Finite Group Databasebeta

← #13080532

Subgroups — #13080532

Order 1408.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623263C211yesmaximal, characteristic, complemented
2#10623257C211yesmaximal, characteristic
3C11×#487C211yesmaximal, characteristic, complemented
4#10622703C211yesmaximal, characteristic, complemented
5#10622700C211yesmaximal, characteristic, complemented
6#10622428C212yesmaximal, complemented
7#10622426C212yesmaximal, complemented
8#10622423C212yesmaximal, complemented
9#10622417C212yesmaximal, complemented
10C4×#4314C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic, complemented
12C2×#4343C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15#67000—21no—
16#66999C2212yes—
17Q8×Dic11—21no—
18C2×#4326C2212yes—
19C2×#4314C2211yescharacteristic
20C2×C8×D11C2212yes—
21#66951—22no—
22#66950C2212yes—
23#66948—21no—
24#66947—22no—
25#66945C2212yes—
26C4⋊C4×D11—21no—
27C4×D44C2211yescharacteristic
28C4×D44C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×#103C2212yes—
31C11×#103C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66899C2212yes—
34#66885C2211yescharacteristic
35(C2×D11)⋊C8C2212yes—
36#66881C2211yescharacteristic
37#66880C2211yescharacteristic
38#66873C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2312yes—
43#4343—24no—
44#4343—42no—
45C2×D44—22no—
46C2×D44D411yescharacteristic
47C2×D44C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—21no—
50C2×C4×D11C2312yes—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2312yes—
58C42×C11C2311yescharacteristic
59#4326—42no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4D412yes—
65C4⋊Dic11—22no—
66C4⋊Dic11D411yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4—21no—
71C4×Dic11—22no—
72C4×Dic11—21no—
73C2×C11⋊C8C2312yes—
74#4314—22no—
75C8×D11—42no—
76#3302—111nomaximal, Sylow
77C22×D11—21no—
78C22×D11C2×D412yes—
79Q8×C11—22no—
80Q8×C11—22no—
81Q8×C11—42no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11C2×D412yes—
91D44—22no—
92D44—21no—
93D44—44no—
94D44#4112yes—
95C4×D11—22no—
96C4×D11—22no—
97C4×D11—44no—
98C4×D11—42no—
99Dic22—21no—
100Dic22—21no—
101C8×C11—21no—
102C8×C11—21no—
103C11⋊C8—22no—
104#556—111no—
105#547—111no—
106#487D1111yescharacteristic, complemented
107#485—112no—
108#474—111no—
109#467—112no—
110#462—111no—
111#452—112no—
112C4×SD16—111no—
113C8×D4—111no—
114#416—112no—
115C22×C11C22×D411yescharacteristic
116C2×D11—22no—
117C2×D11—22no—
118C2×D11—22no—
119C2×D11—22no—
120C2×D11—41no—
121C2×D11—41no—
122C4×C11—21no—
123C4×C11—42no—
124C4×C11—42no—
125C4×C11#13512yes—
126C4×C11C2×#4111yescharacteristic
127C4×C11H(5,𝔽2)11yescharacteristic
128Dic11—22no—
129Dic11—41no—
130Dic11—41no—
131Dic11—41no—
132C2×#41—112no—
133C2×Q16—112no—
134C2×SD16—111no—
135C22×C8—112no—
136C4⋊Q8C2×D1111yescharacteristic
137C4⋊Q8C2×D1111yescharacteristic
138#126—222no—
139#124—221no—
140#123—222no—
141C22⋊Q8—112no—
142C22⋊Q8—112no—
143#121—221no—
144C4×Q8—111no—
145C4×Q8—221no—
146C4×D4—111no—
147C4×D4—111no—
148#117—112no—
149C2×C4⋊C4—221no—
150#107—112no—
151#106—111no—
152C4⋊C8—111no—
153#103—112no—
154#103—111no—
155#103C2×D1112yes—
156#103C2×D1112yes—
157#102—111no—
158#102—112no—
159C22⋊C8—112no—
160C4×C8C2×D1111yescharacteristic
161C2×C11#54611yescharacteristic
162C2×C11C2×#13511yescharacteristic
163C2×C11#57811yescharacteristic
164D11—42no—
165D11—42no—
166#41—224no—
167#41—442no—
168C2×Q8—21no—
169C2×Q8—111no—
170C2×Q8C22×D1112yes—
171C2×D4—111no—
172C2×D4—111no—
173C2×D4—222no—
174C22×C4—112no—
175C22×C4—222no—
176C22×C4—221no—
177Q16—442no—
178SD16—222no—
179C2×C8—112no—
180C2×C8—442no—
181C2×C8C22×D1111yescharacteristic
182C2×C8C22×D1111yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—111no—
187C4⋊C4—111no—
188C4⋊C4—111no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—221no—
192C4⋊C4C22×D1112yes—
193C22⋊C4—112no—
194C22⋊C4—222no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4—221no—
198C42—222no—
199C42—221no—
200C42C22×D1111yescharacteristic
201C11#330211yescharacteristic, complemented, Sylow
202C23—112no—
203C23—221no—
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—221no—
208Q8—221no—
209D4—112no—
210D4—222no—
211D4—221no—
212D4—444no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—112no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—221no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—444no—
222C2×C4—442no—
223C2×C4D4×D1111yescharacteristic
224C2×C4D4×D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—21no—
227C8—21no—
228C8—222no—
229C22—222no—
230C22—222no—
231C22—222no—
232C22—222no—
233C22—441no—
234C22—441no—
235C22C2×D4×D1111yescharacteristic
236C4—21no—
237C4—42no—
238C4—42no—
239C4—222no—
240C4—441no—
241C4—441no—
242C4—441no—
243C4#6696912yes—
244C4#41×D1111yescharacteristic
245C4#6704211yescharacteristic
246C2—442no—
247C2—442no—
248C2#1062320711yescharacteristic
249C2C2×#6696911yescharacteristic
250C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radical#10623257C2
hypercenter#487D11
hypocenterC11#3302
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #10623263C2semidirect
3. C11×#487C2semidirect
4. #10622703C2semidirect
5. #10622700C2semidirect
6. #10622428C2semidirect
7. #10622426C2semidirect
8. #10622423C2semidirect
9. #10622417C2semidirect
10. C4×#4314C2semidirect
11. C8×D44C2semidirect
106. #487D11semidirect
201. C11#3302semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106232572
C11×#4872
#106227032
#106227002
#106224282
#106224262
#106224232
#106224172
C4×#43142
C8×D442
#330211