Finite Group Databasebeta

← #11884103

Subgroups — #11884103

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596101C211yesmaximal, characteristic
2C2×#63945C211yesmaximal, characteristic, complemented
3#10594803C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5051C211yesmaximal, characteristic, complemented
6C3×#5050C211yesmaximal, characteristic, complemented
7#10591629C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591579C211yesmaximal, characteristic, complemented
10#10591183C211yesmaximal, characteristic, complemented
11#10591157C211yesmaximal, characteristic, complemented
12#10590606C211yesmaximal, characteristic, complemented
13#10590565C211yesmaximal, characteristic, complemented
14#10590522C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80771—31nomaximal
17#80204—31nomaximal
18C2×#3832C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×#3797C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23#64156C2211yescharacteristic
24C4×#638C2211yescharacteristic
25#64104—21no—
26#64104C2211yescharacteristic
27#64103—21no—
28#64102C2211yescharacteristic
29#64091—21no—
30C22⋊C4×C3⋊D3—21no—
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#216C2211yescharacteristic, complemented
34C3×#924C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36#63964—21no—
37#63952—21no—
38#63945—24no—
39#63888—21no—
40#63873C2211yescharacteristic, complemented
41#63871C2211yescharacteristic, complemented
42#63843C2211yescharacteristic, complemented
43#63839—21no—
44C2×#3717—24no—
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51C2×#3712C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63Q8×#67—31no—
64C22×#215—31no—
65C2×#918—31no—
66C2×#918—31no—
67C22×#204—31no—
68#5632—31no—
69#5630—31no—
70#5630—31no—
71#5630—61no—
72C3×#467—31no—
73C3×#451—31no—
74#5190—31no—
75#5190—31no—
76#5187—31no—
77#5185—31no—
78#5111—31no—
79#5051D311yescharacteristic, complemented
80#5050D311yescharacteristic, complemented
81#5046—31no—
82#4889—31no—
83#4886—31no—
84#4818—31no—
85#4818—31no—
86#4817—31no—
87#4812—31no—
88#4808—31no—
89#4806—31no—
90#4806—31no—
91#4798—31no—
92#4731—31no—
93#4730—31no—
94C23×C3⋊D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638D411yescharacteristic
98#3832—22no—
99#3832—41no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—21no—
109C2×C4×C3⋊D3C2311yescharacteristic
110C22×C3×Dic3—21no—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6—41no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#624—21no—
119#3797—22no—
120#3797—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3757D411yescharacteristic
125#3752—21no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129#3752D411yescharacteristic
130#3750D411yescharacteristic
131C4×C3⋊Dic3C2311yescharacteristic
132C3×#217—21no—
133C3×#216—22no—
134C3×#216—22no—
135C3×#216—41no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148Dic32—21no—
149#3717—22no—
150#3717—22no—
151#3717—22no—
152#3717—22no—
153#3717—41no—
154#3717D414yescomplemented
155#3712—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—61no—
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—61no—
166C22×Dic6C2×D311yescharacteristic
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C22×C3×C8—31no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175#947—31no—
176#947—31no—
177#947—61no—
178#946—31no—
179#946—61no—
180Q8×Dic3—31no—
181#944—31no—
182#944—31no—
183#944—61no—
184C2×#216C2×D311yescharacteristic, complemented
185C2×#216C2×D311yescharacteristic, complemented
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—64no—
194C4×#67—31no—
195C4×#67—31no—
196C4×#67—61no—
197C4×#67—61no—
198#924—61no—
199#924C2×D311yescharacteristic
200C22×C3⋊C8C2×D311yescharacteristic
201#918—64no—
202#918—64no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—64no—
210C2×ΓL(1,𝔽25)—31no—
211C2×ΓL(1,𝔽25)—31no—
212#897—31no—
213#896—61no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#895—61no—
219#895—62no—
220#894—61no—
221#894—61no—
222#894—62no—
223#893—31no—
224#893—31no—
225#893—61no—
226#888—61no—
227#887—31no—
228#882—61no—
229#882—61no—
230#882—62no—
231#67⋊C4—61no—
232D3×C22⋊C4—61no—
233D3×C22⋊C4—61no—
234D3×C22⋊C4—62no—
235#878—61no—
236C3×#107—31no—
237C3×#103—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#103—31no—
241C3×C22⋊C8—31no—
242#835C2×D311yescharacteristic, complemented
243#830C2×D311yescharacteristic
244#821—31no—
245#821—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248#815—31no—
249#815—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—31no—
252#810C2×D311yescharacteristic, complemented
253#810C2×D311yescharacteristic, complemented
254#810C2×D311yescharacteristic, complemented
255#809—31no—
256#809—31no—
257#807C2×D311yescharacteristic, complemented
258C23×C32C2×D411yescharacteristic
259C22×C3⋊D3—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—81no—
264C22×C3⋊D3C2×D411yescharacteristic
265C32×Q8—21no—
