Finite Group Databasebeta

← #37570849

Subgroups — #37570849

Order 24448.

312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×Dic191⋊C4C211yesmaximal, characteristic
2#27132627C211yesmaximal, characteristic
3#27132388C214yesmaximal, complemented
4#407×C191C211yesmaximal, characteristic
5C23×Dic191C411yescharacteristic
6C23×Dic191C411yescharacteristic
7C2×#15690271—21no—
8C2×Dic191⋊C4—21no—
9C2×Dic191⋊C4—21no—
10C2×Dic191⋊C4—21no—
11C2×Dic191⋊C4—21no—
12C2×Dic191⋊C4C412yes—
13C2×Dic191⋊C4C2212yes—
14C22⋊(C191⋊C8)—21no—
15C22⋊(C191⋊C8)C2212yes—
16C23×C4×C191C2211yescharacteristic
17C2×M16×C191—21no—
18C22⋊C8×C191—21no—
19C22⋊C8×C191C2212yes—
20C22×Dic191—24no—
21C22×Dic191—21no—
22C22×Dic191—21no—
23C22×Dic191—21no—
24C22×Dic191—21no—
25C22×Dic191—42no—
26C22×Dic191C2×C412yes—
27C22×Dic191C2×C412yes—
28#15690271—42no—
29C2×C191⋊C8—22no—
30Dic191⋊C4—22no—
31Dic191⋊C4—22no—
32Dic191⋊C4—22no—
33Dic191⋊C4—22no—
34C24×C191C2×C411yescharacteristic
35C22×C4×C191—42no—
36C22×C4×C191C2×C411yescharacteristic
37C22×C4×C191D411yescharacteristic
38C22×C4×C191D411yescharacteristic
39C22×C4×C191D411yescharacteristic
40C22×C4×C191D411yescharacteristic
41C22×C4×C191C2311yescharacteristic
42M16×C191—42no—
43C2×C8×C191—22no—
44C2×Dic191—24no—
45C2×Dic191—24no—
46C2×Dic191—22no—
47C2×Dic191—22no—
48C2×Dic191—22no—
49C2×Dic191—42no—
50C2×Dic191—42no—
51C2×Dic191—42no—
52C2×Dic191M1614yescomplemented
53C191⋊C8—42no—
54C23×C191—22no—
55C23×C191—22no—
56C23×C191—22no—
57C23×C191C22⋊C411yescharacteristic
58C23×C191C22⋊C411yescharacteristic
59C23×C191C22×C411yescharacteristic
60C2×C4×C191—22no—
61C2×C4×C191—22no—
62C2×C4×C191—41no—
63C2×C4×C191—41no—
64C2×C4×C191—41no—
65C2×C4×C191—41no—
66C2×C4×C191C22⋊C411yescharacteristic
67C2×C4×C191C22⋊C411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—42no—
71C22×C191—28no—
72C22×C191—21no—
73C22×C191—21no—
74C22×C191—21no—
75C22×C191—21no—
76C22×C191—21no—
77C22×C191—21no—
78C22×C191#9912yes—
79C22×C191#10112yes—
80C22×C191C2×C22⋊C411yescharacteristic
81C22×C191C2×M1612yes—
82C4×C191—21no—
83C4×C191—21no—
84C4×C191—21no—
85C4×C191—21no—
86Dic191—24no—
87Dic191—42no—
88C2×C191—22no—
89C2×C191—22no—
90C2×C191—22no—
91C2×C191#40711yescharacteristic
92C2×C191C2×#9911yescharacteristic
93C2×C191C2×#10111yescharacteristic
94C191#146311yescharacteristic, complemented, Sylow
95#1463—1911nomaximal, Sylow
96C22×C4⋊C4—1911no—
97#407—1911no—
98#407D19111yescharacteristic
99#324—1914no—
100C23×C4—1911no—
101C23×C4—1911no—
102C23×C4C2×D19111yescharacteristic
103C2×M16—21no—
104C2×M16—3821no—
105C2×C4⋊C4—3821no—
106C2×C4⋊C4—3821no—
107C2×C4⋊C4—3821no—
108C2×C4⋊C4—3821no—
109C2×C4⋊C4—1912no—
110C2×C4⋊C4—1912no—
111C22⋊C8—21no—
112C22⋊C8—3821no—
113C22⋊C8—1912no—
114C22⋊C8C2×D19112yes—
115C24C4×D19111yescharacteristic
116C22×C4—42no—
117C22×C4—3821no—
118C22×C4—3821no—
119C22×C4—3824no—
120C22×C4—3821no—
121C22×C4—3821no—
122C22×C4—1912no—
123C22×C4—1912no—
124C22×C4—7642no—
125C22×C4C4×D19111yescharacteristic
126C22×C4C22⋊D19111yescharacteristic
127C22×C4C22⋊D19111yescharacteristic
128C22×C4D76411yescharacteristic
129C22×C4D76411yescharacteristic
130C22×C4C22×D19111yescharacteristic
131M16—42no—
132M16—7642no—
133C2×C8—22no—
134C2×C8—3822no—
135C4⋊C4—3822no—
136C4⋊C4—3822no—
137C4⋊C4—3822no—
138C4⋊C4—3822no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23(C2×D191)⋊C411yescharacteristic
143C23(C2×D191)⋊C411yescharacteristic
144C23C2×C4×D19111yescharacteristic
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—3824no—
152C2×C4—3824no—
153C2×C4—3822no—
154C2×C4—3822no—
155C2×C4—3822no—
156C2×C4—1914no—
157C2×C4—7642no—
158C2×C4—7642no—
159C2×C4—7642no—
160C2×C4(C2×D191)⋊C411yescharacteristic
161C2×C4(C2×D191)⋊C411yescharacteristic
162C2×C4C2×C22⋊D19111yescharacteristic
163C2×C4C2×D76411yescharacteristic
164C8—42no—
165C8—7642no—
166C22—28no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22#2025923612yes—
174C22#2025924012yes—
175C22C2×(C2×D191)⋊C411yescharacteristic
176C22M16×D19112yes—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—3824no—
182C4—7642no—
183C2—22no—
184C2—22no—
185C2—22no—
186C2#2713262611yescharacteristic
187C2C2×#2025923611yescharacteristic
188C2C2×#2025924011yescharacteristic
subgroupG/H
centerC22C2×(C2×D191)⋊C4
commutatorC23×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#407×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC24×C191C2×C4
cosocleC22×C4×C191C23
hypercenter#407D191
hypocenterC191#1463
LCSG ▷ C23×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #27132388C2semidirect
52. C2×Dic191M16semidirect
94. C191#1463semidirect

Maximal subgroups

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

subgroupindex
C22×Dic191⋊C42
#271326272
#271323882
#407×C1912
#1463191