Finite Group Databasebeta

← #28393863

Subgroups — #28393863

Order 14464.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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, complemented
2C2×#16813584C211yesmaximal, characteristic
3#20298536C211yesmaximal, characteristic, complemented
4#20298527C212yesmaximal, complemented
5#20298516C211yesmaximal, characteristic
6#20298515C211yesmaximal, characteristic
7#20298511C212yesmaximal, complemented
8#20298445C212yesmaximal, complemented
9#20298445C212yesmaximal, complemented
10#20298443C211yesmaximal, characteristic, complemented
11#400×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2211yescharacteristic
13C22×D452C2211yescharacteristic
14C22×C4×D113C2212yes—
15#16813587—24no—
16#16813584—24no—
17C2×#14268626C2211yescharacteristic
18C2×#14268626C2211yescharacteristic
19C2×#14268624C2212yes—
20C2×#14268624C2212yes—
21C2×#14268624C2212yes—
22C2×#14268624C2212yes—
23C2×#14268624C2212yes—
24C2×C4×Dic113C2211yescharacteristic
25C2×C4×Dic113C2211yescharacteristic
26C2×C4×Dic113C2212yes—
27C2×C4×Dic113C2211yescharacteristic
28#16813529C2212yes—
29#16813529C2212yes—
30#16813529C2211yescharacteristic
31#16813529C2212yes—
32C2×C4⋊C4×C113C2211yescharacteristic
33C2×C4⋊C4×C113C2211yescharacteristic
34#95×C113C2212yes—
35#95×C113C2211yescharacteristic
36#95×C113C2212yes—
37C23×D113C2312yes—
38C2×Dic226—22no—
39C2×Dic226—22no—
40C2×Dic226—22no—
41C2×D452—24no—
42C2×D452—22no—
43C22×Dic113C2311yescharacteristic
44C22×Dic113C2312yes—
45C22×Dic113C2311yescharacteristic
46C22×Dic113C2311yescharacteristic
47C22×Dic113C2311yescharacteristic
48C2×C4×D113—24no—
49C2×C4×D113—24no—
50C2×C4×D113—24no—
51#14268626—22no—
52#14268626—22no—
53#14268624—24no—
54#14268624—24no—
55#14268624—24no—
56#14268624—24no—
57#14268624—24no—
58C4×Dic113—22no—
59C4×Dic113—22no—
60C4×Dic113—24no—
61C4×Dic113D414yes—
62C22×C4×C113C2311yescharacteristic
63C22×C4×C113C2312yes—
64C22×C4×C113C2312yes—
65C22×C4×C113C2311yescharacteristic
66C22×C4×C113C2311yescharacteristic
67C4⋊C4×C113—22no—
68C4⋊C4×C113—22no—
69C23×C113C2411yescharacteristic
70C22×D113—22no—
71C22×D113—22no—
72C22×D113—22no—
73C22×D113—22no—
74C22×D113—22no—
75C22×D113—22no—
76C22×D113#4114yes—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113—21no—
80C2×C4×C113—21no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—22no—
86C2×C4×C113—22no—
87C2×C4×C113—22no—
88C2×C4×C113C2×D412yes—
89C2×C4×C113#4112yes—
90C2×Dic113—21no—
91C2×Dic113—21no—
92C2×Dic113—21no—
93C2×Dic113—21no—
94C2×Dic113—21no—
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113—22no—
98C2×Dic113—22no—
99C2×Dic113C2×D412yes—
100C2×Dic113C2×D412yes—
101C2×Dic113#4112yes—
102C2×Dic113#4114yes—
103D452—28no—
104C4×D113—48no—
105Dic226—28no—
106C22×C113C22×D411yescharacteristic
107C22×C113C2×#4112yes—
108C22×C113C2×#4111yescharacteristic
109C22×C113C2×#4112yes—
110C22×C113C2×#4111yescharacteristic
111C2×D113—24no—
112C2×D113—24no—
113C2×D113—24no—
114C2×D113—42no—
115C2×D113—42no—
116C2×D113—42no—
117C2×D113—42no—
118C4×C113—22no—
119C4×C113—22no—
120C4×C113—41no—
121C4×C113—42no—
122C4×C113—42no—
123Dic113—22no—
124Dic113—22no—
125Dic113—41no—
126Dic113—42no—
127Dic113#12414yes—
