no—
611C4⋊Q8—32no—
612C4⋊Q8—32no—
613C4⋊Q8—62no—
614C4⋊Q8—61no—
615C4⋊Q8—62no—
616C4⋊Q8—61no—
617#127—31no—
618#126—62no—
619#126—62no—
620#126—62no—
621#126—62no—
622#125—31no—
623#125—31no—
624#125—32no—
625#125—32no—
626#125—32no—
627#125—32no—
628#125—62no—
629#125—62no—
630#125—61no—
631#125—61no—
632#125—61no—
633#125—62no—
634#125—62no—
635#125—62no—
636#125—62no—
637#125—62no—
638#125—61no—
639#124—31no—
640#124—31no—
641#124—32no—
642#124—32no—
643#124—62no—
644#123—62no—
645#123—62no—
646#123—62no—
647#123—62no—
648C22⋊Q8—32no—
649C22⋊Q8—32no—
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—
659C22⋊Q8—62no—
660C22⋊Q8—62no—
661C22⋊Q8—61no—
662C22⋊Q8—61no—
663C22⋊Q8—62no—
664#121—61no—
665#121—61no—
666C4×Q8—32no—
667C4×Q8—32no—
668C4×Q8—31no—
669C4×Q8—31no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—32no—
673C4×Q8—32no—
674C4×Q8—62no—
675C4×Q8—62no—
676C4×Q8—62no—
677C4×Q8—61no—
678C4×Q8—61no—
679C4×Q8C22×D312yes—
680C4×Q8C22×D312yes—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—31no—
684C4×D4—31no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—61no—
688C4×D4—61no—
689C4×D4—62no—
690C4×D4—62no—
691C4×D4—62no—
692C4×D4—61no—
693C4×D4—61no—
694C4×D4C22×D312yes—
695C4×D4C22×D312yes—
696#117—21no—
697#117—21no—
698#117—31no—
699#117—31no—
700#117—62no—
701#117—61no—
702#117—61no—
703#117—61no—
704#117—62no—
705#117C22×D311yescharacteristic
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—61no—
710C2×C4⋊C4—61no—
711C2×C4⋊C4—62no—
712C2×C4⋊C4—62no—
713C2×C4⋊C4—61no—
714C2×C4⋊C4—61no—
715C2×C4⋊C4—61no—
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C42—31no—
719C2×C42—61no—
720C2×C42—61no—
721#107—32no—
722#107—32no—
723#107—32no—
724#106—32no—
725#106C22×D312yes—
726#106C22×D312yes—
727C4⋊C8—31no—
728C4⋊C8—31no—
729C4⋊C8—31no—
730C4⋊C8—31no—
731C4⋊C8—32no—
732C4⋊C8—32no—
733C4⋊C8—32no—
734C4⋊C8—32no—
735#103—31no—
736#103—31no—
737#103—32no—
738#103—32no—
739#103—32no—
740#103—31no—
741#103—31no—
742#103—32no—
743#103—32no—
744#103—32no—
745#103—32no—
746#103—32no—
747#103—32no—
748#103C22×D312yes—
749#103C22×D312yes—
750#102—31no—
751#102—31no—
752#102—32no—
753#102—31no—
754#102—31no—
755#102—32no—
756#102—32no—
757#102C22×D312yes—
758#102C22×D312yes—
759#97—32no—
760#97—32no—
761#97C22×D312yes—
762C4×C8—32no—
763C4×C8—32no—
764C4×C8C22×D312yes—
765C23×C3—21no—
766C23×C3—21no—
767C23×C3C22×D411yescharacteristic
768C22×D3—21no—
769C3×Q8—21no—
770C3×Q8—21no—
771C3×Q8—21no—
772C3×Q8C2×#4112yes—
773C3×D4—24no—
774C3×D4—21no—
775C3×D4—21no—
776C3×D4—21no—
777C3×D4—42no—
778C3×D4C2×#4112yes—
779C2×C3×C4—21no—
780C2×C3×C4—24no—
781C2×C3×C4—22no—
782C2×C3×C4—21no—
783C2×C3×C4—22no—
784C2×C3×C4—42no—
785C2×C3×C4—82no—
786C2×C3×C4—82no—
787C2×C3×C4—81no—
788C2×C3×C4—81no—
789C2×C3×C4C22×D412yes—
790C2×C3×C4C22×D412yes—
791C2×C3×C4C22×D411yescharacteristic
792C2×C3×C4C2×#4112yes—
793C2×C3×C42−1+412yes—
794C2×C3×C4C2511yescharacteristic
795#67—42no—
796#67—42no—
797#67—81no—
798C2×Dic3—21no—
799C2×Dic3—21no—
800C2×Dic3—22no—
801C2×Dic3—21no—
802C2×Dic3—22no—
803C2×Dic3—41no—
804C2×Dic3—41no—
805C2×Dic3—42no—
806C2×Dic3—82no—
807C2×Dic3—81no—
