Finite Group Databasebeta

← #34036601

Subgroups — #34036601

Order 18752.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×D4×D293C211yesmaximal, characteristic
2C4×D1172C211yesmaximal, characteristic, complemented
3D4×Dic293C211yesmaximal, characteristic, complemented
4#22627586C211yesmaximal, characteristic, complemented
5C4×C22⋊D293C212yesmaximal, complemented
6#22627584C212yesmaximal, complemented
7#22627582C211yesmaximal, characteristic, complemented
8#22627581C211yesmaximal, characteristic, complemented
9C2×#17989779C212yesmaximal, complemented
10C22⋊C4×D293C212yesmaximal, complemented
11C4×D4×C293C211yesmaximal, characteristic, complemented
12C23×D293C2212yes—
13C2×D1172C2211yescharacteristic
14C2×C22⋊D293C2212yes—
15D4×D293C418yescomplemented
16C22×Dic293C2212yescomplemented
17C2×C4×D293C2211yescharacteristic
18C2×C4×D293C2212yescomplemented
19C2×C4×D293C2212yescomplemented
20C4⋊Dic293C2211yescharacteristic, complemented
21#17989781C2211yescharacteristic, complemented
22#17989781C2211yescharacteristic, complemented
23C22⋊Dic293C2212yescomplemented
24#17989779C2211yescharacteristic
25#17989779C2212yes—
26#17989779C2211yescharacteristic
27#17989779C2212yescomplemented
28#17989779C2212yescomplemented
29C4×Dic293C2212yescomplemented
30C4×Dic293C2211yescharacteristic, complemented
31C2×D4×C293C2211yescharacteristic
32C22×C4×C293C2212yescomplemented
33C4⋊C4×C293C2211yescharacteristic, complemented
34C22⋊C4×C293C2212yescomplemented
35C42×C293C2211yescharacteristic, complemented
36C22×D293—42no—
37C22×D293—42no—
38C22×D293C2×C418yescomplemented
39C22×D293C2311yescharacteristic
40C22×D293C2312yes—
41D1172C2×C414yescomplemented
42C22⋊D293C2×C418yescomplemented
43C2×Dic293—42no—
44C2×Dic293C2311yescharacteristic
45C2×Dic293C2312yes—
46C2×Dic293C2311yescharacteristic
47C2×Dic293C2311yescharacteristic
48C4×D293—42no—
49C4×D293—42no—
50C4×D293C2×C414yescomplemented
51C23×C293C2312yes—
52D4×C293C2×C414yescomplemented
53C2×C4×C293—42no—
54C2×C4×C293C2311yescharacteristic
55C2×C4×C293C2311yescharacteristic
56C2×C4×C293C2312yes—
57C2×C4×C293C2311yescharacteristic
58C22×C293—22no—
59C22×C293—22no—
60C22×C293C22×C414yes—
61C22×C293C2411yescharacteristic
62C2×D293—22no—
63C2×D293—22no—
64C2×D293—21no—
65C2×D293—21no—
66C2×D293—48no—
67C2×D293C22×C412yes—
68C2×D293C22×C414yes—
69C4×C293—21no—
70C4×C293—22no—
71C4×C293—21no—
72C4×C293C22×C412yes—
73Dic293—21no—
74Dic293—22no—
75Dic293—21no—
76Dic293C22×C412yes—
77C2×C293—24no—
78C2×C293C23×C411yescharacteristic
79C2×C293H(5,𝔽2)11yescharacteristic
80C2×C293H(5,𝔽2)11yescharacteristic
81D293—22no—
82D293—24no—
83C293#51811yescharacteristic, complemented, Sylow
84#518—2931nomaximal, Sylow
85C22×D4—2931no—
86C4×D4—2931no—
87C4×D4—2932no—
88C4×D4—2931no—
89C4×D4—2932no—
90C4×D4—2931no—
91C4×D4D29311yescharacteristic, complemented
92#117—2931no—
