Finite Group Databasebeta

← #14271802

Subgroups — #14271802

Order 1856.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#90807C211yesmaximal, characteristic, complemented
2C2×D4×D29C211yesmaximal, characteristic, complemented
3C29×#121C211yesmaximal, characteristic, complemented
4#11745301C211yesmaximal, characteristic, complemented
5#11745299C211yesmaximal, characteristic, complemented
6#11745299C211yesmaximal, characteristic, complemented
7#11745297C211yesmaximal, characteristic, complemented
8C4×C22⋊D29C211yesmaximal, characteristic, complemented
9C2×#90781C211yesmaximal, characteristic, complemented
10#11745258C211yesmaximal, characteristic, complemented
11#11745256C211yesmaximal, characteristic, complemented
12#11745247C211yesmaximal, characteristic, complemented
13#11745246C211yesmaximal, characteristic, complemented
14#11745243C211yesmaximal, characteristic, complemented
15C22⋊C4×D29C211yesmaximal, characteristic, complemented
16C23×D29C2211yescharacteristic
17C23×D29C2211yescharacteristic
18C2×D4×C29C2211yescharacteristic
19C2×D4×C29C2211yescharacteristic, complemented
20C2×D4×C29C2211yescharacteristic, complemented
21C22×C4×C29C2211yescharacteristic, complemented
22C2×C22⋊D29C2211yescharacteristic
23C2×C22⋊D29C2211yescharacteristic
24C2×C22⋊D29C2211yescharacteristic
25C2×C22⋊D29C2211yescharacteristic, complemented
26C2×C22⋊D29C2211yescharacteristic, complemented
27C22×Dic29C2211yescharacteristic, complemented
28C22×Dic29C2211yescharacteristic, complemented
29#90807—24no—
30D4×D29—24no—
31C2×D116C2211yescharacteristic
32C2×C4×D29C2211yescharacteristic
33C2×C4×D29C2211yescharacteristic, complemented
34C2×C4×D29C2211yescharacteristic, complemented
35C2×Dic58C2211yescharacteristic, complemented
36C4⋊C4×C29C2211yescharacteristic, complemented
37C22⋊C4×C29C2211yescharacteristic, complemented
38C22⋊C4×C29C2211yescharacteristic, complemented
39C22⋊Dic29C2211yescharacteristic, complemented
40C22⋊Dic29C2211yescharacteristic, complemented
41C22⋊Dic29C2211yescharacteristic, complemented
42#90781C2211yescharacteristic
43#90781C2211yescharacteristic
44#90781C2211yescharacteristic
45#90781C2211yescharacteristic, complemented
46#90781C2211yescharacteristic, complemented
47#90781C2211yescharacteristic, complemented
48#90781C2211yescharacteristic, complemented
49#90779C2211yescharacteristic, complemented
50#90779C2211yescharacteristic, complemented
51#90779C2211yescharacteristic, complemented
52C4×Dic29C2211yescharacteristic, complemented
53C23×C29C2311yescharacteristic
54C23×C29C2311yescharacteristic
55C23×C29C2311yescharacteristic
56C22×D29—22no—
57C22×D29—22no—
58C22×D29—22no—
59C22×D29—22no—
60C22×D29—41no—
61C22×D29—41no—
62C22×D29C2311yescharacteristic
63C22×D29C2311yescharacteristic
64C22×D29C2311yescharacteristic
65D4×C29—22no—
66D4×C29—22no—
67D4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2311yescharacteristic
70C2×C4×C29C2311yescharacteristic
71C2×C4×C29C2311yescharacteristic
72C2×C4×C29C2311yescharacteristic
73C22⋊D29—22no—
74C22⋊D29—22no—
75C22⋊D29—22no—
76C22⋊D29—41no—
77C22⋊D29D414yescomplemented
78C2×Dic29—22no—
79C2×Dic29—22no—
80C2×Dic29C2311yescharacteristic
81C2×Dic29C2311yescharacteristic
82C2×Dic29C2311yescharacteristic
83C2×Dic29C2311yescharacteristic
84C2×Dic29C2311yescharacteristic
85D116—22no—
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—21no—
98C22×C29C2×D412yes—
99C22×C29C2411yescharacteristic
100C2×D29—21no—
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—21no—
105C2×D29—21no—
106C2×D29—21no—
107C2×D29—44no—
108C2×D29—44no—
109C2×D29C2×D412yes—
