Finite Group Databasebeta

← #13079748

Subgroups — #13079748

Order 1408.

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

normal subgroups only

This group has 370 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×#532C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3#10622692C211yesmaximal, characteristic, complemented
4#10622691C211yesmaximal, characteristic, complemented
5#10622683C211yesmaximal, characteristic, complemented
6#10622683C211yesmaximal, characteristic, complemented
7#10622648C214yesmaximal, complemented
8#10622622C214yesmaximal, complemented
9#10622538C211yesmaximal, characteristic, complemented
10C2×C11×#41—21no—
11C11×C4⋊Q8C2211yescharacteristic
12C11×#127C2211yescharacteristic
13C11×#124—21no—
14C11×#121—21no—
15C11×#121C2212yes—
16C4×D4×C11—21no—
17C4×D4×C11C2212yes—
18C2×C42×C11C2211yescharacteristic
19#66979C2212yes—
20#66977—21no—
21#66977—21no—
22#66923C2212yes—
23#66922C2211yescharacteristic
24#66922C2211yescharacteristic
25C4×Dic22—21no—
26C4×Dic22—21no—
27#66896C2214yes—
28#66896C2214yes—
29C22⋊(C11⋊C8)C2212yes—
30#66872C2214yes—
31#66871C2214yes—
32C4⋊(C11⋊C8)C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C11×#41—44no—
36C2×Q8×C11—21no—
37C2×D4×C11—22no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11C2312yes—
41C22×C4×C11—22no—
42C22×C4×C11D411yescharacteristic
43C22×C4×C11D411yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×Dic22—21no—
46C2×Dic22—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C11×C22⋊C4—22no—
51C42×C11D411yescharacteristic
52C42×C11D411yescharacteristic
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C2×C11⋊C8C2312yes—
64C2×C11⋊C8C2312yes—
65#3228—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11C2×D411yescharacteristic
68Q8×C11—42no—
69D4×C11—24no—
70D4×C11—44no—
71D4×C11—42no—
72D4×C11—42no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—44no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2411yescharacteristic
84C2×Dic11—22no—
85C2×Dic11—22no—
86Dic22—42no—
87Dic22—42no—
88C11⋊C8—22no—
89C11⋊C8—22no—
90#533—111no—
91#532D1111yescharacteristic
92#500—111no—
93#498—111no—
94#486—111no—
95#486—111no—
96#482—114no—
97#478—114no—
98#431—111no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11C22×D411yescharacteristic
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—42no—
110C4×C11#13512yes—
111C4×C11AGL(1,ℤ/8)12yes—
112C4×C112−1+412yes—
113Dic11—42no—
114Dic11—42no—
115C2×#41—21no—
116C4⋊Q8—111no—
117C4⋊Q8—111no—
118C4⋊Q8C2×D1111yescharacteristic
119#127C2×D1111yescharacteristic
120#125—112no—
121#124—21no—
122C22⋊Q8—221no—
123C22⋊Q8—221no—
124#121—21no—
125#121C2×D1112yes—
126C4×Q8—221no—
127C4×Q8—221no—
128C4×D4—21no—
129C4×D4C2×D1112yes—
130#117—112no—
131C2×C42C2×D1111yescharacteristic
132#107—114no—
133#106—114no—
134C4⋊C8—112no—
135#102—114no—
136#102—114no—
137C22⋊C8—112no—
138C4×C8—111no—
139C4×C8—111no—
140C2×C11—41no—
141C2×C11—82no—
142C2×C11#53611yescharacteristic
143C2×C11C2×#13511yescharacteristic
144C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
145#41—44no—
146C2×Q8—21no—
147C2×Q8—221no—
148C2×Q8—221no—
149C2×D4—22no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4C22×D1112yes—
153C22×C4—22no—
154C22×C4C22⋊D1111yescharacteristic
155C22×C4C22⋊D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157C2×C8—112no—
158C2×C8—112no—
159C4⋊C4—21no—
160C4⋊C4—112no—
161C4⋊C4—112no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—221no—
165C4⋊C4—221no—
166C4⋊C4C22×D1112yes—
167C22⋊C4—22no—
168C22⋊C4—22no—
169C22⋊C4—222no—
170C42—222no—
171C42C22⋊D1111yescharacteristic
172C42C22⋊D1111yescharacteristic
173C42C22×D1111yescharacteristic
174C42C22×D1111yescharacteristic
175C11#322811yescharacteristic, complemented, Sylow
176C23—22no—
177C23C2×C22⋊D1111yescharacteristic
178Q8—42no—
179Q8—442no—
180Q8—442no—
181D4—24no—
182D4—44no—
183D4—42no—
184D4—42no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4C2×C22⋊D1111yescharacteristic
193C2×C4C2×C22⋊D1111yescharacteristic
194C2×C4C2×C22⋊D1111yescharacteristic
195C2×C4C2×C22⋊D1111yescharacteristic
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C23×D1111yescharacteristic
198C8—222no—
199C8—222no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C22×C22⋊D1111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—442no—
212C4—442no—
213C4#6698512yes—
214C4#6700312yes—
215C4#6704312yes—
216C2—41no—
217C2—82no—
218C2C2×#6698511yescharacteristic
219C2C2×#6700311yescharacteristic
220C2#1062335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#532C2
socleC22×C11C22×D4
hypercenter#532D11
hypocenterC11#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
3. #10622692C2semidirect
4. #10622691C2semidirect
5. #10622683C2semidirect
6. #10622683C2semidirect
7. #10622648C2semidirect
8. #10622622C2semidirect
9. #10622538C2semidirect
175. C11#3228semidirect

Maximal subgroups

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

subgroupindex
C11×#5322
#106230012
#106226922
#106226912
#106226832
#106226482
#106226222
#106225382
#322811