Finite Group Databasebeta

← #11888691

Subgroups — #11888691

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594530C211yesmaximal, characteristic, complemented
2#10594433C211yesmaximal, characteristic, complemented
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4888C211yesmaximal, characteristic, complemented
5C3×#4886C211yesmaximal, characteristic, complemented
6#10590823C211yesmaximal, characteristic, complemented
7#10590748C211yesmaximal, characteristic, complemented
8#10590724C211yesmaximal, characteristic, complemented
9#10590671C211yesmaximal, characteristic, complemented
10#10590615C211yesmaximal, characteristic, complemented
11#10590610C211yesmaximal, characteristic, complemented
12#10590568C211yesmaximal, characteristic, complemented
13#10590501C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#81546—31nomaximal
17#80819—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64102C2211yescharacteristic
21#64099C2211yescharacteristic
22C2×C3×#204C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63912—21no—
29#63908C2211yescharacteristic
30C4×#625C2211yescharacteristic
31#63900—21no—
32#63898C2211yescharacteristic
33Dic3×D12—21no—
34#63891—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63885—21no—
37#63873C2211yescharacteristic
38#63859—21no—
39#63854—21no—
40#63854—21no—
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#107C2211yescharacteristic
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61#5631—31no—
62#5631—31no—
63#5618—31no—
64#5530—31no—
65C3×#485—31no—
66C3×#468—31no—
67#5172—31no—
68#5162—31no—
69#5133—31no—
70#5127—31no—
71#5048—31no—
72#5043—31no—
73#5037—31no—
74#5002—31no—
75#4891—31no—
76#4891—31no—
77#4891—61no—
78#4888D311yescharacteristic, complemented
79#4886D311yescharacteristic, complemented
80#4869—31no—
81#4862—31no—
82#4818—31no—
83#4810—31no—
84#4804—31no—
85#4803—31no—
86#4797—31no—
87#4797—31no—
88#4785—31no—
89#4778—31no—
90#4734—31no—
91#4730—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×#625—21no—
103C2×#625D411yescharacteristic
104C2×#624—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3799—22no—
109#3799—22no—
110#3799—41no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724—21no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141#3715—41no—
142#3714—22no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×M16—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#117—31no—
155#944—31no—
156#944—31no—
157C2×#215—31no—
158#939—61no—
159#938—31no—
160D4×Dic3—31no—
161D4×Dic3—61no—
162C2×#214—31no—
163C2×#213—31no—
164#930—31no—
165C4×#67—31no—
166C4×#67—31no—
167C2×C4⋊Dic3—31no—
168C22×C3⋊C8—31no—
169C2×D24—31no—
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)C2×D311yescharacteristic
172C2×D3×C8—31no—
173#897C2×D311yescharacteristic
174#897C2×D311yescharacteristic
175#895C2×D311yescharacteristic
176#894—61no—
177#894—61no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—61no—
182#892C2×D311yescharacteristic
183D3×C4⋊C4—31no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186#890—31no—
187#890—31no—
188#890—61no—
189#886—61no—
190#884—61no—
191#884—61no—
192#884—61no—
193#883—61no—
194#883—61no—
195#883—61no—
196#879—61no—
197#876—61no—
198C4×D12—61no—
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic
201C3×#107C2×D311yescharacteristic
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816C2×D311yescharacteristic
221#815—31no—
222#815—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226#810—31no—
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#808C2×D311yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—42no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#626—42no—
268#626—42no—
269#625—41no—
270#625—81no—
271#624—42no—
272#624—42no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—31no—
283#483—91no—
284#478—91no—
285#468—31no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C2×#67—31no—
301C2×#67—31no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308#239—62no—
309#239—62no—
310#239—121no—
311#239—121no—
312#235—62no—
313#235—62no—
314#235—121no—
315#235—121no—
316C2×D12—21no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C3×SD16—121no—
337C3×M16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—61no—
357#217—31no—
358#217—31no—
359#217—61no—
360#217—61no—
361#215—121no—
362#214—121no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
