Finite Group Databasebeta

← #13080050

Subgroups — #13080050

Order 1408.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623150C212yesmaximal, complemented
2C11×#466C211yesmaximal, characteristic, complemented
3#10622763C212yesmaximal, complemented
4#10622728C211yesmaximal, characteristic, complemented
5#10622715C211yesmaximal, characteristic, complemented
6#10622652C212yesmaximal, complemented
7#10622504C212yesmaximal, complemented
8#10622399C212yesmaximal, complemented
9#10622379C212yesmaximal, complemented
10C2×C11×D8C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×#121C2212yes—
13#66993C2212yes—
14#66992—22no—
15#66991—22no—
16D4×Dic11C2212yes—
17C2×#4323C2212yes—
18#66983C2212yes—
19#66979C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21C2×D88C2211yescharacteristic
22#66946C2212yes—
23#66943C2212yes—
24#66939—22no—
25#66936—22no—
26C11×#107C2211yescharacteristic
27C11×#102C2212yes—
28#66896C2212yes—
29#66885C2212yes—
30#66882C2211yescharacteristic
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66873C2212yes—
34#66872C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C2×C22⋊D11—22no—
40C2×C22⋊D11—22no—
41C22×Dic11—22no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C11×D8—41no—
45C2×C8×C11—41no—
46C2×C8×C11C2311yescharacteristic
47C2×C8×C11C2311yescharacteristic
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C22⋊Dic11—22no—
51C22⋊Dic11D412yes—
52#4323—42no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11D411yescharacteristic
57C4⋊Dic11D411yescharacteristic
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60C4×Dic11C2312yes—
61#4318—41no—
62C2×C11⋊C8C2312yes—
63D88—41no—
64#3259—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11C2×D411yescharacteristic
67C22×D11—22no—
68D4×C11—22no—
69D4×C11—22no—
70D4×C11—82no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2411yescharacteristic
76C22⋊D11—82no—
77C22⋊D11—82no—
78C22⋊D11—82no—
79C2×Dic11—22no—
80C2×Dic11—82no—
81C2×Dic11C2×D412yes—
82C2×Dic11C2×D412yes—
83D44—22no—
84D44—22no—
85C4×D11—82no—
86C8×C11—21no—
87C8×C11—21no—
88C11⋊C8—22no—
89#540—112no—
90#478—112no—
91#478—112no—
92#469—112no—
93#466—111no—
94#466D1111yescharacteristic, complemented
95#459—112no—
96#459—112no—
97#424—111no—
98C22×C11—21no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11C22×D411yescharacteristic
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C4×C11—21no—
109C4×C11—42no—
110C4×C11H(5,𝔽2)11yescharacteristic
111C4×C112−1+411yescharacteristic
112Dic11—22no—
113Dic11—22no—
114Dic11—42no—
115C2×D8—112no—
116C2×D8—111no—
117C2×D8C2×D1111yescharacteristic
118C2×M16—111no—
119C22×C8C2×D1111yescharacteristic
120#127—112no—
121#125—112no—
122#123—222no—
123#123—222no—
124#121—112no—
125#121—222no—
126#121—222no—
127#121C2×D1112yes—
128C4×D4—112no—
129C4×D4—112no—
130#117—111no—
131#107—111no—
132#107C2×D1111yescharacteristic
133#106—112no—
134C4⋊C8—112no—
135C4⋊C8—112no—
136#102—112no—
137#102—112no—
138#102—112no—
139#102C2×D1112yes—
140C2×C11—41no—
141C2×C11—82no—
142C2×C11#53711yescharacteristic
143C2×C11#57611yescharacteristic
144C2×C11#57611yescharacteristic
145D11—82no—
146C2×D4—22no—
147C2×D4—112no—
148C2×D4—222no—
149C2×D4—222no—
150C2×D4—222no—
151C2×D4C22×D1112yes—
152C22×C4—222no—
153C22×C4—222no—
154C22×C4C22×D1111yescharacteristic
155D8—41no—
156D8—441no—
157D8—442no—
158M16—441no—
159C2×C8—41no—
160C2×C8—112no—
161C2×C8C22×D1111yescharacteristic
162C2×C8C22×D1111yescharacteristic
163C4⋊C4—111no—
164C4⋊C4—111no—
165C4⋊C4—112no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4C22×D1112yes—
169C22⋊C4—22no—
170C22⋊C4—112no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—112no—
175C11#325911yescharacteristic, complemented, Sylow
176C23—22no—
177C23—222no—
178C23D4×D1111yescharacteristic
179D4—22no—
180D4—22no—
181D4—82no—
182D4—222no—
183D4—222no—
184D4—882no—
185D4—882no—
186D4—882no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—112no—
191C2×C4—112no—
192C2×C4—222no—
193C2×C4—882no—
194C2×C4—882no—
195C2×C4D4×D1111yescharacteristic
196C2×C4C23×D1111yescharacteristic
197C8—21no—
198C8—21no—
199C8—222no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—442no—
207C22—442no—
208C22—442no—
209C22C2×D4×D1111yescharacteristic
210C4—21no—
211C4—42no—
212C4—222no—
213C4—222no—
214C4—442no—
215C4#6703711yescharacteristic
216C4#6704311yescharacteristic
217C2—41no—
218C2—82no—
219C2—882no—
220C2#1062312811yescharacteristic
221C2#1062328811yescharacteristic
222C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3259
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623150C2semidirect
2. C11×#466C2semidirect
3. #10622763C2semidirect
4. #10622728C2semidirect
5. #10622715C2semidirect
6. #10622652C2semidirect
7. #10622504C2semidirect
8. #10622399C2semidirect
9. #10622379C2semidirect
94. #466D11semidirect
175. C11#3259semidirect

Maximal subgroups

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

subgroupindex
#106231502
C11×#4662
#106227632
#106227282
#106227152
#106226522
#106225042
#106223992
#106223792
#325911