266C32×Q8—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273#638—22no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—42no—
281C4⋊(C3⋊D3)—42no—
282C4⋊(C3⋊D3)—81no—
283C4⋊(C3⋊D3)C2×D412yes—
284C4×C3⋊D3—21no—
285C4×C3⋊D3—21no—
286C4×C3⋊D3—42no—
287C4×C3⋊D3—81no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C3×Dic6C2×D412yes—
300#627—42no—
301#624—42no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—91no—
307C22×SD16—91no—
308D4×Q8—91no—
309#546—91no—
310#497—91no—
311#468—91no—
312#467—31no—
313#464—91no—
314#461—91no—
315#452—91no—
316#451—31no—
317#450—91no—
318#448—91no—
319#440—91no—
320#435—91no—
321C23×D3—62no—
322C23×D3—61no—
323C23×D3—61no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—62no—
329C2×C3×Q8—61no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C22×Dic3—21no—
341#239—62no—
342#239—62no—
343#239—122no—
344#239—121no—
345#239—121no—
346#239—122no—
347D3×Q8—62no—
348D3×Q8—62no—
349D3×Q8—121no—
350D3×Q8—121no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—62no—
368C2×D12—122no—
369C2×D12—121no—
370C2×D12—121no—
371C2×D12—122no—
372C2×C4×D3—31no—
373C2×C4×D3—31no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—62no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—62no—
383C2×Dic6—22no—
384C2×Dic6—21no—
385C2×Dic6—41no—
386C2×Dic6—61no—
387C2×Dic6—61no—
388C2×Dic6C22×D311yescharacteristic
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C3×Q16—62no—
392C3×Q16—62no—
393C3×Q16—121no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C3×C4⋊C4—22no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—22no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—61no—
411#217—21no—
412#217—31no—
413#217—31no—
414#217—61no—
415#216—22no—
416#216—22no—
417#216—41no—
418#215—34no—
419#215—62no—
420#215—62no—
421#215—62no—
422#215—62no—
423#215—121no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—61no—
448Dic3⋊C4—61no—
449Dic3⋊C4—61no—
450Dic3⋊C4—61no—
451Dic3⋊C4—61no—
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454C4×Dic3—31no—
455C4×Dic3—31no—
456C4×Dic3—61no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C2×C3⋊C8—22no—
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463C2×C3⋊C8C22×D311yescharacteristic
464#204—34no—
465#204—62no—
466#204—62no—
467#204—62no—
468#204—62no—
469#204—121no—
470ΓL(1,𝔽25)—62no—
471ΓL(1,𝔽25)—62no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32#13712yescomplemented
475C22×C32C22×D411yescharacteristic
476C2×C3⋊D3—22no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—84no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3×Dic3—22no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41—91no—
499C22×Q8—31no—
500C22×Q8—91no—
501C22×D4—91no—
502#137—184no—
503C2×Q16—31no—
504C2×Q16—31no—
505C2×Q16—31no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—184no—
513C2×M16—91no—
514C22×C8—31no—
515C4⋊Q8—91no—
516C4⋊Q8—181no—
517#124—91no—
518#123—181no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521C22⋊Q8—181no—
522C22⋊Q8—181no—
523C22⋊Q8D3211yescharacteristic
524#121—91no—
525#121—181no—
526#120—181no—
527C4×Q8—91no—
528C4×D4—91no—
529C4×D4—91no—
530C4×D4—181no—
531C2×C22⋊C4—181no—
532#107—31no—
533C4⋊C8—91no—
534#103—31no—
535#103—31no—
536#103—31no—
537#103—31no—
538#102—91no—
539#102—91no—
540C22⋊C8—31no—
541C22⋊C8—91no—
542#97—91no—
543C23×C3—21no—
544C23×C3D3×D411yescharacteristic
545C23×C3D3×D411yescharacteristic
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—61no—
549C22×D3—62no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—62no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—124no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—242no—
564C3×Q8—21no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—32no—
569C3×Q8—41no—
570C3×Q8—41no—
571C3×Q8—61no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8—61no—
575C3×Q8—61no—
576C3×Q8—122no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—62no—
601#67—62no—
602#67—122no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—42no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617D12—32no—
618D12—32no—
619D12—62no—
620D12—62no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—124no—
634D12—124no—
635D12—241no—
636D12—241no—
637D12—242no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—121no—
643C4×D3—121no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—124no—
649C4×D3—241no—
650C4×D3—241no—
651C4×D3—242no—
652Dic6—21no—
653Dic6—21no—
654Dic6—21no—
655Dic6—21no—
656Dic6—21no—
657Dic6—42no—
658Dic6—122no—
659Dic6—122no—
660Dic6D3×D412yes—
661C3×C8—32no—
662C3×C8—61no—
663C3×C8—61no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C3⋊C8—21no—
668C3⋊C8D3×D412yes—
669C2×C32—22no—
670C2×C32D4211yescharacteristic
671C2×C32C2×#13711yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—42no—
674C3⋊D3—41no—
675C3⋊D3—81no—
676C24—181no—
677#41—182no—
678#41—361no—
679C2×Q8—31no—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—62no—
683C2×Q8—61no—
684C2×Q8—121no—
685C2×Q8—181no—
686C2×Q8—182no—
