Finite Group Databasebeta

← #34036867

Subgroups — #34036867

Order 18752.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#22627620C211yesmaximal, characteristic, complemented
2#22627619C211yesmaximal, characteristic, complemented
3#22627617C211yesmaximal, characteristic, complemented
4#22627609C211yesmaximal, characteristic, complemented
5#22627608C211yesmaximal, characteristic, complemented
6#22627607C211yesmaximal, characteristic, complemented
7#22627598C211yesmaximal, characteristic, complemented
8#22627597C211yesmaximal, characteristic, complemented
9#22627596C211yesmaximal, characteristic, complemented
10#22627596C211yesmaximal, characteristic, complemented
11#22627595C211yesmaximal, characteristic, complemented
12#22627594C211yesmaximal, characteristic, complemented
13#22627592C211yesmaximal, characteristic, complemented
14#22627592C211yesmaximal, characteristic, complemented
15#121×C293C211yesmaximal, characteristic, complemented
16C23×D293C2211yescharacteristic
17C2×D1172C2211yescharacteristic
18C2×D1172C2211yescharacteristic
19C2×C22⋊D293C2211yescharacteristic
20C2×C22⋊D293C2211yescharacteristic
21C2×C22⋊D293C2211yescharacteristic
22C2×C22⋊D293C2211yescharacteristic
23C2×C22⋊D293C2211yescharacteristic
24C2×C22⋊D293C2211yescharacteristic, complemented
25C2×C22⋊D293C2211yescharacteristic, complemented
26C22×Dic293C2211yescharacteristic, complemented
27C2×C4×D293C2211yescharacteristic, complemented
28C4⋊Dic293C2211yescharacteristic, complemented
29C4⋊Dic293C2211yescharacteristic, complemented
30#17989781C2211yescharacteristic, complemented
31#17989781C2211yescharacteristic, complemented
32#17989781C2211yescharacteristic, complemented
33C22⋊Dic293C2211yescharacteristic
34C22⋊Dic293C2211yescharacteristic
35C22⋊Dic293C2211yescharacteristic, complemented
36#17989779C2211yescharacteristic
37#17989779C2211yescharacteristic
38#17989779C2211yescharacteristic
39#17989779C2211yescharacteristic
40#17989779C2211yescharacteristic
41#17989779C2211yescharacteristic
42#17989779C2211yescharacteristic, complemented
43C4×Dic293C2211yescharacteristic, complemented
44C2×D4×C293C2211yescharacteristic
45C2×D4×C293C2211yescharacteristic
46C2×D4×C293C2211yescharacteristic, complemented
47C22×C4×C293C2211yescharacteristic, complemented
48C4⋊C4×C293C2211yescharacteristic, complemented
49C22⋊C4×C293C2211yescharacteristic
50C22⋊C4×C293C2211yescharacteristic, complemented
51C22×D293—41no—
52C22×D293—41no—
53C22×D293—41no—
54C22×D293C2311yescharacteristic
55C22×D293C2311yescharacteristic
56C22×D293C2311yescharacteristic
57D1172—41no—
58D1172—41no—
59C22⋊D293—41no—
60C22⋊D293—41no—
61C22⋊D293—41no—
62C22⋊D293—41no—
63C22⋊D293—41no—
64C22⋊D293—41no—
65C22⋊D293—41no—
66C2×Dic293—41no—
67C2×Dic293C2311yescharacteristic
68C2×Dic293C2311yescharacteristic
69C2×Dic293C2311yescharacteristic
70C2×Dic293C2311yescharacteristic
71C2×Dic293C2311yescharacteristic
72C4×D293—41no—
73C23×C293C2311yescharacteristic
74C23×C293C2311yescharacteristic
75C23×C293C2311yescharacteristic
76D4×C293—41no—
77D4×C293—41no—
78D4×C293—41no—
79C2×C4×C293—41no—
80C2×C4×C293C2311yescharacteristic
81C2×C4×C293C2311yescharacteristic
82C2×C4×C293C2311yescharacteristic
83C2×C4×C293C2311yescharacteristic
84C22×C293—21no—
85C22×C293—21no—
86C22×C293—21no—
87C22×C293—21no—
88C22×C293—21no—
89C22×C293—21no—
90C22×C293—21no—
91C22×C293—21no—
92C22×C293—21no—
93C22×C293C2411yescharacteristic
94C2×D293—21no—
95C2×D293—21no—
96C2×D293—21no—
97C2×D293—21no—
98C2×D293—21no—
99C2×D293—21no—
100C2×D293—21no—
101C2×D293—21no—
102C2×D293—21no—
103C2×D293—44no—
104C4×C293—21no—
105C4×C293—21no—
106C4×C293—21no—
107C4×C293—21no—
108Dic293—21no—
109Dic293—21no—
110Dic293—21no—
111Dic293—21no—
112Dic293—21no—
113C2×C293—41no—
114C2×C293—41no—
115C2×C293—41no—
