Finite Group Databasebeta

← #11708909

Subgroups — #11708909

Order 768.

6184 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
1C3×#3504C211yesmaximal, characteristic, complemented
2#87038C214yesmaximal, complemented
3#87027C214yesmaximal, complemented
4#86943C218yesmaximal, complemented
5#86941C218yesmaximal, complemented
6#86930C214yesmaximal, complemented
7#86927C214yesmaximal, complemented
8#86604C214yesmaximal, complemented
9#86591C218yesmaximal, complemented
10#86286C211yesmaximal, characteristic, complemented
11#86271C214yesmaximal, complemented
12#86270C211yesmaximal, characteristic, complemented
13#86102C212yesmaximal, complemented
14#86089C212yesmaximal, complemented
15C2×C3⋊#564C212yesmaximal, complemented
16#85895C214yesmaximal, complemented
17#85831C212yesmaximal, complemented
18#63067—31nomaximal, Sylow
19C3×#557C2214yes—
20C3×#554C2214yes—
21C3×#554C2218yes—
22C3×#544C2214yes—
23C3×#544C2212yes—
24C3×#533C2211yescharacteristic
25C3×#533C2212yes—
26C2×C3×#125C2212yes—
27C2×C3×#125C2211yescharacteristic
28C3×#520C2212yes—
29C3×C4×#41C2211yescharacteristic
30#5824C2214yes—
31#5735C2214yes—
32#5735C2218yes—
33#5731C2218yes—
34#5731C2218yes—
35#5730C2214yes—
36#5729C2218yes—
37#5729C2218yes—
38#5729C2214yes—
39#5728C2214yes—
40#5721C2214yes—
41#5721C2218yes—
42#5721C2214yes—
43#5700C2211yescharacteristic
44#5699C2212yes—
45#5699C2214yes—
46#5698C2214yes—
47#5698C2214yes—
48#5696C2218yes—
49#5696C2218yes—
50#5696C2218yes—
51#5696C2218yes—
52#5694C2214yes—
53#5694C2214yes—
54#5693C2218yes—
55#5693C2218yes—
56#5692C2218yes—
57#5689C2214yes—
58D3×#125C2214yes—
59C3⋊#564C2211yescharacteristic
60C3⋊#564C2218yes—
61C3⋊#564C2218yes—
62C3⋊#564C2214yes—
63C3⋊#564C2212yes—
64C3⋊#564C2218yes—
65C3⋊#564C2218yes—
66C3⋊#564C2212yes—
67#5685C2214yes—
68#5685C2214yes—
69#5647C2214yes—
70#5646C2214yes—
71#5646C2218yes—
72#5645C2218yes—
73#5645C2218yes—
74#5642C2218yes—
75#5642C2218yes—
76#5642C2218yes—
77#5639C2218yes—
78#5638C2218yes—
79#5636C2218yes—
80#5636C2218yes—
81#5635C2218yes—
82#5625C2218yes—
83#5625C2218yes—
84#5624C2218yes—
85#5623C2218yes—
86#5623C2218yes—
87#5622C2218yes—
88#5583C2214yes—
89#5583C2214yes—
90#5583C2218yes—
91#5583C2218yes—
92#5581C2214yes—
93#5581C2218yes—
94#5580C2214yes—
95#5579C2212yes—
96#5578C2214yes—
97#5578C2214yes—
98#5570C2214yes—
99#5569C2218yes—
100#5567C2212yes—
101#5567C2214yes—
102#5567C2214yes—
103#5565C2214yes—
104#5564C2218yes—
105#5564C2218yes—
106#5555C2212yes—
107#5555C2214yes—
108#5546C2214yes—
109#5546C2214yes—
110#5543C2212yes—
111#5541C2214yes—
112#5541C2218yes—
113#5540C2218yes—
114#5539C2214yes—
115#5538C2218yes—
116C4×#237C2214yes—
117#5531C2218yes—
