Finite Group Databasebeta

← #13078460

Subgroups — #13078460

Order 1408.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#10623343C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic
3C11×#419C211yesmaximal, characteristic
4C2×#66899C211yesmaximal, characteristic
5#10622734C211yesmaximal, characteristic
6#10622732C211yesmaximal, characteristic
7#10622611C211yesmaximal, characteristic
8#10622412C212yesmaximal, complemented
9#10622409C212yesmaximal, complemented
10#10622407C212yesmaximal, complemented
11#10622404C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15Q8×Dic11—21no—
16Q8×Dic11—21no—
17Q8×Dic11C2212yes—
18Q8×Dic11C2212yes—
19#66979—22no—
20#66979C2211yescharacteristic
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66943C2212yes—
25#66941C2212yes—
26#66931—22no—
27#66923—21no—
28#66922—21no—
29C11×#103C2212yes—
30C11×#103C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33#66882C2212yes—
34#66881C2212yes—
35Dic11⋊C8C2212yes—
36Dic11⋊C8C2212yes—
37#66872C2211yescharacteristic
38#66872C2211yescharacteristic
39#66871C2211yescharacteristic
40#66871C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11—22no—
43C2×Q8×C11Q814yescomplemented
44C2×Q8×C11C2312yes—
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C2×Dic22—22no—
49C11×M16—22no—
50C2×C8×C11C2312yes—
51C11×C4⋊C4C2311yescharacteristic
52C11×C4⋊C4C2311yescharacteristic
53C11×C22⋊C4—21no—
54C42×C11—21no—
55C22⋊Dic11—21no—
56C22⋊Dic11D412yes—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—21no—
61C4⋊Dic11D411yescharacteristic
62C4⋊Dic11D411yescharacteristic
63C4⋊Dic11C2311yescharacteristic
64C4⋊Dic11C2311yescharacteristic
65C4⋊Dic11C2312yes—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68C4×Dic11—22no—
69C4×Dic11—22no—
70C4×Dic11—21no—
71C4×Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#3082—111nomaximal, Sylow
76C23×C11C2×D411yescharacteristic
77Q8×C11—24no—
78Q8×C11—22no—
79Q8×C11C2×Q814yes—
80C2×C4×C11—24no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×Q812yes—
86C2×C4×C11#4112yes—
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—81no—
92C2×Dic11C2×D412yes—
93C2×Dic11C2×D412yes—
94Dic22—82no—
95C8×C11—22no—
96C11⋊C8—21no—
97C11⋊C8—21no—
98#544—111no—
99#519—111no—
100#479—112no—
101#479—112no—
102#477—112no—
103#475—112no—
104#428—111no—
105#427—111no—
106#424—111no—
107#419D1111yescharacteristic
108C2×#103—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11C22⋊Q812yes—
112C22×C11C22×D411yescharacteristic
113C4×C11—24no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11C22⋊Q812yes—
117C4×C11C22×Q811yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—22no—
120Dic11—22no—
121Dic11—42no—
122Dic11—41no—
123Dic11—41no—
124C22×Q8C2×D1111yescharacteristic
125C2×M16C2×D1111yescharacteristic
126C22×C8—111no—
127C4⋊Q8—112no—
128C4⋊Q8—221no—
129#125—112no—
130#125—221no—
131C22⋊Q8—222no—
132C4×Q8—112no—
133C4×Q8—112no—
134C4×Q8—221no—
135C4×Q8—221no—
136#117—111no—
137#117—111no—
138#117—222no—
139#117C2×D1111yescharacteristic
140C2×C4⋊C4—111no—
141#107—112no—
142#107—111no—
143#107—111no—
144#106—112no—
145#106—111no—
146#106—111no—
147C4⋊C8—112no—
148C4⋊C8—112no—
149#103—112no—
150#103—112no—
151#103C2×D1112yes—
152#103C2×D1112yes—
153C2×C11—22no—
154C2×C11C2×C22⋊Q811yescharacteristic
155C2×C11#57711yescharacteristic
156C2×C11#57811yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—222no—
160C2×Q8Dic2214yescomplemented
161C2×Q8C22×D1112yes—
162C22×C4—21no—
163C22×C4—221no—
164C22×C4C22×D1111yescharacteristic
165M16—22no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8—222no—
169C2×C8C22×D1112yes—
170C4⋊C4—111no—
171C4⋊C4—111no—
172C4⋊C4—112no—
173C4⋊C4—111no—
174C4⋊C4—111no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—221no—
181C4⋊C4C22×D1111yescharacteristic
182C4⋊C4C22×D1111yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—112no—
185C22⋊C4—221no—
186C42—21no—
187C42—112no—
188C42—222no—
189C42—222no—
190C42—221no—
191C11#308211yescharacteristic, complemented, Sylow
192C23D4×D1111yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—882no—
196Q8C2×Dic2214yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—112no—
202C2×C4—112no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—222no—
206C2×C4—881no—
207C2×C4C2×Dic2212yes—
208C2×C4D4×D1111yescharacteristic
209C2×C4#434112yes—
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—221no—
213C8—221no—
214C22—21no—
215C22—21no—
216C22#6693112yes—
217C22C2×D4×D1111yescharacteristic
218C4—24no—
219C4—41no—
220C4—41no—
221C4—222no—
222C4—222no—
223C4—442no—
224C4—441no—
225C4—441no—
226C4#6693112yes—
227C4C22×Dic2211yescharacteristic
228C4C2×#434111yescharacteristic
229C2—22no—
230C2C2×#6693111yescharacteristic
231C2#1062330911yescharacteristic
232C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#419D11
hypocenterC11#3082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
8. #10622412C2semidirect
9. #10622409C2semidirect
10. #10622407C2semidirect
11. #10622404C2semidirect
43. C2×Q8×C11Q8semidirect
160. C2×Q8Dic22semidirect
191. C11#3082semidirect

Maximal subgroups

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

subgroupindex
#106233432
#106230502
C11×#4192
C2×#668992
#106227342
#106227322
#106226112
#106224122
#106224092
#106224072
#106224042
#308211