Finite Group Databasebeta

← #34098823

Subgroups — #34098823

Order 20096.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757828C211yesmaximal, characteristic
2#23757295C211yesmaximal, characteristic
3C4⋊C8×D157C211yesmaximal, characteristic
4#23757022C211yesmaximal, characteristic, complemented
5#23757020C211yesmaximal, characteristic, complemented
6#23757018C211yesmaximal, characteristic, complemented
7#333×C157C211yesmaximal, characteristic, complemented
8C2×#14578937—21no—
9C2×C8×D157—21no—
10#19097771C2211yescharacteristic
11#19097762—21no—
12#19097751—21no—
13#19097747C412yes—
14Q8×Dic157C412yes—
15#19097736—21no—
16#19097729—21no—
17C42×D157C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19C4⋊#11929434C2211yescharacteristic
20#19097700—21no—
21#19097700—21no—
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157D411yescharacteristic
29#14578937—42no—
30C2×#11929434—21no—
31C2×#11929434—21no—
32C8×D157—42no—
33C4⋊Dic157—22no—
34C4⋊Dic157—21no—
35C4⋊Dic157C2×C412yes—
36#14578933—22no—
37#14578931—22no—
38C4×Dic157—22no—
39C4×Dic157C2×C411yescharacteristic
40C4×Dic157D411yescharacteristic
41C4×Dic157D411yescharacteristic
42C2×Q8×C157C2×C412yes—
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157—21no—
47C42×C157C2311yescharacteristic
48C22×D157C22⋊C411yescharacteristic
49Dic314—41no—
50Dic314—41no—
51C2×Dic157—22no—
52C2×Dic157C22⋊C411yescharacteristic
53C2×Dic157C22⋊C411yescharacteristic
54C2×Dic157C22⋊C411yescharacteristic
55C4×D157—21no—
56C4×D157—21no—
57C4×D157—41no—
58C4×D157SD1612yes—
59C4×D157Q1612yes—
60#11929434—41no—
61#11929434—41no—
62Q8×C157—42no—
63C2×C4×C157—22no—
64C2×C4×C157C22×C411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C8×C157—41no—
68C8×C157—41no—
69C22×C157C2×C22⋊C411yescharacteristic
70C2×D157—21no—
71C2×D157—21no—
72C2×D157#10312yes—
73C4×C157—21no—
74C4×C157—42no—
75C4×C157C2×SD1611yescharacteristic
76C4×C157C2×Q1611yescharacteristic
77C4×C157AGL(1,ℤ/8)11yescharacteristic
78C4×C157#13711yescharacteristic
79Dic157—21no—
80Dic157—21no—
81Dic157—42no—
82Dic157#10312yes—
83C2×C157#41311yescharacteristic
84C2×C157C2×#10311yescharacteristic
85C2×C157#41711yescharacteristic
86D157—22no—
87C157#155011yescharacteristic, complemented, Sylow
88#1550—1571nomaximal, Sylow
89#533—1571no—
90#423—1571no—
91C2×C4⋊C8—1571no—
92#333—1571no—
93#333D15711yescharacteristic, complemented
94#332—1571no—
95#332—1571no—
96C2×M16—3141no—
97C22×C8—3141no—
98C4⋊Q8—1571no—
99C4⋊Q8C2×D15711yescharacteristic
100#125—3141no—
101C22⋊Q8—3141no—
102C22⋊Q8—1572no—
103C4×Q8—3141no—
104C4×Q8—1572no—
105#117—3141no—
106C2×C42—1571no—
107C4⋊C8—3141no—
108C4⋊C8—3141no—
109C4⋊C8—1571no—
110C4⋊C8—1571no—
111C4⋊C8C2×D15711yescharacteristic
112C4⋊C8C2×D15711yescharacteristic
113C2×Q8—3141no—
114C2×Q8C4×D15712yes—
115C22×C4—1571no—
116C22×C4—1571no—
117C22×C4—1571no—
118M16—6282no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—3141no—
122C2×C8—3141no—
123C2×C8—6282no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3142no—
127C4⋊C4—3142no—
128C4⋊C4—3141no—
129C4⋊C4—1572no—
130C22⋊C4—3142no—
131C42—3142no—
132C42—1571no—
133C42—1571no—
134C42—1571no—
135C42C22×D15711yescharacteristic
136C23—1571no—
137Q8—42no—
138Q8—6281no—
139Q8—6281no—
140C2×C4—22no—
141C2×C4—3141no—
142C2×C4—3141no—
143C2×C4—3142no—
144C2×C4—6281no—
145C2×C4—1571no—
146C2×C4—1571no—
147C2×C4—1571no—
148C2×C4—1572no—
149C2×C4—1572no—
150C2×C4C2×C4×D15711yescharacteristic
151C2×C4D4×D15711yescharacteristic
152C2×C4D4×D15711yescharacteristic
153C8—41no—
154C8—41no—
155C8—6281no—
156C8—6281no—
157C22—3141no—
158C22—3141no—
159C22—1572no—
160C22C22⋊C4×D15711yescharacteristic
161C4—21no—
162C4—42no—
163C4—3141no—
164C4—3141no—
165C4—6282no—
166C4—1572no—
167C4SD16×D15711yescharacteristic
168C4Q16×D15711yescharacteristic
169C4#1909779811yescharacteristic
170C4#1909780311yescharacteristic
171C2—3142no—
172C2#2375725411yescharacteristic
173C2#103×D15711yescharacteristic
174C2#2375727311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#333×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenter#333D157
hypocenterC157#1550
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #23757022C2semidirect
5. #23757020C2semidirect
6. #23757018C2semidirect
7. #333×C157C2semidirect
87. C157#1550semidirect
93. #333D157semidirect

Maximal subgroups

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

subgroupindex
#237578282
#237572952
C4⋊C8×D1572
#237570222
#237570202
#237570182
#333×C1572
#1550157