Finite Group Databasebeta

← #28400366

Subgroups — #28400366

Order 14464.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#20299153C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic
3#20298901C212yesmaximal, complemented
4#20298900C212yesmaximal, complemented
5#20298889C211yesmaximal, characteristic, complemented
6#20298888C211yesmaximal, characteristic, complemented
7#20298875C211yesmaximal, characteristic, complemented
8#20298639C212yesmaximal, complemented
9#20298620C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal
11#474×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113C2211yescharacteristic
13C22×C4×D113—21no—
14C2×#14268630C2212yes—
15#16813622C2211yescharacteristic, complemented
16#16813613C2212yescomplemented
17#16813602—21no—
18#16813598—21no—
19Q8×Dic113—21no—
20#16813587—21no—
21C4×D452C2211yescharacteristic
22D4×Dic113C2211yescharacteristic
23#16813584C2211yescharacteristic
24C4×C22⋊D113—21no—
25#16813582—21no—
26#16813580C2212yes—
27C4⋊C4×D113C2211yescharacteristic
28C22⋊C4×D113—21no—
29C42×D113C2211yescharacteristic
30#16813555C2212yescomplemented
31#16813554C2212yescomplemented
32#16813553C2212yescomplemented
33C4⋊#11744751C2211yescharacteristic, complemented
34#16813551C2212yescomplemented
35#16813544C2212yes—
36#16813543C2212yes—
37#16813542C2212yes—
38C4⋊Q8×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41C4⋊C8×C113C2211yescharacteristic, complemented
42#102×C113C2212yes—
43C23×D113—21no—
44C2×Dic226—21no—
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47D4×D113—22no—
48D4×D113Q814yescomplemented
49C22×Dic113—21no—
50C2×C4×D113—21no—
51C2×C4×D113—21no—
52C2×C4×D113—21no—
53C2×C4×D113—44no—
54C2×C4×D113D411yescharacteristic
55C2×C4×D113D411yescharacteristic
56C2×C4×D113C2311yescharacteristic
57#14268630—24no—
58C2×#11744751C2312yes—
59C4⋊Dic113—21no—
60C4⋊Dic113—22no—
61C4⋊Dic113C2311yescharacteristic
62C4⋊Dic113C2312yes—
63#14268626—21no—
64#14268626—22no—
65C22⋊Dic113—21no—
66#14268624—22no—
67#14268624—21no—
68#14268624—21no—
69C4×Dic113—22no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113—21no—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C2×C8×C113C2312yes—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C22×D113—21no—
84C22×D113—24no—
85C22×D113—42no—
86C22×D113—42no—
87C22×D113C2×D411yescharacteristic
88Q8×C113—42no—
89D4×C113—21no—
90D4×C113C2×Q812yes—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113—42no—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—24no—
98C2×Dic113—22no—
99C2×Dic113—21no—
100C2×Dic113—42no—
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104D452—21no—
105D452C2×Q812yes—
106C4×D113—22no—
107C4×D113—41no—
108C4×D113—42no—
109C4×D113—42no—
110C4×D113—42no—
111C4×D113C2×Q812yes—
112C4×D113#4112yes—
113Dic226—42no—
114C8×C113—22no—
115#11744751—22no—
116C22×C113—22no—
117C22×C113—41no—
118C22×C113—41no—
119C22×C113C22×D411yescharacteristic
120C2×D113—21no—
121C2×D113—21no—
122C2×D113—22no—
123C2×D113—48no—
124C2×D113—41no—
125C2×D113—41no—
126C2×D113C22⋊Q812yes—
127C4×C113—21no—
128C4×C113—41no—
129C4×C113—42no—
130C4×C113AGL(1,ℤ/8)12yes—
131C4×C113C22×Q811yescharacteristic
132C4×C113C2×#4111yescharacteristic
133Dic113—21no—
134Dic113—21no—
135Dic113—41no—
136Dic113—42no—
137Dic113C22⋊Q812yes—
138C2×C113—42no—
139C2×C113C2×C22⋊Q811yescharacteristic
140C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
141C2×C113#57511yescharacteristic
142D113—22no—
143D113—42no—
144#3077—1131nomaximal, Sylow
145C113#307711yescharacteristic, complemented, Sylow
146#533—1131no—
147C2×C4×D4—1131no—
