Finite Group Databasebeta

← #37571820

Subgroups — #37571820

Order 24448.

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

normal subgroups only

This group has 206 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, complemented
2#27133052C211yesmaximal, characteristic
3#27133029C211yesmaximal, characteristic, complemented
4#27133028C211yesmaximal, characteristic, complemented
5#27132404C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic, complemented
7#330×C191C211yesmaximal, characteristic, complemented
8C2×#15690276—21no—
9C2×D1528—21no—
10#20259321—21no—
11#20259319C2211yescharacteristic
12#20259317—21no—
13#20259317—21no—
14#20259314C2211yescharacteristic
15#20259310C2211yescharacteristic
16#20259307—21no—
17#20259302—21no—
18#20259300—21no—
19#20259244—21no—
20#20259244—21no—
21#20259242—21no—
22#20259242—21no—
23#20259233C2211yescharacteristic
24#125×C191C2211yescharacteristic
25#97×C191C2211yescharacteristic
26#97×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382D411yescharacteristic
29C2×D764—21no—
30C2×D764—21no—
31C2×D764—21no—
32C2×D764D411yescharacteristic
33C2×C4×D191—21no—
34#15690276—42no—
35D1528—42no—
36C2×C191⋊C8—21no—
37C4⋊Dic191—21no—
38C4⋊Dic191D411yescharacteristic
39C4⋊Dic191D411yescharacteristic
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42Dic191⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46(C2×D191)⋊C4—21no—
47(C2×D191)⋊C4—21no—
48C4×Dic191—21no—
49C2×C8×C191—21no—
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D411yescharacteristic
54C4⋊C4×C191D411yescharacteristic
55C42×C191C2311yescharacteristic
56C22×D191—21no—
57C22×D191—41no—
58Dic382—41no—
59Dic382—81no—
60D764—41no—
61D764—41no—
62D764—41no—
63D764—42no—
64D764—42no—
65C2×Dic191—21no—
66C2×Dic191—21no—
67C2×Dic191—21no—
68C4×D191—81no—
69C191⋊C8—41no—
70C2×C4×C191—21no—
71C2×C4×C191—21no—
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191C2×D411yescharacteristic
75C8×C191—22no—
76C8×C191—41no—
77C22×C191#12011yescharacteristic
78C2×D191—41no—
79C2×D191—41no—
80C2×D191—41no—
81C2×D191—81no—
82C2×D191—81no—
83C2×D191—81no—
84C4×C191—21no—
85C4×C191—21no—
86C4×C191—21no—
87C4×C191—41no—
88C4×C191—41no—
89Dic191—41no—
90Dic191—41no—
91Dic191—41no—
92C2×C191#45311yescharacteristic
93C2×C191#45411yescharacteristic
94C2×C191#45411yescharacteristic
95D191—81no—
96D191—161no—
97C191#165711yescharacteristic, complemented, Sylow
98#1657—1911nomaximal, Sylow
99#563—1911no—
100#496—1911no—
101#490—1911no—
102#490—1911no—
103#330—1911no—
104#330D19111yescharacteristic, complemented
105#329—1911no—
106C2×SD16—3821no—
107C2×D8—3821no—
108C4⋊Q8—3821no—
109#127—1911no—
110#126—3821no—
111#126—3821no—
112#125—1911no—
113#125C2×D19111yescharacteristic
114#124—1911no—
115#123—3821no—
116C22⋊Q8—3821no—
117C22⋊Q8—3821no—
118#102—3821no—
119#102—3821no—
120#102—3821no—
121#102—3821no—
122#97—1911no—
123#97C2×D19111yescharacteristic
124#97C2×D19111yescharacteristic
125C2×Q8—3821no—
126C2×Q8—1911no—
127C2×D4—3821no—
128C2×D4—3821no—
129C2×D4—3821no—
130C2×D4—1911no—
131C22×C4—3821no—
132SD16—7642no—
133D8—7642no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3821no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3821no—
140C4⋊C4—3821no—
141C4⋊C4—3821no—
142C4⋊C4—3821no—
143C4⋊C4—1911no—
144C4⋊C4—1911no—
145C4⋊C4D76411yescharacteristic
146C4⋊C4D76411yescharacteristic
147C22⋊C4—3821no—
148C22⋊C4—3821no—
149C22⋊C4—3821no—
150C22⋊C4—3821no—
151C22⋊C4—3821no—
152C42—3821no—
153C42C22×D19111yescharacteristic
154C23—3821no—
155C23—7641no—
156Q8—15281no—
157Q8—7641no—
158D4—7641no—
159D4—7641no—
160D4—7642no—
161D4—7642no—
162D4—7641no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—3821no—
166C2×C4—3821no—
167C2×C4—3821no—
168C2×C4—15281no—
169C2×C4D4×D19111yescharacteristic
170C2×C4D4×D19111yescharacteristic
171C2×C4C2×D76411yescharacteristic
172C8—22no—
173C8—41no—
174C8—7641no—
175C22—15281no—
176C22—15281no—
177C22—15281no—
178C22—7641no—
179C22—7641no—
180C22—7641no—
181C22#2025929211yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—7641no—
188C4—7641no—
189C4—7641no—
190C2—30561no—
191C2—15281no—
192C2#2713283211yescharacteristic
193C2#2713283711yescharacteristic
194C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#330×C191C2
socleC22×C191#120
prime radical#27133052C2
hypercenter#330D191
hypocenterC191#1657
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #27133417C2semidirect
3. #27133029C2semidirect
4. #27133028C2semidirect
5. #27132404C2semidirect
6. #27132402C2semidirect
7. #330×C191C2semidirect
97. C191#1657semidirect
104. #330D191semidirect

Maximal subgroups

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

subgroupindex
#271334172
#271330522
#271330292
#271330282
#271324042
#271324022
#330×C1912
#1657191