Finite Group Databasebeta

← #11675946

Subgroups — #11675946

Order 768.

1734 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#85829C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×#2943C211yesmaximal, characteristic
4#83899C211yesmaximal, characteristic
5#83898C211yesmaximal, characteristic
6#82509C211yesmaximal, characteristic, complemented
7#82508C211yesmaximal, characteristic, complemented
8#79856C212yesmaximal, complemented
9#79855C212yesmaximal, complemented
10#79820C212yesmaximal, complemented
11#79819C212yesmaximal, complemented
12#79762C212yesmaximal, complemented
13#79761C212yesmaximal, complemented
14#79760C212yesmaximal, complemented
15#79759C212yesmaximal, complemented
16#79173C211yesmaximal, characteristic, complemented
17#79172C211yesmaximal, characteristic, complemented
18#78824C211yesmaximal, characteristic, complemented
19#78824C211yesmaximal, characteristic, complemented
20#78823C211yesmaximal, characteristic, complemented
21#78823C211yesmaximal, characteristic, complemented
22#78480C211yesmaximal, characteristic, complemented
23C2×#4702C211yesmaximal, characteristic, complemented
24#61380—31nomaximal, Sylow
25C2×C3×#135C2211yescharacteristic
26C3×C4×#41C2211yescharacteristic
27C3×C4×#41C2211yescharacteristic
28#5827C2211yescharacteristic
29#5827C2211yescharacteristic
30#5827C2211yescharacteristic
31#5827C2211yescharacteristic
32#5570C2212yes—
33#5569C2212yes—
34#5569C2212yes—
35Q8×Dic6C2212yes—
36#5543—22no—
37#5543C2212yes—
38#5539—22no—
39#5539—22no—
40#5539C2212yes—
41#5539C2212yes—
42D4×Dic6—22no—
43D4×Dic6C2212yes—
44#5519—21no—
45#5519—21no—
46#5519—21no—
47#5519—21no—
48#5519C2211yescharacteristic
49#5519C2211yescharacteristic
50#5519C2211yescharacteristic
51#5519C2211yescharacteristic
52#5470—21no—
53#5470—21no—
54#5470C2211yescharacteristic
55C2×#870—21no—
56C2×#870C2211yescharacteristic
57C2×#869—21no—
58C2×#869C2211yescharacteristic
59C3×#442C2211yescharacteristic
60C3×#442C2211yescharacteristic
61C3×#441C2211yescharacteristic
62C3×#441C2211yescharacteristic
63C3×#440C2211yescharacteristic
64C3×#440C2211yescharacteristic
65C3×#440C2211yescharacteristic
66C3×#440C2211yescharacteristic
67C3×#427C2211yescharacteristic
68C3×#416C2211yescharacteristic
69C3×#416C2211yescharacteristic
70C2×C3×#97C2211yescharacteristic
71#5232C2211yescharacteristic
72#5232C2211yescharacteristic
73#5232C2211yescharacteristic
74#5232C2211yescharacteristic
75#5184C2212yes—
76Dic3×Q16C2212yes—
77#5164C2212yes—
78#5164C2212yes—
79Dic3×SD16C2212yes—
80Dic3×SD16C2212yes—
81#5152C2212yes—
82Dic3×D8C2212yes—
83C2×#818C2211yescharacteristic
84C2×#818C2211yescharacteristic
85C2×#817C2211yescharacteristic
86C2×#817C2211yescharacteristic
87#5102C2211yescharacteristic
88#5102C2211yescharacteristic
89#5101C2211yescharacteristic
90#5101C2211yescharacteristic
