Finite Group Databasebeta

← #11675952

Subgroups — #11675952

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#85890C211yesmaximal, characteristic, complemented
2#85889C211yesmaximal, characteristic, complemented
3C3×#2952C211yesmaximal, characteristic
4#83898C211yesmaximal, characteristic
5#83897C211yesmaximal, characteristic
6#82560C211yesmaximal, characteristic, complemented
7#82559C211yesmaximal, characteristic, complemented
8#79856C212yesmaximal, complemented
9#79855C212yesmaximal, complemented
10#79820C212yesmaximal, complemented
11#79819C212yesmaximal, complemented
12#79636C212yesmaximal, complemented
13#79636C212yesmaximal, complemented
14#79635C212yesmaximal, complemented
15#79634C212yesmaximal, complemented
16#79110C211yesmaximal, characteristic, complemented
17C2×#4856C211yesmaximal, characteristic, complemented
18#78873C211yesmaximal, characteristic, complemented
19#78872C211yesmaximal, characteristic, complemented
20#78871C211yesmaximal, characteristic, complemented
21#78870C211yesmaximal, characteristic, complemented
22#78546C211yesmaximal, characteristic, complemented
23#78543C211yesmaximal, characteristic, complemented
24#61380—31nomaximal, Sylow
25C2×C3×#135C2211yescharacteristic
26C3×#520C2211yescharacteristic
27C3×#520C2211yescharacteristic
28#5827C2211yescharacteristic
29#5827C2211yescharacteristic
30Dic3×#41C2211yescharacteristic
31Dic3×#41C2211yescharacteristic
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#5519C2211yescharacteristic
47#5519C2211yescharacteristic
48#5517—21no—
49#5517—21no—
50#5517C2211yescharacteristic
51#5500—21no—
52#5500—21no—
53#5500C2211yescharacteristic
54#5500C2211yescharacteristic
55C2×#890—21no—
56C2×#890C2211yescharacteristic
57C2×#888—21no—
58C2×#888C2211yescharacteristic
59C3×#442C2212yes—
60C3×#441C2212yes—
61C3×C4×SD16C2212yes—
62C3×C4×SD16C2212yes—
63C2×C3×#106C2211yescharacteristic
64C3×#417C2211yescharacteristic
65C3×#417C2211yescharacteristic
66C3×#405C2211yescharacteristic
67#5233C2211yescharacteristic
68#5233C2211yescharacteristic
69#5232C2211yescharacteristic
70#5232C2211yescharacteristic
71#5184C2211yescharacteristic
72#5184C2211yescharacteristic
73Dic3×Q16C2212yes—
74#5164C2211yescharacteristic
75#5164C2212yes—
76#5164C2211yescharacteristic
77#5164C2212yes—
78#5164C2211yescharacteristic
79#5164C2211yescharacteristic
80#5152C2211yescharacteristic
81#5152C2211yescharacteristic
82Dic3×D8C2212yes—
83#5121C2211yescharacteristic
84#5121C2211yescharacteristic
85#5119C2211yescharacteristic
86#5118C2211yescharacteristic
87#5106C2211yescharacteristic
88C2×#818C2211yescharacteristic
89#5101C2211yescharacteristic
90C2×#815C2211yescharacteristic
91#5022C2212yes—
92#5022C2212yes—
93#5021C2212yes—
94#5020C2212yes—
95#5009C2212yes—
96#5009C2212yes—
97#5008C2212yes—
98#5007C2212yes—
99#4999C2211yescharacteristic
