Finite Group Databasebeta

← #14271803

Subgroups — #14271803

Order 1856.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊D29C211yesmaximal, characteristic, complemented
2C2×#90805C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C29C211yesmaximal, characteristic, complemented
4#11745315C211yesmaximal, characteristic, complemented
5#11745292C211yesmaximal, characteristic, complemented
6#11745291C211yesmaximal, characteristic, complemented
7C4×C22⋊D29C211yesmaximal, characteristic, complemented
8#11745247C211yesmaximal, characteristic, complemented
9#11745246C211yesmaximal, characteristic, complemented
10#11745246C211yesmaximal, characteristic, complemented
11#11745245C211yesmaximal, characteristic, complemented
12#11745244C211yesmaximal, characteristic, complemented
13#11745243C211yesmaximal, characteristic, complemented
14C22⋊C4×D29C211yesmaximal, characteristic, complemented
15#11745240C211yesmaximal, characteristic, complemented
16C24×C29C2211yescharacteristic
17C23×D29C2211yescharacteristic
18C22×C4×C29C2211yescharacteristic, complemented
19C22×C4×C29C2211yescharacteristic, complemented
20C2×C22⋊D29—24no—
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
29#90805—24no—
30C2×D116C2211yescharacteristic, complemented
31C2×D116C2211yescharacteristic, complemented
32C2×C4×D29C2211yescharacteristic, complemented
33C2×C4×D29C2211yescharacteristic, complemented
34C2×C4×D29C2211yescharacteristic, complemented
35C2×Dic58C2211yescharacteristic, complemented
36C22⋊C4×C29C2211yescharacteristic
37C22⋊C4×C29C2211yescharacteristic
38C22⋊C4×C29C2211yescharacteristic, complemented
39C22⋊C4×C29C2211yescharacteristic, complemented
40C22⋊Dic29C2211yescharacteristic
41C22⋊Dic29C2211yescharacteristic, complemented
42C22⋊Dic29C2211yescharacteristic, complemented
43#90781C2211yescharacteristic, complemented
44#90781C2211yescharacteristic, complemented
45#90781C2211yescharacteristic, complemented
46#90781C2211yescharacteristic, complemented
47#90781C2211yescharacteristic, complemented
48C4⋊Dic29C2211yescharacteristic, complemented
49#90779C2211yescharacteristic, complemented
50#90779C2211yescharacteristic, complemented
51#90779C2211yescharacteristic, complemented
52C4×Dic29C2211yescharacteristic, complemented
53C23×C29—22no—
54C23×C29—22no—
55C23×C29—41no—
56C23×C29C2311yescharacteristic
57C23×C29C2311yescharacteristic
58C23×C29C2311yescharacteristic
59C22×D29—22no—
60C22×D29—22no—
61C22×D29—41no—
62C22×D29C2311yescharacteristic
63C22×D29C2311yescharacteristic
64C22×D29C2311yescharacteristic
65C2×C4×C29—22no—
66C2×C4×C29—41no—
67C2×C4×C29C2311yescharacteristic
68C2×C4×C29C2311yescharacteristic
69C2×C4×C29C2311yescharacteristic
70C2×C4×C29C2311yescharacteristic
71C22⋊D29—22no—
72C22⋊D29—22no—
73C22⋊D29—22no—
74C22⋊D29—22no—
75C22⋊D29—22no—
76C22⋊D29—41no—
77C22⋊D29D414yescomplemented
78C2×Dic29—22no—
79C2×Dic29C2311yescharacteristic
80C2×Dic29C2311yescharacteristic
81C2×Dic29C2311yescharacteristic
82C2×Dic29C2311yescharacteristic
83C2×Dic29C2311yescharacteristic
84D116—22no—
85D116—41no—
86C4×D29—22no—
87C4×D29—22no—
88C4×D29—41no—
89Dic58—22no—
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—21no—
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—21no—
97C22×C29—44no—
98C22×C29C2×D412yes—
99C22×C29#4112yescomplemented
100C22×C29C2411yescharacteristic
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—21no—
105C2×D29—21no—
106C2×D29—21no—
107C2×D29—21no—
108C2×D29—21no—
109C2×D29—44no—
110C2×D29C2×D412yes—
111C4×C29—21no—
112C4×C29—21no—
113C4×C29—21no—
114C4×C29—21no—
115Dic29—21no—
116Dic29—21no—
117Dic29—21no—
118Dic29—21no—
119Dic29C2×D412yes—
120#546—291nomaximal, Sylow
121C2×C29—22no—
122C2×C29—22no—
123C2×C29—41no—
124C2×C29C22×D411yescharacteristic
125C2×C29C2×#4111yescharacteristic
126C2×C29H(5,𝔽2)11yescharacteristic
127D29—22no—
128D29—41no—
129D29—41no—
130C2×#41—291no—
131C22×D4—291no—
