Finite Group Databasebeta

← C2×#23750660 #34061403

Subgroups — C2×#23750660 #34061403

Order 19072.

552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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×#14558745C212yesmaximal, complemented
2#23750660C218yesmaximal, direct product factor
3C2×C4⋊#11924753C211yesmaximal, characteristic, complemented
4C2×C22⋊#11924753C212yesmaximal, complemented
5C2×C4×#11924753C211yesmaximal, characteristic, complemented
6C2×D4×Dic149C211yesmaximal, characteristic
7C2×#14558745—28no—
8C2×#14558745C2218yescomplemented
9C22×#11924753C2212yes—
10C22×#11924753C2211yescharacteristic
11C22×#11924753C2211yescharacteristic
12C4⋊#11924753C2214yescomplemented
13C22⋊#11924753C2218yescomplemented
14C4×#11924753C2214yescomplemented
15C23×Dic149C2212yes—
16D4×Dic149C414yes—
17D4×Dic149C2214yes—
18C2×C4⋊Dic149C411yescharacteristic
19C2×C22⋊Dic149C412yes—
20C2×C4×Dic149C2211yescharacteristic
21C22×D4×C149C411yescharacteristic
22#14558745—216no—
23C2×#11924753—24no—
24C2×#11924753—22no—
25C2×#11924753D414yescomplemented
26C2×#11924753C2312yes—
27C2×#11924753C2314yes—
28C2×#11924753C2312yes—
29C22×Dic149—24no—
30C22×Dic149—24no—
31C22×Dic149C2×C412yes—
32C22×Dic149C2×C414yes—
33C22×Dic149C2×C411yescharacteristic
34C22×Dic149C2314yes—
35C22×Dic149C2311yescharacteristic
36C4⋊Dic149C2×C414yes—
37C22⋊Dic149C2×C418yes—
38C4×Dic149C2×C412yes—
39C4×Dic149C2312yes—
40C24×C149C2×C412yes—
41C2×D4×C149—24no—
42C2×D4×C149C2×C414yes—
43C22×C4×C149C2×C411yescharacteristic
44#11924753—24no—
45#11924753—22no—
46#11924753C2×D414yescomplemented
47C2×Dic149—24no—
48C2×Dic149—22no—
49C2×Dic149—28no—
50C2×Dic149—24no—
51C2×Dic149—24no—
52C2×Dic149C22×C414yes—
53C2×Dic149C22×C412yes—
54C2×Dic149C22×C411yescharacteristic
55C2×Dic149C2×D412yes—
56C2×Dic149#4112yes—
57C2×Dic149C2411yescharacteristic
58C23×C149—24no—
59C23×C149—24no—
60C23×C149—24no—
61C23×C149C22×C414yes—
62C23×C149C22×C411yescharacteristic
63D4×C149—28no—
64C2×C4×C149M1614yescomplemented
65C2×C4×C149C22×C412yes—
66C22×C149—24no—
67C22×C149—24no—
68C22×C149—24no—
69C22×C149—48no—
70C22×C149C4×D412yes—
71C22×C149C2×M1612yes—
72C22×C149#13112yes—
73C22×C149C23×C411yescharacteristic
74C4×C149C2×M1614yescomplemented
75Dic149—24no—
76Dic149—22no—
77Dic149C4×D412yes—
78Dic149C22×D411yescharacteristic
79Dic149C2×#4111yescharacteristic
80C2×C149—44no—
81C2×C149#43614yescomplemented
82C2×C149C2×C4×D411yescharacteristic
83C2×C149C22×M1611yescharacteristic
84C2×C149C2×#13111yescharacteristic
85C149C2×#43611yescharacteristic, complemented, Sylow
86C2×#436—1491nomaximal, Sylow
87C22×M16—1492no—
88C2×C4×D4—1491no—
89#436—1498no—
90C2×C4⋊C8—1491no—
91C2×C22⋊C8—1492no—
92C2×C4×C8—1491no—
93C22×D4#1059701011yescharacteristic
94C23×C4—1492no—
95C2×M16—2988no—
96C2×M16—1498no—
97C22×C8—1492no—
98C22×C8—1491no—
99C22×C8—1491no—
100C4×D4—1494no—
101C4×D4—1494no—
102C2×C4⋊C4—1491no—
103C2×C22⋊C4—1492no—
104C2×C42—1491no—
105C4⋊C8—1494no—
106C22⋊C8—1498no—
107C4×C8—1494no—
108C24C2×#1059701012yes—
109C2×D4—24no—
110C2×D4C2×#1059701014yes—
111C22×C4—2984no—
112C22×C4—2984no—
113C22×C4—1494no—
114C22×C4—1494no—
115C22×C4—1491no—
116C22×C4—1492no—
117C22×C4—1491no—
118C22×C4C2×#1059701011yescharacteristic
119M16—29816no—
120C2×C8—2982no—
121C2×C8—2984no—
122C2×C8—1492no—
123C2×C8—1494no—
124C2×C8—1494no—
125C2×C8—1492no—
126C4⋊C4—1494no—
127C22⋊C4—1498no—
128C42—1492no—
129C42—1492no—
130C23—24no—
131C23—24no—
132C23—24no—
133C23C22×#1059701014yes—
134C23C22×#1059701011yescharacteristic
135D4—28no—
136C2×C4—2984no—
137C2×C4—2982no—
138C2×C4—2984no—
139C2×C4—2984no—
140C2×C4—2988no—
141C2×C4—1492no—
142C2×C4—1494no—
143C2×C4—1492no—
144C2×C4—1492no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4#1455874514yescomplemented
148C2×C4C22×#1059701012yes—
149C8—2982no—
150C8—2984no—
151C8—1494no—
152C22—24no—
153C22—24no—
154C22—24no—
155C22—48no—
156C22D4×#1059701012yes—
157C22C2×#1455874512yes—
158C22#1801199812yes—
159C22C23×#1059701011yescharacteristic
160C4—2984no—
161C4—2982no—
162C4—1491no—
163C4—1491no—
164C4—1492no—
165C4C2×#1455874514yescomplemented
166C2—44no—
167C2#2375066014yesdirect product factor
168C2C2×D4×#1059701011yescharacteristic
169C2C22×#1455874511yescharacteristic
170C2C2×#1801199811yescharacteristic
subgroupG/H
centerC23C22×#10597010
commutatorC22×C149C23×C4
FrattiniC22C23×#10597010
Fitting, prime radicalC22×D4×C149C4
socleC23×C149C22×C4
cosocleC2×Dic149C24
hypercenterC22×D4#10597010
hypocenterC149C2×#436
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14558745C2semidirect
2. #23750660C2direct (N × H)
3. C2×C4⋊#11924753C2semidirect
4. C2×C22⋊#11924753C2semidirect
5. C2×C4×#11924753C2semidirect
8. C2×#14558745C22semidirect
12. C4⋊#11924753C22semidirect
13. C22⋊#11924753C22semidirect
14. C4×#11924753C22semidirect
25. C2×#11924753D4semidirect
46. #11924753C2×D4semidirect
64. C2×C4×C149M16semidirect
74. C4×C149C2×M16semidirect
81. C2×C149#436semidirect
85. C149C2×#436semidirect
147. C2×C4#14558745semidirect
165. C4C2×#14558745semidirect
167. C2#23750660direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587452
#237506602
C2×C4⋊#119247532
C2×C22⋊#119247532
C2×C4×#119247532
C2×D4×Dic1492
C2×#436149