118#5531C2218yes—
119#5531C2218yes—
120#5529C2214yes—
121#5528C2214yes—
122#5518C2214yes—
123#5515C2218yes—
124#5515C2214yes—
125#5514C2218yes—
126#5513C2214yes—
127#5513C2218yes—
128#5511C2214yes—
129#5511C2218yes—
130#5500C2214yes—
131C2×#890C2218yes—
132C2×#889C2218yes—
133C2×#889C2218yes—
134#5479C2212yes—
135#5479C2214yes—
136#5470C2212yes—
137C2×#870C2214yes—
138#3563—34no—
139#3563—38no—
140#3563—38no—
141#3563—34no—
142#3563—34no—
143#3563—32no—
144#3556—34no—
145#3556—31no—
146#3553—38no—
147#3553—32no—
148#3531—31no—
149C2×#564—32no—
150#3515—34no—
151#3515—34no—
152#3515—32no—
153#3504—34no—
154#3504D311yescharacteristic, complemented
155C2×C3×#41C2311yescharacteristic
156C2×#237C2314yes—
157C3×C4⋊Q8C2312yes—
158C3×C4⋊Q8C2314yes—
159C3×C4⋊Q8C2318yes—
160C3×C4⋊Q8C2314yes—
161C3×#125C2314yes—
162C3×#125C2314yes—
163C3×#125C2311yescharacteristic
164C3×#125C2318yes—
165C3×#125C2314yes—
166C3×#125C2312yes—
167C3×#125C2311yescharacteristic
168C3×#125C2318yes—
169C3×#125C2312yes—
170C3×C22⋊Q8C2318yes—
171C3×C22⋊Q8C2318yes—
172C3×C22⋊Q8C2318yes—
173C3×C22⋊Q8C2318yes—
174C3×C22⋊Q8C2314yes—
175C3×C4×Q8C2314yes—
176C3×C4×Q8C2314yes—
177C3×C4×Q8C2312yes—
178C3×C4×Q8C2318yes—
179C3×C4×D4C2314yes—
180C3×C4×D4C2318yes—
181C3×C4×D4C2314yes—
182C3×C4×D4C2312yes—
183C3×#117C2312yes—
184C3×#117C2311yescharacteristic
185C3×#117C2312yes—
186C3×#117C2314yes—
187C2×C3×C4⋊C4C2314yes—
188C2×C3×C4⋊C4C2318yes—
189C2×C3×C4⋊C4C2314yes—
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C42C2312yes—
192C2×C3×C42C2311yescharacteristic
193#947C2314yes—
194#946C2318yes—
195#946C2314yes—
196#946C2318yes—
197#946C2318yes—
198#946C2314yes—
199#946C2318yes—
200#946C2314yes—
201Q8×Dic3C2318yes—
202Q8×Dic3C2318yes—
203Q8×Dic3C2318yes—
204#944C2318yes—
205#944C2318yes—
206#944C2314yes—
207#944C2318yes—
208#944C2314yes—
209#939C2318yes—
210#935C2318yes—
211D4×Dic3C2314yes—
212#930C2314yes—
213#930C2318yes—
214#930C2312yes—
215#929C2318yes—
216#929C2314yes—
217#929C2318yes—
218C4×#67C2318yes—
219C4×#67C2318yes—
220C4×#67C2318yes—
221C4×#67C2318yes—
222C4×#67C2314yes—
223#926C2318yes—
224#926C2314yes—
225C2×C4⋊Dic3C2314yes—
226C2×C4⋊Dic3C2314yes—
227C2×C4⋊Dic3C2318yes—
228#924C2312yes—
229#924C2318yes—
230#924C2314yes—
231#924C2314yes—
232#924C2314yes—
233#924C2318yes—
234C2×Dic3⋊C4C2318yes—
235C2×Dic3⋊C4C2318yes—
236C2×Dic3⋊C4C2318yes—
237C2×Dic3⋊C4C2318yes—
238C2×C4×Dic3C2318yes—
239#898C2318yes—
240#898C2314yes—
241#898C2314yes—
242#898C2318yes—
243#898C2318yes—
244#898C2318yes—
245#898C2318yes—
246#898C2318yes—
247#898C2318yes—
248#898C2318yes—
249#898C2318yes—
250#898C2314yes—
251#897C2314yes—
252#897C2318yes—
