Finite Group Databasebeta

← #11887241

Subgroups — #11887241

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595380C211yesmaximal, characteristic, complemented
2#10595244C211yesmaximal, characteristic
3SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5173C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591612C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591420C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590868C211yesmaximal, characteristic, complemented
13#10590837C211yesmaximal, characteristic, complemented
14#10590718C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#80246—31nomaximal
17#80159—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63908C2211yescharacteristic
32C4×#625C2211yescharacteristic
33#63891—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63878—21no—
36#63872C2211yescharacteristic, complemented
37#63863C2211yescharacteristic
38#63862—21no—
39#63856C2211yescharacteristic
40#63845—21no—
41#63841C2211yescharacteristic, complemented
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5829—31no—
62#5806—31no—
63#5642—31no—
64#5639—31no—
65C3×#452—31no—
66C3×#450—31no—
67#5233—31no—
68C2×#832—31no—
69#5188—31no—
70#5185—31no—
71#5173D311yescharacteristic, complemented
72#5171—31no—
73#5169D311yescharacteristic, complemented
74#5166—31no—
75Dic3×SD16—31no—
76Dic3×SD16—31no—
77Dic3×SD16—61no—
78#5051—31no—
79#5048—31no—
80#4805—31no—
81#4800—31no—
82#4779—31no—
83#4772—31no—
84D3×#102—31no—
85#4768—31no—
86#4766—31no—
87#4763—31no—
88#4737—31no—
89#67⋊C8—31no—
90#67⋊C8—31no—
91#4721—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×#625D411yescharacteristic
109C2×D3×Dic3—21no—
110C32×SD16—22no—
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—41no—
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C2×D311yescharacteristic
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156#953—61no—
157C2×#217—61no—
158#947—31no—
159#946—31no—
160#946C2×D311yescharacteristic
161#946C2×D311yescharacteristic, complemented
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—61no—
165C2×#216C2×D311yescharacteristic, complemented
166C2×#215C2×D311yescharacteristic
167#939—61no—
168#939—61no—
169#938—31no—
170#937—61no—
171#936—31no—
172#935—61no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—61no—
176#930—31no—
177#929—61no—
178C4×#67—31no—
179C4×#67—31no—
180C2×(C2×D3)⋊C4—61no—
181#926—31no—
182C2×C4⋊Dic3—31no—
183#924—31no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188#898—61no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890—31no—
193#890—31no—
194#890—61no—
195#889—61no—
196#886—61no—
197#883—61no—
198#879—61no—
199#877—61no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#821—31no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818—31no—
223#817—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231C8×Dic3—31no—
232C8×Dic3—31no—
233C8×Dic3—61no—
234#810—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—81no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#625—22no—
273#625—81no—
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—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—31no—
289#450—31no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—31no—
316C2×#67—31no—
317C2×#67—61no—
318C2×#67—61no—
319C22×Dic3—21no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—121no—
324#237—22no—
325#237—41no—
326D3×D4—22no—
327D3×D4—41no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—24no—
335C3×SD16—22no—
336C3×SD16—22no—
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349#217—31no—
350#217—31no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#216—41no—
360#215—41no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
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—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—121no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D3×C8—121no—
409D3×C8—121no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C2×C3×D3#13512yes—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C22×D4—31no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16D3211yescharacteristic
441C22×C8—91no—
442C22×C8—91no—
443#126—181no—
444#125—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452#121—91no—
453#121—181no—
454#120—181no—
455C4×Q8—91no—
456C4×D4—91no—
457C4×D4—91no—
458#117—91no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C22⋊C4—181no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3D3×D411yescharacteristic
493C22×D3D3×D411yescharacteristic
494C3×Q8—22no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C3×D4—122no—
510C3×D4#23712yes—
511C3×D4#23712yes—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67—42no—
530#67—62no—
531#67—62no—
532#67—241no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—42no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—122no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—242no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556D12—21no—
557D12—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—122no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32—42no—
576C2×C32#54611yescharacteristic
577C2×C32C2×#13511yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—22no—
580C3×D3—41no—
581C3×D3—81no—
582C24—61no—
583#41—62no—
584#41—121no—
585C2×Q8—31no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—91no—
592C2×D4—121no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—181no—
599C22×C4—181no—
600Q16—121no—
601SD16—22no—
602SD16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—361no—
607C2×C8—361no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—91no—
632C42—181no—
633C42—181no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—84no—
665C2×D3#91612yes—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C2×#23711yescharacteristic
677C3×C4C2×#23711yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4#100411yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—62no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#329611yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701C23—61no—
702C23—122no—
703C23—122no—
704C23—241no—
705Q8—21no—
706Q8—21no—
707Q8—61no—
708Q8—61no—
709D4—21no—
710D4—61no—
711D4—61no—
712D4—122no—
713D4—122no—
714D4—182no—
715D4—721no—
716D4#380512yes—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—62no—
745C2×C3—82no—
746C2×C3—121no—
747C2×C3—241no—
748C2×C3#559111yescharacteristic
749C2×C3#559111yescharacteristic
750C2×C3C2×#91611yescharacteristic
751C2×C3D3×#13511yescharacteristic
752C2×C3#577511yescharacteristic
753C2×C3#577811yescharacteristic
754D3—22no—
755D3—41no—
756D3—81no—
757C22—22no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—244no—
770C22D32×D411yescharacteristic
771C4—41no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—181no—
779C4—361no—
780C4—361no—
781C4#6431311yescharacteristic
782C4C2×#380511yescharacteristic
783C3—21no—
784C3#8015911yescharacteristic, complemented
785C3#8024611yescharacteristic, complemented
786C2—42no—
787C2—62no—
788C2—121no—
789C2—241no—
790C2D3×#91611yescharacteristic
791C2#1059475411yescharacteristic
792C2#1059522511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595244C2
hypercenterC2×SD16D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595380C2semidirect
3. SD16×C3⋊Dic3C2semidirect
4. C3×#5173C2semidirect
5. C3×#5169C2semidirect
6. #10591635C2semidirect
7. #10591634C2semidirect
8. #10591612C2semidirect
9. #10591479C2semidirect
10. #10591420C2semidirect
11. D3×#832C2semidirect
12. #10590868C2semidirect
13. #10590837C2semidirect
14. #10590718C2semidirect
15. #10590675C2semidirect
21. Q8×C3⋊Dic3C22semidirect
24. C3×#946C22semidirect
25. C2×C3×#216C22semidirect
36. #63872C22semidirect
41. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
46. #63644C22semidirect
47. C8×C3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#816C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
71. #5173D3semidirect
73. #5169D3semidirect
161. #946C2×D3semidirect
165. C2×#216C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
228. #816C2×D3semidirect
697. C32#3296semidirect
784. C3#80159semidirect
785. C3#80246semidirect

Maximal subgroups

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

subgroupindex
#105953802
#105952442
SD16×C3⋊Dic32
C3×#51732
C3×#51692
#105916352
#105916342
#105916122
#105914792
#105914202
D3×#8322
#105908682
#105908372
#105907182
#105906752
#802463
#801593