Finite Group Databasebeta

← #34061542

Subgroups — #34061542

Order 19072.

456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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#23750656C218yesmaximal, complemented
2#23750645C212yesmaximal, complemented
3#23750595C212yesmaximal, complemented
4C2×C22⋊#11924753C212yesmaximal, complemented
5C2×D4×Dic149C211yesmaximal, characteristic
6C2×#14558745C2214yescomplemented
7C22×#11924753C2214yescomplemented
8#18011978C2214yescomplemented
9C22⋊#11924753C2214yes—
10C22⋊#11924753C2214yescomplemented
11C22⋊#11924753C2214yescomplemented
12#18011966C2214yescomplemented
13C23×Dic149C2211yescharacteristic
14C23×Dic149C2211yescharacteristic
15D4×Dic149C414yes—
16D4×Dic149C2214yes—
17C2×C4⋊Dic149C411yescharacteristic
18C2×C22⋊Dic149C411yescharacteristic
19C2×C22⋊Dic149C411yescharacteristic
20C2×C4×Dic149C2211yescharacteristic
21C22×D4×C149C411yescharacteristic
22#14558745—44no—
23C2×#11924753—44no—
24C2×#11924753C2318yes—
25C22×Dic149—42no—
26C22×Dic149—42no—
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C22×Dic149C2×C412yes—
30C22×Dic149C2×C412yes—
31C22×Dic149C2×C411yescharacteristic
32C22×Dic149C2311yescharacteristic
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C4⋊Dic149C2×C414yes—
36C22⋊Dic149C2×C414yes—
37C22⋊Dic149C2×C414yes—
38C4×Dic149C2×C412yes—
39C4×Dic149C2312yes—
40C24×C149C2×C411yescharacteristic
41C24×C149C2×C411yescharacteristic
42C2×D4×C149—24no—
43C2×D4×C149C2×C414yes—
44C22×C4×C149C2×C411yescharacteristic
45#11924753—28no—
46C2×Dic149—22no—
47C2×Dic149—24no—
48C2×Dic149—24no—
49C2×Dic149—42no—
50C2×Dic149—42no—
51C2×Dic149—41no—
52C2×Dic149—41no—
53C2×Dic149—41no—
54C2×Dic149C22×C411yescharacteristic
55C2×Dic149C22×C412yes—
56C2×Dic149C22×C412yes—
57C2×Dic149C22×C412yes—
58C2×Dic149C2411yescharacteristic
59C23×C149—22no—
60C23×C149—41no—
61C23×C149—41no—
62C23×C149—41no—
63C23×C149—41no—
64C23×C149M1614yescomplemented
65C23×C149C22×C412yes—
66C23×C149C22×C411yescharacteristic
67C23×C149C22×C412yes—
68D4×C149—28no—
69C2×C4×C149—22no—
70C2×C4×C149C22×C412yes—
71C22×C149—21no—
72C22×C149—22no—
73C22×C149—21no—
74C22×C149—22no—
75C22×C149—22no—
76C22×C149—22no—
77C22×C149—22no—
78C22×C149—44no—
79C22×C149—44no—
80C22×C149C2×M1612yes—
81C22×C149C2×M1614yes—
82C22×C149C23×C411yescharacteristic
83C4×C149—22no—
84Dic149—21no—
85Dic149—22no—
86Dic149—22no—
87Dic149—22no—
88Dic149H(5,𝔽2)12yes—
89C2×C149—22no—
90C2×C149—24no—
91C2×C149—42no—
92C2×C149#51811yescharacteristic
93C2×C149C22×M1611yescharacteristic
94C2×C149#56811yescharacteristic
95C149#297311yescharacteristic, complemented, Sylow
96#2973—1491nomaximal, Sylow
97C2×C4×D4—1491no—
98#435—1498no—
99#432—1492no—
100#407—1492no—
101C2×C22⋊C8—1492no—
102C22×D4#1059701011yescharacteristic
103C23×C4—1491no—
104C23×C4—1491no—
105C2×M16—1494no—
106C22×C8—1494no—
107C4×D4—1494no—
108C4×D4—1494no—
109C2×C4⋊C4—1491no—
110C2×C22⋊C4—1491no—
111C2×C22⋊C4—1491no—
112C2×C42—1491no—
113C4⋊C8—1494no—
114C22⋊C8—1494no—
115C22⋊C8—1494no—
116C22⋊C8—1494no—
117#97—1494no—
118C24C2×#1059701011yescharacteristic
119C24C2×#1059701011yescharacteristic
120C2×D4—24no—
121C2×D4C2×#1059701014yes—
122C22×C4—5962no—
123C22×C4—5962no—
124C22×C4—1491no—
125C22×C4—1492no—
126C22×C4—1492no—
127C22×C4—1491no—
128C22×C4—1491no—
129C22×C4—1491no—
130C22×C4—1492no—
131C22×C4—1492no—
132C22×C4C2×#1059701011yescharacteristic
133M16—5964no—
134C2×C8—5964no—
135C2×C8—1498no—
136C4⋊C4—1494no—
137C22⋊C4—1494no—
138C22⋊C4—1494no—
139C42—1492no—
140C42—1492no—
141C23—22no—
142C23—41no—
143C23—41no—
144C23—41no—
145C23—41no—
146C23#1455874514yescomplemented
147C23C22×#1059701012yes—
148C23C22×#1059701012yes—
149C23C22×#1059701011yescharacteristic
150D4—28no—
151C2×C4—22no—
152C2×C4—2984no—
153C2×C4—2984no—
154C2×C4—2982no—
155C2×C4—5962no—
156C2×C4—5962no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4—5961no—
160C2×C4—1492no—
161C2×C4—1491no—
162C2×C4—1492no—
163C2×C4—1492no—
164C2×C4—1491no—
165C2×C4C22×#1059701012yes—
166C8—2988no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—44no—
175C22—44no—
176C22C2×#1455874512yes—
177C22C2×#1455874514yes—
178C22C23×#1059701011yescharacteristic
179C4—22no—
180C4—2981no—
181C4—2982no—
182C4—2982no—
183C4—2982no—
184C4—1492no—
185C2—22no—
186C2—24no—
187C2—42no—
188C2#2375069211yescharacteristic
189C2C22×#1455874511yescharacteristic
190C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting, prime radicalC22×D4×C149C4
cosocleC2×Dic149C24
hypercenterC22×D4#10597010
hypocenterC149#2973
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750656C2semidirect
2. #23750645C2semidirect
3. #23750595C2semidirect
4. C2×C22⋊#11924753C2semidirect
6. C2×#14558745C22semidirect
7. C22×#11924753C22semidirect
8. #18011978C22semidirect
10. C22⋊#11924753C22semidirect
11. C22⋊#11924753C22semidirect
12. #18011966C22semidirect
64. C23×C149M16semidirect
95. C149#2973semidirect
146. C23#14558745semidirect

Maximal subgroups

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

subgroupindex
#237506562
#237506452
#237505952
C2×C22⋊#119247532
C2×D4×Dic1492
#2973149