Finite Group Databasebeta

← #11667272

Subgroups — #11667272

Order 768.

1800 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic, complemented
2#86219C211yesmaximal, characteristic
3C3×#3131C211yesmaximal, characteristic, complemented
4#83339C211yesmaximal, characteristic, complemented
5#83281C211yesmaximal, characteristic, complemented
6#81649C214yesmaximal, complemented
7#81648C214yesmaximal, complemented
8#81610C211yesmaximal, characteristic, complemented
9#81609C211yesmaximal, characteristic, complemented
10#81608C211yesmaximal, characteristic, complemented
11#81607C211yesmaximal, characteristic, complemented
12#81574C211yesmaximal, characteristic, complemented
13#81573C211yesmaximal, characteristic, complemented
14#81572C211yesmaximal, characteristic, complemented
15#81571C211yesmaximal, characteristic, complemented
16#78842C214yesmaximal, complemented
17#78822C214yesmaximal, complemented
18C2×#4685C211yesmaximal, characteristic, complemented
19#78442C211yesmaximal, characteristic, complemented
20#60846—31nomaximal, Sylow
21C3×#533C2211yescharacteristic
22C3×#532C2211yescharacteristic
23#5828C2212yes—
24Dic3×#41C2212yes—
25#5728C2211yescharacteristic
26#5728C2211yescharacteristic
27#5728C2211yescharacteristic
28#5728C2211yescharacteristic
29D3×C4⋊Q8C2211yescharacteristic
30D3×C4⋊Q8C2211yescharacteristic
31#5716C2211yescharacteristic
32#5716C2211yescharacteristic
33#5688C2212yes—
34D3×#125C2212yes—
35#5680C2212yes—
36#5680C2212yes—
37D3×C22⋊Q8—21no—
38D3×C22⋊Q8—21no—
39#5622—21no—
40#5622—21no—
41#5606—21no—
42#5606—21no—
43#5600—21no—
44#5600—21no—
45#5578—21no—
46#5578—21no—
47C4×D3×Q8—21no—
48C4×D3×Q8—21no—
49#5557—21no—
50#5557—21no—
51C4×#237—21no—
52C4×#237—21no—
53D3×#117C2212yes—
54#5517C2212yes—
55C2×C42×D3C2211yescharacteristic
56#5470C2211yescharacteristic
57#5470C2211yescharacteristic
58C3×#488C2214yescomplemented
59C3×#487C2211yescharacteristic, complemented
60C3×#487C2211yescharacteristic, complemented
61C3×#486C2211yescharacteristic, complemented
62C3×#486C2211yescharacteristic, complemented
63C3×#416C2214yes—
64C2×C3×C4×C8C2211yescharacteristic
65#5233C2214yes—
66C2×(C2×D3)⋊C8C2212yes—
67#5106C2214yes—
68C2×Dic3⋊C8C2212yes—
69#5080C2211yescharacteristic, complemented
70#5080C2211yescharacteristic, complemented
71#5079C2211yescharacteristic, complemented
72#5079C2211yescharacteristic, complemented
73#5078C2211yescharacteristic, complemented
74#5078C2211yescharacteristic, complemented
75#5070C2211yescharacteristic, complemented
76#5070C2211yescharacteristic, complemented
77#5065C2214yescomplemented
78#5056C2214yescomplemented
79#4998C2214yes—
80C2×C4×C3⋊C8C2211yescharacteristic
81#4815C2214yes—
82#4814C2214yes—
83#4811C2214yes—
84#4805C2214yes—
85#4799C2214yescomplemented
86#4796C2214yescomplemented
87#4793C2214yescomplemented
88#4791C2214yescomplemented
89#4784C2214yes—
90#4779C2214yes—
91#4777C2214yes—
92#4774C2214yes—
93#4766C2214yescomplemented
