Finite Group Databasebeta

← #37574504

Subgroups — #37574504

Order 24448.

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

normal subgroups only

This group has 354 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#27132849C212yesmaximal, complemented
2#27132830C211yesmaximal, characteristic, complemented
3#27132456C211yesmaximal, characteristic, complemented
4#27132450C212yesmaximal, complemented
5D42×C191C211yesmaximal, characteristic, complemented
6#20259367C2211yescharacteristic, complemented
7#20259348—21no—
8#20259291—22no—
9#20259250—21no—
10#20259239C2211yescharacteristic, complemented
11#20259237C2212yescomplemented
12#20259236—22no—
13C22×D4×C191—22no—
14#127×C191C2211yescharacteristic
15#121×C191—22no—
16#120×C191—21no—
17#120×C191C2212yes—
18C4×D4×C191—21no—
19#15690287—21no—
20#15690286—41no—
21C2×C22⋊D191—22no—
22C2×C22⋊D191—42no—
23D4×D191—41no—
24#15690275—41no—
25#15690272—41no—
26#15690271—21no—
27C22⋊Dic191—22no—
28C22⋊Dic191—42no—
29C24×C191—21no—
30C24×C191D412yescomplemented
31C2×D4×C191—21no—
32C2×D4×C191—22no—
33C2×D4×C191—22no—
34C2×D4×C191—22no—
35C2×D4×C191—48no—
36C2×D4×C191D411yescharacteristic, complemented
37C2×D4×C191C2311yescharacteristic
38C22×C4×C191—22no—
39C4⋊C4×C191—21no—
40C22⋊C4×C191—21no—
41C22⋊C4×C191—22no—
42C22⋊C4×C191D412yescomplemented
43C42×C191D411yescharacteristic, complemented
44C22×D191—22no—
45Dic382—21no—
46D764—21no—
47C22⋊D191—42no—
48C22⋊D191—41no—
49C22⋊D191—84no—
50C2×Dic191—22no—
51C2×Dic191—42no—
52C4×D191—41no—
53C191⋊C8—41no—
54C23×C191—22no—
55C23×C191—21no—
56C23×C191—44no—
57C23×C191—42no—
58C23×C191—44no—
59C23×C191—81no—
60C23×C191C2×D412yes—
61D4×C191—24no—
62D4×C191—41no—
63D4×C191—41no—
64D4×C191—44no—
65D4×C191—44no—
66D4×C191—44no—
67C2×C4×C191—21no—
68C2×C4×C191—22no—
69C2×C4×C191—44no—
70C2×C4×C191C2×D411yescharacteristic
71C22×C191—24no—
72C22×C191—22no—
73C22×C191—42no—
74C22×C191—42no—
75C22×C191—42no—
76C22×C191—44no—
77C22×C191—42no—
78C22×C191—41no—
79C22×C191—82no—
80C22×C191—84no—
81C22×C191#12011yescharacteristic
82C2×D191—41no—
83C2×D191—82no—
84C4×C191—22no—
85C4×C191—21no—
86C4×C191—42no—
87Dic191—41no—
88Dic191—82no—
89C2×C191—21no—
90C2×C191—42no—
91C2×C191—44no—
92C2×C191—81no—
93C2×C191B(4,𝔽2)11yescharacteristic
94D191—81no—
95C191#219611yescharacteristic, complemented, Sylow
96#2196—1911nomaximal, Sylow
97D42D19111yescharacteristic, complemented
98B(4,𝔽2)—1912no—
99#453—1911no—
100#353—1911no—
101AΣL(1,𝔽16)—1912no—
102H(5,𝔽2)—1911no—
103C22×D4—22no—
104AGL(1,ℤ/8)—3821no—
105#127C2×D19111yescharacteristic
106#121—22no—
107#120—21no—
108#120—3822no—
109#120C2×D19112yes—
110C4×D4—21no—
111#104—3821no—
112#100—1911no—
113#99—3822no—
114#99—1912no—
115C24—21no—
116C24C22⋊D19112yescomplemented
117#41—3821no—
118#41—7641no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—3822no—
125C2×D4—7641no—
126C2×D4—7642no—
127C2×D4C22⋊D19111yescharacteristic, complemented
128C2×D4C22×D19111yescharacteristic
129C22×C4—22no—
130SD16—7641no—
131D8—7641no—
132M16—3821no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—3822no—
137C22⋊C4—7642no—
138C22⋊C4C22⋊D19112yescomplemented
139C42C22⋊D19111yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—3822no—
147C23C2×C22⋊D19112yes—
148Q8—3821no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—3821no—
156D4—15284no—
157D4—7642no—
158D4—7641no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—3822no—
163C2×C4—7641no—
164C2×C4—7642no—
165C2×C4C2×C22⋊D19111yescharacteristic
166C8—7641no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—15282no—
178C22—7641no—
179C22#2025929111yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—15282no—
184C4—7641no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—15281no—
190C2#2713285011yescharacteristic
subgroupG/H
centerC2#27132850
commutator, cosocleC2×D4×C191C23
FrattiniC2×D4C22×D191
FittingD42×C191C2
socleC2×C191B(4,𝔽2)
hypercenterD42D191
hypocenterC191#2196
LCSG ▷ C2×D4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #27132849C2semidirect
2. #27132830C2semidirect
3. #27132456C2semidirect
4. #27132450C2semidirect
5. D42×C191C2semidirect
6. #20259367C22semidirect
10. #20259239C22semidirect
11. #20259237C22semidirect
30. C24×C191D4semidirect
36. C2×D4×C191D4semidirect
42. C22⋊C4×C191D4semidirect
43. C42×C191D4semidirect
95. C191#2196semidirect
97. D42D191semidirect
116. C24C22⋊D191semidirect
127. C2×D4C22⋊D191semidirect
138. C22⋊C4C22⋊D191semidirect
139. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271328492
#271328302
#271324562
#271324502
D42×C1912
#2196191