Finite Group Databasebeta

← #13067751

Subgroups — #13067751

Order 1408.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#10623261C211yesmaximal, characteristic
2#10622705C211yesmaximal, characteristic, complemented
3#10622463C211yesmaximal, characteristic, complemented
4#10622455C211yesmaximal, characteristic
5C11×#333C211yesmaximal, characteristic, complemented
6#10622122C211yesmaximal, characteristic, complemented
7#10622121C211yesmaximal, characteristic
8C11×C4⋊Q8C2211yescharacteristic
9#66999—22no—
10C2×#4326—22no—
11#66950—21no—
12#66946—21no—
13C4⋊C4×D11—21no—
14#66943—21no—
15C4×D44C2211yescharacteristic
16#66922C2211yescharacteristic
17C4×Dic22C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19C11×C4⋊C8C2211yescharacteristic
20#66885—21no—
21#66882—21no—
22#66881—21no—
23#66880—21no—
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11D412yes—
26C2×D44D411yescharacteristic
27C2×C4×D11—22no—
28C2×C4×D11—21no—
29C2×Dic22—21no—
30C2×Dic22D411yescharacteristic
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C42×C11C2311yescharacteristic
36#4326—44no—
37(C2×D11)⋊C4—22no—
38(C2×D11)⋊C4—21no—
39C4⋊Dic11—22no—
40C4⋊Dic11—21no—
41C4⋊Dic11—21no—
42C4⋊Dic11D411yescharacteristic
43C4⋊Dic11D411yescharacteristic
44Dic11⋊C4—22no—
45Dic11⋊C4—21no—
46C4×Dic11—21no—
47C2×C11⋊C8—21no—
48#1632—111nomaximal, Sylow
49C22×D11—21no—
50Q8×C11—42no—
51C2×C4×C11—22no—
52C2×C4×C11C2×D411yescharacteristic
53C2×C4×C11C2×D411yescharacteristic
54C2×C4×C11C2×D411yescharacteristic
55C2×Dic11—21no—
56C2×Dic11—21no—
57C2×Dic11—21no—
58C2×Dic11—41no—
59D44—21no—
60D44Q1612yescomplemented
61C4×D11—41no—
62C4×D11—41no—
63C4×D11—82no—
64Dic22—21no—
65Dic22—21no—
66Dic22—42no—
67C8×C11—41no—
68C8×C11—41no—
69C11⋊C8—22no—
70#554—111no—
71#494—111no—
72#477—111no—
73#476—111no—
74#333D1111yescharacteristic, complemented
75Q8⋊C8—111no—
76D4⋊C8—111no—
77C22×C11#12011yescharacteristic
78C2×D11—22no—
79C2×D11—41no—
80C2×D11—41no—
81C4×C11—21no—
82C4×C11—42no—
83C4×C11C2×Q1611yescharacteristic
84C4×C11#13511yescharacteristic
85C4×C11#13711yescharacteristic
86C4×C11#13711yescharacteristic
87Dic11—41no—
88Dic11—41no—
89Dic11—41no—
90Dic11—81no—
91C2×Q16—222no—
92C4⋊Q8—111no—
93C4⋊Q8C2×D1111yescharacteristic
94#125—221no—
95C22⋊Q8—221no—
96C22⋊Q8—222no—
97C4×Q8—111no—
98C4×D4—111no—
99C4×D4—221no—
100C2×C4⋊C4—221no—
101#107—221no—
102#106—221no—
103C4⋊C8C2×D1111yescharacteristic
104C4⋊C8C2×D1111yescharacteristic
105#103—221no—
106#102—221no—
107C4×C8—111no—
108C2×C11#45111yescharacteristic
109C2×C11#45211yescharacteristic
110C2×C11#45311yescharacteristic
111D11—42no—
112C2×Q8—111no—
113C2×Q8—221no—
114C2×Q8D4412yes—
115C2×D4—111no—
116C22×C4—222no—
117C22×C4—221no—
118Q16—444no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—221no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—111no—
125C4⋊C4—111no—
126C4⋊C4—222no—
127C4⋊C4—222no—
128C4⋊C4—221no—
129C4⋊C4—221no—
130C4⋊C4—221no—
131C22⋊C4—222no—
132C22⋊C4—221no—
133C42—221no—
134C42C22×D1111yescharacteristic
135C11#163211yescharacteristic, complemented, Sylow
136C23—221no—
137Q8—42no—
138Q8—221no—
139Q8—221no—
140Q8—442no—
141D4—112no—
142D4—221no—
143C2×C4—22no—
144C2×C4—221no—
145C2×C4—221no—
146C2×C4—221no—
147C2×C4—441no—
148C2×C4—441no—
149C2×C4—441no—
150C2×C4—882no—
151C2×C4C2×D4411yescharacteristic
152C2×C4D4×D1111yescharacteristic
153C2×C4D4×D1111yescharacteristic
154C8—41no—
155C8—41no—
156C8—222no—
157C22—222no—
158C22—441no—
159C22—441no—
160C22#6693511yescharacteristic
161C4—21no—
162C4—42no—
163C4—441no—
164C4—441no—
165C4—441no—
166C4—881no—
167C4#6696811yescharacteristic
168C4#6696911yescharacteristic
169C4Q16×D1111yescharacteristic
170C4#6697111yescharacteristic
171C2—442no—
172C2#1062236011yescharacteristic
173C2#1062242111yescharacteristic
174C2#1062242311yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#333C2
socleC22×C11#120
prime radicalC2×D44D4
hypercenter#333D11
hypocenterC11#1632
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #10622705C2semidirect
3. #10622463C2semidirect
5. C11×#333C2semidirect
6. #10622122C2semidirect
60. D44Q16semidirect
74. #333D11semidirect
135. C11#1632semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106227052
#106224632
#106224552
C11×#3332
#106221222
#106221212
#163211