Finite Group Databasebeta

← #28401331

Subgroups — #28401331

Order 14464.

468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813601C211yesmaximal, characteristic, complemented
2#20298928C212yesmaximal, complemented
3#20298914C212yesmaximal, complemented
4#20298825C214yesmaximal, complemented
5#20298749C212yesmaximal, complemented
6#20298736C212yesmaximal, complemented
7C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
8C2×#121×C113C211yesmaximal, characteristic
9C22×Dic226C2211yescharacteristic, complemented
10C2×#14268635C2214yescomplemented
11C22×#11744751C2212yescomplemented
12#16813601—21no—
13#16813601—21no—
14#16813601C2212yes—
15#16813601C2212yescomplemented
16C2×C4⋊Dic113C2211yescharacteristic, complemented
17C2×#14268626—21no—
18C2×C22⋊Dic113—21no—
19#16813553C2214yescomplemented
20#16813545C2214yescomplemented
21#16813543C2214yescomplemented
22C22⋊#11744751C2212yes—
23C22⋊#11744751C2212yescomplemented
24C22×D4×C113—21no—
25C22×D4×C113C2211yescharacteristic
26C23×C4×C113C2211yescharacteristic
27#121×C113—21no—
28#121×C113—21no—
29#121×C113C2212yes—
30#121×C113C2212yes—
31C2×C4⋊C4×C113C2211yescharacteristic
32C2×C22⋊C4×C113—21no—
33C2×Dic226—21no—
34C2×Dic226—42no—
35C2×Dic226C2312yes—
36C22×Dic113—21no—
37C22×Dic113—21no—
38#14268635—44no—
39C2×#11744751—42no—
40C2×#11744751C2314yes—
41C4⋊Dic113—21no—
42C4⋊Dic113C2312yes—
43#14268626—22no—
44#14268626—22no—
45C22⋊Dic113—22no—
46C22⋊Dic113—22no—
47C24×C113—21no—
48C24×C113D411yescharacteristic
49C2×D4×C113—22no—
50C2×D4×C113—22no—
51C2×D4×C113—21no—
52C2×D4×C113—42no—
53C2×D4×C113—44no—
54C2×D4×C113C2312yes—
55C22×C4×C113—21no—
56C22×C4×C113—42no—
57C22×C4×C113D411yescharacteristic
58C22×C4×C113D411yescharacteristic
59C22×C4×C113D411yescharacteristic
60C22×C4×C113C2311yescharacteristic
61C22×C4×C113C2311yescharacteristic
62C22×C4×C113C2311yescharacteristic
63C4⋊C4×C113—21no—
64C4⋊C4×C113C2312yes—
65C22⋊C4×C113—22no—
66C22⋊C4×C113—22no—
67C23×C113—22no—
68C23×C113—41no—
69C23×C113—41no—
70C23×C113—42no—
71C23×C113—42no—
72C23×C113—42no—
73C23×C113SD1614yescomplemented
74C23×C113C2×D411yescharacteristic
75C23×C113C2×D411yescharacteristic
76C23×C113C2×D411yescharacteristic
77D4×C113—24no—
78D4×C113—42no—
79D4×C113—44no—
80D4×C113—44no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—41no—
86C2×C4×C113—41no—
87C2×C4×C113—41no—
88C2×C4×C113—42no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2411yescharacteristic
93C2×Dic113—22no—
94C2×Dic113—22no—
95C2×Dic113—42no—
96C2×Dic113—42no—
97Dic226—24no—
98Dic226—42no—
99#11744751—24no—
100C22×C113—21no—
101C22×C113—21no—
102C22×C113—21no—
103C22×C113—21no—
104C22×C113—21no—
105C22×C113—21no—
106C22×C113—44no—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113—42no—
110C22×C113—84no—
111C22×C113C2×SD1612yes—
112C22×C113C2×SD1612yes—
113C22×C113C2×SD1612yes—
114C22×C113C22×D411yescharacteristic
115C4×C113—21no—
116C4×C113—21no—
117C4×C113—21no—
118C4×C113—42no—
119C4×C113H(5,𝔽2)12yes—
120Dic113—42no—
121Dic113—42no—
122C2×C113—22no—
123C2×C113—22no—
124C2×C113—22no—
125C2×C113—82no—
126C2×C113#53411yescharacteristic
127C2×C113C22×SD1611yescharacteristic
128C2×C113#57511yescharacteristic
129#3187—1131nomaximal, Sylow
130C113#318711yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—1131no—
