Finite Group Databasebeta

← #34036763

Subgroups — #34036763

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×D1172C211yesmaximal, characteristic, complemented
2C2×D4×D293C212yesmaximal, complemented
3C2×D4×D293C211yesmaximal, characteristic, complemented
4#22627620C211yesmaximal, characteristic, complemented
5#22627599C211yesmaximal, characteristic, complemented
6#22627597C212yesmaximal, complemented
7#22627594C212yesmaximal, complemented
8#22627592C212yesmaximal, complemented
9#22627586C211yesmaximal, characteristic, complemented
10C4×C22⋊D293C211yesmaximal, characteristic, complemented
11#121×C293C211yesmaximal, characteristic, complemented
12C23×D293C2212yescomplemented
13C23×D293C2212yescomplemented
14C2×D1172—24no—
15C2×D1172C2211yescharacteristic
16C2×D1172C2212yescomplemented
17C2×D1172C2212yescomplemented
18C2×D1172C2211yescharacteristic, complemented
19C2×C22⋊D293C2211yescharacteristic
20C2×C22⋊D293C2212yescomplemented
21C2×C22⋊D293C2212yescomplemented
22C2×C22⋊D293C2212yescomplemented
23D4×D293—24no—
24D4×D293—28no—
25C2×C4×D293C2211yescharacteristic, complemented
26C2×C4×D293C2212yescomplemented
27#17989781C2211yescharacteristic, complemented
28C22⋊Dic293C2211yescharacteristic, complemented
29#17989779C2211yescharacteristic, complemented
30#17989779C2212yescomplemented
31#17989779C2212yescomplemented
32C4×Dic293C2211yescharacteristic, complemented
33C2×D4×C293C2212yescomplemented
34C2×D4×C293C2211yescharacteristic, complemented
35C22×C4×C293C2211yescharacteristic, complemented
36C4⋊C4×C293C2211yescharacteristic, complemented
37C22⋊C4×C293C2212yescomplemented
38C22×D293—24no—
39C22×D293—24no—
40C22×D293—24no—
41C22×D293—24no—
42C22×D293—42no—
43C22×D293—42no—
44C22×D293C2312yes—
45C22×D293C2311yescharacteristic
46C22×D293C2312yes—
47D1172—24no—
48D1172—24no—
49D1172—22no—
50D1172D414yescomplemented
51C22⋊D293—24no—
52C22⋊D293—24no—
53C22⋊D293—42no—
54C22⋊D293D414yescomplemented
55C2×Dic293C2311yescharacteristic
56C2×Dic293C2311yescharacteristic
57C2×Dic293C2311yescharacteristic
58C4×D293—22no—
59C4×D293—24no—
60C23×C293C2312yes—
61C23×C293C2311yescharacteristic
62D4×C293—24no—
63D4×C293—22no—
64C2×C4×C293—22no—
65C2×C4×C293C2311yescharacteristic
66C2×C4×C293C2312yes—
67C2×C4×C293C2311yescharacteristic
68C22×C293—21no—
69C22×C293—21no—
70C22×C293—22no—
71C22×C293—22no—
72C22×C293—22no—
73C22×C293C2×D412yescomplemented
74C22×C293C2411yescharacteristic
75C2×D293—21no—
76C2×D293—22no—
77C2×D293—21no—
78C2×D293—22no—
79C2×D293—22no—
80C2×D293—22no—
81C2×D293—22no—
82C2×D293—48no—
83C2×D293—48no—
84C2×D293C2×D414yescomplemented
85C2×D293C2×D412yescomplemented
86C4×C293—21no—
87C4×C293—22no—
88C4×C293C2×D412yescomplemented
89Dic293—21no—
90Dic293—21no—
91Dic293C2×D412yescomplemented
92C2×C293—22no—
93C2×C293—42no—
94C2×C293C22×D411yescharacteristic
95C2×C293C22×D411yescharacteristic
96C2×C293H(5,𝔽2)11yescharacteristic
97D293—22no—
98D293—24no—
99D293—42no—
100C293D4211yescharacteristic, complemented, Sylow
101D42—2931nomaximal, Sylow
102C22×D4—2932no—
103C22×D4—2931no—
104C22×D4—2931no—
105#127—2931no—
106#121—2931no—
107#121—2932no—
108#121D29311yescharacteristic, complemented
109#120—2932no—
110#120—2932no—
111C4×D4—2931no—
112C4×D4—2931no—
113C24—2932no—