808C2×Dic3—81no—
809C2×Dic3—81no—
810C2×Dic3C22×D411yescharacteristic
811C2×Dic3C22×D411yescharacteristic
812C2×Dic3C22×D412yes—
813C2×Dic3C22×D411yescharacteristic
814C2×Dic3C22×D411yescharacteristic
815C2×Dic3C22×D412yes—
816D12—21no—
817D12—21no—
818C4×D3—42no—
819C4×D3—82no—
820Dic6—22no—
821Dic6—21no—
822Dic6—22no—
823Dic6—21no—
824Dic6—42no—
825Dic6—42no—
826Dic6—42no—
827Dic6—82no—
828Dic6—82no—
829C3×C8—21no—
830C3×C8—21no—
831C3×C8—22no—
832C3⋊C8—21no—
833C3⋊C8—21no—
834C3⋊C8—22no—
835#41—22no—
836#41—22no—
837#41—22no—
838#41—62no—
839#41—62no—
840#41#23514yes—
841C2×Q8—32no—
842C2×Q8—32no—
843C2×Q8—32no—
844C2×Q8—31no—
845C2×Q8—62no—
846C2×Q8—61no—
847C2×Q8—62no—
848C2×Q8—62no—
849C2×Q8—62no—
850C2×Q8C23×D311yescharacteristic
851C2×Q8C23×D311yescharacteristic
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—31no—
855C2×D4—61no—
856C2×D4—61no—
857C2×D4—61no—
858C2×D4C23×D311yescharacteristic
859C2×D4C23×D311yescharacteristic
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—31no—
867C22×C4—31no—
868C22×C4—62no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—62no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4C23×D311yescharacteristic
876Q16—22no—
877Q16—62no—
878Q16—64no—
879SD16—22no—
880SD16—22no—
881SD16—62no—
882SD16—62no—
883SD16—64no—
884D8—22no—
885D8—62no—
886M16—22no—
887M16—62no—
888C2×C8—22no—
889C2×C8—31no—
890C2×C8—32no—
891C2×C8—31no—
892C2×C8—62no—
893C2×C8C23×D312yes—
894C2×C8C23×D311yescharacteristic
895C2×C8C23×D311yescharacteristic
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—31no—
901C4⋊C4—32no—
902C4⋊C4—32no—
903C4⋊C4—31no—
904C4⋊C4—32no—
905C4⋊C4—32no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—31no—
909C4⋊C4—32no—
910C4⋊C4—31no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—62no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4—62no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—61no—
922C4⋊C4—61no—
923C4⋊C4—62no—
924C4⋊C4—61no—
925C4⋊C4—61no—
926C4⋊C4—62no—
927C4⋊C4—62no—
928C4⋊C4—61no—
929C4⋊C4—62no—
930C4⋊C4—62no—
931C4⋊C4—62no—
932C4⋊C4—62no—
933C4⋊C4—62no—
934C4⋊C4D3×D411yescharacteristic
935C4⋊C4D3×D411yescharacteristic
936C4⋊C4C23×D312yes—
937C4⋊C4C23×D312yes—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—32no—
941C22⋊C4—61no—
942C22⋊C4—62no—
943C22⋊C4—61no—
944C22⋊C4—61no—
945C22⋊C4—61no—
946C22⋊C4—61no—
947C22⋊C4—62no—
948C22⋊C4—62no—
949C22⋊C4—61no—
950C22⋊C4—62no—
951C22⋊C4—61no—
952C22⋊C4—62no—
953C22⋊C4—62no—
954C22⋊C4D3×D412yes—
955C42—22no—
956C42—22no—
957C42—31no—
958C42—31no—
959C42—31no—
960C42—32no—
961C42—31no—
962C42—62no—
963C42—62no—
964C42—61no—
965C42—61no—
966C42—62no—
967C42—62no—
968C42—61no—
969C42C23×D312yes—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—22no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3#54812yes—
979C22×C3C23×D411yescharacteristic
980C2×D3—41no—
981C2×D3—41no—
982C2×D3—41no—
983C3×C4—22no—
984C3×C4—22no—
985C3×C4—22no—
986C3×C4—42no—
987C3×C4—42no—
988C3×C4—41no—
989C3×C4#54812yes—
990C3×C4C22×#4111yescharacteristic
991C3×C4C2×2−1+411yescharacteristic
992Dic3—21no—
993Dic3—22no—
994Dic3—21no—
995Dic3—21no—
996Dic3—22no—