94#4763C2214yescomplemented
95#4761C2214yescomplemented
96#4759C2214yescomplemented
97#4685C2211yescharacteristic
98#4685C2211yescharacteristic
99#4685C2211yescharacteristic
100#4685C2211yescharacteristic
101#4685C2212yes—
102#4685C2212yes—
103#4683C2214yescomplemented
104#4682C2211yescharacteristic, complemented
105#4682C2211yescharacteristic, complemented
106#4680C2211yescharacteristic, complemented
107#4680C2211yescharacteristic, complemented
108#3444—31no—
109C2×#533—31no—
110#3233—34no—
111#3232—34no—
112#3231—31no—
113#3231—31no—
114#3230—31no—
115#3229—31no—
116#3228—31no—
117#3228—31no—
118#3227—31no—
119#3226—31no—
120#3160—31no—
121#3160—31no—
122#3131—31no—
123#3131D311yescharacteristic, complemented
124#3091—34no—
125#3076—34no—
126C2×#431—31no—
127C2×C3×#41C2312yes—
128C2×D3×Q8—21no—
129C2×D3×Q8—21no—
130C2×#237—21no—
131C2×#237—21no—
132C22×C4×D3D411yescharacteristic
133C22×C4×D3D411yescharacteristic
134C22×C4×D3C2311yescharacteristic
135C22×C3×C8C2312yes—
136C3×C4⋊Q8C2311yescharacteristic
137C3×C4⋊Q8C2311yescharacteristic
138C3×C4⋊Q8C2311yescharacteristic
139C3×#127C2311yescharacteristic
140C3×#125C2312yes—
141C3×#124C2312yes—
142C3×C22⋊Q8—21no—
143C3×C22⋊Q8—21no—
144C3×#121—21no—
145C3×#121—21no—
146C3×C4×Q8—21no—
147C3×C4×Q8—21no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×#117C2312yes—
151C2×C3×C42C2311yescharacteristic
152#946—21no—
153#946—21no—
154#946C2312yes—
155#946C2312yes—
156Q8×Dic3—21no—
157Q8×Dic3—21no—
158Q8×Dic3C2312yes—
159Q8×Dic3C2312yes—
160#944—21no—
161#944—21no—
162#938—21no—
163#938—21no—
164#938C2312yes—
165#938C2312yes—
166#937—22no—
167#936—21no—
168#936—21no—
169#935—22no—
170D4×Dic3—22no—
171D4×Dic3—22no—
172D4×Dic3—21no—
173D4×Dic3—21no—
174D4×Dic3C2312yes—
175D4×Dic3C2312yes—
176C4×#67—22no—
177C4×#67—22no—
178#926—22no—
179#926C2312yes—
180#926C2312yes—
181#924—21no—
182#924—21no—
183#924—21no—
184#924—21no—
185C2×C4×Dic3—22no—
186C2×C4×Dic3D411yescharacteristic
187C2×C4×Dic3D411yescharacteristic
188C2×C4×Dic3C2311yescharacteristic
189C22×C3⋊C8C2312yes—
190#897—21no—
191#897—21no—
192#897—21no—
193#897—21no—
194#896—22no—
195#896—22no—
196#892—21no—
197#892—21no—
198#892C2312yes—
199#892C2312yes—
200D3×C4⋊C4—22no—
201D3×C4⋊C4—22no—
202D3×C4⋊C4—21no—
203D3×C4⋊C4—21no—
204D3×C4⋊C4C2312yes—
205D3×C4⋊C4C2312yes—
206#890—21no—
207#890—21no—
208#890C2312yes—
209#890C2312yes—
210#889—22no—
211#889—22no—
212#888—21no—
213#888—21no—
214#888C2312yes—
215#888C2312yes—
216#887—22no—
217#887—22no—
218#887—21no—
219#887—21no—
220#887—21no—
221#887—21no—
222#883—22no—
223#883—22no—
224#67⋊C4—22no—
225#67⋊C4—22no—
226D3×C22⋊C4—22no—
227#879—22no—
228#879—22no—
229#878—22no—
230#878—22no—
231#877—22no—
232#877—22no—
233#877—22no—
234#872—22no—
235C42×D3—22no—
236C42×D3D411yescharacteristic
237C42×D3D411yescharacteristic
238C42×D3D411yescharacteristic
239C42×D3D411yescharacteristic
240C42×D3C2311yescharacteristic
241C42×D3C2311yescharacteristic
