Finite Group Databasebeta

← #13080077

Subgroups — #13080077

Order 1408.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623065C212yesmaximal, complemented
2C11×#424C211yesmaximal, characteristic, complemented
3#10622747C212yesmaximal, complemented
4#10622729C211yesmaximal, characteristic, complemented
5#10622728C211yesmaximal, characteristic
6#10622463C212yesmaximal, complemented
7#10622459C212yesmaximal, complemented
8#10622458C212yesmaximal, complemented
9#10622457C212yesmaximal, complemented
10C2×C11×M16C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×#117C2211yescharacteristic
13#66983C2212yes—
14#66977C2212yes—
15C2×Dic44C2211yescharacteristic
16C2×D88C2211yescharacteristic
17C2×#4314C2212yes—
18#66951—22no—
19#66949—22no—
20#66938—22no—
21#66936—22no—
22#66928C2212yes—
23C4×D44C2212yes—
24#66922C2212yes—
25C4×Dic22C2212yes—
26C11×C4⋊C8C2212yes—
27C11×C4⋊C8C2212yes—
28#66885C2212yes—
29#66885C2212yes—
30#66882C2211yescharacteristic
31#66882C2211yescharacteristic
32#66882C2212yes—
33#66880C2212yes—
34#66880C2212yes—
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C2×D44C2312yes—
38C2×C4×D11—22no—
39C2×Dic22—22no—
40C2×Dic22C2312yes—
41C11×M16—41no—
42C2×C8×C11—41no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2312yes—
45C2×C8×C11C2311yescharacteristic
46C11×C4⋊C4D411yescharacteristic
47C11×C4⋊C4D411yescharacteristic
48C11×C22⋊C4D412yes—
49C42×C11C2312yes—
50C22⋊Dic11—22no—
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11C2312yes—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61Dic44—41no—
62D88—41no—
63#4314—42no—
64#3262—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2411yescharacteristic
73C22⋊D11—82no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77D44—22no—
78D44—22no—
79C4×D11—82no—
80Dic22—22no—
81Dic22—22no—
82Dic22—82no—
83C8×C11—22no—
84C8×C11—21no—
85C8×C11—21no—
86#542—112no—
87#477—112no—
88#474—112no—
89#468—112no—
90#467—111no—
91#466—111no—
92#464—112no—
93#463—112no—
94#424D1111yescharacteristic, complemented
95C22×C11—21no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11C22×D411yescharacteristic
99C2×D11—42no—
100C2×D11—42no—
101C2×D11—42no—
102C4×C11—21no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11H(5,𝔽2)11yescharacteristic
106C4×C112−1+411yescharacteristic
107Dic11—42no—
108Dic11—42no—
109Dic11—42no—
110C2×Q16—111no—
111C2×SD16—112no—
112C2×D8—111no—
113C2×M16C2×D1111yescharacteristic
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#121—112no—
123C4×Q8—112no—
124C4×D4—112no—
125#117C2×D1111yescharacteristic
126#107—111no—
127#107—111no—
128#107—112no—
129C4⋊C8C2×D1112yes—
130C4⋊C8C2×D1112yes—
131#103—112no—
132#103—112no—
133#102—112no—
134#102—112no—
135C2×C11—41no—
136C2×C11#53711yescharacteristic
137C2×C11#57611yescharacteristic
138C2×C11#57811yescharacteristic
139D11—82no—
140C2×Q8—112no—
141C2×Q8—222no—
142C2×D4—112no—
143C2×D4—222no—
144C22×C4—222no—
145C22×C4C22×D1111yescharacteristic
146Q16—441no—
147SD16—442no—
148D8—441no—
149M16—41no—
150C2×C8—41no—
151C2×C8C22×D1111yescharacteristic
152C2×C8C22×D1112yes—
153C2×C8C22×D1111yescharacteristic
154C4⋊C4—112no—
155C4⋊C4—112no—
156C4⋊C4—222no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4D4411yescharacteristic
160C4⋊C4D4411yescharacteristic
161C22⋊C4—222no—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C22⋊C4—222no—
166C22⋊C4D4412yes—
167C42—222no—
168C42C22×D1112yes—
169C11#326211yescharacteristic, complemented, Sylow
170C23—222no—
171C23C2×D4411yescharacteristic
172Q8—222no—
173Q8—222no—
174Q8—882no—
175D4—222no—
176D4—222no—
177D4—882no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—882no—
184C2×C4C2×D4412yes—
185C2×C4C2×D4412yes—
186C2×C4C2×D4411yescharacteristic
187C2×C4C23×D1111yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—442no—
195C22—442no—
196C22—442no—
197C22C22×D4411yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—442no—
202C4—442no—
203C4—442no—
204C4#6703711yescharacteristic
205C4#6704011yescharacteristic
206C2—41no—
207C2—882no—
208C2#1062304111yescharacteristic
209C2#1062328311yescharacteristic
210C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#424C2
socleC22×C11C22×D4
prime radical#10622728C2
hypercenter#424D11
hypocenterC11#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #10623065C2semidirect
2. C11×#424C2semidirect
3. #10622747C2semidirect
4. #10622729C2semidirect
6. #10622463C2semidirect
7. #10622459C2semidirect
8. #10622458C2semidirect
9. #10622457C2semidirect
94. #424D11semidirect
169. C11#3262semidirect

Maximal subgroups

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

subgroupindex
#106230652
C11×#4242
#106227472
#106227292
#106227282
#106224632
#106224592
#106224582
#106224572
#326211