Finite Group Databasebeta

← C2×#22627592 #34036614

Subgroups — C2×#22627592 #34036614

Order 18752.

662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C24×D293C211yesmaximal, characteristic, complemented
2C22×C22⋊D293C212yesmaximal, complemented
3#22627592C218yesmaximal, direct product factor
4C2×C22⋊Dic293C211yesmaximal, characteristic, complemented
5C2×#17989779C212yesmaximal, complemented
6C22×D4×C293C211yesmaximal, characteristic, complemented
7C23×D293—28no—
8C23×D293—24no—
9C23×D293C2212yes—
10C23×D293C2214yescomplemented
11C2×C22⋊D293—28no—
12C2×C22⋊D293C2218yescomplemented
13C22×Dic293C2212yescomplemented
14C22⋊Dic293C2214yescomplemented
15#17989779C2218yescomplemented
16C24×C293C2211yescharacteristic
17C24×C293C2211yescharacteristic, complemented
18C2×D4×C293—24no—
19C2×D4×C293C2214yescomplemented
20C22×C4×C293C2211yescharacteristic, complemented
21C22×D293—232no—
22C22×D293—24no—
23C22×D293—24no—
24C22×D293—28no—
25C22×D293—216no—
26C22×D293D418yescomplemented
27C22×D293C2314yes—
28C22⋊D293—216no—
29C2×Dic293—24no—
30C2×Dic293C2314yescomplemented
31C23×C293—24no—
32C23×C293—22no—
33C23×C293—24no—
34C23×C293D414yescomplemented
35C23×C293C2312yes—
36C23×C293C2311yescharacteristic
37C23×C293C2312yescomplemented
38D4×C293—28no—
39C2×C4×C293—22no—
40C2×C4×C293C2312yescomplemented
41C22×C293—28no—
42C22×C293—24no—
43C22×C293—22no—
44C22×C293—24no—
45C22×C293—44no—
46C22×C293C2×D414yes—
47C22×C293C2×D412yes—
48C22×C293C2×D414yescomplemented
49C22×C293C2411yescharacteristic
50C2×D293—232no—
51C2×D293—216no—
52C2×D293—24no—
53C2×D293—24no—
54C2×D293C2×D418yescomplemented
55C4×C293—22no—
56Dic293—24no—
57C2×C293—24no—
58C2×C293—42no—
59C2×C293#12014yescomplemented
60C2×C293C22×D412yes—
61C2×C293C22×D411yescharacteristic
62D293—28no—
63C293C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—2931nomaximal, Sylow
65C25—2931no—
66C22×D4—2932no—
67C22×D4D29311yescharacteristic, complemented
68#120—2938no—
69C2×C22⋊C4—2931no—
70C2×C22⋊C4—2932no—
71C24—2932no—
72C24—2934no—
73C24—5868no—
74C24—5864no—
75C24C2×D29311yescharacteristic
76C24C2×D29311yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—2938no—
79C2×D4—5868no—
80C2×D4C2×D29314yescomplemented
81C22×C4—2932no—
82C22×C4C2×D29311yescharacteristic, complemented
83C22⋊C4—2934no—
84C22⋊C4—2938no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—2938no—
89C23—2934no—
90C23—58616no—
91C23—58632no—
92C23—5864no—
93C23—5864no—
94C23—5868no—
95C23C22⋊D29314yescomplemented
96C23C22×D29312yes—
97C23C22×D29311yescharacteristic
98C23C22×D29312yescomplemented
99D4—28no—
100D4—58616no—
101C2×C4—22no—
102C2×C4—2934no—
103C2×C4—5864no—
104C2×C4C22×D29312yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—2938no—
111C22—58632no—
112C22—58616no—
113C22—5864no—
114C22—5864no—
115C22D4×D29314yes—
116C22C2×C22⋊D29312yes—
117C22C2×C22⋊D29314yescomplemented
118C22C23×D29311yescharacteristic
119C4—22no—
120C4—5864no—
121C2—24no—
122C2—42no—
123C2—5868no—
124C2#2262759214yesdirect product factor
125C2C2×D4×D29312yes—
126C2C22×C22⋊D29311yescharacteristic
subgroupG/H
centerC23C22×D293
commutator, cosocleC22×C293C24
FrattiniC22C23×D293
FittingC22×D4×C293C2
socleC23×C293C23
hypercenterC22×D4D293
hypocenterC293C2×#120
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D293C2semidirect
2. C22×C22⋊D293C2semidirect
3. #22627592C2direct (N × H)
4. C2×C22⋊Dic293C2semidirect
5. C2×#17989779C2semidirect
6. C22×D4×C293C2semidirect
10. C23×D293C22semidirect
12. C2×C22⋊D293C22semidirect
13. C22×Dic293C22semidirect
14. C22⋊Dic293C22semidirect
15. #17989779C22semidirect
17. C24×C293C22semidirect
19. C2×D4×C293C22semidirect
20. C22×C4×C293C22semidirect
26. C22×D293D4semidirect
30. C2×Dic293C23semidirect
34. C23×C293D4semidirect
37. C23×C293C23semidirect
40. C2×C4×C293C23semidirect
48. C22×C293C2×D4semidirect
54. C2×D293C2×D4semidirect
59. C2×C293#120semidirect
63. C293C2×#120semidirect
67. C22×D4D293semidirect
76. C24C2×D293semidirect
80. C2×D4C2×D293semidirect
82. C22×C4C2×D293semidirect
95. C23C22⋊D293semidirect
98. C23C22×D293semidirect
104. C2×C4C22×D293semidirect
117. C22C2×C22⋊D293semidirect
124. C2#22627592direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D2932
C22×C22⋊D2932
#226275922
C2×C22⋊Dic2932
C2×#179897792
C22×D4×C2932
C2×#120293