Finite Group Databasebeta

← #11889099

Subgroups — #11889099

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596113C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic
3C3×#5048C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591652C211yesmaximal, characteristic, complemented
6#10591622C211yesmaximal, characteristic, complemented
7#10591590C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591157C211yesmaximal, characteristic, complemented
10#10591094C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590594C211yesmaximal, characteristic, complemented
13#10590554C211yesmaximal, characteristic, complemented
14#10590513C211yesmaximal, characteristic, complemented
15#10590474C211yesmaximal, characteristic, complemented
16#80685—31nomaximal
17#80160—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic, complemented
22#64155C2211yescharacteristic, complemented
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C4×#638C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26#64107—21no—
27#64101C2211yescharacteristic, complemented
28#64099—21no—
29#64099C2211yescharacteristic, complemented
30#64095—21no—
31#64086—21no—
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic
36C22×C3×C3⋊C8C2211yescharacteristic, complemented
37#63976—21no—
38#63922—21no—
39#63916C2211yescharacteristic
40#63914C2211yescharacteristic
41#63898C2211yescharacteristic
42#63885—21no—
43C2×#3712C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62#5642—31no—
63#5642—31no—
64#5642—61no—
65#5609—31no—
66C3×#465—31no—
67C3×#450—31no—
68C2×#832—31no—
69#5174—31no—
70#5169—31no—
71#5169—31no—
72#5164—31no—
73#5163—31no—
74#5163—31no—
75C2×#821—31no—
76#5111—31no—
77#5048D311yescharacteristic, complemented
78#5046D311yescharacteristic, complemented
79#5033—31no—
80#4871—31no—
81#4866—31no—
82#4817—31no—
83#4812—31no—
84#4784—31no—
85#4770—31no—
86#4770—31no—
87#4766—31no—
88#4764—31no—
89#4764—31no—
90#4736—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117#3757D411yescharacteristic
118#3752—21no—
119#3752—21no—
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128#3750D411yescharacteristic
129C4×C3⋊Dic3—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C3×#215—22no—
133C3×#215—41no—
134C3×#215—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C2×C3×C3⋊C8—41no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3712—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C22×C3×C8—31no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8C2×D311yescharacteristic, complemented
158C3×C22⋊Q8C2×D311yescharacteristic, complemented
159C3×#121—31no—
160#953—61no—
161#946—31no—
162#946—31no—
163#946—61no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—61no—
167C2×#215C2×D311yescharacteristic
168C2×#215C2×D311yescharacteristic, complemented
169C2×#215C2×D311yescharacteristic, complemented
170#940—31no—
171#940—31no—
172#939—61no—
173#938—31no—
174#937—61no—
175#937—61no—
176D4×Dic3—31no—
177#930C2×D311yescharacteristic
178C4×#67—31no—
179C4×#67—31no—
180C4×#67—61no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—61no—
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187#898—61no—
188#898—61no—
189#898—62no—
190#895—31no—
191#893—31no—
192#892—31no—
193#892—31no—
194#892—61no—
195#890—31no—
196#890—31no—
197#890—61no—
198#890—61no—
199#890—61no—
200#890—62no—
201#886—61no—
202#886—61no—
203#886—62no—
204#884—61no—
205#882—61no—
206#877—61no—
207#877—61no—
208#877—62no—
209C3×#106—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#835C2×D311yescharacteristic, complemented
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231#818—31no—
232#818—31no—
233#815—31no—
234#815—31no—
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic, complemented
239#809C2×D311yescharacteristic, complemented
240#808C2×D311yescharacteristic, complemented
241#807—31no—
242#807—31no—
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—81no—
254C32×Q8—21no—
255C32×Q8—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262#638—22no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—42no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—42no—
279C3×D12#4112yes—
280#626—42no—
281#625—42no—
282#625—42no—
283#625—81no—
284D3×Dic3—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—91no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—31no—
297#460—91no—
298#450—31no—
299#450—91no—
300#440—91no—
301#435—91no—
302#418—91no—
303C2×#102—91no—
304C24×C3—61no—
305C23×D3—21no—
306C23×D3—61no—
307C23×D3—61no—
308C2×C3×Q8—21no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—121no—
318C22×C3×C4—21no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—124no—
333C22×Dic3—61no—
334C22×Dic3—62no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—121no—
340D3×D4—121no—
341D3×D4—124no—
342C2×D12—22no—
343C2×D12—21no—
344C2×D12—41no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C3×SD16—62no—
354C3×SD16—121no—
355C3×SD16—121no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—121no—
361C3×C4⋊C4—22no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C22⋊C4—22no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—61no—
372#217—31no—
373#217—31no—
374#217—61no—
375#217—61no—
376#217—61no—
377#215—22no—
378#215—41no—
379#215—41no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—62no—
403C4⋊Dic3—62no—
404C4⋊Dic3—62no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—62no—
425C4×Dic3—62no—
426C2×C3⋊C8—41no—
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431ΓL(1,𝔽25)—121no—
432ΓL(1,𝔽25)—121no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32AGL(1,ℤ/8)12yes—
436C22×C32C22×D411yescharacteristic
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3×D3—22no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—84no—
450D32—84no—
451C32×C4—21no—
452C32×C4—41no—
453C32×C4—41no—
454C32×C4C2×#4111yescharacteristic
455C32×C4H(5,𝔽2)11yescharacteristic
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—41no—
462C22×D4—31no—
463C22×D4—91no—
464C22×D4—181no—
465C2×SD16—31no—
466C2×SD16—31no—
467C2×SD16—31no—
468C2×M16—91no—
469C22×C8—31no—
470#127—91no—
471#126—181no—
472#125—91no—
473#125—181no—
474#123—181no—
