Finite Group Databasebeta

← #14271747

Subgroups — #14271747

Order 1856.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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×#124C211yesmaximal, characteristic, complemented
2#11745309C211yesmaximal, characteristic, complemented
3#11745308C211yesmaximal, characteristic, complemented
4#11745301C211yesmaximal, characteristic, complemented
5#11745299C211yesmaximal, characteristic, complemented
6#11745248C211yesmaximal, characteristic, complemented
7#11745246C211yesmaximal, characteristic, complemented
8#11745246C211yesmaximal, characteristic, complemented
9#11745245C211yesmaximal, characteristic, complemented
10#11745244C211yesmaximal, characteristic, complemented
11#11745243C211yesmaximal, characteristic, complemented
12C22⋊C4×D29C211yesmaximal, characteristic, complemented
13#11745241C211yesmaximal, characteristic, complemented
14#11745238C211yesmaximal, characteristic, complemented
15C4×D116C211yesmaximal, characteristic, complemented
16C23×D29C2211yescharacteristic
17C2×Q8×C29C2211yescharacteristic, complemented
18C2×D4×C29C2211yescharacteristic
19C2×C22⋊D29C2211yescharacteristic
20C2×C22⋊D29C2211yescharacteristic
21C2×C22⋊D29C2211yescharacteristic
22C2×C22⋊D29C2211yescharacteristic, complemented
23C22×Dic29C2211yescharacteristic, complemented
24C2×D116C2211yescharacteristic
25C2×D116C2211yescharacteristic
26C2×C4×D29C2211yescharacteristic
27C2×C4×D29C2211yescharacteristic
28C2×C4×D29C2211yescharacteristic, complemented
29C22⋊C4×C29C2211yescharacteristic
30C22⋊C4×C29C2211yescharacteristic
31C22⋊C4×C29C2211yescharacteristic, complemented
32C22⋊C4×C29C2211yescharacteristic, complemented
33C42×C29C2211yescharacteristic, complemented
34C22⋊Dic29C2211yescharacteristic
35C22⋊Dic29C2211yescharacteristic
36#90781C2211yescharacteristic
37#90781C2211yescharacteristic
38#90781C2211yescharacteristic
39#90781C2211yescharacteristic
40#90781C2211yescharacteristic
41#90781C2211yescharacteristic
42#90781C2211yescharacteristic, complemented
43#90781C2211yescharacteristic, complemented
44C4⋊Dic29C2211yescharacteristic, complemented
45C4⋊Dic29C2211yescharacteristic, complemented
46#90779C2211yescharacteristic, complemented
47#90779C2211yescharacteristic, complemented
48#90779C2211yescharacteristic, complemented
49#90779C2211yescharacteristic, complemented
50C4×Dic29C2211yescharacteristic, complemented
51C23×C29C2311yescharacteristic
52C23×C29C2311yescharacteristic
53C22×D29—22no—
54C22×D29—41no—
55C22×D29—41no—
56C22×D29C2311yescharacteristic
57C22×D29C2311yescharacteristic
58C22×D29C2311yescharacteristic
59Q8×C29—41no—
60D4×C29—41no—
61C2×C4×C29C2311yescharacteristic
62C2×C4×C29C2311yescharacteristic
63C2×C4×C29C2311yescharacteristic
64C2×C4×C29C2311yescharacteristic
65C2×C4×C29C2311yescharacteristic
66C22⋊D29—22no—
67C22⋊D29—41no—
68C22⋊D29—41no—
69C22⋊D29—41no—
70C2×Dic29—41no—
71C2×Dic29C2311yescharacteristic
72C2×Dic29C2311yescharacteristic
73C2×Dic29C2311yescharacteristic
74C2×Dic29C2311yescharacteristic
75C2×Dic29C2311yescharacteristic
76D116—22no—
77D116—41no—
78C4×D29—41no—
79C4×D29—41no—
80C4×D29—41no—
81C22×C29—21no—
82C22×C29—21no—
83C22×C29—21no—
84C22×C29—21no—
85C22×C29—21no—
86C22×C29—21no—
87C22×C29C2411yescharacteristic
88C2×D29—21no—
89C2×D29—21no—
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—21no—
94C2×D29—21no—
95C2×D29—21no—
96C2×D29—44no—
97C2×D29#4112yes—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—21no—