91#5022C2212yes—
92#5022C2212yes—
93#5021C2212yes—
94#5020C2212yes—
95#5009C2212yes—
96#5009C2212yes—
97#5008C2212yes—
98#5007C2212yes—
99#4995C2211yescharacteristic
100#4995C2211yescharacteristic
101#4995C2211yescharacteristic
102#4995C2211yescharacteristic
103#4924C2211yescharacteristic
104#4878C2212yes—
105#4876C2212yes—
106#4876C2212yes—
107#4874C2212yes—
108#4858C2212yes—
109#4856C2212yes—
110#4856C2212yes—
111#4855C2212yes—
112#4799C2212yes—
113#4799C2212yes—
114#4796C2212yes—
115#4796C2212yes—
116#4793C2212yes—
117#4793C2212yes—
118#4791C2212yes—
119#4791C2212yes—
120#4766C2212yes—
121#4766C2212yes—
122#4763C2212yes—
123#4763C2212yes—
124#4761C2212yes—
125#4761C2212yes—
126#4759C2212yes—
127#4759C2212yes—
128#4702C2212yes—
129#4702C2212yes—
130#4702C2212yes—
131#4702C2212yes—
132#4701C2212yes—
133#4701C2212yes—
134#4701C2212yes—
135#4701C2212yes—
136#3504—31no—
137#3503—31no—
138#3390—32no—
139#3389—32no—
140#3388—32no—
141#3388—32no—
142#3387—32no—
143#3386—32no—
144#3385—32no—
145#3384—32no—
146#3164—31no—
147#3163—31no—
148C2×#501—31no—
149#3084—31no—
150#3084—31no—
151#3083—31no—
152#3083—31no—
153#3080—31no—
154#3079—31no—
155#2961—31no—
156#2952—31no—
157#2951—31no—
158#2943D311yescharacteristic
159C2×C3×#41C2311yescharacteristic
160C2×C3×#41C2311yescharacteristic
161C22×Dic6—21no—
162C22×Dic6—22no—
163C3×#135Q818yescomplemented
164C2×C3×Q16C2311yescharacteristic
165C2×C3×SD16C2311yescharacteristic
166C2×C3×SD16C2311yescharacteristic
167C2×C3×D8C2311yescharacteristic
168C22×C3×C8C2311yescharacteristic
169C22×C3×C8C2311yescharacteristic
170C3×C4×Q8C2311yescharacteristic
171C3×C4×Q8C2311yescharacteristic
172C3×C4×Q8C2311yescharacteristic
173C3×C4×Q8C2311yescharacteristic
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4—21no—
178C3×C4×D4C2311yescharacteristic
179C3×C4×D4C2311yescharacteristic
180C3×C4×D4C2311yescharacteristic
181C3×C4×D4C2311yescharacteristic
182C3×#117—21no—
183C3×#117—21no—
184C3×#117C2311yescharacteristic
185C3×#117C2311yescharacteristic
186C2×C3×C42—21no—
187C2×C3×C42—21no—
188C2×C3×C42C2311yescharacteristic
189Q8×Dic3C2312yes—
190Q8×Dic3C2312yes—
191Q8×Dic3C2312yes—
192Q8×Dic3C2312yes—
193D4×Dic3—22no—
194D4×Dic3—22no—
195D4×Dic3—22no—
196D4×Dic3—22no—
197D4×Dic3C2312yes—
198D4×Dic3C2312yes—
199D4×Dic3C2312yes—
200D4×Dic3C2312yes—
201#926—21no—
202#926—21no—
203#926—21no—
204#926—21no—
205#926C2311yescharacteristic
206#926C2311yescharacteristic
207C2×C4⋊Dic3—21no—
208C2×C4⋊Dic3—21no—
209C2×C4⋊Dic3—21no—
210C2×C4⋊Dic3—22no—
211C2×C4⋊Dic3—21no—
212C2×C4⋊Dic3—21no—
213C2×C4⋊Dic3C2311yescharacteristic
214C2×C4⋊Dic3C2311yescharacteristic
215C2×C4⋊Dic3C2311yescharacteristic
216C2×C4⋊Dic3C2311yescharacteristic
217#924—22no—
218#924—22no—
219#924—22no—
220#924—22no—
221#924D412yes—
222#924D412yes—
