Finite Group Databasebeta

← #37583385

Subgroups — #37583385

Order 24448.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#27133227C212yesmaximal, complemented
2#27132988C214yesmaximal, complemented
3#27132916C212yesmaximal, complemented
4#27132899C212yesmaximal, complemented
5#27132799C214yesmaximal, complemented
6#408×C191C211yesmaximal, characteristic, complemented
7C22×D764C2212yescomplemented
8C2×D1528C2212yes—
9C2×D1528C2212yes—
10#20259318—22no—
11#20259311—22no—
12#20259296C2214yes—
13#20259296C2214yescomplemented
14#20259290—22no—
15#20259290—22no—
16#20259281C2212yescomplemented
17#20259256C2212yescomplemented
18#20259254C2212yescomplemented
19#20259244C2214yescomplemented
20#20259244C2214yescomplemented
21C2×#41×C191C2211yescharacteristic
22C2×M16×C191C2211yescharacteristic, complemented
23C22×C8×C191C2211yescharacteristic, complemented
24C22⋊C8×C191C2214yescomplemented
25C23×D191—22no—
26C2×D764—22no—
27C2×D764—42no—
28C2×D764—42no—
29C2×D764C2314yes—
30C2×C22⋊D191—24no—
31C2×C22⋊D191—24no—
32D1528—42no—
33D1528—42no—
34C4⋊Dic191C2314yes—
35C22⋊Dic191—22no—
36(C2×D191)⋊C4—24no—
37(C2×D191)⋊C4—24no—
38C4×Dic191—22no—
39#41×C191—41no—
40#41×C191—41no—
41C2×Q8×C191D411yescharacteristic
42C2×D4×C191D411yescharacteristic
43C2×D4×C191D412yes—
44C22×C4×C191C2312yes—
45C22×C4×C191C2311yescharacteristic
46M16×C191—41no—
47C2×C8×C191—41no—
48C2×C8×C191C2312yes—
49C2×C8×C191C2312yes—
50C22×D191—24no—
51C22×D191—44no—
52C22×D191—84no—
53D764—24no—
54D764—24no—
55D764—44no—
56C22⋊D191—84no—
57C22⋊D191—84no—
58C2×Dic191—24no—
59C23×C191C2×D412yes—
60C23×C191C2×D411yescharacteristic
61Q8×C191—41no—
62D4×C191—41no—
63D4×C191—42no—
64C2×C4×C191—21no—
65C2×C4×C191—21no—
66C2×C4×C191—22no—
67C2×C4×C191—22no—
68C2×C4×C191C2×D412yes—
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2411yescharacteristic
71C8×C191—22no—
72C8×C191—22no—
73C22×C191—21no—
74C22×C191—22no—
75C22×C191—22no—
76C22×C191—24no—
77C22×C191C22×D411yescharacteristic
78C2×D191—44no—
79C2×D191—44no—
80C2×D191—44no—
81C2×D191—88no—
82C4×C191—21no—
83C4×C191—22no—
84C4×C191H(5,𝔽2)11yescharacteristic
85C4×C191H(5,𝔽2)11yescharacteristic
86Dic191—44no—
87C2×C191—42no—
88C2×C191—41no—
89C2×C191#53411yescharacteristic
90C2×C191#57612yes—
91D191—84no—
92C191#319911yescharacteristic, complemented, Sylow
93#3199—1911nomaximal, Sylow
94#535—1912no—
95#482—1914no—
96#469—1912no—
97#466—1912no—
98#447—1914no—
99#408D19111yescharacteristic, complemented
100C2×#41C2×D19111yescharacteristic
101C22×D4—1912no—
102C2×D8—1912no—
103C2×D8—1912no—
104C2×M16C2×D19111yescharacteristic, complemented
105C22×C8C2×D19111yescharacteristic, complemented
106#127—3822no—
107#124—3822no—
108#121—1914no—
109#121—1914no—
110#120—3822no—
111#120—3822no—
112#117—1912no—
113#107—1912no—
114#106—1912no—
115#102—1914no—
116#102—1914no—
117C22⋊C8C2×D19114yescomplemented
118C24—3822no—
119#41—41no—
120#41—41no—
121C2×Q8D76411yescharacteristic
122C2×D4—3824no—
123C2×D4—3824no—
124C2×D4—3822no—
125C2×D4—1914no—
126C2×D4—7642no—
127C2×D4—7642no—
128C2×D4D76411yescharacteristic
129C2×D4D76412yes—
130C22×C4C22×D19112yes—
131C22×C4C22×D19111yescharacteristic
132D8—7642no—
133D8—7642no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D19112yes—
137C2×C8C22×D19112yes—
138C4⋊C4—1914no—
139C22⋊C4—3822no—
140C22⋊C4—3824no—
141C22⋊C4—3824no—
142C42—3822no—
143C23—3824no—
144C23—15284no—
145C23—7644no—
146C23C2×D76412yes—
147C23C2×D76411yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—3824no—
152D4—3824no—
153D4—15284no—
154D4—15284no—
155D4—7644no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—3824no—
161C2×C4C2×D76412yes—
162C2×C4C2×D76411yescharacteristic
163C2×C4C23×D19111yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—15288no—
171C22—7644no—
172C22—7644no—
173C22—7644no—
174C22C22×D76411yescharacteristic
175C4—22no—
176C4—21no—
177C4—7644no—
178C4#2025936711yescharacteristic
179C4#2025936711yescharacteristic
180C2—42no—
181C2—41no—
182C2—15284no—
183C2#2713322511yescharacteristic
184C2#2713346812yes—
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#408×C191C2
socleC22×C191C22×D4
hypercenter#408D191
hypocenterC191#3199
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #27133227C2semidirect
2. #27132988C2semidirect
3. #27132916C2semidirect
4. #27132899C2semidirect
5. #27132799C2semidirect
6. #408×C191C2semidirect
7. C22×D764C22semidirect
13. #20259296C22semidirect
16. #20259281C22semidirect
17. #20259256C22semidirect
18. #20259254C22semidirect
19. #20259244C22semidirect
20. #20259244C22semidirect
22. C2×M16×C191C22semidirect
23. C22×C8×C191C22semidirect
24. C22⋊C8×C191C22semidirect
92. C191#3199semidirect
99. #408D191semidirect
104. C2×M16C2×D191semidirect
105. C22×C8C2×D191semidirect
117. C22⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332272
#271329882
#271329162
#271328992
#271327992
#408×C1912
#3199191