253#897C2314yes—
254#897C2314yes—
255#897C2314yes—
256#896C2314yes—
257#896C2318yes—
258#896C2318yes—
259#896C2314yes—
260#896C2318yes—
261#896C2318yes—
262#896C2318yes—
263#896C2314yes—
264#895C2314yes—
265#894C2318yes—
266#894C2314yes—
267#894C2314yes—
268#894C2318yes—
269#894C2318yes—
270#894C2314yes—
271#893C2318yes—
272#892C2318yes—
273#892C2318yes—
274#892C2318yes—
275#892C2314yes—
276D3×C4⋊C4C2318yes—
277D3×C4⋊C4C2318yes—
278D3×C4⋊C4C2314yes—
279D3×C4⋊C4C2314yes—
280#890C2318yes—
281#890C2318yes—
282#890C2318yes—
283#890C2318yes—
284#890C2318yes—
285#890C2318yes—
286#890C2318yes—
287#890C2318yes—
288#890C2318yes—
289#890C2318yes—
290#890C2314yes—
291#890C2314yes—
292#890C2314yes—
293#890C2318yes—
294#889C2318yes—
295#889C2318yes—
296#889C2318yes—
297#889C2318yes—
298#889C2318yes—
299#889C2318yes—
300#889C2318yes—
301#889C2318yes—
302#889C2314yes—
303#889C2314yes—
304#889C2314yes—
305#889C2318yes—
306#889C2318yes—
307#889C2318yes—
308#889C2318yes—
309#889C2318yes—
310#889C2318yes—
311#889C2318yes—
312#889C2318yes—
313#889C2318yes—
314#889C2318yes—
315#889C2318yes—
316#889C2318yes—
317#889C2318yes—
318#889C2318yes—
319#889C2318yes—
320#888C2318yes—
321#888C2314yes—
322#888C2314yes—
323#888C2318yes—
324#888C2318yes—
325#887C2318yes—
326#887C2318yes—
327#887C2314yes—
328#887C2318yes—
329#887C2314yes—
330#887C2314yes—
331#886C2318yes—
332#886C2318yes—
333#886C2318yes—
334#885C2314yes—
335#884C2314yes—
336#883C2318yes—
337#883C2314yes—
338#67⋊C4C2318yes—
339#67⋊C4C2318yes—
340#67⋊C4C2318yes—
341#879C2318yes—
342#879C2318yes—
343#879C2318yes—
344#879C2314yes—
345#878C2318yes—
346#878C2318yes—
347#878C2318yes—
348#877C2318yes—
349#877C2318yes—
350#877C2318yes—
351#876C2318yes—
352#876C2314yes—
353#876C2318yes—
354#876C2318yes—
355#875C2312yes—
356C4×D12C2314yes—
357C4×D12C2312yes—
358C4×D12C2314yes—
359#872C2314yes—
360#872C2318yes—
361#872C2318yes—
362#872C2318yes—
363#872C2314yes—
364C42×D3C2314yes—
365#870C2312yes—
366#870C2314yes—
367#870C2318yes—
368#870C2314yes—
369#870C2318yes—
370#870C2314yes—
371#870C2318yes—
372#870C2318yes—
373#870C2314yes—
374#869C2312yes—
375#869C2312yes—
376#869C2314yes—
377C4×Dic6C2312yes—
378C4×Dic6C2314yes—
379C4×Dic6C2314yes—
380C4×Dic6C2314yes—
381C4×Dic6C2314yes—
382C4×Dic6C2314yes—
383C4×Dic6C2314yes—
384C4×Dic6C2318yes—
385C4×Dic6C2318yes—
386#564—31no—
387#564—38no—
388#564—32no—
389#564—38no—
390#564—38no—
391#564—34no—
392#564—38no—
393#564—32no—
394#563—34no—
395#563—38no—
396#563—32no—
397#563—34no—
398#563—34no—
399#563—38no—
400#562—31no—
401#562—34no—
402#557—34no—
403#557—34no—
404#557—38no—
405#557—34no—
406#557—34no—
407#557—34no—
408#557—34no—