223C2×Dic3⋊C4—21no—
224C2×Dic3⋊C4—21no—
225C2×Dic3⋊C4—22no—
226C2×Dic3⋊C4—22no—
227C2×#208C2311yescharacteristic
228C2×#208C2311yescharacteristic
229#890—22no—
230#890—22no—
231#890—22no—
232#890—22no—
233#890C2312yes—
234#890C2312yes—
235#890C2312yes—
236#890C2312yes—
237#888—22no—
238#888—22no—
239#888—22no—
240#888—22no—
241#888C2312yes—
242#888C2312yes—
243#888C2312yes—
244#888C2312yes—
245#878—22no—
246#878—22no—
247#878—22no—
248#878—22no—
249#878—22no—
250#878—22no—
251#878—22no—
252#878—22no—
253#878—22no—
254#878—22no—
255#878—22no—
256#878—22no—
257#870—21no—
258#870—21no—
259#870—21no—
260#870—21no—
261#870—21no—
262#870—21no—
263#870—22no—
264#870—22no—
265#870D411yescharacteristic
266#870D411yescharacteristic
267#870C2312yes—
268#870C2312yes—
269#869—22no—
270#869—21no—
271#869—21no—
272#869—21no—
273#869—21no—
274#869—22no—
275#869—21no—
276#869—21no—
277#869D411yescharacteristic
278#869D411yescharacteristic
279#869C2312yes—
280#869C2312yes—
281C4×Dic6—22no—
282C4×Dic6—22no—
283C4×Dic6—22no—
284C4×Dic6—22no—
285C4×Dic6C2312yes—
286C4×Dic6C2312yes—
287C3×#107C2311yescharacteristic
288C3×#107C2311yescharacteristic
289C3×#106C2311yescharacteristic
290C3×#106C2311yescharacteristic
291C3×#103C2311yescharacteristic
292C3×#103C2311yescharacteristic
293C3×#103C2311yescharacteristic
294C3×#103C2311yescharacteristic
295C3×#102C2311yescharacteristic
296C3×#102C2311yescharacteristic
297C3×#102C2311yescharacteristic
298C3×#102C2311yescharacteristic
299C3×#97C2311yescharacteristic
300C3×#97C2311yescharacteristic
301C3×#97C2311yescharacteristic
302C3×#97C2311yescharacteristic
303#835C2312yes—
304#835C2312yes—
305#835C2312yes—
306#835C2312yes—
307#832C2312yes—
308#832C2312yes—
309#832C2312yes—
310#832C2312yes—
311#818C2312yes—
312#818C2312yes—
313#818C2312yes—
314#818C2312yes—
315#817C2312yes—
316#817C2312yes—
317#817C2312yes—
318#817C2312yes—
319#815C2312yes—
320#815C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2312yes—
324Dic3⋊C8C2312yes—
325C8×Dic3C2312yes—
326C8×Dic3C2312yes—
327#808C2312yes—
328#808C2312yes—
329#808C2312yes—
330#808C2312yes—
331#807C2312yes—
332#807C2312yes—
333#807C2312yes—
334#807C2312yes—
335C4⋊(C3⋊C8)C2312yes—
336C4⋊(C3⋊C8)C2312yes—
337C2×#135C2×D311yescharacteristic
338Q82—32no—
339#557—32no—
340#557—32no—
341#557—32no—
342#554—32no—
343#554—32no—
344#554—32no—
345#554—62no—
346#554—62no—
347#554—62no—
348D4×Q8—32no—
349D4×Q8—62no—
350#544—31no—
351#544—31no—
352#544—31no—
353#544—31no—
354#544—61no—
355#544—61no—
356#544—61no—
357#544—61no—
358#533—31no—
359#533—61no—
360#533—61no—
361C2×C4⋊Q8—31no—
362C2×C4⋊Q8—61no—
363C2×#125—31no—
364C2×#125—61no—
365#520—31no—
366#520—31no—
367#520—31no—
368#520—31no—
369C4×#41C2×D311yescharacteristic
370C4×#41C2×D311yescharacteristic
371#501—32no—
372#501—32no—
373#501—32no—
374#501—32no—
