Finite Group Databasebeta

← #34099696

Subgroups — #34099696

Order 20096.

176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757619C211yesmaximal, characteristic, complemented
2#23757479C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic
4#23757350C211yesmaximal, characteristic, complemented
5#23757023C211yesmaximal, characteristic, complemented
6#23757018C211yesmaximal, characteristic, complemented
7#331×C157C211yesmaximal, characteristic, complemented
8C2×#14578943—21no—
9C2×#14578939—21no—
10C2×#14578937—21no—
11#19097771C2211yescharacteristic
12C4×D628C2211yescharacteristic
13C4⋊#11929434C2211yescharacteristic
14#19097696—21no—
15#19097692—21no—
16#19097692—21no—
17#19097692—21no—
18#19097683—21no—
19C4×#11929434C2211yescharacteristic
20#127×C157C2211yescharacteristic
21C4⋊C8×C157C2211yescharacteristic
22C4⋊C8×C157C2211yescharacteristic
23C2×Dic314—21no—
24C2×D628D411yescharacteristic
25C2×C4×D157—21no—
26#14578943—42no—
27#14578939—42no—
28#14578937—42no—
29C2×#11929434—21no—
30C2×#11929434D411yescharacteristic
31C2×#11929434D411yescharacteristic
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35#14578931—21no—
36C2×D4×C157—21no—
37C2×D4×C157—21no—
38C2×D4×C157—21no—
39C2×C8×C157—21no—
40C2×C8×C157—21no—
41C42×C157C2311yescharacteristic
42C22×D157—21no—
43Dic314—41no—
44Dic314—41no—
45D628—21no—
46D628—21no—
47C2×Dic157—21no—
48C2×Dic157—41no—
49C4×D157—41no—
50C4×D157—41no—
51#11929434—21no—
52#11929434—21no—
53#11929434—41no—
54C23×C157—41no—
55D4×C157—41no—
56D4×C157—41no—
57D4×C157—41no—
58D4×C157—41no—
59D4×C157—81no—
60C2×C4×C157C2×D411yescharacteristic
61C2×C4×C157C2×D411yescharacteristic
62C2×C4×C157#4111yescharacteristic
63C8×C157—41no—
64C8×C157—41no—
65C22×C157—81no—
66C22×C157—81no—
67C22×C157—81no—
68C22×C157#12111yescharacteristic
69C2×D157—41no—
70C2×D157—41no—
71C2×D157—41no—
72C4×C157—21no—
73C4×C157#13511yescharacteristic
74C4×C157AGL(1,ℤ/8)11yescharacteristic
75C4×C157AGL(1,ℤ/8)11yescharacteristic
76C4×C157AGL(1,ℤ/8)11yescharacteristic
77Dic157—41no—
78Dic157—81no—
79C2×C157—161no—
80C2×C157#46311yescharacteristic
81C2×C157#46911yescharacteristic
82C2×C157#47111yescharacteristic
83D157—81no—
84C157#170111yescharacteristic, complemented, Sylow
85#1701—1571nomaximal, Sylow
86#486—1571no—
87#461—1571no—
88#459—1571no—
89#436—1571no—
90#334—1571no—
91#332—1571no—
92#331D15711yescharacteristic, complemented
93C2×SD16—3141no—
94C2×D8—3141no—
95C2×M16—3141no—
96C4⋊Q8—1571no—
97#127C2×D15711yescharacteristic
98C4×D4—1571no—
99C4⋊C8—1571no—
100C4⋊C8C2×D15711yescharacteristic
101C4⋊C8C2×D15711yescharacteristic
102#103—3141no—
103#102—3141no—
104#102—3141no—
105#102—3141no—
106C22⋊C8—3141no—
107C4×C8—1571no—
108C2×Q8—3141no—
109C2×D4—21no—
110C2×D4—21no—
111C2×D4—21no—
112C2×D4—1571no—
113C22×C4—3141no—
114SD16—6282no—
115D8—6282no—
116M16—6282no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—3141no—
120C2×C8—1571no—
121C2×C8—1571no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—1571no—
125C22⋊C4—3141no—
126C42C22×D15711yescharacteristic
127C23—41no—
128C23—3141no—
129Q8—6281no—
130Q8—6281no—
131D4—41no—
132D4—41no—
133D4—41no—
134D4—41no—
135D4—81no—
136D4—3141no—
137D4—3141no—
138C2×C4—3141no—
139C2×C4—6281no—
140C2×C4—6281no—
141C2×C4—6281no—
142C2×C4D4×D15711yescharacteristic
143C2×C4D4×D15711yescharacteristic
144C2×C4#1457895411yescharacteristic
145C8—41no—
146C8—41no—
147C8—3141no—
148C8—3141no—
149C8—6281no—
150C22—81no—
151C22—81no—
152C22—81no—
153C22—6281no—
154C22—6281no—
155C22—6281no—
156C22#1909774411yescharacteristic
157C4—21no—
158C4—6281no—
159C4—12561no—
160C4#1909779211yescharacteristic
161C4#1909779511yescharacteristic
162C4#1909779511yescharacteristic
163C4#1909779811yescharacteristic
164C2—161no—
165C2—12561no—
166C2#2375748711yescharacteristic
167C2#2375752511yescharacteristic
168C2#2375753511yescharacteristic
subgroupG/H
centerC22#19097744
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#331×C157C2
socleC22×C157#121
prime radical#23757465C2
hypercenter#331D157
hypocenterC157#1701
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #23757619C2semidirect
2. #23757479C2semidirect
4. #23757350C2semidirect
5. #23757023C2semidirect
6. #23757018C2semidirect
7. #331×C157C2semidirect
84. C157#1701semidirect
92. #331D157semidirect

Maximal subgroups

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

subgroupindex
#237576192
#237574792
#237574652
#237573502
#237570232
#237570182
#331×C1572
#1701157