Finite Group Databasebeta

← #28393866

Subgroups — #28393866

Order 14464.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#16813587C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic
3#20298532C212yesmaximal
4#20298529C211yesmaximal, characteristic
5#20298519C211yesmaximal, characteristic
6#20298518C212yesmaximal
7#20298518C211yesmaximal, characteristic
8C4⋊C4×Dic113C212yesmaximal
9#20298449C212yesmaximal
10#20298443C211yesmaximal, characteristic
11#398×C113C211yesmaximal, characteristic
12C22×Dic226C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14#16813587—24no—
15#16813587—24no—
16C2×C4⋊Dic113C2212yes—
17C2×#14268626C2212yes—
18C2×#14268626C2212yes—
19C2×#14268626C2212yes—
20C2×#14268626C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×C4×Dic113C2211yescharacteristic
23C2×C4×Dic113C2212yes—
24C2×C4×Dic113C2211yescharacteristic
25C2×C4×Dic113C2211yescharacteristic
26C2×C4×Dic113C2212yes—
27#16813529C2212yes—
28#16813529C2212yes—
29#16813529C2211yescharacteristic
30#16813529C2212yes—
31#16813529C2212yes—
32C2×C4⋊C4×C113C2211yescharacteristic
33C2×C4⋊C4×C113C2212yes—
34C2×C4⋊C4×C113C2211yescharacteristic
35#95×C113C2211yescharacteristic
36#95×C113C2212yes—
37C2×Dic226—22no—
38C2×Dic226—22no—
39C2×Dic226—22no—
40C2×Dic226—22no—
41C2×Dic226—24no—
42C22×Dic113C2311yescharacteristic
43C22×Dic113C2311yescharacteristic
44C22×Dic113C2312yes—
45C22×Dic113C2311yescharacteristic
46C22×Dic113C2312yes—
47C22×Dic113C2311yescharacteristic
48C4⋊Dic113—24no—
49#14268626—22no—
50#14268626—24no—
51#14268626—22no—
52#14268626—24no—
53#14268626—24no—
54C4×Dic113—22no—
55C4×Dic113—24no—
56C4×Dic113—22no—
57C4×Dic113D414yes—
58C4×Dic113Q818yescomplemented
59C22×C4×C113C2311yescharacteristic
60C22×C4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62C22×C4×C113C2312yes—
63C22×C4×C113C2311yescharacteristic
64C4⋊C4×C113—22no—
65C4⋊C4×C113—22no—
66C4⋊C4×C113—24no—
67C23×C113C2411yescharacteristic
68C2×C4×C113—21no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113C2×D412yes—
79C2×C4×C113C2×Q814yes—
80C2×C4×C113#4112yes—
81C2×Dic113—21no—
82C2×Dic113—22no—
83C2×Dic113—22no—
84C2×Dic113—22no—
85C2×Dic113—21no—
86C2×Dic113—22no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113—22no—
91C2×Dic113C2×D412yes—
92C2×Dic113C2×D412yes—
93C2×Dic113C2×Q814yes—
94C2×Dic113C2×Q814yes—
95C2×Dic113#4112yes—
96C2×Dic113#4114yes—
97Dic226—28no—
98Dic226—28no—
99C22×C113C22×D411yescharacteristic
100C22×C113C22×Q812yes—
101C22×C113C2×#4112yes—
102C22×C113C2×#4111yescharacteristic
103C22×C113C2×#4111yescharacteristic
104C4×C113—22no—
105C4×C113—22no—
106C4×C113—24no—
107C4×C113—41no—
108C4×C113—42no—
109Dic113—22no—
110Dic113—24no—
111Dic113—22no—
112Dic113—24no—
113Dic113—41no—
114Dic113C4⋊Q814yes—
115C2×C113#52511yescharacteristic
116C2×C113#52511yescharacteristic
117C2×C113C2×C4⋊Q811yescharacteristic
118C2×C113#53312yes—
119C2×C113#53312yes—
120#2399—1131nomaximal, Sylow
121C113#239911yescharacteristic, complemented, Sylow
122C2×C4×Q8—1131no—
123C2×C4×Q8—1131no—
124#398—1131no—
125#398—1132no—
126#398D11311yescharacteristic
127#395—1132no—
128#395—1131no—
129#395—1131no—
130C4×C4⋊C4—1132no—
131C4×C4⋊C4—1132no—
132#376—1131no—
133C22×Q8—1131no—
134C22×Q8—1131no—
135C4×Q8—2264no—
136C4×Q8—2264no—
137C2×C4⋊C4—1132no—
138C2×C4⋊C4—1131no—
139C2×C4⋊C4—1131no—
140C2×C4⋊C4—1132no—
141C2×C4⋊C4—1132no—
142C2×C4⋊C4—1132no—
143C2×C4⋊C4C2×D11311yescharacteristic
144C2×C4⋊C4C2×D11311yescharacteristic
145C2×C4⋊C4C2×D11312yes—
146C2×C42—1131no—
147C2×C42—1132no—
148C2×C42—1132no—
149C2×C42—1131no—
150C2×C42—1131no—
151#95—1131no—
152#95—1132no—
153#95—1132no—
154#95—1132no—
155#95—1132no—
156#95C2×D11311yescharacteristic
157#95C2×D11312yes—
158C2×Q8—2262no—
159C2×Q8—2264no—
160C2×Q8—2262no—
161C2×Q8—2262no—
162C2×Q8—2262no—
163C22×C4—1131no—
164C22×C4—1132no—
165C22×C4—1131no—
166C22×C4—1132no—
167C22×C4—1131no—
168C22×C4—1131no—
169C22×C4C22×D11312yes—
170C22×C4C22×D11311yescharacteristic
171C22×C4C22×D11311yescharacteristic
172C22×C4C22×D11312yes—
173C22×C4C22×D11311yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—2262no—
178C4⋊C4—2264no—
179C4⋊C4—2264no—
180C4⋊C4—2264no—
181C4⋊C4—2264no—
182C4⋊C4—2262no—
183C42—1134no—
184C42—1138no—
185C42—2262no—
186C42—2262no—
187C42—2264no—
188C23C23×D11311yescharacteristic
189Q8—2268no—
190Q8—2268no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—1132no—
202C2×C4—1134no—
203C2×C4—1132no—
204C2×C4—1134no—
205C2×C4—1134no—
206C2×C4—1132no—
207C2×C4—2261no—
208C2×C4—2262no—
209C2×C4—2262no—
210C2×C4—2261no—
211C2×C4—2262no—
212C2×C4—2262no—
213C2×C4—2262no—
214C2×C4—2261no—
215C2×C4—2261no—
216C2×C4—2261no—
217C2×C4D4×D11312yes—
218C2×C4Q8×D11314yes—
219C2×C4#1426864612yes—
220C22C2×D4×D11311yescharacteristic
221C22C2×Q8×D11312yes—
222C22#41×D11312yes—
223C22#41×D11311yescharacteristic
224C22C2×#1426864611yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—1134no—
231C4—4521no—
232C4—2264no—
233C4—2262no—
234C4—2262no—
235C4—2264no—
236C2#2029910611yescharacteristic
237C2#2029910811yescharacteristic
238C2C4⋊Q8×D11311yescharacteristic
239C2#2029915012yes—
240C2#2029915412yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, prime radical, cosocleC23×C113C24
Fitting#398×C113C2
hypercenter#398D113
hypocenterC113#2399
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic113Q8semidirect
121. C113#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#168135872
#202985322
#202985292
#202985192
#202985182
C4⋊C4×Dic1132
#202984492
#202984432
#398×C1132
#2399113