375#501—32no—
376#501—32no—
377#501—32no—
378#501—32no—
379#500—32no—
380#499—32no—
381#499—32no—
382#498—32no—
383#479—32no—
384#479—32no—
385#479—32no—
386#479—32no—
387#479—32no—
388#479—32no—
389#478—32no—
390#478—32no—
391#478—32no—
392#478—32no—
393#478—32no—
394#478—32no—
395#477—32no—
396#477—32no—
397#477—32no—
398#476—32no—
399#476—32no—
400#476—32no—
401#475—32no—
402#475—32no—
403#475—32no—
404#474—32no—
405#474—32no—
406#474—32no—
407#446—32no—
408#446—32no—
409#446—32no—
410#446—32no—
411#442—32no—
412#442C2×D311yescharacteristic
413#442C2×D311yescharacteristic
414#441—32no—
415#441C2×D311yescharacteristic
416#441C2×D311yescharacteristic
417#440—32no—
418#440—32no—
419#440C2×D311yescharacteristic
420#440C2×D311yescharacteristic
421#440C2×D311yescharacteristic
422#440C2×D311yescharacteristic
423C4×Q16—32no—
424C4×SD16—32no—
425C4×SD16—32no—
426C4×D8—32no—
427#428—31no—
428#428—31no—
429#428—31no—
430#428—31no—
431#427C2×D311yescharacteristic
432C2×#107—31no—
433C2×#107—31no—
434C2×#106—31no—
435C2×#106—31no—
436#424—31no—
437#424—31no—
438#423—31no—
439#417—31no—
440#417—31no—
441#417—31no—
442#417—31no—
443#416C2×D311yescharacteristic
444#416C2×D311yescharacteristic
445#405—31no—
446#405—31no—
447C2×#97C2×D311yescharacteristic
448C3×#41—22no—
449C3×#41—22no—
450C3×#41C2×Q814yes—
451C3×#41C2×Q814yescomplemented
452C2×C3×Q8C2411yescharacteristic
453C2×C3×Q8C2411yescharacteristic
454C2×C3×D4—21no—
455C2×C3×D4—21no—
456C2×C3×D4C2411yescharacteristic
457C2×C3×D4C2411yescharacteristic
458C22×C3×C4—21no—
459C22×C3×C4—21no—
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4C2×D411yescharacteristic
465C22×C3×C4C2×D411yescharacteristic
466C22×C3×C4C2411yescharacteristic
467C22×Dic3—21no—
468C22×Dic3—21no—
469C22×Dic3—21no—
470C22×Dic3—21no—
471C22×Dic3—22no—
472C22×Dic3—22no—
473C22×Dic3—22no—
474C22×Dic3—22no—
475C2×Dic6—22no—
476C2×Dic6—22no—
477C2×Dic6—22no—
478C2×Dic6—22no—
479C2×Dic6—22no—
480C2×Dic6—22no—
481C2×Dic6—84no—
482C2×Dic6—82no—
483C2×Dic6C2×D412yes—
484C2×Dic6C2×D412yes—
485C3×Q16C2×Q814yescomplemented
486C3×SD16C2×Q814yescomplemented
487C3×SD16C2×Q814yescomplemented
488C3×D8C2×Q814yescomplemented
489C2×C3×C8—22no—
490C2×C3×C8C2×Q814yescomplemented
491C2×C3×C8C2411yescharacteristic
492C2×C3×C8C2411yescharacteristic
493C2×C3×C8C2411yescharacteristic
494C2×C3×C8C2411yescharacteristic
495C3×C4⋊C4—21no—
496C3×C4⋊C4—21no—
497C3×C4⋊C4—21no—
498C3×C4⋊C4—21no—
499C3×C4⋊C4C2411yescharacteristic
500C3×C4⋊C4C2411yescharacteristic
501C3×C4⋊C4C2411yescharacteristic
502C3×C4⋊C4C2411yescharacteristic
503C3×C22⋊C4—21no—
504C3×C22⋊C4—21no—
505C3×C22⋊C4—21no—
506C3×C22⋊C4—21no—
507C3×C22⋊C4—21no—
508C3×C22⋊C4—21no—
509C3×C42—21no—
510C3×C42—21no—
511C3×C42—21no—
512C3×C42—21no—
513C3×C42—21no—
514C3×C42—21no—
515C3×C42C2×D411yescharacteristic