116C2×C293H(5,𝔽2)11yescharacteristic
117C2×C293H(5,𝔽2)11yescharacteristic
118C2×C293H(5,𝔽2)11yescharacteristic
119D293—41no—
120D293—41no—
121D293—41no—
122C293#56011yescharacteristic, complemented, Sylow
123#560—2931nomaximal, Sylow
124#127—2931no—
125#126—2931no—
126#126—2931no—
127#123—2931no—
128#123—2931no—
129#123—2931no—
130#121—2931no—
131#121—2931no—
132#121—2931no—
133#121—2931no—
134#121—2931no—
135#121D29311yescharacteristic, complemented
136#120—2931no—
137#120—2931no—
138#120—2931no—
139C24—2931no—
140C2×D4—2931no—
141C2×D4—2931no—
142C2×D4—2931no—
143C2×D4—2931no—
144C2×D4—2931no—
145C2×D4—2931no—
146C2×D4—2931no—
147C2×D4—2931no—
148C2×D4—2931no—
149C2×D4C2×D29311yescharacteristic
150C2×D4C2×D29311yescharacteristic
151C2×D4C2×D29311yescharacteristic, complemented
152C22×C4—2931no—
153C22×C4—2931no—
154C22×C4C2×D29311yescharacteristic, complemented
155C4⋊C4—2931no—
156C4⋊C4—2931no—
157C4⋊C4—2931no—
158C4⋊C4—2931no—
159C4⋊C4—2931no—
160C4⋊C4C2×D29311yescharacteristic, complemented
161C22⋊C4—2931no—
162C22⋊C4—2931no—
163C22⋊C4—2931no—
164C22⋊C4—2931no—
165C22⋊C4—2931no—
166C22⋊C4—2931no—
167C22⋊C4—2931no—
168C22⋊C4—2931no—
169C22⋊C4—2931no—
170C22⋊C4—2931no—
171C22⋊C4C2×D29311yescharacteristic
172C22⋊C4C2×D29311yescharacteristic, complemented
173C42—2931no—
174C23—2931no—
175C23—2931no—
176C23—2931no—
177C23—11721no—
178C23—11721no—
179C23—11721no—
180C23C22×D29311yescharacteristic
181C23C22×D29311yescharacteristic
182C23C22×D29311yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—11721no—
187D4—11721no—
188D4—11721no—
189D4—11721no—
190D4—11721no—
191D4—11721no—
192D4—11721no—
193D4—11721no—
194D4—11721no—
195C2×C4—41no—
196C2×C4—2931no—
197C2×C4—2931no—
198C2×C4—2931no—
199C2×C4—2931no—
200C2×C4—2931no—
201C2×C4—11721no—
202C2×C4—11721no—
203C2×C4C22×D29311yescharacteristic
204C2×C4C22×D29311yescharacteristic
205C2×C4C22×D29311yescharacteristic
206C2×C4C22×D29311yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—5861no—
217C22—5861no—
218C22—5861no—
219C22—5861no—
220C22—5861no—
221C22—5861no—
222C22—5861no—
223C22—5861no—
224C22—5861no—
225C22—11724no—
226C22C23×D29311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—5861no—
232C4—5861no—
233C4—5861no—
234C4—5861no—
235C4—5861no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—11721no—
240C2—11721no—
241C2—11721no—
242C2#2262766911yescharacteristic
243C2#2262766911yescharacteristic
244C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#121×C293C2
hypercenter#121D293
hypocenterC293#560
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #22627620C2semidirect
2. #22627619C2semidirect
3. #22627617C2semidirect
4. #22627609C2semidirect
5. #22627608C2semidirect
6. #22627607C2semidirect
7. #22627598C2semidirect
8. #22627597C2semidirect
9. #22627596C2semidirect
10. #22627596C2semidirect
11. #22627595C2semidirect
12. #22627594C2semidirect
13. #22627592C2semidirect
14. #22627592C2semidirect
15. #121×C293C2semidirect
24. C2×C22⋊D293C22semidirect
25. C2×C22⋊D293C22semidirect
26. C22×Dic293C22semidirect
27. C2×C4×D293C22semidirect
28. C4⋊Dic293C22semidirect
29. C4⋊Dic293C22semidirect
30. #17989781C22semidirect
31. #17989781C22semidirect
32. #17989781C22semidirect
35. C22⋊Dic293C22semidirect
42. #17989779C22semidirect
43. C4×Dic293C22semidirect
46. C2×D4×C293C22semidirect
47. C22×C4×C293C22semidirect
48. C4⋊C4×C293C22semidirect
50. C22⋊C4×C293C22semidirect
122. C293#560semidirect
135. #121D293semidirect
151. C2×D4C2×D293semidirect
154. C22×C4C2×D293semidirect
160. C4⋊C4C2×D293semidirect
172. C22⋊C4C2×D293semidirect

Maximal subgroups

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

subgroupindex
#226276202
#226276192
#226276172
#226276092
#226276082
#226276072
#226275982
#226275972
#226275962
#226275952
#226275942
#226275922
#121×C2932
#560293