Finite Group Databasebeta

← #11887251

Subgroups — #11887251

Order 1152.

923 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595984C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic
3C3×#4971C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591148C211yesmaximal, characteristic, complemented
8#10590618C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590539C211yesmaximal, characteristic, complemented
11#10590538C211yesmaximal, characteristic, complemented
12#10590513C211yesmaximal, characteristic, complemented
13#10590507C211yesmaximal, characteristic, complemented
14#10590474C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#78759—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64138—21no—
22C4×#638C2211yescharacteristic
23#64135—21no—
24#64133C2211yescharacteristic
25#64107—21no—
26#64106C2211yescharacteristic, complemented
27#64101C2211yescharacteristic, complemented
28#64099C2211yescharacteristic, complemented
29#64098—21no—
30#64096C2211yescharacteristic, complemented
31C3×#924C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63977—21no—
34D3×#217—21no—
35#63916C2211yescharacteristic
36#63898C2211yescharacteristic
37#63886—21no—
38#63884—21no—
39#63863C2211yescharacteristic
40C2×#3719C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5806—31no—
62#5630—31no—
63#5513—31no—
64#5513—31no—
65#5513—61no—
66C3×#483—31no—
67C2×C3×#102—31no—
68#5218—31no—
69#5116—31no—
70C8×#67—31no—
71#5051—31no—
72#4971D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4871—31no—
75#4866—31no—
76#4864—31no—
77#4852—31no—
78#4808—31no—
79#4804—31no—
80#4800—31no—
81#4798—31no—
82#4784—31no—
83#4783—31no—
84#4778—31no—
85#4772—31no—
86#4768—31no—
87#4767—31no—
88#4766—31no—
89#4758—31no—
90#4731—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114#3757D411yescharacteristic
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123#3750—21no—
124#3750D411yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#217—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3719—41no—
141#3716—22no—
142#3716—41no—
143#3710—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154#953—61no—
155C2×#217—61no—
156#947—31no—
157C2×#216—31no—
158#939—61no—
159#938—31no—
160#936—31no—
161#935—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164C2×#214—31no—
165#929—61no—
166#929—61no—
167#929—62no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—61no—
171#926—61no—
172#926—61no—
173#926—62no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924C2×D311yescharacteristic
178C22×C3⋊C8C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×#204—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#898—61no—
185#898—61no—
186#898—62no—
187#897—31no—
188#897—31no—
189#897—61no—
190#895—31no—
191#895—61no—
192#894—61no—
193#893—31no—
194#892—31no—
195#892—31no—
196#892—61no—
197#890—31no—
198#890—31no—
199#890—61no—
200#889—61no—
201#889—61no—
202#889—62no—
203#887—31no—
204#887—31no—
205#887—61no—
206#882—61no—
207D3×C22⋊C4—61no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#835—31no—
218#832—31no—
219#832—31no—
220#830C2×D311yescharacteristic
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#810C2×D311yescharacteristic, complemented
234#810C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic
239#808C2×D311yescharacteristic, complemented
240#808C2×D311yescharacteristic, complemented
241#807—31no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—22no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264#634—21no—
265#634—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×D12#4112yes—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—42no—
276#626—81no—
277D3×Dic3—42no—
278D3×Dic3—81no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—91no—
284#546—91no—
285#488—91no—
286#483—31no—
287#482—91no—
288#478—91no—
289#467—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294C4×SD16—91no—
295C8×D4—91no—
296#416—91no—
297C2×#102—31no—
298C24×C3—61no—
299C23×D3—21no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—121no—
306C22×C3×C4—22no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319#239—62no—
320#239—121no—
321#237—62no—
322#237—121no—
323C2×D12—22no—
324C2×D12—21no—
325C2×D12—41no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—121no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356#217—21no—
357#217—31no—
358#217—31no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—62no—
365#217—61no—
366#217—61no—
367#216—121no—
368#214—62no—
369#214—121no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—62no—
382(C2×D3)⋊C4—62no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—62no—
391C4⋊Dic3—62no—
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—62no—
414C4×Dic3—62no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420Dic12—121no—
421#204—62no—
422#204—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32#13512yes—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4C2×#4111yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3⋊Dic3—21no—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—91no—
452C22×D4—31no—
453C2×Q16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C22×C8—31no—
457C22×C8—91no—
458#126—181no—
459#125—91no—