409#557—32no—
410#557—34no—
411#557—38no—
412#557C2×D314yes—
413#554—34no—
414#554—38no—
415#554—38no—
416#554—38no—
417#554—32no—
418#554—34no—
419#554—32no—
420#554—38no—
421#554—34no—
422#554C2×D314yes—
423#554C2×D318yes—
424#553—38no—
425#553—34no—
426#553—38no—
427#552—38no—
428#552—38no—
429#552—34no—
430#552—34no—
431#552—38no—
432#552—38no—
433#552—38no—
434#552—38no—
435#552—34no—
436#552—38no—
437#552—38no—
438#552—34no—
439#552—34no—
440#552—38no—
441#552—38no—
442#552—38no—
443#552—34no—
444#552—38no—
445#547—34no—
446#547—34no—
447#547—32no—
448#544—34no—
449#544—38no—
450#544—38no—
451#544—34no—
452#544—38no—
453#544—38no—
454#544—34no—
455#544C2×D314yes—
456#544C2×D312yes—
457#541—38no—
458#541—38no—
459#541—38no—
460#541—38no—
461#541—38no—
462#541—38no—
463#541—34no—
464#541—34no—
465#541—38no—
466#541—38no—
467#541—34no—
468#541—34no—
469#541—38no—
470#541—38no—
471#541—34no—
472#539—38no—
473#539—38no—
474#539—38no—
475#539—38no—
476#539—38no—
477#539—38no—
478#539—38no—
479#539—34no—
480#533—34no—
481#533—38no—
482#533—34no—
483#533—34no—
484#533—32no—
485#533C2×D311yescharacteristic
486#533C2×D312yes—
487#529—38no—
488#529—34no—
489#529—38no—
490#529—34no—
491#529—32no—
492#529—34no—
493C2×#125—34no—
494C2×#125—38no—
495C2×#125—38no—
496C2×#125—38no—
497C2×#125—34no—
498C2×#125C2×D312yes—
499C2×#125C2×D311yescharacteristic
500#520—34no—
501#520—34no—
502#520C2×D312yes—
503C4×#41—34no—
504C4×#41C2×D311yescharacteristic
505C3×#41—24no—
506C2×C3×Q8C2411yescharacteristic
507C2×C3×Q8C2414yes—
508C2×C3×Q8C2418yes—
509C2×C3×D4C2412yes—
510C2×C3×D4C2411yescharacteristic
511C22×C3×C4C2412yes—
512C22×C3×C4C2411yescharacteristic
513C22×C3×C4C2418yes—
514C22×C3×C4C2414yes—
515C22×C3×C4C2412yes—
516C22×C3×C4C2414yes—
517C2×#67C2418yes—
518C2×#67C2414yes—
519C22×Dic3C2418yes—
520C22×Dic3C2418yes—
521#237—216no—
522C2×D12C2412yes—
523C2×D12C2414yes—
524C2×C4×D3C2414yes—
525C2×C4×D3C2414yes—
526C2×C4×D3C2414yes—
527C2×C4×D3C2418yes—
528C2×C4×D3C2418yes—
529C2×Dic6C2414yes—
530C2×Dic6C2412yes—
531C2×Dic6C2414yes—
532C2×Dic6C2414yes—
533C2×Dic6C2418yes—
534C3×C4⋊C4C2414yes—
535C3×C4⋊C4C2414yes—
536C3×C4⋊C4C2412yes—
537C3×C4⋊C4C2418yes—
538C3×C4⋊C4C2418yes—
539C3×C4⋊C4C2418yes—
540C3×C4⋊C4C2414yes—
541C3×C4⋊C4C2418yes—
542C3×C4⋊C4C2412yes—
543C3×C4⋊C4C2418yes—
544C3×C4⋊C4C2414yes—
545C3×C4⋊C4C2412yes—
546C3×C4⋊C4C2414yes—
547C3×C4⋊C4C2414yes—
548C3×C4⋊C4C2418yes—
549C3×C22⋊C4C2414yes—
550C3×C22⋊C4C2418yes—
551C3×C22⋊C4C2414yes—
552C3×C22⋊C4C2412yes—
553C3×C42C2411yescharacteristic
554C3×C42C2412yes—
555C3×C42C2414yes—
556C3×C42C2418yes—
557C3×C42C2414yes—
558C3×C42C2411yescharacteristic
559C3×C42C2412yes—