242C42×D3C2311yescharacteristic
243C42×D3C2311yescharacteristic
244#870C2312yes—
245#870C2312yes—
246#869C2311yescharacteristic
247#869C2311yescharacteristic
248#869C2311yescharacteristic
249#869C2311yescharacteristic
250C4×Dic6—21no—
251C4×Dic6—21no—
252C4×Dic6—21no—
253C4×Dic6—21no—
254C4×Dic6—22no—
255C4×Dic6—22no—
256C3×#103C2314yes—
257C3×#103C2314yes—
258C3×#102C2314yes—
259C3×#102C2314yes—
260C3×C4×C8C2311yescharacteristic
261C3×C4×C8C2311yescharacteristic
262C3×C4×C8C2312yes—
263#835C2314yes—
264#835C2314yes—
265#832C2314yes—
266#832C2314yes—
267(C2×D3)⋊C8C2312yes—
268(C2×D3)⋊C8C2312yes—
269(C2×D3)⋊C8C2312yes—
270(C2×D3)⋊C8C2312yes—
271#818C2314yes—
272#818C2314yes—
273#817C2314yes—
274#817C2314yes—
275Dic3⋊C8C2312yes—
276Dic3⋊C8C2312yes—
277Dic3⋊C8C2312yes—
278Dic3⋊C8C2312yes—
279#808C2314yes—
280#808C2314yes—
281#807C2314yes—
282#807C2314yes—
283C4×C3⋊C8C2312yes—
284C4×C3⋊C8C2311yescharacteristic
285C4×C3⋊C8C2311yescharacteristic
286#533—31no—
287#533—31no—
288#533—32no—
289#533—32no—
290#533—31no—
291#533—31no—
292#533—31no—
293#533—31no—
294#533—61no—
295#533—61no—
296#533—61no—
297#533—61no—
298#533C2×D311yescharacteristic
299#532—31no—
300#532—31no—
301#532C2×D311yescharacteristic
302C2×C4⋊Q8—31no—
303C2×C4⋊Q8—31no—
304#529—32no—
305#529—32no—
306#529—61no—
307#529—61no—
308#529—61no—
309#529—61no—
310C2×#125—32no—
311#525—32no—
312#525—61no—
313#525—61no—
314C2×C22⋊Q8—61no—
315C2×C22⋊Q8—61no—
316C4×#41—32no—
317C4×#41—61no—
318C4×#41—61no—
319C2×C4×Q8—61no—
320C2×C4×Q8—61no—
321C2×#117—32no—
322C22×C42—31no—
323#500—31no—
324#500—31no—
325#500—31no—
326#500—31no—
327#499—34no—
328#499—34no—
329#498—31no—
330#498—31no—
331#498—31no—
332#498—31no—
333#488—34no—
334#488C2×D314yescomplemented
335#487—31no—
336#487—31no—
337#487C2×D311yescharacteristic, complemented
338#487C2×D311yescharacteristic, complemented
339#486—31no—
340#486—31no—
341#486C2×D311yescharacteristic, complemented
342#486C2×D311yescharacteristic, complemented
343#485—34no—
344#485—34no—
345#484—34no—
346#483—34no—
347#482—34no—
348#482—34no—
349#481—34no—
350#480—34no—
351#479—34no—
352#479—34no—
353#478—34no—
354#478—34no—
355#477—34no—
356#476—34no—
357#475—34no—
358#474—34no—
359#431—31no—
360#431—31no—
361#431—31no—
362#431—31no—
363#431—32no—
364#431—32no—
365#427—34no—
366#427—34no—
367C2×C4⋊C8—32no—
368#416—34no—
369#416C2×D314yes—
370C2×C22⋊C8—32no—
371C2×C4×C8—31no—
372C2×C4×C8C2×D311yescharacteristic
373C23×D3C2×D411yescharacteristic
374C3×#41—28no—
375C2×C3×Q8—21no—
376C2×C3×Q8—21no—
377C2×C3×Q8C2412yes—
378C2×C3×D4—22no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4C2412yes—
382C22×C3×C4—22no—
383C22×C3×C4C2×D411yescharacteristic
384C22×C3×C4C2×D411yescharacteristic
385C22×C3×C4C2411yescharacteristic
386C2×#67—22no—
387C2×#67—22no—
388C22×Dic3—22no—
389C22×Dic3—22no—
390C22×Dic3C2×D411yescharacteristic
391C22×Dic3C2×D411yescharacteristic
392C22×Dic3C2×D411yescharacteristic
