Finite Group Databasebeta

← #13081339

Subgroups — #13081339

Order 1408.

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

normal subgroups only

This group has 372 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#10623258C211yesmaximal, characteristic, complemented
3C11×#487C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622696C211yesmaximal, characteristic, complemented
6#10622432C212yesmaximal
7#10622430C212yesmaximal, complemented
8#10622408C212yesmaximal, complemented
9#10622407C212yesmaximal, complemented
10C4×D88C211yesmaximal, characteristic
11#10622292C211yesmaximal, characteristic, complemented
12C2×Q8×D11—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15#67000C2212yes—
16#66999—21no—
17Q8×Dic11C2212yes—
18C2×#4325C2212yes—
19C2×D88C2211yescharacteristic
20#66951—22no—
21#66950—21no—
22#66949—22no—
23#66946C2212yes—
24#66945—21no—
25#66941C2212yes—
26C4×D44C2211yescharacteristic
27C4×D44C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#103C2212yes—
30C11×#103C2212yes—
31C4×C8×C11C2211yescharacteristic
32#66899C2212yes—
33#66885C2211yescharacteristic
34#66885C2211yescharacteristic
35#66882C2211yescharacteristic
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2312yes—
43Q8×D11—44no—
44C2×D44C2311yescharacteristic
45C2×D44C2311yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11—21no—
48C2×C4×D11—21no—
49C2×Dic22—22no—
50C2×Dic22D411yescharacteristic
51C2×C8×C11C2311yescharacteristic
52C2×C8×C11C2311yescharacteristic
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2312yes—
57C42×C11C2311yescharacteristic
58#4325—24no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64C4⋊Dic11—22no—
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—22no—
69Dic11⋊C4D412yes—
70C4×Dic11—22no—
71C4×Dic11C2312yes—
72C2×C11⋊C8C2312yes—
73D88—22no—
74#3367—111nomaximal, Sylow
75C22×D11—21no—
76C22×D11—21no—
77Q8×C11—22no—
78Q8×C11—22no—
79Q8×C11—42no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89D44—21no—
90D44—21no—
91D44—21no—
92D44#4112yes—
93C4×D11—44no—
94C4×D11—42no—
95C4×D11—42no—
96Dic22—22no—
97Dic22—44no—
98C8×C11—21no—
99C8×C11—21no—
100C11⋊C8—22no—
101#556—111no—
102D4×Q8—111no—
103#489—112no—
104#487D1111yescharacteristic, complemented
105#477—112no—
106#474—111no—
107#463—112no—
108#461—111no—
109#446—111no—
110#440—112no—
111C4×D8—111no—
112C22×C11C22×D411yescharacteristic
113C2×D11—22no—
114C2×D11—41no—
115C2×D11—41no—
116C2×D11—41no—
117C2×D11—41no—
118C2×D11—41no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11AGL(1,ℤ/8)12yes—
123C4×C11C2×#4111yescharacteristic
124C4×C112−1+411yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—41no—
128Dic11—41no—
129C22×Q8—221no—
130C2×SD16—112no—
131C2×D8—111no—
132C4⋊Q8—112no—
133C4⋊Q8C2×D1111yescharacteristic
134C4⋊Q8C2×D1111yescharacteristic
135#126—222no—
136#124—112no—
137C22⋊Q8—222no—
138C22⋊Q8—221no—
139C22⋊Q8—221no—
140C4×Q8—111no—
141C4×Q8—112no—
142C4×D4—112no—
143C4×D4—111no—
144C4×D4—111no—
145#117—221no—
146#107—111no—
147#107—112no—
148C4⋊C8—112no—
149C4⋊C8—111no—
150#103—112no—
151#103C2×D1112yes—
152#103C2×D1112yes—
153#102—111no—
154#102—111no—
155#102—112no—
156#97—112no—
157C4×C8C2×D1111yescharacteristic
158C2×C11#54811yescharacteristic
159C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
160C2×C11#57811yescharacteristic
161D11—42no—
162D11—81no—
163C2×Q8—21no—
164C2×Q8—111no—
165C2×Q8—222no—
166C2×Q8—444no—
167C2×Q8C22×D1112yes—
168C2×D4—111no—
169C2×D4—111no—
170C22×C4—222no—
171C22×C4—221no—
172C22×C4—221no—
173SD16—224no—
174D8—222no—
175C2×C8—112no—
176C2×C8C22×D1111yescharacteristic
177C2×C8C22×D1111yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—112no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4C22×D1112yes—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—221no—
192C22⋊C4—221no—
193C42—112no—
194C42—222no—
195C42C22×D1111yescharacteristic
196C11#336711yescharacteristic, complemented, Sylow
197C23—221no—
198C23—221no—
199Q8—22no—
200Q8—22no—
201Q8—42no—
202Q8—222no—
203Q8—444no—
204D4—112no—
205D4—221no—
206D4—221no—
207D4—221no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—112no—
211C2×C4—112no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—444no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4D4×D1111yescharacteristic
218C2×C4D4×D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—21no—
221C8—21no—
222C8—222no—
223C22—222no—
224C22—441no—
225C22—441no—
226C22—441no—
227C22—441no—
228C22—441no—
229C22C2×D4×D1111yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—222no—
234C4—222no—
235C4—441no—
236C4—441no—
237C4#6696712yes—
238C4#41×D1111yescharacteristic
239C4#6704311yescharacteristic
240C2—442no—
241C2—881no—
242C2#1062320811yescharacteristic
243C2C2×#6696711yescharacteristic
244C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radicalC2×D88C22
hypercenter#487D11
hypocenterC11#3367
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
2. #10623258C2semidirect
3. C11×#487C2semidirect
4. #10622700C2semidirect
5. #10622696C2semidirect
7. #10622430C2semidirect
8. #10622408C2semidirect
9. #10622407C2semidirect
11. #10622292C2semidirect
104. #487D11semidirect
196. C11#3367semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106232582
C11×#4872
#106227002
#106226962
#106224322
#106224302
#106224082
#106224072
C4×D882
#106222922
#336711