Finite Group Databasebeta

← #13079262

Subgroups — #13079262

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#10623093C212yesmaximal, complemented
2C4×C11×D8C211yesmaximal, characteristic, complemented
3#10622770C211yesmaximal, characteristic, complemented
4#10622764C211yesmaximal, characteristic, complemented
5#10622627C212yesmaximal, complemented
6#10622496C211yesmaximal, characteristic, complemented
7#10622491C211yesmaximal, characteristic, complemented
8#10622395C212yesmaximal, complemented
9#10622377C212yesmaximal, complemented
10C4×D88C211yesmaximal, characteristic, complemented
11#10622302C211yesmaximal, characteristic, complemented
12C2×C11×D8C2211yescharacteristic
13C4×D4×C11C2212yes—
14#66993C2212yes—
15#66991C2212yes—
16C2×#4323C2212yes—
17#66983—22no—
18#66982—22no—
19C2×D88C2211yescharacteristic
20C2×#4313C2211yescharacteristic
21C2×C8×D11C2211yescharacteristic
22#66948C2212yes—
23#66943C2212yes—
24#66937—22no—
25#66936—22no—
26C4×D44C2212yes—
27#66925C2211yescharacteristic
28C11×#107C2211yescharacteristic
29C11×#102C2212yes—
30C4×C8×C11C2211yescharacteristic
31#66896C2212yes—
32#66885C2212yes—
33#66882C2211yescharacteristic
34#66879C2211yescharacteristic
35C8×Dic11C2211yescharacteristic
36#66873C2212yes—
37#66872C2212yes—
38#66867C2211yescharacteristic
39C2×D4×C11C2312yes—
40C22×C4×C11—22no—
41C2×C22⋊D11—22no—
42C2×C22⋊D11—22no—
43C2×C22⋊D11—22no—
44C2×D44—22no—
45C2×D44C2312yes—
46C2×C4×D11—22no—
47C2×C4×D11C2311yescharacteristic
48C11×D8—22no—
49C2×C8×C11C2311yescharacteristic
50C2×C8×C11C2311yescharacteristic
51C11×C4⋊C4C2312yes—
52C11×C22⋊C4—22no—
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55#4323—24no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4D411yescharacteristic
59(C2×D11)⋊C4D411yescharacteristic
60C4⋊Dic11—22no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4D411yescharacteristic
64Dic11⋊C4D411yescharacteristic
65C4×Dic11C2311yescharacteristic
66C2×C11⋊C8C2311yescharacteristic
67C2×C11⋊C8C2311yescharacteristic
68D88—22no—
69#4313—22no—
70C8×D11—22no—
71#3176—111nomaximal, Sylow
72C23×C11—22no—
73C22×D11—22no—
74C22×D11C2×D411yescharacteristic
75D4×C11—22no—
76D4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—82no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2411yescharacteristic
82C22⋊D11—82no—
83C22⋊D11—82no—
84C22⋊D11—82no—
85C2×Dic11—22no—
86C2×Dic11C2×D411yescharacteristic
87C2×Dic11C2×D411yescharacteristic
88C2×Dic11C2×D411yescharacteristic
89D44—22no—
90D44—22no—
91D44—82no—
92C4×D11—21no—
93C4×D11—21no—
94C4×D11—82no—
95C8×C11—21no—
96C8×C11#4112yes—
97C11⋊C8—21no—
98C11⋊C8#4112yes—
99#540—112no—
100#499—111no—
101#493—111no—
102#490—112no—
103#469—112no—
104#466—111no—
105#466—111no—
106#442—112no—
107C4×D8—111no—
108C4×D8D1111yescharacteristic, complemented
109#405—111no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11—42no—
113C22×C11C22×D411yescharacteristic
114C2×D11—21no—
115C2×D11—21no—
116C2×D11—21no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—42no—
123C4×C11C2×#4111yescharacteristic
124C4×C11C2×#4111yescharacteristic
125Dic11—21no—
126Dic11—21no—
127Dic11—21no—
128Dic11—42no—
129C2×D8—112no—
130C2×D8—111no—
131C2×D8C2×D1111yescharacteristic
132C2×M16—111no—
133C22×C8—111no—
134#127—112no—
135#125—112no—
136#123—222no—
137#123—222no—
138#121—112no—
139#121—112no—
140#121—222no—
141#121—222no—
142C4×D4—112no—
143C4×D4C2×D1112yes—
144#117—111no—
145#107—111no—
146#107C2×D1111yescharacteristic
147#106—112no—
148#102—112no—
149#102—112no—
150#102—112no—
151#102C2×D1112yes—
152#97—111no—
153#97—111no—
154C4×C8—111no—
155C4×C8C2×D1111yescharacteristic
156C2×C11—82no—
157C2×C11#53211yescharacteristic
158C2×C11#57611yescharacteristic
159C2×C11#57611yescharacteristic
160D11—41no—
161D11—82no—
162C2×D4—112no—
163C2×D4—222no—
164C2×D4—222no—
165C2×D4—222no—
166C2×D4—222no—
167C2×D4C22×D1112yes—
168C22×C4—22no—
169C22×C4—111no—
170C22×C4—222no—
171D8—22no—
172D8—224no—
173D8—222no—
174M16—222no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8—222no—
178C2×C8C22×D1111yescharacteristic
179C2×C8C22×D1111yescharacteristic
180C4⋊C4—111no—
181C4⋊C4—111no—
182C4⋊C4—112no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4C22×D1112yes—
186C22⋊C4—22no—
187C22⋊C4—111no—
188C22⋊C4—111no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C42—111no—
193C42C22×D1111yescharacteristic
194C11#317611yescharacteristic, complemented, Sylow
195C23—22no—
196C23—111no—
197C23—222no—
198D4—22no—
199D4—22no—
200D4—222no—
201D4—222no—
202D4—882no—
203D4—882no—
204D4—882no—
205D4—882no—
206C2×C4—22no—
207C2×C4—82no—
208C2×C4—111no—
209C2×C4—111no—
210C2×C4—111no—
211C2×C4—221no—
212C2×C4—221no—
213C2×C4—222no—
214C2×C4—882no—
215C2×C4D4×D1111yescharacteristic
216C2×C4D4×D1111yescharacteristic
217C2×C4C23×D1111yescharacteristic
218C8—21no—
219C8—112no—
220C8—221no—
221C8#433912yes—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—221no—
226C22—221no—
227C22—221no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22C2×D4×D1111yescharacteristic
232C4—21no—
233C4—21no—
234C4—42no—
235C4—221no—
236C4—221no—
237C4—221no—
238C4—442no—
239C4C2×#433911yescharacteristic
240C4#41×D1111yescharacteristic
241C2—82no—
242C2—441no—
243C2—882no—
244C2#1062307911yescharacteristic
245C2#1062328811yescharacteristic
246C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
hypercenterC4×D8D11
hypocenterC11#3176
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623093C2semidirect
2. C4×C11×D8C2semidirect
3. #10622770C2semidirect
4. #10622764C2semidirect
5. #10622627C2semidirect
6. #10622496C2semidirect
7. #10622491C2semidirect
8. #10622395C2semidirect
9. #10622377C2semidirect
10. C4×D88C2semidirect
11. #10622302C2semidirect
108. C4×D8D11semidirect
194. C11#3176semidirect

Maximal subgroups

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

subgroupindex
#106230932
C4×C11×D82
#106227702
#106227642
#106226272
#106224962
#106224912
#106223952
#106223772
C4×D882
#106223022
#317611