Finite Group Databasebeta

← #34098736

Subgroups — #34098736

Order 20096.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D157C211yesmaximal, characteristic
2#23757328C211yesmaximal, characteristic
3#23757225C211yesmaximal, characteristic
4#23757015C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757014C211yesmaximal, characteristic, complemented
7#330×C157C211yesmaximal, characteristic, complemented
8C2×#14578937—21no—
9#19097763C2211yescharacteristic
10#19097762C411yescharacteristic
11#19097762C411yescharacteristic
12#19097761—21no—
13#19097761—21no—
14C4⋊C4×D157—21no—
15C4⋊C4×D157—21no—
16C4⋊C4×D157C411yescharacteristic
17C4⋊C4×D157C411yescharacteristic
18C42×D157C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21#19097682C2211yescharacteristic
22#19097682C2211yescharacteristic
23C8×Dic157—21no—
24#125×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×C4×D157—21no—
28C2×C4×D157—21no—
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157D411yescharacteristic
32#14578937—24no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157C2×C411yescharacteristic
38C4⋊Dic157C2×C411yescharacteristic
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578933—21no—
44#14578933—21no—
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C2×C8×C157—21no—
49C2×C8×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157C2×C411yescharacteristic
53C4⋊C4×C157C2×C411yescharacteristic
54C42×C157C2311yescharacteristic
55C22×D157C22⋊C411yescharacteristic
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157C22⋊C411yescharacteristic
59C2×Dic157C22⋊C411yescharacteristic
60C2×Dic157C22⋊C411yescharacteristic
61C4×D157—22no—
62C4×D157—22no—
63C4×D157—41no—
64C4×D157—42no—
65C4×D157—42no—
66#11929434—22no—
67#11929434—41no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157C22×C411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—22no—
74C8×C157—41no—
75C22×C157C2×C22⋊C411yescharacteristic
76C2×D157—21no—
77C2×D157—21no—
78C2×D157#10412yes—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82C4×C157—41no—
83C4×C157—41no—
84Dic157—21no—
85Dic157—21no—
86Dic157—41no—
87Dic157—41no—
88Dic157#10112yes—
89C2×C157C2×#10111yescharacteristic
90C2×C157C2×#10411yescharacteristic
91C2×C157#42111yescharacteristic
92D157—22no—
93C157#152811yescharacteristic, complemented, Sylow
94#1528—1571nomaximal, Sylow
95C2×#125—1571no—
96#432—1571no—
97C4×M16—1571no—
98#330—1571no—
99#330—1571no—
100#330—1571no—
101#330D15711yescharacteristic, complemented
102C2×M16—3141no—
103#125—3141no—
104#125—3141no—
105#125—1571no—
106#125—1571no—
107#125—1571no—
108#125C2×D15711yescharacteristic
109C2×C4⋊C4—3141no—
110C2×C4⋊C4—3141no—
111C2×C4⋊C4—1571no—
112C2×C4⋊C4—1571no—
113C2×C42—1571no—
114C4⋊C8—3141no—
115C22⋊C8—3141no—
116#97—1571no—
117#97—1571no—
118#97C2×D15711yescharacteristic
119#97C2×D15711yescharacteristic
120C4×C8—3141no—
121C22×C4—3141no—
122C22×C4—3141no—
123C22×C4—1571no—
124C22×C4—1571no—
125C22×C4—1571no—
126M16—3144no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—3141no—
130C2×C8—3141no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—3141no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C4⋊C4C4×D15711yescharacteristic
144C4⋊C4C4×D15711yescharacteristic
145C42—1571no—
146C42—1571no—
147C42—1571no—
148C42C22×D15711yescharacteristic
149C23—1571no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—3142no—
153C2×C4—3142no—
154C2×C4—3141no—
155C2×C4—3141no—
156C2×C4—6281no—
157C2×C4—6282no—
158C2×C4—6282no—
159C2×C4—1571no—
160C2×C4—1571no—
161C2×C4—1571no—
162C2×C4C2×C4×D15711yescharacteristic
163C2×C4D4×D15711yescharacteristic
164C2×C4D4×D15711yescharacteristic
165C8—22no—
166C8—41no—
167C8—3142no—
168C8—6281no—
169C22—3141no—
170C22—3141no—
171C22—1572no—
172C22C22⋊C4×D15711yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—3141no—
179C4—3141no—
180C4—6281no—
181C4—6281no—
182C4—1572no—
183C2—3142no—
184C2#101×D15711yescharacteristic
185C2#104×D15711yescharacteristic
186C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenter#330D157
hypocenterC157#1528
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #23757015C2semidirect
5. #23757014C2semidirect
6. #23757014C2semidirect
7. #330×C157C2semidirect
93. C157#1528semidirect
101. #330D157semidirect

Maximal subgroups

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

subgroupindex
#125×D1572
#237573282
#237572252
#237570152
#237570142
#330×C1572
#1528157