102C4×C29—21no—
103Dic29—21no—
104Dic29—21no—
105Dic29—21no—
106Dic29—21no—
107Dic29—21no—
108#538—291nomaximal, Sylow
109C2×C29—41no—
110C2×C29—41no—
111C2×C29C2×#4111yescharacteristic
112C2×C29H(5,𝔽2)11yescharacteristic
113C2×C29H(5,𝔽2)11yescharacteristic
114D29—22no—
115D29—41no—
116D29—41no—
117#126—291no—
118#126—291no—
119#124—291no—
120#124D2911yescharacteristic, complemented
121#123—291no—
122#123—291no—
123C22⋊Q8—291no—
124#121—291no—
125#121—291no—
126#121—291no—
127#120—291no—
128#120—291no—
129C4×D4—291no—
130C4×D4—291no—
131C2×C22⋊C4—291no—
132C29#53811yescharacteristic, complemented, Sylow
133C24—291no—
134C2×Q8C2×D2911yescharacteristic, complemented
135C2×D4—291no—
136C2×D4—291no—
137C2×D4—291no—
138C2×D4—291no—
139C2×D4—291no—
140C2×D4—291no—
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⋊C4C2×D2911yescharacteristic
163C22⋊C4C2×D2911yescharacteristic
164C22⋊C4C2×D2911yescharacteristic, complemented
165C22⋊C4C2×D2911yescharacteristic, complemented
166C42—291no—
167C42C2×D2911yescharacteristic, complemented
168C23—291no—
169C23—291no—
170C23—291no—
171C23—582no—
172C23—1161no—
173C23—1161no—
174C23C22×D2911yescharacteristic
175C23C22×D2911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—582no—
179D4—582no—
180D4—1161no—
181D4—1161no—
182D4—1161no—
183D4—1161no—
184C2×C4—291no—
185C2×C4—291no—
186C2×C4—291no—
187C2×C4—291no—
188C2×C4—291no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4C22×D2911yescharacteristic
194C2×C4C22×D2911yescharacteristic
195C2×C4C22×D2911yescharacteristic
196C2×C4C22×D2911yescharacteristic
197C2×C4C22×D2911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—292no—
205C22—581no—
206C22—581no—
207C22—581no—
208C22—581no—
209C22—581no—
210C22—581no—
211C22—581no—
212C22—581no—
213C22—1164no—
214C22C23×D2911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—581no—
221C4—581no—
222C4—581no—
223C4—581no—
224C4—581no—
225C2—41no—
226C2—41no—
227C2—582no—
228C2—1161no—
229C2—1161no—
230C2#1174535911yescharacteristic
231C2#41×D2911yescharacteristic
232C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#124C2
hypercenter#124D29
hypocenterC29#538
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C29×#124C2semidirect
2. #11745309C2semidirect
3. #11745308C2semidirect
4. #11745301C2semidirect
5. #11745299C2semidirect
6. #11745248C2semidirect
7. #11745246C2semidirect
8. #11745246C2semidirect
9. #11745245C2semidirect
10. #11745244C2semidirect
11. #11745243C2semidirect
12. C22⋊C4×D29C2semidirect
13. #11745241C2semidirect
14. #11745238C2semidirect
15. C4×D116C2semidirect
17. C2×Q8×C29C22semidirect
22. C2×C22⋊D29C22semidirect
23. C22×Dic29C22semidirect
28. C2×C4×D29C22semidirect
31. C22⋊C4×C29C22semidirect
32. C22⋊C4×C29C22semidirect
33. C42×C29C22semidirect
42. #90781C22semidirect
43. #90781C22semidirect
44. C4⋊Dic29C22semidirect
45. C4⋊Dic29C22semidirect
46. #90779C22semidirect
47. #90779C22semidirect
48. #90779C22semidirect
49. #90779C22semidirect
50. C4×Dic29C22semidirect
120. #124D29semidirect
132. C29#538semidirect
134. C2×Q8C2×D29semidirect
164. C22⋊C4C2×D29semidirect
165. C22⋊C4C2×D29semidirect
167. C42C2×D29semidirect

Maximal subgroups

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

subgroupindex
C29×#1242
#117453092
#117453082
#117453012
#117452992
#117452482
#117452462
#117452452
#117452442
#117452432
C22⋊C4×D292
#117452412
#117452382
C4×D1162
#53829