560#217C2418yes—
561#217C2418yes—
562#217C2414yes—
563(C2×D3)⋊C4C2418yes—
564(C2×D3)⋊C4C2414yes—
565(C2×D3)⋊C4C2414yes—
566(C2×D3)⋊C4C2414yes—
567(C2×D3)⋊C4C2414yes—
568(C2×D3)⋊C4C2414yes—
569(C2×D3)⋊C4C2418yes—
570(C2×D3)⋊C4C2414yes—
571(C2×D3)⋊C4C2418yes—
572(C2×D3)⋊C4C2414yes—
573(C2×D3)⋊C4C2414yes—
574(C2×D3)⋊C4C2418yes—
575(C2×D3)⋊C4C2418yes—
576C4⋊Dic3C2414yes—
577C4⋊Dic3C2414yes—
578C4⋊Dic3C2418yes—
579C4⋊Dic3C2414yes—
580C4⋊Dic3C2412yes—
581C4⋊Dic3C2414yes—
582C4⋊Dic3C2418yes—
583C4⋊Dic3C2414yes—
584C4⋊Dic3C2418yes—
585C4⋊Dic3C2412yes—
586C4⋊Dic3C2418yes—
587C4⋊Dic3C2418yes—
588C4⋊Dic3C2418yes—
589C4⋊Dic3C2418yes—
590C4⋊Dic3C2414yes—
591Dic3⋊C4C2418yes—
592Dic3⋊C4C2418yes—
593Dic3⋊C4C2418yes—
594Dic3⋊C4C2418yes—
595Dic3⋊C4C2418yes—
596Dic3⋊C4C2418yes—
597Dic3⋊C4C2414yes—
598Dic3⋊C4C2414yes—
599Dic3⋊C4C2418yes—
600Dic3⋊C4C2414yes—
601Dic3⋊C4C2414yes—
602Dic3⋊C4C2414yes—
603Dic3⋊C4C2414yes—
604Dic3⋊C4C2418yes—
605Dic3⋊C4C2418yes—
606Dic3⋊C4C2418yes—
607Dic3⋊C4C2418yes—
608Dic3⋊C4C2418yes—
609Dic3⋊C4C2418yes—
610Dic3⋊C4C2414yes—
611Dic3⋊C4C2418yes—
612Dic3⋊C4C2418yes—
613Dic3⋊C4C2414yes—
614Dic3⋊C4C2418yes—
615Dic3⋊C4C2418yes—
616C4×Dic3C2414yes—
617C4×Dic3C2414yes—
618C4×Dic3C2418yes—
619C4×Dic3C2418yes—
620C4×Dic3C2418yes—
621C4×Dic3C2418yes—
622C4×Dic3C2418yes—
623C4×Dic3C2418yes—
624C4×Dic3C2414yes—
625C4×Dic3C2418yes—
626C2×#41—34no—
627C2×#41C22×D311yescharacteristic
628C4⋊Q8—38no—
629C4⋊Q8—34no—
630C4⋊Q8—34no—
631C4⋊Q8—38no—
632C4⋊Q8—38no—
633C4⋊Q8—38no—
634C4⋊Q8—34no—
635C4⋊Q8—34no—
636C4⋊Q8—38no—
637C4⋊Q8—38no—
638C4⋊Q8—34no—
639C4⋊Q8—32no—
640C4⋊Q8—32no—
641C4⋊Q8C22×D314yes—
642C4⋊Q8C22×D314yes—
643C4⋊Q8C22×D312yes—
644C4⋊Q8C22×D318yes—
645#126—38no—
646#126—38no—
647#126—38no—
648#126—34no—
649#126—34no—
650#126—34no—
651#126—38no—
652#126—38no—
653#126—38no—
654#126—38no—
655#126—38no—
656#126—38no—
657#126—38no—
658#126—34no—
659#126—38no—
660#126—38no—
661#126—38no—
662#126—34no—
663#126—38no—
664#126—38no—
665#125—34no—
666#125—34no—
667#125—34no—
668#125—38no—
669#125—38no—
670#125—38no—
671#125—38no—
672#125—38no—
673#125—38no—
674#125—38no—
675#125—38no—
676#125—38no—
677#125—38no—
678#125—38no—
679#125—38no—
680#125—38no—
681#125—38no—
682#125—38no—
683#125—38no—
684#125—38no—
685#125—38no—
686#125—38no—
687#125—38no—
688#125—34no—
689#125—34no—
690#125—38no—
691#125—38no—
692#125—34no—
693#125—38no—
694#125—38no—
695#125—38no—
696#125—38no—
697#125—38no—
698#125—38no—
699#125—38no—
700#125—38no—
701#125—38no—
702#125—38no—
703#125—38no—
704#125—38no—
705#125—32no—
706#125—34no—
707#125—38no—
708#125—34no—
709#125—34no—
710#125—38no—
711#125—34no—
712#125—38no—
713#125—38no—
