Finite Group Databasebeta

← #34098740

Subgroups — #34098740

Order 20096.

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

normal subgroups only

This group has 216 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#23757802C211yesmaximal, characteristic
2#23757328C211yesmaximal, characteristic, complemented
3#23757225C211yesmaximal, characteristic, complemented
4#23757014C211yesmaximal, characteristic, complemented
5#23757014C211yesmaximal, characteristic, complemented
6#23757013C211yesmaximal, characteristic, complemented
7#329×C157C211yesmaximal, characteristic, complemented
8C2×#14578937—21no—
9#19097764—21no—
10#19097763C2211yescharacteristic
11#19097753—21no—
12#19097747C411yescharacteristic
13#19097742C411yescharacteristic
14Q8×Dic157C411yescharacteristic
15D4×Dic157C411yescharacteristic
16#19097731—21no—
17#19097727—21no—
18C42×D157C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21#19097682C2211yescharacteristic
22#19097682C2211yescharacteristic
23C8×Dic157—21no—
24#124×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×C22⋊D157—21no—
28C22×Dic157—21no—
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157D411yescharacteristic
32#14578937—24no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157C2×C411yescharacteristic
37C4⋊Dic157C2×C411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43#14578931—21no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C2×Q8×C157C2×C411yescharacteristic
49C2×D4×C157C2×C411yescharacteristic
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C22⋊C4×C157—21no—
53C22⋊C4×C157—21no—
54C42×C157C2311yescharacteristic
55C22×D157C22⋊C411yescharacteristic
56C22⋊D157—42no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—42no—
60C2×Dic157C22⋊C411yescharacteristic
61C2×Dic157C22⋊C411yescharacteristic
62C2×Dic157C22⋊C411yescharacteristic
63C4×D157—22no—
64C4×D157—41no—
65C4×D157—41no—
66#11929434—22no—
67#11929434—41no—
68C23×C157—21no—
69Q8×C157—41no—
70D4×C157—41no—
71C2×C4×C157—21no—
72C2×C4×C157C22×C411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C8×C157—22no—
76C8×C157—41no—
77C22×C157—41no—
78C22×C157—41no—
79C22×C157—41no—
80C22×C157C2×C22⋊C411yescharacteristic
81C2×D157—21no—
82C2×D157—21no—
83C2×D157—21no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—21no—
87C4×C157—41no—
88Dic157—21no—
89Dic157—21no—
90Dic157—41no—
91Dic157—41no—
92Dic157#10412yes—
93C2×C157—81no—
94C2×C157#41311yescharacteristic
95C2×C157C2×#10411yescharacteristic
96C2×C157#42111yescharacteristic
97D157—41no—
98C157#152911yescharacteristic, complemented, Sylow
99#1529—1571nomaximal, Sylow
100#529—1571no—
101#432—1571no—
102C4×M16—1571no—
103#330—1571no—
104#330—1571no—
105#329—1571no—
106#329D15711yescharacteristic, complemented
107C2×M16—3141no—
108#126—3141no—
109#125—1571no—
110#124C2×D15711yescharacteristic
111#123—3141no—
112C22⋊Q8—1571no—
113#121—1571no—
114C4×Q8—1571no—
115C4×D4—3141no—
116C4×D4—1571no—
117#117—3141no—
118C2×C42—1571no—
119C4⋊C8—3141no—
120C22⋊C8—3141no—
121#97—1571no—
122#97—1571no—
123#97C2×D15711yescharacteristic
124#97C2×D15711yescharacteristic
125C4×C8—3141no—
126C2×Q8C4×D15711yescharacteristic
127C2×D4—3141no—
128C2×D4C4×D15711yescharacteristic
129C22×C4—3141no—
130C22×C4—1571no—
131C22×C4—1571no—
132C22×C4—1571no—
133M16—3144no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3141no—
137C2×C8—3141no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—1571no—
143C4⋊C4—1571no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—3141no—
147C22⋊C4—3141no—
148C22⋊C4—3141no—
149C42—3141no—
150C42—1571no—
151C42—1571no—
152C42—1571no—
153C42C22×D15711yescharacteristic
154C23—21no—
155C23—1571no—
156Q8—41no—
157D4—41no—
158D4—6282no—
159C2×C4—21no—
160C2×C4—3142no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—6281no—
164C2×C4—6281no—
165C2×C4—6282no—
166C2×C4—1571no—
167C2×C4—1571no—
168C2×C4—1571no—
169C2×C4C2×C4×D15711yescharacteristic
170C2×C4D4×D15711yescharacteristic
171C2×C4D4×D15711yescharacteristic
172C8—22no—
173C8—41no—
174C8—3142no—
175C8—6281no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—3141no—
180C22—3141no—
181C22—3141no—
182C22C22⋊C4×D15711yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—3141no—
188C4—3141no—
189C4—6281no—
190C4—6281no—
191C4—1572no—
192C2—81no—
193C2—6281no—
194C2#2375725411yescharacteristic
195C2#104×D15711yescharacteristic
196C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097742C4
cosocleC42×C157C23
hypercenter#329D157
hypocenterC157#1529
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. #23757225C2semidirect
4. #23757014C2semidirect
5. #23757014C2semidirect
6. #23757013C2semidirect
7. #329×C157C2semidirect
98. C157#1529semidirect
106. #329D157semidirect

Maximal subgroups

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

subgroupindex
#237578022
#237573282
#237572252
#237570142
#237570132
#329×C1572
#1529157