516C3×C42C2×D411yescharacteristic
517C3×C42C2411yescharacteristic
518C3×C42C2411yescharacteristic
519#217—22no—
520#217—22no—
521#217—22no—
522#217—22no—
523#217C2×D412yes—
524#217C2×D412yes—
525C4⋊Dic3—22no—
526C4⋊Dic3—21no—
527C4⋊Dic3—21no—
528C4⋊Dic3—22no—
529C4⋊Dic3—21no—
530C4⋊Dic3—21no—
531C4⋊Dic3—22no—
532C4⋊Dic3—22no—
533C4⋊Dic3—22no—
534C4⋊Dic3—22no—
535C4⋊Dic3—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3C2×D412yes—
540C4⋊Dic3C2×D412yes—
541C4⋊Dic3C2×D411yescharacteristic
542C4⋊Dic3C2×D411yescharacteristic
543C4⋊Dic3C2×D411yescharacteristic
544C4⋊Dic3C2×D411yescharacteristic
545C4⋊Dic3C2412yes—
546C4⋊Dic3C2412yes—
547C4⋊Dic3C2412yes—
548C4⋊Dic3C2412yes—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561Dic3⋊C4C2×D412yes—
562Dic3⋊C4C2×D412yes—
563Dic3⋊C4C2×D412yes—
564Dic3⋊C4C2×D412yes—
565C4×Dic3—22no—
566C4×Dic3—22no—
567C4×Dic3—22no—
568C4×Dic3—22no—
569C4×Dic3C2412yes—
570C4×Dic3C2412yes—
571#208—22no—
572#208—22no—
573C2×C3⋊C8C2412yes—
574C2×C3⋊C8C2412yes—
575C2×#41C22×D311yescharacteristic
576C2×#41C22×D311yescharacteristic
577C22×Q8—62no—
578C22×Q8—61no—
579#135Dic618yescomplemented
580C2×Q16C22×D311yescharacteristic
581C2×SD16C22×D311yescharacteristic
582C2×SD16C22×D311yescharacteristic
583C2×D8C22×D311yescharacteristic
584C2×M16—31no—
585C2×M16—31no—
586C22×C8C22×D311yescharacteristic
587C22×C8C22×D311yescharacteristic
588C4⋊Q8—32no—
589C4⋊Q8—32no—
590C4⋊Q8—32no—
591C4⋊Q8—32no—
592C4⋊Q8—31no—
593C4⋊Q8—31no—
594C4⋊Q8—32no—
595C4⋊Q8—32no—
596C4⋊Q8—61no—
597C4⋊Q8—61no—
598C4⋊Q8—62no—
599C4⋊Q8—61no—
600C4⋊Q8—61no—
601C4⋊Q8—62no—
602C4⋊Q8—62no—
603C4⋊Q8—62no—
604C4⋊Q8—62no—
605C4⋊Q8—62no—
606C4⋊Q8—61no—
607C4⋊Q8—61no—
608#125—32no—
609#125—32no—
610#125—32no—
611#125—32no—
612#125—31no—
613#125—31no—
614#125—32no—
615#125—32no—
616#125—61no—
617#125—61no—
618#125—62no—
619#125—62no—
620#125—61no—
621#125—61no—
622#125—62no—
623#125—62no—
624#125—62no—
625#125—62no—
626#125—61no—
627#125—61no—
628C22⋊Q8—32no—
629C22⋊Q8—32no—
630C22⋊Q8—62no—
631C22⋊Q8—62no—
632C22⋊Q8—62no—
633C22⋊Q8—62no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—62no—
645C22⋊Q8—62no—
646C4×Q8—32no—
647C4×Q8—32no—
648C4×Q8—32no—
649C4×Q8—32no—
650C4×Q8—32no—
651C4×Q8—32no—
652C4×Q8—62no—
653C4×Q8—62no—
654C4×Q8—62no—
655C4×Q8—62no—
656C4×Q8C22×D311yescharacteristic
657C4×Q8C22×D311yescharacteristic
658C4×Q8C22×D311yescharacteristic
659C4×Q8C22×D311yescharacteristic
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—32no—
665C4×D4—32no—
666C4×D4—32no—
667C4×D4—32no—
668C4×D4—62no—
669C4×D4—62no—
670C4×D4—62no—
671C4×D4—62no—
672C4×D4C22×D311yescharacteristic
673C4×D4C22×D311yescharacteristic
674C4×D4C22×D311yescharacteristic
675C4×D4C22×D311yescharacteristic
676#117—21no—
677#117—21no—
678#117—31no—
679#117—31no—
680#117—61no—
681#117—61no—
