Finite Group Databasebeta

← #13079568

Subgroups — #13079568

Order 1408.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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×#533C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic
3#10622706C211yesmaximal, characteristic, complemented
4#10622705C211yesmaximal, characteristic, complemented
5#10622701C211yesmaximal, characteristic, complemented
6#10622698C211yesmaximal, characteristic, complemented
7#10622660C214yesmaximal, complemented
8#10622641C214yesmaximal, complemented
9#10622538C211yesmaximal, characteristic, complemented
10C2×#4339C2212yes—
11C11×C4⋊Q8C2211yescharacteristic
12C11×C4⋊Q8C2211yescharacteristic
13C11×#125—21no—
14C11×C22⋊Q8—21no—
15C11×C22⋊Q8C2212yes—
16C4×Q8×C11—21no—
17C4×Q8×C11C2212yes—
18C11×#117—21no—
19C2×C42×C11C2211yescharacteristic
20C2×#4326C2214yes—
21C2×#4325C2214yes—
22#66983—21no—
23#66983—21no—
24#66928C2212yes—
25#66927C2211yescharacteristic
26C4×D44—21no—
27C4×D44—21no—
28#66922C2211yescharacteristic
29C22⋊(C11⋊C8)C2212yes—
30#66874C2214yes—
31#66873C2214yes—
32C4⋊(C11⋊C8)C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11C2312yes—
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—22no—
41#4339—44no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44C2312yes—
45C2×C4×D11—22no—
46C2×Dic22C2312yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—22no—
54C42×C11—22no—
55C42×C11D411yescharacteristic
56C42×C11D411yescharacteristic
57C42×C11C2311yescharacteristic
58C42×C11C2311yescharacteristic
59#4326—44no—
60#4325—44no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3210—111nomaximal, Sylow
68C23×C11C2×D411yescharacteristic
69C22×D11—22no—
70Q8×C11—24no—
71Q8×C11—42no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2411yescharacteristic
83C22⋊D11—44no—
84C2×Dic11—22no—
85D44—24no—
86D44—42no—
87D44—42no—
88C4×D11—44no—
89Dic22—24no—
90C11⋊C8—22no—
91C11⋊C8—22no—
92#533D1111yescharacteristic, complemented
93#532—111no—
94#494—111no—
95#492—111no—
96#487—111no—
97#486—111no—
98#464—114no—
99#452—114no—
100#431—111no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11C22×D411yescharacteristic
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11—42no—
113C4×C11#13512yes—
114C4×C11#13712yes—
115C4×C11H(5,𝔽2)12yes—
116Dic11—42no—
117C2×#41—112no—
118C2×Q16—114no—
119C2×SD16—114no—
120C4⋊Q8—111no—
121C4⋊Q8C2×D1111yescharacteristic
122C4⋊Q8C2×D1111yescharacteristic
123#127—111no—
124#125—21no—
125#124—112no—
126C22⋊Q8—21no—
127C22⋊Q8C2×D1112yes—
128#121—221no—
129#121—221no—
130C4×Q8—21no—
131C4×Q8C2×D1112yes—
132C4×D4—221no—
133C4×D4—221no—
134#117—21no—
135C2×C42C2×D1111yescharacteristic
136C4⋊C8—112no—
137#103—114no—
138#102—114no—
139C22⋊C8—112no—
140C4×C8—111no—
141C4×C8—111no—
142C2×C11—41no—
143C2×C11#53511yescharacteristic
144C2×C11C2×#13511yescharacteristic
145C2×C11C2×#13711yescharacteristic
146D11—82no—
147#41—444no—
148C2×Q8—21no—
149C2×Q8—112no—
150C2×Q8C22×D1112yes—
151C2×D4—112no—
152C2×D4—222no—
153C2×D4—221no—
154C2×D4—221no—
155C22×C4—222no—
156C22×C4C22⋊D1111yescharacteristic
157C22×C4C22⋊D1111yescharacteristic
158C22×C4C22×D1111yescharacteristic
159Q16—444no—
160SD16—444no—
161C2×C8—112no—
162C2×C8—112no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—221no—
169C4⋊C4—221no—
170C4⋊C4C22×D1112yes—
171C22⋊C4—22no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—22no—
175C42C22⋊D1111yescharacteristic
176C42C22⋊D1111yescharacteristic
177C42C22×D1111yescharacteristic
178C42C22×D1111yescharacteristic
179C11#321011yescharacteristic, complemented, Sylow
180C23—222no—
181C23C2×C22⋊D1111yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—224no—
185D4—224no—
186D4—444no—
187D4—442no—
188D4—442no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—222no—
195C2×C4—444no—
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C2×C22⋊D1111yescharacteristic
198C2×C4C2×C22⋊D1111yescharacteristic
199C2×C4C2×C22⋊D1111yescharacteristic
200C2×C4C2×C22⋊D1111yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—222no—
203C8—222no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—442no—
208C22—442no—
209C22—442no—
210C22C22×C22⋊D1111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—442no—
217C4#6699512yes—
218C4#6700312yes—
219C4#6704212yes—
220C2—41no—
221C2—882no—
222C2C2×#6699511yescharacteristic
223C2C2×#6700311yescharacteristic
224C2#1062336111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenter#533D11
hypocenterC11#3210
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
3. #10622706C2semidirect
4. #10622705C2semidirect
5. #10622701C2semidirect
6. #10622698C2semidirect
7. #10622660C2semidirect
8. #10622641C2semidirect
9. #10622538C2semidirect
92. #533D11semidirect
179. C11#3210semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230082
#106227062
#106227052
#106227012
#106226982
#106226602
#106226412
#106225382
#321011