Finite Group Databasebeta

← #34101804

Subgroups — #34101804

Order 20096.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757841C211yesmaximal, characteristic
2#99×D157C212yesmaximal, complemented
3#23757068C211yesmaximal, characteristic, complemented
4#23757065C212yesmaximal, complemented
5#354×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C411yescharacteristic, complemented
7C2×D4×D157C2211yescharacteristic
8#19097768C411yescharacteristic, complemented
9#19097767C2211yescharacteristic
10#19097760C411yescharacteristic, complemented
11#19097744—22no—
12#19097741—22no—
13#19097728C411yescharacteristic, complemented
14C22⋊C4×D157—22no—
15#19097686C2212yes—
16#19097685—22no—
17#124×C157C2211yescharacteristic
18#99×C157C2212yes—
19C23×D157D412yes—
20#14578955—42no—
21C2×D628—21no—
22C2×D628—22no—
23C2×D628C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic, complemented
25C2×C22⋊D157—22no—
26C2×C22⋊D157D412yes—
27D4×D157—42no—
28C2×C4×D157—21no—
29C2×C4×D157—42no—
30C2×C4×D157C2×C411yescharacteristic
31#14578933—21no—
32C22⋊Dic157—22no—
33#14578931—21no—
34#14578931—22no—
35#14578931—42no—
36C4×Dic157C2×C411yescharacteristic, complemented
37C2×Q8×C157C2×C411yescharacteristic, complemented
38C2×D4×C157C2311yescharacteristic
39C22⋊C4×C157—22no—
40C22⋊C4×C157—22no—
41C42×C157C2×C411yescharacteristic, complemented
42C22×D157—22no—
43C22×D157—22no—
44C22×D157—21no—
45C22×D157—82no—
46C22×D157C22⋊C412yes—
47C22×D157C22⋊C411yescharacteristic
48D628—41no—
49D628—41no—
50D628—42no—
51D628—82no—
52C22⋊D157—42no—
53C22⋊D157—82no—
54C2×Dic157—21no—
55C2×Dic157—42no—
56C2×Dic157C22⋊C411yescharacteristic
57C4×D157—22no—
58C4×D157—42no—
59C4×D157—84no—
60C23×C157C2×D412yes—
61Q8×C157—41no—
62D4×C157—41no—
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157—42no—
66C2×C4×C157C22×C411yescharacteristic
67C22×C157—22no—
68C22×C157—42no—
69C22×C157C2×C22⋊C411yescharacteristic
70C2×D157—22no—
71C2×D157—41no—
72C2×D157—44no—
73C2×D157—42no—
74C2×D157—42no—
75C2×D157—41no—
76C2×D157—82no—
77C2×D157#9912yes—
78C4×C157—21no—
79C4×C157—41no—
80C4×C157—41no—
81C4×C157—82no—
82Dic157—21no—
83Dic157—41no—
84Dic157—82no—
85C2×C157—21no—
86C2×C157—42no—
87C2×C157C2×#9911yescharacteristic
88D157—22no—
89D157—42no—
90D157—81no—
91C157#212711yescharacteristic, complemented, Sylow
92#2127—1571nomaximal, Sylow
93#535—1571no—
94C2×#99—1572no—
95#354—1571no—
96#354D15711yescharacteristic, complemented
97#353—1572no—
98C2×#41—1571no—
99C22×D4—1571no—
100#127—1571no—
101#127—1571no—
102#124—1571no—
103#124C2×D15711yescharacteristic
104#121—3142no—
105#120—3142no—
106#117—1571no—
107C2×C22⋊C4—3142no—
108#99—3142no—
109#99—1572no—
110#99C2×D15712yes—
111C24—1572no—
112#41—6282no—
113C2×Q8C4×D15711yescharacteristic, complemented
114C2×D4—3141no—
115C2×D4—3142no—
116C2×D4—3142no—
117C2×D4—6282no—
118C2×D4—1572no—
119C2×D4—1571no—
120C2×D4—1571no—
121C2×D4C22×D15711yescharacteristic
122C22×C4—3141no—
123C22×C4—6282no—
124C22×C4—1571no—
125C4⋊C4—3141no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—3141no—
129C22⋊C4—3142no—
130C22⋊C4—3142no—
131C22⋊C4—6282no—
132C42—1571no—
133C42C4×D15711yescharacteristic, complemented
134C23—3142no—
135C23—3142no—
136C23—3141no—
137C23—1572no—
138C23—1571no—
139C23—12562no—
140C23D4×D15712yes—
141Q8—41no—
142D4—41no—
143D4—6281no—
144D4—6281no—
145D4—6282no—
146D4—6282no—
147D4—12562no—
148D4—12562no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—3142no—
153C2×C4—3141no—
154C2×C4—6282no—
155C2×C4—6282no—
156C2×C4—1571no—
157C2×C4—12564no—
158C2×C4C2×C4×D15711yescharacteristic
159C22—22no—
160C22—42no—
161C22—3142no—
162C22—6281no—
163C22—6282no—
164C22—6282no—
165C22—6284no—
166C22—6281no—
167C22—1572no—
168C22—12562no—
169C22C22⋊C4×D15711yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—3141no—
175C4—6281no—
176C4—12562no—
177C2—21no—
178C2—42no—
179C2—3142no—
180C2—6282no—
181C2—12561no—
182C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#354×C157C2
socleC2×C157C2×#99
prime radical#23757841C2
cosocleC2×D4×C157C23
hypercenter#354D157
hypocenterC157#2127
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D157C2semidirect
3. #23757068C2semidirect
4. #23757065C2semidirect
5. #354×C157C2semidirect
6. C2×#14578955C4semidirect
8. #19097768C4semidirect
10. #19097760C4semidirect
13. #19097728C4semidirect
24. C2×D628C2×C4semidirect
36. C4×Dic157C2×C4semidirect
37. C2×Q8×C157C2×C4semidirect
41. C42×C157C2×C4semidirect
91. C157#2127semidirect
96. #354D157semidirect
113. C2×Q8C4×D157semidirect
133. C42C4×D157semidirect

Maximal subgroups

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

subgroupindex
#237578412
#99×D1572
#237570682
#237570652
#354×C1572
#2127157