Finite Group Databasebeta

← #34098758

Subgroups — #34098758

Order 20096.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D157C211yesmaximal, characteristic
2#23757328C212yesmaximal, complemented
3#23757013C211yesmaximal, characteristic, complemented
4#23757012C212yesmaximal, complemented
5#329×C157C211yesmaximal, characteristic, complemented
6C2×Q8×D157C411yescharacteristic
7C2×D4×D157C411yescharacteristic
8#19097760C411yescharacteristic
9#19097759C2211yescharacteristic
10#19097758C411yescharacteristic
11#19097757—22no—
12C22⋊C4×D157—22no—
13C42×D157C2211yescharacteristic
14#19097700—22no—
15#19097683—22no—
16#19097682C2212yescomplemented
17#124×C157C2211yescharacteristic
18#97×C157C2212yescomplemented
19C23×D157—21no—
20C2×Dic314—21no—
21C2×Dic314C2×C411yescharacteristic
22Q8×D157—42no—
23C2×D628C2×C411yescharacteristic
24C2×C22⋊D157—21no—
25D4×D157—42no—
26C2×C4×D157—21no—
27C2×C4×D157C2×C411yescharacteristic
28C2×C4×D157D412yes—
29C2×#11929434—22no—
30C22⋊Dic157—22no—
31#14578931—22no—
32#14578931—22no—
33C4×Dic157C2×C411yescharacteristic
34C4×Dic157D412yes—
35C2×Q8×C157C2×C411yescharacteristic
36C2×D4×C157C2×C411yescharacteristic
37C2×C8×C157—22no—
38C22⋊C4×C157—22no—
39C42×C157C2311yescharacteristic
40C22×D157—21no—
41C22×D157—44no—
42C22×D157—42no—
43C22×D157C22⋊C411yescharacteristic
44Dic314—42no—
45Dic314—41no—
46D628—41no—
47C22⋊D157—42no—
48C2×Dic157—21no—
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C22⋊C412yes—
51C4×D157—22no—
52C4×D157—42no—
53C4×D157—42no—
54#11929434—42no—
55C23×C157—21no—
56Q8×C157—41no—
57D4×C157—41no—
58C2×C4×C157—21no—
59C2×C4×C157C22×C411yescharacteristic
60C2×C4×C157C2×D412yes—
61C8×C157—42no—
62C22×C157—41no—
63C22×C157—42no—
64C22×C157C2×C22⋊C411yescharacteristic
65C2×D157—22no—
66C2×D157—41no—
67C2×D157—42no—
68C2×D157—84no—
69C2×D157#10012yes—
70C4×C157—21no—
71C4×C157—22no—
72C4×C157—41no—
73Dic157—21no—
74Dic157—22no—
75Dic157—41no—
76C2×C157—81no—
77C2×C157C2×#10011yescharacteristic
78C2×C157#42112yes—
79D157—22no—
80D157—81no—
81C157#153311yescharacteristic, complemented, Sylow
82#1533—1571nomaximal, Sylow
83C2×#124—1571no—
84#432—1572no—
85#329—1571no—
86#329—1572no—
87#329D15711yescharacteristic, complemented
88C22×Q8—1571no—
89C22×D4—1571no—
90#124—3142no—
91#124—1571no—
92#124—1571no—
93#124—1571no—
94#124C2×D15711yescharacteristic
95C2×C22⋊C4—3142no—
96C2×C42—1571no—
97C4⋊C8—3142no—
98C22⋊C8—3142no—
99#97—1572no—
100#97C2×D15712yescomplemented
101C24—3141no—
102C2×Q8—3141no—
103C2×Q8—6282no—
104C2×Q8—1571no—
105C2×Q8C4×D15711yescharacteristic
106C2×D4—3141no—
107C2×D4—6282no—
108C2×D4—1571no—
109C2×D4C4×D15711yescharacteristic
110C22×C4—3141no—
111C22×C4—1571no—
112C22×C4—1572no—
113C2×C8—22no—
114C2×C8—3142no—
115C22⋊C4—22no—
116C22⋊C4—3142no—
117C22⋊C4—3142no—
118C22⋊C4—3142no—
119C42—1571no—
120C42—1572no—
121C42C22×D15711yescharacteristic
122C23—21no—
123C23—3141no—
124C23—6284no—
125C23—6282no—
126C23—1571no—
127Q8—41no—
128Q8—6281no—
129Q8—6282no—
130D4—41no—
131D4—6281no—
132D4—6282no—
133C2×C4—21no—
134C2×C4—3142no—
135C2×C4—3141no—
136C2×C4—6282no—
137C2×C4—6282no—
138C2×C4—1572no—
139C2×C4—1571no—
140C2×C4C2×C4×D15711yescharacteristic
141C2×C4D4×D15712yes—
142C8—42no—
143C8—6282no—
144C22—41no—
145C22—42no—
146C22—3142no—
147C22—6281no—
148C22—6282no—
149C22—1572no—
150C22—12564no—
151C22C22⋊C4×D15711yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—3141no—
156C4—3142no—
157C4—6281no—
158C2—81no—
159C2—3142no—
160C2—12561no—
161C2#100×D15711yescharacteristic
162C2#2375728812yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×D4×D157C4
cosocleC42×C157C23
hypercenter#329D157
hypocenterC157#1533
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23757328C2semidirect
3. #23757013C2semidirect
4. #23757012C2semidirect
5. #329×C157C2semidirect
16. #19097682C22semidirect
18. #97×C157C22semidirect
81. C157#1533semidirect
87. #329D157semidirect
100. #97C2×D157semidirect

Maximal subgroups

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

subgroupindex
#124×D1572
#237573282
#237570132
#237570122
#329×C1572
#1533157