Finite Group Databasebeta

← #37571793

Subgroups — #37571793

Order 24448.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#27133383C211yesmaximal, characteristic
2#27133061C211yesmaximal, characteristic, complemented
3#27132943C211yesmaximal, characteristic
4#27132874C211yesmaximal, characteristic, complemented
5#27132408C211yesmaximal, characteristic, complemented
6#27132395C211yesmaximal, characteristic, complemented
7D4⋊C8×C191C211yesmaximal, characteristic
8C2×Dic764—21no—
9#20259322C2211yescharacteristic
10#20259322C2211yescharacteristic
11#20259315—22no—
12#20259309—21no—
13#20259301—21no—
14C4×Dic382C2211yescharacteristic
15#20259287—21no—
16#20259281—21no—
17#20259255—21no—
18#20259254—22no—
19C4⋊(C191⋊C8)C2211yescharacteristic
20#20259247—21no—
21#20259243—21no—
22C4×D4×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4×C8×C191C2211yescharacteristic
25C2×Dic382—21no—
26C2×Dic382—21no—
27C2×Dic382D411yescharacteristic
28Dic764—42no—
29C2×C191⋊C8—21no—
30C4⋊Dic191—21no—
31C4⋊Dic191—21no—
32C4⋊Dic191—21no—
33C4⋊Dic191D411yescharacteristic
34C4⋊Dic191D412yes—
35Dic191⋊C4—22no—
36Dic191⋊C4—21no—
37C22⋊Dic191—22no—
38C22⋊Dic191—22no—
39C4×Dic191—22no—
40C4×Dic191—21no—
41C2×D4×C191D411yescharacteristic
42C22×C4×C191—21no—
43C2×C8×C191—21no—
44C2×C8×C191—21no—
45C4⋊C4×C191D411yescharacteristic
46C22⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48Dic382—21no—
49Dic382—21no—
50Dic382—41no—
51Dic382—41no—
52Dic382—41no—
53Dic382—41no—
54C2×Dic191—21no—
55C2×Dic191—21no—
56C2×Dic191—22no—
57C2×Dic191—41no—
58C191⋊C8—41no—
59C23×C191—21no—
60D4×C191—21no—
61D4×C191—21no—
62C2×C4×C191—21no—
63C2×C4×C191—41no—
64C2×C4×C191—41no—
65C2×C4×C191C2×D411yescharacteristic
66C2×C4×C191C2×D411yescharacteristic
67C2×C4×C191C2×D411yescharacteristic
68C8×C191—22no—
69C8×C191—41no—
70C22×C191—41no—
71C22×C191—41no—
72C22×C191—41no—
73C22×C191#12011yescharacteristic
74C4×C191—21no—
75C4×C191—41no—
76C4×C191#13511yescharacteristic
77C4×C191#13511yescharacteristic
78C4×C191AGL(1,ℤ/8)11yescharacteristic
79C4×C191#13711yescharacteristic
80Dic191—41no—
81Dic191—42no—
82Dic191—41no—
83Dic191—81no—
84C2×C191—81no—
85C2×C191#44911yescharacteristic
86C2×C191#45211yescharacteristic
87C2×C191#45611yescharacteristic
88C191#165211yescharacteristic, complemented, Sylow
89#1652—1911nomaximal, Sylow
90#556—1911no—
91#498—1911no—
92#474—1911no—
93#462—1911no—
94#332—1911no—
95Q8⋊C8—1911no—
96D4⋊C8D19111yescharacteristic
97C2×Q16—3821no—
98C4⋊Q8—1911no—
99C4⋊Q8—1911no—
100#126—3822no—
101#124—3821no—
102C22⋊Q8—3821no—
103C4×Q8—3821no—
104C4×Q8—1911no—
105C4×D4C2×D19111yescharacteristic
106#117—3821no—
107#107—3821no—
108#106—3822no—
109C4⋊C8—1911no—
110C4⋊C8C2×D19111yescharacteristic
111#103—3821no—
112#102—3821no—
113C4×C8C2×D19111yescharacteristic
114C2×Q8—3821no—
115C2×Q8—3821no—
116C2×Q8—1911no—
117C2×D4D76411yescharacteristic
118C22×C4—21no—
119Q16—7642no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—3821no—
123C4⋊C4—3822no—
124C4⋊C4—3821no—
125C4⋊C4—3821no—
126C4⋊C4—3821no—
127C4⋊C4—3821no—
128C4⋊C4—1911no—
129C4⋊C4—1912no—
130C4⋊C4D76411yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—3822no—
133C22⋊C4—3822no—
134C42—3822no—
135C42—3821no—
136C42C22×D19111yescharacteristic
137C23—21no—
138Q8—3821no—
139Q8—3821no—
140Q8—7641no—
141Q8—7641no—
142Q8—7641no—
143Q8—7641no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3821no—
150C2×C4—3821no—
151C2×C4—3822no—
152C2×C4—7641no—
153C2×C4D4×D19111yescharacteristic
154C2×C4D4×D19111yescharacteristic
155C2×C4C2×D76411yescharacteristic
156C8—22no—
157C8—41no—
158C8—7641no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#2025929211yescharacteristic
163C4—21no—
164C4—41no—
165C4—15281no—
166C4—7641no—
167C4—7642no—
168C4—7641no—
169C4#2025934311yescharacteristic
170C4#2025934411yescharacteristic
171C4#2025934611yescharacteristic
172C4#2025935511yescharacteristic
173C2—81no—
174C2#2713280911yescharacteristic
175C2#2713282711yescharacteristic
176C2#2713284711yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
FittingD4⋊C8×C191C2
socleC22×C191#120
prime radicalC2×D4×C191D4
hypercenterD4⋊C8D191
hypocenterC191#1652
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #27133061C2semidirect
4. #27132874C2semidirect
5. #27132408C2semidirect
6. #27132395C2semidirect
88. C191#1652semidirect

Maximal subgroups

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

subgroupindex
#271333832
#271330612
#271329432
#271328742
#271324082
#271323952
D4⋊C8×C1912
#1652191