132C2×#121D11311yescharacteristic
133#483—1132no—
134#481—1132no—
135#465—1134no—
136#450—1132no—
137#448—1132no—
138C2×C22⋊C8—1131no—
139C22×Q8—1131no—
140C22×D4—21no—
141C22×D4C2×D11311yescharacteristic
142C23×C4C2×D11311yescharacteristic
143C2×SD16—1134no—
144C22×C8—1132no—
145C22⋊Q8—1132no—
146C22⋊Q8—1132no—
147C22⋊Q8—2261no—
148C22⋊Q8—2261no—
149#121—21no—
150#121—21no—
151#121C2×D11312yes—
152#121C2×D11312yes—
153C2×C4⋊C4—1131no—
154C2×C4⋊C4—2261no—
155C2×C4⋊C4C2×D11311yescharacteristic
156C2×C22⋊C4—21no—
157C2×C22⋊C4—2261no—
158#106—1134no—
159#103—1134no—
160#102—1134no—
161C22⋊C8—1132no—
162C22⋊C8—1132no—
163C24—21no—
164C24C22⋊D11311yescharacteristic
165C2×Q8—1132no—
166C2×Q8—4522no—
167C2×Q8—2261no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—42no—
172C2×D4—44no—
173C2×D4C22×D11312yes—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—2261no—
177C22×C4—2261no—
178C22×C4C22⋊D11311yescharacteristic
179C22×C4C22⋊D11311yescharacteristic
180C22×C4C22⋊D11311yescharacteristic
181C22×C4C22×D11311yescharacteristic
182C22×C4C22×D11311yescharacteristic
183C22×C4C22×D11311yescharacteristic
184SD16—4524no—
185C2×C8—1134no—
186C2×C8—4522no—
187C4⋊C4—21no—
188C4⋊C4—1132no—
189C4⋊C4—2261no—
190C4⋊C4—2262no—
191C4⋊C4—2262no—
192C4⋊C4C22×D11312yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—2262no—
196C22⋊C4—2262no—
197C23—22no—
198C23—41no—
199C23—41no—
200C23—42no—
201C23—42no—
202C23—42no—
203C23#1426863514yescomplemented
204C23C2×C22⋊D11311yescharacteristic
205C23C2×C22⋊D11311yescharacteristic
206C23C2×C22⋊D11311yescharacteristic
207Q8—4522no—
208Q8—2264no—
209D4—24no—
210D4—42no—
211D4—44no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—4522no—
222C2×C4—4522no—
223C2×C4—2262no—
224C2×C4—2262no—
225C2×C4C2×C22⋊D11311yescharacteristic
226C2×C4C2×C22⋊D11311yescharacteristic
227C2×C4C2×C22⋊D11311yescharacteristic
228C2×C4C23×D11311yescharacteristic
229C8—2264no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—44no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—84no—
241C22C2×#1426863512yes—
242C22C2×#1426863512yes—
243C22C2×#1426863512yes—
244C22C22×C22⋊D11311yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—4522no—
250C4—4522no—
251C4#1681366712yes—
252C2—22no—
253C2—22no—
254C2—22no—
255C2—82no—
256C2#2029915711yescharacteristic
257C2C22×#1426863511yescharacteristic
258C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radicalC2×#121×C113C2
socleC22×C113C22×D4
hypercenterC2×#121D113
hypocenterC113#3187
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16813601C2semidirect
2. #20298928C2semidirect
3. #20298914C2semidirect
4. #20298825C2semidirect
5. #20298749C2semidirect
6. #20298736C2semidirect
7. C2×C22⋊#11744751C2semidirect
9. C22×Dic226C22semidirect
10. C2×#14268635C22semidirect
11. C22×#11744751C22semidirect
15. #16813601C22semidirect
16. C2×C4⋊Dic113C22semidirect
19. #16813553C22semidirect
20. #16813545C22semidirect
21. #16813543C22semidirect
23. C22⋊#11744751C22semidirect
73. C23×C113SD16semidirect
130. C113#3187semidirect
203. C23#14268635semidirect

Maximal subgroups

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

subgroupindex
C2×#168136012
#202989282
#202989142
#202988252
#202987492
#202987362
C2×C22⋊#117447512
C2×#121×C1132
#3187113