100#4964C2211yescharacteristic
101#4964C2211yescharacteristic
102C2×#808C2211yescharacteristic
103C2×#807C2211yescharacteristic
104#4858C2212yes—
105#4856C2212yes—
106#4856C2212yes—
107#4856C2212yes—
108#4856C2212yes—
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#4701C2212yes—
131#4701C2212yes—
132#4683C2212yes—
133#4682C2212yes—
134#4679C2212yes—
135#4679C2212yes—
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#2952D311yescharacteristic
157#2951—31no—
158#2943—31no—
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
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
183Q8×Dic3C2312yes—
184Q8×Dic3C2312yes—
185Q8×Dic3C2311yescharacteristic
186Q8×Dic3C2311yescharacteristic
187Q8×Dic3C2311yescharacteristic
188Q8×Dic3C2311yescharacteristic
189D4×Dic3—21no—
190D4×Dic3—21no—
191D4×Dic3—21no—
192D4×Dic3—21no—
193D4×Dic3—22no—
194D4×Dic3—22no—
195D4×Dic3C2312yes—
196D4×Dic3C2312yes—
197D4×Dic3C2311yescharacteristic
198D4×Dic3C2311yescharacteristic
199D4×Dic3C2311yescharacteristic
200D4×Dic3C2311yescharacteristic
201#926—21no—
202#926—21no—
203#926—21no—
204#926—21no—
205#926C2311yescharacteristic
206#926C2311yescharacteristic
207#926C2311yescharacteristic
208C2×C4⋊Dic3—21no—
209C2×C4⋊Dic3—21no—
210C2×C4⋊Dic3—21no—
211C2×C4⋊Dic3—22no—
212C2×C4⋊Dic3C2311yescharacteristic
213C2×C4⋊Dic3C2311yescharacteristic
214#924—22no—
215#924—22no—
216#924—22no—
217#924—22no—
218#924—22no—
219#924—22no—
220C2×Dic3⋊C4—21no—
221C2×Dic3⋊C4—21no—
222C2×Dic3⋊C4—22no—
223C2×Dic3⋊C4—22no—
224C2×C4×Dic3—21no—
225C2×C4×Dic3—21no—
226C2×C4×Dic3C2311yescharacteristic
227C2×#208C2311yescharacteristic
228C22×C3⋊C8C2311yescharacteristic
229#890—21no—
230#890—21no—
231#890—21no—
232#890—22no—
233#890—21no—
234#890—22no—
235#890—22no—
236#890—22no—
237#890—21no—
238#890—21no—
239#890D411yescharacteristic
240#890D411yescharacteristic
241#890C2312yes—
242#890C2312yes—
243#890C2312yes—
244#890C2312yes—
245#888—22no—
246#888—22no—
247#888—21no—
248#888—21no—
249#888—21no—
250#888—21no—
251#888—22no—
252#888—22no—
253#888—21no—
254#888—21no—
255#888D411yescharacteristic
256#888D411yescharacteristic
257#888C2312yes—
258#888C2312yes—
259#888C2312yes—
260#888C2312yes—
261#878—22no—
262#878—22no—
263#878—22no—
264#878—22no—
265#878—22no—
266#878—22no—
267#878—22no—
268#878—22no—
269#878—22no—
270#878—22no—
271#878D412yes—
272#878D412yes—
273#870—22no—
274#870—22no—
275#870C2312yes—
276#870C2312yes—
277#869—22no—
278#869—22no—
279#869C2312yes—
280#869C2312yes—
281C4×Dic6—22no—
282C4×Dic6—22no—
283C4×Dic6—22no—
284C4×Dic6—22no—
285C4×Dic6C2312yes—
286C4×Dic6C2312yes—
287C3×#106C2312yes—
288C3×#106C2312yes—
289C3×#103C2312yes—
290C3×#103C2312yes—
291C3×#102C2312yes—
292C3×#102C2312yes—
293C3×#97C2312yes—
294C3×C4×C8C2312yes—
295#835C2312yes—
296#835C2312yes—
297#835C2311yescharacteristic