714#125C22×D314yes—
715#125C22×D311yescharacteristic
716#125C22×D312yes—
717#125C22×D318yes—
718#125C22×D312yes—
719#125C22×D314yes—
720#125C22×D314yes—
721#125C22×D311yescharacteristic
722#125C22×D318yes—
723#124—34no—
724#124—34no—
725#124—32no—
726#123—38no—
727#123—38no—
728#123—34no—
729#123—38no—
730#123—34no—
731#123—34no—
732#123—34no—
733#123—38no—
734#123—38no—
735#123—38no—
736#123—38no—
737#123—38no—
738#123—38no—
739#123—34no—
740#123—38no—
741C22⋊Q8—34no—
742C22⋊Q8—38no—
743C22⋊Q8—34no—
744C22⋊Q8—34no—
745C22⋊Q8—38no—
746C22⋊Q8—38no—
747C22⋊Q8—38no—
748C22⋊Q8—32no—
749C22⋊Q8—34no—
750C22⋊Q8—34no—
751C22⋊Q8—38no—
752C22⋊Q8—34no—
753C22⋊Q8—38no—
754C22⋊Q8—34no—
755C22⋊Q8—38no—
756C22⋊Q8—34no—
757C22⋊Q8—34no—
758C22⋊Q8—34no—
759C22⋊Q8—34no—
760C22⋊Q8—34no—
761C22⋊Q8—34no—
762C22⋊Q8—38no—
763C22⋊Q8—38no—
764C22⋊Q8—38no—
765C22⋊Q8—38no—
766C22⋊Q8—38no—
767C22⋊Q8—38no—
768C22⋊Q8—38no—
769C22⋊Q8—38no—
770C22⋊Q8C22×D318yes—
771C22⋊Q8C22×D318yes—
772C22⋊Q8C22×D318yes—
773C22⋊Q8C22×D314yes—
774C22⋊Q8C22×D318yes—
775#121—38no—
776#121—38no—
777#121—34no—
778#121—32no—
779#121—34no—
780#121—34no—
781C4×Q8—38no—
782C4×Q8—38no—
783C4×Q8—38no—
784C4×Q8—34no—
785C4×Q8—34no—
786C4×Q8—34no—
787C4×Q8—38no—
788C4×Q8—38no—
789C4×Q8—38no—
790C4×Q8—34no—
791C4×Q8—34no—
792C4×Q8—34no—
793C4×Q8—34no—
794C4×Q8—32no—
795C4×Q8—38no—
796C4×Q8—34no—
797C4×Q8—38no—
798C4×Q8—34no—
799C4×Q8C22×D312yes—
800C4×Q8C22×D314yes—
801C4×Q8C22×D314yes—
802C4×Q8C22×D318yes—
803C4×D4—34no—
804C4×D4—38no—
805C4×D4—38no—
806C4×D4—38no—
807C4×D4—34no—
808C4×D4—38no—
809C4×D4—38no—
810C4×D4—38no—
811C4×D4—38no—
812C4×D4—38no—
813C4×D4—34no—
814C4×D4—32no—
815C4×D4—34no—
816C4×D4C22×D314yes—
817C4×D4C22×D312yes—
818C4×D4C22×D314yes—
819C4×D4C22×D318yes—
820#117—38no—
821#117—34no—
822#117—34no—
823#117—38no—
824#117—38no—
825#117—38no—
826#117—38no—
827#117—38no—
828#117—38no—
829#117—34no—
830#117—34no—
831#117—38no—
832#117—38no—
833#117—38no—
834#117C22×D311yescharacteristic
835#117C22×D312yes—
836#117C22×D312yes—
837#117C22×D314yes—
838C2×C4⋊C4—38no—
839C2×C4⋊C4—38no—
840C2×C4⋊C4—38no—
841C2×C4⋊C4—38no—
842C2×C4⋊C4—34no—
843C2×C4⋊C4—38no—
844C2×C4⋊C4—34no—
845C2×C4⋊C4—34no—
846C2×C4⋊C4—34no—
847C2×C4⋊C4—38no—
848C2×C4⋊C4—38no—
849C2×C4⋊C4C22×D314yes—
850C2×C4⋊C4C22×D312yes—
851C2×C4⋊C4C22×D318yes—
852C2×C4⋊C4C22×D314yes—
853C2×C42—38no—
854C2×C42—34no—
855C2×C42C22×D312yes—
856C2×C42C22×D311yescharacteristic
857C23×C3C2511yescharacteristic
858C23×C3C2512yes—
859C22×D3C2514yes—
860C3×Q8—22no—
861C3×Q8—44no—
862C3×Q8—48no—
863C3×D4—24no—
864C3×D42−1+414yes—
865C2×C3×C4—24no—
866C2×C3×C4—22no—
867C2×C3×C4—42no—
868C2×C3×C4—44no—
