Finite Group Databasebeta

← #13074534

Subgroups — #13074534

Order 1408.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic
3#10622844C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622824C211yesmaximal, characteristic, complemented
6#10622606C211yesmaximal, characteristic, complemented
7#10622602C212yesmaximal, complemented
8#10622593C211yesmaximal, characteristic, complemented
9#10622591C212yesmaximal, complemented
10#10622572C212yesmaximal
11#10622565C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C11×C22⋊Q8—24no—
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C4×C22⋊D11—24no—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C2×Q8×C11—22no—
40C2×Q8×C11—42no—
41C22×C4×C11—42no—
42C22×C4×C11D414yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—22no—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—22no—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—42no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—24no—
59C11×C22⋊C4—24no—
60C22⋊Dic11—22no—
61C22⋊Dic11—42no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—42no—
65Dic11⋊C4—24no—
66Dic11⋊C4—22no—
67Dic11⋊C4—42no—
68C4×Dic11—22no—
69#2638—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11C2×D412yes—
75C23×C11C2411yescharacteristic
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11#4112yes—
81Q8×C11—44no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—44no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D412yes—
93C22⋊D11—28no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11#4112yes—
107C4×D11—44no—
108C2×C22⋊Q8D1111yescharacteristic, complemented
109C2×C4×D4—111no—
110#398—111no—
111#397—111no—
112#397—112no—
113#395—111no—
114#394—112no—
115#393—111no—
116#387—112no—
117#385—112no—
118#381—111no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11C22×D411yescharacteristic
125C22×C11C2×#4111yescharacteristic
126C22×C11C2×#4111yescharacteristic
127C22×C11H(5,𝔽2)12yes—
128C22×C112−1+412yes—
129C2×D11—22no—
130C2×D11—24no—
131C2×D11—41no—
132C2×D11—41no—
133C2×D11—42no—
134C4×C11—22no—
135C4×C11—22no—
136C4×C11—42no—
137C4×C11—42no—
138Dic11—22no—
139Dic11—41no—
140Dic11—41no—
141Dic11—42no—
142Dic11—42no—
143C22×Q8C2×D1111yescharacteristic
144C22×D4—111no—
145C23×C4—111no—
146C23×C4C2×D1111yescharacteristic
147C22⋊Q8—24no—
148C4×D4—224no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4C2×D1112yes—
153C2×C4⋊C4C2×D1111yescharacteristic
154C2×C22⋊C4—111no—
155C2×C22⋊C4—111no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4C2×D1112yes—
160C2×C42—111no—
161#95—112no—
162#95—111no—
163#95—111no—
164#95—112no—
165#95—112no—
166#95—112no—
167#95—112no—
168C2×C11—42no—
169C2×C11#52511yescharacteristic
170C2×C11#53411yescharacteristic
171C2×C11#53611yescharacteristic
172C2×C11#53912yes—
173C2×C11#54212yes—
174D11—42no—
175C24—111no—
176C24C22×D1111yescharacteristic
177C2×Q8—22no—
178C2×Q8—42no—
179C2×D4—222no—
180C2×D4—222no—
181C2×D4—222no—
182C22×C4—42no—
183C22×C4—111no—
184C22×C4—111no—
185C22×C4—112no—
186C22×C4—112no—
187C22×C4—111no—
188C22×C4—222no—
189C22×C4—442no—
190C22×C4C22⋊D1114yes—
191C22×C4C22×D1112yes—
192C22×C4C22×D1112yes—
193C22×C4C22×D1111yescharacteristic
194C22×C4C22×D1111yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—224no—
198C4⋊C4—222no—
199C4⋊C4—442no—
200C22⋊C4—24no—
201C22⋊C4—224no—
202C22⋊C4—222no—
203C22⋊C4—222no—
204C22⋊C4—442no—
205C22⋊C4—442no—
206C42—222no—
207C11#263811yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—21no—
211C23—21no—
212C23—112no—
213C23—222no—
214C23—222no—
215C23—221no—
216C23—221no—
217C23C2×C22⋊D1112yes—
218C23C23×D1111yescharacteristic
219Q8—44no—
220D4—228no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—112no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—221no—
242C2×C4—221no—
243C2×C4—444no—
244C2×C4C2×C22⋊D1112yes—
245C2×C4C2×C22⋊D1112yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—222no—
252C22—224no—
253C22—441no—
254C22—441no—
255C22—442no—
256C22#6703712yes—
257C22#6704012yes—
258C22#41×D1111yescharacteristic
259C22#41×D1111yescharacteristic
260C22C22×C22⋊D1111yescharacteristic
261C4—22no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—222no—
266C4—441no—
267C4—441no—
268C4—442no—
269C4—442no—
270C2—42no—
271C2—442no—
272C2#1062316912yes—
273C2#1062317112yes—
274C2#1062333511yescharacteristic
275C2#1062334711yescharacteristic
276C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
3. #10622844C2semidirect
4. #10622842C2semidirect
5. #10622824C2semidirect
6. #10622606C2semidirect
7. #10622602C2semidirect
8. #10622593C2semidirect
9. #10622591C2semidirect
11. #10622565C2semidirect
108. C2×C22⋊Q8D11semidirect
207. C11#2638semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×C4×C22⋊D112
#106228442
#106228422
#106228242
#106226062
#106226022
#106225932
#106225912
#106225722
#106225652
#263811