460#125—181no—
461#124—91no—
462#123—181no—
463#123—181no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467#121—91no—
468#121—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—91no—
472C4×D4—91no—
473#117—91no—
474#117—181no—
475C2×C4⋊C4D3211yescharacteristic
476C2×C22⋊C4—181no—
477#107—91no—
478#106—31no—
479#106—31no—
480C4⋊C8—91no—
481#103—31no—
482#103—31no—
483#103—91no—
484#103—91no—
485#102—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—91no—
490#102—91no—
491C22⋊C8—31no—
492C22⋊C8—91no—
493C4×C8—91no—
494C23×C3—21no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C23×C3D3×D411yescharacteristic
501C23×C3D3×D411yescharacteristic
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—61no—
509C22×D3—81no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—32no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—122no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—44no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—62no—
541#67—62no—
542#67—122no—
543#67—122no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—122no—
563C2×Dic3—241no—
564D12—21no—
565D12—21no—
566D12—21no—
567D12—42no—
568D12—122no—
569D12—241no—
570D12#23512yes—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—121no—
576C4×D3—121no—
577C4×D3—122no—
578C4×D3—241no—
579Dic6—21no—
580Dic6—21no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586Dic6—121no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32—22no—
596C2×C32#54611yescharacteristic
597C2×C32C2×#13511yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—41no—
600C3×D3—42no—
601C3×D3—81no—
602C24—61no—
603#41—182no—
604#41—361no—
605C2×Q8—31no—
606C2×Q8—91no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—91no—
612C2×D4—121no—
613C2×D4—181no—
614C2×D4—181no—
615C22×C4—21no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620Q16—361no—
621SD16—182no—
622SD16—361no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—121no—
628C2×C8—361no—
629C4⋊C4—21no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—61no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—91no—
652C42—181no—
653C42—181no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—62no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—244no—
669C22×C3#91212yes—
670C22×C3#91612yes—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—22no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—84no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C2×#23511yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4#100911yescharacteristic
706Dic3—41no—
707Dic3—41no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—122no—
718Dic3—122no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723C32#329611yescharacteristic, complemented, Sylow
724C23—61no—
725C23—61no—
726C23—91no—
727C23—122no—
728C23—122no—
729C23—241no—
730C23#381111yescharacteristic
731Q8—61no—
732Q8—61no—
733Q8—181no—
734Q8—181no—
735D4—32no—
736D4—61no—
737D4—61no—
738D4—61no—
739D4—122no—
740D4—182no—
741D4—362no—
742D4—721no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—91no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—362no—
758C2×C4—721no—
759C2×C4#381111yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—61no—
764C8—61no—
765C2×C3—22no—
766C2×C3—22no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—42no—
771C2×C3—122no—
772C2×C3—241no—
773C2×C3#549011yescharacteristic
774C2×C3#565411yescharacteristic
775C2×C3C2×#91211yescharacteristic
776C2×C3C2×#91611yescharacteristic
777C2×C3#576211yescharacteristic
778C2×C3#577811yescharacteristic
779D3—42no—
780D3—81no—
781D3—121no—
782D3—121no—
783D3—241no—
784C22—21no—
785C22—21no—
786C22—62no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—244no—
796C22#6393612yes—
797C22C2×#381111yescharacteristic
798C4—21no—
799C4—41no—
800C4—41no—
801C4—121no—
802C4—121no—
803C4—181no—
804C4—181no—
805C4—181no—
806C4—361no—
807C4—361no—
808C4D3×#23511yescharacteristic
809C4#6430711yescharacteristic
810C3—21no—
811C3#7875911yescharacteristic, complemented
812C3#8144511yescharacteristic, complemented
813C2—22no—
814C2—122no—
815C2—241no—
816C2—361no—
817C2#1059507711yescharacteristic
818C2C2×#6393611yescharacteristic
819C2#1059532411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595984C2semidirect
3. C3×#4971C2semidirect
4. C2×C3×#809C2semidirect
5. #10591187C2semidirect
6. #10591172C2semidirect
7. #10591148C2semidirect
8. #10590618C2semidirect
9. #10590611C2semidirect
10. #10590539C2semidirect
11. #10590538C2semidirect
12. #10590513C2semidirect
13. #10590507C2semidirect
14. #10590474C2semidirect
15. #10590460C2semidirect
26. #64106C22semidirect
27. #64101C22semidirect
28. #64099C22semidirect
30. #64096C22semidirect
40. C2×#3719C22semidirect
43. C2×#3710C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #4971D3semidirect
73. C2×#809D3semidirect
233. #810C2×D3semidirect
234. #810C2×D3semidirect
239. #808C2×D3semidirect
240. #808C2×D3semidirect
723. C32#3296semidirect
811. C3#78759semidirect
812. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105959842
#105948892
C3×#49712
C2×C3×#8092
#105911872
#105911722
#105911482
#105906182
#105906112
#105905392
#105905382
#105905132
#105905072
#105904742
#105904602
#814453
#787593