475C22⋊Q8—91no—
476C22⋊Q8D3211yescharacteristic, complemented
477#121—31no—
478#121—91no—
479#121—181no—
480#120—181no—
481#120—181no—
482C4×Q8—91no—
483C4×D4—91no—
484C4×D4—91no—
485#117—91no—
486#117—181no—
487C2×C4⋊C4—91no—
488#107—91no—
489#107—91no—
490#106—31no—
491C4⋊C8—91no—
492#103—31no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500#102—91no—
501#102—91no—
502C22⋊C8—31no—
503C22⋊C8—91no—
504#97—91no—
505C23×C3—21no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—241no—
512C23×C3D3×D411yescharacteristic
513C23×C3D3×D411yescharacteristic
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—31no—
518C22×D3—31no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—61no—
522C22×D3—81no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—241no—
528C22×D3—241no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×D4—32no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—122no—
542C3×D4—122no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4D3×D411yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—42no—
563#67—62no—
564#67—62no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—241no—
572#67—241no—
573C2×Dic3—21no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—122no—
590C2×Dic3—124no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593D12—21no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—42no—
599D12—122no—
600D12#23712yes—
601C4×D3—61no—
602C4×D3—61no—
603C4×D3—61no—
604C4×D3—61no—
605C4×D3—121no—
606C4×D3—121no—
607C4×D3—122no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32#54611yescharacteristic
618C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—41no—
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624C24—61no—
625C24—181no—
626C2×Q8C2×D3211yescharacteristic
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—121no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—182no—
640C2×D4—361no—
641C2×D4—364no—
642C22×C4—91no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646SD16—62no—
647SD16—121no—
648SD16—121no—
649M16—361no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—121no—
655C4⋊C4—21no—
656C4⋊C4—31no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—91no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—61no—
668C22⋊C4—91no—
669C22⋊C4—91no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C42—91no—
675C42—181no—
676C42—181no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—22no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—62no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3#91412yes—
696C22×C3#91412yes—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—84no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—244no—
719C2×D3—244no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—121no—
732C3×C4C2×#23711yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4#100411yescharacteristic
735C3×C4D3×#4111yescharacteristic
736Dic3—41no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—122no—
747Dic3—122no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752C32#331011yescharacteristic, complemented, Sylow
753C23—61no—
754C23—61no—
755C23—61no—
756C23—91no—
757C23—122no—
758C23—122no—
759C23—241no—
760C23—362no—
761C23—362no—
762C23—721no—
763C23#381111yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—32no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—122no—
773D4—122no—
774D4—182no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—61no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—362no—
792C2×C4—362no—
793C2×C4#381111yescharacteristic
794C2×C4C22×D3211yescharacteristic
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—122no—
806C2×C3—241no—
807C2×C3—241no—
808C2×C3#559111yescharacteristic
809C2×C3#561011yescharacteristic
810C2×C3C2×#91411yescharacteristic
811C2×C3C2×#91411yescharacteristic
812C2×C3#577011yescharacteristic
813C2×C3#577511yescharacteristic
814D3—42no—
815D3—81no—
816D3—81no—
817D3—121no—
818D3—121no—
819D3—241no—
820C22—21no—
821C22—21no—
822C22—62no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—244no—
835C22—724no—
836C22#6394112yes—
837C22C2×#381111yescharacteristic
838C4—21no—
839C4—41no—
840C4—41no—
841C4—121no—
842C4—181no—
843C4—181no—
844C4—181no—
845C4—361no—
846C4—361no—
847C4D3×#23711yescharacteristic
848C4#6431311yescharacteristic
849C3—21no—
850C3#8016011yescharacteristic, complemented
851C3#8068511yescharacteristic, complemented
852C2—22no—
853C2—122no—
854C2—241no—
855C2—241no—
856C2—361no—
857C2#1059530711yescharacteristic
858C2C2×#6394111yescharacteristic
859C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595069C2
hypercenterC22⋊Q8D32
hypocenterC32#3310
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. #10596113C2semidirect
3. C3×#5048C2semidirect
4. C3×#5046C2semidirect
5. #10591652C2semidirect
6. #10591622C2semidirect
7. #10591590C2semidirect
8. #10591572C2semidirect
9. #10591157C2semidirect
10. #10591094C2semidirect
11. C2×#63563C2semidirect
12. #10590594C2semidirect
13. #10590554C2semidirect
14. #10590513C2semidirect
15. #10590474C2semidirect
21. C32×C22⋊Q8C22semidirect
22. #64155C22semidirect
23. Q8×C3⋊Dic3C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
27. #64101C22semidirect
29. #64099C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#215C22semidirect
36. C22×C3×C3⋊C8C22semidirect
43. C2×#3712C22semidirect
44. C3×#835C22semidirect
45. C3×#830C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. #63572C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
77. #5048D3semidirect
78. #5046D3semidirect
157. C3×C22⋊Q8C2×D3semidirect
158. C3×C22⋊Q8C2×D3semidirect
168. C2×#215C2×D3semidirect
169. C2×#215C2×D3semidirect
184. C22×C3⋊C8C2×D3semidirect
215. #835C2×D3semidirect
222. #830C2×D3semidirect
238. #809C2×D3semidirect
239. #809C2×D3semidirect
240. #808C2×D3semidirect
476. C22⋊Q8D32semidirect
752. C32#3310semidirect
850. C3#80160semidirect
851. C3#80685semidirect

Maximal subgroups

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

subgroupindex
#105961132
#105950692
C3×#50482
C3×#50462
#105916522
#105916222
#105915902
#105915722
#105911572
#105910942
C2×#635632
#105905942
#105905542
#105905132
#105904742
#806853
#801603