Finite Group Databasebeta

← #37582449

Subgroups — #37582449

Order 24448.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20259281C211yesmaximal, characteristic, complemented
2#27133001C214yesmaximal, complemented
3#27132984C214yesmaximal, complemented
4#27132706C212yesmaximal, complemented
5#27132664C212yesmaximal, complemented
6#27132627C211yesmaximal, characteristic, complemented
7#525×C191C211yesmaximal, characteristic
8C2×#15690271C2212yes—
9#20259281—22no—
10#20259281C2214yes—
11C2×C4⋊Dic191C2212yes—
12C2×C22⋊Dic191—21no—
13C2×C4×Dic191—21no—
14#20259255C2214yescomplemented
15#20259253C2214yescomplemented
16#20259246C2214yescomplemented
17#20259243C2214yescomplemented
18C22⋊(C191⋊C8)C2214yes—
19C2×#41×C191C2211yescharacteristic
20C23×C4×C191C2211yescharacteristic
21#123×C191—21no—
22C22⋊Q8×C191C2212yes—
23#121×C191C2212yes—
24#120×C191—21no—
25C4×D4×C191—22no—
26#117×C191C2211yescharacteristic
27C22×Dic191—22no—
28#15690271—24no—
29C2×C191⋊C8C2314yes—
30C4⋊Dic191—22no—
31C4⋊Dic191C2314yes—
32C22⋊Dic191—24no—
33C4×Dic191—24no—
34C24×C191D411yescharacteristic
35#41×C191—24no—
36C2×Q8×C191C2311yescharacteristic
37C2×D4×C191—22no—
38C2×D4×C191—21no—
39C2×D4×C191C2311yescharacteristic
40C22×C4×C191—24no—
41C22×C4×C191—21no—
42C22×C4×C191D412yes—
43C22×C4×C191D411yescharacteristic
44C22×C4×C191C2312yes—
45C22×C4×C191C2311yescharacteristic
46C4⋊C4×C191—22no—
47C4⋊C4×C191C2312yes—
48C22⋊C4×C191—21no—
49C22⋊C4×C191—22no—
50C22⋊C4×C191—22no—
51C42×C191—21no—
52C2×Dic191—24no—
53C2×Dic191—44no—
54C191⋊C8—24no—
55C23×C191—22no—
56C23×C191—21no—
57C23×C191—42no—
58C23×C191C2×D412yes—
59C23×C191C2×D411yescharacteristic
60Q8×C191—22no—
61D4×C191—22no—
62D4×C191—44no—
63D4×C191—42no—
64C2×C4×C191—22no—
65C2×C4×C191—24no—
66C2×C4×C191—24no—
67C2×C4×C191—22no—
68C2×C4×C191—21no—
69C2×C4×C191—42no—
70C2×C4×C191C2×D412yes—
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191#4114yes—
73C2×C4×C191C2411yescharacteristic
74C22×C191—22no—
75C22×C191—22no—
76C22×C191—22no—
77C22×C191—22no—
78C22×C191—44no—
79C22×C191—41no—
80C22×C191—42no—
81C22×C191#12312yes—
82C22×C191C22×D411yescharacteristic
83C4×C191—22no—
84C4×C191—41no—
85C4×C191—42no—
86C4×C191#12312yes—
87C4×C191C2×#4112yes—
88Dic191—44no—
89C2×C191—22no—
90C2×C191—42no—
91C2×C191—81no—
92C2×C191C2×#12311yescharacteristic
93C2×C191#57512yes—
94C191#309311yescharacteristic, complemented, Sylow
95#3093—1911nomaximal, Sylow
96#525D19111yescharacteristic
97C2×#117—1911no—
98#485—1914no—
99#482—1914no—
100#428—1912no—
101#417—1912no—
102#407—1911no—
103C2×#41C2×D19111yescharacteristic
104C23×C4C2×D19111yescharacteristic
105C2×M16—1912no—
106#123—21no—
107C22⋊Q8C2×D19112yes—
108#121C2×D19112yes—
109#120—21no—
110C4×D4—22no—
111#117—3822no—
112#117—1914no—
113#117C2×D19111yescharacteristic
114C2×C4⋊C4—1912no—
115C2×C22⋊C4—3821no—
116C2×C42—3821no—
117#107—1914no—
118#106—1914no—
119#103—1914no—
120#102—1914no—
121C22⋊C8—1914no—
122C24C22⋊D19111yescharacteristic
123#41—24no—
124C2×Q8C22×D19111yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D19111yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—3822no—
131C22×C4C22⋊D19111yescharacteristic
132C22×C4C22⋊D19112yes—
133C22×C4C22×D19112yes—
134C22×C4C22×D19111yescharacteristic
135M16—3824no—
136C2×C8—1914no—
137C4⋊C4—22no—
138C4⋊C4—3822no—
139C4⋊C4—1914no—
140C4⋊C4C22×D19112yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—3824no—
145C42—21no—
146C42—3824no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D19112yes—
151C23C2×C22⋊D19111yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—3824no—
163C2×C4—7644no—
164C2×C4C2×C22⋊D19112yes—
165C2×C4C2×C22⋊D19111yescharacteristic
166C2×C4#1569028614yes—
167C2×C4C23×D19111yescharacteristic
168C8—3824no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—42no—
175C22—41no—
176C22#2025930312yes—
177C22C22×C22⋊D19111yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4—7644no—
182C4#2025930312yes—
183C4C2×#1569028612yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#2025930311yescharacteristic
188C2#2713346112yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting, prime radical#525×C191C2
socleC22×C191C22×D4
hypercenter#525D191
hypocenterC191#3093
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#20259281C2semidirect
2. #27133001C2semidirect
3. #27132984C2semidirect
4. #27132706C2semidirect
5. #27132664C2semidirect
6. #27132627C2semidirect
14. #20259255C22semidirect
15. #20259253C22semidirect
16. #20259246C22semidirect
17. #20259243C22semidirect
94. C191#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#202592812
#271330012
#271329842
#271327062
#271326642
#271326272
#525×C1912
#3093191