Finite Group Databasebeta

← #34115639

Subgroups — #34115639

Order 20096.

246 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 62 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#23758290C212yesmaximal, complemented
2#23758133C212yesmaximal, complemented
3#23758131C212yesmaximal, complemented
4#23757819C211yesmaximal, characteristic
5#19097838C2214yes—
6C22⋊#11929441—22no—
7C4×#11929441—22no—
8C2×#14578954C411yescharacteristic
9#19097769C2211yescharacteristic
10#19097767C2211yescharacteristic
11#19097760C411yescharacteristic
12#19097758C411yescharacteristic
13#19097743—22no—
14C4×C22⋊D157—22no—
15C2×C4×Dic157C2211yescharacteristic
16C2×#41×C157C411yescharacteristic
17C2×#11929441—24no—
18#14578954—42no—
19C2×Dic314C2×C411yescharacteristic
20C2×D628C2×C411yescharacteristic
21C2×C22⋊D157—22no—
22C2×C22⋊D157—21no—
23C22×Dic157D412yes—
24C2×C4×D157—21no—
25#14578933—22no—
26C22⋊Dic157—22no—
27#14578931—22no—
28C4×Dic157C2×C411yescharacteristic
29C4×Dic157D412yes—
30C4×Dic157C2311yescharacteristic
31#41×C157—42no—
32C2×Q8×C157C2×C411yescharacteristic
33C2×D4×C157—21no—
34C2×D4×C157C2×C411yescharacteristic
35C22×C4×C157—21no—
36C22×C4×C157C2×C411yescharacteristic
37#11929441—44no—
38C22×D157—21no—
39Dic314—41no—
40D628—41no—
41C22⋊D157—42no—
42C22⋊D157—44no—
43C2×Dic157—24no—
44C2×Dic157—21no—
45C2×Dic157C22⋊C412yes—
46C2×Dic157C2×D412yes—
47C4×D157—42no—
48C23×C157—21no—
49C23×C157C22⋊C411yescharacteristic
50Q8×C157—41no—
51D4×C157—41no—
52D4×C157—42no—
53C2×C4×C157—22no—
54C2×C4×C157—21no—
55C2×C4×C157—42no—
56C2×C4×C157C22⋊C411yescharacteristic
57C2×C4×C157C22×C411yescharacteristic
58C22×C157—21no—
59C22×C157—22no—
60C22×C157—41no—
61C22×C157—42no—
62C22×C157C2×C22⋊C411yescharacteristic
63C2×D157—41no—
64C2×D157—42no—
65C4×C157—21no—
66C4×C157—41no—
67C4×C157#10012yes—
68Dic157—22no—
69Dic157—41no—
70Dic157#13514yes—
71C2×C157—41no—
72C2×C157—81no—
73C2×C157C2×#10011yescharacteristic
74C2×C157#41612yes—
75D157—81no—
76C157#154311yescharacteristic, complemented, Sylow
77#1543—1571nomaximal, Sylow
78#532—1571no—
79#431—1572no—
80#333—1572no—
81#331—1572no—
82C2×#41—1571no—
83C2×#41#1059784511yescharacteristic
84C4⋊Q8—1571no—
85#127—1571no—
86#124—1571no—
87#124—1571no—
88#121—3142no—
89C4×D4—3142no—
90C2×C42—1571no—
91C4⋊C8—1574no—
92C22⋊C8—3142no—
93C4×C8—3142no—
94#41—42no—
95#41—6282no—
96C2×Q8—1571no—
97C2×Q8C2×#1059784511yescharacteristic
98C2×D4—21no—
99C2×D4—3141no—
100C2×D4—3142no—
101C2×D4—1571no—
102C2×D4C2×#1059784511yescharacteristic
103C22×C4—21no—
104C22×C4—3141no—
105C22×C4—1572no—
106C22×C4C2×#1059784511yescharacteristic
107C2×C8—3144no—
108C4⋊C4—3142no—
109C22⋊C4—3142no—
110C22⋊C4—3142no—
111C42—1572no—
112C42—1571no—
113C42—1571no—
114C23—21no—
115C23—3141no—
116C23C22⋊#1059784511yescharacteristic
117Q8—41no—
118Q8—6281no—
119D4—41no—
120D4—42no—
121D4—6281no—
122D4—6282no—
123D4—6284no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—42no—
127C2×C4—3144no—
128C2×C4—3141no—
129C2×C4—6282no—
130C2×C4—1572no—
131C2×C4—1572no—
132C2×C4C22⋊#1059784511yescharacteristic
133C2×C4C22×#1059784511yescharacteristic
134C8—6284no—
135C22—21no—
136C22—22no—
137C22—41no—
138C22—42no—
139C22—6281no—
140C22—6282no—
141C22C2×C22⋊#1059784511yescharacteristic
142C4—21no—
143C4—41no—
144C4—3142no—
145C4—6281no—
146C4—1574no—
147C4#1909783112yes—
148C2—41no—
149C2—81no—
150C2—12561no—
151C2C2×#1909783111yescharacteristic
152C2#2375826312yes—
subgroupG/H
centerC2×C4C22⋊#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC2×#41×C157C4
socleC22×C157C2×C22⋊C4
prime radical#23757819C2
cosocleC4×Dic157C23
hypercenterC2×#41#10597845
hypocenterC157#1543
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23758290C2semidirect
2. #23758133C2semidirect
3. #23758131C2semidirect
76. C157#1543semidirect

Maximal subgroups

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

subgroupindex
#237582902
#237581332
#237581312
#237578192
#1543157