Finite Group Databasebeta

← #34100664

Subgroups — #34100664

Order 20096.

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#23758040C211yesmaximal, characteristic, complemented
2#23757278C212yesmaximal, complemented
3#23757247C211yesmaximal, characteristic, complemented
4#23757029C212yesmaximal, complemented
5#535×C157C211yesmaximal, characteristic
6#19097778—24no—
7C2×#14578938—22no—
8C2×#14578938C2212yes—
9#19097730C2212yes—
10#19097692—24no—
11#19097686—22no—
12C2×#41×C157C2211yescharacteristic
13C22×D4×C157C2211yescharacteristic
14#127×C157C412yescomplemented
15#124×C157C412yescomplemented
16#121×C157—22no—
17#120×C157—22no—
18#117×C157C2211yescharacteristic
19#14578938—24no—
20#14578938—22no—
21#14578938—22no—
22C2×#11929434—24no—
23C2×#11929434D414yescomplemented
24C4⋊Dic157—22no—
25C22⋊Dic157—22no—
26C4×Dic157—22no—
27C24×C157—21no—
28#41×C157—22no—
29#41×C157—22no—
30C2×Q8×C157C2×C411yescharacteristic
31C2×D4×C157—24no—
32C2×D4×C157—22no—
33C2×D4×C157—21no—
34C2×D4×C157—22no—
35C2×D4×C157C2×C412yes—
36C2×D4×C157C2×C411yescharacteristic
37C2×D4×C157D412yes—
38C22×C4×C157D412yes—
39C22×C4×C157C2311yescharacteristic
40C4⋊C4×C157—21no—
41C22⋊C4×C157—21no—
42C22⋊C4×C157—24no—
43C42×C157C2×C412yes—
44C2×Dic157—42no—
45#11929434—24no—
46C23×C157—22no—
47C23×C157—42no—
48C23×C157—82no—
49C23×C157C22⋊C412yes—
50C23×C157C2×D411yescharacteristic
51Q8×C157—22no—
52D4×C157—24no—
53D4×C157—22no—
54D4×C157—24no—
55D4×C157—41no—
56D4×C157—41no—
57D4×C157—84no—
58C2×C4×C157—22no—
59C2×C4×C157—22no—
60C2×C4×C157—22no—
61C2×C4×C157C22⋊C412yes—
62C2×C4×C157C22×C411yescharacteristic
63C2×C4×C157C2×D412yes—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157#4112yes—
66C22×C157—22no—
67C22×C157—41no—
68C22×C157—42no—
69C22×C157—44no—
70C22×C157—42no—
71C22×C157—84no—
72C22×C157C2×C22⋊C411yescharacteristic
73C22×C157#12112yes—
74C4×C157—22no—
75C4×C157—42no—
76C4×C157C4×D412yes—
77C4×C157#12011yescharacteristic
78C4×C157#12311yescharacteristic
79Dic157—82no—
80C2×C157—22no—
81C2×C157—21no—
82C2×C157—42no—
83C2×C157—82no—
84C2×C157#38611yescharacteristic
85C157#191011yescharacteristic, complemented, Sylow
86#1910—1571nomaximal, Sylow
87#568—1571no—
88#535D15711yescharacteristic
89#418—1572no—
90#410—1571no—
91H(3,ℤ/4)—1572no—
92C2×#41C2×D15711yescharacteristic
93C22×D4C2×D15711yescharacteristic
94#131—3144no—
95C2×M16—3142no—
96C2×M16—1572no—
97#127Dic15712yescomplemented
98#124Dic15712yescomplemented
99#121—22no—
100#120—22no—
101#117—1572no—
102#117C2×D15711yescharacteristic
103#102—3144no—
104#99—3142no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic15711yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic15712yes—
114C2×D4C2×Dic15711yescharacteristic
115C2×D4C22⋊D15712yes—
116C22×C4C22⋊D15712yes—
117C22×C4C22×D15711yescharacteristic
118M16—3144no—
119M16—3142no—
120M16—3142no—
121C2×C8—3144no—
122C2×C8—1574no—
123C4⋊C4—21no—
124C4⋊C4—3142no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—3142no—
128C42—3142no—
129C42C2×Dic15712yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic15712yes—
134C23C2×C22⋊D15711yescharacteristic
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—6282no—
146C2×C4C22⋊Dic15712yes—
147C2×C4C22×Dic15711yescharacteristic
148C2×C4D4×D15712yes—
149C2×C4C2×C22⋊D15711yescharacteristic
150C2×C4#1457895312yes—
151C8—3144no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic15711yescharacteristic
159C22#1909774312yes—
160C4—22no—
161C4—42no—
162C4—12562no—
163C4D4×Dic15712yes—
164C4#1909773911yescharacteristic
165C4#1909775211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2375715311yescharacteristic
subgroupG/H
centerC2#23757153
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting, prime radical#535×C157C2
socleC2×C157#386
cosocleC22×C4×C157C23
hypercenter#535D157
hypocenterC157#1910
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23758040C2semidirect
2. #23757278C2semidirect
3. #23757247C2semidirect
4. #23757029C2semidirect
14. #127×C157C4semidirect
15. #124×C157C4semidirect
23. C2×#11929434D4semidirect
85. C157#1910semidirect
97. #127Dic157semidirect
98. #124Dic157semidirect

Maximal subgroups

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

subgroupindex
#237580402
#237572782
#237572472
#237570292
#535×C1572
#1910157