Finite Group Databasebeta

← #11858043

Subgroups — #11858043

Order 1152.

1374 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1374 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C211yesmaximal, characteristic
2C2×#64287C211yesmaximal, characteristic, complemented
3#10595219C211yesmaximal, characteristic, complemented
4#10593498C212yesmaximal, complemented
5#10593496C212yesmaximal, complemented
6#10593493C212yesmaximal, complemented
7C2×#63739C212yesmaximal, complemented
8#10593365C211yesmaximal, characteristic, complemented
9#10593363C211yesmaximal, characteristic, complemented
10#10593360C211yesmaximal, characteristic, complemented
11#10593349C211yesmaximal, characteristic, complemented
12C2×#3830C2211yescharacteristic
13C2×C3×D3×D4—21no—
14C2×D3×#67—22no—
15C22×#625C2212yes—
16C2×#3805C2212yes—
17#64313—24no—
18#64313C418yescomplemented
19C2×#3802C2211yescharacteristic
20C2×#3798C2211yescharacteristic
21C2×#3795—21no—
22C2×#3792C2212yescomplemented
23C22×#622C2212yescomplemented
24#64287—24no—
25C2×#3788C2211yescharacteristic, complemented
26C2×#3787C2211yescharacteristic, complemented
27C3×D4×Dic3—21no—
28C2×#3724C2212yescomplemented
29#63957C2212yescomplemented
30#63952—22no—
31#63900C2211yescharacteristic, complemented
32#63874C2211yescharacteristic, complemented
33#63844—21no—
34#63740C2211yescharacteristic, complemented
35#63740C2211yescharacteristic, complemented
36#63740C2212yescomplemented
37#63739C2211yescharacteristic, complemented
38#63739C2211yescharacteristic, complemented
39#63739C2212yescomplemented
40#63739C2212yescomplemented
41#63739C2212yescomplemented
42#63739C2212yescomplemented
43#63739C2212yescomplemented
44C2×#1004—61no—
45#5546—61no—
46C23×C3×D3—22no—
47C22×D32—21no—
48C2×C32×D4D411yescharacteristic
49C2×#638D412yes—
50C22×C3⋊Dic3C2312yes—
51#3830C2×C414yes—
52#3830D414yes—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#634D411yescharacteristic
55C2×C3×#67—22no—
56C22×C3×Dic3—22no—
57C3×D3×D4—28no—
58C2×C3×D12—21no—
59C2×C3×C4×D3—21no—
60D3×#67—216no—
61C2×#627C2311yescharacteristic
62C2×#626—21no—
63C2×#625—22no—
64C2×#625—24no—
65C2×#625C2×C418yescomplemented
66C2×#625C2311yescharacteristic
67C2×#625C2312yes—
68C2×#624—21no—
69#3805—24no—
70#3805C2×C418yescomplemented
71C2×D3×Dic3—22no—
72#3802—22no—
73#3802C2×C414yescomplemented
74#3798—22no—
75#3798C2×C414yescomplemented
76#3795—28no—
77#3792—24no—
78C2×#622—24no—
79C2×#622C2311yescharacteristic
80C2×#622C2311yescharacteristic
81C2×#622C2312yes—
82#3788—22no—
83#3787—22no—
84C3×#217—22no—
85C3×C4⋊Dic3—21no—
86C3×C4×Dic3—21no—
87#3724—22no—
88#3724C2311yescharacteristic
89#3724C2311yescharacteristic
90#3724C2312yes—
91#3722—21no—
92Dic32—22no—
93#2897—91nomaximal, Sylow
94C22×C3×D4—61no—
95C22×#67—62no—
96C22×#67—62no—
97#1004—68no—
98#1004—68no—
99C2×#237—62no—
100C2×#237—61no—
101C2×#237—61no—
102C2×#237—61no—
103C2×D3×D4—21no—
104C2×D3×D4—61no—
105C2×D3×D4—62no—
106C2×#235—61no—
107C2×#235—61no—
108C3×C4×D4—61no—
109D4×Dic3—21no—
110C4×#67—62no—
111C2×Dic3⋊C4—62no—
112D3×C4⋊C4—61no—
113#887—61no—
114#67⋊C4—62no—
115#877—62no—
116#872—61no—
117C4×Dic6—61no—
118C23×C32C2×D412yes—
119C22×C3⋊D3C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—21no—
122C22×C3×D3—28no—
123C22×C3×D3—82no—
124C22×C3×D3—82no—
125C2×D32—24no—
126C2×D32—81no—
127C2×D32—81no—
128C32×D4C22⋊C414yes—
129C2×C32×C4C2×D411yescharacteristic
130#638C22⋊C418yes—
131C2×C3⋊Dic3C22×C414yes—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D414yes—
134C2×C3⋊Dic3C2411yescharacteristic
135C4×C3⋊D3C22×C412yes—
136C4×C3⋊D3C2×D412yes—
137#634C22⋊C414yes—
138C3×#67—28no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—82no—
144C3×D12—24no—
145C3×C4×D3—24no—
