Finite Group Databasebeta

← #34098697

Subgroups — #34098697

Order 20096.

264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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#23757823C211yesmaximal, characteristic
2#23757139C211yesmaximal, characteristic, complemented
3#23757008C214yesmaximal, complemented
4#431×C157C211yesmaximal, characteristic, complemented
5C2×#14578954—21no—
6#19097771C411yescharacteristic, complemented
7#19097768C411yescharacteristic, complemented
8#19097759—21no—
9#19097745—21no—
10#19097745C2212yes—
11C4×D628—21no—
12C4×D628C412yescomplemented
13C2×C4⋊Dic157—21no—
14#19097678—21no—
15#19097678C2212yes—
16C2×C42×C157C2211yescharacteristic
17C4⋊C8×C157—21no—
18C22⋊C8×C157C2212yes—
19C4×C8×C157—21no—
20#14578954—42no—
21#14578954—42no—
22C2×Dic314—21no—
23C2×D628—21no—
24C2×D628—21no—
25C2×D628C2×C412yes—
26C2×C22⋊D157—22no—
27C22×Dic157—22no—
28C2×C4×D157—22no—
29C4⋊Dic157—21no—
30C4⋊Dic157—42no—
31C4⋊Dic157C2×C412yes—
32#14578931—22no—
33#14578931—22no—
34C22×C4×C157D411yescharacteristic
35C22×C4×C157D411yescharacteristic
36C22×C4×C157C2311yescharacteristic
37C2×C8×C157—22no—
38C42×C157C2×C411yescharacteristic
39C42×C157C2×C411yescharacteristic
40C42×C157D411yescharacteristic
41C42×C157D411yescharacteristic
42C22×D157—22no—
43Dic314—42no—
44D628—42no—
45D628—42no—
46D628—42no—
47C22⋊D157—42no—
48C22⋊D157—42no—
49C2×Dic157—22no—
50C2×Dic157—42no—
51C2×Dic157—42no—
52C2×Dic157—42no—
53C4×D157—44no—
54C23×C157C2×D411yescharacteristic
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157C22⋊C411yescharacteristic
58C2×C4×C157C22⋊C411yescharacteristic
59C2×C4×C157C22⋊C411yescharacteristic
60C2×C4×C157C22⋊C411yescharacteristic
61C2×C4×C157D812yes—
62C2×C4×C157SD1612yes—
63C2×C4×C157C22×C411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C8×C157—42no—
66C22×C157—21no—
67C22×C157—21no—
68C22×C157C2×C22⋊C411yescharacteristic
69C22×C157C2×D811yescharacteristic
70C22×C157C2×SD1611yescharacteristic
71C2×D157—42no—
72C2×D157—42no—
73C2×D157—42no—
74C4×C157—21no—
75C4×C157—21no—
76C4×C157—21no—
77C4×C157—21no—
78C4×C157#10212yes—
79C4×C157#10212yes—
80Dic157—42no—
81Dic157—82no—
82C2×C157—21no—
83C2×C157—21no—
84C2×C157#41011yescharacteristic
85C2×C157C2×#10211yescharacteristic
86C2×C157#42111yescharacteristic
87D157—82no—
88C157#151711yescharacteristic, complemented, Sylow
89#1517—1571nomaximal, Sylow
90#532—1571no—
91#431D15711yescharacteristic, complemented
92#382—1571no—
93#327—1574no—
94C2×#41—3141no—
95C4⋊Q8—1571no—
96#127—1571no—
97#124—3141no—
98#121—3141no—
99#121—1572no—
100C4×D4—3141no—
101C4×D4—1572no—
102C2×C4⋊C4—3141no—
103C2×C42C2×D15711yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C2×D15712yes—
106C4×C8—21no—
107#95—3141no—
108#95—1572no—
109#41—6282no—
110#41—6282no—
111C2×Q8—3141no—
112C2×D4—3142no—
113C2×D4—3141no—
114C2×D4—3141no—
115C2×D4—1572no—
116C22×C4—3142no—
117C22×C4—3142no—
118C22×C4D62811yescharacteristic
119C22×C4D62811yescharacteristic
120C22×C4C22×D15711yescharacteristic
121C2×C8—22no—
122C4⋊C4—3141no—
123C4⋊C4—6282no—
124C4⋊C4—1572no—
125C22⋊C4—3142no—
126C22⋊C4—3142no—
127C42C4×D15711yescharacteristic
128C42C4×D15711yescharacteristic
129C42C22⋊D15711yescharacteristic
130C42C22⋊D15711yescharacteristic
131C23—3142no—
132C23C2×D62811yescharacteristic
133Q8—6282no—
134D4—6282no—
135D4—6282no—
136D4—6282no—
137D4—6282no—
138D4—6282no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—3142no—
142C2×C4—6284no—
143C2×C4—6282no—
144C2×C4—6282no—
145C2×C4—6282no—
146C2×C4#1457893111yescharacteristic
147C2×C4#1457893111yescharacteristic
148C2×C4#1457893111yescharacteristic
149C2×C4#1457893111yescharacteristic
150C2×C4D125612yes—
151C2×C4#1457894312yes—
152C2×C4C2×C4×D15711yescharacteristic
153C2×C4C2×C22⋊D15711yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—6282no—
158C22—6282no—
159C22—6282no—
160C22C2×#1457893111yescharacteristic
161C22C2×D125611yescharacteristic
162C22C2×#1457894311yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—6282no—
168C4—12562no—
169C4#1909769312yes—
170C4#1909769312yes—
171C2—21no—
172C2—21no—
173C2—12562no—
174C2#2375724611yescharacteristic
175C2C2×#1909769311yescharacteristic
176C2#2375728911yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#431×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757823C2
cosocleC22×C4×C157C23
hypercenter#431D157
hypocenterC157#1517
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #23757139C2semidirect
3. #23757008C2semidirect
4. #431×C157C2semidirect
6. #19097771C4semidirect
7. #19097768C4semidirect
12. C4×D628C4semidirect
88. C157#1517semidirect
91. #431D157semidirect

Maximal subgroups

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

subgroupindex
#237578232
#237571392
#237570082
#431×C1572
#1517157