Finite Group Databasebeta

← #13073798

Subgroups — #13073798

Order 1408.

584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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
5C2×C11⋊#95C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622602C212yesmaximal, complemented
8#10622595C211yesmaximal, characteristic, complemented
9#10622591C212yesmaximal, complemented
10#10622571C212yesmaximal
11#10622555C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C23×Dic11C2212yes—
16C22×C4×D11C2211yescharacteristic
17C11×C22⋊Q8—24no—
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2212yes—
21C2×C22⋊Dic11C2211yescharacteristic
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⋊#95C2211yescharacteristic
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
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⋊D11Q814yescomplemented
50C22×Dic11—24no—
51C22×Dic11—24no—
52C22×Dic11—42no—
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C2×C4×D11—22no—
59C2×C4×D11—42no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—24no—
62C11×C22⋊C4—24no—
63C22⋊Dic11—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—42no—
67Dic11⋊C4—24no—
68Dic11⋊C4—22no—
69Dic11⋊C4—42no—
70C4×Dic11—22no—
71#2564—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11C2×D412yes—
75C23×C11C2×Q812yes—
76C23×C11#4112yes—
77C23×C11C2411yescharacteristic
78C22×D11—21no—
79C22×D11—22no—
80C22×D11—21no—
81C22×D11—22no—
82C22×D11C2×Q812yes—
83Q8×C11—44no—
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—22no—
91C2×C4×C11—22no—
92C2×C4×C11—44no—
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D412yes—
95C22⋊D11—28no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—48no—
108C2×Dic11C2×Q812yes—
109C2×Dic11#4114yes—
110C4×D11—44no—
111C2×C22⋊Q8D1111yescharacteristic, complemented
112C2×C4×D4—111no—
113#400—111no—
114#399—111no—
115#395—111no—
116#393—111no—
117#387—112no—
118#386—112no—
119#385—112no—
120#380—112no—
121C2×#95—111no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—24no—
125C22×C11—24no—
126C22×C11C22⋊Q814yes—
127C22×C11C22×D411yescharacteristic
128C22×C11C22×Q811yescharacteristic
129C22×C11C2×#4111yescharacteristic
130C22×C11C2×#4112yes—
131C22×C11H(5,𝔽2)12yes—
132C2×D11—22no—
133C2×D11—24no—
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—42no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—42no—
141Dic11—22no—
142Dic11—24no—
143Dic11—41no—
144Dic11—41no—
145Dic11—42no—
146C22×Q8C2×D1111yescharacteristic
147C22×D4—111no—
148C23×C4—112no—
149C23×C4—111no—
150C23×C4C2×D1111yescharacteristic
151C22⋊Q8—24no—
152C4×D4—224no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4C2×D1112yes—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4—111no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4C2×D1112yes—
163C2×C42—111no—
164#95—112no—
165#95—111no—
166#95—111no—
167#95—112no—
168#95—112no—
169#95—112no—
170#95—112no—
171C2×C11—24no—
172C2×C11C2×C22⋊Q811yescharacteristic
173C2×C11#53211yescharacteristic
174C2×C11#53411yescharacteristic
175C2×C11#55112yes—
176C2×C11#55412yes—
177D11—42no—
178C24—111no—
179C24C22×D1111yescharacteristic
180C2×Q8—22no—
181C2×Q8—42no—
182C2×D4—114no—
183C2×D4—222no—
184C2×D4—222no—
185C22×C4—42no—
186C22×C4—111no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4—111no—
190C22×C4—111no—
191C22×C4—224no—
192C22×C4—224no—
193C22×C4—222no—
194C22×C4—442no—
195C22×C4—442no—
196C22×C4C22⋊D1114yes—
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—24no—
203C4⋊C4—224no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C22⋊C4—24no—
207C22⋊C4—224no—
208C22⋊C4—222no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C42—222no—
212C11#256411yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—112no—
216C23—222no—
217C23—221no—
218C23—222no—
219C23—221no—
220C23Q8×D1112yes—
221C23#434312yes—
222C23C2×C22⋊D1112yes—
223C23C23×D1111yescharacteristic
224Q8—44no—
225D4—228no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—44no—
235C2×C4—112no—
236C2×C4—114no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—221no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—444no—
249C2×C4—448no—
250C2×C4C2×C22⋊D1112yes—
251C2×C4C2×C22⋊D1112yes—
252C22—22no—
253C22—22no—
254C22—24no—
255C22—24no—
256C22—222no—
257C22—224no—
258C22—441no—
259C22—441no—
260C22—442no—
261C22#6699914yes—
262C22#6703712yes—
263C22C2×Q8×D1111yescharacteristic
264C22C2×#434311yescharacteristic
265C22#41×D1112yes—
266C22C22×C22⋊D1111yescharacteristic
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—222no—
272C4—224no—
273C4—441no—
274C4—441no—
275C4—442no—
276C2—24no—
277C2—442no—
278C2#1062316712yes—
279C2#1062316812yes—
280C2#1062333511yescharacteristic
281C2C2×#6699911yescharacteristic
282C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2564
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. C2×C11⋊#95C2semidirect
6. #10622605C2semidirect
7. #10622602C2semidirect
8. #10622595C2semidirect
9. #10622591C2semidirect
11. #10622555C2semidirect
49. C2×C22⋊D11Q8semidirect
111. C2×C22⋊Q8D11semidirect
212. C11#2564semidirect

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
C2×C11⋊#952
#106226052
#106226022
#106225952
#106225912
#106225712
#106225552
#256411