110C2×D29#4112yescomplemented
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—41no—
123C2×C29—41no—
124C2×C29C22×D411yescharacteristic
125C2×C29C2×#4111yescharacteristic
126C2×C29H(5,𝔽2)11yescharacteristic
127D29—22no—
128D29—22no—
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#121D2911yescharacteristic, complemented
139#120—291no—
140#120—291no—
141C4×D4—291no—
142C4×D4—291no—
143C2×C22⋊C4—291no—
144C2×C22⋊C4—291no—
145C29#54611yescharacteristic, complemented, Sylow
146C24—291no—
147C24—291no—
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—584no—
157C2×D4C2×D2911yescharacteristic
158C2×D4C2×D2911yescharacteristic, complemented
159C2×D4C2×D2911yescharacteristic, complemented
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4—291no—
165C22×C4C2×D2911yescharacteristic, complemented
166C4⋊C4—291no—
167C4⋊C4—291no—
168C4⋊C4—291no—
169C4⋊C4C2×D2911yescharacteristic, complemented
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⋊C4—291no—
179C22⋊C4—291no—
180C22⋊C4C2×D2911yescharacteristic, complemented
181C22⋊C4C2×D2911yescharacteristic, complemented
182C42—291no—
183C23—291no—
184C23—291no—
185C23—291no—
186C23—582no—
187C23—582no—
188C23—582no—
189C23—582no—
190C23—1161no—
191C23—1161no—
192C23C22×D2911yescharacteristic
193C23C22×D2911yescharacteristic
194C23C22×D2911yescharacteristic
195Q8—582no—
196D4—22no—
197D4—22no—
198D4—41no—
199D4—294no—
200D4—582no—
201D4—582no—
202D4—582no—
203D4—582no—
204D4—1161no—
205C2×C4—41no—
206C2×C4—291no—
207C2×C4—291no—
208C2×C4—291no—
209C2×C4—291no—
210C2×C4—291no—
211C2×C4—582no—
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—21no—
228C22—292no—
229C22—292no—
230C22—581no—
231C22—581no—
232C22—581no—
233C22—581no—
234C22—581no—
235C22—581no—
236C22—581no—
237C22—1164no—
238C22—1164no—
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—41no—
252C2—41no—
253C2—582no—
254C2—582no—
255C2—1161no—
256C2C2×D4×D2911yescharacteristic
257C2#1174535911yescharacteristic
258C2#41×D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#121C2
hypercenter#121D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#90807C2semidirect
2. C2×D4×D29C2semidirect
3. C29×#121C2semidirect
4. #11745301C2semidirect
5. #11745299C2semidirect
6. #11745299C2semidirect
7. #11745297C2semidirect
8. C4×C22⋊D29C2semidirect
9. C2×#90781C2semidirect
10. #11745258C2semidirect
11. #11745256C2semidirect
12. #11745247C2semidirect
13. #11745246C2semidirect
14. #11745243C2semidirect
15. C22⋊C4×D29C2semidirect
19. C2×D4×C29C22semidirect
20. C2×D4×C29C22semidirect
21. C22×C4×C29C22semidirect
25. C2×C22⋊D29C22semidirect
26. C2×C22⋊D29C22semidirect
27. C22×Dic29C22semidirect
28. C22×Dic29C22semidirect
33. C2×C4×D29C22semidirect
34. C2×C4×D29C22semidirect
35. C2×Dic58C22semidirect
36. C4⋊C4×C29C22semidirect
37. C22⋊C4×C29C22semidirect
38. C22⋊C4×C29C22semidirect
39. C22⋊Dic29C22semidirect
40. C22⋊Dic29C22semidirect
41. C22⋊Dic29C22semidirect
45. #90781C22semidirect
46. #90781C22semidirect
47. #90781C22semidirect
48. #90781C22semidirect
49. #90779C22semidirect
50. #90779C22semidirect
51. #90779C22semidirect
52. C4×Dic29C22semidirect
77. C22⋊D29D4semidirect
110. C2×D29#41semidirect
138. #121D29semidirect
145. C29#546semidirect
158. C2×D4C2×D29semidirect
159. C2×D4C2×D29semidirect
165. C22×C4C2×D29semidirect
169. C4⋊C4C2×D29semidirect
180. C22⋊C4C2×D29semidirect
181. C22⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#908072
C2×D4×D292
C29×#1212
#117453012
#117452992
#117452972
C4×C22⋊D292
C2×#907812
#117452582
#117452562
#117452472
#117452462
#117452432
C22⋊C4×D292
#54629