Finite Group Databasebeta

← #34036761

Subgroups — #34036761

Order 18752.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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×C22⋊D293C212yesmaximal, complemented
2C2×D4×D293C212yesmaximal, complemented
3#22627620C211yesmaximal, characteristic, complemented
4#22627597C212yesmaximal, complemented
5#22627596C212yesmaximal, complemented
6#22627594C212yesmaximal, complemented
7#22627592C211yesmaximal, characteristic, complemented
8#22627584C212yesmaximal, complemented
9#120×C293C211yesmaximal, characteristic, complemented
10C23×D293C2211yescharacteristic, complemented
11C23×D293C2212yescomplemented
12C2×D1172C2212yescomplemented
13C2×D1172C2211yescharacteristic, complemented
14C2×C22⋊D293—28no—
15C2×C22⋊D293C2212yes—
16C2×C22⋊D293C2212yescomplemented
17C2×C22⋊D293C2212yescomplemented
18C2×C22⋊D293C2212yescomplemented
19C2×C22⋊D293C2212yescomplemented
20D4×D293—28no—
21C22×Dic293C2212yescomplemented
22C2×C4×D293C2212yescomplemented
23#17989781C2212yescomplemented
24C22⋊Dic293C2211yescharacteristic, complemented
25#17989779C2212yescomplemented
26#17989779C2212yescomplemented
27C4×Dic293C2211yescharacteristic, complemented
28C24×C293C2211yescharacteristic, complemented
29C2×D4×C293C2212yescomplemented
30C2×D4×C293C2211yescharacteristic, complemented
31C22⋊C4×C293C2212yescomplemented
32C22⋊C4×C293C2211yescharacteristic, complemented
33C22×D293—24no—
34C22×D293—24no—
35C22×D293—24no—
36C22×D293—41no—
37C22×D293—42no—
38C22×D293C2312yes—
39C22×D293C2312yes—
40D1172—24no—
41D1172—41no—
42C22⋊D293—24no—
43C22⋊D293—24no—
44C22⋊D293—24no—
45C22⋊D293—24no—
46C22⋊D293D418yescomplemented
47C2×Dic293—24no—
48C2×Dic293C2312yes—
49C2×Dic293C2312yes—
50C4×D293—24no—
51C23×C293—24no—
52C23×C293—41no—
53C23×C293C2311yescharacteristic
54C23×C293C2311yescharacteristic
55C23×C293C2312yes—
56D4×C293—24no—
57D4×C293—41no—
58C2×C4×C293C2311yescharacteristic
59C2×C4×C293C2312yes—
60C22×C293—22no—
61C22×C293—22no—
62C22×C293—22no—
63C22×C293—22no—
64C22×C293—21no—
65C22×C293—21no—
66C22×C293—44no—
67C22×C293C2×D414yescomplemented
68C22×C293C2411yescharacteristic
69C2×D293—22no—
70C2×D293—22no—
71C2×D293—22no—
72C2×D293—22no—
73C2×D293—22no—
74C2×D293—44no—
75C2×D293—48no—
76C2×D293C2×D414yescomplemented
77C4×C293—22no—
78C4×C293—21no—
79Dic293—22no—
80Dic293C2×D414yescomplemented
81C2×C293—24no—
82C2×C293—41no—
83C2×C293—41no—
84C2×C293C22×D412yes—
85C2×C293H(5,𝔽2)11yescharacteristic
86D293—24no—
87D293—42no—
88C293D4211yescharacteristic, complemented, Sylow
89D42—2931nomaximal, Sylow
90C22×D4—2932no—
91C22×D4—2932no—
92#127—2931no—
93#121—2932no—
94#121—2932no—
95#120—2931no—
96#120—2932no—
97#120D29311yescharacteristic, complemented
98C4×D4—2932no—
99C24—2931no—
100C24—2932no—
101C24C2×D29311yescharacteristic, complemented
102C2×D4—2932no—
103C2×D4—2932no—
104C2×D4—2932no—
105C2×D4—2932no—
106C2×D4—2932no—
107C2×D4—2932no—
108C2×D4—2931no—
109C2×D4—5868no—
110C2×D4—5868no—
111C2×D4C2×D29312yescomplemented
112C2×D4C2×D29311yescharacteristic, complemented
113C22×C4—2932no—
114C22×C4—2932no—
115C4⋊C4—2932no—
116C22⋊C4—2931no—
117C22⋊C4—2932no—
118C22⋊C4—2932no—
119C22⋊C4C2×D29312yescomplemented
120C22⋊C4C2×D29311yescharacteristic, complemented
121C42—2931no—
122C23—24no—
123C23—41no—
124C23—2932no—
125C23—2932no—
126C23—5864no—
127C23—5864no—
128C23—5864no—
129C23—11722no—
130C23—11721no—
131C23C22×D29311yescharacteristic
132C23C22×D29311yescharacteristic
133C23C22×D29312yes—
134D4—24no—
135D4—41no—
136D4—2938no—
137D4—5864no—
138D4—5864no—
139D4—5864no—
140D4—5864no—
141D4—5864no—
142D4—11721no—
143C2×C4—2932no—
144C2×C4—2932no—
145C2×C4—5864no—
146C2×C4—5864no—
147C2×C4C22×D29311yescharacteristic
148C2×C4C22×D29312yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—2934no—
157C22—5862no—
158C22—5862no—
159C22—5862no—
160C22—5862no—
161C22—5862no—
162C22—11728no—
163C22—11724no—
164C22D4×D29314yescomplemented
165C22C23×D29311yescharacteristic
166C4—22no—
167C4—21no—
168C4—2934no—
169C4—5862no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—5864no—
174C2—11722no—
175C2C2×D4×D29312yes—
176C2#2262766911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#120×C293C2
hypercenter#120D293
hypocenterC293D42
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D293C2semidirect
2. C2×D4×D293C2semidirect
3. #22627620C2semidirect
4. #22627597C2semidirect
5. #22627596C2semidirect
6. #22627594C2semidirect
7. #22627592C2semidirect
8. #22627584C2semidirect
9. #120×C293C2semidirect
10. C23×D293C22semidirect
11. C23×D293C22semidirect
12. C2×D1172C22semidirect
13. C2×D1172C22semidirect
16. C2×C22⋊D293C22semidirect
17. C2×C22⋊D293C22semidirect
18. C2×C22⋊D293C22semidirect
19. C2×C22⋊D293C22semidirect
21. C22×Dic293C22semidirect
22. C2×C4×D293C22semidirect
23. #17989781C22semidirect
24. C22⋊Dic293C22semidirect
25. #17989779C22semidirect
26. #17989779C22semidirect
27. C4×Dic293C22semidirect
28. C24×C293C22semidirect
29. C2×D4×C293C22semidirect
30. C2×D4×C293C22semidirect
31. C22⋊C4×C293C22semidirect
32. C22⋊C4×C293C22semidirect
46. C22⋊D293D4semidirect
67. C22×C293C2×D4semidirect
76. C2×D293C2×D4semidirect
80. Dic293C2×D4semidirect
88. C293D42semidirect
97. #120D293semidirect
101. C24C2×D293semidirect
111. C2×D4C2×D293semidirect
112. C2×D4C2×D293semidirect
119. C22⋊C4C2×D293semidirect
120. C22⋊C4C2×D293semidirect
164. C22D4×D293semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D2932
C2×D4×D2932
#226276202
#226275972
#226275962
#226275942
#226275922
#226275842
#120×C2932
D42293