Finite Group Databasebeta

← #11872809

Subgroups — #11872809

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596096C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3C3×#5046C211yesmaximal, characteristic
4C3×#5045C211yesmaximal, characteristic, complemented
5#10591572C211yesmaximal, characteristic, complemented
6#10591571C211yesmaximal, characteristic, complemented
7#10591569C211yesmaximal, characteristic, complemented
8#10591569C211yesmaximal, characteristic, complemented
9#10591172C211yesmaximal, characteristic
10#10591134C211yesmaximal, characteristic, complemented
11#10591062C211yesmaximal, characteristic, complemented
12#10590474C211yesmaximal, characteristic, complemented
13#10590473C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81498—31nomaximal
17#80137—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21#64153C2211yescharacteristic, complemented
22#64135C2211yescharacteristic
23#64133C2211yescharacteristic
24#64099—21no—
25#64099C2211yescharacteristic, complemented
26#64098—21no—
27#64096C2211yescharacteristic, complemented
28#64088—21no—
29#64088—21no—
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#926C2211yescharacteristic
33D3×#217—21no—
34D3×#217—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic
39Dic3×D12—21no—
40Dic3×D12—21no—
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C3×#835C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5625—31no—
63#5625—31no—
64#5625—61no—
65#5521—31no—
66C3×#485—31no—
67C3×#450—31no—
68#5218—31no—
69#5164—31no—
70#5162—31no—
71#5162—31no—
72Dic3×SD16—31no—
73#5046D311yescharacteristic
74#5045D311yescharacteristic, complemented
75#4996—31no—
76#4891—31no—
77#4889—31no—
78#4871—31no—
79#4852—31no—
80#4818—31no—
81#4818—31no—
82#4817—31no—
83#4788—31no—
84#4766—31no—
85#4763—31no—
86#4758—31no—
87#4757—31no—
88#4731—31no—
89#4723—31no—
90#4720—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12—22no—
98C2×C3×D12—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108#3757—21no—
109#3757D411yescharacteristic
110#3757D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)D411yescharacteristic
114C4⋊(C3⋊Dic3)D411yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#217—21no—
126C3×#215—22no—
127C3×#215—22no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3716—22no—
140#3716—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8C2×D311yescharacteristic
148C3×C22⋊Q8C2×D311yescharacteristic
149C3×#117—31no—
150C2×#217—61no—
151C2×#217—61no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155#944—31no—
156#944—31no—
157#944—61no—
158C2×#215C2×D311yescharacteristic
159C2×#215C2×D311yescharacteristic
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166C2×#214—31no—
167C2×#214—31no—
168#926—31no—
169#926—31no—
170#926—61no—
171#926C2×D311yescharacteristic
172#924—31no—
173#924—31no—
174#924—61no—
175C2×#204—31no—
176C2×#204—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#890—31no—
182#890—31no—
183#890—61no—
184#890—61no—
185#890—61no—
186#890—62no—
187#889—61no—
188#889—61no—
189#889—62no—
190#887—31no—
191#887—31no—
192#887—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#879—61no—
197#879—61no—
198#879—61no—
199#879—62no—
200#879—62no—
201C4×D12—61no—
202C4×D12—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#830C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#818—31no—
220#817—31no—
221#816—31no—
222#816—31no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#808—31no—
236#808C2×D311yescharacteristic, complemented
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—24no—
243C22×C3×D3—81no—
244C22×C3×D3—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259#634—21no—
260#634—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—24no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×D12#4112yes—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#541—91no—
277#518—91no—
278#485—31no—
279#485—91no—
280#478—91no—
281#478—91no—
282#461—91no—
283#461—91no—
284#450—31no—
285#450—91no—
286#440—91no—
287#440—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290#433—91no—
291C24×C3—61no—
292C23×D3—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C2×D12—21no—
309C2×D12—22no—
310C2×D12—22no—
311C2×D12C22×D311yescharacteristic
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×SD16—62no—
321C3×SD16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C22⋊C4—22no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—61no—
338C3×C42—61no—
339#217—21no—
340#217—31no—
341#217—31no—
342#217—31no—
343#217—31no—
344#217—61no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—62no—
351#217—61no—
352#217—61no—
353#215—22no—
354#215—22no—
355#214—62no—
356#214—62no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—62no—
