Finite Group Databasebeta

← #37571812

Subgroups — #37571812

Order 24448.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#27133411C211yesmaximal, characteristic, complemented
2#27133050C212yesmaximal, complemented
3#27132405C211yesmaximal, characteristic, complemented
4#27132402C212yesmaximal, complemented
5#490×C191C211yesmaximal, characteristic, complemented
6C2×#15690275—22no—
7C2×#15690272—22no—
8#20259310C2212yes—
9#20259307—22no—
10#20259300—22no—
11#20259297—22no—
12#20259233C2212yes—
13#127×C191C2211yescharacteristic
14#125×C191C2211yescharacteristic
15#102×C191—22no—
16#97×C191C2211yescharacteristic
17C2×Dic382D412yes—
18C2×D764—22no—
19C2×D764D412yes—
20C2×C4×D191—22no—
21#15690275—44no—
22#15690272—44no—
23C2×C191⋊C8—22no—
24Dic191⋊C4—22no—
25(C2×D191)⋊C4—22no—
26(C2×D191)⋊C4—22no—
27(C2×D191)⋊C4—22no—
28C2×D4×C191—22no—
29C2×D4×C191—21no—
30C2×C8×C191—21no—
31C4⋊C4×C191—22no—
32C4⋊C4×C191D412yes—
33C42×C191C2311yescharacteristic
34C22×D191—22no—
35Dic382—42no—
36D764—42no—
37D764—82no—
38C2×Dic191—22no—
39C4×D191—82no—
40C191⋊C8—24no—
41C23×C191—41no—
42D4×C191—42no—
43D4×C191—42no—
44D4×C191—42no—
45C2×C4×C191—22no—
46C2×C4×C191C2×D412yes—
47C2×C4×C191C2×D411yescharacteristic
48C8×C191—41no—
49C22×C191—82no—
50C22×C191—81no—
51C22×C191#12011yescharacteristic
52C2×D191—42no—
53C2×D191—42no—
54C2×D191—42no—
55C4×C191—22no—
56C4×C191—21no—
57C4×C191—42no—
58Dic191—42no—
59C2×C191—161no—
60C2×C191#45312yes—
61C2×C191#45411yescharacteristic
62D191—82no—
63C191#165611yescharacteristic, complemented, Sylow
64#1656—1911nomaximal, Sylow
65#562—1911no—
66#496—1912no—
67#490D19111yescharacteristic, complemented
68#330—1911no—
69#329—1912no—
70C2×SD16—3822no—
71C2×D8—3822no—
72#127C2×D19111yescharacteristic
73#125C2×D19111yescharacteristic
74#124—1912no—
75#123—3822no—
76C22⋊Q8—3822no—
77#121—3822no—
78#102—22no—
79#97—1912no—
80#97C2×D19111yescharacteristic
81C2×Q8—1912no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—3822no—
85C2×D4—1912no—
86C22×C4—3822no—
87SD16—7644no—
88D8—7644no—
89C2×C8—21no—
90C2×C8—3822no—
91C4⋊C4—22no—
92C4⋊C4—3822no—
93C4⋊C4C22⋊D19112yes—
94C22⋊C4—3822no—
95C22⋊C4—3822no—
96C22⋊C4—3822no—
97C42C22×D19111yescharacteristic
98C23—41no—
99C23—3822no—
100Q8—7642no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—15282no—
105D4—7642no—
106C2×C4—22no—
107C2×C4—3822no—
108C2×C4—15282no—
109C2×C4D4×D19112yes—
110C2×C4C2×C22⋊D19111yescharacteristic
111C8—41no—
112C8—3824no—
113C22—82no—
114C22—81no—
115C22—7642no—
116C22—7642no—
117C22—7642no—
118C22#2025929011yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—7642no—
123C2—161no—
124C2—15282no—
125C2#2713282912yes—
126C2#2713283511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#490×C191C2
socleC22×C191#120
hypercenter#490D191
hypocenterC191#1656
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #27133411C2semidirect
2. #27133050C2semidirect
3. #27132405C2semidirect
4. #27132402C2semidirect
5. #490×C191C2semidirect
63. C191#1656semidirect
67. #490D191semidirect

Maximal subgroups

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

subgroupindex
#271334112
#271330502
#271324052
#271324022
#490×C1912
#1656191