Finite Group Databasebeta

← #11887316

Subgroups — #11887316

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594629C211yesmaximal, characteristic
2#10594553C211yesmaximal, characteristic, complemented
3#10592563C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590956C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590906C211yesmaximal, characteristic, complemented
9#10590813C211yesmaximal, characteristic, complemented
10#10590618C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590451C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#81186—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22#64106C2211yescharacteristic, complemented
23#64104C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909—21no—
31C4×#626C2211yescharacteristic
32#63890—21no—
33#63864C2211yescharacteristic
34#63857C2211yescharacteristic
35#63850—21no—
36#63849C2211yescharacteristic, complemented
37#63848—21no—
38#63845—21no—
39#63844C2211yescharacteristic, complemented
40#63841—21no—
41C2×#3719C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5694—31no—
62#5630—31no—
63#5554—31no—
64#5513—31no—
65C3×#483—31no—
66C3×#478—31no—
67#5068—31no—
68#5051—31no—
69C4×#214—31no—
70C2×#809—31no—
71#4887—31no—
72#4885—31no—
73#4871D311yescharacteristic, complemented
74#4866—31no—
75#4864—31no—
76#4864—31no—
77#4864—61no—
78#4862D311yescharacteristic, complemented
79#4852—31no—
80#4845—31no—
81#4834—31no—
82#4808—31no—
83#4804—31no—
84#4800—31no—
85#4798—31no—
86#4783—31no—
87#4776—31no—
88#4772—31no—
89D3×#102—31no—
90#4731—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626D411yescharacteristic
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3744—41no—
118C8×C3⋊D3—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3719—41no—
142#3716—22no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C22×D12—31no—
149C3×#125—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154C2×#216—31no—
155C2×#214—31no—
156#930—61no—
157#929—61no—
158C4×#67—31no—
159C2×(C2×D3)⋊C4—61no—
160#926—61no—
161#924—31no—
162C22×C3⋊C8—31no—
163C2×Dic12—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—61no—
168C2×D3×C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172#898—61no—
173#898—61no—
174#897—31no—
175#897—31no—
176#897—31no—
177#897—61no—
178#897C2×D311yescharacteristic
179#895—31no—
180#895—31no—
181#895—61no—
182#895—61no—
183#894—61no—
184#894—61no—
185#893C2×D311yescharacteristic
186#892—31no—
187#892—31no—
188#892—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#890—61no—
191#890C2×D311yescharacteristic, complemented
192#889—61no—
193#887—31no—
194#886—61no—
195#882—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198#875—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C2×D311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212#835—31no—
213#832—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#816C2×D311yescharacteristic, complemented
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—22no—
272#626—42no—
273#626—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—31no—
283#482—91no—
284#478—31no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—31no—
302C2×#67—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305#239—62no—
306#239—121no—
307#237—62no—
308#237—121no—
309D3×D4—62no—
310D3×D4—121no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—121no—
321C2×D12—121no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6C22×D311yescharacteristic
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354#217—31no—
355#217—61no—
356#216—121no—
357#214—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402Dic12—121no—
403#204—62no—
404#204—121no—
405#204—121no—
406#204—122no—
407D3×C8—121no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13512yes—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444#126—181no—
445#125—31no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106D3211yescharacteristic, complemented
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479C4×C8—91no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3D3×D411yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—32no—
499C3×D4—61no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4—241no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—62no—
520#67—122no—
521#67—122no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—21no—
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—121no—
543D12—122no—
544D12—122no—
545D12—241no—
546D12—241no—
547D12—242no—
548D12#23912yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—81no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—122no—
560Dic6—21no—
561Dic6—21no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567Dic6—121no—
568C3×C8—22no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C2×C32#54611yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57711yescharacteristic
581C3⋊D3—41no—
582C3⋊D3—81no—
583C3×D3—22no—
584C3×D3—42no—
585C24—181no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—91no—
602C22×C4—181no—
603Q16—361no—
604SD16—182no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—361no—
610C2×C8—361no—
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4C2×D3211yescharacteristic
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C42—181no—
637C22×C3—21no—
638C22×C3—32no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—62no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#91612yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23911yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689C3×C4#100911yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—91no—
706C23—181no—
707C23—362no—
708C23—362no—
709C23—721no—
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714D4—32no—
715D4—61no—
716D4—182no—
717D4—181no—
718D4—181no—
719D4—362no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—91no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—362no—
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—61no—
742C8—61no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—62no—
748C2×C3—122no—
749C2×C3#563011yescharacteristic
750C2×C3#565411yescharacteristic
751C2×C3C2×#91611yescharacteristic
752C2×C3D3×#13511yescharacteristic
753C2×C3#577511yescharacteristic
754C2×C3#577811yescharacteristic
755D3—22no—
756D3—42no—
757D3—122no—
758D3—121no—
759D3—121no—
760D3—241no—
761D3—241no—
762D3—481no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22D32×D411yescharacteristic
777C4—41no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4—361no—
787C4#6430811yescharacteristic
788C4D3×#23911yescharacteristic
789C3—21no—
790C3#8118611yescharacteristic, complemented
791C3#8144511yescharacteristic, complemented
792C2—62no—
793C2—122no—
794C2—361no—
795C2—721no—
796C2#1059462011yescharacteristic
797C2D3×#91611yescharacteristic
798C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594629C2
hypercenter#106D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594553C2semidirect
3. #10592563C2semidirect
4. C3×#4871C2semidirect
5. C3×#4862C2semidirect
6. #10590956C2semidirect
7. #10590946C2semidirect
8. #10590906C2semidirect
9. #10590813C2semidirect
10. #10590618C2semidirect
11. D3×#809C2semidirect
12. #10590579C2semidirect
13. #10590537C2semidirect
14. #10590479C2semidirect
15. #10590451C2semidirect
21. C2×C8×C3⋊D3C22semidirect
22. #64106C22semidirect
27. C3×#890C22semidirect
36. #63849C22semidirect
39. #63844C22semidirect
41. C2×#3719C22semidirect
44. C32×#106C22semidirect
45. #63637C22semidirect
49. C3×#816C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
53. C3×#808C22semidirect
54. C3×#807C22semidirect
55. #63565C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
73. #4871D3semidirect
78. #4862D3semidirect
191. #890C2×D3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C2×D3semidirect
220. #816C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
227. #810C2×D3semidirect
235. #808C2×D3semidirect
236. #807C2×D3semidirect
465. #106D32semidirect
702. C32#3296semidirect
790. C3#81186semidirect
791. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105946292
#105945532
#105925632
C3×#48712
C3×#48622
#105909562
#105909462
#105909062
#105908132
#105906182
D3×#8092
#105905792
#105905372
#105904792
#105904512
#814453
#811863