132#124—291no—
133#123—291no—
134#123—291no—
135C22⋊Q8—291no—
136#121—291no—
137#121—291no—
138#121—291no—
139#120—291no—
140#120—291no—
141C4×D4—291no—
142C4×D4—291no—
143C2×C22⋊C4—291no—
144C2×C22⋊C4D2911yescharacteristic, complemented
145C29#54611yescharacteristic, complemented, Sylow
146C24—291no—
147C24C2×D2911yescharacteristic
148#41—584no—
149C2×Q8—291no—
150C2×D4—291no—
151C2×D4—291no—
152C2×D4—291no—
153C2×D4—291no—
154C2×D4—291no—
155C2×D4—291no—
156C2×D4—291no—
157C2×D4—291no—
158C2×D4—291no—
159C2×D4—584no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4C2×D2911yescharacteristic, complemented
165C22×C4C2×D2911yescharacteristic, complemented
166C4⋊C4—291no—
167C4⋊C4—291no—
168C4⋊C4—291no—
169C4⋊C4—291no—
170C22⋊C4—291no—
171C22⋊C4—291no—
172C22⋊C4—291no—
173C22⋊C4—291no—
174C22⋊C4—291no—
175C22⋊C4—291no—
176C22⋊C4—291no—
177C22⋊C4—291no—
178C22⋊C4C2×D2911yescharacteristic
179C22⋊C4C2×D2911yescharacteristic
180C22⋊C4C2×D2911yescharacteristic, complemented
181C22⋊C4C2×D2911yescharacteristic, complemented
182C42—291no—
183C23—22no—
184C23—22no—
185C23—41no—
186C23—291no—
187C23—291no—
188C23—291no—
189C23—582no—
190C23—582no—
191C23—1161no—
192C23C22×D2911yescharacteristic
193C23C22×D2911yescharacteristic
194C23C22×D2911yescharacteristic
195Q8—582no—
196D4—294no—
197D4—582no—
198D4—582no—
199D4—582no—
200D4—582no—
201D4—582no—
202D4—582no—
203D4—1161no—
204D4—1161no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—291no—
208C2×C4—291no—
209C2×C4—291no—
210C2×C4—291no—
211C2×C4—291no—
212C2×C4—582no—
213C2×C4—582no—
214C2×C4—582no—
215C2×C4—1161no—
216C2×C4C22×D2911yescharacteristic
217C2×C4C22×D2911yescharacteristic
218C2×C4C22×D2911yescharacteristic
219C2×C4C22×D2911yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—44no—
228C22—292no—
229C22—581no—
230C22—581no—
231C22—581no—
232C22—581no—
233C22—581no—
234C22—581no—
235C22—581no—
236C22—581no—
237C22—1164no—
238C22#9080512yescomplemented
239C22D4×D2912yes—
240C22C23×D2911yescharacteristic
241C4—21no—
242C4—21no—
243C4—21no—
244C4—21no—
245C4—292no—
246C4—581no—
247C4—581no—
248C4—581no—
249C4—581no—
250C2—22no—
251C2—22no—
252C2—41no—
253C2—582no—
254C2—1161no—
255C2—1161no—
256C2C2×#9080511yescharacteristic
257C2C2×D4×D2911yescharacteristic
258C2#1174535911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC2×C22⋊C4×C29C2
hypercenterC2×C22⋊C4D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D29C2semidirect
2. C2×#90805C2semidirect
3. C2×C22⋊C4×C29C2semidirect
4. #11745315C2semidirect
5. #11745292C2semidirect
6. #11745291C2semidirect
7. C4×C22⋊D29C2semidirect
8. #11745247C2semidirect
9. #11745246C2semidirect
10. #11745246C2semidirect
11. #11745245C2semidirect
12. #11745244C2semidirect
13. #11745243C2semidirect
14. C22⋊C4×D29C2semidirect
15. #11745240C2semidirect
18. C22×C4×C29C22semidirect
19. C22×C4×C29C22semidirect
26. C2×C22⋊D29C22semidirect
27. C2×C22⋊D29C22semidirect
30. C2×D116C22semidirect
31. C2×D116C22semidirect
32. C2×C4×D29C22semidirect
33. C2×C4×D29C22semidirect
34. C2×C4×D29C22semidirect
35. C2×Dic58C22semidirect
38. C22⋊C4×C29C22semidirect
39. C22⋊C4×C29C22semidirect
41. C22⋊Dic29C22semidirect
42. C22⋊Dic29C22semidirect
43. #90781C22semidirect
44. #90781C22semidirect
45. #90781C22semidirect
46. #90781C22semidirect
47. #90781C22semidirect
48. C4⋊Dic29C22semidirect
49. #90779C22semidirect
50. #90779C22semidirect
51. #90779C22semidirect
52. C4×Dic29C22semidirect
77. C22⋊D29D4semidirect
99. C22×C29#41semidirect
144. C2×C22⋊C4D29semidirect
145. C29#546semidirect
164. C22×C4C2×D29semidirect
165. C22×C4C2×D29semidirect
180. C22⋊C4C2×D29semidirect
181. C22⋊C4C2×D29semidirect
238. C22#90805semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D292
C2×#908052
C2×C22⋊C4×C292
#117453152
#117452922
#117452912
C4×C22⋊D292
#117452472
#117452462
#117452452
#117452442
#117452432
C22⋊C4×D292
#117452402
#54629