682#117—61no—
683#117—61no—
684#117C22×D311yescharacteristic
685#117C22×D311yescharacteristic
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—61no—
691C2×C4⋊C4—61no—
692C2×C4⋊C4—61no—
693C2×C4⋊C4—61no—
694C2×C4⋊C4—62no—
695C2×C4⋊C4—62no—
696C2×C4⋊C4—62no—
697C2×C4⋊C4—61no—
698C2×C4⋊C4—61no—
699C2×C4⋊C4—61no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42C22×D311yescharacteristic
703#107—32no—
704#107—32no—
705#107—32no—
706#107—32no—
707#107—32no—
708#107—32no—
709#107—32no—
710#107—32no—
711#107C22×D311yescharacteristic
712#107C22×D311yescharacteristic
713#106—32no—
714#106—32no—
715#106—32no—
716#106—32no—
717#106—32no—
718#106—32no—
719#106—32no—
720#106—32no—
721#106C22×D311yescharacteristic
722#106C22×D311yescharacteristic
723C4⋊C8—32no—
724C4⋊C8—32no—
725C4⋊C8—32no—
726C4⋊C8—32no—
727C4⋊C8—32no—
728C4⋊C8—32no—
729#103—32no—
730#103—32no—
731#103—32no—
732#103—32no—
733#103C22×D311yescharacteristic
734#103C22×D311yescharacteristic
735#103C22×D311yescharacteristic
736#103C22×D311yescharacteristic
737#102—32no—
738#102—32no—
739#102—32no—
740#102—32no—
741#102C22×D311yescharacteristic
742#102C22×D311yescharacteristic
743#102C22×D311yescharacteristic
744#102C22×D311yescharacteristic
745#97—32no—
746#97—32no—
747#97C22×D311yescharacteristic
748#97C22×D311yescharacteristic
749#97C22×D311yescharacteristic
750#97C22×D311yescharacteristic
751C4×C8—32no—
752C4×C8—32no—
753C23×C3—21no—
754C23×C3—21no—
755C23×C3C22×D411yescharacteristic
756C3×Q8—21no—
757C3×Q8—21no—
758C3×Q8C22×Q812yes—
759C3×Q8C22×Q812yes—
760C3×D4—24no—
761C3×D4—24no—
762C3×D4—21no—
763C3×D4—21no—
764C3×D4C22×Q812yes—
765C3×D4C22×Q812yes—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—24no—
769C2×C3×C4—24no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—41no—
775C2×C3×C4—41no—
776C2×C3×C4—42no—
777C2×C3×C4—42no—
778C2×C3×C4—81no—
779C2×C3×C4—81no—
780C2×C3×C4C22×D411yescharacteristic
781C2×C3×C4C22×D411yescharacteristic
782C2×C3×C4C22×D411yescharacteristic
783C2×C3×C4C22×D411yescharacteristic
784C2×C3×C4C22×D411yescharacteristic
785C2×C3×C4C22×Q812yes—
786C2×C3×C42−1+412yes—
787C2×C3×C4C2511yescharacteristic
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—22no—
791C2×Dic3—22no—
792C2×Dic3—82no—
793C2×Dic3—82no—
794C2×Dic3—82no—
795C2×Dic3—82no—
796C2×Dic3—81no—
797C2×Dic3—81no—
798C2×Dic3—81no—
799C2×Dic3—81no—
800C2×Dic3C22×D412yes—
801C2×Dic3C22×D412yes—
802C2×Dic3C22×D412yes—
803C2×Dic3C22×D412yes—
804Dic6—42no—
805Dic6—42no—
806Dic6—44no—
807Dic6—82no—
808Dic6—82no—
809Dic6—82no—
810Dic6—82no—
811Dic6—82no—
812C3×C8—21no—
813C3×C8—21no—
814C3×C8C22×Q812yes—
815C3×C8C22×Q812yes—
816C3⋊C8—22no—
817C3⋊C8—22no—
818#41—22no—
819#41—22no—
820#41C2×Dic614yes—
821#41C2×Dic614yescomplemented
822C2×Q8—32no—
823C2×Q8—32no—
824C2×Q8—62no—
825C2×Q8—62no—
