Finite Group Databasebeta

← #13079993

Subgroups — #13079993

Order 1408.

430 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623127C212yesmaximal, complemented
2C11×#469C211yesmaximal, characteristic, complemented
3#10622763C212yesmaximal, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622731C211yesmaximal, characteristic, complemented
6#10622652C212yesmaximal, complemented
7#10622483C212yesmaximal, complemented
8#10622399C212yesmaximal, complemented
9#10622374C212yesmaximal, complemented
10C2×#4341—22no—
11C2×C11×D8C2211yescharacteristic
12C2×C11×M16C2211yescharacteristic
13C11×#121C2212yes—
14#66993C2212yes—
15#66992—22no—
16D4×Dic11C2212yes—
17C2×#4323C2212yes—
18#66983C2212yes—
19C2×C4×Dic11C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21C2×D88C2211yescharacteristic
22#66946C2212yes—
23#66941C2212yes—
24#66938—22no—
25(C22⋊D11)⋊C4—22no—
26C11×#106C2211yescharacteristic
27C11×#102C2212yes—
28#66896C2212yes—
29#66885C2212yes—
30#66881C2211yescharacteristic
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66873C2212yes—
34#66872C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C2×C22⋊D11—22no—
40C2×C22⋊D11—22no—
41C22×Dic11—22no—
42C22×Dic11D412yes—
43#4341—48no—
44C2×D44C2312yes—
45C2×C4×D11—22no—
46C2×Dic22—22no—
47C11×D8—41no—
48C11×M16—41no—
49C2×C8×C11C2311yescharacteristic
50C2×C8×C11C2311yescharacteristic
51C11×C4⋊C4C2312yes—
52C11×C22⋊C4—22no—
53C22⋊Dic11—22no—
54#4323—42no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—22no—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59C4×Dic11D411yescharacteristic
60C4×Dic11D411yescharacteristic
61C4×Dic11C2312yes—
62#4318—41no—
63C2×C11⋊C8C2312yes—
64D88—41no—
65#3253—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11C2×D411yescharacteristic
68C22×D11—22no—
69D4×C11—22no—
70D4×C11—22no—
71D4×C11—44no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2411yescharacteristic
77C22⋊D11—44no—
78C22⋊D11—44no—
79C22⋊D11—44no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11—44no—
83C2×Dic11C2×D412yes—
84C2×Dic11C2×D412yes—
85D44—22no—
86D44—22no—
87C4×D11—44no—
88Dic22—44no—
89C8×C11—21no—
90C8×C11—21no—
91C11⋊C8—22no—
92#532—112no—
93#476—112no—
94#476—112no—
95#469—111no—
96#469—112no—
97#469D1111yescharacteristic, complemented
98#459—112no—
99#459—112no—
100#423—111no—
101C22×C11—21no—
102C22×C11—22no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11C22×D411yescharacteristic
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11H(5,𝔽2)11yescharacteristic
113C4×C112−1+411yescharacteristic
114Dic11—22no—
115Dic11—42no—
116Dic11AGL(1,ℤ/8)14yes—
117C2×#41—222no—
118C2×D8—112no—
119C2×D8—111no—
120C2×D8C2×D1111yescharacteristic
121C2×M16—111no—
122C2×M16C2×D1111yescharacteristic
123C4⋊Q8—112no—
124#127—112no—
125#124—222no—
126#121—112no—
127#121—222no—
128#121C2×D1112yes—
129C4×D4—112no—
130C4×D4—112no—
131C4×D4—222no—
132C2×C42—111no—
133#106—111no—
134#106—112no—
135#106C2×D1111yescharacteristic
136C4⋊C8—112no—
137C4⋊C8—112no—
138#102—112no—
139#102—112no—
140#102—112no—
141#102C2×D1112yes—
142C2×C11—41no—
143C2×C11—82no—
144C2×C11#53711yescharacteristic
145C2×C11C2×AGL(1,ℤ/8)12yes—
146D11—82no—
147#41—448no—
148C2×Q8—222no—
149C2×D4—22no—
150C2×D4—112no—
151C2×D4—222no—
152C2×D4—222no—
153C2×D4—222no—
154C2×D4C22×D1112yes—
155C22×C4—112no—
156C22×C4—222no—
157C22×C4—222no—
158C22×C4C22×D1111yescharacteristic
159D8—41no—
160D8—441no—
161D8—442no—
162M16—41no—
163M16—441no—
164C2×C8—112no—
165C2×C8C22×D1111yescharacteristic
166C2×C8C22×D1111yescharacteristic
167C4⋊C4—112no—
168C4⋊C4—222no—
169C4⋊C4C22×D1112yes—
170C22⋊C4—22no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—111no—
175C42—111no—
176C42—112no—
177C11#325311yescharacteristic, complemented, Sylow
178C23—22no—
179C23—222no—
180C23D4×D1111yescharacteristic
181Q8—444no—
182D4—22no—
183D4—22no—
184D4—44no—
185D4—222no—
186D4—222no—
187D4—444no—
188D4—444no—
189D4—444no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—112no—
194C2×C4—112no—
195C2×C4—224no—
196C2×C4—222no—
197C2×C4—444no—
198C2×C4—444no—
199C2×C4D4×D1111yescharacteristic
200C2×C4C23×D1111yescharacteristic
201C8—21no—
202C8—21no—
203C8—222no—
204C22—22no—
205C22—21no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—442no—
210C22—442no—
211C22—442no—
212C22C2×D4×D1111yescharacteristic
213C4—21no—
214C4—42no—
215C4—114no—
216C4—222no—
217C4—442no—
218C4#6703711yescharacteristic
219C4#6704311yescharacteristic
220C2—41no—
221C2—82no—
222C2—882no—
223C2#1062312811yescharacteristic
224C2D11×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#469C2
socleC22×C11C22×D4
hypercenter#469D11
hypocenterC11#3253
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. #10623127C2semidirect
2. C11×#469C2semidirect
3. #10622763C2semidirect
4. #10622748C2semidirect
5. #10622731C2semidirect
6. #10622652C2semidirect
7. #10622483C2semidirect
8. #10622399C2semidirect
9. #10622374C2semidirect
97. #469D11semidirect
177. C11#3253semidirect

Maximal subgroups

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

subgroupindex
#106231272
C11×#4692
#106227632
#106227482
#106227312
#106226522
#106224832
#106223992
#106223742
#325311