Finite Group Databasebeta

← #13079701

Subgroups — #13079701

Order 1408.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623057C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622462C212yesmaximal, complemented
5#10622458C212yesmaximal, complemented
6#10622352C212yesmaximal, complemented
7#10622346C212yesmaximal
8#10622328C211yesmaximal, characteristic, complemented
9#10622316C211yesmaximal, characteristic, complemented
10#10622312C211yesmaximal, characteristic, complemented
11#10622310C211yesmaximal, characteristic, complemented
12C2×#4339C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C11×#117C2211yescharacteristic
15#66977C2212yes—
16C2×Dic44C2212yes—
17C2×Dic44C2212yes—
18C2×Dic44C2212yes—
19C2×#4314C2212yes—
20#66950—22no—
21#66942—22no—
22#66939—22no—
23#66932—22no—
24#66928C2211yescharacteristic
25#66928C2211yescharacteristic
26#66923C2211yescharacteristic
27#66922C2211yescharacteristic
28#66922C2211yescharacteristic
29#66922C2211yescharacteristic
30C4×Dic22C2212yes—
31C11×C4⋊C8C2212yes—
32C11×C22⋊C8C2212yes—
33C11×#97C2211yescharacteristic
34C4×C8×C11C2211yescharacteristic
35#66885C2212yes—
36#66880C2212yes—
37#66880C2212yes—
38#66880C2212yes—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—21no—
41C22×Dic11—21no—
42#4339—42no—
43C2×D44C2311yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22—21no—
46C2×Dic22—42no—
47C2×Dic22C2311yescharacteristic
48C2×Dic22C2311yescharacteristic
49C2×Dic22C2311yescharacteristic
50C2×Dic22C2312yes—
51C2×C8×C11C2312yes—
52C2×C8×C11C2312yes—
53C11×C4⋊C4D412yes—
54C11×C22⋊C4D412yes—
55C42×C11C2311yescharacteristic
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11C2312yes—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67C4×Dic11—22no—
68Dic44—42no—
69Dic44—42no—
70Dic44—42no—
71#4314—42no—
72#3223—111nomaximal, Sylow
73C23×C11C2×D411yescharacteristic
74C22×D11—21no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2411yescharacteristic
80C22⋊D11—42no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—42no—
87D44—22no—
88C4×D11—42no—
89Dic22—22no—
90Dic22—22no—
91Dic22—22no—
92Dic22—22no—
93Dic22—22no—
94Dic22—42no—
95C8×C11—22no—
96C8×C11—22no—
97#541—111no—
98#536—111no—
99#497—111no—
100#494—111no—
101#491—111no—
102#488—111no—
103#464—112no—
104#462—112no—
105#452—112no—
106#451—112no—
107#433D1111yescharacteristic, complemented
108C22×C11—21no—
109C22×C11—22no—
110C22×C11C22×D411yescharacteristic
111C2×D11—41no—
112C2×D11—42no—
113C4×C11—21no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11H(5,𝔽2)12yes—
117Dic11—41no—
118Dic11—41no—
119Dic11—41no—
120Dic11—42no—
121Dic11—42no—
122C2×#41—111no—
123C22×Q8—111no—
124C2×Q16—112no—
125C2×Q16—112no—
126C2×Q16—112no—
127C2×SD16—112no—
128C4⋊Q8—111no—
129C4⋊Q8—111no—
130C4⋊Q8—111no—
131#126—222no—
132#125—111no—
133#125—222no—
134#124—111no—
135#124—111no—
136#123—222no—
137C22⋊Q8—112no—
138C22⋊Q8—222no—
139C4×Q8—112no—
140#117C2×D1111yescharacteristic
141C4⋊C8C2×D1112yes—
142#103—112no—
143#103—112no—
144#103—112no—
145#102—112no—
146C22⋊C8C2×D1112yes—
147#97C2×D1111yescharacteristic
148C4×C8C2×D1111yescharacteristic
149C2×C11—41no—
150C2×C11#53511yescharacteristic
151C2×C11#57812yes—
152D11—81no—
153#41—442no—
154C2×Q8—111no—
155C2×Q8—111no—
156C2×Q8—111no—
157C2×Q8—112no—
158C2×Q8—221no—
159C2×Q8—442no—
160C2×D4—111no—
161C2×D4—221no—
162C22×C4—221no—
163C22×C4—221no—
164C22×C4C22×D1111yescharacteristic
165Q16—442no—
166Q16—442no—
167Q16—442no—
168SD16—442no—
169C2×C8C22×D1112yes—
170C2×C8C22×D1112yes—
171C4⋊C4—112no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4D4412yes—
179C22⋊C4—222no—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C22⋊C4D4412yes—
183C42—222no—
184C42C22×D1111yescharacteristic
185C42C22×D1111yescharacteristic
186C11#322311yescharacteristic, complemented, Sylow
187C23—221no—
188C23C2×D4411yescharacteristic
189Q8—222no—
190Q8—222no—
191Q8—222no—
192Q8—222no—
193Q8—222no—
194Q8—442no—
195D4—222no—
196D4—442no—
197C2×C4—22no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—221no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4C2×D4412yes—
206C2×C4C2×D4412yes—
207C2×C4C2×D4411yescharacteristic
208C2×C4C23×D1111yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—442no—
214C22—441no—
215C22C22×D4411yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—442no—
220C4—441no—
221C4—441no—
222C4—441no—
223C4—442no—
224C4#6704212yes—
225C2—41no—
226C2—881no—
227C2#1062305611yescharacteristic
228C2#1062328412yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#433D11
hypocenterC11#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
3. C11×#433C2semidirect
4. #10622462C2semidirect
5. #10622458C2semidirect
6. #10622352C2semidirect
8. #10622328C2semidirect
9. #10622316C2semidirect
10. #10622312C2semidirect
11. #10622310C2semidirect
107. #433D11semidirect
186. C11#3223semidirect

Maximal subgroups

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

subgroupindex
#106230572
#106230492
C11×#4332
#106224622
#106224582
#106223522
#106223462
#106223282
#106223162
#106223122
#106223102
#322311