93#117—2931no—
94C2×C22⋊C4—2932no—
95C2×C22⋊C4—2932no—
96C24—2932no—
97C2×D4—2932no—
98C2×D4—2938no—
99C2×D4—2931no—
100C2×D4C2×D29311yescharacteristic
101C22×C4—2931no—
102C22×C4—2932no—
103C22×C4—2932no—
104C22×C4—2932no—
105C22×C4C2×D29312yescomplemented
106C4⋊C4—2931no—
107C4⋊C4—2931no—
108C4⋊C4—2931no—
109C4⋊C4C2×D29311yescharacteristic, complemented
110C22⋊C4—2932no—
111C22⋊C4—2932no—
112C22⋊C4—2931no—
113C22⋊C4—2931no—
114C22⋊C4—2932no—
115C22⋊C4—2932no—
116C22⋊C4C2×D29312yescomplemented
117C42—2932no—
118C42—2931no—
119C42C2×D29311yescharacteristic, complemented
120C23—2931no—
121C23—2932no—
122C23—2938no—
123C23—11722no—
124C23—11722no—
125C23C22×D29312yes—
126D4—2938no—
127D4—2934no—
128D4C4×D29314yescomplemented
129C2×C4—42no—
130C2×C4—2931no—
131C2×C4—2934no—
132C2×C4—2931no—
133C2×C4—2932no—
134C2×C4—2931no—
135C2×C4—11722no—
136C2×C4—11722no—
137C2×C4—11722no—
138C2×C4C22×D29312yes—
139C2×C4C22×D29311yescharacteristic
140C2×C4C22×D29311yescharacteristic
141C2×C4C22×D29311yescharacteristic
142C22—22no—
143C22—22no—
144C22—2932no—
145C22—2934no—
146C22—5862no—
147C22—5861no—
148C22—5862no—
149C22—5861no—
150C22—11728no—
151C22C2×C4×D29314yes—
152C22C23×D29311yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—2932no—
157C4—5861no—
158C4—5862no—
159C4—5861no—
160C4C2×C4×D29312yes—
161C2—24no—
162C2—5862no—
163C2—5864no—
164C2C22×C4×D29311yescharacteristic
165C2#2262766911yescharacteristic
166C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutatorC2×C293C23×C4
FittingC4×D4×C293C2
socle, cosocleC22×C293C24
prime radicalC2×D4×D293C2
hypercenterC4×D4D293
hypocenterC293#518
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1172C2semidirect
3. D4×Dic293C2semidirect
4. #22627586C2semidirect
5. C4×C22⋊D293C2semidirect
6. #22627584C2semidirect
7. #22627582C2semidirect
8. #22627581C2semidirect
9. C2×#17989779C2semidirect
10. C22⋊C4×D293C2semidirect
11. C4×D4×C293C2semidirect
15. D4×D293C4semidirect
16. C22×Dic293C22semidirect
18. C2×C4×D293C22semidirect
19. C2×C4×D293C22semidirect
20. C4⋊Dic293C22semidirect
21. #17989781C22semidirect
22. #17989781C22semidirect
23. C22⋊Dic293C22semidirect
27. #17989779C22semidirect
28. #17989779C22semidirect
29. C4×Dic293C22semidirect
30. C4×Dic293C22semidirect
32. C22×C4×C293C22semidirect
33. C4⋊C4×C293C22semidirect
34. C22⋊C4×C293C22semidirect
35. C42×C293C22semidirect
38. C22×D293C2×C4semidirect
41. D1172C2×C4semidirect
42. C22⋊D293C2×C4semidirect
50. C4×D293C2×C4semidirect
52. D4×C293C2×C4semidirect
83. C293#518semidirect
91. C4×D4D293semidirect
105. C22×C4C2×D293semidirect
109. C4⋊C4C2×D293semidirect
116. C22⋊C4C2×D293semidirect
119. C42C2×D293semidirect
128. D4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2932
C4×D11722
D4×Dic2932
#226275862
C4×C22⋊D2932
#226275842
#226275822
#226275812
C2×#179897792
C22⋊C4×D2932
C4×D4×C2932
#518293