Finite Group Databasebeta

← #13079829

Subgroups — #13079829

Order 1408.

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

normal subgroups only

This group has 322 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#10623259C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic
3C11×#475C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622634C211yesmaximal, characteristic, complemented
6#10622480C212yesmaximal
7#10622469C212yesmaximal, complemented
8#10622463C211yesmaximal, characteristic, complemented
9#10622448C211yesmaximal, characteristic
10#10622427C212yesmaximal
11#10622410C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14#66999—21no—
15#66999C2211yescharacteristic
16Q8×Dic11—21no—
17#66997C2211yescharacteristic
18#66950—21no—
19#66950C2211yescharacteristic
20#66949—21no—
21#66945C2212yes—
22#66943C2212yes—
23#66942—21no—
24#66941C2211yescharacteristic
25#66940—21no—
26#66925—21no—
27C42×D11C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×Dic22—21no—
30C4×Dic22C2211yescharacteristic
31C11×#106C2212yes—
32C11×C4⋊C8C2211yescharacteristic
33C11×#103C2212yes—
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66882C2212yes—
37#66880C2212yes—
38#66879C2212yes—
39#66874C2212yes—
40#66872C2212yes—
41#66871C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×Q8×C11C2311yescharacteristic
45C2×C4×D11D411yescharacteristic
46C2×C4×D11D411yescharacteristic
47C2×C4×D11C2311yescharacteristic
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22C2311yescharacteristic
51C2×C8×C11C2312yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2312yes—
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58(C2×D11)⋊C4—21no—
59(C2×D11)⋊C4—21no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11C2312yes—
65C4⋊Dic11C2311yescharacteristic
66Dic11⋊C4—21no—
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71Dic11⋊C4—21no—
72C4×Dic11—22no—
73C4×Dic11—21no—
74C4×Dic11D411yescharacteristic
75C4×Dic11D411yescharacteristic
76C4×Dic11C2311yescharacteristic
77C2×C11⋊C8C2312yes—
78#3237—111nomaximal, Sylow
79C22×D11C2×D411yescharacteristic
80Q8×C11—21no—
81Q8×C11—21no—
82Q8×C11—42no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11C2×D411yescharacteristic
93C2×Dic11C2×D411yescharacteristic
94C2×Dic11C2×D411yescharacteristic
95C4×D11—22no—
96C4×D11—21no—
97C4×D11—21no—
98C4×D11—41no—
99Dic22—21no—
100Dic22—21no—
101Dic22—42no—
102Dic22—42no—
103C8×C11—22no—
104C11⋊C8—22no—
105#533—111no—
106#533—111no—
107#501—112no—
108#491—112no—
109#485—112no—
110#485—112no—
111#477—111no—
112#477—111no—
113#475—111no—
114#475D1111yescharacteristic, complemented
115#432—111no—
116C22×C11C22×D411yescharacteristic
117C2×D11—21no—
118C2×D11—21no—
119C2×D11—21no—
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—42no—
123C4×C11—41no—
124C4×C11#13712yes—
125C4×C112−1+411yescharacteristic
126C4×C112−1+411yescharacteristic
127Dic11—21no—
128Dic11—21no—
129Dic11—21no—
130Dic11—41no—
131Dic11—41no—
132Dic11—42no—
133C4⋊Q8—111no—
134C4⋊Q8—111no—
135C4⋊Q8—111no—
136C4⋊Q8C2×D1111yescharacteristic
137#125—112no—
138#125—221no—
139C22⋊Q8—111no—
140C22⋊Q8—111no—
141C22⋊Q8—221no—
142C22⋊Q8—221no—
143C22⋊Q8—221no—
144C4×Q8—111no—
145C4×Q8—221no—
146C4×Q8—221no—
147C4×Q8—221no—
148C4×Q8C2×D1111yescharacteristic
149#117—112no—
150#117—221no—
151C2×C42—111no—
152#107—112no—
153#107—112no—
154#106—112no—
155#106C2×D1112yes—
156C4⋊C8—111no—
157C4⋊C8C2×D1111yescharacteristic
158#103—112no—
159#103—112no—
160#103—112no—
161#103C2×D1112yes—
162C22⋊C8—112no—
163#97—112no—
164C2×C11#53611yescharacteristic
165C2×C11C2×#13711yescharacteristic
166C2×C11#57511yescharacteristic
167D11—41no—
168C2×Q8—21no—
169C2×Q8—111no—
170C2×Q8—221no—
171C2×Q8—221no—
172C2×Q8C22×D1111yescharacteristic
173C22×C4—111no—
174C22×C4—111no—
175C22×C4—111no—
176C2×C8—112no—
177C2×C8C22×D1112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—112no—
181C4⋊C4—111no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4C22×D1112yes—
192C4⋊C4C22×D1111yescharacteristic
193C22⋊C4—222no—
194C22⋊C4—221no—
195C22⋊C4—221no—
196C42—21no—
197C42—111no—
198C42—111no—
199C42—111no—
200C42—222no—
201C42—221no—
202C42C22×D1111yescharacteristic
203C11#323711yescharacteristic, complemented, Sylow
204C23—111no—
205Q8—21no—
206Q8—21no—
207Q8—42no—
208Q8—221no—
209Q8—221no—
210Q8—442no—
211Q8—442no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—111no—
216C2×C4—111no—
217C2×C4—111no—
218C2×C4—222no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—222no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—441no—
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—22no—
229C8—222no—
230C22—221no—
231C22—221no—
232C22—221no—
233C22C2×D4×D1111yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—221no—
239C4—221no—
240C4—221no—
241C4—442no—
242C4—441no—
243C4—441no—
244C4#6696812yes—
245C4#6704011yescharacteristic
246C4#6704311yescharacteristic
247C2—441no—
248C2#1062315911yescharacteristic
249C2C2×#6696811yescharacteristic
250C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#475D11
hypocenterC11#3237
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C11×#475C2semidirect
4. #10622707C2semidirect
5. #10622634C2semidirect
7. #10622469C2semidirect
8. #10622463C2semidirect
11. #10622410C2semidirect
114. #475D11semidirect
203. C11#3237semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106231092
C11×#4752
#106227072
#106226342
#106224802
#106224692
#106224632
#106224482
#106224272
#106224102
#323711