Finite Group Databasebeta

← #324×D191 #37570828

Subgroups — #324×D191 #37570828

Order 24448.

328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C4×D191C211yesmaximal, characteristic
2C22⋊C8×D191C212yesmaximal
3#27132389C211yesmaximal, characteristic, complemented
4#27132388C212yesmaximal, complemented
5#324×C191C211yesmaximal, characteristic, complemented
6C22×C4×D191C411yescharacteristic
7C22×C4×D191C411yescharacteristic
8C22×C4×D191C2211yescharacteristic
9C2×C8×D191—22no—
10C2×C4⋊Dic191C411yescharacteristic
11C2×Dic191⋊C4C411yescharacteristic
12C2×Dic191⋊C4C2211yescharacteristic
13C4⋊C4×D191—22no—
14C4⋊C4×D191—22no—
15C22⋊(C191⋊C8)C2212yes—
16(C2×D191)⋊C8—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×D191—21no—
27C2×C4×D191—21no—
28C2×C4×D191—42no—
29C2×C4×D191—42no—
30C2×C4×D191C814yescomplemented
31C2×C4×D191D412yes—
32C2×C4×D191D412yes—
33C2×C191⋊C8—22no—
34C8×D191—44no—
35C4⋊Dic191—22no—
36Dic191⋊C4—22no—
37Dic191⋊C4—22no—
38C22×C4×C191C2×C411yescharacteristic
39C22×C4×C191C2×C411yescharacteristic
40C22×C4×C191C2311yescharacteristic
41C2×C8×C191—22no—
42C4⋊C4×C191—22no—
43C22×D191—22no—
44C22×D191—22no—
45C22×D191C22⋊C411yescharacteristic
46C22×D191C22⋊C411yescharacteristic
47C22×D191C2×C812yes—
48C22×D191M1612yes—
49C2×Dic191—21no—
50C2×Dic191—21no—
51C2×Dic191—21no—
52C2×Dic191—41no—
53C2×Dic191—41no—
54C2×Dic191C22⋊C412yes—
55C2×Dic191C2×C812yescomplemented
56C4×D191—24no—
57C4×D191—24no—
58C4×D191—24no—
59C4×D191—42no—
60C4×D191—42no—
61C4×D191—42no—
62C191⋊C8—42no—
63C23×C191C22×C411yescharacteristic
64C2×C4×C191—21no—
65C2×C4×C191—21no—
66C2×C4×C191—21no—
67C2×C4×C191—41no—
68C2×C4×C191—41no—
69C2×C4×C191C2×C812yescomplemented
70C2×C4×C191C2×D412yes—
71C8×C191—42no—
72C22×C191—21no—
73C22×C191—21no—
74C22×C191C2×C22⋊C411yescharacteristic
75C22×C191C22×C811yescharacteristic
76C22×C191C2×M1611yescharacteristic
77C2×D191—21no—
78C2×D191—21no—
79C2×D191—24no—
80C2×D191—24no—
81C2×D191C22⋊C812yes—
82C2×D191C22⋊C812yes—
83C2×D191#9912yes—
84C2×D191#10112yes—
85C4×C191—22no—
86C4×C191—22no—
87C4×C191—41no—
88Dic191—22no—
89Dic191—22no—
90Dic191—41no—
91C2×C191—21no—
92C2×C191—21no—
93C2×C191C2×C22⋊C811yescharacteristic
94C2×C191C2×#9911yescharacteristic
95C2×C191C2×#10111yescharacteristic
96D191—22no—
97D191#32414yesdirect product factor
98C191C2×#32411yescharacteristic, complemented, Sylow
99C2×#324—1911nomaximal, Sylow
100C22×C4⋊C4—1911no—
101C2×C22⋊C8—1912no—
102#324—1911no—
103#324—1912no—
104#324D19111yescharacteristic, direct product factor
105C23×C4—1911no—
106C23×C4—1911no—
107C23×C4—1911no—
108C22×C8—3822no—
109C2×C4⋊C4—3822no—
110C2×C4⋊C4—3822no—
111C2×C4⋊C4—1911no—
112C2×C4⋊C4—1911no—
113C2×C4⋊C4—1911no—
114C2×C4⋊C4C2×D19111yescharacteristic
115C22⋊C8—3822no—
116C22⋊C8—1912no—
117C22⋊C8C2×D19112yes—
118C24—1911no—
119C22×C4—3821no—
120C22×C4—3821no—
121C22×C4—3822no—
122C22×C4—3821no—
123C22×C4—3821no—
124C22×C4—1911no—
125C22×C4—1914no—
126C22×C4—1912no—
127C22×C4—1911no—
128C22×C4—1911no—
129C22×C4—1912no—
130C22×C4—7642no—
131C22×C4—7642no—
132C22×C4C4×D19111yescharacteristic
133C22×C4C4×D19111yescharacteristic
134C22×C4C22×D19111yescharacteristic
135C2×C8—22no—
136C2×C8—3822no—
137C2×C8—7644no—
138C4⋊C4—22no—
139C4⋊C4—3822no—
140C4⋊C4—3822no—
141C4⋊C4—3822no—
142C23—3822no—
143C23—3822no—
144C23—1911no—
145C23—1912no—
146C23—1912no—
147C23—1911no—
148C23C2×C4×D19111yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—3824no—
155C2×C4—3824no—
156C2×C4—3824no—
157C2×C4—3821no—
158C2×C4—3821no—
159C2×C4—3821no—
160C2×C4—1912no—
161C2×C4—1912no—
162C2×C4—7642no—
163C2×C4—7642no—
164C2×C4—7642no—
165C2×C4—7641no—
166C2×C4—7641no—
167C2×C4C8×D19112yescomplemented
168C2×C4D4×D19112yes—
169C8—42no—
170C8—7642no—
171C22—21no—
172C22—21no—
173C22—3824no—
174C22—3824no—
175C22—3821no—
176C22—3821no—
177C22—1912no—
178C22—1912no—
179C22—1912no—
180C22—1912no—
181C22C22⋊C4×D19111yescharacteristic
182C22C2×C8×D19111yescharacteristic
183C22M16×D19111yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—3822no—
188C4—3822no—
189C4—7641no—
190C2—21no—
191C2—21no—
192C2—3822no—
193C2—1914no—
194C2C22⋊C8×D19111yescharacteristic
195C2#99×D19111yescharacteristic
196C2#101×D19111yescharacteristic
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
hypocenterC191C2×#324
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
3. #27132389C2semidirect
4. #27132388C2semidirect
5. #324×C191C2semidirect
30. C2×C4×D191C8semidirect
55. C2×Dic191C2×C8semidirect
69. C2×C4×C191C2×C8semidirect
97. D191#324direct (N × H)
98. C191C2×#324semidirect
104. #324D191direct (N × H)
167. C2×C4C8×D191semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1912
C22⋊C8×D1912
#271323892
#271323882
#324×C1912
C2×#324191