393D3×Q8—44no—
394D3×Q8—44no—
395#237—44no—
396#237—44no—
397C2×C4×D3—24no—
398C2×C4×D3—24no—
399C2×C4×D3—22no—
400C2×C4×D3—22no—
401C2×C4×D3—42no—
402C2×C4×D3C2×D411yescharacteristic
403C2×C4×D3C2×D411yescharacteristic
404C2×C4×D3C2×D411yescharacteristic
405C2×C4×D3C2×D411yescharacteristic
406C2×C4×D3C2×D411yescharacteristic
407C2×C4×D3C2×D411yescharacteristic
408C2×C4×D3C2×D411yescharacteristic
409C2×C4×D3C2×D411yescharacteristic
410C2×C4×D3C2×D411yescharacteristic
411C2×C4×D3C2×D411yescharacteristic
412C2×C4×D3C2411yescharacteristic
413C2×C4×D3C2411yescharacteristic
414C2×Dic6—21no—
415C2×Dic6—21no—
416C2×Dic6—21no—
417C2×Dic6—21no—
418C2×Dic6—22no—
419C2×Dic6—22no—
420C2×C3×C8—24no—
421C2×C3×C8C2412yes—
422C2×C3×C8C2412yes—
423C3×C4⋊C4—21no—
424C3×C4⋊C4—21no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—22no—
427C3×C4⋊C4—21no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4C2412yes—
430C3×C4⋊C4C2412yes—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C42—22no—
435C3×C42C2×D411yescharacteristic
436C3×C42C2×D411yescharacteristic
437C3×C42C2411yescharacteristic
438C3×C42C2411yescharacteristic
439#217—22no—
440#217—22no—
441#217—22no—
442#217—22no—
443#217—22no—
444#217—22no—
445(C2×D3)⋊C4—22no—
446(C2×D3)⋊C4—22no—
447(C2×D3)⋊C4—22no—
448(C2×D3)⋊C4—22no—
449C4⋊Dic3—21no—
450C4⋊Dic3—21no—
451C4⋊Dic3—21no—
452C4⋊Dic3—21no—
453C4⋊Dic3—22no—
454C4⋊Dic3—22no—
455C4⋊Dic3—22no—
456C4⋊Dic3—22no—
457C4⋊Dic3C2412yes—
458C4⋊Dic3C2412yes—
459C4⋊Dic3C2412yes—
460C4⋊Dic3C2412yes—
461Dic3⋊C4—22no—
462Dic3⋊C4—22no—
463Dic3⋊C4—22no—
464Dic3⋊C4—22no—
465Dic3⋊C4—22no—
466Dic3⋊C4—22no—
467Dic3⋊C4—22no—
468Dic3⋊C4—22no—
469Dic3⋊C4—22no—
470Dic3⋊C4—22no—
471Dic3⋊C4—22no—
472Dic3⋊C4—22no—
473C4×Dic3—22no—
474C4×Dic3—22no—
475C4×Dic3—22no—
476C4×Dic3—22no—
477C4×Dic3—22no—
478C4×Dic3—22no—
479C4×Dic3C2×D411yescharacteristic
480C4×Dic3C2×D411yescharacteristic
481C4×Dic3C2×D411yescharacteristic
482C4×Dic3C2×D411yescharacteristic
483C4×Dic3C2×D411yescharacteristic
484C4×Dic3C2×D411yescharacteristic
485C4×Dic3C2×D411yescharacteristic
486C4×Dic3C2×D411yescharacteristic
487C4×Dic3C2×D411yescharacteristic
488C4×Dic3C2×D411yescharacteristic
489C4×Dic3C2411yescharacteristic
490C4×Dic3C2411yescharacteristic
491C2×C3⋊C8—24no—
492C2×C3⋊C8C2412yes—
493C2×C3⋊C8C2412yes—
494C2×#41—61no—
495C2×#41—61no—
496C2×#41C22×D312yes—
497C22×Q8—61no—
498C22×Q8—61no—
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—31no—
502C22×C8—32no—
503C22×C8C22×D312yes—
504C4⋊Q8—32no—
505C4⋊Q8—32no—
506C4⋊Q8—31no—
507C4⋊Q8—31no—
508C4⋊Q8—31no—
509C4⋊Q8—31no—
510C4⋊Q8—61no—
511C4⋊Q8—61no—
512C4⋊Q8—61no—
513C4⋊Q8—61no—
514C4⋊Q8C22×D311yescharacteristic
515C4⋊Q8C22×D311yescharacteristic
516C4⋊Q8C22×D311yescharacteristic
517#127C22×D311yescharacteristic
518#126—62no—
519#126—62no—
520#125—32no—
521#125—32no—
522#125—32no—
523#125—32no—
524#125—62no—
525#125—62no—
526#125—61no—
527#125—61no—
528#125C22×D312yes—
529#124—61no—
