Finite Group Databasebeta

← #14271838

Subgroups — #14271838

Order 1856.

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

normal subgroups only

This group has 248 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×#126C211yesmaximal, characteristic, complemented
2#11745259C211yesmaximal, characteristic, complemented
3#11745258C211yesmaximal, characteristic, complemented
4#11745256C211yesmaximal, characteristic, complemented
5#11745256C211yesmaximal, characteristic, complemented
6#11745255C211yesmaximal, characteristic, complemented
7#11745254C211yesmaximal, characteristic, complemented
8#11745247C211yesmaximal, characteristic, complemented
9#11745245C211yesmaximal, characteristic, complemented
10#11745244C211yesmaximal, characteristic
11C22⋊C4×D29C211yesmaximal, characteristic, complemented
12C22⋊C4×D29C211yesmaximal, characteristic, complemented
13#11745241C211yesmaximal, characteristic, complemented
14C4×D116C211yesmaximal, characteristic, complemented
15#11745234C211yesmaximal, characteristic, complemented
16C23×D29C2211yescharacteristic
17C2×C22⋊D29C2211yescharacteristic
18C2×D116C2211yescharacteristic
19C2×D116C2211yescharacteristic
20C2×C4×D29C2211yescharacteristic
21C2×C4×D29C2211yescharacteristic
22C2×C4×D29C2211yescharacteristic
23C2×C4×D29C2211yescharacteristic
24C2×C4×D29C2211yescharacteristic, complemented
25C2×Dic58C2211yescharacteristic, complemented
26C4⋊C4×C29C2211yescharacteristic, complemented
27C4⋊C4×C29C2211yescharacteristic, complemented
28C4⋊C4×C29C2211yescharacteristic, complemented
29C22⋊C4×C29C2211yescharacteristic
30C22⋊C4×C29C2211yescharacteristic
31C22⋊C4×C29C2211yescharacteristic
32C42×C29C2211yescharacteristic, complemented
33C22⋊Dic29C2211yescharacteristic
34C22⋊Dic29C2211yescharacteristic
35#90781C2211yescharacteristic
36#90781C2211yescharacteristic
37#90781C2211yescharacteristic
38#90781C2211yescharacteristic
39#90781C2211yescharacteristic
40#90781C2211yescharacteristic
41#90781C2211yescharacteristic, complemented
42#90781C2211yescharacteristic, complemented
43#90781C2211yescharacteristic, complemented
44C4⋊Dic29C2211yescharacteristic, complemented
45C4⋊Dic29C2211yescharacteristic, complemented
46#90779C2211yescharacteristic, complemented
47#90779C2211yescharacteristic, complemented
48#90779C2211yescharacteristic, complemented
49C4×Dic29C2211yescharacteristic, complemented
50C4×Dic29C2211yescharacteristic, complemented
51C23×C29C2311yescharacteristic
52C22×D29—22no—
53C22×D29—22no—
54C22×D29—41no—
55C22×D29C2311yescharacteristic
56C22×D29C2311yescharacteristic
57C22×D29C2311yescharacteristic
58C2×C4×C29C2311yescharacteristic
59C2×C4×C29C2311yescharacteristic
60C2×C4×C29C2311yescharacteristic
61C2×C4×C29C2311yescharacteristic
62C2×C4×C29C2311yescharacteristic
63C2×C4×C29C2311yescharacteristic
64C22⋊D29—41no—
65C2×Dic29C2311yescharacteristic
66C2×Dic29C2311yescharacteristic
67C2×Dic29C2311yescharacteristic
68C2×Dic29C2311yescharacteristic
69C2×Dic29C2311yescharacteristic
70D116—22no—
71D116—22no—
72C4×D29—22no—
73C4×D29—22no—
74C4×D29—41no—
75C4×D29—41no—
76C4×D29—41no—
77Dic58—41no—
78C22×C29—21no—
79C22×C29—21no—
80C22×C29—21no—
81C22×C29C2411yescharacteristic
82C2×D29—21no—
83C2×D29—21no—
84C2×D29—21no—
85C2×D29—21no—
86C2×D29—21no—
87C2×D29—21no—
88C2×D29—21no—
89C2×D29—44no—
90C2×D29#4112yes—
91C2×D29#4112yes—
92C4×C29—21no—
93C4×C29—21no—
94C4×C29—21no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—21no—
98Dic29—21no—
99Dic29—21no—
100Dic29—21no—
101Dic29—21no—
102Dic29—21no—
103#551—291nomaximal, Sylow
