Finite Group Databasebeta

← #34101800

Subgroups — #34101800

Order 20096.

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

normal subgroups only

This group has 258 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#23757822C211yesmaximal, characteristic
2#23757245C212yesmaximal, complemented
3#23757068C211yesmaximal, characteristic, complemented
4#23757065C212yesmaximal, complemented
5#354×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C411yescharacteristic, complemented
7C2×#14578953C2211yescharacteristic
8#19097769C411yescharacteristic, complemented
9#19097767C2211yescharacteristic
10#19097759C411yescharacteristic, complemented
11#19097744—22no—
12#19097731—22no—
13#19097727—22no—
14C42×D157C411yescharacteristic, complemented
15#19097686C2212yes—
16#19097685—22no—
17#124×C157C2211yescharacteristic
18#99×C157C2212yes—
19#14578955—41no—
20#14578955—41no—
21#14578953—41no—
22#14578953—41no—
23C2×Dic314C2×C411yescharacteristic
24C2×D628—21no—
25C2×D628C2×C411yescharacteristic
26C2×C22⋊D157—22no—
27C2×C22⋊D157D412yes—
28C22×Dic157D412yes—
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×C4×D157C2×C411yescharacteristic
32#14578933—22no—
33#14578933—42no—
34C22⋊Dic157—22no—
35#14578931—22no—
36C4×Dic157—21no—
37C4×Dic157—42no—
38C4×Dic157C2×C411yescharacteristic
39C2×Q8×C157C2×C411yescharacteristic
40C2×D4×C157C2311yescharacteristic
41C22⋊C4×C157—22no—
42C22⋊C4×C157—22no—
43C42×C157C2×C411yescharacteristic
44C22×D157—21no—
45C22×D157C22⋊C411yescharacteristic
46Dic314—41no—
47D628—41no—
48D628—42no—
49C22⋊D157—42no—
50C22⋊D157—44no—
51C2×Dic157—21no—
52C2×Dic157—22no—
53C2×Dic157—22no—
54C2×Dic157—42no—
55C2×Dic157C22⋊C412yes—
56C2×Dic157C22⋊C411yescharacteristic
57C4×D157—21no—
58C4×D157—21no—
59C4×D157—42no—
60C4×D157—41no—
61C4×D157—41no—
62C23×C157C2×D412yes—
63Q8×C157—41no—
64D4×C157—41no—
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—42no—
68C2×C4×C157C22×C411yescharacteristic
69C22×C157—22no—
70C22×C157—42no—
71C22×C157C2×C22⋊C411yescharacteristic
72C2×D157—21no—
73C2×D157—41no—
74C2×D157—42no—
75C2×D157—41no—
76C4×C157—21no—
77C4×C157—41no—
78C4×C157—41no—
79C4×C157—82no—
80Dic157—22no—
81Dic157—22no—
82Dic157—82no—
83Dic157#9911yescharacteristic
84Dic157#9911yescharacteristic
85C2×C157—21no—
86C2×C157—42no—
87C2×C157C2×#9911yescharacteristic
88D157—41no—
89D157—81no—
90C157#212611yescharacteristic, complemented, Sylow
91#2126—1571nomaximal, Sylow
92#532—1571no—
93#410—1572no—
94#354—1571no—
95#354D15711yescharacteristic, complemented
96#353—1572no—
97C2×#41—1571no—
98C2×#41—1571no—
99C4⋊Q8—1571no—
100#127—1571no—
101#124—1571no—
102#124C2×D15711yescharacteristic
103#121—3142no—
104C4×D4—3142no—
105#117—3142no—
106C2×C42—1571no—
107#99—3142no—
108#99—1572no—
109#99C2×D15712yes—
110#41—6281no—
111#41—6281no—
112#41—6281no—
113#41—6281no—
114C2×Q8—1571no—
115C2×Q8C4×D15711yescharacteristic
116C2×D4—3141no—
117C2×D4—3142no—
118C2×D4—1572no—
119C2×D4—1571no—
120C2×D4C22×D15711yescharacteristic
121C22×C4—3141no—
122C22×C4—3141no—
123C22×C4—1572no—
124C22×C4—1571no—
125C4⋊C4—3142no—
126C4⋊C4—6282no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—3142no—
130C22⋊C4—3142no—
131C42—3141no—
132C42—6282no—
133C42—1571no—
134C42C4×D15711yescharacteristic
135C23—3141no—
136C23—1571no—
137C23D4×D15712yes—
138Q8—41no—
139Q8—6281no—
140D4—41no—
141D4—6281no—
142D4—6282no—
143D4—6282no—
144D4—6284no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—3141no—
149C2×C4—3141no—
150C2×C4—3141no—
151C2×C4—3142no—
152C2×C4—3142no—
153C2×C4—6282no—
154C2×C4—6281no—
155C2×C4—6281no—
156C2×C4—6282no—
157C2×C4—1572no—
158C2×C4—1571no—
159C2×C4C2×C4×D15711yescharacteristic
160C22—22no—
161C22—42no—
162C22—3141no—
163C22—6281no—
164C22—6282no—
165C22—6281no—
166C22C22⋊C4×D15711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—3142no—
172C4—3142no—
173C4—1571no—
174C4—1571no—
175C4—12562no—
176C2—21no—
177C2—42no—
178C2—6281no—
179C2—12561no—
180C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#354×C157C2
socleC2×C157C2×#99
prime radical#23757822C2
cosocleC2×D4×C157C23
hypercenter#354D157
hypocenterC157#2126
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. #23757245C2semidirect
3. #23757068C2semidirect
4. #23757065C2semidirect
5. #354×C157C2semidirect
6. C2×#14578955C4semidirect
8. #19097769C4semidirect
10. #19097759C4semidirect
14. C42×D157C4semidirect
90. C157#2126semidirect
95. #354D157semidirect

Maximal subgroups

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

subgroupindex
#237578222
#237572452
#237570682
#237570652
#354×C1572
#2126157