Finite Group Databasebeta

← #37571095

Subgroups — #37571095

Order 24448.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#27133197C211yesmaximal, characteristic
2#27132716C211yesmaximal, characteristic, complemented
3#27132399C212yesmaximal, complemented
4#27132396C212yesmaximal
5#383×C191C211yesmaximal, characteristic, complemented
6#20259316—21no—
7#20259314C411yescharacteristic, complemented
8#20259310C411yescharacteristic, complemented
9#20259305—21no—
10#20259301C2211yescharacteristic
11#20259296C2211yescharacteristic
12C4×Dic382C411yescharacteristic, complemented
13C4×D764C411yescharacteristic, complemented
14C4×C22⋊D191—21no—
15#20259279—21no—
16C4⋊(C191⋊C8)—21no—
17C22⋊(C191⋊C8)C2212yes—
18C4×C191⋊C8—21no—
19C2×C42×C191C2211yescharacteristic
20#95×C191—21no—
21#95×C191—21no—
22#95×C191C2212yes—
23C2×Dic382C2×C411yescharacteristic
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—21no—
26C2×C4×D191—21no—
27C2×C191⋊C8—22no—
28C4⋊Dic191C2×C411yescharacteristic
29C4⋊Dic191C2×C411yescharacteristic
30Dic191⋊C4—21no—
31Dic191⋊C4—21no—
32Dic191⋊C4—21no—
33Dic191⋊C4—21no—
34C22⋊Dic191—21no—
35(C2×D191)⋊C4—21no—
36(C2×D191)⋊C4—21no—
37(C2×D191)⋊C4—21no—
38(C2×D191)⋊C4—21no—
39C4×Dic191—21no—
40C22×C4×C191—22no—
41C22×C4×C191D411yescharacteristic
42C22×C4×C191D411yescharacteristic
43C22×C4×C191C2311yescharacteristic
44C42×C191C2×C411yescharacteristic
45C42×C191C2×C411yescharacteristic
46C42×C191D411yescharacteristic
47C42×C191D411yescharacteristic
48C22×D191—21no—
49Dic382—41no—
50D764—41no—
51C22⋊D191—42no—
52C2×Dic191—21no—
53C2×Dic191—21no—
54C2×Dic191—21no—
55C4×D191—42no—
56C191⋊C8—42no—
57C23×C191C2×D411yescharacteristic
58C2×C4×C191—22no—
59C2×C4×C191—41no—
60C2×C4×C191—41no—
61C2×C4×C191—42no—
62C2×C4×C191—42no—
63C2×C4×C191—42no—
64C2×C4×C191C22⋊C411yescharacteristic
65C2×C4×C191C22⋊C411yescharacteristic
66C2×C4×C191C22⋊C411yescharacteristic
67C2×C4×C191C22⋊C411yescharacteristic
68C2×C4×C191C22×C411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C22×C191—21no—
71C22×C191—21no—
72C22×C191C2×C22⋊C411yescharacteristic
73C22×C191#13512yes—
74C2×D191—41no—
75C2×D191—41no—
76C2×D191—41no—
77C4×C191—21no—
78C4×C191—21no—
79C4×C191—21no—
80C4×C191—21no—
81C4×C191—21no—
82C4×C191—21no—
83C4×C191—82no—
84Dic191—41no—
85Dic191—41no—
86Dic191—41no—
87C2×C191—22no—
88C2×C191#41011yescharacteristic
89C2×C191#41611yescharacteristic
90C2×C191#42111yescharacteristic
91D191—81no—
92C191#152111yescharacteristic, complemented, Sylow
93#1521—1911nomaximal, Sylow
94#529—1911no—
95#431—1911no—
96#383D19111yescharacteristic, complemented
97#328—1912no—
98#327—1912no—
99#126—3821no—
100#125—1911no—
101#124—1911no—
102#123—3821no—
103C22⋊Q8—1911no—
104#121—1911no—
105C4×Q8—1911no—
106C4×D4—3821no—
107C4×D4—1911no—
108#117—3821no—
109C2×C42C2×D19111yescharacteristic
110C4⋊C8—3821no—
111C22⋊C8—1912no—
112C4×C8—3821no—
113#95—21no—
114#95—21no—
115#95C2×D19112yes—
116C2×Q8—1911no—
117C2×D4—3821no—
118C2×D4—1911no—
119C22×C4—22no—
120C22×C4—3821no—
121C22×C4C22⋊D19111yescharacteristic
122C22×C4C22⋊D19111yescharacteristic
123C22×C4C22×D19111yescharacteristic
124C2×C8—3822no—
125C4⋊C4—3821no—
126C4⋊C4—3821no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—1911no—
130C4⋊C4—1911no—
131C22⋊C4—3821no—
132C22⋊C4—3821no—
133C22⋊C4—3821no—
134C22⋊C4—3821no—
135C22⋊C4—3821no—
136C42—3821no—
137C42C4×D19111yescharacteristic
138C42C4×D19111yescharacteristic
139C42D76411yescharacteristic
140C42D76411yescharacteristic
141C23—3821no—
142C23C2×C22⋊D19111yescharacteristic
143Q8—7641no—
144D4—7641no—
145D4—7642no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—3821no—
155C2×C4—7642no—
156C2×C4(C2×D191)⋊C411yescharacteristic
157C2×C4(C2×D191)⋊C411yescharacteristic
158C2×C4(C2×D191)⋊C411yescharacteristic
159C2×C4(C2×D191)⋊C411yescharacteristic
160C2×C4C2×C4×D19111yescharacteristic
161C2×C4C2×D76411yescharacteristic
162C8—7642no—
163C22—21no—
164C22—21no—
165C22—7641no—
166C22—7641no—
167C22—7641no—
168C22C2×(C2×D191)⋊C411yescharacteristic
169C22#2025934212yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—7641no—
178C4—7641no—
179C4—7641no—
180C2—22no—
181C2—15281no—
182C2#2713263611yescharacteristic
183C2#2713265711yescharacteristic
184C2#2713268111yescharacteristic
subgroupG/H
centerC22C2×(C2×D191)⋊C4
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#383×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259296C22
cosocleC22×C4×C191C23
hypercenter#383D191
hypocenterC191#1521
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #27132716C2semidirect
3. #27132399C2semidirect
5. #383×C191C2semidirect
7. #20259314C4semidirect
8. #20259310C4semidirect
12. C4×Dic382C4semidirect
13. C4×D764C4semidirect
92. C191#1521semidirect
96. #383D191semidirect

Maximal subgroups

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

subgroupindex
#271331972
#271327162
#271323992
#271323962
#383×C1912
#1521191