530#124—61no—
531#124C22×D312yes—
532#123—62no—
533#123—62no—
534#123—62no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—32no—
538C22⋊Q8—32no—
539C22⋊Q8—62no—
540C22⋊Q8—62no—
541C22⋊Q8—62no—
542C22⋊Q8—62no—
543C22⋊Q8—61no—
544C22⋊Q8—61no—
545C22⋊Q8—61no—
546C22⋊Q8—61no—
547C22⋊Q8—61no—
548C22⋊Q8—61no—
549C22⋊Q8—61no—
550C22⋊Q8—61no—
551C22⋊Q8—61no—
552C22⋊Q8—61no—
553#121—21no—
554#121—21no—
555#121—32no—
556#121—32no—
557#121—61no—
558#121—61no—
559#120—62no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—32no—
563C4×Q8—32no—
564C4×Q8—62no—
565C4×Q8—62no—
566C4×Q8—62no—
567C4×Q8—61no—
568C4×Q8—61no—
569C4×Q8—62no—
570C4×Q8—61no—
571C4×Q8—61no—
572C4×Q8—61no—
573C4×Q8—61no—
574C4×Q8—61no—
575C4×Q8—61no—
576C4×Q8—61no—
577C4×Q8—61no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—32no—
581C4×D4—32no—
582C4×D4—61no—
583C4×D4—61no—
584C4×D4—62no—
585C4×D4—62no—
586C4×D4—62no—
587C4×D4—62no—
588C4×D4—62no—
589C4×D4—62no—
590#117—32no—
591#117—32no—
592#117—32no—
593#117—32no—
594#117—62no—
595#117—62no—
596#117—62no—
597#117—62no—
598#117—62no—
599#117—61no—
600#117—61no—
601#117C22×D312yes—
602C2×C4⋊C4—32no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—62no—
605C2×C4⋊C4—62no—
606C2×C4⋊C4—61no—
607C2×C4⋊C4—61no—
608C2×C22⋊C4—62no—
609C2×C42—31no—
610C2×C42—31no—
611C2×C42—31no—
612C2×C42—31no—
613C2×C42—31no—
614C2×C42—31no—
615C2×C42—31no—
616C2×C42—31no—
617C2×C42—31no—
618C2×C42—31no—
619C2×C42—31no—
620C2×C42—62no—
621C2×C42—62no—
622C2×C42C22×D311yescharacteristic
623#107—34no—
624#107—34no—
625#107—34no—
626#107—34no—
627#106—34no—
628#106—34no—
629#106—34no—
630#106—34no—
631C4⋊C8—32no—
632C4⋊C8—32no—
633C4⋊C8—32no—
634C4⋊C8—32no—
635#103—34no—
636#103—34no—
637#103C22×D314yes—
638#103C22×D314yes—
639#102—34no—
640#102—34no—
641#102C22×D314yes—
642#102C22×D314yes—
643C22⋊C8—32no—
644C22⋊C8—32no—
645C22⋊C8—32no—
646C22⋊C8—32no—
647C4×C8—31no—
648C4×C8—31no—
649C4×C8—32no—
650C4×C8C22×D311yescharacteristic
651C4×C8C22×D311yescharacteristic
652C4×C8C22×D312yes—
653C23×C3—22no—
654C23×C3C22×D411yescharacteristic
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—41no—
658C22×D3C22×D411yescharacteristic
659C22×D3C22×D411yescharacteristic
660C3×Q8—24no—
661C3×Q8—42no—
662C3×Q8—42no—
663C3×D4—24no—
664C3×D4—44no—
665C3×D4—42no—
666C3×D4—42no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—44no—
673C2×C3×C4C22×D411yescharacteristic
674C2×C3×C4C22×D411yescharacteristic
675C2×C3×C4C22×D411yescharacteristic
676C2×C3×C4C22×D411yescharacteristic
677C2×C3×C4C22×D411yescharacteristic
678C2×C3×C42−1+414yes—
679C2×C3×C4C2511yescharacteristic
680#67—44no—
681#67—44no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—41no—
689C2×Dic3—44no—
690C2×Dic3—44no—
691C2×Dic3C22×D411yescharacteristic
692C2×Dic3C22×D411yescharacteristic
693C2×Dic3C22×D411yescharacteristic
694C2×Dic3C22×D411yescharacteristic
695C2×Dic3C22×D411yescharacteristic
696C2×Dic3C22×D411yescharacteristic
