Finite Group Databasebeta

← #13079968

Subgroups — #13079968

Order 1408.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#10623010C212yesmaximal, complemented
2C2×C11×C4⋊C8C211yesmaximal, characteristic, complemented
3#10622729C211yesmaximal, characteristic, complemented
4#10622728C211yesmaximal, characteristic
5#10622727C212yesmaximal, complemented
6#10622460C212yesmaximal, complemented
7#10622458C212yesmaximal, complemented
8#10622457C212yesmaximal, complemented
9#10622442C212yesmaximal, complemented
10C22×C8×C11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13#66983C2212yes—
14#66982—22no—
15C4×C22⋊D11—22no—
16#66977C2212yes—
17C2×Dic44C2211yescharacteristic
18C2×D88C2211yescharacteristic
19C2×#4314C2212yes—
20#66929—22no—
21#66928C2212yes—
22C4×D44C2212yes—
23#66925—22no—
24#66923C2212yes—
25C4×Dic22C2212yes—
26C11×C4⋊C8C2212yes—
27C11×C4⋊C8C2212yes—
28#66885C2212yes—
29#66885C2212yes—
30#66882C2211yescharacteristic
31#66882C2211yescharacteristic
32#66881C2212yes—
33#66880C2212yes—
34#66880C2212yes—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C2×D44C2312yes—
40C2×C4×D11—22no—
41C2×Dic22C2312yes—
42C2×C8×C11—41no—
43C2×C8×C11—41no—
44C2×C8×C11C2311yescharacteristic
45C2×C8×C11C2312yes—
46C2×C8×C11C2311yescharacteristic
47C42×C11D412yes—
48C42×C11C2312yes—
49C22⋊Dic11—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—22no—
54C4⋊Dic11C2312yes—
55C4⋊Dic11C2312yes—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61Dic44—41no—
62D88—41no—
63#4314—42no—
64#3250—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—41no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2411yescharacteristic
75C22⋊D11—44no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79D44—22no—
80D44—22no—
81C4×D11—44no—
82Dic22—22no—
83Dic22—22no—
84C8×C11—22no—
85C8×C11—21no—
86C8×C11—21no—
87#529—112no—
88#479—112no—
89#478—112no—
90#467—111no—
91#466—111no—
92#465—112no—
93#464—112no—
94#463—112no—
95C2×C4⋊C8D1111yescharacteristic, complemented
96C22×C11—21no—
97C22×C11—21no—
98C22×C11#13512yes—
99C22×C11C22×D411yescharacteristic
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—42no—
103C4×C11—21no—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11H(5,𝔽2)11yescharacteristic
107C4×C112−1+411yescharacteristic
108Dic11—42no—
109Dic11—42no—
110Dic11—42no—
111C2×Q16—111no—
112C2×SD16—112no—
113C2×D8—111no—
114C22×C8C2×D1111yescharacteristic
115C22×C8C2×D1111yescharacteristic
116#126—222no—
117#125—112no—
118#124—112no—
119#123—222no—
120C22⋊Q8—112no—
121#121—112no—
122C4×Q8—112no—
123C4×D4—112no—
124C4×D4—222no—
125#117—222no—
126C2×C42C2×D1111yescharacteristic
127#107—111no—
128#107—111no—
129#106—112no—
130C4⋊C8C2×D1112yes—
131C4⋊C8C2×D1112yes—
132#103—112no—
133#103—112no—
134#102—112no—
135#102—112no—
136C2×C11—22no—
137C2×C11#53711yescharacteristic
138C2×C11C2×#13511yescharacteristic
139C2×C11#57511yescharacteristic
140D11—82no—
141C2×Q8—112no—
142C2×D4—112no—
143C2×D4—222no—
144C22×C4—222no—
145C22×C4D4411yescharacteristic
146C22×C4D4411yescharacteristic
147C22×C4C22×D1111yescharacteristic
148Q16—441no—
149SD16—442no—
150D8—441no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8C22×D1111yescharacteristic
154C2×C8C22×D1112yes—
155C2×C8C22×D1111yescharacteristic
156C4⋊C4—112no—
157C4⋊C4—112no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—222no—
161C4⋊C4—222no—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C22⋊C4—222no—
166C22⋊C4—222no—
167C42—222no—
168C42D4412yes—
169C42C22×D1112yes—
170C11#325011yescharacteristic, complemented, Sylow
171C23—222no—
172C23C2×D4411yescharacteristic
173Q8—222no—
174Q8—222no—
175D4—222no—
176D4—222no—
177D4—444no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—444no—
186C2×C4C2×D4412yes—
187C2×C4C2×D4412yes—
188C2×C4C2×D4411yescharacteristic
189C2×C4C23×D1111yescharacteristic
190C8—21no—
191C8—22no—
192C8—21no—
193C22—21no—
194C22—21no—
195C22—442no—
196C22—442no—
197C22—442no—
198C22#6695712yes—
199C22C22×D4411yescharacteristic
200C4—22no—
201C4—22no—
202C4—21no—
203C4—442no—
204C4—442no—
205C4—442no—
206C4#6703711yescharacteristic
207C4#6704011yescharacteristic
208C2—22no—
209C2—882no—
210C2#1062304111yescharacteristic
211C2C2×#6695711yescharacteristic
212C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C4⋊C8C2
socleC22×C11C22×D4
prime radical#10622728C2
hypercenterC2×C4⋊C8D11
hypocenterC11#3250
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. C2×C11×C4⋊C8C2semidirect
3. #10622729C2semidirect
5. #10622727C2semidirect
6. #10622460C2semidirect
7. #10622458C2semidirect
8. #10622457C2semidirect
9. #10622442C2semidirect
95. C2×C4⋊C8D11semidirect
170. C11#3250semidirect

Maximal subgroups

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

subgroupindex
#106230102
C2×C11×C4⋊C82
#106227292
#106227282
#106227272
#106224602
#106224582
#106224572
#106224422
#325011