869C2×C3×C4—48no—
870C2×C3×C4—44no—
871C2×C3×C4C2512yes—
872C2×C3×C4C2514yes—
873C2×C3×C4C2514yes—
874C2×C3×C4C2518yes—
875C2×C3×C4C2514yes—
876C2×C3×C4C2512yes—
877C2×C3×C4C2511yescharacteristic
878C2×C3×C4C2512yes—
879C2×C3×C4C2511yescharacteristic
880#67—216no—
881#67—44no—
882C2×Dic3—216no—
883C2×Dic3—48no—
884C2×Dic3C2514yes—
885C2×Dic3C2518yes—
886C2×Dic3C2514yes—
887C2×Dic3C2518yes—
888C2×Dic3C2514yes—
889D12—42no—
890D12—44no—
891C4×D3—28no—
892C4×D3—44no—
893C4×D3—48no—
894C4×D3—48no—
895C4×D3—44no—
896Dic6—28no—
897Dic6—42no—
898Dic6—48no—
899Dic6—44no—
900Dic6—44no—
901#41—24no—
902#41—616no—
903C2×Q8—34no—
904C2×Q8—38no—
905C2×Q8—34no—
906C2×Q8—32no—
907C2×Q8—34no—
908C2×Q8C23×D311yescharacteristic
909C2×Q8C23×D318yes—
910C2×Q8C23×D314yes—
911C2×D4—38no—
912C2×D4—34no—
913C2×D4—34no—
914C2×D4—32no—
915C2×D4C23×D312yes—
916C2×D4C23×D311yescharacteristic
917C22×C4—38no—
918C22×C4—38no—
919C22×C4—34no—
920C22×C4—34no—
921C22×C4—34no—
922C22×C4—38no—
923C22×C4—38no—
924C22×C4C23×D312yes—
925C22×C4C23×D311yescharacteristic
926C22×C4C23×D318yes—
927C22×C4C23×D314yes—
928C22×C4C23×D312yes—
929C22×C4C23×D314yes—
930C4⋊C4—34no—
931C4⋊C4—38no—
932C4⋊C4—38no—
933C4⋊C4—34no—
934C4⋊C4—34no—
935C4⋊C4—34no—
936C4⋊C4—34no—
937C4⋊C4—32no—
938C4⋊C4—34no—
939C4⋊C4—32no—
940C4⋊C4—38no—
941C4⋊C4—38no—
942C4⋊C4—38no—
943C4⋊C4—38no—
944C4⋊C4—34no—
945C4⋊C4—38no—
946C4⋊C4—38no—
947C4⋊C4—34no—
948C4⋊C4—38no—
949C4⋊C4—38no—
950C4⋊C4—38no—
951C4⋊C4—38no—
952C4⋊C4—38no—
953C4⋊C4—38no—
954C4⋊C4—38no—
955C4⋊C4—38no—
956C4⋊C4—38no—
957C4⋊C4—38no—
958C4⋊C4—38no—
959C4⋊C4—38no—
960C4⋊C4—34no—
961C4⋊C4—34no—
962C4⋊C4—38no—
963C4⋊C4—38no—
964C4⋊C4—34no—
965C4⋊C4—34no—
966C4⋊C4—34no—
967C4⋊C4—38no—
968C4⋊C4—34no—
969C4⋊C4—38no—
970C4⋊C4C23×D312yes—
971C4⋊C4C23×D314yes—
972C4⋊C4C23×D318yes—
973C4⋊C4C23×D318yes—
974C4⋊C4C23×D314yes—
975C4⋊C4C23×D312yes—
976C4⋊C4C23×D314yes—
977C4⋊C4C23×D318yes—
978C4⋊C4C23×D318yes—
979C4⋊C4C23×D318yes—
980C4⋊C4C23×D318yes—
981C4⋊C4C23×D312yes—
982C4⋊C4C23×D314yes—
983C4⋊C4C23×D314yes—
984C4⋊C4C23×D314yes—
985C22⋊C4—38no—
986C22⋊C4—38no—
987C22⋊C4—34no—
988C22⋊C4—38no—
989C22⋊C4—38no—
990C22⋊C4—38no—
991C22⋊C4—38no—
992C22⋊C4—34no—
993C22⋊C4—34no—
994C22⋊C4—34no—
995C22⋊C4—34no—
996C22⋊C4—34no—
997C22⋊C4—34no—
998C22⋊C4—34no—
999C22⋊C4—34no—
1000C22⋊C4—38no—
1001C22⋊C4C23×D314yes—
1002C22⋊C4C23×D318yes—
1003C22⋊C4C23×D314yes—
1004C22⋊C4C23×D312yes—
1005C42—34no—
1006C42—38no—
1007C42—34no—
1008C42—34no—
1009C42—38no—
1010C42—38no—
1011C42—38no—
1012C42—38no—
1013C42—38no—
1014C42—38no—
1015C42C23×D314yes—
1016C42C23×D311yescharacteristic
1017C42C23×D312yes—
1018C42C23×D312yes—