687C2×Q8—361no—
688C2×Q8C2×D3211yescharacteristic
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—91no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—361no—
697C22×C4—61no—
698C22×C4—91no—
699C22×C4—181no—
700C22×C4—181no—
701C22×C4—181no—
702C22×C4C2×D3211yescharacteristic
703Q16—62no—
704Q16—62no—
705Q16—121no—
706SD16—94no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—182no—
711SD16—361no—
712M16—182no—
713C2×C8—31no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C4⋊C4—21no—
719C4⋊C4—31no—
720C4⋊C4—61no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4—181no—
724C4⋊C4—181no—
725C4⋊C4—181no—
726C4⋊C4C2×D3211yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—61no—
729C22⋊C4—91no—
730C22⋊C4—91no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C42—91no—
737C42—181no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—22no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3#91812yescomplemented
747C22×C3#91812yescomplemented
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—64no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—62no—
757C2×D3—61no—
758C2×D3—62no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—122no—
763C2×D3—122no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—244no—
778C2×D3—244no—
779C2×D3—248no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—42no—
786C3×C4—42no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—62no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4#100911yescharacteristic
799Dic3—22no—
800Dic3—41no—
801Dic3—41no—
802Dic3—41no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—61no—
808Dic3—61no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812C32#326611yescharacteristic, complemented, Sylow
813C23—91no—
814C23—181no—
815C23—181no—
816C23—362no—
817C23—362no—
818C23—721no—
819C23#381111yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—32no—
823Q8—61no—
824Q8—61no—
825Q8—61no—
826Q8—61no—
827Q8—61no—
828Q8—122no—
829Q8—362no—
830D4—92no—
831D4—182no—
832D4—181no—
833D4—181no—
834D4—181no—
835D4—362no—
836D4—362no—
837D4—721no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—91no—
847C2×C4—91no—
848C2×C4—91no—
849C2×C4—122no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—362no—
853C2×C4—362no—
854C2×C4—721no—
855C2×C4#381111yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C8—32no—
858C8—61no—
859C8—61no—
860C8—61no—
861C2×C3—22no—
862C2×C3—22no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3#559011yescharacteristic
868C2×C3#560911yescharacteristic
869C2×C3C2×#91811yescharacteristic
870C2×C3C2×#91811yescharacteristic
871C2×C3#577011yescharacteristic
872C2×C3#577811yescharacteristic
873D3—124no—
874D3—121no—
875D3—122no—
876D3—121no—
877D3—122no—
878D3—241no—
879D3—242no—
880D3—241no—
881D3—241no—
882C22—21no—
883C22—21no—
884C22—181no—
885C22—181no—
886C22—181no—
887C22—182no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—361no—
892C22—361no—
893C22—724no—
894C22#6394512yescomplemented
895C22C2×#381111yescharacteristic
896C4—21no—
897C4—41no—
898C4—41no—
899C4—62no—
900C4—121no—
901C4—121no—
902C4—121no—
903C4—181no—
904C4—181no—
905C4—181no—
906C4D32×D411yescharacteristic
907C4#6431411yescharacteristic
908C3—21no—
909C3#8020411yescharacteristic, complemented
910C3#8077111yescharacteristic, complemented
911C2—22no—
912C2—361no—
913C2—362no—
914C2—721no—
915C2#1059529211yescharacteristic
916C2C2×#6394511yescharacteristic
917C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10596101C2
hypercenterC22⋊Q8D32
hypocenterC32#3266
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
2. C2×#63945C2semidirect
3. #10594803C2semidirect
4. C22×#3717C2semidirect
5. C3×#5051C2semidirect
6. C3×#5050C2semidirect
7. #10591629C2semidirect
8. #10591602C2semidirect
9. #10591579C2semidirect
10. #10591183C2semidirect
11. #10591157C2semidirect
12. #10590606C2semidirect
13. #10590565C2semidirect
14. #10590522C2semidirect
15. #10590484C2semidirect
21. C2×#3797C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#216C22semidirect
40. #63873C22semidirect
41. #63871C22semidirect
42. #63843C22semidirect
51. C2×#3712C22semidirect
52. C3×#835C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. #63572C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
79. #5051D3semidirect
80. #5050D3semidirect
154. #3717D4semidirect
184. C2×#216C2×D3semidirect
185. C2×#216C2×D3semidirect
186. C2×#216C2×D3semidirect
242. #835C2×D3semidirect
252. #810C2×D3semidirect
253. #810C2×D3semidirect
254. #810C2×D3semidirect
257. #807C2×D3semidirect
474. C22×C32#137semidirect
746. C22×C3#918semidirect
747. C22×C3#918semidirect
812. C32#3266semidirect
894. C22#63945semidirect
909. C3#80204semidirect
910. C3#80771semidirect

Maximal subgroups

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

subgroupindex
#105961012
C2×#639452
#105948032
C22×#37172
C3×#50512
C3×#50502
#105916292
#105916022
#105915792
#105911832
#105911572
#105906062
#105905652
#105905222
#105904842
#807713
#802043