Finite Group Databasebeta

← #13067786

Subgroups — #13067786

Order 1408.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#10623073C211yesmaximal, characteristic
2C11×#476C211yesmaximal, characteristic
3#10622704C211yesmaximal, characteristic, complemented
4#10622694C211yesmaximal, characteristic, complemented
5D4⋊(C11⋊C8)C211yesmaximal, characteristic
6#10622122C211yesmaximal, characteristic, complemented
7#10622120C211yesmaximal, characteristic, complemented
8C11×C4⋊Q8C2211yescharacteristic
9C4×D4×C11C2211yescharacteristic
10#66989—21no—
11#66979—21no—
12#66977—21no—
13#66940—21no—
14#66932—22no—
15#66922C2211yescharacteristic
16C4×Dic22C2211yescharacteristic
17C11×#106—21no—
18C11×C4⋊C8C2211yescharacteristic
19C11×#102—21no—
20#66899—22no—
21#66874—21no—
22#66871—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×D4×C11D411yescharacteristic
27C22×C4×C11—21no—
28C2×Dic22—21no—
29C2×Dic22D411yescharacteristic
30C2×C8×C11—21no—
31C11×C4⋊C4—21no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4D411yescharacteristic
34C11×C22⋊C4—21no—
35C42×C11C2311yescharacteristic
36C22⋊Dic11—22no—
37C22⋊Dic11—22no—
38C4⋊Dic11—21no—
39C4⋊Dic11D411yescharacteristic
40C4⋊Dic11D412yes—
41Dic11⋊C4—22no—
42Dic11⋊C4—21no—
43C4×Dic11—22no—
44C4×Dic11—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47#1638—111nomaximal, Sylow
48C23×C11—21no—
49Q8×C11—42no—
50D4×C11—21no—
51D4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—41no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11C2×D411yescharacteristic
58C2×C4×C11C2×D411yescharacteristic
59C2×Dic11—21no—
60C2×Dic11—21no—
61C2×Dic11—22no—
62Dic22—21no—
63Dic22—21no—
64Dic22—41no—
65Dic22—41no—
66C8×C11—41no—
67C11⋊C8—41no—
68C11⋊C8—41no—
69#556—111no—
70#487—111no—
71#477—111no—
72#476D1111yescharacteristic
73#332—111no—
74Q8⋊C8—111no—
75D4⋊C8—111no—
76C22×C11—41no—
77C22×C11—41no—
78C22×C11—41no—
79C22×C11#12011yescharacteristic
80C4×C11—21no—
81C4×C11—41no—
82C4×C11—81no—
83C4×C11#13511yescharacteristic
84C4×C11#13511yescharacteristic
85C4×C11#13711yescharacteristic
86C4×C11#13711yescharacteristic
87Dic11—41no—
88Dic11—42no—
89Dic11—41no—
90C4⋊Q8—111no—
91C4⋊Q8C2×D1111yescharacteristic
92#126—222no—
93#124—221no—
94C22⋊Q8—221no—
95C4×Q8—111no—
96C4×Q8—221no—
97C4×D4C2×D1111yescharacteristic
98#117—221no—
99#107—221no—
100#106—21no—
101C4⋊C8—111no—
102C4⋊C8C2×D1111yescharacteristic
103#103—221no—
104#103—222no—
105#102—21no—
106C4×C8—111no—
107C2×C11—81no—
108C2×C11#45211yescharacteristic
109C2×C11#45211yescharacteristic
110C2×C11#45411yescharacteristic
111C2×Q8—21no—
112C2×Q8—111no—
113C2×Q8—221no—
114C2×D4C22⋊D1111yescharacteristic
115C22×C4—21no—
116C2×C8—21no—
117C2×C8—221no—
118C2×C8—221no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—112no—
122C4⋊C4—111no—
123C4⋊C4—222no—
124C4⋊C4—221no—
125C4⋊C4—221no—
126C4⋊C4C22⋊D1111yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—222no—
129C22⋊C4—222no—
130C42—222no—
131C42—221no—
132C42C22×D1111yescharacteristic
133C11#163811yescharacteristic, complemented, Sylow
134C23—21no—
135Q8—42no—
136Q8—221no—
137Q8—221no—
138Q8—441no—
139Q8—441no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—221no—
147C2×C4—222no—
148C2×C4—221no—
149C2×C4D4×D1111yescharacteristic
150C2×C4D4×D1111yescharacteristic
151C2×C4C2×C22⋊D1111yescharacteristic
152C8—41no—
153C8—441no—
154C8—441no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#6699011yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—441no—
163C4—441no—
164C4—442no—
165C4#6696811yescharacteristic
166C4#6696911yescharacteristic
167C4#6699511yescharacteristic
168C4#6700311yescharacteristic
169C2—81no—
170C2#1062266011yescharacteristic
171C2#1062278611yescharacteristic
172C2#1062281411yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#476C2
socleC22×C11#120
prime radicalC2×D4×C11D4
hypercenter#476D11
hypocenterC11#1638
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
3. #10622704C2semidirect
4. #10622694C2semidirect
6. #10622122C2semidirect
7. #10622120C2semidirect
133. C11#1638semidirect

Maximal subgroups

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

subgroupindex
#106230732
C11×#4762
#106227042
#106226942
D4⋊(C11⋊C8)2
#106221222
#106221202
#163811