Finite Group Databasebeta

← #13073992

Subgroups — #13073992

Order 1408.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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×#66999C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622602C212yesmaximal
6#10622596C211yesmaximal, characteristic, complemented
7#10622586C212yesmaximal, complemented
8#10622281C212yesmaximal
9#10622279C211yesmaximal, characteristic
10#10622274C211yesmaximal, characteristic, complemented
11#10622260C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18#66999—24no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2212yes—
30C4⋊C4×D11—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—42no—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C2×C4×D11—22no—
51C2×C4×D11—22no—
52C2×C4×D11—22no—
53C2×C4×D11—22no—
54C2×C4×D11—42no—
55C2×C4×D11—42no—
56C2×C4×D11D414yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4Q818yescomplemented
61C4⋊Dic11—22no—
62C4⋊Dic11—24no—
63C4⋊Dic11—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—24no—
66Dic11⋊C4—22no—
67Dic11⋊C4—24no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70#2583—111nomaximal, Sylow
71C23×C11C2411yescharacteristic
72C22×D11—21no—
73C22×D11—21no—
74C22×D11—22no—
75C22×D11C2×D412yes—
76C22×D11C2×Q814yes—
77Q8×C11—44no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11C2×D412yes—
89C2×C4×C11C2×Q814yes—
90C2×C4×C11#4112yes—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11C2×D412yes—
102C2×Dic11C2×Q814yes—
103C2×Dic11#4112yes—
104C4×D11—28no—
105C4×D11—44no—
106C4×D11—44no—
107C2×C22⋊Q8—111no—
108C22×C4⋊C4—111no—
109#398—111no—
110#398—111no—
111#395—111no—
112#395D1111yescharacteristic, complemented
113#389—112no—
114#389—112no—
115#385—112no—
116#385—112no—
117C4×C22⋊C4—111no—
118C22×C11C22×D411yescharacteristic
119C22×C11C22×Q812yes—
120C22×C11C2×#4111yescharacteristic
121C22×C11C2×#4111yescharacteristic
122C22×C11H(5,𝔽2)12yes—
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—24no—
126C2×D11—24no—
127C2×D11C4⋊Q814yes—
128C4×C11—22no—
129C4×C11—22no—
130C4×C11—24no—
131C4×C11—42no—
132C4×C11—41no—
133Dic11—22no—
134Dic11—22no—
135Dic11—24no—
136Dic11—42no—
137Dic11—41no—
138C22×Q8C2×D1111yescharacteristic
139C23×C4—111no—
140C23×C4—111no—
141C23×C4—111no—
142C22⋊Q8—224no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—224no—
152C2×C4⋊C4C2×D1111yescharacteristic
153C2×C4⋊C4C2×D1112yes—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C42—112no—
157#95—111no—
158#95—112no—
159#95—112no—
160#95—112no—
161#95C2×D1111yescharacteristic
162#95C2×D1112yes—
163C2×C11#52511yescharacteristic
164C2×C11C2×C4⋊Q811yescharacteristic
165C2×C11#53411yescharacteristic
166C2×C11#55412yes—
167C2×C11#55412yes—
168D11—24no—
169C24—111no—
170C2×Q8—22no—
171C2×Q8—42no—
172C22×C4—112no—
173C22×C4—111no—
174C22×C4—111no—
175C22×C4—114no—
176C22×C4—112no—
177C22×C4—111no—
178C22×C4—222no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4—442no—
183C22×C4—442no—
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1112yes—
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1112yes—
188C22×C4C22×D1111yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—224no—
194C4⋊C4—224no—
195C4⋊C4—222no—
196C4⋊C4—222no—
197C4⋊C4—224no—
198C4⋊C4—442no—
199C22⋊C4—118no—
200C22⋊C4—224no—
201C42—442no—
202C11#258311yescharacteristic, complemented, Sylow
203C23—112no—
204C23—114no—
205C23—222no—
206C23—221no—
207C23—221no—
208C23C23×D1111yescharacteristic
209Q8—44no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—112no—
221C2×C4—114no—
222C2×C4—112no—
223C2×C4—228no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—221no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—444no—
235C2×C4—444no—
236C2×C4D4×D1112yes—
237C2×C4Q8×D1114yes—
238C2×C4#434312yes—
239C22—114no—
240C22—224no—
241C22—222no—
242C22—222no—
243C22—224no—
244C22C2×D4×D1111yescharacteristic
245C22#6703712yes—
246C22C2×Q8×D1112yes—
247C22C2×#434311yescharacteristic
248C22#41×D1111yescharacteristic
249C4—22no—
250C4—22no—
251C4—24no—
252C4—41no—
253C4—42no—
254C4—224no—
255C4—222no—
256C4—222no—
257C4—441no—
258C4—442no—
259C2—224no—
260C2#1062312011yescharacteristic
261C2#1062315811yescharacteristic
262C2#1062316712yes—
263C2D11×C4⋊Q811yescharacteristic
264C2#1062326112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC23×D11C23
hypercenter#395D11
hypocenterC11#2583
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. C11×#395C2semidirect
4. #10622842C2semidirect
6. #10622596C2semidirect
7. #10622586C2semidirect
10. #10622274C2semidirect
11. #10622260C2semidirect
60. (C2×D11)⋊C4Q8semidirect
112. #395D11semidirect
202. C11#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4⋊C4×D112
C11×#3952
#106228422
#106226022
#106225962
#106225862
#106222812
#106222792
#106222742
#106222602
#258311