Finite Group Databasebeta

← #13078461

Subgroups — #13078461

Order 1408.

362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623050C211yesmaximal, characteristic
2#10623047C211yesmaximal, characteristic
3C11×#427C211yesmaximal, characteristic
4C2×#66880C211yesmaximal, characteristic
5#10622715C211yesmaximal, characteristic
6#10622617C211yesmaximal, characteristic
7#10622608C211yesmaximal, characteristic
8#10622490C212yesmaximal, complemented
9#10622488C212yesmaximal, complemented
10#10622470C212yesmaximal, complemented
11#10622467C212yesmaximal, complemented
12C22×Dic22C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C11×#117C2211yescharacteristic
15C11×#117C2211yescharacteristic
16#66979C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66943C2212yes—
20#66941C2212yes—
21#66940C2212yes—
22#66940C2212yes—
23#66931—22no—
24#66930—22no—
25#66923—21no—
26#66922—21no—
27C4×Dic22—21no—
28C4×Dic22—21no—
29C11×#107C2211yescharacteristic
30C11×#107C2211yescharacteristic
31C11×#106C2211yescharacteristic
32C11×#106C2211yescharacteristic
33#66880C2212yes—
34#66880C2212yes—
35Dic11⋊C8C2212yes—
36Dic11⋊C8C2212yes—
37#66874C2212yes—
38#66874C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—21no—
43C22×Dic11—21no—
44C2×Dic22—22no—
45C2×Dic22—21no—
46C2×Dic22—22no—
47C2×Dic22Q814yescomplemented
48C2×Dic22C2312yes—
49C2×C8×C11—22no—
50C2×C8×C11C2311yescharacteristic
51C2×C8×C11C2311yescharacteristic
52C11×C4⋊C4C2311yescharacteristic
53C11×C4⋊C4C2311yescharacteristic
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2311yescharacteristic
56C11×C22⋊C4—21no—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59C42×C11—21no—
60C22⋊Dic11D412yes—
61C4⋊Dic11—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2312yes—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C4×Dic11—22no—
72C4×Dic11C2312yes—
73#4318—22no—
74C2×C11⋊C8C2312yes—
75#3082—111nomaximal, Sylow
76C23×C11C2×D411yescharacteristic
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×Q812yes—
83C2×C4×C11#4112yes—
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—24no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—81no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D412yes—
91Dic22—24no—
92Dic22—22no—
93Dic22—82no—
94Dic22C2×Q814yes—
95C8×C11—21no—
96C8×C11—21no—
97C11⋊C8—22no—
98#544—111no—
99#519—111no—
100#479—112no—
101#479—112no—
102#477—112no—
103#475—112no—
104#428—111no—
105#427D1111yescharacteristic
106#424—111no—
107#419—111no—
108C2×#103—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11C22⋊Q812yes—
112C22×C11C22×D411yescharacteristic
113C4×C11—41no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11—41no—
117C4×C11C22⋊Q812yes—
118C4×C11C22×Q811yescharacteristic
119C4×C11C2×#4111yescharacteristic
120Dic11—24no—
121Dic11—22no—
122Dic11—22no—
123Dic11—42no—
124C22×Q8—111no—
125C2×M16—111no—
126C22×C8C2×D1111yescharacteristic
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—222no—
138#117C2×D1111yescharacteristic
139#117C2×D1111yescharacteristic
140C2×C4⋊C4—111no—
141#107—112no—
142#107C2×D1111yescharacteristic
143#107C2×D1111yescharacteristic
144#106—112no—
145#106C2×D1111yescharacteristic
146#106C2×D1111yescharacteristic
147C4⋊C8—112no—
148C4⋊C8—112no—
149#103—112no—
150#103—112no—
151#103—112no—
152#103—112no—
153C2×C11—22no—
154C2×C11C2×C22⋊Q811yescharacteristic
155C2×C11#57711yescharacteristic
156C2×C11#57811yescharacteristic
157C2×Q8—114no—
158C2×Q8—112no—
159C2×Q8—222no—
160C2×Q8—222no—
161C2×Q8—221no—
162C22×C4—221no—
163C22×C4—221no—
164C22×C4C22×D1111yescharacteristic
165M16—222no—
166C2×C8—22no—
167C2×C8—112no—
168C2×C8C22×D1111yescharacteristic
169C2×C8C22×D1111yescharacteristic
170C4⋊C4—111no—
171C4⋊C4—111no—
172C4⋊C4—112no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—221no—
179C4⋊C4C22×D1111yescharacteristic
180C4⋊C4C22×D1111yescharacteristic
181C4⋊C4C22×D1111yescharacteristic
182C4⋊C4C22×D1111yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—21no—
185C22⋊C4—112no—
186C42—21no—
187C42—21no—
188C42—112no—
189C42—222no—
190C42—222no—
191C11#308211yescharacteristic, complemented, Sylow
192C23D4×D1111yescharacteristic
193Q8—114no—
194Q8—224no—
195Q8—222no—
196Q8—882no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—112no—
202C2×C4—112no—
203C2×C4—224no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—881no—
207C2×C4#433912yes—
208C2×C4D4×D1111yescharacteristic
209C2×C4Q8×D1112yes—
210C2×C4C23×D1111yescharacteristic
211C8—21no—
212C8—21no—
213C8—222no—
214C22—21no—
215C22—21no—
216C22#6694912yes—
217C22C2×D4×D1111yescharacteristic
218C4—41no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—224no—
223C4—222no—
224C4—222no—
225C4—442no—
226C4#6694912yes—
227C4C2×#433911yescharacteristic
228C4C2×Q8×D1111yescharacteristic
229C2—22no—
230C2C2×#6694911yescharacteristic
231C2#1062330111yescharacteristic
232C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#427C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#427D11
hypocenterC11#3082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
8. #10622490C2semidirect
9. #10622488C2semidirect
10. #10622470C2semidirect
11. #10622467C2semidirect
47. C2×Dic22Q8semidirect
191. C11#3082semidirect

Maximal subgroups

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

subgroupindex
#106230502
#106230472
C11×#4272
C2×#668802
#106227152
#106226172
#106226082
#106224902
#106224882
#106224702
#106224672
#308211