Finite Group Databasebeta

← #37570782

Subgroups — #37570782

Order 24448.

476 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×C191⋊#95C213yesmaximal
2C2×C191⋊#95C213yesmaximal
3C2×#95×C191C211yesmaximal, characteristic
4C23×Dic191C2213yes—
5C23×Dic191C2211yescharacteristic
6C191⋊#95—26no—
7C191⋊#95—26no—
8C23×C4×C191C2213yes—
9#95×C191C414yescomplemented
10C22×Dic191—23no—
11C22×Dic191—23no—
12C22×Dic191—23no—
13C22×Dic191—23no—
14C22×Dic191—23no—
15C22×Dic191—23no—
16C22×Dic191—23no—
17C22×Dic191—23no—
18C22×Dic191D416yes—
19C22×Dic191Q812yes—
20C24×C191C2311yescharacteristic
21C22×C4×C191—23no—
22C22×C4×C191—23no—
23C22×C4×C191—23no—
24C22×C4×C191—23no—
25C22×C4×C191—23no—
26C22×C4×C191—23no—
27C22×C4×C191C2×C416yes—
28C2×Dic191—26no—
29C2×Dic191—26no—
30C2×Dic191—26no—
31C2×Dic191—26no—
32C2×Dic191—43no—
33C2×Dic191—43no—
34C2×Dic191—43no—
35C2×Dic191—41no—
36C2×Dic191—43no—
37C2×Dic191—43no—
38C23×C191C22×C411yescharacteristic
39C23×C191C2×D413yes—
40C23×C191C2×Q811yescharacteristic
41C23×C191#4113yes—
42C23×C191#4113yes—
43C23×C191#4113yes—
44C23×C191#4111yescharacteristic
45C2×C4×C191—26no—
46C2×C4×C191—26no—
47C2×C4×C191—26no—
48C2×C4×C191—43no—
49C2×C4×C191—43no—
50C2×C4×C191—43no—
51C2×C4×C191—43no—
52C22×C191#11713yes—
53C22×C191C4×D413yes—
54C22×C191C4×Q811yescharacteristic
55C22×C191#12113yes—
56C22×C191C22⋊Q813yes—
57C22×C191#12313yes—
58C22×C191#12313yes—
59C22×C191#12413yes—
60C22×C191#12513yes—
61C22×C191#12613yes—
62C22×C191#12611yescharacteristic
63C22×C191#12613yes—
64C22×C191#12613yes—
65C4×C191—46no—
66Dic191—42no—
67Dic191—46no—
68C2×C191#38311yescharacteristic
69C2×C191#38713yes—
70C2×C191#38813yes—
71C2×C191#39611yescharacteristic
72C2×C191#39713yes—
73C2×C191#40013yes—
74C2×C191#40111yescharacteristic
75C191#144311yescharacteristic, complemented, Sylow
76#1443—1911nomaximal, Sylow
77C2×#95—1913no—
78C2×#95—1913no—
79C2×#95D19111yescharacteristic
80C23×C4—1911no—
81C23×C4—1913no—
82C23×C4C2×D19113yes—
83#95—3826no—
84#95—3826no—
85#95Dic19114yescomplemented
86C24C22×D19111yescharacteristic
87C22×C4—23no—
88C22×C4—23no—
89C22×C4—23no—
90C22×C4—23no—
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—3823no—
94C22×C4—3823no—
95C22×C4—3823no—
96C22×C4—3823no—
97C22×C4—3823no—
98C22×C4—3823no—
99C22×C4—3823no—
100C22×C4—3823no—
101C22×C4—1916no—
102C22×C4—1912no—
103C22×C4C2×Dic19116yes—
104C23C22×Dic19111yescharacteristic
105C23D4×D19113yes—
106C23Q8×D19111yescharacteristic
107C23#1569028613yes—
108C23#1569028713yes—
109C23#1569028713yes—
110C23#1569028811yescharacteristic
111C2×C4—26no—
112C2×C4—26no—
113C2×C4—26no—
114C2×C4—43no—
115C2×C4—43no—
116C2×C4—43no—
117C2×C4—43no—
118C2×C4—3826no—
119C2×C4—3826no—
120C2×C4—3826no—
121C2×C4—3826no—
122C2×C4—7643no—
123C2×C4—7643no—
124C2×C4—7643no—
125C2×C4—7641no—
126C2×C4—7643no—
127C2×C4—7643no—
128C22#2025928113yes—
129C22D4×Dic19113yes—
130C22Q8×Dic19111yescharacteristic
131C22#2025929513yes—
132C22#2025930013yes—
133C22#2025930413yes—
134C22#2025930713yes—
135C22#2025930813yes—
136C22#2025931213yes—
137C22#2025931513yes—
138C22#2025931611yescharacteristic
139C22#2025931613yes—
140C22#2025931713yes—
141C4—46no—
142C4—7642no—
143C4—7646no—
144C2#2713253111yescharacteristic
145C2#2713254913yes—
146C2#2713255613yes—
147C2#2713258711yescharacteristic
148C2#2713259213yes—
149C2#2713260413yes—
150C2C191⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D191
commutatorC23×C191C22×C4
FittingC2×#95×C191C2
socle, prime radical, cosocleC24×C191C23
hypercenterC2×#95D191
hypocenterC191#1443
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
9. #95×C191C4semidirect
75. C191#1443semidirect
85. #95Dic191semidirect

Maximal subgroups

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

subgroupindex
C2×C191⋊#952
C2×#95×C1912
#1443191