826C2×Q8—62no—
827C2×Q8—62no—
828C2×Q8—62no—
829C2×Q8—62no—
830C2×Q8—242no—
831C2×Q8—244no—
832C2×Q8C23×D311yescharacteristic
833C2×Q8C23×D311yescharacteristic
834C2×D4—21no—
835C2×D4—21no—
836C2×D4C23×D311yescharacteristic
837C2×D4C23×D311yescharacteristic
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—62no—
845C22×C4—62no—
846C22×C4—62no—
847C22×C4—62no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4D3×D411yescharacteristic
853C22×C4D3×D411yescharacteristic
854C22×C4C23×D311yescharacteristic
855Q16C2×Dic614yescomplemented
856SD16C2×Dic614yescomplemented
857SD16C2×Dic614yescomplemented
858D8C2×Dic614yescomplemented
859M16—62no—
860M16—62no—
861C2×C8—22no—
862C2×C8—32no—
863C2×C8—32no—
864C2×C8C2×Dic614yescomplemented
865C2×C8C23×D311yescharacteristic
866C2×C8C23×D311yescharacteristic
867C2×C8C23×D311yescharacteristic
868C2×C8C23×D311yescharacteristic
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—31no—
876C4⋊C4—32no—
877C4⋊C4—32no—
878C4⋊C4—32no—
879C4⋊C4—31no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—62no—
890C4⋊C4—62no—
891C4⋊C4—62no—
892C4⋊C4—62no—
893C4⋊C4—62no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—62no—
898C4⋊C4—62no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—61no—
904C4⋊C4—61no—
905C4⋊C4—61no—
906C4⋊C4—61no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—62no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4C23×D311yescharacteristic
914C4⋊C4C23×D311yescharacteristic
915C4⋊C4C23×D311yescharacteristic
916C4⋊C4C23×D311yescharacteristic
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—21no—
920C22⋊C4—21no—
921C22⋊C4—21no—
922C22⋊C4—21no—
923C22⋊C4—32no—
924C22⋊C4—32no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C22⋊C4—62no—
928C22⋊C4—62no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—32no—
936C42—32no—
937C42—62no—
938C42—62no—
939C42—62no—
940C42—62no—
941C42D3×D411yescharacteristic
942C42D3×D411yescharacteristic
943C42C23×D311yescharacteristic
944C42C23×D311yescharacteristic
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—22no—
948C22×C3—22no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3D4×Q812yes—
954C22×C3C23×D411yescharacteristic
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—21no—
958C3×C4—21no—
959C3×C4—22no—
960C3×C4—22no—
961C3×C4—41no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—41no—
965C3×C4D4×Q812yes—
966C3×C4C23×Q811yescharacteristic
967C3×C4C2×2−1+411yescharacteristic
968Dic3—22no—
969Dic3—22no—
970Dic3—22no—
971Dic3—22no—
972Dic3—42no—
973Dic3—42no—
974Dic3—42no—
975Dic3—42no—
976C23—21no—
977C23—21no—
978C23C2×D3×D411yescharacteristic
979Q8—21no—
980Q8—21no—
981Q8—122no—
982Q8—122no—
983Q8—124no—
984Q8—242no—
985Q8—242no—
986Q8—242no—
987Q8—242no—
988Q8—242no—
989Q8C22×Dic612yes—
990Q8C22×Dic612yes—
991D4—24no—
992D4—24no—