697C4×D3—22no—
698C4×D3—22no—
699C4×D3—22no—
700C4×D3—22no—
701C4×D3—22no—
702C4×D3—22no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—22no—
706C4×D3—41no—
707C4×D3—41no—
708C4×D3—44no—
709C4×D3—44no—
710C4×D3#13514yes—
711Dic6—44no—
712Dic6—42no—
713Dic6—42no—
714Dic6—42no—
715Dic6—42no—
716Dic6—44no—
717C3×C8—22no—
718C3×C8—22no—
719C3⋊C8—22no—
720C3⋊C8—22no—
721C24—31no—
722#41—28no—
723#41—124no—
724#41—124no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—62no—
728C2×Q8—62no—
729C2×Q8—61no—
730C2×Q8—61no—
731C2×Q8—61no—
732C2×Q8—61no—
733C2×Q8—124no—
734C2×Q8—124no—
735C2×Q8C23×D312yes—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—62no—
740C2×D4—62no—
741C2×D4C23×D312yes—
742C22×C4—22no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—64no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—64no—
764C22×C4—122no—
765C22×C4D3×D411yescharacteristic
766C22×C4D3×D411yescharacteristic
767C22×C4C23×D311yescharacteristic
768C2×C8—24no—
769C2×C8—32no—
770C2×C8—32no—
771C2×C8—64no—
772C2×C8C23×D312yes—
773C2×C8C23×D312yes—
774C4⋊C4—22no—
775C4⋊C4—22no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—32no—
781C4⋊C4—32no—
782C4⋊C4—32no—
783C4⋊C4—32no—
784C4⋊C4—62no—
785C4⋊C4—62no—
786C4⋊C4—62no—
787C4⋊C4—62no—
788C4⋊C4—62no—
789C4⋊C4—62no—
790C4⋊C4—62no—
791C4⋊C4—62no—
792C4⋊C4—62no—
793C4⋊C4—62no—
794C4⋊C4—62no—
795C4⋊C4—62no—
796C4⋊C4—62no—
797C4⋊C4—62no—
798C4⋊C4—61no—
799C4⋊C4—61no—
800C4⋊C4—61no—
801C4⋊C4—61no—
802C4⋊C4—62no—
803C4⋊C4—62no—
804C4⋊C4C23×D312yes—
805C4⋊C4C23×D312yes—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—62no—
810C22⋊C4—62no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—62no—
819C42—22no—
820C42—31no—
821C42—31no—
822C42—31no—
823C42—31no—
824C42—31no—
825C42—31no—
826C42—31no—
827C42—31no—
828C42—31no—
829C42—31no—
830C42—31no—
831C42—31no—
832C42—62no—
833C42—62no—
834C42—62no—
835C42—62no—
836C42—62no—
837C42—62no—
838C42D3×D411yescharacteristic
839C42D3×D411yescharacteristic
840C42C23×D311yescharacteristic
841C42C23×D311yescharacteristic
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3#53612yes—
848C22×C3C23×D411yescharacteristic
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—44no—
855C2×D3C2×#13512yes—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4#53612yes—
862C3×C4C2×#13512yes—
863C3×C4#57512yes—
864C3×C4C2×2−1+412yes—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—21no—
869Dic3—21no—
870Dic3—42no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3C2×#13512yes—
875C23—22no—
876C23—31no—
877C23—31no—
878C23—62no—
879C23—62no—
880C23—121no—
881C23C2×D3×D411yescharacteristic
882Q8—24no—
883Q8—42no—
884Q8—42no—
885Q8—124no—
886Q8—124no—
887Q8—122no—
888Q8—122no—
889Q8—122no—
890Q8—122no—
891D4—24no—
892D4—44no—
893D4—42no—
894D4—42no—
895D4—124no—
896D4—124no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—31no—
903C2×C4—34no—
904C2×C4—31no—
905C2×C4—31no—
