Finite Group Databasebeta

← #28399036

Subgroups — #28399036

Order 14464.

716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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×#16813669C211yesmaximal, characteristic
2#20299075C212yesmaximal, complemented
3#20298572C211yesmaximal, characteristic, complemented
4#20298571C212yesmaximal, complemented
5#20298570C218yesmaximal, complemented
6#410×C113C211yesmaximal, characteristic, complemented
7#16813669—24no—
8#16813669—24no—
9C2×#14268647C412yescomplemented
10C2×#14268647C2211yescharacteristic
11C2×#14268646C412yescomplemented
12C2×#14268646C2214yes—
13C22×Dic226C412yescomplemented
14C22×Dic226C2211yescharacteristic
15C2×Q8×D113C412yescomplemented
16C4×Dic226—24no—
17#16813587—24no—
18#16813581C2212yes—
19#16813578C2218yes—
20#16813537C2214yes—
21#16813536C2218yes—
22C2×#41×C113C2211yescharacteristic
23#117×C113C2212yes—
24#99×C113C2214yes—
25#14268647—22no—
26#14268647—22no—
27#14268647—24no—
28#14268647—24no—
29#14268646—216no—
30#14268646—28no—
31C2×Dic226—24no—
32C2×Dic226—24no—
33C2×Dic226C2×C414yes—
34C2×Dic226C2×C411yescharacteristic
35C2×Dic226C2×C412yes—
36C2×Dic226C2×C412yes—
37C2×Dic226D414yes—
38C2×Dic226D414yes—
39Q8×D113—28no—
40C2×D452C2×C411yescharacteristic
41C2×C22⋊D113C2×C414yes—
42C2×C22⋊D113C2312yes—
43C22×Dic113C2×C414yes—
44C22×Dic113C2312yes—
45C2×C4×D113C2×C412yes—
46C2×C4×D113C2×C414yes—
47C4⋊Dic113—22no—
48#14268626—28no—
49C22⋊Dic113C2314yes—
50C4×Dic113—22no—
51C4×Dic113—28no—
52#41×C113—22no—
53#41×C113—22no—
54C2×Q8×C113C2×C411yescharacteristic
55C2×D4×C113C2×C411yescharacteristic
56C2×D4×C113C2312yes—
57C22×C4×C113C2×C412yes—
58C22×C4×C113C2311yescharacteristic
59C4⋊C4×C113—22no—
60C22⋊C4×C113C2314yes—
61C42×C113—22no—
62C23×C113C22×C412yes—
63C23×C113C2411yescharacteristic
64C22×D113C22×C412yes—
65Q8×C113—22no—
66D4×C113—24no—
67D4×C113—22no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—24no—
71C2×C4×C113C22×C412yes—
72C2×C4×C113C22×C411yescharacteristic
73C2×C4×C113C22×C411yescharacteristic
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2×D412yes—
76C22⋊D113—24no—
77C22⋊D113—28no—
78C2×Dic113—28no—
79C2×Dic113—24no—
80C2×Dic113C22×C412yes—
81C2×Dic113C22×C414yes—
82C2×Dic113C2×D418yes—
83D452—21no—
84D452—21no—
85C4×D113—24no—
86C4×D113—28no—
87Dic226—21no—
88Dic226—21no—
89Dic226—28no—
90Dic226C22⋊C418yes—
91Dic226C22⋊C414yes—
92Dic226C22⋊C414yes—
93C22×C113—22no—
94C22×C113—41no—
95C22×C113—42no—
96C22×C113C23×C411yescharacteristic
97C22×C113C22×D412yes—
98C2×D113—22no—
99C2×D113—42no—
100C4×C113—22no—
101C4×C113—44no—
102C4×C113C2×C22⋊C411yescharacteristic
103C4×C113C2×C22⋊C411yescharacteristic
104C4×C113C2×C22⋊C412yes—
105Dic113—22no—
106Dic113—44no—
107Dic113C2×C22⋊C418yes—
108C2×C113—22no—
109C2×C113—21no—
110C2×C113—42no—
111C2×C113C22×C22⋊C411yescharacteristic