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—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—121no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406#204—41no—
407ΓL(1,𝔽25)—41no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—21no—
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—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—91no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—91no—
439C2×M16—31no—
440C22×C8—91no—
441C4⋊Q8—91no—
442#126—181no—
443#125—91no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—31no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107D3211yescharacteristic
461#106—31no—
462#106—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—31no—
466#103—31no—
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⋊C8—91no—
476#97—91no—
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—121no—
484C22×D3D3×D411yescharacteristic
485C22×D3D3×D411yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—122no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—122no—
512#67—122no—
513#67—121no—
514#67—121no—
515#67—241no—
516#67—241no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533D12—21no—
534D12—21no—
535D12—32no—
536D12—32no—
537D12—42no—
538D12—62no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—122no—
543D12—122no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—242no—
555C4×D3—241no—
556C4×D3—241no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32#54611yescharacteristic
572C2×C32#57511yescharacteristic
573C2×C32#57711yescharacteristic
574C3⋊D3—42no—
575C3×D3—41no—
576C3×D3—41no—
577C3×D3—81no—
578#41—182no—
579#41—182no—
580#41—361no—
581#41—361no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598SD16—121no—
599SD16—361no—
600D8—182no—
601M16—121no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—361no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—91no—
630C22×C3—21no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—241no—
659C2×D3—241no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4#100411yescharacteristic
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4#100911yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691C32#330711yescharacteristic, complemented, Sylow
692C23—31no—
693C23—31no—
694C23—61no—
695C23—181no—
696Q8—61no—
697Q8—61no—
698Q8—61no—
699Q8—61no—
700D4—61no—
701D4—61no—
702D4—92no—
703D4—122no—
704D4—181no—
705D4—362no—
706D4—362no—
707D4—361no—
708D4—721no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4—721no—
727C2×C4—721no—
728C2×C4C22×D3211yescharacteristic
729C8—21no—
730C8—61no—
731C8—61no—
732C8—181no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—121no—
737C2×C3—121no—
738C2×C3—241no—
739C2×C3#561011yescharacteristic
740C2×C3#565411yescharacteristic
741C2×C3#576811yescharacteristic
742C2×C3#577311yescharacteristic
743C2×C3#577811yescharacteristic
744C2×C3#577811yescharacteristic
745D3—41no—
746D3—41no—
747D3—81no—
748D3—122no—
749D3—122no—
750D3—242no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—182no—
761C22—361no—
762C22—361no—
763C22D32×D411yescharacteristic
764C4—41no—
765C4—41no—
766C4—61no—
767C4—61no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—181no—
772C4—181no—
773C4—361no—
774C4#6430711yescharacteristic
775C4#6431911yescharacteristic
776C3—21no—
777C3#8081911yescharacteristic, complemented
778C3#8154611yescharacteristic, complemented
779C2—121no—
780C2—121no—
781C2—241no—
782C2—362no—
783C2#1059461711yescharacteristic
784C2#1059472911yescharacteristic
785C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594530C2semidirect
2. #10594433C2semidirect
3. #10592590C2semidirect
4. C3×#4888C2semidirect
5. C3×#4886C2semidirect
6. #10590823C2semidirect
7. #10590748C2semidirect
8. #10590724C2semidirect
9. #10590671C2semidirect
10. #10590615C2semidirect
11. #10590610C2semidirect
12. #10590568C2semidirect
13. #10590501C2semidirect
14. #10590462C2semidirect
15. #10590439C2semidirect
78. #4888D3semidirect
79. #4886D3semidirect
691. C32#3307semidirect
777. C3#80819semidirect
778. C3#81546semidirect

Maximal subgroups

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

subgroupindex
#105945302
#105944332
#105925902
C3×#48882
C3×#48862
#105908232
#105907482
#105907242
#105906712
#105906152
#105906102
#105905682
#105905012
#105904622
#105904392
#815463
#808193