Finite Group Databasebeta

← #37570833

Subgroups — #37570833

Order 24448.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#20259280C211yesmaximal, characteristic
2#27132713C212yesmaximal, complemented
3#27132389C211yesmaximal, characteristic, complemented
4#27132386C212yesmaximal
5#324×C191C211yesmaximal, characteristic, complemented
6C22×C4×D191C411yescharacteristic
7#20259280—22no—
8#20259280—22no—
9C2×C4⋊Dic191C411yescharacteristic
10C2×(C2×D191)⋊C4C411yescharacteristic
11C2×(C2×D191)⋊C4C2211yescharacteristic
12C2×C4×Dic191C411yescharacteristic
13C2×C4×Dic191C2211yescharacteristic
14Dic191⋊C8—22no—
15C22⋊(C191⋊C8)C2212yes—
16C8×Dic191—22no—
17C2×C4⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yes—
19C23×D191C2×C411yescharacteristic
20C22×Dic191C2×C411yescharacteristic
21C22×Dic191C2×C411yescharacteristic
22C22×Dic191C2×C411yescharacteristic
23C2×C4×D191—21no—
24C2×C4×D191—21no—
25C2×C4×D191—22no—
26C2×C4×D191C814yescomplemented
27C2×C191⋊C8—22no—
28C4⋊Dic191—22no—
29(C2×D191)⋊C4—22no—
30(C2×D191)⋊C4—22no—
31C4×Dic191—21no—
32C4×Dic191—21no—
33C4×Dic191D412yes—
34C4×Dic191D412yes—
35C22×C4×C191C2×C411yescharacteristic
36C22×C4×C191C2×C411yescharacteristic
37C22×C4×C191C2311yescharacteristic
38C2×C8×C191—22no—
39C4⋊C4×C191—22no—
40C22×D191—21no—
41C22×D191—21no—
42C22×D191—41no—
43C22×D191—41no—
44C22×D191C2×C812yes—
45C2×Dic191—21no—
46C2×Dic191—41no—
47C2×Dic191—41no—
48C2×Dic191C22⋊C412yes—
49C2×Dic191C22⋊C411yescharacteristic
50C2×Dic191C22⋊C411yescharacteristic
51C2×Dic191C2×C812yes—
52C2×Dic191M1612yes—
53C4×D191—24no—
54C4×D191—24no—
55C191⋊C8—42no—
56C23×C191C22×C411yescharacteristic
57C2×C4×C191—21no—
58C2×C4×C191—21no—
59C2×C4×C191—21no—
60C2×C4×C191—41no—
61C2×C4×C191—41no—
62C2×C4×C191C2×C812yes—
63C2×C4×C191C2×D412yes—
64C8×C191—42no—
65C22×C191—21no—
66C22×C191—21no—
67C22×C191C2×C22⋊C411yescharacteristic
68C22×C191C22×C811yescharacteristic
69C22×C191C2×M1611yescharacteristic
70C2×D191—22no—
71C2×D191—42no—
72C2×D191—41no—
73C2×D191—41no—
74C2×D191—42no—
75C4×C191—22no—
76C4×C191—22no—
77C4×C191—41no—
78Dic191—22no—
79Dic191—41no—
80Dic191C22⋊C812yes—
81Dic191C22⋊C812yes—
82C2×C191—21no—
83C2×C191—21no—
84C2×C191C2×C22⋊C811yescharacteristic
85C2×C191#41011yescharacteristic
86C2×C191#41311yescharacteristic
87D191—42no—
88C191#145811yescharacteristic, complemented, Sylow
89#1458—1911nomaximal, Sylow
90C2×#117—1911no—
91#431—1912no—
92#324—1911no—
93#324D19111yescharacteristic, complemented
94#323—1912no—
95C23×C4—1911no—
96#117—3822no—
97#117—3822no—
98C2×C4⋊C4—1911no—
99C2×C4⋊C4C2×D19111yescharacteristic
100C2×C22⋊C4—1911no—
101C2×C22⋊C4—1911no—
102C2×C42—1911no—
103C2×C42—1911no—
104C4⋊C8—3822no—
105C22⋊C8—1912no—
106C22⋊C8C2×D19112yes—
107C4×C8—3822no—
108C24—1911no—
109C22×C4—3821no—
110C22×C4—3821no—
111C22×C4—3822no—
112C22×C4—1914no—
113C22×C4—1911no—
114C22×C4—1911no—
115C22×C4—1911no—
116C22×C4C4×D19111yescharacteristic
117C22×C4C4×D19111yescharacteristic
118C22×C4C22×D19111yescharacteristic
119C2×C8—22no—
120C2×C8—3822no—
121C4⋊C4—22no—
122C4⋊C4—3822no—
123C22⋊C4—3822no—
124C22⋊C4—3822no—
125C42—3821no—
126C42—3821no—
127C42—1912no—
128C42—1912no—
129C23—3821no—
130C23—3821no—
131C23—1912no—
132C23—7641no—
133C23—7641no—
134C23C2×C4×D19111yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3824no—
141C2×C4—3824no—
142C2×C4—3821no—
143C2×C4—1912no—
144C2×C4—1911no—
145C2×C4—1911no—
146C2×C4—1912no—
147C2×C4—1912no—
148C2×C4—7641no—
149C2×C4—7641no—
150C2×C4C8×D19112yes—
151C2×C4D4×D19112yes—
152C8—42no—
153C8—7642no—
154C22—21no—
155C22—21no—
156C22—3822no—
157C22—7642no—
158C22—7642no—
159C22—7641no—
160C22—7641no—
161C22C22⋊C4×D19111yescharacteristic
162C22C2×C8×D19111yescharacteristic
163C22M16×D19111yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—3822no—
168C4—1912no—
169C4—1912no—
170C4—7641no—
171C2—21no—
172C2—21no—
173C2—7642no—
174C2C22⋊C8×D19111yescharacteristic
175C2#2713263511yescharacteristic
176C2#2713264611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC22×C191C22×C8
FrattiniC22×C4C22×D191
Fitting#324×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC23×D191C2×C4
cosocleC22×C4×C191C23
hypercenter#324D191
hypocenterC191#1458
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #27132713C2semidirect
3. #27132389C2semidirect
5. #324×C191C2semidirect
26. C2×C4×D191C8semidirect
88. C191#1458semidirect
93. #324D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592802
#271327132
#271323892
#271323862
#324×C1912
#1458191