Finite Group Databasebeta

← #14271748

Subgroups — #14271748

Order 1856.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×#120C211yesmaximal, characteristic, complemented
2#11745315C211yesmaximal, characteristic, complemented
3C2×C22⋊Dic29C211yesmaximal, characteristic, complemented
4#11745301C211yesmaximal, characteristic, complemented
5#11745301C211yesmaximal, characteristic, complemented
6#11745300C211yesmaximal, characteristic, complemented
7#11745298C211yesmaximal, characteristic, complemented
8#11745297C211yesmaximal, characteristic, complemented
9D4×Dic29C211yesmaximal, characteristic, complemented
10#11745247C211yesmaximal, characteristic, complemented
11#11745245C211yesmaximal, characteristic, complemented
12#11745243C211yesmaximal, characteristic, complemented
13#11745241C211yesmaximal, characteristic, complemented
14#11745241C211yesmaximal, characteristic, complemented
15#11745240C211yesmaximal, characteristic, complemented
16C24×C29C2211yescharacteristic
17C2×D4×C29C2211yescharacteristic
18C2×D4×C29C2211yescharacteristic
19C2×D4×C29C2211yescharacteristic
20C2×C22⋊D29C2211yescharacteristic
21C2×C22⋊D29C2211yescharacteristic
22C2×C22⋊D29C2211yescharacteristic
23C2×C22⋊D29C2211yescharacteristic, complemented
24C22×Dic29C2211yescharacteristic
25C22×Dic29C2211yescharacteristic
26C22×Dic29C2211yescharacteristic, complemented
27C2×C4×D29C2211yescharacteristic, complemented
28C2×Dic58C2211yescharacteristic, complemented
29C22⋊C4×C29C2211yescharacteristic
30C22⋊C4×C29C2211yescharacteristic
31C22⋊C4×C29C2211yescharacteristic
32C22⋊Dic29C2211yescharacteristic
33C22⋊Dic29C2211yescharacteristic
34C22⋊Dic29C2211yescharacteristic
35C22⋊Dic29C2211yescharacteristic
36C22⋊Dic29C2211yescharacteristic
37C22⋊Dic29C2211yescharacteristic
38C22⋊Dic29C2211yescharacteristic
39C22⋊Dic29C2211yescharacteristic, complemented
40C22⋊Dic29C2211yescharacteristic, complemented
41#90781C2211yescharacteristic, complemented
42#90781C2211yescharacteristic, complemented
43C4⋊Dic29C2211yescharacteristic, complemented
44C4⋊Dic29C2211yescharacteristic, complemented
45#90779C2211yescharacteristic, complemented
46#90779C2211yescharacteristic, complemented
47#90779C2211yescharacteristic, complemented
48#90779C2211yescharacteristic, complemented
49C4×Dic29C2211yescharacteristic, complemented
50C4×Dic29C2211yescharacteristic, complemented
51C23×C29—22no—
52C23×C29—41no—
53C23×C29—41no—
54C23×C29C2311yescharacteristic
55C23×C29C2311yescharacteristic
56C23×C29C2311yescharacteristic
57C23×C29C2311yescharacteristic
58C22×D29C2311yescharacteristic
59D4×C29—22no—
60D4×C29—41no—
61D4×C29—41no—
62C2×C4×C29C2311yescharacteristic
63C2×C4×C29C2311yescharacteristic
64C2×C4×C29C2311yescharacteristic
65C22⋊D29—22no—
66C22⋊D29—41no—
67C22⋊D29—41no—
68C22⋊D29—41no—
69C2×Dic29—41no—
70C2×Dic29—41no—
71C2×Dic29—41no—
72C2×Dic29C2311yescharacteristic
73C2×Dic29C2311yescharacteristic
74C2×Dic29C2311yescharacteristic
75C2×Dic29C2311yescharacteristic
76C2×Dic29C2311yescharacteristic
77C2×Dic29C2311yescharacteristic
78C2×Dic29C2311yescharacteristic
79C4×D29—41no—
80Dic58—41no—
81C22×C29—21no—
82C22×C29—21no—
83C22×C29—21no—
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—44no—
93C22×C29#4112yes—
94C22×C29C2411yescharacteristic
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—21no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101Dic29—21no—
102Dic29—21no—
103Dic29—21no—
104Dic29—21no—
105Dic29—21no—