114C24—2932no—
115C2×D4—2931no—
116C2×D4—2932no—
117C2×D4—2932no—
118C2×D4—2932no—
119C2×D4—2931no—
120C2×D4—2932no—
121C2×D4—2932no—
122C2×D4—2931no—
123C2×D4—5864no—
124C2×D4—5868no—
125C2×D4—5864no—
126C2×D4C2×D29312yescomplemented
127C2×D4C2×D29311yescharacteristic, complemented
128C22×C4—2932no—
129C22×C4—2931no—
130C22×C4C2×D29311yescharacteristic, complemented
131C4⋊C4—2931no—
132C4⋊C4C2×D29311yescharacteristic, complemented
133C22⋊C4—2931no—
134C22⋊C4—2932no—
135C22⋊C4—2931no—
136C22⋊C4—2932no—
137C22⋊C4C2×D29312yescomplemented
138C42—2931no—
139C23—2931no—
140C23—2932no—
141C23—2932no—
142C23—5864no—
143C23—5864no—
144C23—5864no—
145C23—5864no—
146C23—11722no—
147C23—11722no—
148C23C22×D29312yes—
149C23C22×D29311yescharacteristic
150D4—24no—
151D4—22no—
152D4—2934no—
153D4—2934no—
154D4—5864no—
155D4—5864no—
156D4—5864no—
157D4—5864no—
158D4—5862no—
159D4—11722no—
160C2×C4—22no—
161C2×C4—2931no—
162C2×C4—2931no—
163C2×C4—2931no—
164C2×C4—5864no—
165C2×C4—5862no—
166C2×C4C22×D29312yes—
167C2×C4C22×D29311yescharacteristic
168C2×C4C22×D29311yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—2932no—
175C22—2934no—
176C22—5862no—
177C22—5861no—
178C22—5862no—
179C22—5861no—
180C22—5862no—
181C22—5862no—
182C22—5862no—
183C22—11728no—
184C22—11728no—
185C22D4×D29312yescomplemented
186C22C23×D29311yescharacteristic
187C4—21no—
188C4—22no—
189C4—2932no—
190C4—5861no—
191C4—5861no—
192C4D4×D29312yescomplemented
193C2—22no—
194C2—42no—
195C2—5864no—
196C2—5862no—
197C2—11722no—
198C2C2×D4×D29311yescharacteristic
199C2C2×D4×D29311yescharacteristic
200C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#121×C293C2
hypercenter#121D293
hypocenterC293D42
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D1172C2semidirect
2. C2×D4×D293C2semidirect
3. C2×D4×D293C2semidirect
4. #22627620C2semidirect
5. #22627599C2semidirect
6. #22627597C2semidirect
7. #22627594C2semidirect
8. #22627592C2semidirect
9. #22627586C2semidirect
10. C4×C22⋊D293C2semidirect
11. #121×C293C2semidirect
12. C23×D293C22semidirect
13. C23×D293C22semidirect
16. C2×D1172C22semidirect
17. C2×D1172C22semidirect
18. C2×D1172C22semidirect
20. C2×C22⋊D293C22semidirect
21. C2×C22⋊D293C22semidirect
22. C2×C22⋊D293C22semidirect
25. C2×C4×D293C22semidirect
26. C2×C4×D293C22semidirect
27. #17989781C22semidirect
28. C22⋊Dic293C22semidirect
29. #17989779C22semidirect
30. #17989779C22semidirect
31. #17989779C22semidirect
32. C4×Dic293C22semidirect
33. C2×D4×C293C22semidirect
34. C2×D4×C293C22semidirect
35. C22×C4×C293C22semidirect
36. C4⋊C4×C293C22semidirect
37. C22⋊C4×C293C22semidirect
50. D1172D4semidirect
54. C22⋊D293D4semidirect
73. C22×C293C2×D4semidirect
84. C2×D293C2×D4semidirect
85. C2×D293C2×D4semidirect
88. C4×C293C2×D4semidirect
91. Dic293C2×D4semidirect
100. C293D42semidirect
108. #121D293semidirect
126. C2×D4C2×D293semidirect
127. C2×D4C2×D293semidirect
130. C22×C4C2×D293semidirect
132. C4⋊C4C2×D293semidirect
137. C22⋊C4C2×D293semidirect
185. C22D4×D293semidirect
192. C4D4×D293semidirect

Maximal subgroups

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

subgroupindex
C22×D11722
C2×D4×D2932
#226276202
#226275992
#226275972
#226275942
#226275922
#226275862
C4×C22⋊D2932
#121×C2932
D42293