298#835C2311yescharacteristic
299#835C2311yescharacteristic
300#835C2311yescharacteristic
301#832C2312yes—
302#832C2312yes—
303#832C2311yescharacteristic
304#832C2311yescharacteristic
305#832C2311yescharacteristic
306#832C2311yescharacteristic
307#818C2312yes—
308#818C2312yes—
309#818C2312yes—
310#818C2311yescharacteristic
311#818C2312yes—
312#818C2311yescharacteristic
313#817C2312yes—
314#817C2312yes—
315#817C2311yescharacteristic
316#817C2311yescharacteristic
317#815C2311yescharacteristic
318#815C2311yescharacteristic
319#815C2311yescharacteristic
320#815C2311yescharacteristic
321#815C2312yes—
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2312yes—
324Dic3⋊C8C2312yes—
325Dic3⋊C8C2312yes—
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#520C2×D311yescharacteristic
368#520C2×D311yescharacteristic
369C4×#41—31no—
370C4×#41—31no—
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—31no—
412#442—31no—
413#442C2×D312yes—
414#441—31no—
415#441—31no—
416#441C2×D312yes—
417#440—31no—
418#440—32no—
419#440—31no—
420#440—32no—
421#440—31no—
422#440—31no—
423C4×Q16—32no—
424C4×SD16C2×D312yes—
425C4×SD16C2×D312yes—
426C4×D8—32no—
427#428—31no—
428#428—31no—
429#428—31no—
430#428—31no—
431#427—31no—
432C2×#107—31no—
433C2×#107—31no—
434C2×#106—31no—
435C2×#106C2×D311yescharacteristic
436#424—31no—
437#424—31no—
438#423—31no—
439#417—31no—
440#417—31no—
441#417C2×D311yescharacteristic
442#417C2×D311yescharacteristic
443#416—31no—
444#416—31no—
445#405—31no—
446#405C2×D311yescharacteristic
447C2×#97—31no—
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—22no—
463C22×C3×C4—22no—
464C22×C3×C4C2411yescharacteristic
465C22×Dic3—21no—
466C22×Dic3—21no—
467C22×Dic3—21no—
468C22×Dic3—21no—
469C22×Dic3—21no—
470C22×Dic3—21no—
471C22×Dic3—22no—
472C22×Dic3—22no—
473C22×Dic3C2×D411yescharacteristic
474C22×Dic3C2×D411yescharacteristic
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
489C3×M16—22no—
490C2×C3×C8C2×Q814yescomplemented
491C2×C3×C8C2412yes—
492C2×C3×C8C2411yescharacteristic
493C2×C3×C8C2411yescharacteristic
494C3×C4⋊C4—21no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—21no—
497C3×C4⋊C4—22no—
498C3×C4⋊C4C2×D411yescharacteristic
499C3×C4⋊C4C2×D411yescharacteristic
500C3×C4⋊C4C2412yes—
501C3×C4⋊C4C2412yes—
502C3×C22⋊C4—22no—
503C3×C22⋊C4—22no—
504C3×C22⋊C4C2×D412yes—
505C3×C42—22no—
506C3×C42—22no—
507C3×C42C2412yes—
508#217—21no—
509#217—21no—
510#217—21no—
511#217—21no—
512#217—21no—
513#217—21no—
514#217—22no—
515#217—22no—
516#217C2×D412yes—
517C4⋊Dic3—22no—
518C4⋊Dic3—22no—
519C4⋊Dic3—21no—
520C4⋊Dic3—21no—
521C4⋊Dic3—22no—
522C4⋊Dic3—22no—
523C4⋊Dic3—21no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—22no—
529C4⋊Dic3—21no—
530C4⋊Dic3—21no—
531C4⋊Dic3C2×D412yes—
532C4⋊Dic3C2×D412yes—
533C4⋊Dic3C2×D411yescharacteristic
534C4⋊Dic3C2×D411yescharacteristic