128C2×C113#52511yescharacteristic
129C2×C113#52511yescharacteristic
130C2×C113C2×#12411yescharacteristic
131C2×C113#52912yes—
132C2×C113#52912yes—
133D113—44no—
134#2398—1131nomaximal, Sylow
135C113#239811yescharacteristic, complemented, Sylow
136C2×C4×Q8—1131no—
137C2×C4×D4—1131no—
138#400—1131no—
139#400D11311yescharacteristic, complemented
140#397—1132no—
141#394—1131no—
142#394—1131no—
143#393—1132no—
144C4×C22⋊C4—1132no—
145C4×C22⋊C4—1132no—
146#376—1131no—
147C22×Q8—1131no—
148C22×D4—1131no—
149C23×C4—1132no—
150C4×Q8—2264no—
151C4×D4—2264no—
152C2×C4⋊C4—1131no—
153C2×C4⋊C4—1131no—
154C2×C4⋊C4C2×D11311yescharacteristic
155C2×C4⋊C4C2×D11311yescharacteristic
156C2×C22⋊C4—1132no—
157C2×C22⋊C4—1132no—
158C2×C22⋊C4—1132no—
159C2×C22⋊C4—1132no—
160C2×C22⋊C4—1132no—
161C2×C42—1131no—
162C2×C42—1131no—
163C2×C42—1131no—
164C2×C42—1132no—
165#95—1132no—
166#95—1131no—
167#95—1132no—
168#95—1132no—
169#95C2×D11311yescharacteristic
170#95C2×D11312yes—
171#95C2×D11312yes—
172C24—1132no—
173C2×Q8—2262no—
174C2×Q8—2262no—
175C2×Q8—2262no—
176C2×D4—2264no—
177C2×D4—2262no—
178C22×C4—1131no—
179C22×C4—1131no—
180C22×C4—1131no—
181C22×C4—1132no—
182C22×C4—1131no—
183C22×C4—2264no—
184C22×C4—2264no—
185C22×C4—2264no—
186C22×C4C22×D11312yes—
187C22×C4C22×D11312yes—
188C22×C4C22×D11311yescharacteristic
189C22×C4C22×D11311yescharacteristic
190C22×C4C22×D11311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—2262no—
194C4⋊C4—2262no—
195C22⋊C4—2264no—
196C22⋊C4—2264no—
197C22⋊C4—2264no—
198C22⋊C4—2264no—
199C22⋊C4—2264no—
200C42—1134no—
201C42—2262no—
202C42—2262no—
203C42—2264no—
204C23—1134no—
205C23—2262no—
206C23—2262no—
207C23—2262no—
208C23—2262no—
209C23—2262no—
210C23—2262no—
211C23C23×D11311yescharacteristic
212Q8—2268no—
213D4—2268no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—1132no—
226C2×C4—1134no—
227C2×C4—1132no—
228C2×C4—1132no—
229C2×C4—4528no—
230C2×C4—2261no—
231C2×C4—2262no—
232C2×C4—2262no—
233C2×C4—2262no—
234C2×C4—2262no—
235C2×C4—2261no—
236C2×C4—2261no—
237C2×C4—2261no—
238C2×C4—2261no—
239C2×C4D4×D11312yes—
240C2×C4#1426864812yes—
241C22—4522no—
242C22—4522no—
243C22—4522no—
244C22—4522no—
245C22—2264no—
246C22—2264no—
247C22—2264no—
248C22C2×D4×D11311yescharacteristic
249C22#41×D11312yes—
250C22#41×D11311yescharacteristic
251C22#41×D11312yes—
252C22C2×#1426864811yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—42no—
258C4—1134no—
259C4—4521no—
260C4—4522no—
261C4—2262no—
262C4—2262no—
263C2—4524no—
264C2#2029910611yescharacteristic
265C2#2029911111yescharacteristic
266C2#124×D11311yescharacteristic
267C2#2029913112yes—
268C2#2029913312yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#400×C113C2
prime radicalC22×D452C22
hypercenter#400D113
hypocenterC113#2398
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#16813587C2semidirect
3. #20298536C2semidirect
4. #20298527C2semidirect
7. #20298511C2semidirect
8. #20298445C2semidirect
9. #20298445C2semidirect
10. #20298443C2semidirect
11. #400×C113C2semidirect
135. C113#2398semidirect
139. #400D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135872
C2×#168135842
#202985362
#202985272
#202985162
#202985152
#202985112
#202984452
#202984432
#400×C1132
#2398113