Finite Group Databasebeta

← #37571617

Subgroups — #37571617

Order 24448.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133388C211yesmaximal, characteristic, complemented
2#27133011C211yesmaximal, characteristic
3#27132864C211yesmaximal, characteristic
4#27132864C211yesmaximal, characteristic
5#27132393C211yesmaximal, characteristic, complemented
6#27132393C211yesmaximal, characteristic, complemented
7#332×C191C211yesmaximal, characteristic, complemented
8C2×#15690276—21no—
9C2×#15690276—21no—
10#20259320—21no—
11#20259319C2211yescharacteristic
12#20259313—21no—
13#20259312—22no—
14Q8×Dic191—21no—
15C4×Dic382C2211yescharacteristic
16C4×Dic382C2211yescharacteristic
17#20259287—21no—
18#20259244—21no—
19#20259244—21no—
20#20259242—22no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25C2×Dic382D411yescharacteristic
26C2×Dic382D411yescharacteristic
27C2×D764—21no—
28C2×D764—21no—
29C2×D764—21no—
30#15690276—42no—
31#15690276—42no—
32C2×C191⋊C8—21no—
33C4⋊Dic191—22no—
34C4⋊Dic191D411yescharacteristic
35C4⋊Dic191D411yescharacteristic
36Dic191⋊C4—22no—
37Dic191⋊C4—22no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40C4×Dic191—22no—
41C4×Dic191—21no—
42C4×Dic191—21no—
43C2×Q8×C191—21no—
44C2×C8×C191—21no—
45C2×C8×C191—21no—
46C4⋊C4×C191—21no—
47C4⋊C4×C191D412yes—
48C42×C191C2311yescharacteristic
49C22×D191—41no—
50Dic382—21no—
51Dic382—21no—
52Dic382—21no—
53Dic382SD1612yescomplemented
54D764—42no—
55D764—41no—
56D764—41no—
57D764—41no—
58D764—41no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—21no—
63C191⋊C8—41no—
64Q8×C191—41no—
65Q8×C191—41no—
66C2×C4×C191—22no—
67C2×C4×C191C2×D411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—41no—
71C8×C191—41no—
72C22×C191#12011yescharacteristic
73C2×D191—81no—
74C2×D191—81no—
75C2×D191—81no—
76C4×C191—21no—
77C4×C191—42no—
78C4×C191C2×SD1611yescharacteristic
79C4×C191#13511yescharacteristic
80C4×C191AGL(1,ℤ/8)11yescharacteristic
81C4×C191#13711yescharacteristic
82Dic191—22no—
83Dic191—41no—
84Dic191—41no—
85Dic191—41no—
86C2×C191#44811yescharacteristic
87C2×C191#44911yescharacteristic
88C2×C191#45411yescharacteristic
89D191—161no—
90C191#162611yescharacteristic, complemented, Sylow
91#1626—1911nomaximal, Sylow
92#557—1911no—
93#486—1911no—
94#460—1911no—
95#460—1911no—
96#332D19111yescharacteristic, complemented
97Q8⋊C8—1911no—
98Q8⋊C8—1911no—
99C2×SD16—3821no—
100C2×SD16—3821no—
101C4⋊Q8—3821no—
102C4⋊Q8C2×D19111yescharacteristic
103#127—1911no—
104#125—3821no—
105#125—3822no—
106C4×Q8—3821no—
107C4×Q8—3821no—
108C4×Q8—1911no—
109C4×Q8—1911no—
110C4⋊C8C2×D19111yescharacteristic
111C4⋊C8C2×D19111yescharacteristic
112#102—3821no—
113#102—3821no—
114#102—3822no—
115C4×C8—1911no—
116C2×Q8—21no—
117C2×Q8—1911no—
118C2×Q8—1911no—
119C2×D4—3821no—
120C2×D4—3821no—
121C2×D4—3821no—
122SD16—7642no—
123SD16—7642no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—3821no—
127C4⋊C4—21no—
128C4⋊C4—3822no—
129C4⋊C4—3822no—
130C4⋊C4—3822no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C4⋊C4D76412yes—
136C42—3822no—
137C42—3821no—
138C42—3821no—
139C42C22×D19111yescharacteristic
140C23—7641no—
141Q8—41no—
142Q8—41no—
143Q8—3821no—
144Q8—3821no—
145Q8—3821no—
146Q8—1912no—
147D4—7642no—
148D4—7641no—
149D4—7641no—
150D4—7641no—
151D4—7641no—
152C2×C4—22no—
153C2×C4—3821no—
154C2×C4—3821no—
155C2×C4—3821no—
156C2×C4—3821no—
157C2×C4D4×D19111yescharacteristic
158C2×C4D4×D19111yescharacteristic
159C2×C4C2×D76411yescharacteristic
160C8—41no—
161C8—41no—
162C8—7641no—
163C22—15281no—
164C22—15281no—
165C22—15281no—
166C22#2025929211yescharacteristic
167C4—21no—
168C4—42no—
169C4—3822no—
170C4—7641no—
171C4—7641no—
172C4—7641no—
173C4SD16×D19111yescharacteristic
174C4#2025934311yescharacteristic
175C4#2025934611yescharacteristic
176C4#2025935411yescharacteristic
177C2—30561no—
178C2#2713280311yescharacteristic
179C2#2713280911yescharacteristic
180C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#332×C191C2
socleC22×C191#120
prime radical#20259319C22
hypercenter#332D191
hypocenterC191#1626
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #27133388C2semidirect
5. #27132393C2semidirect
6. #27132393C2semidirect
7. #332×C191C2semidirect
53. Dic382SD16semidirect
90. C191#1626semidirect
96. #332D191semidirect

Maximal subgroups

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

subgroupindex
#271333882
#271330112
#271328642
#271323932
#332×C1912
#1626191