535C4⋊Dic3C2411yescharacteristic
536C4⋊Dic3C2411yescharacteristic
537C4⋊Dic3C2412yes—
538C4⋊Dic3C2411yescharacteristic
539C4⋊Dic3C2411yescharacteristic
540C4⋊Dic3C2412yes—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4C2×D412yes—
554Dic3⋊C4C2×D412yes—
555Dic3⋊C4C2×D412yes—
556Dic3⋊C4C2×D412yes—
557C4×Dic3—21no—
558C4×Dic3—21no—
559C4×Dic3—21no—
560C4×Dic3—21no—
561C4×Dic3—22no—
562C4×Dic3—22no—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3C2×D411yescharacteristic
566C4×Dic3C2×D411yescharacteristic
567C4×Dic3C2412yes—
568C4×Dic3C2411yescharacteristic
569C4×Dic3C2411yescharacteristic
570#208—22no—
571C2×C3⋊C8—22no—
572C2×C3⋊C8C2412yes—
573C2×C3⋊C8C2411yescharacteristic
574C2×C3⋊C8C2411yescharacteristic
575C2×#41C22×D311yescharacteristic
576C2×#41C22×D311yescharacteristic
577C22×Q8—61no—
578C22×Q8—62no—
579#135Dic618yescomplemented
580C2×Q16C22×D311yescharacteristic
581C2×SD16C22×D311yescharacteristic
582C2×SD16C22×D311yescharacteristic
583C2×D8C22×D311yescharacteristic
584C2×M16—31no—
585C2×M16C22×D311yescharacteristic
586C22×C8—31no—
587C22×C8C22×D311yescharacteristic
588C4⋊Q8—31no—
589C4⋊Q8—31no—
590C4⋊Q8—32no—
591C4⋊Q8—32no—
592C4⋊Q8—32no—
593C4⋊Q8—32no—
594C4⋊Q8—32no—
595C4⋊Q8—32no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8—61no—
599C4⋊Q8—61no—
600C4⋊Q8—61no—
601C4⋊Q8—62no—
602C4⋊Q8—61no—
603C4⋊Q8—62no—
604C4⋊Q8—62no—
605C4⋊Q8—62no—
606C4⋊Q8—61no—
607C4⋊Q8—61no—
608#125—31no—
609#125—31no—
610#125—32no—
611#125—32no—
612#125—32no—
613#125—32no—
614#125—32no—
615#125—32no—
616#125—62no—
617#125—62no—
618#125—61no—
619#125—61no—
620#125—61no—
621#125—62no—
622#125—62no—
623#125—61no—
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—31no—
649C4×Q8—31no—
650C4×Q8—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—62no—
655C4×Q8—62no—
656C4×Q8—62no—
657C4×Q8—62no—
658C4×Q8C22×D312yes—
659C4×Q8C22×D312yes—
660C4×D4—22no—
661C4×D4—22no—
662C4×D4—31no—
663C4×D4—31no—
664C4×D4—31no—
665C4×D4—31no—
666C4×D4—32no—
667C4×D4—32no—
668C4×D4—62no—
669C4×D4—62no—
670C4×D4—61no—
671C4×D4—61no—
672C4×D4—61no—
673C4×D4—61no—
674C4×D4C22×D312yes—
675C4×D4C22×D312yes—
676#117—21no—
677#117—21no—
678#117—31no—
679#117—31no—
680#117—31no—
681#117—61no—
682#117—61no—
683#117—61no—
684#117—61no—
685#117C22×D311yescharacteristic
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—61no—
691C2×C4⋊C4—61no—
692C2×C4⋊C4—62no—
693C2×C4⋊C4—62no—
694C2×C4⋊C4—62no—
695C2×C4⋊C4—61no—
696C2×C4⋊C4—61no—
697C2×C4⋊C4—61no—
698C2×C4⋊C4C22×D311yescharacteristic
699C2×C4⋊C4C22×D311yescharacteristic
700C2×C42—31no—
701C2×C42—61no—
702C2×C42—61no—
703#107—32no—
704#107—32no—
705#107—31no—
706#107—31no—
707#107—32no—
708#107—32no—
709#107—32no—
710#107—32no—
711#107—32no—
712#107—32no—
713#106—31no—
714#106—31no—
715#106—32no—
716#106—32no—
717#106—32no—
