Finite Group Databasebeta

← #28400404

Subgroups — #28400404

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299228C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic
3#20298900C211yesmaximal, characteristic, complemented
4#20298897C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298889C211yesmaximal, characteristic, complemented
7#20298886C211yesmaximal, characteristic, complemented
8#20298878C211yesmaximal, characteristic, complemented
9#20298877C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#20298633C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic
14#102×D113C211yesmaximal, characteristic
15#478×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic, complemented
20#16813621—21no—
21#16813621C2211yescharacteristic, complemented
22#16813613C2211yescharacteristic, complemented
23#16813612—21no—
24#16813602—21no—
25#16813600—21no—
26C4×D452C2211yescharacteristic
27D4×Dic113C2211yescharacteristic
28#16813584C2211yescharacteristic
29C4×C22⋊D113—21no—
30#16813582—21no—
31#16813580C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813579C2211yescharacteristic
34C4⋊C4×D113C2211yescharacteristic
35C2×#14268624—21no—
36C22⋊C4×D113—21no—
37#16813555C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43C4⋊#11744751C2211yescharacteristic, complemented
44#16813551C2211yescharacteristic, complemented
45#16813551C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813542C2211yescharacteristic
51#16813542C2211yescharacteristic
52#125×C113C2211yescharacteristic, complemented
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64D4×D113—22no—
65D4×D113Q814yescomplemented
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268630—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—22no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91#14268624D411yescharacteristic
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113—21no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C42×C113C2311yescharacteristic
106C23×C113—21no—
107C22×D113—21no—
108C22×D113—24no—
109C22×D113—81no—
110C22×D113—81no—
111C22×D113C2×D411yescharacteristic
112D4×C113—21no—
113D4×C113C2×Q812yes—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—81no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—24no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—81no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—21no—
130D452C2×Q812yes—
131C4×D113—81no—
132C4×D113—81no—
133C4×D113—81no—
134C4×D113C2×Q812yes—
135C4×D113#4112yes—
136Dic226—81no—
137Dic226—81no—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—22no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113C22×D411yescharacteristic
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—22no—
149C2×D113—41no—
150C2×D113—41no—
151C2×D113—84no—
152C2×D113C22⋊Q812yes—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C22×Q811yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113C22⋊Q812yes—
166C2×C113—42no—
167C2×C113C2×C22⋊Q811yescharacteristic
168C2×C113#57611yescharacteristic
169C2×C113#57711yescharacteristic
170D113—22no—
171D113—42no—
172#3081—1131nomaximal, Sylow
173C113#308111yescharacteristic, complemented, Sylow
174#544—1131no—
175#518—1131no—
176#478—1131no—
177#478—1131no—
178#478—1131no—
179#478D11311yescharacteristic, complemented
180#476—1131no—
181#476—1131no—
182#474—1131no—
183#474—1131no—
184#428—1131no—
185#427—1131no—
186#424—1131no—
187#418—1131no—
188C2×#102—1131no—
189C22×D4—1131no—
190C2×M16—1131no—
191C22×C8—1131no—
192C4⋊Q8—1131no—
193C4⋊Q8—1131no—
194C4⋊Q8—2261no—
195#125—1131no—
196#125—2261no—
197#125C2×D11311yescharacteristic, complemented
198C22⋊Q8—2261no—
199C22⋊Q8—2261no—
200C4×D4—1131no—
201C4×D4—1131no—
202C4×D4—1131no—
203C4×D4—2261no—
204C4×D4—2261no—
205C4×D4C2×D11311yescharacteristic
206#117—1131no—
207#117—1131no—
208#117—1131no—
209C2×C4⋊C4—1131no—
210C2×C22⋊C4—2261no—
211C2×C22⋊C4—2261no—
212#107—1131no—
213#107—1131no—
214#107—1131no—
215#107C2×D11311yescharacteristic, complemented
216#106—1131no—
217#106—1131no—
218#106—1131no—
219#106C2×D11311yescharacteristic, complemented
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223C4⋊C8C2×D11311yescharacteristic, complemented
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102C2×D11311yescharacteristic
231#102C2×D11311yescharacteristic
232C24—2261no—
233C2×Q8—2261no—
234C2×Q8—2261no—
235C2×D4—1134no—
236C2×D4—1131no—
237C2×D4—2262no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—1131no—
242C22×C4—2261no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246M16—2262no—
247C2×C8—1131no—
248C2×C8—1131no—
249C2×C8—2262no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4C22×D11311yescharacteristic
265C4⋊C4C22×D11311yescharacteristic
266C4⋊C4C22×D11311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1131no—
269C22⋊C4—1131no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—1131no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—1131no—
281C23—9041no—
282C23—9041no—
283C23—2264no—
284C23—2261no—
285Q8—9041no—
286Q8—9041no—
287D4—21no—
288D4—1132no—
289D4—2264no—
290D4—2261no—
291D4Q8×D11312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—1131no—
297C2×C4—1132no—
298C2×C4—1132no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—9041no—
302C2×C4—9041no—
303C2×C4—9041no—
304C2×C4—9041no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—1132no—
319C22—9044no—
320C22—4521no—
321C22—4521no—
322C22—2262no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1132no—
332C4—4521no—
333C4—4521no—
334C4—4521no—
335C4—2261no—
336C4—2261no—
337C4C2×Q8×D11311yescharacteristic
338C4#41×D11311yescharacteristic
339C2—42no—
340C2—4522no—
341C2—2262no—
342C2C22⋊Q8×D11311yescharacteristic
343C2#2029940211yescharacteristic
344C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#478D113
hypocenterC113#3081
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299228C2semidirect
3. #20298900C2semidirect
4. #20298897C2semidirect
5. #20298895C2semidirect
6. #20298889C2semidirect
7. #20298886C2semidirect
8. #20298878C2semidirect
9. #20298877C2semidirect
10. #20298639C2semidirect
11. #20298633C2semidirect
12. #20298623C2semidirect
15. #478×C113C2semidirect
19. #16813622C22semidirect
21. #16813621C22semidirect
22. #16813613C22semidirect
37. #16813555C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. C4⋊#11744751C22semidirect
44. #16813551C22semidirect
45. #16813551C22semidirect
52. #125×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. C4⋊C8×C113C22semidirect
65. D4×D113Q8semidirect
173. C113#3081semidirect
179. #478D113semidirect
197. #125C2×D113semidirect
215. #107C2×D113semidirect
219. #106C2×D113semidirect
223. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992282
#202990702
#202989002
#202988972
#202988952
#202988892
#202988862
#202988782
#202988772
#202986392
#202986332
#202986232
#202986012
#102×D1132
#478×C1132
#3081113