Finite Group Databasebeta

← #34098766

Subgroups — #34098766

Order 20096.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757808C211yesmaximal, characteristic
2#23757328C211yesmaximal, characteristic, complemented
3#23757328C211yesmaximal, characteristic, complemented
4#23757015C211yesmaximal, characteristic, complemented
5#23757012C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#330×C157C211yesmaximal, characteristic, complemented
8#19097766—21no—
9#19097759C2211yescharacteristic
10#19097756—21no—
11#19097751C411yescharacteristic
12#19097746C411yescharacteristic
13#19097736C411yescharacteristic
14#19097733—21no—
15#19097733C411yescharacteristic
16#19097729—21no—
17C42×D157C2211yescharacteristic
18#19097700—21no—
19#19097700—21no—
20#19097683—21no—
21#19097683—21no—
22#19097682C2211yescharacteristic
23#19097682C2211yescharacteristic
24#125×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×Dic314C2×C411yescharacteristic
28C2×D628—21no—
29C2×D628C2×C411yescharacteristic
30C2×C4×D157—21no—
31C2×C4×D157C2×C411yescharacteristic
32C2×C4×D157D411yescharacteristic
33C2×C4×D157D411yescharacteristic
34C2×#11929434—21no—
35C2×#11929434—21no—
36C4⋊Dic157—21no—
37#14578933—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42#14578931—21no—
43C4×Dic157—21no—
44C4×Dic157C2×C411yescharacteristic
45C4×Dic157D411yescharacteristic
46C4×Dic157D411yescharacteristic
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157C2×C411yescharacteristic
52C4⋊C4×C157C2×C411yescharacteristic
53C42×C157C2311yescharacteristic
54C22×D157—21no—
55C22×D157C22⋊C411yescharacteristic
56Dic314—41no—
57D628—41no—
58D628—42no—
59C2×Dic157—21no—
60C2×Dic157C22⋊C411yescharacteristic
61C2×Dic157C22⋊C411yescharacteristic
62C2×Dic157C22⋊C411yescharacteristic
63C4×D157—41no—
64C4×D157—41no—
65C4×D157—41no—
66C4×D157—42no—
67#11929434—41no—
68#11929434—41no—
69C2×C4×C157—21no—
70C2×C4×C157—21no—
71C2×C4×C157C22×C411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—41no—
75C8×C157—41no—
76C22×C157C2×C22⋊C411yescharacteristic
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—21no—
80C2×D157—41no—
81C2×D157—41no—
82C2×D157—41no—
83C4×C157—21no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—41no—
87C4×C157—41no—
88Dic157—21no—
89Dic157—21no—
90Dic157—21no—
91Dic157—41no—
92C2×C157#41311yescharacteristic
93C2×C157#42111yescharacteristic
94C2×C157#42111yescharacteristic
95D157—41no—
96D157—81no—
97C157#153511yescharacteristic, complemented, Sylow
98#1535—1571nomaximal, Sylow
99#529—1571no—
100#432—1571no—
101#432—1571no—
102#330—1571no—
103#330D15711yescharacteristic, complemented
104#329—1571no—
105#329—1571no—
106#126—3141no—
107#125C2×D15711yescharacteristic
108#124—1571no—
109#123—3141no—
110C22⋊Q8—1571no—
111#121—1571no—
112C4×Q8—1571no—
113C4×D4—3141no—
114C4×D4—1571no—
115#117—3141no—
116C2×C42—1571no—
117C4⋊C8—3141no—
118C4⋊C8—3141no—
119C22⋊C8—3141no—
120C22⋊C8—3141no—
121#97—1571no—
122#97—1571no—
123#97C2×D15711yescharacteristic
124#97C2×D15711yescharacteristic
125C2×Q8—1571no—
126C2×D4—3141no—
127C2×D4—1571no—
128C22×C4—3141no—
129C22×C4—1571no—
130C22×C4—1571no—
131C22×C4—1571no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—3141no—
135C2×C8—3141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4C4×D15711yescharacteristic
141C4⋊C4C4×D15711yescharacteristic
142C22⋊C4—3141no—
143C22⋊C4—3141no—
144C22⋊C4—3141no—
145C22⋊C4—3141no—
146C22⋊C4—3141no—
147C42—3141no—
148C42—1571no—
149C42—1571no—
150C42—1571no—
151C42C22×D15711yescharacteristic
152C23—3141no—
153C23—1571no—
154Q8—6281no—
155D4—6281no—
156D4—6282no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—6281no—
162C2×C4—6281no—
163C2×C4—6282no—
164C2×C4—1571no—
165C2×C4—1571no—
166C2×C4—1571no—
167C2×C4C2×C4×D15711yescharacteristic
168C2×C4D4×D15711yescharacteristic
169C2×C4D4×D15711yescharacteristic
170C8—41no—
171C8—41no—
172C8—6281no—
173C8—6281no—
174C22—3141no—
175C22—3141no—
176C22—3141no—
177C22—6281no—
178C22—6281no—
179C22—6281no—
180C22C22⋊C4×D15711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—3141no—
187C4—3141no—
188C4—3141no—
189C4—6281no—
190C2—6281no—
191C2—12561no—
192C2#2375725611yescharacteristic
193C2#2375728811yescharacteristic
194C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097746C4
cosocleC42×C157C23
hypercenter#330D157
hypocenterC157#1535
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
2. #23757328C2semidirect
3. #23757328C2semidirect
4. #23757015C2semidirect
5. #23757012C2semidirect
6. #23757012C2semidirect
7. #330×C157C2semidirect
97. C157#1535semidirect
103. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237578082
#237573282
#237570152
#237570122
#330×C1572
#1535157