Finite Group Databasebeta

← #13073684

Subgroups — #13073684

Order 1408.

696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66992C212yesmaximal, complemented
2C2×#66938C212yesmaximal, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622601C211yesmaximal, characteristic, complemented
5#10622592C211yesmaximal, characteristic, complemented
6#10622573C212yesmaximal, complemented
7#10622571C212yesmaximal, complemented
8C22⋊C4×Dic11C212yesmaximal, complemented
9#10622282C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C23×Dic11C2212yes—
14C22×D44C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20#66992—28no—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66938—28no—
29C11×#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C24×C11C2312yes—
34C23×D11C2312yes—
35C2×D4×C11—24no—
36C2×D4×C11—41no—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—24no—
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—42no—
46C2×C22⋊D11—42no—
47C22×Dic11—24no—
48C22×Dic11—24no—
49C22×Dic11—42no—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C2×D44—22no—
54C2×D44—41no—
55C2×D44—41no—
56C2×Dic22—24no—
57C2×Dic22—41no—
58C11×C4⋊C4—41no—
59C11×C22⋊C4—24no—
60C11×C22⋊C4—24no—
61C22⋊Dic11D418yescomplemented
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66Dic11⋊C4—24no—
67C4×Dic11—24no—
68C4×Dic11—41no—
69#2555—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11C2×D414yes—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85D4×C11—44no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11#4112yes—
96C22⋊D11—48no—
97C22⋊D11—48no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—48no—
105C2×Dic11C2×D414yes—
106C2×Dic11C2×D414yes—
107C2×Dic11#4114yes—
108D44—44no—
109Dic22—44no—
110C2×#124—112no—
111C2×#121—112no—
112#395—111no—
113#394D1111yescharacteristic, complemented
114#392—112no—
115#390—111no—
116#388—112no—
117#386—112no—
118C4×C22⋊C4—112no—
119C22×C11—24no—
120C22×C11—24no—
121C22×C11—24no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11C22×D412yes—
127C22×C11C2×#4111yescharacteristic
128C22×C11C2×#4112yes—
129C22×C11H(5,𝔽2)11yescharacteristic
130C22×C11H(5,𝔽2)11yescharacteristic
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—41no—
141C4×C11—41no—
142Dic11—24no—
143Dic11—24no—
144Dic11—24no—
145C22×Q8—111no—
146C22×D4—112no—
147C22×D4—112no—
148C22×D4—111no—
149C22×D4C2×D1111yescharacteristic
150C23×C4—112no—
151#124—228no—
152#121—228no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4C2×D1112yes—
161C2×C22⋊C4C2×D1112yes—
162C2×C42—112no—
163C2×C42—111no—
164#95—112no—
165#95—112no—
166#95—111no—
167#95C2×D1111yescharacteristic
168C2×C11—44no—
169C2×C11#53212yes—
170C2×C11#53811yescharacteristic
171C2×C11D4211yescharacteristic
172C2×C11#54612yes—
173C2×C11#55511yescharacteristic
174D11—82no—
175C24—112no—
176C24C22×D1112yes—
177C2×Q8—224no—
178C2×Q8—441no—
179C2×D4—24no—
180C2×D4—41no—
181C2×D4—224no—
182C2×D4—224no—
183C2×D4—224no—
184C2×D4—224no—
185C2×D4—222no—
186C2×D4—441no—
187C2×D4—441no—
188C2×D4—442no—
189C2×D4—442no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—112no—
193C22×C4—224no—
194C22×C4—224no—
195C22×C4—442no—
196C22×C4C22×D1112yes—
197C22×C4C22×D1111yescharacteristic
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C4⋊C4—41no—
201C4⋊C4—224no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—118no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—224no—
208C22⋊C4—224no—
209C42—224no—
210C42—441no—
211C11#255511yescharacteristic, complemented, Sylow
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—222no—
219C23—222no—
220C23—222no—
221C23—222no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23D4×D1114yes—
226C23C23×D1111yescharacteristic
227Q8—444no—
228D4—44no—
229D4—444no—
230D4—448no—
231D4—448no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—114no—
242C2×C4—114no—
243C2×C4—114no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—448no—
251C2×C4#434112yes—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—442no—
260C22—442no—
261C22—442no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22C2×D4×D1112yes—
267C22C2×#434111yescharacteristic
268C22#6703711yescharacteristic
269C22#41×D1112yes—
270C22#6704211yescharacteristic
271C4—22no—
272C4—41no—
273C4—41no—
274C4—42no—
275C4—224no—
276C4—224no—
277C4—224no—
278C2—44no—
279C2—882no—
280C2#1062312111yescharacteristic
281C2#1062312712yes—
282C2#1062314811yescharacteristic
283C2#1062318512yes—
284C2#1062320111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2555
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C2×#66938C2semidirect
3. C11×#394C2semidirect
4. #10622601C2semidirect
5. #10622592C2semidirect
6. #10622573C2semidirect
7. #10622571C2semidirect
8. C22⋊C4×Dic11C2semidirect
9. #10622282C2semidirect
61. C22⋊Dic11D4semidirect
113. #394D11semidirect
211. C11#2555semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669382
C11×#3942
#106226012
#106225922
#106225732
#106225712
C22⋊C4×Dic112
#106222822
#255511