Finite Group Databasebeta

← #37571855

Subgroups — #37571855

Order 24448.

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

normal subgroups only

This group has 184 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#27133417C211yesmaximal, characteristic
2#27133072C211yesmaximal, characteristic, complemented
3#27133033C211yesmaximal, characteristic, complemented
4#27133023C211yesmaximal, characteristic
5#27132404C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic
7#330×C191C211yesmaximal, characteristic, complemented
8#20259322C2211yescharacteristic
9#20259321—21no—
10#20259317—21no—
11#20259317—21no—
12#20259314C2211yescharacteristic
13#20259310C2211yescharacteristic
14#20259307—21no—
15#20259302—21no—
16#20259300—21no—
17#20259256—21no—
18#20259254—21no—
19#20259247—21no—
20#20259245—21no—
21#20259245—21no—
22#20259244—21no—
23#20259233C2211yescharacteristic
24#125×C191C2211yescharacteristic
25#97×C191C2211yescharacteristic
26#97×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382—21no—
29C2×Dic382D411yescharacteristic
30C2×D764D411yescharacteristic
31C2×C4×D191—21no—
32C2×C191⋊C8—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37C4⋊Dic191D411yescharacteristic
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46C4×Dic191—21no—
47C2×C8×C191—21no—
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191D411yescharacteristic
52C4⋊C4×C191D411yescharacteristic
53C42×C191C2311yescharacteristic
54C22×D191—21no—
55Dic382—41no—
56Dic382—42no—
57Dic382—81no—
58D764—41no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—41no—
63C4×D191—81no—
64C191⋊C8—41no—
65C2×C4×C191—21no—
66C2×C4×C191—21no—
67C2×C4×C191C2×D411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—22no—
71C8×C191—41no—
72C22×C191#12011yescharacteristic
73C2×D191—41no—
74C2×D191—41no—
75C2×D191—41no—
76C4×C191—21no—
77C4×C191—21no—
78C4×C191—21no—
79C4×C191—41no—
80C4×C191—41no—
81Dic191—41no—
82Dic191—41no—
83Dic191—41no—
84Dic191—81no—
85C2×C191#45411yescharacteristic
86C2×C191#45511yescharacteristic
87C2×C191#45611yescharacteristic
88D191—81no—
89C191#166411yescharacteristic, complemented, Sylow
90#1664—1911nomaximal, Sylow
91#563—1911no—
92#501—1911no—
93#491—1911no—
94#489—1911no—
95#330—1911no—
96#330D19111yescharacteristic, complemented
97#329—1911no—
98C4⋊Q8—3821no—
99C4⋊Q8—1911no—
100#126—3821no—
101#126—3821no—
102#125—1911no—
103#125C2×D19111yescharacteristic
104#124—1911no—
105#123—3821no—
106C22⋊Q8—3821no—
107C22⋊Q8—3821no—
108#107—3821no—
109#106—3821no—
110#103—3821no—
111#103—3821no—
112#103—3821no—
113#102—3821no—
114#97—1911no—
115#97C2×D19111yescharacteristic
116#97C2×D19111yescharacteristic
117C2×Q8—3821no—
118C2×Q8—3821no—
119C2×Q8—1911no—
120C2×D4—1911no—
121C22×C4—3821no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—3821no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—3821no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C4⋊C4D76411yescharacteristic
136C4⋊C4D76411yescharacteristic
137C22⋊C4—3821no—
138C22⋊C4—3821no—
139C22⋊C4—3821no—
140C22⋊C4—3821no—
141C22⋊C4—3821no—
142C42—3821no—
143C42C22×D19111yescharacteristic
144C23—3821no—
145Q8—15281no—
146Q8—7642no—
147Q8—7641no—
148D4—7641no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—15281no—
155C2×C4—7641no—
156C2×C4D4×D19111yescharacteristic
157C2×C4D4×D19111yescharacteristic
158C2×C4C2×D76411yescharacteristic
159C8—22no—
160C8—41no—
161C8—7641no—
162C22—7641no—
163C22—7641no—
164C22—7641no—
165C22#2025929211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—15281no—
172C4—7641no—
173C4—7641no—
174C4—7641no—
175C2—15281no—
176C2#2713283811yescharacteristic
177C2#2713284211yescharacteristic
178C2#2713284711yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#330×C191C2
socleC22×C191#120
prime radicalC2×D764D4
hypercenter#330D191
hypocenterC191#1664
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #27133072C2semidirect
3. #27133033C2semidirect
5. #27132404C2semidirect
7. #330×C191C2semidirect
89. C191#1664semidirect
96. #330D191semidirect

Maximal subgroups

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

subgroupindex
#271334172
#271330722
#271330332
#271330232
#271324042
#271324022
#330×C1912
#1664191