146#627—21no—
147#627C22×C412yes—
148#626—24no—
149#625—28no—
150#625—21no—
151#625—22no—
152#625C22×C412yes—
153#625C22×C414yes—
154#624—81no—
155D3×Dic3—28no—
156#622—21no—
157#622—21no—
158#622—22no—
159C2×H(5,𝔽2)—91no—
160C2×#131—91no—
161#520—91no—
162#418—91no—
163#418—92no—
164#417—91no—
165#417—92no—
166#416—91no—
167#416—92no—
168C2×#102—91no—
169C2×#102—92no—
170C24×C3—62no—
171C23×D3—22no—
172C23×D3—62no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—61no—
176C2×C3×D4—68no—
177C2×C3×D4—62no—
178C22×C3×C4—61no—
179C22×C3×C4—62no—
180C2×#67—22no—
181C2×#67—68no—
182C2×#67—61no—
183C2×#67—62no—
184C2×#67—62no—
185C2×#67—62no—
186C2×#67—61no—
187C2×#67—616no—
188C2×#67—62no—
189C2×#67—62no—
190C2×#67—68no—
191C22×Dic3—22no—
192C22×Dic3—62no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195#237—68no—
196#237—64no—
197#237—64no—
198#237—64no—
199#237—64no—
200#237—68no—
201#237—68no—
202D3×D4—28no—
203D3×D4—64no—
204D3×D4—64no—
205D3×D4—616no—
206#235—64no—
207#235—64no—
208#235—68no—
209C2×D12—21no—
210C2×D12—61no—
211C2×C4×D3—21no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C3×C4⋊C4—61no—
220C3×C22⋊C4—62no—
221C3×C42—61no—
222#217—22no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225C4⋊Dic3—21no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231C4×Dic3—21no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C22×C32—22no—
235C22×C32—22no—
236C22×C32C2×C22⋊C414yes—
237C22×C32C22×D411yescharacteristic
238C2×C3⋊D3—21no—
239C2×C3⋊D3—21no—
240C2×C3⋊D3C2×C22⋊C412yes—
241C2×C3×D3—24no—
242C2×C3×D3—22no—
243C2×C3×D3—42no—
244C2×C3×D3—41no—
245C2×C3×D3—42no—
246C2×C3×D3—41no—
247C2×C3×D3—88no—
248D32—84no—
249C32×C4C2×C22⋊C412yes—
250C3⋊Dic3C2×C22⋊C414yes—
251C3⋊Dic3C23×C411yescharacteristic
252C3⋊Dic3C22×D411yescharacteristic
253C3×Dic3—22no—
254C3×Dic3—42no—
255C3×Dic3—41no—
256C3×Dic3—41no—
257H(5,𝔽2)—98no—
258H(5,𝔽2)—184no—
259C2×#41—91no—
260C2×#41—91no—
261C2×#41—92no—
262C2×#41—181no—
263C22×D4—61no—
264C22×D4—91no—
265C22×D4—92no—
266C22×D4—182no—
267#131—184no—
268C2×M16—91no—
269C2×M16—92no—
270C22×C8—91no—
271C22×C8—92no—
272C4×Q8—181no—
273C4×D4—61no—
274C4×D4—182no—
275#117—91no—
276#117—92no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—92no—
279#103—91no—
280#103—91no—
281#103—92no—
282#102—92no—
283#102—91no—
284#102—92no—
285#102—92no—
286#102—92no—
287#102—91no—
288#102—92no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—62no—
292C23×C3—61no—
293C23×C3—68no—
294C23×C3—242no—
295C23×C3—242no—
296C22×D3—21no—
297C22×D3—22no—
298C22×D3—28no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—68no—
302C22×D3—82no—
303C22×D3—82no—
304C22×D3—242no—
305C22×D3—242no—
306C3×D4—24no—
307C3×D4—24no—
308C3×D4—64no—
309C3×D4—68no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—64no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—61no—
317C2×C3×C4—242no—
318#67—28no—
319#67—62no—
320#67—64no—
321#67—68no—
322#67—68no—
323#67—64no—
324#67—68no—
325#67—62no—
326#67—68no—
327#67—64no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—22no—
332C2×Dic3—64no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—68no—
341C2×Dic3—82no—
342D12—24no—
343D12—64no—
344C4×D3—24no—
345C4×D3—62no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—68no—
350C4×D3—242no—
351Dic6—62no—
352Dic6—64no—
353Dic6—64no—
354Dic6—62no—
355C2×C32—24no—
356C2×C32C22×C22⋊C411yescharacteristic
357C2×C32#57611yescharacteristic
358C2×C32#57711yescharacteristic
359C3⋊D3—22no—
360C3×D3—44no—
361C3×D3—42no—
362C24—62no—
363C24—181no—
364#41—94no—
365#41—94no—
366#41—94no—
367#41—98no—
368#41—182no—
369#41—188no—
370#41—184no—
371C2×Q8—91no—
372C2×Q8—91no—
373C2×D4—62no—
374C2×D4—68no—
