Finite Group Databasebeta

← #37574595

Subgroups — #37574595

Order 24448.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#27133101C211yesmaximal, characteristic, complemented
2#27133099C211yesmaximal, characteristic, complemented
3#27133038C211yesmaximal, characteristic, complemented
4#27132779C211yesmaximal, characteristic, complemented
5#27132483C211yesmaximal, characteristic, complemented
6#27132475C211yesmaximal, characteristic, complemented
7#361×C191C211yesmaximal, characteristic, complemented
8#20259344C2211yescharacteristic
9C2×D1528C2211yescharacteristic
10C2×#15690272—21no—
11#20259330—21no—
12#20259318—21no—
13#20259267—21no—
14#20259266—21no—
15D3056—21no—
16#20259263—21no—
17#20259262C2211yescharacteristic
18#20259248—21no—
19C8×Dic191C2211yescharacteristic
20C2×D8×C191C2211yescharacteristic
21M32×C191C2211yescharacteristic
22#108×C191C2211yescharacteristic
23#15690287—21no—
24C2×D764—21no—
25C2×C22⋊D191—42no—
26Dic764D411yescharacteristic, complemented
27#15690276—21no—
28D1528—21no—
29D1528—21no—
30D1528D411yescharacteristic, complemented
31#15690272—41no—
32#15690272—41no—
33#15690270—41no—
34C2×C191⋊C8D411yescharacteristic
35C8×D191—41no—
36C4×Dic191D411yescharacteristic
37C191⋊C16—21no—
38C2×D4×C191—21no—
39D8×C191—21no—
40D8×C191—21no—
41M16×C191—21no—
42C2×C8×C191C2311yescharacteristic
43C16×C191—21no—
44C22×D191—41no—
45Dic382—21no—
46D764—21no—
47D764—41no—
48D764—41no—
49C22⋊D191—41no—
50C22⋊D191—84no—
51C2×Dic191—21no—
52C4×D191—41no—
53C191⋊C8D811yescharacteristic
54C191⋊C8D811yescharacteristic
55C23×C191—41no—
56D4×C191—41no—
57D4×C191—41no—
58C2×C4×C191C2×D411yescharacteristic
59C8×C191—41no—
60C8×C191C2×D411yescharacteristic
61C8×C191#4111yescharacteristic
62C22×C191—82no—
63C22×C191—81no—
64C22×C191AGL(1,ℤ/8)11yescharacteristic
65C2×D191—41no—
66C2×D191—82no—
67C2×D191—81no—
68C4×C191#12111yescharacteristic
69C4×C191C2×D811yescharacteristic
70Dic191—22no—
71Dic191—41no—
72C2×C191—21no—
73C2×C191—161no—
74C2×C191#45911yescharacteristic
75D191—81no—
76D191—161no—
77C191#221311yescharacteristic, complemented, Sylow
78#2213—1911nomaximal, Sylow
79#509—1911no—
80#509—1911no—
81#493—1911no—
82#443—1911no—
83#364—1911no—
84#361—1911no—
85#361D19111yescharacteristic, complemented
86#135—1911no—
87C2×D8—3821no—
88C2×D8—1911no—
89C2×D8C2×D19111yescharacteristic
90#131—3821no—
91#127—3821no—
92SD32—3821no—
93SD32—3821no—
94D16—3821no—
95D16—3821no—
96M32—1911no—
97M32C2×D19111yescharacteristic
98#108C2×D19111yescharacteristic
99#104—3821no—
100C4×C8—1911no—
101#41—3821no—
102C2×D4—21no—
103C2×D4—3821no—
104C2×D4—7642no—
105Q16—1911no—
106SD16—3821no—
107D8—21no—
108D8—21no—
109D8—3821no—
110D8—3821no—
111D8—1911no—
112D8—7641no—
113D8—7641no—
114M16—21no—
115M16—7641no—
116C2×C8—1911no—
117C2×C8—7641no—
118C2×C8C22×D19111yescharacteristic
119C42—1911no—
120C16—21no—
121C16—3821no—
122C23—41no—
123C23—7641no—
124Q8—3821no—
125D4—41no—
126D4—41no—
127D4—3821no—
128D4—15284no—
129D4—7641no—
130D4—7641no—
131D4—7641no—
132C2×C4—3821no—
133C2×C4—7641no—
134C2×C4D4×D19111yescharacteristic
135C8—41no—
136C8—1911no—
137C8—1911no—
138C8D4×D19111yescharacteristic
139C8#1569028711yescharacteristic
140C22—82no—
141C22—81no—
142C22—15282no—
143C22—15281no—
144C22—7641no—
145C22#2025934911yescharacteristic
146C4—3822no—
147C4—7641no—
148C4#2025929511yescharacteristic
149C4D8×D19111yescharacteristic
150C2—21no—
151C2—161no—
152C2—30561no—
153C2—15281no—
154C2#2713285711yescharacteristic
subgroupG/H
centerC2#27132857
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
Fitting#361×C191C2
socleC2×C191#459
hypercenter#361D191
hypocenterC191#2213
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #27133101C2semidirect
2. #27133099C2semidirect
3. #27133038C2semidirect
4. #27132779C2semidirect
5. #27132483C2semidirect
6. #27132475C2semidirect
7. #361×C191C2semidirect
26. Dic764D4semidirect
30. D1528D4semidirect
77. C191#2213semidirect
85. #361D191semidirect

Maximal subgroups

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

subgroupindex
#271331012
#271330992
#271330382
#271327792
#271324832
#271324752
#361×C1912
#2213191