Finite Group Databasebeta

← #28401651

Subgroups — #28401651

Order 14464.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299174C211yesmaximal, characteristic
2#20298990C211yesmaximal, characteristic, complemented
3#20298977C211yesmaximal, characteristic, complemented
4#20298968C211yesmaximal, characteristic, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298820C212yesmaximal, complemented
7#20298808C212yesmaximal, complemented
8#20298758C212yesmaximal
9#20298753C212yesmaximal, complemented
10#20298659C211yesmaximal, characteristic, complemented
11#541×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14C2×#14268637C2212yes—
15C2×#14268637C2212yes—
16C2×#14268637C2212yes—
17C2×#14268634C2212yes—
18#16813622C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813610C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813606—22no—
23#16813602—22no—
24C4⋊#11744751C2212yes—
25#16813545C2212yes—
26#16813545C2212yes—
27#16813545C2212yes—
28#16813542C2212yes—
29C22⋊#11744751C2212yes—
30#16813533C2211yescharacteristic
31C4×#11744751C2211yescharacteristic
32C4⋊Q8×C113C2211yescharacteristic
33#126×C113—22no—
34#125×C113—22no—
35#125×C113C2211yescharacteristic
36C22⋊Q8×C113C2212yes—
37C4×Q8×C113C2212yes—
38#117×C113C2211yescharacteristic
39#14268647—42no—
40C2×Dic226—21no—
41C2×Dic226—42no—
42C2×Dic226C2311yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×Dic226C2311yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47C22×Dic113—21no—
48C2×C4×D113—21no—
49#14268637—42no—
50#14268637—42no—
51#14268637—42no—
52#14268634—42no—
53C2×#11744751C2312yes—
54C2×#11744751C2312yes—
55C4⋊Dic113—22no—
56C4⋊Dic113—22no—
57#14268624—22no—
58#14268624—22no—
59C2×Q8×C113C2312yes—
60C22×C4×C113C2311yescharacteristic
61C4⋊C4×C113—22no—
62C4⋊C4×C113—22no—
63C4⋊C4×C113—22no—
64C4⋊C4×C113—22no—
65C4⋊C4×C113D412yes—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C22⋊C4×C113D412yes—
69C42×C113—22no—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113C2×D411yescharacteristic
73C22×D113—21no—
74Q8×C113—22no—
75Q8×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D412yes—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—42no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113—21no—
87C2×Dic113—42no—
88D452—22no—
89C4×D113—42no—
90Dic226—22no—
91Dic226—22no—
92Dic226—22no—
93Dic226—42no—
94#11744751—22no—
95#11744751—22no—
96C22×C113—21no—
97C22×C113—22no—
98C22×C113C22×D411yescharacteristic
99C2×D113—41no—
100C2×D113—42no—
101C4×C113—21no—
102C4×C113—22no—
103C4×C113—22no—
104C4×C113—42no—
105C4×C113—42no—
106C4×C113H(5,𝔽2)12yes—
107Dic113—41no—
108Dic113—41no—
109Dic113—41no—
110C2×C113—41no—
111C2×C113#53511yescharacteristic
112C2×C113#57812yes—
113D113—81no—
114#3223—1131nomaximal, Sylow
115C113#322311yescharacteristic, complemented, Sylow
116#541D11311yescharacteristic, complemented
117#536—1131no—
118#497—1131no—
119#494—1131no—
120#491—1131no—
121#488—1131no—
122#464—1132no—
123#462—1132no—
124#452—1132no—
125#451—1132no—
126#433—1131no—
127C2×#41—1131no—
128C22×Q8—1131no—
129C2×Q16—1132no—
130C2×Q16—1132no—
131C2×Q16—1132no—
132C2×SD16—1132no—
133C4⋊Q8—1131no—
134C4⋊Q8—1131no—
135C4⋊Q8C2×D11311yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D11311yescharacteristic
139#124—1131no—
140#124—1131no—
141#123—2262no—
142C22⋊Q8—2262no—
143C22⋊Q8C2×D11312yes—
144C4×Q8C2×D11312yes—
145#117C2×D11311yescharacteristic
146C4⋊C8—1132no—
147#103—1132no—
148#103—1132no—
149#103—1132no—
150#102—1132no—
151C22⋊C8—1132no—
152#97—1131no—
153C4×C8—1131no—
154#41—4522no—
155C2×Q8—1131no—
156C2×Q8—1131no—
157C2×Q8—1131no—
158C2×Q8—4522no—
159C2×Q8—2261no—
160C2×Q8C22×D11312yes—
161C2×D4—1131no—
162C2×D4—2261no—
163C22×C4—2261no—
164C22×C4—2261no—
165C22×C4C22×D11311yescharacteristic
166Q16—4522no—
167Q16—4522no—
168Q16—4522no—
169SD16—4522no—
170C2×C8—1132no—
171C2×C8—1132no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—2262no—
177C4⋊C4—2262no—
178C4⋊C4C22⋊D11312yes—
179C4⋊C4C22×D11312yes—
180C22⋊C4—22no—
181C22⋊C4—2262no—
182C22⋊C4—2262no—
183C22⋊C4C22⋊D11312yes—
184C42—22no—
185C42C22×D11311yescharacteristic
186C42C22×D11311yescharacteristic
187C23—2261no—
188C23C2×C22⋊D11311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—4522no—
192Q8—2262no—
193Q8—2262no—
194Q8—2262no—
195D4—4522no—
196D4—2262no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—4522no—
201C2×C4—4522no—
202C2×C4—2261no—
203C2×C4—2261no—
204C2×C4—2261no—
205C2×C4C2×C22⋊D11312yes—
206C2×C4C2×C22⋊D11312yes—
207C2×C4C2×C22⋊D11311yescharacteristic
208C2×C4C23×D11311yescharacteristic
209C8—2262no—
210C8—2262no—
211C22—22no—
212C22—21no—
213C22—4522no—
214C22—4521no—
215C22C22×C22⋊D11311yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—4521no—
222C4—4521no—
223C4—4521no—
224C4#1681366812yes—
225C2—41no—
226C2—9041no—
227C2#2029916211yescharacteristic
228C2#2029941312yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#541×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#541D113
hypocenterC113#3223
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20298990C2semidirect
3. #20298977C2semidirect
4. #20298968C2semidirect
5. #20298955C2semidirect
6. #20298820C2semidirect
7. #20298808C2semidirect
9. #20298753C2semidirect
10. #20298659C2semidirect
11. #541×C113C2semidirect
115. C113#3223semidirect
116. #541D113semidirect

Maximal subgroups

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

subgroupindex
#202991742
#202989902
#202989772
#202989682
#202989552
#202988202
#202988082
#202987582
#202987532
#202986592
#541×C1132
#3223113