375C4⋊Dic3—62no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4—62no—
389Dic3⋊C4—62no—
390Dic3⋊C4—62no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—21no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—62no—
405C4×Dic3—62no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—62no—
411#204—62no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C22×D4—31no—
437C2×SD16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×SD16—91no—
441C4⋊Q8—91no—
442#126—181no—
443#126—181no—
444#125—91no—
445#125—181no—
446#125—181no—
447C22⋊Q8—91no—
448C22⋊Q8D3211yescharacteristic
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—31no—
458#117—91no—
459C2×C22⋊C4—181no—
460C2×C22⋊C4—181no—
461#107—31no—
462#107—91no—
463#106—31no—
464#106—91no—
465C4⋊C8—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—31no—
477#97—91no—
478C4×C8—91no—
479C23×C3—21no—
480C23×C3—64no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—241no—
484C23×C3—241no—
485C23×C3D3×D411yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—24no—
490C22×D3—81no—
491C22×D3—81no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—32no—
499C3×D4—32no—
500C3×D4—64no—
501C3×D4—61no—
502C3×D4—61no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547D12—24no—
548D12—21no—
549D12—21no—
550D12#23712yes—
551D12#23712yes—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561Dic6—121no—
562C3×C8—61no—
563C3×C8—61no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C2×C32—41no—
571C2×C32#52511yescharacteristic
572C2×C32#57711yescharacteristic
573C2×C32#57711yescharacteristic
574C3×D3—42no—
575C3×D3—42no—
576C24—61no—
577C2×Q8—91no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—62no—
582C2×D4—62no—
583C2×D4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4C2×D3211yescharacteristic
589SD16—62no—
590SD16—62no—
591SD16—182no—
592SD16—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—31no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—61no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—61no—
621C42—91no—
622C42—91no—
623C42—181no—
624C42—181no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—244no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—84no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4C2×#23711yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—41no—
669Dic3—41no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688C32#312311yescharacteristic, complemented, Sylow
689C23—64no—
690C23—61no—
691C23—61no—
692C23—241no—
693C23—241no—
694C23#381111yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—181no—
698Q8—181no—
699D4—32no—
700D4—32no—
701D4—64no—
702D4—61no—
703D4—61no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4#381111yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—61no—
723C8—61no—
724C8—61no—
725C8—61no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—81no—
732C2×C3—122no—
733C2×C3—122no—
734C2×C3#558611yescharacteristic
735C2×C3#565611yescharacteristic
736C2×C3#576211yescharacteristic
737C2×C3#577011yescharacteristic
738C2×C3#577511yescharacteristic
739C2×C3#577811yescharacteristic
740D3—42no—
741D3—42no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—62no—
746C22—62no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22C2×#381111yescharacteristic
753C4—21no—
754C4—41no—
755C4—41no—
756C4—121no—
757C4—121no—
758C4—181no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—361no—
763C4—361no—
764C4D3×#23711yescharacteristic
765C4D3×#23711yescharacteristic
766C3—21no—
767C3#8013711yescharacteristic, complemented
768C3#8149811yescharacteristic, complemented
769C2—41no—
770C2—122no—
771C2—122no—
772C2#1059516011yescharacteristic
773C2#1059532411yescharacteristic
774C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC22⋊Q8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596096C2semidirect
4. C3×#5045C2semidirect
5. #10591572C2semidirect
6. #10591571C2semidirect
7. #10591569C2semidirect
8. #10591569C2semidirect
10. #10591134C2semidirect
11. #10591062C2semidirect
12. #10590474C2semidirect
13. #10590473C2semidirect
14. #10590461C2semidirect
15. #10590460C2semidirect
20. Q8×C3⋊Dic3C22semidirect
21. #64153C22semidirect
25. #64099C22semidirect
27. #64096C22semidirect
43. C3×#835C22semidirect
44. C3×#835C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
74. #5045D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
236. #808C2×D3semidirect
238. #807C2×D3semidirect
688. C32#3123semidirect
767. C3#80137semidirect
768. C3#81498semidirect

Maximal subgroups

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

subgroupindex
#105960962
#105949822
C3×#50462
C3×#50452
#105915722
#105915712
#105915692
#105911722
#105911342
#105910622
#105904742
#105904732
#105904612
#105904602
#814983
#801373