Finite Group Databasebeta

← #14271901

Subgroups — #14271901

Order 1856.

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
1C29×#121C211yesmaximal, characteristic, complemented
2#11745302C211yesmaximal, characteristic, complemented
3#11745301C211yesmaximal, characteristic, complemented
4#11745301C211yesmaximal, characteristic, complemented
5#11745300C211yesmaximal, characteristic, complemented
6#11745299C211yesmaximal, characteristic, complemented
7#11745299C211yesmaximal, characteristic, complemented
8#11745292C211yesmaximal, characteristic, complemented
9#11745291C211yesmaximal, characteristic, complemented
10#11745260C211yesmaximal, characteristic, complemented
11#11745256C211yesmaximal, characteristic, complemented
12#11745248C211yesmaximal, characteristic, complemented
13#11745246C211yesmaximal, characteristic, complemented
14#11745244C211yesmaximal, characteristic, complemented
15#11745241C211yesmaximal, characteristic, complemented
16C23×D29C2211yescharacteristic
17C2×D4×C29C2211yescharacteristic
18C2×D4×C29C2211yescharacteristic
19C2×D4×C29C2211yescharacteristic, complemented
20C22×C4×C29C2211yescharacteristic, complemented
21C2×C22⋊D29C2211yescharacteristic
22C2×C22⋊D29C2211yescharacteristic
23C2×C22⋊D29C2211yescharacteristic
24C2×C22⋊D29C2211yescharacteristic
25C2×C22⋊D29C2211yescharacteristic
26C2×C22⋊D29C2211yescharacteristic, complemented
27C2×C22⋊D29C2211yescharacteristic, complemented
28C22×Dic29C2211yescharacteristic, complemented
29C2×D116C2211yescharacteristic
30C2×D116C2211yescharacteristic
31C2×C4×D29C2211yescharacteristic, complemented
32C4⋊C4×C29C2211yescharacteristic, complemented
33C22⋊C4×C29C2211yescharacteristic
34C22⋊C4×C29C2211yescharacteristic, complemented
35C22⋊Dic29C2211yescharacteristic
36C22⋊Dic29C2211yescharacteristic
37C22⋊Dic29C2211yescharacteristic, complemented
38#90781C2211yescharacteristic
39#90781C2211yescharacteristic
40#90781C2211yescharacteristic
41#90781C2211yescharacteristic
42#90781C2211yescharacteristic
43#90781C2211yescharacteristic
44#90781C2211yescharacteristic, complemented
45C4⋊Dic29C2211yescharacteristic, complemented
46C4⋊Dic29C2211yescharacteristic, complemented
47#90779C2211yescharacteristic, complemented
48#90779C2211yescharacteristic, complemented
49#90779C2211yescharacteristic, complemented
50C4×Dic29C2211yescharacteristic, complemented
51C23×C29C2311yescharacteristic
52C23×C29C2311yescharacteristic
53C23×C29C2311yescharacteristic
54C22×D29—41no—
55C22×D29—41no—
56C22×D29—41no—
57C22×D29C2311yescharacteristic
58C22×D29C2311yescharacteristic
59C22×D29C2311yescharacteristic
60D4×C29—41no—
61D4×C29—41no—
62D4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29C2311yescharacteristic
65C2×C4×C29C2311yescharacteristic
66C2×C4×C29C2311yescharacteristic
67C2×C4×C29C2311yescharacteristic
68C22⋊D29—41no—
69C22⋊D29—41no—
70C22⋊D29—41no—
71C22⋊D29—41no—
72C22⋊D29—41no—
73C22⋊D29—41no—
74C22⋊D29—41no—
75C2×Dic29—41no—
76C2×Dic29C2311yescharacteristic
77C2×Dic29C2311yescharacteristic
78C2×Dic29C2311yescharacteristic
79C2×Dic29C2311yescharacteristic
80C2×Dic29C2311yescharacteristic
81D116—41no—
82D116—41no—
83C4×D29—41no—
84C22×C29—21no—
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—21no—
93C22×C29C2411yescharacteristic
94C2×D29—21no—
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—21no—
98C2×D29—21no—
99C2×D29—21no—
100C2×D29—21no—
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—44no—
104C4×C29—21no—
105C4×C29—21no—
106C4×C29—21no—
107C4×C29—21no—
108Dic29—21no—
109Dic29—21no—
110Dic29—21no—
111Dic29—21no—
112Dic29—21no—
113#560—291nomaximal, Sylow
114C2×C29—41no—
