Finite Group Databasebeta

← #37571830

Subgroups — #37571830

Order 24448.

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

normal subgroups only

This group has 196 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#27133069C211yesmaximal, characteristic, complemented
3#27133055C211yesmaximal, characteristic
4#27132405C211yesmaximal, characteristic, complemented
5#27132404C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic
7#501×C191C211yesmaximal, characteristic, complemented
8C2×#15690277—21no—
9C2×#15690274—21no—
10#20259321—21no—
11#20259317—21no—
12#20259317—21no—
13#20259314C2211yescharacteristic
14#20259310C2211yescharacteristic
15#20259307—21no—
16#20259302—21no—
17#20259300—21no—
18#20259255—21no—
19#20259253—21no—
20#20259233C2211yescharacteristic
21#20259233C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#125×C191C2211yescharacteristic
24#107×C191—21no—
25#106×C191—21no—
26#97×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382D411yescharacteristic
29C2×D764D411yescharacteristic
30C2×C4×D191—21no—
31#15690277—42no—
32#15690274—42no—
33C2×C191⋊C8—21no—
34C2×C191⋊C8—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×Q8×C191—21no—
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D411yescharacteristic
54C4⋊C4×C191D411yescharacteristic
55C42×C191C2311yescharacteristic
56C22×D191—21no—
57Dic382—41no—
58Dic382—81no—
59D764—41no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—21no—
63C4×D191—81no—
64C191⋊C8—22no—
65C191⋊C8—22no—
66Q8×C191—41no—
67Q8×C191—41no—
68C2×C4×C191—21no—
69C2×C4×C191—21no—
70C2×C4×C191—41no—
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191C2×D411yescharacteristic
74C8×C191—22no—
75C22×C191#12011yescharacteristic
76C2×D191—41no—
77C2×D191—41no—
78C2×D191—41no—
79C4×C191—21no—
80C4×C191—21no—
81C4×C191—21no—
82C4×C191—41no—
83C4×C191—41no—
84C4×C191—81no—
85Dic191—41no—
86Dic191—41no—
87Dic191—41no—
88C2×C191#45311yescharacteristic
89C2×C191#45611yescharacteristic
90C2×C191#45611yescharacteristic
91D191—81no—
92C191#166011yescharacteristic, complemented, Sylow
93#1660—1911nomaximal, Sylow
94#563—1911no—
95#501—1911no—
96#501D19111yescharacteristic, complemented
97#497—1911no—
98#330—1911no—
99#330—1911no—
100#329—1911no—
101C2×Q16—3821no—
102C2×SD16—3821no—
103C4⋊Q8—3821no—
104C4⋊Q8C2×D19111yescharacteristic
105#126—3821no—
106#126—3821no—
107#125—1911no—
108#125C2×D19111yescharacteristic
109#124—1911no—
110#123—3821no—
111C22⋊Q8—3821no—
112C22⋊Q8—3821no—
113#107—21no—
114#107—3821no—
115#106—21no—
116#106—3821no—
117#97—1911no—
118#97—1911no—
119#97C2×D19111yescharacteristic
120C2×Q8—21no—
121C2×Q8—3821no—
122C2×Q8—1911no—
123C2×D4—1911no—
124C22×C4—3821no—
125Q16—7642no—
126SD16—7642no—
127C2×C8—21no—
128C2×C8—3821no—
129C2×C8—3821no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3821no—
135C4⋊C4—3821no—
136C4⋊C4—3821no—
137C4⋊C4—3821no—
138C4⋊C4—1911no—
139C4⋊C4—1911no—
140C4⋊C4C22⋊D19111yescharacteristic
141C4⋊C4C22⋊D19111yescharacteristic
142C22⋊C4—3821no—
143C22⋊C4—3821no—
144C22⋊C4—3821no—
145C22⋊C4—3821no—
146C22⋊C4—3821no—
147C42—3821no—
148C42C22×D19111yescharacteristic
149C23—3821no—
150Q8—41no—
151Q8—41no—
152Q8—15281no—
153Q8—7641no—
154D4—7641no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—3821no—
159C2×C4—3821no—
160C2×C4—3821no—
161C2×C4—15281no—
162C2×C4D4×D19111yescharacteristic
163C2×C4D4×D19111yescharacteristic
164C2×C4C2×C22⋊D19111yescharacteristic
165C8—22no—
166C8—3822no—
167C8—3822no—
168C22—7641no—
169C22—7641no—
170C22—7641no—
171C22#2025929011yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—7641no—
179C4—7641no—
180C4—7641no—
181C2—15281no—
182C2#2713282911yescharacteristic
183C2#2713284411yescharacteristic
184C2#2713284511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#501×C191C2
socleC22×C191#120
prime radicalC2×D764D4
hypercenter#501D191
hypocenterC191#1660
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #27133069C2semidirect
4. #27132405C2semidirect
5. #27132404C2semidirect
7. #501×C191C2semidirect
92. C191#1660semidirect
96. #501D191semidirect

Maximal subgroups

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

subgroupindex
#271334172
#271330692
#271330552
#271324052
#271324042
#271324022
#501×C1912
#1660191