Finite Group Databasebeta

← #11888603

Subgroups — #11888603

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594995C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic, complemented
3#10592420C211yesmaximal, characteristic, complemented
4C3×#4734C211yesmaximal, characteristic, complemented
5C3×#4728C211yesmaximal, characteristic, complemented
6#10591176C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic, complemented
8#10590962C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590898C211yesmaximal, characteristic, complemented
11#10590829C211yesmaximal, characteristic, complemented
12#10590772C211yesmaximal, characteristic, complemented
13#10590771C211yesmaximal, characteristic, complemented
14#10590752C211yesmaximal, characteristic, complemented
15#10590711C211yesmaximal, characteristic, complemented
16#80108—31nomaximal
17#79500—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63980—21no—
29#67⋊Dic3—21no—
30#63970—21no—
31#63969—21no—
32#63908C2211yescharacteristic
33#63905—21no—
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63891—21no—
37D3×Dic3⋊C4—21no—
38#63869C2211yescharacteristic
39#63866C2211yescharacteristic
40#63861—21no—
41#63856C2211yescharacteristic
42#63841C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63644C2211yescharacteristic
46#63644C2211yescharacteristic
47#63643C2211yescharacteristic
48#63643C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5824—31no—
62#5618—31no—
63#5565—31no—
64#5551—31no—
65C3×#449—31no—
66C3×#435—31no—
67#5232—31no—
68#5171—31no—
69#5162—31no—
70#5158—31no—
71#5152—31no—
72#5134—31no—
73#5133—31no—
74#5114—31no—
75#5113—31no—
76#5042—31no—
77#4847—31no—
78#4841—31no—
79#4815—31no—
80#4797—31no—
81#4772—31no—
82#4763—31no—
83#4734—31no—
84#4734D311yescharacteristic, complemented
85#4728D311yescharacteristic, complemented
86#4723—31no—
87#4721—31no—
88#4721—31no—
89#4721—61no—
90#4711—31no—
91#4703—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C3×#208—41no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130C3×#204—41no—
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#235—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#946—31no—
156#944—31no—
157#939—61no—
158#939—61no—
159#939—61no—
160#938—31no—
161#938—61no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166C2×#214—31no—
167#930—31no—
168#930C2×D311yescharacteristic
169#929—61no—
170C4×#67C2×D311yescharacteristic
171#926—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924—31no—
176#924—31no—
177#924—31no—
178#924—61no—
179C2×Dic3⋊C4—61no—
180C2×#208C2×D311yescharacteristic
181C2×D24C2×D311yescharacteristic
182C2×#204—31no—
183C2×#204C2×D311yescharacteristic
184C2×D3×C8C2×D311yescharacteristic
185#898—61no—
186#892—31no—
187D3×C4⋊C4—61no—
188#890—31no—
189#886—61no—
190#883—61no—
191#883—61no—
192#883—61no—
193#67⋊C4—61no—
194#879—61no—
195C4×D12—31no—
196C4×D12—31no—
197#870—31no—
198#869—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#817—61no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—61no—
232#816—61no—
233#816C2×D311yescharacteristic
234#815C2×D311yescharacteristic
235Dic3⋊C8C2×D311yescharacteristic
236#810—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251#634—21no—
252#634—21no—
253C3×#67—41no—
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#625—42no—
271#625—81no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—31no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67D1211yescharacteristic
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—62no—
321#237—121no—
322#235—22no—
323#235—41no—
324#235—62no—
325#235—121no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—121no—
338C3×D8—62no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217D1211yescharacteristic
364#214—121no—
365(C2×D3)⋊C4—21no—
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)⋊C4D1211yescharacteristic
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—121no—
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398Dic3⋊C4D1211yescharacteristic
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402#208—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—22no—
406#204—41no—
407#204—121no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3⋊Dic3—41no—
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—31no—
439C2×M16—31no—
440C22×C8—31no—
441C4⋊Q8—91no—
442#126—181no—
443#125—91no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474C22⋊C8—31no—
475C22⋊C8D3211yescharacteristic
476#97—31no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3C2×D1211yescharacteristic
482C23×C3D3×D411yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3C2×D1211yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C3×D4—32no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—121no—
493C3×D4—122no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—122no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—41no—
516#67—42no—
517#67—42no—
518#67—122no—
519#67—122no—
520#67—241no—
521#67—241no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—241no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3—242no—
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545D12—21no—
546D12—21no—
547D12—21no—
548D12#23712yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—241no—
555Dic6—21no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—41no—
578C3×D3—42no—
579C3×D3—81no—
580#41—62no—
581#41—121no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4C2×D3211yescharacteristic
600SD16—121no—
601SD16—361no—
602D8—62no—
603M16—121no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—121no—
607C2×C8C2×D3211yescharacteristic
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—181no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—61no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C22×D1211yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23711yescharacteristic
673C3×C4#100411yescharacteristic
674C3×C4#100411yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691Dic3—241no—
692Dic3—241no—
693C32#330711yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23—61no—
697C23D3×D1211yescharacteristic
698Q8—61no—
699Q8—61no—
700Q8—181no—
701Q8—181no—
702D4—32no—
703D4—61no—
704D4—61no—
705D4—61no—
706D4—121no—
707D4—122no—
708D4—122no—
709D4—362no—
710D4—721no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—122no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4—362no—
727C2×C4—721no—
728C2×C4—721no—
729C2×C4D3×D1211yescharacteristic
730C2×C4C22×D3211yescharacteristic
731C8—21no—
732C8—21no—
733C8—61no—
734C8—61no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—122no—
742C2×C3—121no—
743C2×C3—241no—
744C2×C3#555411yescharacteristic
745C2×C3#559111yescharacteristic
746C2×C3#574811yescharacteristic
747C2×C3#575111yescharacteristic
748C2×C3#577011yescharacteristic
749C2×C3#577311yescharacteristic
750D3—41no—
751D3—42no—
752D3—81no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—62no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22C2×D3×D1211yescharacteristic
766C4—21no—
767C4—61no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4—361no—
773C4—361no—
774C4—361no—
775C4—361no—
776C4D3×#23711yescharacteristic
777C4#6431311yescharacteristic
778C3—21no—
779C3#7950011yescharacteristic, complemented
780C3#8010811yescharacteristic, complemented
781C2—41no—
782C2—121no—
783C2—122no—
784C2—241no—
785C2#1059429211yescharacteristic
786C2#1059467911yescharacteristic
787C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594995C2semidirect
2. #10594887C2semidirect
3. #10592420C2semidirect
4. C3×#4734C2semidirect
5. C3×#4728C2semidirect
6. #10591176C2semidirect
7. #10591088C2semidirect
8. #10590962C2semidirect
9. #10590954C2semidirect
10. #10590898C2semidirect
11. #10590829C2semidirect
12. #10590772C2semidirect
13. #10590771C2semidirect
14. #10590752C2semidirect
15. #10590711C2semidirect
84. #4734D3semidirect
85. #4728D3semidirect
693. C32#3307semidirect
779. C3#79500semidirect
780. C3#80108semidirect

Maximal subgroups

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

subgroupindex
#105949952
#105948872
#105924202
C3×#47342
C3×#47282
#105911762
#105910882
#105909622
#105909542
#105908982
#105908292
#105907722
#105907712
#105907522
#105907112
#801083
#795003