Finite Group Databasebeta

← #34101802

Subgroups — #34101802

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#23757836C211yesmaximal, characteristic
2#99×D157C212yesmaximal, complemented
3#23757067C212yesmaximal, complemented
4#23757066C211yesmaximal, characteristic, complemented
5#353×C157C211yesmaximal, characteristic, complemented
6C2×#14578953C411yescharacteristic, complemented
7C2×D4×D157C2211yescharacteristic
8#19097767C411yescharacteristic, complemented
9#19097759C411yescharacteristic, complemented
10#19097758C2211yescharacteristic
11#19097743—22no—
12#19097739—22no—
13#19097728C411yescharacteristic, complemented
14C22⋊C4×D157—22no—
15#19097686C2212yes—
16#19097685—22no—
17#127×C157C2211yescharacteristic
18#99×C157C2212yes—
19C23×D157D412yes—
20#14578953—42no—
21C2×Dic314C2×C411yescharacteristic, complemented
22C2×D628C2×C411yescharacteristic
23C2×C22⋊D157—21no—
24C2×C22⋊D157—22no—
25C2×C22⋊D157D412yes—
26D4×D157—42no—
27C22×Dic157—21no—
28C2×C4×D157—42no—
29C2×C4×D157C2×C411yescharacteristic
30#14578933—21no—
31C22⋊Dic157—22no—
32C22⋊Dic157—22no—
33#14578931—21no—
34#14578931—22no—
35#14578931—42no—
36C4×Dic157C2×C411yescharacteristic, complemented
37C2×D4×C157—22no—
38C2×D4×C157C2×C411yescharacteristic, complemented
39C2×D4×C157C2311yescharacteristic
40C22⋊C4×C157—22no—
41C42×C157C2×C411yescharacteristic, complemented
42C22×D157—22no—
43C22×D157—22no—
44C22×D157—82no—
45C22×D157C22⋊C412yes—
46C22×D157C22⋊C411yescharacteristic
47Dic314—41no—
48D628—41no—
49C22⋊D157—42no—
50C22⋊D157—42no—
51C22⋊D157—82no—
52C2×Dic157—21no—
53C2×Dic157—21no—
54C2×Dic157—42no—
55C2×Dic157—42no—
56C2×Dic157C22⋊C411yescharacteristic
57C4×D157—22no—
58C4×D157—84no—
59C23×C157—21no—
60C23×C157C2×D412yes—
61D4×C157—41no—
62D4×C157—41no—
63D4×C157—82no—
64C2×C4×C157—21no—
65C2×C4×C157—42no—
66C2×C4×C157C22×C411yescharacteristic
67C22×C157—22no—
68C22×C157—42no—
69C22×C157—42no—
70C22×C157—41no—
71C22×C157C2×C22⋊C411yescharacteristic
72C2×D157—22no—
73C2×D157—41no—
74C2×D157—44no—
75C2×D157—42no—
76C2×D157—82no—
77C2×D157#9912yes—
78C4×C157—21no—
79C4×C157—41no—
80C4×C157—82no—
81Dic157—21no—
82Dic157—41no—
83Dic157—41no—
84Dic157—82no—
85C2×C157—21no—
86C2×C157—42no—
87C2×C157—81no—
88C2×C157C2×#9911yescharacteristic
89D157—22no—
90D157—42no—
91C157#212711yescharacteristic, complemented, Sylow
92#2127—1571nomaximal, Sylow
93#535—1571no—
94C2×#99—1572no—
95#354—1572no—
96#353—1571no—
97#353D15711yescharacteristic, complemented
98C2×#41—1571no—
99C22×D4—1571no—
100#127—1571no—
101#127C2×D15711yescharacteristic
102#124—1571no—
103#124—1571no—
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×Q8—1571no—
114C2×D4—22no—
115C2×D4—3141no—
116C2×D4—3142no—
117C2×D4—6282no—
118C2×D4—1572no—
119C2×D4—1571no—
120C2×D4C4×D15711yescharacteristic, complemented
121C2×D4C22×D15711yescharacteristic
122C22×C4—3141no—
123C22×C4—6282no—
124C22×C4—1571no—
125C4⋊C4—3141no—
126C22⋊C4—22no—
127C22⋊C4—3141no—
128C22⋊C4—3142no—
129C22⋊C4—3142no—
130C22⋊C4—3142no—
131C22⋊C4—6282no—
132C42—1571no—
133C42C4×D15711yescharacteristic, complemented
134C23—21no—
135C23—3142no—
136C23—3142no—
137C23—1572no—
138C23—1571no—
139C23—12562no—
140C23D4×D15712yes—
141Q8—6281no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—6281no—
146D4—6282no—
147D4—6282no—
148D4—12562no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—3142no—
152C2×C4—3141no—
153C2×C4—3141no—
154C2×C4—6282no—
155C2×C4—6282no—
156C2×C4—1571no—
157C2×C4—12564no—
158C2×C4C2×C4×D15711yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—3142no—
164C22—6281no—
165C22—6282no—
166C22—6284no—
167C22—1572no—
168C22—12562no—
169C22C22⋊C4×D15711yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—3141no—
174C4—6281no—
175C4—6281no—
176C4—12562no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—3142no—
181C2—6282no—
182C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#353×C157C2
socleC2×C157C2×#99
prime radical#23757836C2
cosocleC2×D4×C157C23
hypercenter#353D157
hypocenterC157#2127
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D157C2semidirect
3. #23757067C2semidirect
4. #23757066C2semidirect
5. #353×C157C2semidirect
6. C2×#14578953C4semidirect
8. #19097767C4semidirect
9. #19097759C4semidirect
13. #19097728C4semidirect
21. C2×Dic314C2×C4semidirect
36. C4×Dic157C2×C4semidirect
38. C2×D4×C157C2×C4semidirect
41. C42×C157C2×C4semidirect
91. C157#2127semidirect
97. #353D157semidirect
120. C2×D4C4×D157semidirect
133. C42C4×D157semidirect

Maximal subgroups

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

subgroupindex
#237578362
#99×D1572
#237570672
#237570662
#353×C1572
#2127157