Finite Group Databasebeta

← #37581430

Subgroups — #37581430

Order 24448.

458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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#27133430C212yesmaximal, complemented
2#27132785C214yesmaximal, complemented
3#27132780C214yesmaximal, complemented
4#27132712C211yesmaximal, characteristic, complemented
5C2×#20259249C212yesmaximal, complemented
6M16×Dic191C211yesmaximal, characteristic, complemented
7#575×C191C211yesmaximal, characteristic
8#20259329—24no—
9#20259329C2218yescomplemented
10C2×#15690271—24no—
11C2×#15690271C2212yes—
12C2×#15690271C2211yescharacteristic
13C2×C4×Dic191C2211yescharacteristic
14#20259258C2214yescomplemented
15#20259249C2214yescomplemented
16#20259249C2214yescomplemented
17#20259232C2212yescomplemented
18C8×Dic191C2212yescomplemented
19C2×#41×C191C2212yes—
20#137×C191C414yescomplemented
21AGL(1,ℤ/8)×C191C414yescomplemented
22#135×C191C2214yes—
23C2×M16×C191C2211yescharacteristic
24C22×Dic191—21no—
25#15690271—28no—
26#15690271—22no—
27#15690271D414yes—
28#15690271C2314yes—
29C2×C191⋊C8—28no—
30C2×C191⋊C8—22no—
31C2×C191⋊C8C2312yes—
32C4×Dic191—21no—
33C4×Dic191C2311yescharacteristic
34C4×Dic191C2311yescharacteristic
35#41×C191—22no—
36#41×C191—22no—
37#41×C191C2×C414yes—
38#41×C191C2314yes—
39C2×Q8×C191C2×C412yes—
40C2×D4×C191—22no—
41C2×D4×C191C2×C412yes—
42C22×C4×C191—22no—
43C22×C4×C191C2311yescharacteristic
44Q16×C191C2×C414yescomplemented
45SD16×C191C2×C418yescomplemented
46D8×C191C2×C414yescomplemented
47M16×C191C2×C414yes—
48C2×C8×C191C2312yes—
49C2×Dic191—21no—
50C2×Dic191—21no—
51C2×Dic191—42no—
52C191⋊C8—24no—
53C191⋊C8C2×D414yes—
54C23×C191—22no—
55C23×C191#4111yescharacteristic
56Q8×C191—22no—
57Q8×C191C22×C414yes—
58D4×C191—24no—
59D4×C191—24no—
60D4×C191—22no—
61D4×C191C22×C414yes—
62C2×C4×C191—22no—
63C2×C4×C191—24no—
64C2×C4×C191—24no—
65C2×C4×C191C22×C412yes—
66C2×C4×C191C2×D412yes—
67C2×C4×C191#4111yescharacteristic
68C2×C4×C191C2411yescharacteristic
69C8×C191C22×C414yes—
70C22×C191—24no—
71C22×C191—41no—
72C22×C191—82no—
73C22×C191C4×D412yes—
74C22×C191C2×#4111yescharacteristic
75C4×C191—24no—
76C4×C191C4×D412yes—
77C4×C191C23×C411yescharacteristic
78C4×C191C22×D411yescharacteristic
79Dic191—22no—
80Dic191—41no—
81C2×C191—21no—
82C2×C191—22no—
83C2×C191—44no—
84C2×C191C2×C4×D411yescharacteristic
85C191#295611yescharacteristic, complemented, Sylow
86#2956—1911nomaximal, Sylow
87#575D19111yescharacteristic
88#568—1912no—
89#444—1914no—
90#443—1914no—
91#430—1911no—
92C2×#104—1912no—
93C4×M16—1911no—
94C2×#41C2×D19112yes—
95#137Dic19114yescomplemented
96AGL(1,ℤ/8)Dic19114yescomplemented
97#135C2×D19114yes—
98#131—3824no—
99#131—1918no—
100C2×M16—3824no—
101C2×M16—1912no—
102C2×M16—1911no—
103C2×M16C2×D19111yescharacteristic
104C2×C42—1911no—
105#108—1914no—
106#104—1914no—
107#104—1914no—
108#97—1912no—
109C4×C8—1912no—
110#41—22no—
111#41—22no—
112#41C2×Dic19114yes—
113#41C22×D19114yes—
114C2×Q8C2×Dic19112yes—
115C2×D4—22no—
116C2×D4C2×Dic19112yes—
117C22×C4—22no—
118C22×C4—3821no—
119C22×C4C22×D19111yescharacteristic
120Q16C2×Dic19114yescomplemented
121SD16C2×Dic19118yescomplemented
122D8C2×Dic19114yescomplemented
123M16—3822no—
124M16—3828no—
125M16—1914no—
126M16—1914no—
127M16C2×Dic19114yes—
128C2×C8—3822no—
129C2×C8—3828no—
130C2×C8—1912no—
131C2×C8C22×D19112yes—
132C42—3821no—
133C42—1911no—
134C42—1911no—
135C23—22no—
136C23#1569028611yescharacteristic
137Q8—22no—
138Q8C22×Dic19114yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic19114yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—3821no—
147C2×C4—3821no—
148C2×C4—7642no—
149C2×C4C22×Dic19112yes—
150C2×C4D4×D19112yes—
151C2×C4#1569028611yescharacteristic
152C2×C4C23×D19111yescharacteristic
153C8—3824no—
154C8—1914no—
155C8C22×Dic19114yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic19112yes—
160C22C2×#1569028611yescharacteristic
161C4—24no—
162C4—3822no—
163C4—7641no—
164C4D4×Dic19112yes—
165C4C23×Dic19111yescharacteristic
166C4C2×D4×D19111yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic19111yescharacteristic
subgroupG/H
centerC4C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting, prime radical#575×C191C2
socleC2×C191C2×C4×D4
cosocleC2×C4×C191C24
hypercenter#575D191
hypocenterC191#2956
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #27133430C2semidirect
2. #27132785C2semidirect
3. #27132780C2semidirect
4. #27132712C2semidirect
5. C2×#20259249C2semidirect
6. M16×Dic191C2semidirect
9. #20259329C22semidirect
14. #20259258C22semidirect
15. #20259249C22semidirect
16. #20259249C22semidirect
17. #20259232C22semidirect
18. C8×Dic191C22semidirect
20. #137×C191C4semidirect
21. AGL(1,ℤ/8)×C191C4semidirect
44. Q16×C191C2×C4semidirect
45. SD16×C191C2×C4semidirect
46. D8×C191C2×C4semidirect
85. C191#2956semidirect
95. #137Dic191semidirect
96. AGL(1,ℤ/8)Dic191semidirect
120. Q16C2×Dic191semidirect
121. SD16C2×Dic191semidirect
122. D8C2×Dic191semidirect

Maximal subgroups

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

subgroupindex
#271334302
#271327852
#271327802
#271327122
C2×#202592492
M16×Dic1912
#575×C1912
#2956191