Finite Group Databasebeta

← #13080051

Subgroups — #13080051

Order 1408.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#540C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic, complemented
3#10622685C212yesmaximal, complemented
4#10622679C212yesmaximal, complemented
5#10622652C212yesmaximal, complemented
6#10622651C212yesmaximal, complemented
7#10622628C212yesmaximal, complemented
8#10622622C212yesmaximal, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C11×#127C2211yescharacteristic
11C11×#125C2211yescharacteristic
12C11×#123—22no—
13C11×#121—22no—
14C11×#121C2212yes—
15C4×D4×C11C2212yes—
16C11×#117C2211yescharacteristic
17C2×#4323C2212yes—
18C2×#4323C2212yes—
19#66983C2212yes—
20C2×#4318C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66947—22no—
23#66937—22no—
24#66927C2211yescharacteristic
25C4×D44C2212yes—
26#66923C2211yescharacteristic
27#66896C2212yes—
28#66896C2212yes—
29#66873C2212yes—
30#66873C2212yes—
31#66872C2212yes—
32#66871C2212yes—
33C4⋊(C11⋊C8)C2212yes—
34C4⋊(C11⋊C8)C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11C2312yes—
38C22×C4×C11—22no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—22no—
41C2×D44—22no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4D412yes—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C11×C22⋊C4—22no—
49C11×C22⋊C4D412yes—
50C42×C11C2311yescharacteristic
51C42×C11C2311yescharacteristic
52#4323—42no—
53#4323—42no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—22no—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58#4318—41no—
59C2×C11⋊C8—41no—
60C2×C11⋊C8C2312yes—
61C2×C11⋊C8C2312yes—
62#3259—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11C2×D411yescharacteristic
65C22×D11—22no—
66D4×C11—22no—
67D4×C11—22no—
68D4×C11—82no—
69D4×C11—82no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—82no—
74C2×C4×C11C2×D412yes—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2411yescharacteristic
78C22⋊D11—82no—
79C2×Dic11—22no—
80D44—22no—
81D44—22no—
82D44—82no—
83C4×D11—82no—
84C11⋊C8—22no—
85C11⋊C8—22no—
86#540—111no—
87#540D1111yescharacteristic, complemented
88#478—112no—
89#478—112no—
90#469—112no—
91#466—112no—
92#459—112no—
93#459—112no—
94#424—111no—
95C22×C11—21no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11—42no—
100C22×C11C22×D411yescharacteristic
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—42no—
104C4×C11—21no—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—42no—
108C4×C11H(5,𝔽2)11yescharacteristic
109C4×C112−1+411yescharacteristic
110Dic11—42no—
111C2×D8—112no—
112C2×D8—112no—
113C2×M16—111no—
114C22×C8—111no—
115#127—111no—
116#127C2×D1111yescharacteristic
117#125—111no—
118#125C2×D1111yescharacteristic
119#123—22no—
120#123—222no—
121#121—22no—
122#121—112no—
123#121—222no—
124#121C2×D1112yes—
125C4×D4—112no—
126C4×D4C2×D1112yes—
127#117C2×D1111yescharacteristic
128#107—112no—
129#106—112no—
130C4⋊C8—112no—
131C4⋊C8—112no—
132#102—112no—
133#102—112no—
134#102—112no—
135#102—112no—
136C2×C11—41no—
137C2×C11—82no—
138C2×C11#53711yescharacteristic
139C2×C11#57612yes—
140D11—82no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—112no—
144C2×D4—222no—
145C2×D4—222no—
146C2×D4C22×D1112yes—
147C22×C4—22no—
148C22×C4—222no—
149C22×C4C22×D1111yescharacteristic
150D8—442no—
151D8—442no—
152M16—441no—
153C2×C8—112no—
154C2×C8—112no—
155C2×C8—441no—
156C4⋊C4—22no—
157C4⋊C4—112no—
158C4⋊C4—222no—
159C4⋊C4C22⋊D1112yes—
160C4⋊C4C22×D1112yes—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C22⋊C4C22⋊D1112yes—
166C42C22×D1111yescharacteristic
167C42C22×D1111yescharacteristic
168C11#325911yescharacteristic, complemented, Sylow
169C23—22no—
170C23—222no—
171C23C2×C22⋊D1111yescharacteristic
172D4—22no—
173D4—22no—
174D4—82no—
175D4—82no—
176D4—222no—
177D4—222no—
178D4—882no—
179D4—882no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—82no—
184C2×C4—222no—
185C2×C4—882no—
186C2×C4C2×C22⋊D1112yes—
187C2×C4C2×C22⋊D1112yes—
188C2×C4C2×C22⋊D1111yescharacteristic
189C2×C4C23×D1111yescharacteristic
190C8—222no—
191C8—222no—
192C22—21no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—442no—
198C22—442no—
199C22—442no—
200C22C22×C22⋊D1111yescharacteristic
201C4—21no—
202C4—22no—
203C4—22no—
204C4—42no—
205C4—442no—
206C4#6704211yescharacteristic
207C4#6704311yescharacteristic
208C2—41no—
209C2—82no—
210C2—882no—
211C2#1062336411yescharacteristic
212C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#540C2
socleC22×C11C22×D4
hypercenter#540D11
hypocenterC11#3259
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C11×#540C2semidirect
2. #10623066C2semidirect
3. #10622685C2semidirect
4. #10622679C2semidirect
5. #10622652C2semidirect
6. #10622651C2semidirect
7. #10622628C2semidirect
8. #10622622C2semidirect
9. #10622612C2semidirect
87. #540D11semidirect
168. C11#3259semidirect

Maximal subgroups

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

subgroupindex
C11×#5402
#106230662
#106226852
#106226792
#106226522
#106226512
#106226282
#106226222
#106226122
#325911