375C2×D4—61no—
376C2×D4—94no—
377C2×D4—92no—
378C2×D4—91no—
379C2×D4—92no—
380C2×D4—98no—
381C2×D4—181no—
382C2×D4—182no—
383C2×D4—182no—
384C2×D4—184no—
385C2×D4—1816no—
386C2×D4GO+(4,𝔽2)11yescharacteristic
387C22×C4—61no—
388C22×C4—62no—
389C22×C4—92no—
390C22×C4—91no—
391C22×C4—181no—
392C22×C4—182no—
393M16—182no—
394M16—184no—
395C2×C8—91no—
396C2×C8—91no—
397C2×C8—92no—
398C2×C8—182no—
399C2×C8—184no—
400C4⋊C4—61no—
401C4⋊C4—91no—
402C4⋊C4—92no—
403C4⋊C4—91no—
404C4⋊C4—182no—
405C22⋊C4—62no—
406C22⋊C4—181no—
407C42—61no—
408C42—182no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—64no—
418C22×C3—62no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—248no—
424C2×D3—22no—
425C2×D3—24no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—88no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—248no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—62no—
441C3×C4—122no—
442C3×C4—121no—
443C3×C4—121no—
444Dic3—22no—
445Dic3—42no—
446Dic3—41no—
447Dic3—41no—
448Dic3—64no—
449Dic3—61no—
450Dic3—61no—
451Dic3—64no—
452Dic3—61no—
453Dic3—61no—
454C32#289711yescharacteristic, complemented, Sylow
455C23—61no—
456C23—62no—
457C23—68no—
458C23—91no—
459C23—184no—
460C23—242no—
461C23—242no—
462C23—721no—
463C23—721no—
464C23C2×GO+(4,𝔽2)12yes—
465Q8—92no—
466Q8—94no—
467Q8—181no—
468D4—68no—
469D4—64no—
470D4—92no—
471D4—94no—
472D4—98no—
473D4—184no—
474D4—181no—
475D4—182no—
476D4—188no—
477D4D32⋊C414yes—
478C2×C4—61no—
479C2×C4—64no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—92no—
484C2×C4—91no—
485C2×C4—94no—
486C2×C4—94no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—188no—
490C2×C4—242no—
491C2×C4—721no—
492C2×C4C2×GO+(4,𝔽2)11yescharacteristic
493C8—181no—
494C8—181no—
495C8—182no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—44no—
503C2×C3—44no—
504C2×C3—124no—
505C2×C3—122no—
506D3—42no—
507D3—44no—
508D3—122no—
509D3—122no—
510C22—22no—
511C22—22no—
512C22—62no—
513C22—64no—
514C22—92no—
515C22—121no—
516C22—122no—
517C22—121no—
518C22—122no—
519C22—181no—
520C22—181no—
521C22—248no—
522C22—724no—
523C22C2×D32⋊C414yes—
524C22C22×GO+(4,𝔽2)11yescharacteristic
525C4—62no—
526C4—91no—
527C4—91no—
528C4—94no—
529C4—121no—
530C4—122no—
531C4—121no—
532C4C2×D32⋊C412yes—
533C3—21no—
534C3—21no—
535C2—24no—
536C2—122no—
537C2—124no—
538C2—182no—
539C2#1059651411yescharacteristic
540C2#1059651511yescharacteristic
541C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC2×C32×D4D4
socleC22×C32C22×D4
prime radicalC2×#64313C2
cosocleC2×C3⋊Dic3C24
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#2897
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×#64287C2semidirect
3. #10595219C2semidirect
4. #10593498C2semidirect
5. #10593496C2semidirect
6. #10593493C2semidirect
7. C2×#63739C2semidirect
8. #10593365C2semidirect
9. #10593363C2semidirect
10. #10593360C2semidirect
11. #10593349C2semidirect
18. #64313C4semidirect
22. C2×#3792C22semidirect
23. C22×#622C22semidirect
25. C2×#3788C22semidirect
26. C2×#3787C22semidirect
28. C2×#3724C22semidirect
29. #63957C22semidirect
31. #63900C22semidirect
32. #63874C22semidirect
34. #63740C22semidirect
35. #63740C22semidirect
36. #63740C22semidirect
37. #63739C22semidirect
38. #63739C22semidirect
39. #63739C22semidirect
40. #63739C22semidirect
41. #63739C22semidirect
42. #63739C22semidirect
43. #63739C22semidirect
65. C2×#625C2×C4semidirect
70. #3805C2×C4semidirect
73. #3802C2×C4semidirect
75. #3798C2×C4semidirect
454. C32#2897semidirect

Maximal subgroups

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

subgroupindex
C2×#643132
C2×#642872
#105952192
#105934982
#105934962
#105934932
C2×#637392
#105933652
#105933632
#105933602
#105933492
#28979