1019C42C23×D311yescharacteristic
1020C42C23×D314yes—
1021C42C23×D318yes—
1022C22×C3—24no—
1023C22×C3—21no—
1024C22×C3—22no—
1025C22×C3C2×2−1+414yes—
1026C22×C3C2611yescharacteristic
1027C2×D3—24no—
1028C2×D3—24no—
1029C2×D3—24no—
1030C3×C4—21no—
1031C3×C4—22no—
1032C3×C4—22no—
1033C3×C4—28no—
1034C3×C4—24no—
1035C3×C4—22no—
1036C3×C4—24no—
1037C3×C4—24no—
1038C3×C4C2×2−1+412yes—
1039Dic3—28no—
1040Dic3—24no—
1041Dic3—24no—
1042Dic3—28no—
1043Dic3—24no—
1044C23—34no—
1045C23C24×D311yescharacteristic
1046C23C24×D312yes—
1047Q8—22no—
1048Q8—44no—
1049Q8—48no—
1050Q8—68no—
1051Q8—122no—
1052Q8—128no—
1053Q8—124no—
1054Q8—124no—
1055D4—24no—
1056D4—616no—
1057D4—122no—
1058D4—124no—
1059D4—124no—
1060D4#100714yes—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—34no—
1064C2×C4—38no—
1065C2×C4—34no—
1066C2×C4—38no—
1067C2×C4—34no—
1068C2×C4—44no—
1069C2×C4—42no—
1070C2×C4—48no—
1071C2×C4—44no—
1072C2×C4—616no—
1073C2×C4—68no—
1074C2×C4—124no—
1075C2×C4—128no—
1076C2×C4—128no—
1077C2×C4—124no—
1078C2×C4—128no—
1079C2×C4C24×D312yes—
1080C2×C4C24×D314yes—
1081C2×C4C24×D318yes—
1082C2×C4C24×D314yes—
1083C2×C4C24×D314yes—
1084C2×C4C24×D312yes—
1085C2×C4C24×D311yescharacteristic
1086C2×C4C24×D312yes—
1087C2×C4C24×D311yescharacteristic
1088C2×C3—24no—
1089C2×C3—41no—
1090C2×C3C22×2−1+411yescharacteristic
1091C2×C32−1+612yes—
1092D3—44no—
1093C22—24no—
1094C22—21no—
1095C22—22no—
1096C22—64no—
1097C22—64no—
1098C22—64no—
1099C22C2×#100714yes—
1100C22C25×D311yescharacteristic
1101C4—21no—
1102C4—22no—
1103C4—22no—
1104C4—24no—
1105C4—28no—
1106C4—24no—
1107C4—22no—
1108C4—24no—
1109C4—64no—
1110C4—68no—
1111C4—64no—
1112C4—68no—
1113C4—64no—
1114C4C2×#100712yes—
1115C3#6306711yescharacteristic, complemented, Sylow
1116C2—24no—
1117C2—41no—
1118C2—124no—
1119C2C22×#100711yescharacteristic
1120C2#8757212yes—
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3504C2
hypercenter#3504D3
hypocenterC3#63067
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. C3×#3504C2semidirect
2. #87038C2semidirect
3. #87027C2semidirect
4. #86943C2semidirect
5. #86941C2semidirect
6. #86930C2semidirect
7. #86927C2semidirect
8. #86604C2semidirect
9. #86591C2semidirect
10. #86286C2semidirect
11. #86271C2semidirect
12. #86270C2semidirect
13. #86102C2semidirect
14. #86089C2semidirect
15. C2×C3⋊#564C2semidirect
16. #85895C2semidirect
17. #85831C2semidirect
154. #3504D3semidirect
1115. C3#63067semidirect

Maximal subgroups

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

subgroupindex
C3×#35042
#870382
#870272
#869432
#869412
#869302
#869272
#866042
#865912
#862862
#862712
#862702
#861022
#860892
C2×C3⋊#5642
#858952
#858312
#630673