Finite Group Databasebeta

← #28393859

Subgroups — #28393859

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×#16813582C211yesmaximal, characteristic
3#20298539C212yesmaximal, complemented
4#20298524C211yesmaximal, characteristic, complemented
5#20298513C212yesmaximal
6#20298511C211yesmaximal, characteristic, complemented
7#20298510C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic113C212yesmaximal, complemented
9#20298445C212yesmaximal, complemented
10#20298443C211yesmaximal, characteristic, complemented
11#397×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2211yescharacteristic
13C22×C22⋊D113C2211yescharacteristic
14C23×Dic113C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16#16813587—24no—
17#16813582—24no—
18C2×#14268626C2212yes—
19C2×#14268626C2211yescharacteristic
20C2×C22⋊Dic113C2212yes—
21C2×#14268624C2212yes—
22C2×#14268624C2211yescharacteristic
23C2×#14268624C2212yes—
24C2×C4×Dic113C2212yes—
25C2×C4×Dic113C2212yes—
26C2×C4×Dic113C2211yescharacteristic
27#16813529C2211yescharacteristic
28#16813529C2212yes—
29#16813529C2212yes—
30#16813529C2212yes—
31#16813529C2212yes—
32C2×C4⋊C4×C113C2211yescharacteristic
33C2×C22⋊C4×C113C2211yescharacteristic
34C2×C22⋊C4×C113C2212yes—
35#95×C113C2211yescharacteristic
36#95×C113C2212yes—
37C23×D113C2311yescharacteristic
38C2×Dic226—22no—
39C2×Dic226—24no—
40C2×C22⋊D113—22no—
41C2×C22⋊D113—22no—
42C2×C22⋊D113—22no—
43C22×Dic113—22no—
44C22×Dic113—24no—
45C22×Dic113C2312yes—
46C22×Dic113C2311yescharacteristic
47C22×Dic113C2311yescharacteristic
48C22×Dic113C2312yes—
49C22×Dic113C2311yescharacteristic
50C2×C4×D113—22no—
51C2×C4×D113—24no—
52#14268626—22no—
53#14268626—24no—
54C22⋊Dic113—24no—
55#14268624—24no—
56#14268624—22no—
57#14268624—24no—
58C4×Dic113—24no—
59C4×Dic113—24no—
60C4×Dic113D414yes—
61C24×C113C2311yescharacteristic
62C22×C4×C113C2312yes—
63C22×C4×C113C2312yes—
64C22×C4×C113C2311yescharacteristic
65C22×C4×C113C2311yescharacteristic
66C4⋊C4×C113—22no—
67C22⋊C4×C113—24no—
68C22⋊C4×C113—22no—
69C23×C113—21no—
70C23×C113—22no—
71C23×C113—22no—
72C23×C113—21no—
73C23×C113#4112yes—
74C23×C113C2411yescharacteristic
75C22×D113—21no—
76C22×D113—22no—
77C22×D113—22no—
78C22×D113—21no—
79C22×D113#4112yes—
80C2×C4×C113—22no—
81C2×C4×C113—21no—
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×C113—22no—
89C2×C4×C113C2×D412yes—
90C22⋊D113—28no—
91C2×Dic113—22no—
92C2×Dic113—21no—
93C2×Dic113—21no—
94C2×Dic113—22no—
95C2×Dic113—21no—
96C2×Dic113—22no—
97C2×Dic113—22no—
98C2×Dic113—22no—
99C2×Dic113—22no—
100C2×Dic113—44no—
101C2×Dic113C2×D412yes—
102C2×Dic113C2×D412yes—
103C2×Dic113#4114yes—
104C2×Dic113#4114yes—
105C4×D113—44no—
106Dic226—28no—
107C22×C113—22no—
108C22×C113—24no—
109C22×C113—41no—
110C22×C113—41no—
111C22×C113—42no—
112C22×C113C22×D411yescharacteristic
113C22×C113C2×#4111yescharacteristic
114C22×C113C2×#4112yes—
115C22×C113C2×#4112yes—
116C22×C113C2×#4111yescharacteristic
117C2×D113—22no—
118C2×D113—24no—
119C2×D113—41no—
120C2×D113—41no—
121C2×D113—42no—
122C4×C113—22no—
123C4×C113—42no—
124C4×C113—41no—
125C4×C113—42no—
126Dic113—24no—
127Dic113—22no—
128Dic113—41no—
129Dic113—42no—
130Dic113#12414yes—
131C2×C113—42no—
132C2×C113#52511yescharacteristic
133C2×C113#52511yescharacteristic
