Finite Group Databasebeta

← #37570839

Subgroups — #37570839

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
1C2×(C22⋊D191)⋊C4C211yesmaximal, characteristic
2#27132713C212yesmaximal, complemented
3#27132387C211yesmaximal, characteristic, complemented
4#27132386C212yesmaximal, complemented
5#323×C191C211yesmaximal, characteristic, complemented
6C22×C22⋊D191C411yescharacteristic
7C23×Dic191C411yescharacteristic
8C22×C4×D191C411yescharacteristic
9(C22⋊D191)⋊C4—22no—
10(C22⋊D191)⋊C4—22no—
11C2×Dic191⋊C4C411yescharacteristic
12C2×(C2×D191)⋊C4C2211yescharacteristic
13C2×C4×Dic191C2211yescharacteristic
14Dic191⋊C8—22no—
15C22⋊(C191⋊C8)C2212yes—
16C8×Dic191—22no—
17C2×C22⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yes—
19C23×D191C2×C411yescharacteristic
20C2×C22⋊D191—22no—
21C2×C22⋊D191—22no—
22C2×C22⋊D191C814yescomplemented
23C22×Dic191—21no—
24C22×Dic191—21no—
25C22×Dic191—42no—
26C22×Dic191C2×C411yescharacteristic
27C22×Dic191C2×C411yescharacteristic
28C22×Dic191C2×C411yescharacteristic
29C2×C4×D191—21no—
30C2×C4×D191—21no—
31C2×C4×D191—42no—
32C2×C191⋊C8—22no—
33Dic191⋊C4—22no—
34(C2×D191)⋊C4—22no—
35C4×Dic191D412yes—
36C4×Dic191D412yes—
37C24×C191C2×C411yescharacteristic
38C22×C4×C191C2×C411yescharacteristic
39C22×C4×C191C2311yescharacteristic
40C2×C8×C191—22no—
41C22⋊C4×C191—22no—
42C22×D191—21no—
43C22×D191—21no—
44C22×D191—41no—
45C22×D191—41no—
46C22×D191C2×C812yes—
47C22⋊D191—28no—
48C2×Dic191—22no—
49C2×Dic191—21no—
50C2×Dic191—42no—
51C2×Dic191—42no—
52C2×Dic191—41no—
53C2×Dic191C22⋊C411yescharacteristic
54C2×Dic191C22⋊C412yes—
55C2×Dic191C22⋊C411yescharacteristic
56C2×Dic191C2×C812yes—
57C2×Dic191M1612yes—
58C4×D191—42no—
59C4×D191—42no—
60C191⋊C8—42no—
61C23×C191—21no—
62C23×C191—21no—
63C23×C191—41no—
64C23×C191—41no—
65C23×C191C2×C812yes—
66C23×C191C22×C411yescharacteristic
67C2×C4×C191—21no—
68C2×C4×C191—41no—
69C2×C4×C191—41no—
70C2×C4×C191C2×D412yes—
71C8×C191—42no—
72C22×C191—21no—
73C22×C191—21no—
74C22×C191—22no—
75C22×C191—42no—
76C22×C191—42no—
77C22×C191—41no—
78C22×C191—41no—
79C22×C191C2×C22⋊C411yescharacteristic
80C22×C191C22×C811yescharacteristic
81C22×C191C2×M1611yescharacteristic
82C2×D191—22no—
83C2×D191—42no—
84C2×D191—41no—
85C2×D191—41no—
86C2×D191—42no—
87C4×C191—22no—
88C4×C191—41no—
89Dic191—21no—
90Dic191—41no—
91Dic191C22⋊C814yes—
92Dic191#10012yes—
93C2×C191—21no—
94C2×C191—21no—
95C2×C191—42no—
96C2×C191C2×C22⋊C811yescharacteristic
97C2×C191#41011yescharacteristic
98C2×C191C2×#10011yescharacteristic
99D191—42no—
100C191#146011yescharacteristic, complemented, Sylow
101#1460—1911nomaximal, Sylow
102C2×C4×D4—1911no—
103#431—1912no—
104#323—1911no—
105#323—1912no—
106#323D19111yescharacteristic, complemented
107C22×D4—1911no—
108C23×C4—1911no—
109C23×C4—1911no—
110C4×D4—3822no—
111C4×D4—3822no—
112C2×C4⋊C4—1911no—
113C2×C22⋊C4—1911no—
114C2×C22⋊C4C2×D19111yescharacteristic
115C2×C42—1911no—
116C4⋊C8—3822no—
117C22⋊C8—1912no—
118C22⋊C8C2×D19112yes—
119C4×C8—3822no—
120C24—1911no—
121C24C4×D19111yescharacteristic
122C2×D4—3822no—
123C2×D4—3822no—
124C2×D4—1914no—
125C22×C4—3821no—
126C22×C4—3821no—
127C22×C4—3821no—
128C22×C4—3821no—
129C22×C4—1911no—
130C22×C4—1911no—
131C22×C4—1911no—
132C22×C4—7642no—
133C22×C4—7642no—
134C22×C4C4×D19111yescharacteristic
135C22×C4C22×D19111yescharacteristic
136C2×C8—22no—
137C2×C8—3822no—
138C4⋊C4—3822no—
139C22⋊C4—22no—
140C22⋊C4—3822no—
141C42—1912no—
142C42—1912no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—3821no—
148C23—3821no—
149C23—1912no—
150C23—7641no—
151C23—7641no—
152C23C8×D19112yes—
153C23C2×C4×D19111yescharacteristic
154D4—3828no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3822no—
159C2×C4—3821no—
160C2×C4—1911no—
161C2×C4—1912no—
162C2×C4—1911no—
163C2×C4—1912no—
164C2×C4—1912no—
165C2×C4—7642no—
166C2×C4—7642no—
167C2×C4—7642no—
168C2×C4—7642no—
169C2×C4—7641no—
170C2×C4D4×D19112yes—
171C8—42no—
172C8—7642no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—3822no—
181C22—7642no—
182C22—7642no—
183C22—7641no—
184C22—7641no—
185C22C22⋊C4×D19111yescharacteristic
186C22C2×C8×D19111yescharacteristic
187C22M16×D19111yescharacteristic
188C4—22no—
189C4—41no—
190C4—3821no—
191C4—1914no—
192C4—1912no—
193C4—7641no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—7642no—
198C2C22⋊C8×D19111yescharacteristic
199C2#2713263511yescharacteristic
200C2#100×D19111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC22×C191C22×C8
FrattiniC22×C4C22×D191
Fitting#323×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC22×C22⋊D191C4
cosocleC22×C4×C191C23
hypercenter#323D191
hypocenterC191#1460
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #27132713C2semidirect
3. #27132387C2semidirect
4. #27132386C2semidirect
5. #323×C191C2semidirect
22. C2×C22⋊D191C8semidirect
100. C191#1460semidirect
106. #323D191semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D191)⋊C42
#271327132
#271323872
#271323862
#323×C1912
#1460191