Finite Group Databasebeta

← #28400745

Subgroups — #28400745

Order 14464.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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#20299132C211yesmaximal, characteristic
2#20298933C211yesmaximal, characteristic, complemented
3#20298916C211yesmaximal, characteristic
4#20298905C212yesmaximal, complemented
5#20298820C212yesmaximal, complemented
6#20298754C211yesmaximal, characteristic, complemented
7#20298737C211yesmaximal, characteristic
8#20298703C212yesmaximal, complemented
9#20298696C212yesmaximal, complemented
10#20298655C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C113C211yesmaximal, characteristic, complemented
12C2×#14268637C2212yes—
13C2×#14268634C2212yes—
14#16813616—21no—
15#16813614C2211yescharacteristic
16#16813610C2211yescharacteristic
17#16813605—21no—
18#16813601C2211yescharacteristic
19#16813596C2211yescharacteristic
20C4×Dic226C2211yescharacteristic
21C4×D452C2211yescharacteristic
22C4×C22⋊D113—21no—
23#16813579—21no—
24#16813555C2212yes—
25#16813553C2212yes—
26C4⋊#11744751C2212yes—
27#16813546C2212yes—
28#16813546C2212yes—
29#16813545C2212yes—
30#16813542C2212yes—
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33#16813533C2212yes—
34C22×Q8×C113C2211yescharacteristic
35C4×Q8×C113—21no—
36C4×Q8×C113—21no—
37C4×Q8×C113C2212yes—
38C4×Q8×C113C2212yes—
39C2×C4⋊C4×C113—21no—
40C2×C4⋊C4×C113C2211yescharacteristic
41C2×C42×C113—21no—
42C2×C42×C113C2211yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C2×C4×D113—21no—
47#14268637—24no—
48#14268634—24no—
49C2×#11744751C2312yes—
50C2×#11744751C2312yes—
51C4⋊Dic113C2311yescharacteristic
52C4⋊Dic113C2311yescharacteristic
53#14268626—21no—
54#14268626—21no—
55#14268626—21no—
56#14268626—21no—
57C22⋊Dic113—21no—
58#14268624—21no—
59#14268624—21no—
60#14268624—21no—
61#14268624—21no—
62C4×Dic113—21no—
63C2×Q8×C113—24no—
64C2×Q8×C113—21no—
65C2×Q8×C113C2312yes—
66C22×C4×C113—21no—
67C22×C4×C113—21no—
68C22×C4×C113D411yescharacteristic
69C22×C4×C113D411yescharacteristic
70C22×C4×C113C2311yescharacteristic
71C4⋊C4×C113—22no—
72C4⋊C4×C113—22no—
73C4⋊C4×C113—21no—
74C4⋊C4×C113C2312yes—
75C42×C113—22no—
76C42×C113—22no—
77C42×C113D411yescharacteristic
78C42×C113D411yescharacteristic
79C42×C113C2311yescharacteristic
80C42×C113C2311yescharacteristic
81C23×C113C2×D411yescharacteristic
82C22×D113—21no—
83Q8×C113—24no—
84Q8×C113—22no—
85Q8×C113#4114yes—
86C2×C4×C113—24no—
87C2×C4×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—41no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—42no—
100C2×Dic113—21no—
101C2×Dic113—21no—
102C2×Dic113—21no—
103D452—22no—
104C4×D113—42no—
105Dic226—22no—
106#11744751—22no—
107#11744751—22no—
108C22×C113—21no—
109C22×C113—21no—
110C22×C113#13712yes—
111C22×C113C22×D411yescharacteristic
112C2×D113—41no—
113C2×D113—41no—
114C2×D113—41no—
115C4×C113—24no—
116C4×C113—21no—
117C4×C113—21no—
118C4×C113—21no—
119C4×C113—21no—
120C4×C113—21no—
121C4×C113—42no—
122C4×C113C2×#4112yes—
123Dic113—41no—
124Dic113—41no—
125Dic113—41no—
126C2×C113—22no—
127C2×C113#52511yescharacteristic
128C2×C113C2×#13711yescharacteristic
129C2×C113#57511yescharacteristic
130D113—81no—
131#3117—1131nomaximal, Sylow