112D113—42no—
113#2884—1131nomaximal, Sylow
114C113#288411yescharacteristic, complemented, Sylow
115C2×2−1+4—1131no—
116#519—1132no—
117#410—1131no—
118#410—1132no—
119#410—1138no—
120#410D11311yescharacteristic, complemented
1212−1+4—2264no—
1222−1+4—2264no—
123C2×#41—1132no—
124C2×#41—1134no—
125C2×#41—1132no—
126C2×#41—1131no—
127C2×#41C2×D11311yescharacteristic
128C22×Q8—1132no—
129C22×Q8—1132no—
130C22×Q8—1131no—
131C4×Q8—2264no—
132C4×Q8—2264no—
133#117—1132no—
134#117—1138no—
135#117C2×D11312yes—
136#99—1134no—
137#99—1138no—
138#99C2×D11314yes—
139#41—22no—
140#41—22no—
141#41—2264no—
142#41—2264no—
143#41—22616no—
144#41—2268no—
145#41—2262no—
146#41—2262no—
147C2×Q8—1132no—
148C2×Q8—1132no—
149C2×Q8—1134no—
150C2×Q8—1131no—
151C2×Q8—1134no—
152C2×Q8—1134no—
153C2×Q8—2264no—
154C2×Q8—2264no—
155C2×Q8—2268no—
156C2×Q8C4×D11311yescharacteristic
157C2×D4—1134no—
158C2×D4—1132no—
159C2×D4—1131no—
160C2×D4C4×D11311yescharacteristic
161C2×D4C22×D11312yes—
162C22×C4—1132no—
163C22×C4—1134no—
164C22×C4—1134no—
165C22×C4—1132no—
166C22×C4C4×D11312yes—
167C22×C4C22×D11311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—2268no—
170C4⋊C4—2262no—
171C22⋊C4—1134no—
172C22⋊C4C22×D11314yes—
173C42—22no—
174C42—2268no—
175C42—2262no—
176C23—1132no—
177C23C2×C4×D11312yes—
178C23C23×D11311yescharacteristic
179Q8—22no—
180Q8—1134no—
181Q8—1134no—
182Q8—1138no—
183Q8—2268no—
184Q8—2261no—
185Q8—2261no—
186D4—24no—
187D4—22no—
188D4—2268no—
189D4—2264no—
190D4—2261no—
191D4—2261no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—1134no—
196C2×C4—1138no—
197C2×C4—1132no—
198C2×C4—2268no—
199C2×C4—2268no—
200C2×C4—2264no—
201C2×C4—2264no—
202C2×C4C2×C4×D11312yes—
203C2×C4C2×C4×D11311yescharacteristic
204C2×C4C2×C4×D11311yescharacteristic
205C2×C4D4×D11312yes—
206C2×C4D4×D11312yes—
207C22—22no—
208C22—41no—
209C22—42no—
210C22—4522no—
211C22—2262no—
212C22C22×C4×D11311yescharacteristic
213C22C2×D4×D11312yes—
214C4—22no—
215C4—44no—
216C4—1138no—
217C4—4524no—
218C4—2262no—
219C4C22⋊C4×D11311yescharacteristic
220C4C22⋊C4×D11311yescharacteristic
221C4C22⋊C4×D11312yes—
222C2—22no—
223C2—21no—
224C2—42no—
225C2—4522no—
226C2C2×C22⋊C4×D11311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
Fitting#410×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813669C2
cosocleC23×C113C24
hypercenter#410D113
hypocenterC113#2884
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20299075C2semidirect
3. #20298572C2semidirect
4. #20298571C2semidirect
5. #20298570C2semidirect
6. #410×C113C2semidirect
9. C2×#14268647C4semidirect
11. C2×#14268646C4semidirect
13. C22×Dic226C4semidirect
15. C2×Q8×D113C4semidirect
114. C113#2884semidirect
120. #410D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
#202990752
#202985722
#202985712
#202985702
#410×C1132
#2884113