Finite Group Databasebeta

← #13079260

Subgroups — #13079260

Order 1408.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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#10622686C211yesmaximal, characteristic, complemented
4#10622684C211yesmaximal, characteristic, complemented
5#10622680C211yesmaximal, characteristic, complemented
6#10622677C211yesmaximal, characteristic, complemented
7#10622652C212yesmaximal, complemented
8#10622651C212yesmaximal, complemented
9#10622627C212yesmaximal, complemented
10C4×#4323C212yesmaximal, complemented
11#10622610C211yesmaximal, characteristic, complemented
12C11×#127C2211yescharacteristic
13C11×#125C2211yescharacteristic
14C11×#123—22no—
15C11×#121—22no—
16C11×#121C2212yes—
17C4×D4×C11C2212yes—
18C11×#117C2211yescharacteristic
19C2×#4323C2212yes—
20C2×#4323C2212yes—
21#66983C2212yes—
22C2×#4318C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66947—22no—
25#66937—22no—
26#66927C2211yescharacteristic
27C4×D44C2212yes—
28#66923C2211yescharacteristic
29#66896C2212yes—
30#66896C2212yes—
31#66873C2212yes—
32#66873C2212yes—
33#66872C2212yes—
34#66871C2212yes—
35#66867C2211yescharacteristic
36#66867C2211yescharacteristic
37C4×C11⋊C8C2211yescharacteristic
38C4×C11⋊C8C2211yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11C2312yes—
42C22×C4×C11—22no—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×D44—22no—
46C2×D44C2312yes—
47C2×C4×D11—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4D412yes—
50C11×C4⋊C4C2312yes—
51C11×C22⋊C4—22no—
52C11×C22⋊C4—22no—
53C11×C22⋊C4D412yes—
54C42×C11C2311yescharacteristic
55C42×C11C2311yescharacteristic
56#4323—24no—
57#4323—24no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—22no—
62#4318—22no—
63C2×C11⋊C8—22no—
64C2×C11⋊C8C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66C2×C11⋊C8C2311yescharacteristic
67C2×C11⋊C8C2311yescharacteristic
68#3176—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11C2×D411yescharacteristic
71C22×D11—22no—
72D4×C11—22no—
73D4×C11—22no—
74D4×C11—82no—
75D4×C11—82no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—82no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2411yescharacteristic
84C22⋊D11—82no—
85C2×Dic11—22no—
86D44—22no—
87D44—22no—
88D44—82no—
89C4×D11—82no—
90C11⋊C8—21no—
91C11⋊C8—21no—
92C11⋊C8#4112yes—
93C11⋊C8#4112yes—
94#540—111no—
95#540D1111yescharacteristic, complemented
96#499—111no—
97#493—111no—
98#490—111no—
99#490—111no—
100#469—112no—
101#466—112no—
102#442—112no—
103C4×D8—112no—
104#405—111no—
105C22×C11—21no—
106C22×C11—22no—
107C22×C11—42no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11C22×D411yescharacteristic
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C4×C11—21no—
115C4×C11—22no—
116C4×C11—22no—
117C4×C11—42no—
118C4×C11C2×#4111yescharacteristic
119C4×C11C2×#4111yescharacteristic
120Dic11—42no—
121C2×D8—112no—
122C2×D8—112no—
123C2×M16—111no—
124C22×C8—111no—
125#127—111no—
126#127C2×D1111yescharacteristic
127#125—111no—
128#125C2×D1111yescharacteristic
129#123—22no—
130#123—222no—
131#121—22no—
132#121—112no—
133#121—222no—
134#121C2×D1112yes—
135C4×D4—112no—
136C4×D4C2×D1112yes—
137#117C2×D1111yescharacteristic
138#107—112no—
139#106—112no—
140#102—112no—
141#102—112no—
142#102—112no—
143#102—112no—
144#97—111no—
145#97—111no—
146C4×C8—111no—
147C4×C8—111no—
148C2×C11—41no—
149C2×C11—82no—
150C2×C11#53211yescharacteristic
151C2×C11#57612yes—
152D11—82no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—112no—
156C2×D4—222no—
157C2×D4—222no—
158C2×D4C22×D1112yes—
159C22×C4—22no—
160C22×C4—222no—
161C22×C4C22×D1111yescharacteristic
162D8—224no—
163D8—224no—
164M16—222no—
165C2×C8—111no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8—111no—
169C2×C8—222no—
170C4⋊C4—22no—
171C4⋊C4—112no—
172C4⋊C4—222no—
173C4⋊C4C22⋊D1112yes—
174C4⋊C4C22×D1112yes—
175C22⋊C4—22no—
176C22⋊C4—22no—
177C22⋊C4—222no—
178C22⋊C4—222no—
179C22⋊C4C22⋊D1112yes—
180C42C22×D1111yescharacteristic
181C42C22×D1111yescharacteristic
182C11#317611yescharacteristic, complemented, Sylow
183C23—22no—
184C23—222no—
185C23C2×C22⋊D1111yescharacteristic
186D4—22no—
187D4—22no—
188D4—82no—
189D4—82no—
190D4—222no—
191D4—222no—
192D4—882no—
193D4—882no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—222no—
199C2×C4—882no—
200C2×C4C2×C22⋊D1112yes—
201C2×C4C2×C22⋊D1112yes—
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—112no—
205C8—112no—
206C8—221no—
207C8—221no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—442no—
214C22—442no—
215C22—442no—
216C22C22×C22⋊D1111yescharacteristic
217C4—21no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—442no—
222C4#41×D1111yescharacteristic
223C4#41×D1111yescharacteristic
224C2—41no—
225C2—82no—
226C2—882no—
227C2#1062336311yescharacteristic
228C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#540C2
socleC22×C11C22×D4
hypercenter#540D11
hypocenterC11#3176
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. #10622686C2semidirect
4. #10622684C2semidirect
5. #10622680C2semidirect
6. #10622677C2semidirect
7. #10622652C2semidirect
8. #10622651C2semidirect
9. #10622627C2semidirect
10. C4×#4323C2semidirect
11. #10622610C2semidirect
95. #540D11semidirect
182. C11#3176semidirect

Maximal subgroups

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

subgroupindex
C11×#5402
#106230662
#106226862
#106226842
#106226802
#106226772
#106226522
#106226512
#106226272
C4×#43232
#106226102
#317611