Finite Group Databasebeta

← #13072271

Subgroups — #13072271

Order 1408.

852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D11C211yesmaximal, characteristic, complemented
2C2×C11×#124C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic
4C2×#66989C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622569C214yesmaximal, complemented
7#10622560C214yesmaximal, complemented
8C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9#10622542C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C2×Q8×D11—24no—
14C2×Q8×D11—24no—
15C2×Q8×D11—24no—
16C22×C4×D11C2212yes—
17C22×C4×D11C2211yescharacteristic
18C22×Dic22C2212yes—
19C22×Dic22C2211yescharacteristic
20C11×#124—24no—
21C2×C11×C22⋊C4C2214yes—
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2214yes—
25#66991—24no—
26#66989—24no—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30C11⋊#95C2214yes—
31C11⋊#95C2212yes—
32C11⋊#95C2214yes—
33C24×C11C2312yes—
34C23×D11C2311yescharacteristic
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11D414yescomplemented
38C2×D4×C11—22no—
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—24no—
45C2×C22⋊D11—28no—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2312yes—
50Q8×D11—232no—
51C2×C4×D11—24no—
52C2×C4×D11—24no—
53C2×C4×D11—22no—
54C2×C4×D11—24no—
55C2×C4×D11—22no—
56C2×C4×D11D414yes—
57C2×Dic22—24no—
58C2×Dic22—24no—
59C2×Dic22—22no—
60C2×Dic22—24no—
61C2×Dic22—22no—
62C2×Dic22D414yescomplemented
63C11×C22⋊C4—28no—
64C42×C11—22no—
65C22⋊Dic11—28no—
66C22⋊Dic11—24no—
67(C2×D11)⋊C4—24no—
68C4⋊Dic11—22no—
69C4×Dic11—22no—
70#2436—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—24no—
75C23×C11—24no—
76C23×C11C2411yescharacteristic
77C22×D11—21no—
78C22×D11—21no—
79C22×D11—22no—
80C22×D11C2×D412yes—
81C22×D11#4114yes—
82Q8×C11—28no—
83D4×C11—44no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11C2×D412yes—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D414yes—
92C2×C4×C11C2×D412yes—
93C22⋊D11—48no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—24no—
102C2×Dic11—22no—
103C2×Dic11C2×D412yes—
104C2×Dic11C2×D414yes—
105C4×D11—216no—
106C4×D11—28no—
107Dic22—216no—
108Dic22—28no—
109C23×Q8—111no—
110C2×#124—111no—
111C2×#124D1111yescharacteristic, complemented
112C2×#121—111no—
113#393—114no—
114#391—111no—
115#391—111no—
116#386—114no—
117C4×C22⋊C4—111no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—44no—
122C22×C11—44no—
123C22×C11C22×D411yescharacteristic
124C22×C11C22×D411yescharacteristic
125C22×C11C22×D411yescharacteristic
126C22×C11C2×#4112yes—
127C22×C112−1+412yes—
128C2×D11—22no—
129C2×D11—22no—
130C2×D11—24no—
131C2×D11—24no—
132C2×D11#12414yescomplemented
133C4×C11—24no—
134C4×C11—42no—
135C4×C11#12014yes—
136Dic11—22no—
137Dic11—24no—
138Dic11—42no—
139Dic11—42no—
140C22×Q8—111no—
141C22×Q8—112no—
142C22×Q8—224no—
143C22×Q8—224no—
144C22×Q8—224no—
145C22×Q8C2×D1111yescharacteristic
146C22×D4—112no—
147C22×D4C2×D1111yescharacteristic
148C23×C4—111no—
149C23×C4—112no—
150#124—24no—
151#124—224no—
152#121—224no—
153C2×C4⋊C4—111no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—114no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4C2×D1114yes—
158C2×C42—111no—
159C2×C42C2×D1111yescharacteristic
160#95—112no—
161#95—114no—
162#95—114no—
163C2×C11—82no—
164C2×C11C2×#12011yescharacteristic
165C2×C11C2×#12411yescharacteristic
166C2×C11#53611yescharacteristic
167C2×C11#54812yes—
168C2×C11#54812yes—
169D11—24no—
170C24—111no—
171C24C22×D1112yes—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—114no—
175C2×Q8—224no—
176C2×Q8—224no—
177C2×Q8—2232no—
178C2×Q8—222no—
179C2×Q8—224no—
180C2×Q8—222no—
181C2×Q8C22⋊D1114yescomplemented
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—224no—
186C2×D4—228no—
187C22×C4—111no—
188C22×C4—112no—
189C22×C4—114no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—222no—
195C22×C4—224no—
196C22×C4—222no—
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C4⋊C4—222no—
201C22⋊C4—28no—
202C22⋊C4—224no—
203C22⋊C4—224no—
204C22⋊C4—228no—
205C42—22no—
206C42—222no—
207C11#243611yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—24no—
211C23—24no—
212C23—22no—
213C23—112no—
214C23—114no—
215C23—221no—
216C23—222no—
217C23—221no—
218C23C23×D1111yescharacteristic
219Q8—28no—
220Q8—2216no—
221Q8—228no—
222D4—44no—
223D4—448no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—112no—
230C2×C4—114no—
231C2×C4—2216no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—228no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—224no—
241C2×C4—222no—
242C2×C4D4×D1112yes—
243C2×C4D4×D1112yes—
244C2×C4C2×C22⋊D1114yes—
245C2×C4C2×C22⋊D1112yes—
246C22—42no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—44no—
251C22—114no—
252C22—222no—
253C22—224no—
254C22—222no—
255C22—224no—
256C22C2×D4×D1111yescharacteristic
257C22C2×D4×D1111yescharacteristic
258C22#41×D1112yes—
259C22#6704312yes—
260C22C22×C22⋊D1111yescharacteristic
261C4—24no—
262C4—42no—
263C4—222no—
264C4—224no—
265C4—442no—
266C4—442no—
267C4#6699014yes—
268C2—82no—
269C2—224no—
270C2D11×#12411yescharacteristic
271C2#1062320611yescharacteristic
272C2#1062320812yes—
273C2C2×#6699011yescharacteristic
274C2#1062336212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC2×#66991C2
hypercenterC2×#124D11
hypocenterC11#2436
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D11C2semidirect
2. C2×C11×#124C2semidirect
4. C2×#66989C2semidirect
5. #10622843C2semidirect
6. #10622569C2semidirect
7. #10622560C2semidirect
8. C4×(C2×D11)⋊C4C2semidirect
9. #10622542C2semidirect
37. C2×Q8×C11D4semidirect
62. C2×Dic22D4semidirect
111. C2×#124D11semidirect
132. C2×D11#124semidirect
181. C2×Q8C22⋊D11semidirect
207. C11#2436semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D112
C2×C11×#1242
C2×#669912
C2×#669892
#106228432
#106225692
#106225602
C4×(C2×D11)⋊C42
#106225422
#243611