993D4—21no—
994D4—21no—
995D4C22×Dic612yes—
996D4C22×Dic612yes—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—81no—
1018C2×C4—81no—
1019C2×C4—242no—
1020C2×C4—242no—
1021C2×C4—242no—
1022C2×C4—242no—
1023C2×C4—241no—
1024C2×C4—241no—
1025C2×C4—241no—
1026C2×C4—241no—
1027C2×C4C22×Dic612yes—
1028C2×C4C2×D3×D411yescharacteristic
1029C2×C4C2×D3×D411yescharacteristic
1030C2×C4C2×D3×D411yescharacteristic
1031C2×C4C2×D3×D411yescharacteristic
1032C2×C4C2×D3×D411yescharacteristic
1033C2×C4#101012yes—
1034C2×C4C24×D311yescharacteristic
1035C8—21no—
1036C8—21no—
1037C8—62no—
1038C8—62no—
1039C8C22×Dic612yes—
1040C8C22×Dic612yes—
1041C2×C3—22no—
1042C2×C3—42no—
1043C2×C3—42no—
1044C2×C3C2×D4×Q811yescharacteristic
1045C2×C3#358511yescharacteristic
1046C2×C3#358611yescharacteristic
1047C22—21no—
1048C22—21no—
1049C22—22no—
1050C22—22no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22D4×Dic612yes—
1056C22C22×D3×D411yescharacteristic
1057C4—21no—
1058C4—21no—
1059C4—21no—
1060C4—21no—
1061C4—22no—
1062C4—22no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—62no—
1071C4—122no—
1072C4—122no—
1073C4—122no—
1074C4—122no—
1075C4D4×Dic612yes—
1076C4C23×Dic611yescharacteristic
1077C4C2×#101011yescharacteristic
1078C3#6138011yescharacteristic, complemented, Sylow
1079C2—22no—
1080C2—42no—
1081C2—42no—
1082C2C2×D4×Dic611yescharacteristic
1083C2#8720011yescharacteristic
1084C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2943C2
socleC22×C3C23×D4
prime radicalC2×C3×#135C22
hypercenter#2943D3
hypocenterC3#61380
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2943

Complements

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

NH ≅ G/Ntype
1. #85829C2semidirect
2. #85828C2semidirect
6. #82509C2semidirect
7. #82508C2semidirect
8. #79856C2semidirect
9. #79855C2semidirect
10. #79820C2semidirect
11. #79819C2semidirect
12. #79762C2semidirect
13. #79761C2semidirect
14. #79760C2semidirect
15. #79759C2semidirect
16. #79173C2semidirect
17. #79172C2semidirect
18. #78824C2semidirect
19. #78824C2semidirect
20. #78823C2semidirect
21. #78823C2semidirect
22. #78480C2semidirect
23. C2×#4702C2semidirect
163. C3×#135Q8semidirect
451. C3×#41C2×Q8semidirect
485. C3×Q16C2×Q8semidirect
486. C3×SD16C2×Q8semidirect
487. C3×SD16C2×Q8semidirect
488. C3×D8C2×Q8semidirect
490. C2×C3×C8C2×Q8semidirect
579. #135Dic6semidirect
821. #41C2×Dic6semidirect
855. Q16C2×Dic6semidirect
856. SD16C2×Dic6semidirect
857. SD16C2×Dic6semidirect
858. D8C2×Dic6semidirect
864. C2×C8C2×Dic6semidirect
1078. C3#61380semidirect

Maximal subgroups

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

subgroupindex
#858292
#858282
C3×#29432
#838992
#838982
#825092
#825082
#798562
#798552
#798202
#798192
#797622
#797612
#797602
#797592
#791732
#791722
#788242
#788232
#784802
C2×#47022
#613803