115C2×C29—41no—
116C2×C29—41no—
117C2×C29H(5,𝔽2)11yescharacteristic
118C2×C29H(5,𝔽2)11yescharacteristic
119C2×C29H(5,𝔽2)11yescharacteristic
120D29—41no—
121D29—41no—
122D29—41no—
123#127—291no—
124#126—291no—
125#126—291no—
126#123—291no—
127#123—291no—
128#123—291no—
129#121—291no—
130#121—291no—
131#121—291no—
132#121—291no—
133#121—291no—
134#121D2911yescharacteristic, complemented
135#120—291no—
136#120—291no—
137#120—291no—
138C29#56011yescharacteristic, complemented, Sylow
139C24—291no—
140C2×D4—291no—
141C2×D4—291no—
142C2×D4—291no—
143C2×D4—291no—
144C2×D4—291no—
145C2×D4—291no—
146C2×D4—291no—
147C2×D4—291no—
148C2×D4—291no—
149C2×D4C2×D2911yescharacteristic
150C2×D4C2×D2911yescharacteristic
151C2×D4C2×D2911yescharacteristic, complemented
152C22×C4—291no—
153C22×C4—291no—
154C22×C4C2×D2911yescharacteristic, complemented
155C4⋊C4—291no—
156C4⋊C4—291no—
157C4⋊C4—291no—
158C4⋊C4—291no—
159C4⋊C4—291no—
160C4⋊C4C2×D2911yescharacteristic, complemented
161C22⋊C4—291no—
162C22⋊C4—291no—
163C22⋊C4—291no—
164C22⋊C4—291no—
165C22⋊C4—291no—
166C22⋊C4—291no—
167C22⋊C4—291no—
168C22⋊C4—291no—
169C22⋊C4—291no—
170C22⋊C4—291no—
171C22⋊C4C2×D2911yescharacteristic
172C22⋊C4C2×D2911yescharacteristic, complemented
173C42—291no—
174C23—291no—
175C23—291no—
176C23—291no—
177C23—1161no—
178C23—1161no—
179C23—1161no—
180C23C22×D2911yescharacteristic
181C23C22×D2911yescharacteristic
182C23C22×D2911yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1161no—
187D4—1161no—
188D4—1161no—
189D4—1161no—
190D4—1161no—
191D4—1161no—
192D4—1161no—
193D4—1161no—
194D4—1161no—
195C2×C4—41no—
196C2×C4—291no—
197C2×C4—291no—
198C2×C4—291no—
199C2×C4—291no—
200C2×C4—291no—
201C2×C4—1161no—
202C2×C4—1161no—
203C2×C4C22×D2911yescharacteristic
204C2×C4C22×D2911yescharacteristic
205C2×C4C22×D2911yescharacteristic
206C2×C4C22×D2911yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—581no—
217C22—581no—
218C22—581no—
219C22—581no—
220C22—581no—
221C22—581no—
222C22—581no—
223C22—581no—
224C22—581no—
225C22—1164no—
226C22C23×D2911yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—581no—
232C4—581no—
233C4—581no—
234C4—581no—
235C4—581no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1161no—
240C2—1161no—
241C2—1161no—
242C2#1174535911yescharacteristic
243C2#1174535911yescharacteristic
244C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#121C2
hypercenter#121D29
hypocenterC29#560
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C29×#121C2semidirect
2. #11745302C2semidirect
3. #11745301C2semidirect
4. #11745301C2semidirect
5. #11745300C2semidirect
6. #11745299C2semidirect
7. #11745299C2semidirect
8. #11745292C2semidirect
9. #11745291C2semidirect
10. #11745260C2semidirect
11. #11745256C2semidirect
12. #11745248C2semidirect
13. #11745246C2semidirect
14. #11745244C2semidirect
15. #11745241C2semidirect
19. C2×D4×C29C22semidirect
20. C22×C4×C29C22semidirect
26. C2×C22⋊D29C22semidirect
27. C2×C22⋊D29C22semidirect
28. C22×Dic29C22semidirect
31. C2×C4×D29C22semidirect
32. C4⋊C4×C29C22semidirect
34. C22⋊C4×C29C22semidirect
37. C22⋊Dic29C22semidirect
44. #90781C22semidirect
45. C4⋊Dic29C22semidirect
46. C4⋊Dic29C22semidirect
47. #90779C22semidirect
48. #90779C22semidirect
49. #90779C22semidirect
50. C4×Dic29C22semidirect
134. #121D29semidirect
138. C29#560semidirect
151. C2×D4C2×D29semidirect
154. C22×C4C2×D29semidirect
160. C4⋊C4C2×D29semidirect
172. C22⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
C29×#1212
#117453022
#117453012
#117453002
#117452992
#117452922
#117452912
#117452602
#117452562
#117452482
#117452462
#117452442
#117452412
#56029