148#478—1132no—
149#478—1132no—
150#476—1131no—
151#476—1131no—
152#474—1131no—
153#474D11311yescharacteristic, complemented
154#428—1132no—
155#423—1131no—
156#418—1132no—
157C22×D4—1131no—
158C23×C4—2261no—
159C2×M16—1132no—
160C4⋊Q8—1131no—
161C4⋊Q8C2×D11311yescharacteristic, complemented
162#125—1132no—
163C22⋊Q8—2261no—
164C22⋊Q8—2261no—
165C4×Q8—2261no—
166C4×Q8—2261no—
167C4×D4—1131no—
168C4×D4—1131no—
169C4×D4—1131no—
170C4×D4—2261no—
171C4×D4—2261no—
172C4×D4C2×D11311yescharacteristic
173#117—1132no—
174C2×C4⋊C4—1131no—
175C2×C22⋊C4—2261no—
176C2×C42—1131no—
177#107—1132no—
178#107C2×D11312yescomplemented
179#106—1132no—
180#106—1132no—
181C4⋊C8—1132no—
182C4⋊C8—1131no—
183C4⋊C8C2×D11311yescharacteristic, complemented
184#102—1132no—
185#102—1132no—
186#102—1132no—
187#102C2×D11312yes—
188C24—2261no—
189C2×Q8—21no—
190C2×Q8—2261no—
191C2×D4—1134no—
192C2×D4—1131no—
193C2×D4—2262no—
194C2×D4—2261no—
195C2×D4C22×D11311yescharacteristic
196C22×C4—21no—
197C22×C4—1131no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—4524no—
201C22×C4—2261no—
202C22×C4—2261no—
203C22×C4—2261no—
204C22×C4—2261no—
205M16—2264no—
206C2×C8—1132no—
207C2×C8C22×D11312yes—
208C4⋊C4—21no—
209C4⋊C4—1132no—
210C4⋊C4—1131no—
211C4⋊C4—2261no—
212C4⋊C4—2262no—
213C4⋊C4—2262no—
214C4⋊C4—2261no—
215C4⋊C4C22×D11312yes—
216C4⋊C4C22×D11311yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—2261no—
219C22⋊C4—2262no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C42—1131no—
223C42—1131no—
224C42—1131no—
225C42—2262no—
226C42C22×D11311yescharacteristic
227C23—21no—
228C23—1131no—
229C23—4522no—
230C23—4522no—
231C23—2264no—
232C23—2261no—
233Q8—42no—
234Q8—4522no—
235D4—21no—
236D4—1132no—
237D4—2264no—
238D4—2261no—
239D4Q8×D11312yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—1131no—
244C2×C4—1132no—
245C2×C4—1132no—
246C2×C4—1131no—
247C2×C4—1131no—
248C2×C4—4521no—
249C2×C4—4522no—
250C2×C4—4522no—
251C2×C4—4522no—
252C2×C4—4522no—
253C2×C4—2262no—
254C2×C4—2261no—
255C2×C4—2262no—
256C2×C4D4×D11311yescharacteristic
257C2×C4D4×D11311yescharacteristic
258C2×C4C23×D11311yescharacteristic
259C8—22no—
260C8—2262no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—1132no—
265C22—4528no—
266C22—4521no—
267C22—4521no—
268C22—2262no—
269C22—2261no—
270C22—2261no—
271C22C2×D4×D11311yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—1132no—
276C4—4521no—
277C4—4522no—
278C4—2261no—
279C4—2261no—
280C4#1681364612yes—
281C4C2×Q8×D11311yescharacteristic
282C4#41×D11311yescharacteristic
283C2—42no—
284C2—4522no—
285C2—2262no—
286C2C22⋊Q8×D11311yescharacteristic
287C2C2×#1681364611yescharacteristic
288C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#474D113
hypocenterC113#3077
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298901C2semidirect
4. #20298900C2semidirect
5. #20298889C2semidirect
6. #20298888C2semidirect
7. #20298875C2semidirect
8. #20298639C2semidirect
9. #20298620C2semidirect
11. #474×C113C2semidirect
15. #16813622C22semidirect
16. #16813613C22semidirect
30. #16813555C22semidirect
31. #16813554C22semidirect
32. #16813553C22semidirect
33. C4⋊#11744751C22semidirect
34. #16813551C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #107×C113C22semidirect
41. C4⋊C8×C113C22semidirect
48. D4×D113Q8semidirect
145. C113#3077semidirect
153. #474D113semidirect
161. C4⋊Q8C2×D113semidirect
178. #107C2×D113semidirect
183. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
C4×D4×D1132
#202989012
#202989002
#202988892
#202988882
#202988752
#202986392
#202986202
#202986012
#474×C1132
#3077113