132C113#311711yescharacteristic, complemented, Sylow
133#529—1131no—
134C2×C4×Q8D11311yescharacteristic, complemented
135#484—1131no—
136#481—1131no—
137#479—1132no—
138#464—1132no—
139#451—1131no—
140#448—1131no—
141#441—1132no—
142#440—1132no—
143#432—1131no—
144C22×Q8C2×D11311yescharacteristic
145C2×Q16—1132no—
146C2×SD16—1132no—
147#126—2261no—
148#125—1131no—
149#124—1131no—
150#123—2261no—
151C22⋊Q8—1131no—
152#121—1131no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—1131no—
156C4×Q8C2×D11312yes—
157C4×Q8C2×D11312yes—
158C4×D4—1131no—
159C4×D4—2261no—
160#117—2261no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×D11311yescharacteristic
163C2×C42—21no—
164C2×C42C2×D11311yescharacteristic
165#107—1132no—
166#106—1132no—
167C4⋊C8—1132no—
168#103—1132no—
169#103—1132no—
170#103—1132no—
171#102—1132no—
172C22⋊C8—1131no—
173C22⋊C8—1131no—
174#97—1132no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—1131no—
178C2×Q8C22×D11312yes—
179C2×D4—1131no—
180C2×D4—2261no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—2261no—
184C22×C4C22⋊D11311yescharacteristic
185C22×C4C22⋊D11311yescharacteristic
186C22×C4C22×D11311yescharacteristic
187Q16—2264no—
188SD16—2264no—
189C2×C8—1132no—
190C2×C8—1132no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—1131no—
195C4⋊C4—1131no—
196C4⋊C4—2261no—
197C4⋊C4—2261no—
198C4⋊C4—2261no—
199C4⋊C4—2261no—
200C4⋊C4C22×D11312yes—
201C22⋊C4—2261no—
202C22⋊C4—2261no—
203C22⋊C4—2261no—
204C22⋊C4—2261no—
205C22⋊C4—2261no—
206C42—22no—
207C42—22no—
208C42—2261no—
209C42C22⋊D11311yescharacteristic
210C42C22⋊D11311yescharacteristic
211C42C22×D11311yescharacteristic
212C42C22×D11311yescharacteristic
213C23—2261no—
214C23C2×C22⋊D11311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—2262no—
218Q8#1426864714yes—
219D4—4522no—
220D4—2262no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—4522no—
229C2×C4—2261no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4C2×C22⋊D11311yescharacteristic
233C2×C4C2×C22⋊D11311yescharacteristic
234C2×C4C2×C22⋊D11311yescharacteristic
235C2×C4C2×C22⋊D11311yescharacteristic
236C2×C4C2×C22⋊D11311yescharacteristic
237C2×C4C23×D11311yescharacteristic
238C8—2262no—
239C8—2262no—
240C22—21no—
241C22—21no—
242C22—4521no—
243C22—4521no—
244C22—4521no—
245C22#1681365312yes—
246C22C22×C22⋊D11311yescharacteristic
247C4—24no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—42no—
254C4—4521no—
255C4—4521no—
256C4—4521no—
257C4C2×#1426864712yes—
258C2—22no—
259C2—9041no—
260C2#2029910911yescharacteristic
261C2C2×#1681365311yescharacteristic
262C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×Q8×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenterC2×C4×Q8D113
hypocenterC113#3117
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #20298933C2semidirect
4. #20298905C2semidirect
5. #20298820C2semidirect
6. #20298754C2semidirect
8. #20298703C2semidirect
9. #20298696C2semidirect
10. #20298655C2semidirect
11. C2×C4×Q8×C113C2semidirect
132. C113#3117semidirect
134. C2×C4×Q8D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202989332
#202989162
#202989052
#202988202
#202987542
#202987372
#202987032
#202986962
#202986552
C2×C4×Q8×C1132
#3117113