Finite Group Databasebeta

← #14271840

Subgroups — #14271840

Order 1856.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×C22⋊Q8C211yesmaximal, characteristic, complemented
2#11745309C211yesmaximal, characteristic, complemented
3#11745308C211yesmaximal, characteristic, complemented
4C4×C22⋊D29C211yesmaximal, characteristic, complemented
5C2×#90781C211yesmaximal, characteristic, complemented
6#11745260C211yesmaximal, characteristic, complemented
7#11745260C211yesmaximal, characteristic, complemented
8#11745256C211yesmaximal, characteristic, complemented
9#11745256C211yesmaximal, characteristic, complemented
10#11745255C211yesmaximal, characteristic, complemented
11#11745254C211yesmaximal, characteristic, complemented
12#11745248C211yesmaximal, characteristic, complemented
13#11745244C211yesmaximal, characteristic
14C22⋊C4×D29C211yesmaximal, characteristic, complemented
15#11745239C211yesmaximal, characteristic, complemented
16C23×D29C2211yescharacteristic
17C2×Q8×C29C2211yescharacteristic, complemented
18C22×C4×C29C2211yescharacteristic
19C2×C22⋊D29C2211yescharacteristic
20C22×Dic29C2211yescharacteristic
21C2×D116C2211yescharacteristic
22C2×D116C2211yescharacteristic
23C2×C4×D29C2211yescharacteristic
24C2×C4×D29C2211yescharacteristic
25C2×C4×D29C2211yescharacteristic, complemented
26C4⋊C4×C29C2211yescharacteristic, complemented
27C4⋊C4×C29C2211yescharacteristic, complemented
28C4⋊C4×C29C2211yescharacteristic, complemented
29C22⋊C4×C29C2211yescharacteristic
30C22⋊C4×C29C2211yescharacteristic
31C22⋊Dic29C2211yescharacteristic
32#90781C2211yescharacteristic
33#90781C2211yescharacteristic
34#90781C2211yescharacteristic
35#90781C2211yescharacteristic
36#90781C2211yescharacteristic
37#90781C2211yescharacteristic
38#90781C2211yescharacteristic
39#90781C2211yescharacteristic
40#90781C2211yescharacteristic, complemented
41#90781C2211yescharacteristic, complemented
42#90781C2211yescharacteristic, complemented
43C4⋊Dic29C2211yescharacteristic, complemented
44C4⋊Dic29C2211yescharacteristic, complemented
45#90779C2211yescharacteristic, complemented
46#90779C2211yescharacteristic, complemented
47#90779C2211yescharacteristic, complemented
48C4×Dic29C2211yescharacteristic, complemented
49C4×Dic29C2211yescharacteristic, complemented
50C4×Dic29C2211yescharacteristic, complemented
51C23×C29C2311yescharacteristic
52C22×D29—22no—
53C22×D29—22no—
54C22×D29—41no—
55C22×D29C2311yescharacteristic
56C22×D29C2311yescharacteristic
57C22×D29C2311yescharacteristic
58Q8×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C2311yescharacteristic
61C2×C4×C29C2311yescharacteristic
62C2×C4×C29C2311yescharacteristic
63C2×C4×C29C2311yescharacteristic
64C2×C4×C29C2311yescharacteristic
65C2×C4×C29C2311yescharacteristic
66C22⋊D29—22no—
67C2×Dic29—22no—
68C2×Dic29C2311yescharacteristic
69C2×Dic29C2311yescharacteristic
70C2×Dic29C2311yescharacteristic
71C2×Dic29C2311yescharacteristic
72C2×Dic29C2311yescharacteristic
73D116—22no—
74D116—41no—
75C4×D29—22no—
76C4×D29—41no—
77C4×D29—41no—
78C22×C29—21no—
79C22×C29—21no—
80C22×C29#4112yes—
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—21no—
90C2×D29—44no—
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—22no—
105C2×C29C2×#4111yescharacteristic
106C2×C29C2×#4111yescharacteristic
107C2×C29H(5,𝔽2)11yescharacteristic
108D29—22no—
109D29—41no—
110D29—41no—
111#126—291no—
112#126—291no—
113#124—291no—
114#123—291no—
115#123—291no—
116#123—291no—
117C22⋊Q8—291no—
118C22⋊Q8D2911yescharacteristic, complemented
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×Q8C2×D2911yescharacteristic, complemented
129C2×D4—291no—
130C2×D4—291no—
131C2×D4—291no—
132C22×C4—291no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4C2×D2911yescharacteristic
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⋊C4—291no—
157C22⋊C4C2×D2911yescharacteristic
158C22⋊C4C2×D2911yescharacteristic
159C42—291no—
160C42—291no—
161C42—291no—
162C23—291no—
163C23—291no—
164C23—291no—
165C23—582no—
166C23—582no—
167C23—1161no—
168C23C22×D2911yescharacteristic
169Q8—41no—
170D4—582no—
171D4—582no—
172D4—1161no—
173C2×C4—41no—
174C2×C4—291no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—582no—
180C2×C4—582no—
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—292no—
192C22—581no—
193C22—581no—
194C22—581no—
195C22—581no—
196C22—581no—
197C22—581no—
198C22—581no—
199C22—581no—
200C22—1164no—
201C22#9080912yes—
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—22no—
215C2—582no—
216C2—1161no—
217C2—1161no—
218C2#1174535911yescharacteristic
219C2C2×#9080911yescharacteristic
220C2#41×D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×C22⋊Q8C2
prime radical#11745244C2
hypercenterC22⋊Q8D29
hypocenterC29#551
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C29×C22⋊Q8C2semidirect
2. #11745309C2semidirect
3. #11745308C2semidirect
4. C4×C22⋊D29C2semidirect
5. C2×#90781C2semidirect
6. #11745260C2semidirect
7. #11745260C2semidirect
8. #11745256C2semidirect
9. #11745256C2semidirect
10. #11745255C2semidirect
11. #11745254C2semidirect
12. #11745248C2semidirect
14. C22⋊C4×D29C2semidirect
15. #11745239C2semidirect
17. C2×Q8×C29C22semidirect
25. C2×C4×D29C22semidirect
26. C4⋊C4×C29C22semidirect
27. C4⋊C4×C29C22semidirect
28. C4⋊C4×C29C22semidirect
40. #90781C22semidirect
41. #90781C22semidirect
42. #90781C22semidirect
43. C4⋊Dic29C22semidirect
44. C4⋊Dic29C22semidirect
45. #90779C22semidirect
46. #90779C22semidirect
47. #90779C22semidirect
48. C4×Dic29C22semidirect
49. C4×Dic29C22semidirect
50. C4×Dic29C22semidirect
118. C22⋊Q8D29semidirect
126. C29#551semidirect
128. C2×Q8C2×D29semidirect
142. C4⋊C4C2×D29semidirect
143. C4⋊C4C2×D29semidirect
144. C4⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
C29×C22⋊Q82
#117453092
#117453082
C4×C22⋊D292
C2×#907812
#117452602
#117452562
#117452552
#117452542
#117452482
#117452442
C22⋊C4×D292
#117452392
#55129