104C2×C29—41no—
105C2×C29C2×#4111yescharacteristic
106C2×C29C2×#4111yescharacteristic
107C2×C29H(5,𝔽2)11yescharacteristic
108D29—22no—
109D29—22no—
110D29—41no—
111#126—291no—
112#126D2911yescharacteristic, complemented
113#124—291no—
114#123—291no—
115#123—291no—
116#123—291no—
117C22⋊Q8—291no—
118C22⋊Q8—291no—
119#120—291no—
120C4×D4—291no—
121C4×D4—291no—
122#117—291no—
123#117—291no—
124C2×C22⋊C4—291no—
125C2×C22⋊C4—291no—
126C29#55111yescharacteristic, complemented, Sylow
127C24—291no—
128C2×Q8—291no—
129C2×D4—291no—
130C2×D4—291no—
131C2×D4—291no—
132C22×C4—291no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—291no—
137C4⋊C4—291no—
138C4⋊C4—291no—
139C4⋊C4—291no—
140C4⋊C4—291no—
141C4⋊C4—291no—
142C4⋊C4C2×D2911yescharacteristic, complemented
143C4⋊C4C2×D2911yescharacteristic, complemented
144C4⋊C4C2×D2911yescharacteristic, complemented
145C22⋊C4—291no—
146C22⋊C4—291no—
147C22⋊C4—291no—
148C22⋊C4—291no—
149C22⋊C4—291no—
150C22⋊C4—291no—
151C22⋊C4—291no—
152C22⋊C4—291no—
153C22⋊C4—291no—
154C22⋊C4—291no—
155C22⋊C4—291no—
156C22⋊C4C2×D2911yescharacteristic
157C22⋊C4C2×D2911yescharacteristic
158C22⋊C4C2×D2911yescharacteristic
159C42—291no—
160C42—291no—
161C42C2×D2911yescharacteristic, complemented
162C23—291no—
163C23—291no—
164C23—291no—
165C23—582no—
166C23—582no—
167C23—1161no—
168C23C22×D2911yescharacteristic
169Q8—1161no—
170D4—582no—
171D4—582no—
172D4—1161no—
173C2×C4—291no—
174C2×C4—291no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—582no—
179C2×C4—582no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4—1161no—
183C2×C4C22×D2911yescharacteristic
184C2×C4C22×D2911yescharacteristic
185C2×C4C22×D2911yescharacteristic
186C2×C4C22×D2911yescharacteristic
187C2×C4C22×D2911yescharacteristic
188C2×C4C22×D2911yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—292no—
193C22—292no—
194C22—581no—
195C22—581no—
196C22—581no—
197C22—581no—
198C22—581no—
199C22—581no—
200C22—581no—
201C22—1164no—
202C22C23×D2911yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—581no—
210C4—581no—
211C4—581no—
212C4—581no—
213C4—581no—
214C2—41no—
215C2—582no—
216C2—582no—
217C2—1161no—
218C2#41×D2911yescharacteristic
219C2#41×D2911yescharacteristic
220C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#126C2
prime radical#11745244C2
hypercenter#126D29
hypocenterC29#551
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. C29×#126C2semidirect
2. #11745259C2semidirect
3. #11745258C2semidirect
4. #11745256C2semidirect
5. #11745256C2semidirect
6. #11745255C2semidirect
7. #11745254C2semidirect
8. #11745247C2semidirect
9. #11745245C2semidirect
11. C22⋊C4×D29C2semidirect
12. C22⋊C4×D29C2semidirect
13. #11745241C2semidirect
14. C4×D116C2semidirect
15. #11745234C2semidirect
24. C2×C4×D29C22semidirect
25. C2×Dic58C22semidirect
26. C4⋊C4×C29C22semidirect
27. C4⋊C4×C29C22semidirect
28. C4⋊C4×C29C22semidirect
32. C42×C29C22semidirect
41. #90781C22semidirect
42. #90781C22semidirect
43. #90781C22semidirect
44. C4⋊Dic29C22semidirect
45. C4⋊Dic29C22semidirect
46. #90779C22semidirect
47. #90779C22semidirect
48. #90779C22semidirect
49. C4×Dic29C22semidirect
50. C4×Dic29C22semidirect
112. #126D29semidirect
126. C29#551semidirect
142. C4⋊C4C2×D29semidirect
143. C4⋊C4C2×D29semidirect
144. C4⋊C4C2×D29semidirect
161. C42C2×D29semidirect

Maximal subgroups

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

subgroupindex
C29×#1262
#117452592
#117452582
#117452562
#117452552
#117452542
#117452472
#117452452
#117452442
C22⋊C4×D292
#117452412
C4×D1162
#117452342
#55129