Finite Group Databasebeta

← #28400522

Subgroups — #28400522

Order 14464.

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

normal subgroups only

This group has 410 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
2#20298939C214yesmaximal, complemented
3#20298933C212yesmaximal, complemented
4#20298928C212yesmaximal, complemented
5#20298641C212yesmaximal, complemented
6#20298606C212yesmaximal, complemented
7#20298562C211yesmaximal, characteristic
8C2×#117×C113C211yesmaximal, characteristic
9C22×Dic226C2211yescharacteristic
10C2×#14268631C2212yes—
11#16813601—21no—
12#16813601—21no—
13#16813601C2212yes—
14#16813601C2212yes—
15C2×C4⋊Dic113C2211yescharacteristic
16C2×#14268626—21no—
17C2×C22⋊Dic113—21no—
18#16813555C2214yescomplemented
19#16813553C2214yescomplemented
20#16813545C2214yescomplemented
21#16813545C2214yescomplemented
22C22⋊#11744751C2212yes—
23C22⋊#11744751C2212yes—
24C23×C4×C113C2211yescharacteristic
25#117×C113—21no—
26#117×C113—21no—
27#117×C113C2212yes—
28#117×C113C2212yes—
29C2×C4⋊C4×C113C2211yescharacteristic
30C2×C4⋊C4×C113C2211yescharacteristic
31C2×C22⋊C4×C113—21no—
32C2×C42×C113—21no—
33C2×Dic226—24no—
34C2×Dic226—21no—
35C2×Dic226C2312yes—
36C22×Dic113—21no—
37C22×Dic113—21no—
38#14268631—24no—
39C2×#11744751C2314yes—
40C4⋊Dic113—21no—
41C4⋊Dic113C2312yes—
42#14268626—22no—
43#14268626—22no—
44C22⋊Dic113—22no—
45C22⋊Dic113—22no—
46C24×C113D411yescharacteristic
47C22×C4×C113—24no—
48C22×C4×C113—21no—
49C22×C4×C113—21no—
50C22×C4×C113D411yescharacteristic
51C22×C4×C113D411yescharacteristic
52C22×C4×C113D411yescharacteristic
53C22×C4×C113C2311yescharacteristic
54C22×C4×C113C2311yescharacteristic
55C22×C4×C113C2311yescharacteristic
56C4⋊C4×C113—21no—
57C4⋊C4×C113—21no—
58C4⋊C4×C113C2312yes—
59C4⋊C4×C113C2312yes—
60C22⋊C4×C113—22no—
61C22⋊C4×C113—22no—
62C42×C113—22no—
63C42×C113—22no—
64C23×C113—22no—
65C23×C113—22no—
66C23×C113—41no—
67C23×C113C2×D411yescharacteristic
68C23×C113C2×D411yescharacteristic
69C23×C113C2×D411yescharacteristic
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—42no—
78C2×C4×C113—42no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113#4114yes—
83C2×C4×C113C2411yescharacteristic
84C2×Dic113—22no—
85C2×Dic113—22no—
86C2×Dic113—42no—
87C2×Dic113—42no—
88Dic226—24no—
89Dic226—42no—
90#11744751—24no—
91C22×C113—21no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—21no—
96C22×C113—21no—
97C22×C113—21no—
98C22×C113—44no—
99C22×C113#12312yes—
100C22×C113#13712yes—
101C22×C113C22×D411yescharacteristic
102C4×C113—21no—
103C4×C113—21no—
104C4×C113—42no—
105C4×C113—42no—
106C4×C113#12312yes—
107C4×C113C2×#4112yes—
108Dic113—42no—
109Dic113—42no—
110C2×C113—22no—
111C2×C113—22no—
112C2×C113—41no—
113C2×C113C2×#12311yescharacteristic
114C2×C113C2×#13711yescharacteristic
115C2×C113#57511yescharacteristic
116#3095—1131nomaximal, Sylow
117C113#309511yescharacteristic, complemented, Sylow
118C2×C22⋊Q8—1131no—
119C2×#117D11311yescharacteristic
120#485—1134no—
121#484—1132no—
122#483—1132no—
123#428—1132no—
124#419—1132no—
125#407—1131no—
126C22×Q8—1131no—
127C23×C4C2×D11311yescharacteristic
128C2×M16—1132no—
129C22⋊Q8—1132no—
130C22⋊Q8—1132no—
131C22⋊Q8—2261no—
132C22⋊Q8—2261no—
133#117—21no—
134#117—21no—
135#117C2×D11312yes—
136#117C2×D11312yes—
137C2×C4⋊C4—1131no—
138C2×C4⋊C4—2261no—
139C2×C4⋊C4C2×D11311yescharacteristic
140C2×C4⋊C4C2×D11311yescharacteristic
141C2×C22⋊C4—21no—
142C2×C22⋊C4—2261no—
143C2×C42—21no—
144#107—1134no—
145#106—1134no—
146#103—1134no—
147#103—1134no—
148C22⋊C8—1132no—
149C22⋊C8—1132no—
150C24C22⋊D11311yescharacteristic
151C2×Q8—1132no—
152C2×Q8—2264no—
153C2×Q8—2261no—
154C22×C4—24no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—2261no—
158C22×C4—2261no—
159C22×C4C22⋊D11311yescharacteristic
160C22×C4C22⋊D11311yescharacteristic
161C22×C4C22⋊D11311yescharacteristic
162C22×C4C22×D11311yescharacteristic
163C22×C4C22×D11311yescharacteristic
164C22×C4C22×D11311yescharacteristic
165M16—2264no—
166C2×C8—1134no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1132no—
170C4⋊C4—2261no—
171C4⋊C4—2262no—
172C4⋊C4—2262no—
173C4⋊C4C22×D11312yes—
174C4⋊C4C22×D11312yes—
175C22⋊C4—22no—
176C22⋊C4—22no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C42—22no—
180C42—22no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×C22⋊D11311yescharacteristic
185C23C2×C22⋊D11311yescharacteristic
186C23C2×C22⋊D11311yescharacteristic
187Q8—4522no—
188Q8—2264no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—4522no—
199C2×C4—4522no—
200C2×C4—2262no—
201C2×C4—2262no—
202C2×C4C2×C22⋊D11311yescharacteristic
203C2×C4C2×C22⋊D11311yescharacteristic
204C2×C4C2×C22⋊D11311yescharacteristic
205C2×C4#1426864714yes—
206C2×C4C23×D11311yescharacteristic
207C8—2264no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1681360512yes—
217C22#1681365212yes—
218C22C22×C22⋊D11311yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—42no—
223C4—4522no—
224C4—4522no—
225C4#1681360512yes—
226C4C2×#1426864712yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1681360511yescharacteristic
231C2C2×#1681365211yescharacteristic
232C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#117×C113C2
socleC22×C113C22×D4
prime radicalC24×C113D4
hypercenterC2×#117D113
hypocenterC113#3095
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20298939C2semidirect
3. #20298933C2semidirect
4. #20298928C2semidirect
5. #20298641C2semidirect
6. #20298606C2semidirect
18. #16813555C22semidirect
19. #16813553C22semidirect
20. #16813545C22semidirect
21. #16813545C22semidirect
117. C113#3095semidirect

Maximal subgroups

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

subgroupindex
C2×#168136012
#202989392
#202989332
#202989282
#202986412
#202986062
#202985622
C2×#117×C1132
#3095113