Finite Group Databasebeta

← #37571506

Subgroups — #37571506

Order 24448.

280 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 57 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#27132974C212yesmaximal, complemented
2#27132588C211yesmaximal, characteristic, complemented
3#27132397C212yesmaximal, complemented
4#27132387C211yesmaximal, characteristic, complemented
5#534×C191C211yesmaximal, characteristic
6C2×C4⋊Dic191C2211yescharacteristic, complemented
7C2×C22⋊Dic191—21no—
8#20259255—22no—
9#20259243—22no—
10C22⋊(C191⋊C8)C2212yescomplemented
11C191⋊#95—21no—
12C191⋊#95C2211yescharacteristic, complemented
13C22×D4×C191—21no—
14#123×C191—22no—
15#121×C191—21no—
16#121×C191C2212yes—
17#120×C191—22no—
18C2×C22⋊C4×C191C2211yescharacteristic
19C22×Dic191—21no—
20C22×Dic191—21no—
21C2×C191⋊C8—22no—
22C4⋊Dic191—22no—
23C22⋊Dic191—42no—
24C24×C191—21no—
25C24×C191D411yescharacteristic
26C2×D4×C191—22no—
27C2×D4×C191—22no—
28C2×D4×C191—21no—
29C2×D4×C191—42no—
30C2×D4×C191—42no—
31C2×D4×C191D412yes—
32C22×C4×C191—21no—
33C22×C4×C191D411yescharacteristic
34C22×C4×C191C2311yescharacteristic
35C4⋊C4×C191—21no—
36C4⋊C4×C191D412yes—
37C22⋊C4×C191—22no—
38C22⋊C4×C191—22no—
39C22⋊C4×C191—22no—
40C2×Dic191—41no—
41C2×Dic191—41no—
42C2×Dic191—41no—
43C2×Dic191—41no—
44C2×Dic191—41no—
45C2×Dic191—41no—
46C191⋊C8—42no—
47C23×C191—21no—
48C23×C191—21no—
49C23×C191—22no—
50C23×C191—41no—
51C23×C191—41no—
52C23×C191—42no—
53C23×C191—81no—
54C23×C191—81no—
55C23×C191D812yes—
56C23×C191C2×D411yescharacteristic
57D4×C191—42no—
58D4×C191—44no—
59D4×C191—42no—
60D4×C191—42no—
61D4×C191—81no—
62C2×C4×C191—21no—
63C2×C4×C191—22no—
64C2×C4×C191—41no—
65C2×C4×C191—42no—
66C2×C4×C191—41no—
67C2×C4×C191C2×D412yes—
68C22×C191—21no—
69C22×C191—21no—
70C22×C191—22no—
71C22×C191—42no—
72C22×C191—41no—
73C22×C191—41no—
74C22×C191—42no—
75C22×C191—42no—
76C22×C191—42no—
77C22×C191—81no—
78C22×C191—84no—
79C22×C191#12011yescharacteristic
80C22×C191C2×D811yescharacteristic
81C22×C191AGL(1,ℤ/8)11yescharacteristic
82C4×C191—22no—
83C4×C191—42no—
84C4×C191—41no—
85Dic191—81no—
86Dic191—81no—
87C2×C191—21no—
88C2×C191—21no—
89C2×C191—42no—
90C2×C191—82no—
91C2×C191#44711yescharacteristic
92C2×C191#45511yescharacteristic
93C2×C191#45811yescharacteristic
94C191#160711yescharacteristic, complemented, Sylow
95#1607—1911nomaximal, Sylow
96#534D19111yescharacteristic
97#480—1912no—
98#397—1911no—
99#327—1912no—
100#323—1911no—
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D19112yes—
105#120—22no—
106C2×C4⋊C4—1911no—
107C2×C22⋊C4—3821no—
108C2×C22⋊C4C2×D19111yescharacteristic
109#107—3822no—
110#102—3822no—
111C22⋊C8—1912no—
112#95—3821no—
113#95—1911no—
114C24—21no—
115C24C22⋊D19111yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4C22⋊D19112yes—
122C22×C4—21no—
123C22×C4—3821no—
124C22×C4—3821no—
125C22×C4C22⋊D19111yescharacteristic
126C22×C4C22×D19111yescharacteristic
127C2×C8—3822no—
128C4⋊C4—21no—
129C4⋊C4—3822no—
130C4⋊C4C22⋊D19112yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—7642no—
135C23—21no—
136C23—21no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23—81no—
142C23—81no—
143C23#1569027212yes—
144C23C2×C22⋊D19111yescharacteristic
145D4—42no—
146D4—44no—
147D4—42no—
148D4—42no—
149D4—81no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—7641no—
156C2×C4—7641no—
157C2×C4—7641no—
158C2×C4—7641no—
159C2×C4—7641no—
160C2×C4—7641no—
161C2×C4C2×C22⋊D19112yes—
162C8—7642no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—81no—
173C22—84no—
174C22#2025929111yescharacteristic
175C22C2×#1569027211yescharacteristic
176C22#2025934811yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—15281no—
181C4—15281no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—82no—
186C2#2713279711yescharacteristic
187C2#2713284111yescharacteristic
188C2#2713285311yescharacteristic
subgroupG/H
centerC22#20259291
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting, prime radical#534×C191C2
socleC22×C191#120
hypercenter#534D191
hypocenterC191#1607
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #27132974C2semidirect
2. #27132588C2semidirect
3. #27132397C2semidirect
4. #27132387C2semidirect
6. C2×C4⋊Dic191C22semidirect
10. C22⋊(C191⋊C8)C22semidirect
12. C191⋊#95C22semidirect
94. C191#1607semidirect

Maximal subgroups

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

subgroupindex
#271329742
#271325882
#271323972
#271323872
#534×C1912
#1607191