106Dic29—21no—
107Dic29—21no—
108#538—291nomaximal, Sylow
109C2×C29—22no—
110C2×C29—41no—
111C2×C29—41no—
112C2×C29—41no—
113C2×C29C2×#4111yescharacteristic
114C2×C29H(5,𝔽2)11yescharacteristic
115C2×C29H(5,𝔽2)11yescharacteristic
116D29—41no—
117#126—291no—
118#126—291no—
119#124—291no—
120#124—291no—
121#123—291no—
122#123—291no—
123C22⋊Q8—291no—
124#121—291no—
125#121—291no—
126#121—291no—
127#120—291no—
128#120D2911yescharacteristic, complemented
129C4×D4—291no—
130C4×D4—291no—
131C2×C22⋊C4—291no—
132C29#53811yescharacteristic, complemented, Sylow
133C24C2×D2911yescharacteristic
134C2×Q8—291no—
135C2×D4—291no—
136C2×D4—291no—
137C2×D4—291no—
138C2×D4—291no—
139C2×D4C2×D2911yescharacteristic
140C2×D4C2×D2911yescharacteristic
141C2×D4C2×D2911yescharacteristic
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—291no—
146C4⋊C4—291no—
147C4⋊C4—291no—
148C4⋊C4—291no—
149C4⋊C4—291no—
150C4⋊C4—291no—
151C4⋊C4—291no—
152C22⋊C4—291no—
153C22⋊C4—291no—
154C22⋊C4—291no—
155C22⋊C4—291no—
156C22⋊C4—291no—
157C22⋊C4—291no—
158C22⋊C4—291no—
159C22⋊C4—291no—
160C22⋊C4—291no—
161C22⋊C4—291no—
162C22⋊C4—291no—
163C22⋊C4C2×D2911yescharacteristic
164C22⋊C4C2×D2911yescharacteristic
165C22⋊C4C2×D2911yescharacteristic
166C42—291no—
167C42—291no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—291no—
172C23C22×D2911yescharacteristic
173C23C22×D2911yescharacteristic
174C23C22×D2911yescharacteristic
175C23C22×D2911yescharacteristic
176Q8—1161no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—582no—
181D4—1161no—
182D4—1161no—
183D4—1161no—
184C2×C4—291no—
185C2×C4—291no—
186C2×C4—291no—
187C2×C4—291no—
188C2×C4—291no—
189C2×C4—291no—
190C2×C4—291no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4C22×D2911yescharacteristic
196C2×C4C22×D2911yescharacteristic
197C2×C4C22×D2911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—581no—
211C22—581no—
212C22—581no—
213C22#9080712yes—
214C22C23×D2911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—581no—
219C4—581no—
220C4—581no—
221C4—581no—
222C4—581no—
223C4—581no—
224C4—581no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—1161no—
230C2C2×#9080711yescharacteristic
231C2#1174535911yescharacteristic
232C2#1174535911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#120C2
hypercenter#120D29
hypocenterC29#538
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C29×#120C2semidirect
2. #11745315C2semidirect
3. C2×C22⋊Dic29C2semidirect
4. #11745301C2semidirect
5. #11745301C2semidirect
6. #11745300C2semidirect
7. #11745298C2semidirect
8. #11745297C2semidirect
9. D4×Dic29C2semidirect
10. #11745247C2semidirect
11. #11745245C2semidirect
12. #11745243C2semidirect
13. #11745241C2semidirect
14. #11745241C2semidirect
15. #11745240C2semidirect
23. C2×C22⋊D29C22semidirect
26. C22×Dic29C22semidirect
27. C2×C4×D29C22semidirect
28. C2×Dic58C22semidirect
39. C22⋊Dic29C22semidirect
40. C22⋊Dic29C22semidirect
41. #90781C22semidirect
42. #90781C22semidirect
43. C4⋊Dic29C22semidirect
44. C4⋊Dic29C22semidirect
45. #90779C22semidirect
46. #90779C22semidirect
47. #90779C22semidirect
48. #90779C22semidirect
49. C4×Dic29C22semidirect
50. C4×Dic29C22semidirect
128. #120D29semidirect
132. C29#538semidirect

Maximal subgroups

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

subgroupindex
C29×#1202
#117453152
C2×C22⋊Dic292
#117453012
#117453002
#117452982
#117452972
D4×Dic292
#117452472
#117452452
#117452432
#117452412
#117452402
#53829