906C2×C4—31no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—44no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—124no—
928C2×C4—124no—
929C2×C4—124no—
930C2×C4—121no—
931C2×C4—124no—
932C2×C4C2×D3×D411yescharacteristic
933C2×C4C2×D3×D411yescharacteristic
934C2×C4C2×D3×D411yescharacteristic
935C2×C4C2×D3×D411yescharacteristic
936C2×C4C2×D3×D411yescharacteristic
937C2×C4#101014yes—
938C2×C4C24×D311yescharacteristic
939C8—22no—
940C8—22no—
941C8—62no—
942C8—62no—
943C2×C3—22no—
944C2×C3—82no—
945C2×C3C2×#53611yescharacteristic
946C2×C3C22×#13511yescharacteristic
947C2×C3C2×#57511yescharacteristic
948D3—22no—
949D3—41no—
950C22—21no—
951C22—21no—
952C22—32no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—61no—
957C22—61no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—124no—
962C22#567512yes—
963C22C22×D3×D411yescharacteristic
964C4—21no—
965C4—21no—
966C4—32no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—61no—
971C4—61no—
972C4—61no—
973C4—61no—
974C4—61no—
975C4—122no—
976C4—122no—
977C4—122no—
978C4—122no—
979C4#567512yes—
980C4D3×#13512yes—
981C4#576812yes—
982C4C2×#101012yes—
983C3#6084611yescharacteristic, complemented, Sylow
984C2—22no—
985C2—62no—
986C2—82no—
987C2—121no—
988C2C2×#567511yescharacteristic
989C2C2×D3×#13511yescharacteristic
990C2C2×#576811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3131C2
socleC22×C3C23×D4
prime radical#86219C2
hypercenter#3131D3
hypocenterC3#60846
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. D3×#533C2semidirect
3. C3×#3131C2semidirect
4. #83339C2semidirect
5. #83281C2semidirect
6. #81649C2semidirect
7. #81648C2semidirect
8. #81610C2semidirect
9. #81609C2semidirect
10. #81608C2semidirect
11. #81607C2semidirect
12. #81574C2semidirect
13. #81573C2semidirect
14. #81572C2semidirect
15. #81571C2semidirect
16. #78842C2semidirect
17. #78822C2semidirect
18. C2×#4685C2semidirect
19. #78442C2semidirect
58. C3×#488C22semidirect
59. C3×#487C22semidirect
60. C3×#487C22semidirect
61. C3×#486C22semidirect
62. C3×#486C22semidirect
69. #5080C22semidirect
70. #5080C22semidirect
71. #5079C22semidirect
72. #5079C22semidirect
73. #5078C22semidirect
74. #5078C22semidirect
75. #5070C22semidirect
76. #5070C22semidirect
77. #5065C22semidirect
78. #5056C22semidirect
85. #4799C22semidirect
86. #4796C22semidirect
87. #4793C22semidirect
88. #4791C22semidirect
93. #4766C22semidirect
94. #4763C22semidirect
95. #4761C22semidirect
96. #4759C22semidirect
103. #4683C22semidirect
104. #4682C22semidirect
105. #4682C22semidirect
106. #4680C22semidirect
107. #4680C22semidirect
123. #3131D3semidirect
334. #488C2×D3semidirect
337. #487C2×D3semidirect
338. #487C2×D3semidirect
341. #486C2×D3semidirect
342. #486C2×D3semidirect
983. C3#60846semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
#862192
C3×#31312
#833392
#832812
#816492
#816482
#816102
#816092
#816082
#816072
#815742
#815732
#815722
#815712
#788422
#788222
C2×#46852
#784422
#608463