Finite Group Databasebeta

← #46811413

Subgroups — #46811413

Order 34432.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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#31771372C211yesmaximal, characteristic, complemented
2#31770610C212yesmaximal, complemented
3#31770579C211yesmaximal, characteristic, complemented
4#31770361C212yesmaximal, complemented
5#535×C269C211yesmaximal, characteristic
6#22575460—24no—
7C2×#16864386—22no—
8C2×#16864386C2212yes—
9#22575412C2212yes—
10#22575374—24no—
11#22575368—22no—
12C2×#41×C269C2211yescharacteristic
13C22×D4×C269C2211yescharacteristic
14#127×C269C412yescomplemented
15#124×C269C412yescomplemented
16#121×C269—22no—
17#120×C269—22no—
18#117×C269C2211yescharacteristic
19#16864386—24no—
20#16864386—22no—
21#16864386—22no—
22C2×#14524130—24no—
23C2×#14524130D414yescomplemented
24C4⋊Dic269—22no—
25C22⋊Dic269—22no—
26C4×Dic269—22no—
27C24×C269—21no—
28#41×C269—22no—
29#41×C269—22no—
30C2×Q8×C269C2×C411yescharacteristic
31C2×D4×C269—24no—
32C2×D4×C269—22no—
33C2×D4×C269—21no—
34C2×D4×C269—22no—
35C2×D4×C269C2×C412yes—
36C2×D4×C269C2×C411yescharacteristic
37C2×D4×C269D412yes—
38C22×C4×C269D412yes—
39C22×C4×C269C2311yescharacteristic
40C4⋊C4×C269—21no—
41C22⋊C4×C269—21no—
42C22⋊C4×C269—24no—
43C42×C269C2×C412yes—
44C2×Dic269—42no—
45#14524130—24no—
46C23×C269—22no—
47C23×C269—42no—
48C23×C269—82no—
49C23×C269C22⋊C412yes—
50C23×C269C2×D411yescharacteristic
51Q8×C269—22no—
52D4×C269—24no—
53D4×C269—22no—
54D4×C269—24no—
55D4×C269—41no—
56D4×C269—41no—
57D4×C269—84no—
58C2×C4×C269—22no—
59C2×C4×C269—22no—
60C2×C4×C269—22no—
61C2×C4×C269C22⋊C412yes—
62C2×C4×C269C22×C411yescharacteristic
63C2×C4×C269C2×D412yes—
64C2×C4×C269C2×D411yescharacteristic
65C2×C4×C269#4112yes—
66C22×C269—22no—
67C22×C269—41no—
68C22×C269—42no—
69C22×C269—44no—
70C22×C269—42no—
71C22×C269—84no—
72C22×C269C2×C22⋊C411yescharacteristic
73C22×C269#12112yes—
74C4×C269—22no—
75C4×C269—42no—
76C4×C269C4×D412yes—
77C4×C269#12011yescharacteristic
78C4×C269#12311yescharacteristic
79Dic269—82no—
80C2×C269—22no—
81C2×C269—21no—
82C2×C269—42no—
83C2×C269—82no—
84C2×C269#38611yescharacteristic
85C269#191011yescharacteristic, complemented, Sylow
86#1910—2691nomaximal, Sylow
87#568—2691no—
88#535D26911yescharacteristic
89#418—2692no—
90#410—2691no—
91H(3,ℤ/4)—2692no—
92C2×#41C2×D26911yescharacteristic
93C22×D4C2×D26911yescharacteristic
94#131—5384no—
95C2×M16—2692no—
96C2×M16—5382no—
97#127Dic26912yescomplemented
98#124Dic26912yescomplemented
99#121—22no—
100#120—22no—
101#117—2692no—
102#117C2×D26911yescharacteristic
103#102—5384no—
104#99—5382no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic26911yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic26912yes—
114C2×D4C2×Dic26911yescharacteristic
115C2×D4C22⋊D26912yes—
116C22×C4C22⋊D26912yes—
117C22×C4C22×D26911yescharacteristic
118M16—5384no—
119M16—5382no—
120M16—5382no—
121C2×C8—2694no—
122C2×C8—5384no—
123C4⋊C4—21no—
124C4⋊C4—5382no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—5382no—
128C42—5382no—
129C42C2×Dic26912yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic26912yes—
134C23C2×C22⋊D26911yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—10762no—
146C2×C4C22⋊Dic26912yes—
147C2×C4C22×Dic26911yescharacteristic
148C2×C4D4×D26912yes—
149C2×C4C2×C22⋊D26911yescharacteristic
150C2×C4#1686440112yes—
151C8—5384no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic26911yescharacteristic
159C22#2257542512yes—
160C4—22no—
161C4—42no—
162C4—21522no—
163C4D4×Dic26912yes—
164C4#2257542111yescharacteristic
165C4#2257543411yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#3177048511yescharacteristic
subgroupG/H
centerC2#31770485
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting, prime radical#535×C269C2
socleC2×C269#386
cosocleC22×C4×C269C23
hypercenter#535D269
hypocenterC269#1910
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #31771372C2semidirect
2. #31770610C2semidirect
3. #31770579C2semidirect
4. #31770361C2semidirect
14. #127×C269C4semidirect
15. #124×C269C4semidirect
23. C2×#14524130D4semidirect
85. C269#1910semidirect
97. #127Dic269semidirect
98. #124Dic269semidirect

Maximal subgroups

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

subgroupindex
#317713722
#317706102
#317705792
#317703612
#535×C2692
#1910269