Finite Group Databasebeta

← #34061540

Subgroups — #34061540

Order 19072.

500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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#23750652C218yesmaximal, complemented
2#23750642C212yesmaximal, complemented
3D149⋊(C22⋊C8)C212yesmaximal, complemented
4C2×C22⋊#11924753C212yesmaximal, complemented
5C2×#18011871C211yesmaximal, characteristic
6C2×D149⋊C8C2214yescomplemented
7C22×#11924753C2214yescomplemented
8#18011978C2214yescomplemented
9#18011968C2214yescomplemented
10C22⋊#11924753C2214yes—
11C22⋊#11924753C2214yescomplemented
12C4×#11924753C2214yescomplemented
13C22×C22⋊D149C411yescharacteristic
14C23×Dic149C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16#18011871C414yes—
17#18011871C2214yes—
18C2×#14558715C411yescharacteristic
19C2×#14558713C411yescharacteristic
20C2×C4×Dic149C2211yescharacteristic
21C2×C22⋊C4×C149C411yescharacteristic
22D149⋊C8—44no—
23C2×#11924753—44no—
24C2×#11924753C2318yes—
25C23×D149C2×C411yescharacteristic
26C2×C22⋊D149C818yescomplemented
27C2×C22⋊D149C2×C414yes—
28C22×Dic149—42no—
29C22×Dic149C2×C411yescharacteristic
30C22×Dic149C2×C412yes—
31C22×Dic149C2×C411yescharacteristic
32C22×Dic149C2311yescharacteristic
33C22×Dic149C2312yes—
34C2×C4×D149—42no—
35C2×C4×D149C2×C412yes—
36C2×C4×D149C2312yes—
37#14558715C2×C414yes—
38#14558713C2×C414yes—
39C4×Dic149C2×C412yes—
40C4×Dic149C2312yes—
41C24×C149C2×C411yescharacteristic
42C22×C4×C149C2×C411yescharacteristic
43C22×C4×C149C2×C411yescharacteristic
44C22⋊C4×C149C2×C414yes—
45#11924753—28no—
46C22×D149—41no—
47C22×D149—41no—
48C22×D149C2×C814yescomplemented
49C22×D149C22×C412yes—
50C22⋊D149C2×C8116yescomplemented
51C2×Dic149—22no—
52C2×Dic149—24no—
53C2×Dic149—42no—
54C2×Dic149—41no—
55C2×Dic149C2×C814yescomplemented
56C2×Dic149C22×C411yescharacteristic
57C2×Dic149C22×C412yes—
58C2×Dic149C22×C412yes—
59C2×Dic149C2411yescharacteristic
60C4×D149—24no—
61C4×D149—42no—
62C23×C149—41no—
63C23×C149—41no—
64C23×C149C2×C814yescomplemented
65C23×C149C22×C411yescharacteristic
66C23×C149C22×C412yes—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C2×C4×C149C22×C412yes—
70C2×C4×C149C22×C412yes—
71C22×C149—21no—
72C22×C149—22no—
73C22×C149—21no—
74C22×C149—22no—
75C22×C149—44no—
76C22×C149C22×C812yes—
77C22×C149C22×C814yes—
78C22×C149C23×C411yescharacteristic
79C2×D149—22no—
80C2×D149—22no—
81C2×D149—44no—
82C2×D149C22×C814yes—
83C4×C149—22no—
84C4×C149—22no—
85Dic149—21no—
86Dic149—22no—
87Dic149C22×C814yes—
88Dic149H(5,𝔽2)12yes—
89C2×C149—22no—
90C2×C149—24no—
91C2×C149#51811yescharacteristic
92C2×C149C23×C811yescharacteristic
93C2×C149#56811yescharacteristic
94D149—24no—
95C149#297211yescharacteristic, complemented, Sylow
96#2972—1491nomaximal, Sylow
97C2×C4×D4—1491no—
98C8×D4—1498no—
99#431—1492no—
100C2×C22⋊C8—1492no—
101C2×C22⋊C8—1492no—
102C22×D4—1491no—
103C23×C4—1491no—
104C23×C4—1491no—
105C22×C8—1494no—
106C22×C8—1494no—
107C4×D4—1494no—
108C4×D4—1494no—
109C2×C4⋊C4—1491no—
110C2×C22⋊C4—1491no—
111C2×C22⋊C4#1059701011yescharacteristic
112C2×C42—1491no—
113C4⋊C8—1494no—
114C22⋊C8—1494no—
115C22⋊C8—1494no—
116C22⋊C8—1494no—
117C4×C8—1494no—
118C24—1491no—
119C24C2×#1059701011yescharacteristic
120C2×D4—1498no—
121C2×D4—1494no—
122C22×C4—5962no—
123C22×C4—5962no—
124C22×C4—1491no—
125C22×C4—1492no—
126C22×C4—1492no—
127C22×C4—1491no—
128C22×C4—1492no—
129C22×C4—1492no—
130C22×C4—1491no—
131C22×C4C2×#1059701011yescharacteristic
132C22×C4C2×#1059701011yescharacteristic
133C2×C8—5964no—
134C2×C8—5964no—
135C2×C8—1498no—
136C4⋊C4—1494no—
137C22⋊C4—1494no—
138C22⋊C4C2×#1059701014yes—
139C42—1492no—
140C42—1492no—
141C23—41no—
142C23—41no—
143C23—5961no—
144C23—5961no—
145C23—1492no—
146C23—1494no—
147C23D149⋊C814yescomplemented
148C23C22×#1059701012yes—
149C23C22×#1059701011yescharacteristic
150D4—14916no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—2984no—
154C2×C4—2984no—
155C2×C4—2982no—
156C2×C4—5962no—
157C2×C4—5962no—
158C2×C4—5961no—
159C2×C4—1491no—
160C2×C4—1492no—
161C2×C4—1494no—
162C2×C4—1492no—
163C2×C4—1491no—
164C2×C4C22×#1059701012yes—
165C2×C4C22×#1059701012yes—
166C8—2988no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—44no—
172C22—2982no—
173C22—2982no—
174C22—5964no—
175C22—1494no—
176C22C2×D149⋊C812yes—
177C22C2×D149⋊C814yes—
178C22C23×#1059701011yescharacteristic
179C4—22no—
180C4—22no—
181C4—2981no—
182C4—2982no—
183C4—1492no—
184C4—1494no—
185C2—22no—
186C2—24no—
187C2—2984no—
188C2#2375069211yescharacteristic
189C2C22×D149⋊C811yescharacteristic
190C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutatorC2×C149C23×C8
FittingC2×C22⋊C4×C149C4
socleC22×C149C23×C4
prime radicalC22×C22⋊D149C4
cosocleC2×Dic149C24
hypercenterC2×C22⋊C4#10597010
hypocenterC149#2972
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750652C2semidirect
2. #23750642C2semidirect
3. D149⋊(C22⋊C8)C2semidirect
4. C2×C22⋊#11924753C2semidirect
6. C2×D149⋊C8C22semidirect
7. C22×#11924753C22semidirect
8. #18011978C22semidirect
9. #18011968C22semidirect
11. C22⋊#11924753C22semidirect
12. C4×#11924753C22semidirect
26. C2×C22⋊D149C8semidirect
48. C22×D149C2×C8semidirect
50. C22⋊D149C2×C8semidirect
55. C2×Dic149C2×C8semidirect
64. C23×C149C2×C8semidirect
95. C149#2972semidirect
147. C23D149⋊C8semidirect

Maximal subgroups

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

subgroupindex
#237506522
#237506422
D149⋊(C22⋊C8)2
C2×C22⋊#119247532
C2×#180118712
#2972149