Finite Group Databasebeta

← #13079821

Subgroups — #13079821

Order 1408.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623153C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic
3C11×#484C211yesmaximal, characteristic
4#10622656C211yesmaximal, characteristic
5#10622583C211yesmaximal, characteristic
6#10622490C212yesmaximal, complemented
7#10622489C212yesmaximal, complemented
8#10622412C212yesmaximal, complemented
9#10622410C212yesmaximal, complemented
10#10622334C211yesmaximal, characteristic
11#10622332C211yesmaximal, characteristic
12C11×C22⋊Q8C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14Q8×Dic11C2211yescharacteristic
15#66997C2211yescharacteristic
16C2×C4⋊Dic11—21no—
17C2×C4⋊Dic11C2211yescharacteristic
18#66977C2211yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×C4×Dic11C2211yescharacteristic
21#66943—21no—
22#66943—21no—
23#66943C2212yes—
24#66943C2212yes—
25#66942—21no—
26#66941C2211yescharacteristic
27#66940—21no—
28#66940C2211yescharacteristic
29#66931—21no—
30#66930—21no—
31C11×#107C2212yes—
32C11×#103C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66899C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66881C2212yes—
37#66880C2212yes—
38#66879C2212yes—
39Dic11⋊C8C2212yes—
40#66874C2212yes—
41#66872C2212yes—
42#66871C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11D411yescharacteristic
48C22×Dic11D411yescharacteristic
49C2×Dic22—21no—
50C2×Dic22C2311yescharacteristic
51C2×C8×C11C2312yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C4⋊C4C2311yescharacteristic
56C11×C22⋊C4—21no—
57C22⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11C2311yescharacteristic
63C4⋊Dic11C2312yes—
64Dic11⋊C4—21no—
65Dic11⋊C4—21no—
66Dic11⋊C4—21no—
67Dic11⋊C4—21no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—21no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73C4×Dic11D411yescharacteristic
74C4×Dic11D411yescharacteristic
75C4×Dic11C2311yescharacteristic
76C4×Dic11C2311yescharacteristic
77C2×C11⋊C8C2312yes—
78#3236—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80Q8×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—42no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—22no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—41no—
93C2×Dic11—42no—
94C2×Dic11C2×D411yescharacteristic
95C2×Dic11C2×D411yescharacteristic
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98Dic22—22no—
99Dic22—42no—
100C8×C11—22no—
101C11⋊C8—22no—
102#533—111no—
103C2×#125—111no—
104#501—112no—
105#491—112no—
106#484—111no—
107#484D1111yescharacteristic
108#483—111no—
109#483—111no—
110#479—112no—
111#479—112no—
112#432—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11#13712yes—
116C22×C11C22×D411yescharacteristic
117C4×C11—21no—
118C4×C11—41no—
119C4×C11—42no—
120C4×C11—41no—
121C4×C112−1+412yes—
122Dic11—21no—
123Dic11—21no—
124Dic11—21no—
125Dic11—21no—
126Dic11—41no—
127Dic11—42no—
128Dic11—41no—
129C4⋊Q8—111no—
130C4⋊Q8—111no—
131#125—112no—
132#125—112no—
133#125—221no—
134#125—221no—
135#125—221no—
136C22⋊Q8—111no—
137C22⋊Q8—221no—
138C22⋊Q8C2×D1111yescharacteristic
139C4×Q8—111no—
140C4×Q8—111no—
141C4×Q8—221no—
142#117—221no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4C2×D1111yescharacteristic
147C2×C42—111no—
148#107—112no—
149#107C2×D1112yes—
150#106—112no—
151#106—112no—
152C4⋊C8—112no—
153#103—112no—
154#103—112no—
155#103—112no—
156#103C2×D1112yes—
157C22⋊C8—111no—
158C22⋊C8C2×D1111yescharacteristic
159#97—112no—
160C2×C11—22no—
161C2×C11#53611yescharacteristic
162C2×C11C2×#13711yescharacteristic
163C2×C11#57511yescharacteristic
164C2×Q8—111no—
165C2×Q8—221no—
166C2×Q8C22×D1111yescharacteristic
167C22×C4—21no—
168C22×C4—111no—
169C22×C4—111no—
170C22×C4—221no—
171C22×C4C22×D1111yescharacteristic
172C2×C8—112no—
173C2×C8C22×D1112yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—112no—
177C4⋊C4—111no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4C22×D1112yes—
190C4⋊C4C22×D1111yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—221no—
193C42—111no—
194C42—111no—
195C42—111no—
196C42—111no—
197C42—221no—
198C42—221no—
199C11#323611yescharacteristic, complemented, Sylow
200C23D4×D1111yescharacteristic
201Q8—22no—
202Q8—222no—
203Q8—442no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—111no—
210C2×C4—111no—
211C2×C4—111no—
212C2×C4—111no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4—441no—
218C2×C4—442no—
219C2×C4D4×D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—22no—
222C8—222no—
223C22—21no—
224C22—21no—
225C22#6697112yes—
226C22C2×D4×D1111yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—221no—
232C4—221no—
233C4—221no—
234C4—221no—
235C4—442no—
236C4—441no—
237C4—441no—
238C4#6704312yes—
239C2—22no—
240C2#1062317911yescharacteristic
241C2C2×#6697111yescharacteristic
242C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#484D11
hypocenterC11#3236
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
6. #10622490C2semidirect
7. #10622489C2semidirect
8. #10622412C2semidirect
9. #10622410C2semidirect
199. C11#3236semidirect

Maximal subgroups

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

subgroupindex
#106231532
C2×#669432
C11×#4842
#106226562
#106225832
#106224902
#106224892
#106224122
#106224102
#106223342
#106223322
#323611