Finite Group Databasebeta

← #37582453

Subgroups — #37582453

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
1#27133174C211yesmaximal, characteristic
2C2×#20259281C211yesmaximal, characteristic, complemented
3#27133005C214yesmaximal, complemented
4#27132988C214yesmaximal, complemented
5#27132705C212yesmaximal, complemented
6#27132665C212yesmaximal, complemented
7#407×C191C211yesmaximal, characteristic, complemented
8C2×#15690287C2211yescharacteristic
9#20259305—21no—
10#20259301C2212yes—
11#20259296C2212yes—
12#20259291—21no—
13C4×C22⋊D191—22no—
14#20259281—22no—
15#20259281C2211yescharacteristic
16#20259281C2214yes—
17C2×C4⋊Dic191C2212yes—
18C2×C22⋊Dic191—21no—
19C2×C4×Dic191—21no—
20#20259256C2214yescomplemented
21#20259254C2214yescomplemented
22#20259247C2214yescomplemented
23#20259244C2214yescomplemented
24C23×C4×C191C2211yescharacteristic
25C2×M16×C191C2212yes—
26C22⋊C8×C191C2214yes—
27#15690287—24no—
28C2×Dic382C2311yescharacteristic
29C2×D764C2311yescharacteristic
30C2×C22⋊D191—21no—
31C2×C22⋊D191—22no—
32C22×Dic191—22no—
33C2×C4×D191—21no—
34C4⋊Dic191—22no—
35C4⋊Dic191C2314yes—
36C4⋊Dic191C2312yes—
37Dic191⋊C4—22no—
38C22⋊Dic191—24no—
39C22⋊Dic191—21no—
40C22⋊Dic191—22no—
41(C2×D191)⋊C4—22no—
42C4×Dic191—24no—
43C4×Dic191—21no—
44C24×C191D411yescharacteristic
45C22×C4×C191—24no—
46C22×C4×C191D411yescharacteristic
47C22×C4×C191D412yes—
48C22×C4×C191C2312yes—
49C22×C4×C191C2311yescharacteristic
50M16×C191—24no—
51C2×C8×C191C2314yes—
52C22×D191—21no—
53Dic382—22no—
54D764—22no—
55C22⋊D191—44no—
56C22⋊D191—42no—
57C2×Dic191—24no—
58C2×Dic191—22no—
59C2×Dic191—21no—
60C2×Dic191—44no—
61C4×D191—42no—
62C23×C191—22no—
63C23×C191—42no—
64C23×C191C2×D412yes—
65C23×C191C2×D411yescharacteristic
66C2×C4×C191—22no—
67C2×C4×C191—24no—
68C2×C4×C191—24no—
69C2×C4×C191C2×D412yes—
70C2×C4×C191C2×D411yescharacteristic
71C2×C4×C191#4114yes—
72C2×C4×C191C2411yescharacteristic
73C8×C191—24no—
74C22×C191—22no—
75C22×C191—22no—
76C22×C191—22no—
77C22×C191—22no—
78C22×C191—44no—
79C22×C191#12312yes—
80C22×C191C22×D411yescharacteristic
81C2×D191—41no—
82C2×D191—42no—
83C4×C191—22no—
84C4×C191#12312yes—
85C4×C191C2×#4112yes—
86Dic191—41no—
87Dic191—44no—
88Dic191—42no—
89C2×C191—22no—
90C2×C191—42no—
91C2×C191C2×#12311yescharacteristic
92C2×C191#57512yes—
93D191—81no—
94C191#309311yescharacteristic, complemented, Sylow
95#3093—1911nomaximal, Sylow
96#525—1911no—
97C2×#117—1911no—
98#485—1914no—
99#482—1914no—
100#428—1912no—
101#417—1912no—
102#407D19111yescharacteristic, complemented
103C2×#41—1911no—
104C23×C4C2×D19111yescharacteristic
105C2×M16C2×D19112yes—
106#123—3821no—
107C22⋊Q8—1912no—
108#121—1912no—
109#120—3821no—
110C4×D4—3822no—
111#117—3822no—
112#117—1914no—
113#117—1911no—
114C2×C4⋊C4—1912no—
115C2×C22⋊C4—3821no—
116C2×C42—3821no—
117#107—1914no—
118#106—1914no—
119#103—1914no—
120#102—1914no—
121C22⋊C8C2×D19114yes—
122C24D76411yescharacteristic
123#41—3824no—
124C2×Q8—1911no—
125C2×D4—3822no—
126C2×D4—3821no—
127C2×D4—1911no—
128C22×C4—24no—
129C22×C4—3822no—
130C22×C4—3821no—
131C22×C4D76411yescharacteristic
132C22×C4D76412yes—
133C22×C4C22×D19112yes—
134C22×C4C22×D19111yescharacteristic
135M16—24no—
136C2×C8C22×D19114yes—
137C4⋊C4—3822no—
138C4⋊C4—3822no—
139C4⋊C4—1914no—
140C4⋊C4—1912no—
141C22⋊C4—3824no—
142C22⋊C4—3821no—
143C22⋊C4—3822no—
144C22⋊C4—3822no—
145C42—3824no—
146C42—3821no—
147C23—22no—
148C23—42no—
149C23—3821no—
150C23C2×D76412yes—
151C23C2×D76411yescharacteristic
152Q8—3822no—
153D4—3822no—
154D4—7644no—
155D4—7642no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—3824no—
160C2×C4—3822no—
161C2×C4—3821no—
162C2×C4—7644no—
163C2×C4—7642no—
164C2×C4C2×D76412yes—
165C2×C4C2×D76411yescharacteristic
166C2×C4#1569028614yes—
167C2×C4C23×D19111yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—7642no—
175C22—7641no—
176C22#2025930612yes—
177C22C22×D76411yescharacteristic
178C4—22no—
179C4—7644no—
180C4—7642no—
181C4—7641no—
182C4#2025930612yes—
183C4C2×#1569028612yes—
184C2—22no—
185C2—42no—
186C2—15281no—
187C2C2×#2025930611yescharacteristic
188C2#2713346312yes—
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#407×C191C2
socleC22×C191C22×D4
prime radical#27133174C2
hypercenter#407D191
hypocenterC191#3093
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#20259281C2semidirect
3. #27133005C2semidirect
4. #27132988C2semidirect
5. #27132705C2semidirect
6. #27132665C2semidirect
7. #407×C191C2semidirect
20. #20259256C22semidirect
21. #20259254C22semidirect
22. #20259247C22semidirect
23. #20259244C22semidirect
94. C191#3093semidirect
102. #407D191semidirect

Maximal subgroups

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

subgroupindex
#271331742
C2×#202592812
#271330052
#271329882
#271327052
#271326652
#407×C1912
#3093191