718#106—32no—
719#106—32no—
720#106—32no—
721#106C22×D312yes—
722#106C22×D312yes—
723C4⋊C8—32no—
724C4⋊C8—32no—
725C4⋊C8—32no—
726C4⋊C8—32no—
727C4⋊C8—32no—
728C4⋊C8—32no—
729#103—31no—
730#103—31no—
731#103—31no—
732#103—31no—
733#103—32no—
734#103—32no—
735#103C22×D312yes—
736#103C22×D312yes—
737#102—31no—
738#102—31no—
739#102—31no—
740#102—31no—
741#102—32no—
742#102—32no—
743#102C22×D312yes—
744#102C22×D312yes—
745#97—31no—
746#97—31no—
747#97—31no—
748#97—31no—
749#97—32no—
750#97C22×D312yes—
751C4×C8—32no—
752C4×C8C22×D312yes—
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—22no—
771C2×C3×C4—22no—
772C2×C3×C4—82no—
773C2×C3×C4—82no—
774C2×C3×C4—81no—
775C2×C3×C4—81no—
776C2×C3×C4C22×D412yes—
777C2×C3×C4C22×D412yes—
778C2×C3×C4C22×D411yescharacteristic
779C2×C3×C4C22×Q812yes—
780C2×C3×C42−1+412yes—
781C2×C3×C4C2511yescharacteristic
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—41no—
789C2×Dic3—41no—
790C2×Dic3—42no—
791C2×Dic3—42no—
792C2×Dic3—82no—
793C2×Dic3—82no—
794C2×Dic3—81no—
795C2×Dic3—81no—
796C2×Dic3—81no—
797C2×Dic3—81no—
798C2×Dic3C22×D412yes—
799C2×Dic3C22×D411yescharacteristic
800C2×Dic3C22×D411yescharacteristic
801C2×Dic3C22×D411yescharacteristic
802C2×Dic3C22×D411yescharacteristic
803C2×Dic3C22×D412yes—
804Dic6—42no—
805Dic6—42no—
806Dic6—44no—
807Dic6—82no—
808Dic6—82no—
809Dic6—82no—
810Dic6—82no—
811Dic6—82no—
812C3×C8—22no—
813C3×C8C22×Q812yes—
814C3×C8C22×Q812yes—
815C3⋊C8—21no—
816C3⋊C8—21no—
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—244no—
831C2×Q8—242no—
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—22no—
843C22×C4—22no—
844C22×C4—31no—
845C22×C4—31no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—62no—
851C22×C4—62no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4C23×D311yescharacteristic
855Q16C2×Dic614yescomplemented
856SD16C2×Dic614yescomplemented
857SD16C2×Dic614yescomplemented
858D8C2×Dic614yescomplemented
859M16—22no—
860M16—62no—
861C2×C8—32no—
862C2×C8—31no—
863C2×C8—31no—
864C2×C8—62no—
865C2×C8C2×Dic614yescomplemented
866C2×C8C23×D312yes—
867C2×C8C23×D311yescharacteristic
868C2×C8C23×D311yescharacteristic
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—31no—
874C4⋊C4—32no—
875C4⋊C4—32no—
876C4⋊C4—32no—
877C4⋊C4—31no—
878C4⋊C4—32no—
879C4⋊C4—32no—
880C4⋊C4—32no—
881C4⋊C4—31no—
882C4⋊C4—32no—
883C4⋊C4—31no—
884C4⋊C4—31no—
885C4⋊C4—32no—
886C4⋊C4—31no—
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—61no—
899C4⋊C4—61no—
900C4⋊C4—61no—
901C4⋊C4—61no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
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⋊C4D3×D411yescharacteristic
914C4⋊C4D3×D411yescharacteristic
915C4⋊C4C23×D312yes—
916C4⋊C4C23×D312yes—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—32no—
920C22⋊C4—61no—
921C22⋊C4—61no—
922C22⋊C4—61no—
923C22⋊C4—61no—
