Finite Group Databasebeta

← #13080071

Subgroups — #13080071

Order 1408.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623134C212yesmaximal, complemented
2C11×#466C211yesmaximal, characteristic
3#10622766C212yesmaximal, complemented
4#10622729C211yesmaximal, characteristic, complemented
5#10622715C211yesmaximal, characteristic, complemented
6#10622655C212yesmaximal, complemented
7#10622488C212yesmaximal, complemented
8#10622380C212yesmaximal, complemented
9#10622372C212yesmaximal, complemented
10C2×C11×D8C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×#121C2212yes—
13#66989—22no—
14#66989C2212yes—
15#66988—22no—
16D4×Dic11C2212yes—
17C2×#4324C2212yes—
18#66979C2211yescharacteristic
19#66977C2212yes—
20C2×#4318C2211yescharacteristic
21C2×Dic44C2211yescharacteristic
22#66941C2212yes—
23#66940C2212yes—
24#66932—22no—
25#66931—22no—
26C11×#107C2211yescharacteristic
27C11×#102C2212yes—
28#66896C2212yes—
29#66882C2211yescharacteristic
30#66880C2212yes—
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66874C2212yes—
34#66871C2212yes—
35C2×D4×C11—22no—
36C2×D4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—22no—
39C2×Dic22—22no—
40C2×Dic22C2312yes—
41C11×D8—41no—
42C2×C8×C11—41no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2311yescharacteristic
45C11×C4⋊C4C2312yes—
46C11×C22⋊C4—22no—
47C22⋊Dic11—22no—
48C22⋊Dic11—22no—
49C22⋊Dic11—22no—
50C22⋊Dic11—22no—
51C22⋊Dic11D412yes—
52#4324—42no—
53C4⋊Dic11D411yescharacteristic
54C4⋊Dic11D411yescharacteristic
55C4⋊Dic11C2312yes—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59C4×Dic11—22no—
60C4×Dic11C2312yes—
61#4318—41no—
62C2×C11⋊C8C2312yes—
63Dic44—41no—
64#3262—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11C2×D411yescharacteristic
67D4×C11—22no—
68D4×C11—22no—
69D4×C11—82no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2411yescharacteristic
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—82no—
78C2×Dic11C2×D412yes—
79C2×Dic11C2×D412yes—
80Dic22—22no—
81Dic22—22no—
82Dic22—82no—
83C8×C11—21no—
84C8×C11—21no—
85C11⋊C8—22no—
86#542—112no—
87#477—112no—
88#474—112no—
89#468—112no—
90#467—111no—
91#466D1111yescharacteristic
92#464—112no—
93#463—112no—
94#424—111no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11—42no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11C22×D411yescharacteristic
102C4×C11—21no—
103C4×C11—42no—
104C4×C11H(5,𝔽2)11yescharacteristic
105C4×C112−1+411yescharacteristic
106Dic11—22no—
107Dic11—22no—
108Dic11—42no—
109Dic11—42no—
110C2×Q16—111no—
111C2×SD16—112no—
112C2×D8C2×D1111yescharacteristic
113C2×M16—111no—
114C22×C8C2×D1111yescharacteristic
115C4⋊Q8—112no—
116#126—222no—
117#124—112no—
118#124—222no—
119#123—222no—
120C22⋊Q8—112no—
121C22⋊Q8—222no—
122#121C2×D1112yes—
123C4×Q8—112no—
124C4×D4—112no—
125#117—111no—
126#107—111no—
127#107—112no—
128#107C2×D1111yescharacteristic
129C4⋊C8—112no—
130C4⋊C8—112no—
131#103—112no—
132#103—112no—
133#102—112no—
134#102C2×D1112yes—
135C2×C11—41no—
136C2×C11—82no—
137C2×C11#53711yescharacteristic
138C2×C11#57611yescharacteristic
139C2×C11#57811yescharacteristic
140C2×Q8—112no—
141C2×Q8—222no—
142C2×D4—22no—
143C2×D4C22×D1112yes—
144C22×C4—222no—
145C22×C4C22×D1111yescharacteristic
146Q16—441no—
147SD16—442no—
148D8—41no—
149M16—441no—
150C2×C8—41no—
151C2×C8—112no—
152C2×C8C22×D1111yescharacteristic
153C2×C8C22×D1111yescharacteristic
154C4⋊C4—111no—
155C4⋊C4—111no—
156C4⋊C4—112no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4C22×D1112yes—
161C22⋊C4—22no—
162C22⋊C4—112no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C22⋊C4—222no—
166C22⋊C4—222no—
167C42—112no—
168C42—222no—
169C11#326211yescharacteristic, complemented, Sylow
170C23—22no—
171C23D4×D1111yescharacteristic
172Q8—222no—
173Q8—222no—
174Q8—882no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—112no—
182C2×C4—112no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—882no—
186C2×C4D4×D1111yescharacteristic
187C2×C4C23×D1111yescharacteristic
188C8—21no—
189C8—21no—
190C8—222no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D1111yescharacteristic
198C4—21no—
199C4—42no—
200C4—222no—
201C4—222no—
202C4—442no—
203C4—442no—
204C4#6703711yescharacteristic
205C4#6704311yescharacteristic
206C2—41no—
207C2—82no—
208C2#1062312811yescharacteristic
209C2#1062328811yescharacteristic
210C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623134C2semidirect
3. #10622766C2semidirect
4. #10622729C2semidirect
5. #10622715C2semidirect
6. #10622655C2semidirect
7. #10622488C2semidirect
8. #10622380C2semidirect
9. #10622372C2semidirect
169. C11#3262semidirect

Maximal subgroups

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

subgroupindex
#106231342
C11×#4662
#106227662
#106227292
#106227152
#106226552
#106224882
#106223802
#106223722
#326211