Finite Group Databasebeta

← #34098792

Subgroups — #34098792

Order 20096.

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

normal subgroups only

This group has 212 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#23757325C211yesmaximal, characteristic
3C4⋊C8×D157C211yesmaximal, characteristic
4#23757021C211yesmaximal, characteristic, complemented
5#23757021C211yesmaximal, characteristic, complemented
6#23757019C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8C2×C8×D157—21no—
9#19097771C2211yescharacteristic
10#19097762—21no—
11#19097751C412yes—
12#19097747—21no—
13Q8×Dic157—21no—
14#19097736C412yes—
15#19097729—21no—
16C42×D157C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21C8×Dic157—21no—
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25C2×Dic314C2×C412yes—
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157D411yescharacteristic
29C2×#11929434—21no—
30C2×#11929434—21no—
31C8×D157—42no—
32C4⋊Dic157—22no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35#14578933—22no—
36#14578931—22no—
37C4×Dic157—22no—
38C4×Dic157C2×C411yescharacteristic
39C4×Dic157D411yescharacteristic
40C4×Dic157D411yescharacteristic
41C2×Q8×C157—21no—
42C2×C8×C157—21no—
43C2×C8×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157C2×C412yes—
46C42×C157C2311yescharacteristic
47C22×D157C22⋊C411yescharacteristic
48Dic314—42no—
49C2×Dic157—22no—
50C2×Dic157C22⋊C411yescharacteristic
51C2×Dic157C22⋊C411yescharacteristic
52C2×Dic157C22⋊C411yescharacteristic
53C4×D157—21no—
54C4×D157—21no—
55C4×D157—41no—
56C4×D157SD1612yes—
57C4×D157Q1612yes—
58#11929434—41no—
59#11929434—41no—
60Q8×C157—41no—
61Q8×C157—41no—
62C2×C4×C157—22no—
63C2×C4×C157C22×C411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C8×C157—41no—
67C8×C157—41no—
68C22×C157C2×C22⋊C411yescharacteristic
69C2×D157—21no—
70C2×D157—21no—
71C2×D157#10312yes—
72C4×C157—21no—
73C4×C157—42no—
74C4×C157C2×SD1611yescharacteristic
75C4×C157C2×Q1611yescharacteristic
76C4×C157#13511yescharacteristic
77C4×C157#13511yescharacteristic
78Dic157—21no—
79Dic157—21no—
80Dic157—42no—
81Dic157#10312yes—
82C2×C157#41311yescharacteristic
83C2×C157C2×#10311yescharacteristic
84C2×C157#41611yescharacteristic
85D157—22no—
86C157#154211yescharacteristic, complemented, Sylow
87#1542—1571nomaximal, Sylow
88#533—1571no—
89#431—1571no—
90C2×C4⋊C8—1571no—
91#333—1571no—
92#333—1571no—
93#332—1571no—
94#332D15711yescharacteristic, complemented
95C22×C8—3141no—
96C4⋊Q8—1571no—
97C4⋊Q8C2×D15711yescharacteristic
98#125—3141no—
99C22⋊Q8—3141no—
100C22⋊Q8—1572no—
101C4×Q8—3141no—
102C4×Q8—1572no—
103#117—3141no—
104C2×C42—1571no—
105C4⋊C8—3141no—
106C4⋊C8—1571no—
107C4⋊C8—1571no—
108C4⋊C8C2×D15711yescharacteristic
109C4⋊C8C2×D15711yescharacteristic
110C22⋊C8—3141no—
111C4×C8—3141no—
112C2×Q8—21no—
113C2×Q8—1572no—
114C22×C4—1571no—
115C22×C4—1571no—
116C22×C4—1571no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—3141no—
120C2×C8—3141no—
121C2×C8—6282no—
122C4⋊C4—21no—
123C4⋊C4—3142no—
124C4⋊C4—3142no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4C4×D15712yes—
128C22⋊C4—3142no—
129C42—3142no—
130C42—1571no—
131C42—1571no—
132C42—1571no—
133C42C22×D15711yescharacteristic
134C23—1571no—
135Q8—41no—
136Q8—41no—
137Q8—6282no—
138C2×C4—22no—
139C2×C4—3141no—
140C2×C4—3141no—
141C2×C4—3142no—
142C2×C4—6281no—
143C2×C4—1571no—
144C2×C4—1571no—
145C2×C4—1571no—
146C2×C4—1572no—
147C2×C4—1572no—
148C2×C4C2×C4×D15711yescharacteristic
149C2×C4D4×D15711yescharacteristic
150C2×C4D4×D15711yescharacteristic
151C8—41no—
152C8—41no—
153C8—6281no—
154C8—6281no—
155C22—3141no—
156C22—3141no—
157C22—1572no—
158C22C22⋊C4×D15711yescharacteristic
159C4—21no—
160C4—42no—
161C4—3141no—
162C4—3141no—
163C4—6282no—
164C4—1572no—
165C4SD16×D15711yescharacteristic
166C4Q16×D15711yescharacteristic
167C4#1909779011yescharacteristic
168C4#1909779211yescharacteristic
169C2—3142no—
170C2#2375725611yescharacteristic
171C2#103×D15711yescharacteristic
172C2#2375726611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenter#332D157
hypocenterC157#1542
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #23757021C2semidirect
5. #23757021C2semidirect
6. #23757019C2semidirect
7. #332×C157C2semidirect
86. C157#1542semidirect
94. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237578282
#237573252
C4⋊C8×D1572
#237570212
#237570192
#332×C1572
#1542157