997Dic3—21no—
998Dic3—41no—
999Dic3—42no—
1000Dic3—41no—
1001Dic3—42no—
1002Dic3—41no—
1003C23—21no—
1004C23—21no—
1005C23—61no—
1006C23C2×D3×D411yescharacteristic
1007Q8—21no—
1008Q8—21no—
1009Q8—21no—
1010Q8—62no—
1011Q8—61no—
1012Q8—62no—
1013Q8—61no—
1014Q8—122no—
1015Q8—122no—
1016Q8—122no—
1017Q8—242no—
1018Q8—242no—
1019Q8C2×#23512yes—
1020D4—24no—
1021D4—21no—
1022D4—21no—
1023D4—21no—
1024D4—42no—
1025D4—61no—
1026D4—61no—
1027D4—122no—
1028D4—122no—
1029D4—241no—
1030D4C2×#23512yes—
1031C2×C4—21no—
1032C2×C4—24no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—32no—
1041C2×C4—32no—
1042C2×C4—42no—
1043C2×C4—62no—
1044C2×C4—61no—
1045C2×C4—61no—
1046C2×C4—61no—
1047C2×C4—62no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—81no—
1051C2×C4—81no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—122no—
1055C2×C4—122no—
1056C2×C4—242no—
1057C2×C4—241no—
1058C2×C4—242no—
1059C2×C4—241no—
1060C2×C4—241no—
1061C2×C4C2×#23512yes—
1062C2×C4C2×D3×D412yes—
1063C2×C4C2×D3×D412yes—
1064C2×C4C2×D3×D411yescharacteristic
1065C2×C4#101012yes—
1066C2×C4C24×D311yescharacteristic
1067C8—21no—
1068C8—21no—
1069C8—22no—
1070C8—61no—
1071C8—61no—
1072C8—62no—
1073C2×C3—22no—
1074C2×C3—42no—
1075C2×C3—81no—
1076C2×C3C2×#54811yescharacteristic
1077C2×C3#358411yescharacteristic
1078C2×C3#358611yescharacteristic
1079D3—81no—
1080C22—21no—
1081C22—21no—
1082C22—22no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—121no—
1089C22—121no—
1090C22—121no—
1091C22#555212yes—
1092C22C22×D3×D411yescharacteristic
1093C4—22no—
1094C4—22no—
1095C4—22no—
1096C4—42no—
1097C4—42no—
1098C4—41no—
1099C4—61no—
1100C4—61no—
1101C4—62no—
1102C4—61no—
1103C4—61no—
1104C4—62no—
1105C4—122no—
1106C4—121no—
1107C4—121no—
1108C4—121no—
1109C4—122no—
1110C4#555212yes—
1111C4C22×#23511yescharacteristic
1112C4C2×#101011yescharacteristic
1113C3#6135011yescharacteristic, complemented, Sylow
1114C2—22no—
1115C2—42no—
1116C2—81no—
1117C2—241no—
1118C2C2×#555211yescharacteristic
1119C2#8720611yescharacteristic
1120C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2952C2
socleC22×C3C23×D4
prime radical#83900C2
hypercenter#2952D3
hypocenterC3#61350
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #2952

Complements

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

NH ≅ G/Ntype
1. #85892C2semidirect
2. #85890C2semidirect
3. C3×#2952C2semidirect
4. #83902C2semidirect
6. #82572C2semidirect
7. #82559C2semidirect
8. #79854C2semidirect
9. #79852C2semidirect
10. #79818C2semidirect
11. #79817C2semidirect
12. #79628C2semidirect
13. #79627C2semidirect
14. #79623C2semidirect
15. #79620C2semidirect
16. C2×#4857C2semidirect
17. #79130C2semidirect
18. #78879C2semidirect
19. #78877C2semidirect
20. #78868C2semidirect
21. #78867C2semidirect
22. #78575C2semidirect
23. #78544C2semidirect
156. #2952D3semidirect
1113. C3#61350semidirect

Maximal subgroups

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

subgroupindex
#858922
#858902
C3×#29522
#839022
#839002
#825722
#825592
#798542
#798522
#798182
#798172
#796282
#796272
#796232
#796202
C2×#48572
#791302
#788792
#788772
#788682
#788672
#785752
#785442
#613503