Finite Group Databasebeta

← #13079700

Subgroups — #13079700

Order 1408.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623255C211yesmaximal, characteristic
2#10623228C211yesmaximal, characteristic, complemented
3C11×#491C211yesmaximal, characteristic, complemented
4#10622705C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622423C212yesmaximal
7#10622421C212yesmaximal, complemented
8#10622411C212yesmaximal, complemented
9#10622406C212yesmaximal, complemented
10#10622328C211yesmaximal, characteristic, complemented
11#10622322C211yesmaximal, characteristic, complemented
12C2×#4343C2211yescharacteristic
13C2×Q8×D11C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15C11×#125C2211yescharacteristic
16#67000C2211yescharacteristic
17#66997C2211yescharacteristic
18C2×#4326C2212yes—
19C2×#4326C2212yes—
20C2×Dic44C2212yes—
21C2×#4314C2212yes—
22#66951—22no—
23#66950C2212yes—
24#66949—22no—
25#66947—22no—
26#66943—22no—
27#66940C2212yes—
28#66928C2211yescharacteristic
29#66925C2211yescharacteristic
30#66922C2211yescharacteristic
31C11×#103C2212yes—
32C11×#103C2212yes—
33C11×#97C2211yescharacteristic
34(C2×D11)⋊C8C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2212yes—
37#66873C2212yes—
38C4×C11⋊C8C2211yescharacteristic
39C2×Q8×C11C2311yescharacteristic
40C2×Q8×C11C2311yescharacteristic
41#4343—42no—
42Q8×D11—42no—
43C2×D44—21no—
44C2×D44C2311yescharacteristic
45C2×C4×D11—21no—
46C2×C4×D11—21no—
47C2×C4×D11C2311yescharacteristic
48C2×Dic22—21no—
49C2×Dic22C2311yescharacteristic
50C2×Dic22C2312yes—
51C2×C8×C11C2312yes—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4C2312yes—
55C42×C11C2311yescharacteristic
56#4326—42no—
57#4326—42no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4D412yes—
62C4⋊Dic11—22no—
63C4⋊Dic11—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4D412yes—
67C4×Dic11—22no—
68C4×Dic11C2311yescharacteristic
69C2×C11⋊C8C2312yes—
70Dic44—42no—
71#4314—42no—
72#3223—111nomaximal, Sylow
73C22×D11—21no—
74C22×D11C2×D411yescharacteristic
75Q8×C11—22no—
76Q8×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2411yescharacteristic
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11C2×D412yes—
85C2×Dic11C2×D411yescharacteristic
86D44—22no—
87D44—42no—
88C4×D11—22no—
89C4×D11—42no—
90C4×D11—42no—
91Dic22—22no—
92Dic22—22no—
93Dic22—22no—
94Dic22—42no—
95C8×C11—22no—
96C11⋊C8—22no—
97#541—111no—
98#536—111no—
99#497—111no—
100#494—111no—
101#491D1111yescharacteristic, complemented
102#488—111no—
103#464—112no—
104#462—112no—
105#452—112no—
106#451—112no—
107#433—111no—
108C22×C11C22×D411yescharacteristic
109C2×D11—21no—
110C2×D11—22no—
111C2×D11—41no—
112C2×D11—42no—
113C4×C11—22no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11—42no—
117C4×C11H(5,𝔽2)12yes—
118Dic11—21no—
119Dic11—22no—
120Dic11—41no—
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⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#125—222no—
133#125C2×D1111yescharacteristic
134#124—111no—
135#124—111no—
136#123—222no—
137C22⋊Q8—112no—
138C22⋊Q8—222no—
139C4×Q8—112no—
140#117—111no—
141C4⋊C8—112no—
142#103—112no—
143#103C2×D1112yes—
144#103C2×D1112yes—
145#102—112no—
146C22⋊C8—112no—
147#97C2×D1111yescharacteristic
148C4×C8—111no—
149C2×C11#53511yescharacteristic
150C2×C11#57812yes—
151D11—41no—
152D11—81no—
153#41—442no—
154C2×Q8—111no—
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—442no—
158C2×Q8C22×D1111yescharacteristic
159C2×Q8C22×D1111yescharacteristic
160C2×D4—111no—
161C2×D4—221no—
162C22×C4—111no—
163C22×C4—221no—
164C22×C4—221no—
165Q16—442no—
166Q16—442no—
167Q16—442no—
168SD16—442no—
169C2×C8—112no—
170C2×C8C22×D1112yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—112no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4C22×D1112yes—
179C22⋊C4—112no—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C22⋊C4—222no—
183C42—111no—
184C42—222no—
185C42C22×D1111yescharacteristic
186C11#322311yescharacteristic, complemented, Sylow
187C23—111no—
188C23—221no—
189Q8—22no—
190Q8—22no—
191Q8—222no—
192Q8—222no—
193Q8—222no—
194Q8—442no—
195D4—222no—
196D4—442no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—112no—
201C2×C4—111no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—221no—
205C2×C4—442no—
206C2×C4—442no—
207C2×C4D4×D1112yes—
208C2×C4C23×D1111yescharacteristic
209C8—22no—
210C8—222no—
211C22—222no—
212C22—221no—
213C22—442no—
214C22—441no—
215C22C2×D4×D1111yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—222no—
221C4—221no—
222C4—441no—
223C4—442no—
224C4#6704212yes—
225C2—441no—
226C2—881no—
227C2#1062320511yescharacteristic
228C2#1062331012yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#491C2
socleC22×C11C22×D4
prime radicalC2×#4343C22
hypercenter#491D11
hypocenterC11#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #10623228C2semidirect
3. C11×#491C2semidirect
4. #10622705C2semidirect
5. #10622681C2semidirect
7. #10622421C2semidirect
8. #10622411C2semidirect
9. #10622406C2semidirect
10. #10622328C2semidirect
11. #10622322C2semidirect
101. #491D11semidirect
186. C11#3223semidirect

Maximal subgroups

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

subgroupindex
#106232552
#106232282
C11×#4912
#106227052
#106226812
#106224232
#106224212
#106224112
#106224062
#106223282
#106223222
#322311