924C22⋊C4—62no—
925C22⋊C4—62no—
926C22⋊C4—61no—
927C22⋊C4—61no—
928C22⋊C4D3×D412yes—
929C42—22no—
930C42—22no—
931C42—31no—
932C42—31no—
933C42—32no—
934C42—31no—
935C42—31no—
936C42—61no—
937C42—61no—
938C42—61no—
939C42—61no—
940C42—62no—
941C42—62no—
942C42—61no—
943C42—61no—
944C42C23×D312yes—
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—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—22no—
959C3×C4—42no—
960C3×C4—42no—
961C3×C4D4×Q812yes—
962C3×C4C23×Q811yescharacteristic
963C3×C4C2×2−1+411yescharacteristic
964Dic3—21no—
965Dic3—22no—
966Dic3—21no—
967Dic3—21no—
968Dic3—22no—
969Dic3—21no—
970Dic3—42no—
971Dic3—41no—
972Dic3—41no—
973Dic3—42no—
974Dic3—41no—
975Dic3—41no—
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—22no—
1002C2×C4—22no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—31no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—82no—
1016C2×C4—82no—
1017C2×C4—81no—
1018C2×C4—81no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—122no—
1022C2×C4—122no—
1023C2×C4—242no—
1024C2×C4—241no—
1025C2×C4—242no—
1026C2×C4—241no—
1027C2×C4—241no—
1028C2×C4—241no—
1029C2×C4C22×Dic612yes—
1030C2×C4C2×D3×D412yes—
1031C2×C4C2×D3×D412yes—
1032C2×C4C2×D3×D411yescharacteristic
1033C2×C4#101012yes—
1034C2×C4C24×D311yescharacteristic
1035C8—22no—
1036C8—61no—
1037C8—61no—
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—22no—
1058C4—22no—
1059C4—22no—
1060C4—22no—
1061C4—42no—
1062C4—42no—
1063C4—61no—
1064C4—61no—
1065C4—62no—
1066C4—61no—
1067C4—61no—
1068C4—62no—
1069C4—121no—
1070C4—122no—
1071C4—122no—
1072C4—121no—
1073C4—121no—
1074C4—121no—
1075C4D4×Dic612yes—
1076C4C23×Dic611yescharacteristic
1077C4C2×#101011yescharacteristic
1078C3#6138011yescharacteristic, complemented, Sylow
1079C2—22no—
1080C2—42no—
1081C2—42no—
1082C2C2×D4×Dic611yescharacteristic
1083C2#8720711yescharacteristic
1084C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2952C2
socleC22×C3C23×D4
prime radicalC2×C3×#135C22
hypercenter#2952D3
hypocenterC3#61380
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. #85890C2semidirect
2. #85889C2semidirect
6. #82560C2semidirect
7. #82559C2semidirect
8. #79856C2semidirect
9. #79855C2semidirect
10. #79820C2semidirect
11. #79819C2semidirect
12. #79636C2semidirect
13. #79636C2semidirect
14. #79635C2semidirect
15. #79634C2semidirect
16. #79110C2semidirect
17. C2×#4856C2semidirect
18. #78873C2semidirect
19. #78872C2semidirect
20. #78871C2semidirect
21. #78870C2semidirect
22. #78546C2semidirect
23. #78543C2semidirect
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
865. 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
#858902
#858892
C3×#29522
#838982
#838972
#825602
#825592
#798562
#798552
#798202
#798192
#796362
#796352
#796342
#791102
C2×#48562
#788732
#788722
#788712
#788702
#785462
#785432
#613803