Finite Group Databasebeta

← #13069864

Subgroups — #13069864

Order 1408.

382 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C11×#534C211yesmaximal, characteristic
2#10622833C212yesmaximal, complemented
3C2×#66898C212yesmaximal, complemented
4#10622559C211yesmaximal, characteristic, complemented
5#10622164C211yesmaximal, characteristic, complemented
6C22×D4×C11C2212yes—
7C23×Dic11C2211yescharacteristic
8C11×#123—22no—
9C11×#121—21no—
10C11×#121—21no—
11C11×#120—22no—
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C22⋊Dic11—22no—
14C2×C22⋊Dic11C2212yes—
15C2×C22⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4—21no—
17#66898—24no—
18C11⋊#95—21no—
19C11⋊#95—22no—
20C24×C11D412yes—
21C24×C11C2311yescharacteristic
22C2×D4×C11—22no—
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11—22no—
26C2×D4×C11—22no—
27C2×D4×C11—22no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C22×C4×C11D412yes—
31C22×C4×C11D411yescharacteristic
32C22×C4×C11D411yescharacteristic
33C22×Dic11—21no—
34C22×Dic11—21no—
35C22×Dic11—22no—
36C22×Dic11—22no—
37C22×Dic11—42no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C22⋊C4—22no—
41C11×C22⋊C4—22no—
42C11×C22⋊C4—22no—
43C22⋊Dic11—22no—
44C22⋊Dic11—21no—
45C22⋊Dic11—22no—
46C22⋊Dic11—44no—
47C22⋊Dic11D412yescomplemented
48Dic11⋊C4—42no—
49#2044—111nomaximal, Sylow
50C23×C11—22no—
51C23×C11—22no—
52C23×C11—22no—
53C23×C11—41no—
54C23×C11—41no—
55C23×C11—42no—
56C23×C11—42no—
57C23×C11C2×D411yescharacteristic
58C23×C11C2×D412yes—
59C23×C11C2×D411yescharacteristic
60C23×C11#4111yescharacteristic
61C23×C11#4112yes—
62D4×C11—42no—
63D4×C11—42no—
64D4×C11—42no—
65D4×C11—42no—
66D4×C11—81no—
67D4×C11—81no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×Dic11—22no—
76C2×Dic11—24no—
77C2×Dic11—22no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—42no—
82C2×Dic11—41no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C2×Dic11—42no—
86#534D1111yescharacteristic
87C2×#99—112no—
88#386—112no—
89#385—111no—
90#342—111no—
91C22×C11—21no—
92C22×C11—22no—
93C22×C11—21no—
94C22×C11—22no—
95C22×C11—41no—
96C22×C11—41no—
97C22×C11—42no—
98C22×C11—44no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—82no—
103C22×C11#12011yescharacteristic
104C22×C11#12111yescharacteristic
105C22×C11#12112yes—
106C22×C11#12312yes—
107C22×C11#12411yescharacteristic
108C4×C11—42no—
109C4×C11—41no—
110C4×C11—41no—
111Dic11—42no—
112Dic11—42no—
113Dic11—82no—
114C22×D4C2×D1112yes—
115C23×C4—111no—
116#123—22no—
117#121—21no—
118#121—21no—
119#120—22no—
120C2×C4⋊C4—221no—
121C2×C22⋊C4—111no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—222no—
124C2×C22⋊C4C2×D1111yescharacteristic
125#99—224no—
126#95—221no—
127#95—222no—
128C2×C11—21no—
129C2×C11—22no—
130C2×C11—22no—
131C2×C11—21no—
132C2×C11—82no—
133C2×C11#39411yescharacteristic
134C2×C11B(4,𝔽2)11yescharacteristic
135C2×C11#45811yescharacteristic
136C24C22⋊D1112yes—
137C24C22×D1111yescharacteristic
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—21no—
145C2×D4—21no—
146C22×C4—221no—
147C22×C4—222no—
148C22×C4—221no—
149C22×C4—222no—
150C22×C4—442no—
151C22×C4C22⋊D1112yes—
152C22×C4C22⋊D1111yescharacteristic
153C22×C4C22⋊D1111yescharacteristic
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—442no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—112no—
161C22⋊C4—221no—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C22⋊C4—444no—
165C11#204411yescharacteristic, complemented, Sylow
166C23—22no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—42no—
172C23—42no—
173C23D4×D1111yescharacteristic
174C23#434111yescharacteristic
175C23#434112yes—
176C23C2×C22⋊D1112yes—
177C23C2×C22⋊D1111yescharacteristic
178D4—42no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—81no—
183D4—81no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—224no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—441no—
195C2×C4—441no—
196C2×C4—442no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4—442no—
200C2×C4—442no—
201C2×C4—442no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—44no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—82no—
214C22#6698812yes—
215C22#6698911yescharacteristic
216C22#6699111yescharacteristic
217C22#6699212yes—
218C22#6700611yescharacteristic
219C4—42no—
220C4—41no—
221C4—41no—
222C4—442no—
223C4—442no—
224C4—882no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—82no—
230C2#1062283511yescharacteristic
231C2#1062285611yescharacteristic
232C2#1062285711yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
Fitting, prime radicalC11×#534C2
socleC22×C11#120
hypercenter#534D11
hypocenterC11#2044
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
2. #10622833C2semidirect
3. C2×#66898C2semidirect
4. #10622559C2semidirect
5. #10622164C2semidirect
47. C22⋊Dic11D4semidirect
165. C11#2044semidirect

Maximal subgroups

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

subgroupindex
C11×#5342
#106228332
C2×#668982
#106225592
#106221642
#204411