Finite Group Databasebeta

← #13079261

Subgroups — #13079261

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#10623150C212yesmaximal, complemented
2C11×#469C211yesmaximal, characteristic, complemented
3#10622765C211yesmaximal, characteristic, complemented
4#10622764C211yesmaximal, characteristic, complemented
5#10622748C211yesmaximal, characteristic, complemented
6#10622735C211yesmaximal, characteristic, complemented
7#10622651C212yesmaximal, complemented
8#10622482C211yesmaximal, characteristic, complemented
9#10622471C211yesmaximal, characteristic, complemented
10#10622377C212yesmaximal, complemented
11#10622369C212yesmaximal, complemented
12C2×C11×D8C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#121C2212yes—
15#66993C2212yes—
16#66992—22no—
17#66991—22no—
18D4×Dic11C2212yes—
19C2×#4323C2212yes—
20#66983C2212yes—
21#66979C2211yescharacteristic
22C22×C11⋊C8C2211yescharacteristic
23C2×D88C2211yescharacteristic
24#66946C2212yes—
25#66943C2212yes—
26#66939—22no—
27#66936—22no—
28C11×#106C2211yescharacteristic
29C11×#102C2212yes—
30#66896C2212yes—
31#66885C2212yes—
32#66881C2211yescharacteristic
33#66879C2211yescharacteristic
34#66879C2211yescharacteristic
35C8×Dic11C2211yescharacteristic
36C8×Dic11C2211yescharacteristic
37#66873C2212yes—
38#66871C2212yes—
39C2×D4×C11—22no—
40C2×D4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—22no—
43C2×C22⋊D11—22no—
44C2×C22⋊D11—22no—
45C22×Dic11—22no—
46C2×D44C2312yes—
47C2×C4×D11—22no—
48C11×D8—22no—
49C11×M16—22no—
50C2×C8×C11C2311yescharacteristic
51C2×C8×C11C2311yescharacteristic
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—22no—
54C22⋊Dic11—22no—
55C22⋊Dic11D412yes—
56#4323—24no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11D412yes—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63C4×Dic11C2311yescharacteristic
64C4×Dic11C2311yescharacteristic
65C2×C11⋊C8—22no—
66C2×C11⋊C8C2311yescharacteristic
67C2×C11⋊C8C2311yescharacteristic
68D88—22no—
69#3176—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11C2×D411yescharacteristic
72C22×D11—22no—
73D4×C11—22no—
74D4×C11—22no—
75D4×C11—82no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—82no—
82C22⋊D11—82no—
83C22⋊D11—82no—
84C2×Dic11—22no—
85C2×Dic11—82no—
86C2×Dic11C2×D412yes—
87C2×Dic11C2×D412yes—
88D44—22no—
89D44—22no—
90C4×D11—82no—
91C8×C11—21no—
92C8×C11#4112yes—
93C11⋊C8—21no—
94C11⋊C8#4112yes—
95#540—112no—
96#499—111no—
97#493—111no—
98#490—112no—
99#469—111no—
100#469D1111yescharacteristic, complemented
101#466—112no—
102#442—111no—
103#442—111no—
104C4×D8—112no—
105#405—111no—
106C22×C11—21no—
107C22×C11—22no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11C22×D411yescharacteristic
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—42no—
115C4×C11—21no—
116C4×C11—42no—
117C4×C11C2×#4111yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—22no—
120Dic11—22no—
121Dic11—42no—
122C2×D8—112no—
123C2×D8—111no—
124C2×D8C2×D1111yescharacteristic
125C2×M16C2×D1111yescharacteristic
126C22×C8—111no—
127#127—112no—
128#125—112no—
129#123—222no—
130#123—222no—
131#121—112no—
132#121—222no—
133#121—222no—
134#121C2×D1112yes—
135C4×D4—112no—
136C4×D4—112no—
137#117—111no—
138#107—112no—
139#106—111no—
140#106C2×D1111yescharacteristic
141#102—112no—
142#102—112no—
143#102—112no—
144#102C2×D1112yes—
145#97—111no—
146#97—111no—
147C4×C8—111no—
148C4×C8—111no—
149C2×C11—41no—
150C2×C11—82no—
151C2×C11#53211yescharacteristic
152C2×C11#57612yes—
153D11—82no—
154C2×D4—22no—
155C2×D4—112no—
156C2×D4—222no—
157C2×D4—222no—
158C2×D4—222no—
159C2×D4C22×D1112yes—
160C22×C4—222no—
161C22×C4—222no—
162C22×C4C22×D1111yescharacteristic
163D8—22no—
164D8—224no—
165D8—222no—
166M16—22no—
167C2×C8—111no—
168C2×C8—111no—
169C2×C8—222no—
170C2×C8C22×D1111yescharacteristic
171C2×C8C22×D1111yescharacteristic
172C4⋊C4—112no—
173C4⋊C4—112no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4C22×D1112yes—
177C22⋊C4—22no—
178C22⋊C4—112no—
179C22⋊C4—222no—
180C22⋊C4—222no—
181C22⋊C4—222no—
182C42—111no—
183C42—111no—
184C11#317611yescharacteristic, complemented, Sylow
185C23—22no—
186C23—222no—
187C23D4×D1111yescharacteristic
188D4—22no—
189D4—22no—
190D4—82no—
191D4—222no—
192D4—222no—
193D4—882no—
194D4—882no—
195D4—882no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—112no—
200C2×C4—112no—
201C2×C4—222no—
202C2×C4—882no—
203C2×C4—882no—
204C2×C4D4×D1111yescharacteristic
205C2×C4C23×D1111yescharacteristic
206C8—21no—
207C8—112no—
208C8—221no—
209C8#434112yes—
210C22—22no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—442no—
216C22—442no—
217C22—442no—
218C22C2×D4×D1111yescharacteristic
219C4—21no—
220C4—42no—
221C4—222no—
222C4—222no—
223C4—442no—
224C4C2×#434111yescharacteristic
225C4#41×D1111yescharacteristic
226C2—41no—
227C2—82no—
228C2—882no—
229C2#1062312711yescharacteristic
230C2#1062330512yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#469C2
socleC22×C11C22×D4
hypercenter#469D11
hypocenterC11#3176
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #10623150C2semidirect
2. C11×#469C2semidirect
3. #10622765C2semidirect
4. #10622764C2semidirect
5. #10622748C2semidirect
6. #10622735C2semidirect
7. #10622651C2semidirect
8. #10622482C2semidirect
9. #10622471C2semidirect
10. #10622377C2semidirect
11. #10622369C2semidirect
100. #469D11semidirect
184. C11#3176semidirect

Maximal subgroups

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

subgroupindex
#106231502
C11×#4692
#106227652
#106227642
#106227482
#106227352
#106226512
#106224822
#106224712
#106223772
#106223692
#317611