134C2×C113C2×#12411yescharacteristic
135C2×C113#52912yes—
136C2×C113#52912yes—
137D113—42no—
138#2398—1131nomaximal, Sylow
139C113#239811yescharacteristic, complemented, Sylow
140C2×C4×Q8—1131no—
141C2×C4×D4—1131no—
142#400—1132no—
143#397—1131no—
144#397D11311yescharacteristic, complemented
145#394—1132no—
146#393—1131no—
147#393—1131no—
148C4×C22⋊C4—1132no—
149C4×C22⋊C4—1132no—
150#376—1131no—
151C22×Q8—1131no—
152C22×D4—1131no—
153C23×C4—1131no—
154C23×C4—1131no—
155C4×Q8—2264no—
156C4×D4—2264no—
157C2×C4⋊C4—1131no—
158C2×C4⋊C4—1132no—
159C2×C4⋊C4C2×D11311yescharacteristic
160C2×C22⋊C4—1132no—
161C2×C22⋊C4—1131no—
162C2×C22⋊C4—1132no—
163C2×C22⋊C4—1132no—
164C2×C22⋊C4C2×D11311yescharacteristic
165C2×C22⋊C4C2×D11312yes—
166C2×C42—1131no—
167C2×C42—1132no—
168C2×C42—1132no—
169#95—1131no—
170#95—1132no—
171#95—1132no—
172#95—1132no—
173#95—1132no—
174#95C2×D11311yescharacteristic
175#95C2×D11312yes—
176C24—1131no—
177C24C22×D11311yescharacteristic
178C2×Q8—2264no—
179C2×Q8—2262no—
180C2×D4—2262no—
181C2×D4—2262no—
182C2×D4—2262no—
183C22×C4—1131no—
184C22×C4—1132no—
185C22×C4—1131no—
186C22×C4—1132no—
187C22×C4—1131no—
188C22×C4—2262no—
189C22×C4—2264no—
190C22×C4—2262no—
191C22×C4—2264no—
192C22×C4C22×D11312yes—
193C22×C4C22×D11311yescharacteristic
194C22×C4C22×D11312yes—
195C22×C4C22×D11311yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—2262no—
198C4⋊C4—2264no—
199C22⋊C4—24no—
200C22⋊C4—22no—
201C22⋊C4—2264no—
202C22⋊C4—2264no—
203C22⋊C4—2264no—
204C22⋊C4—2262no—
205C42—1134no—
206C42—2264no—
207C42—2264no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—1132no—
213C23—2261no—
214C23—2262no—
215C23—2262no—
216C23—2261no—
217C23#1426864612yes—
218C23C23×D11311yescharacteristic
219Q8—2268no—
220D4—2268no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—1132no—
231C2×C4—1134no—
232C2×C4—1132no—
233C2×C4—1134no—
234C2×C4—4524no—
235C2×C4—4524no—
236C2×C4—2261no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4—2262no—
240C2×C4—2262no—
241C2×C4—2262no—
242C2×C4—2261no—
243C2×C4—2262no—
244C2×C4—2261no—
245C2×C4D4×D11312yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—4521no—
252C22—4521no—
253C22—4522no—
254C22—2262no—
255C22—2264no—
256C22C2×D4×D11311yescharacteristic
257C22#41×D11312yes—
258C22#41×D11311yescharacteristic
259C22#41×D11312yes—
260C22C2×#1426864611yescharacteristic
261C4—22no—
262C4—42no—
263C4—41no—
264C4—42no—
265C4—1134no—
266C4—4521no—
267C4—4522no—
268C4—2264no—
269C4—2262no—
270C2—42no—
271C2—4522no—
272C2#2029910611yescharacteristic
273C2#2029910811yescharacteristic
274C2#124×D11311yescharacteristic
275C2#2029912512yes—
276C2#2029913112yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#397×C113C2
prime radicalC22×C22⋊D113C22
hypercenter#397D113
hypocenterC113#2398
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#16813587C2semidirect
3. #20298539C2semidirect
4. #20298524C2semidirect
6. #20298511C2semidirect
7. #20298510C2semidirect
8. C22⋊C4×Dic113C2semidirect
9. #20298445C2semidirect
10. #20298443C2semidirect
11. #397×C113C2semidirect
139. C113#2398semidirect
144. #397D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135872
C2×#168135822
#202985392
#202985242
#202985132
#202985112
#202985102
C22⋊C4×Dic1132
#202984452
#202984432
#397×C1132
#2398113