Finite Group Databasebeta

← #28409615

Subgroups — #28409615

Order 14528.

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
1#20300283C211yesmaximal, characteristic, complemented
2#20300282C211yesmaximal, characteristic, complemented
3#20300276C211yesmaximal, characteristic, complemented
4#20300274C211yesmaximal, characteristic, complemented
5#20300273C211yesmaximal, characteristic, complemented
6#20300271C211yesmaximal, characteristic, complemented
7#20300265C211yesmaximal, characteristic, complemented
8#20300262C211yesmaximal, characteristic, complemented
9#20300261C211yesmaximal, characteristic, complemented
10#20300260C211yesmaximal, characteristic, complemented
11#20300258C211yesmaximal, characteristic, complemented
12#20300256C211yesmaximal, characteristic, complemented
13C4×C22⋊D227C211yesmaximal, characteristic, complemented
14C2×(C2×D227)⋊C4C211yesmaximal, characteristic, complemented
15C4×D4×C227C211yesmaximal, characteristic, complemented
16C23×D227C2211yescharacteristic
17C2×Dic454C2211yescharacteristic, complemented
18C2×D908C2211yescharacteristic
19C2×D908C2211yescharacteristic
20C2×C22⋊D227C2211yescharacteristic
21C2×C22⋊D227C2211yescharacteristic
22C2×C22⋊D227C2211yescharacteristic
23C2×C22⋊D227C2211yescharacteristic, complemented
24C22×Dic227C2211yescharacteristic
25C2×C4×D227C2211yescharacteristic, complemented
26C4⋊Dic227C2211yescharacteristic, complemented
27Dic227⋊C4C2211yescharacteristic, complemented
28Dic227⋊C4C2211yescharacteristic, complemented
29Dic227⋊C4C2211yescharacteristic, complemented
30Dic227⋊C4C2211yescharacteristic, complemented
31C22⋊Dic227C2211yescharacteristic
32C22⋊Dic227C2211yescharacteristic, complemented
33(C2×D227)⋊C4C2211yescharacteristic
34(C2×D227)⋊C4C2211yescharacteristic
35(C2×D227)⋊C4C2211yescharacteristic
36(C2×D227)⋊C4C2211yescharacteristic
37(C2×D227)⋊C4C2211yescharacteristic
38(C2×D227)⋊C4C2211yescharacteristic
39(C2×D227)⋊C4C2211yescharacteristic
40(C2×D227)⋊C4C2211yescharacteristic
41(C2×D227)⋊C4C2211yescharacteristic, complemented
42(C2×D227)⋊C4C2211yescharacteristic, complemented
43C4×Dic227C2211yescharacteristic, complemented
44C2×D4×C227C2211yescharacteristic
45C22×C4×C227C2211yescharacteristic
46C22×C4×C227C2211yescharacteristic, complemented
47C4⋊C4×C227C2211yescharacteristic, complemented
48C22⋊C4×C227C2211yescharacteristic
49C22⋊C4×C227C2211yescharacteristic, complemented
50C42×C227C2211yescharacteristic, complemented
51C22×D227—22no—
52C22×D227—41no—
53C22×D227—41no—
54C22×D227C2311yescharacteristic
55C22×D227C2311yescharacteristic
56C22×D227C2311yescharacteristic
57Dic454—41no—
58D908—41no—
59D908—41no—
60C22⋊D227—22no—
61C22⋊D227—41no—
62C22⋊D227—41no—
63C22⋊D227—41no—
64C2×Dic227—41no—
65C2×Dic227C2311yescharacteristic
66C2×Dic227C2311yescharacteristic
67C2×Dic227C2311yescharacteristic
68C2×Dic227C2311yescharacteristic
69C2×Dic227C2311yescharacteristic
70C4×D227—41no—
71C23×C227C2311yescharacteristic
72C23×C227C2311yescharacteristic
73D4×C227—22no—
74C2×C4×C227—41no—
75C2×C4×C227—41no—
76C2×C4×C227C2311yescharacteristic
77C2×C4×C227C2311yescharacteristic
78C2×C4×C227C2311yescharacteristic
79C2×C4×C227C2311yescharacteristic
80C2×C4×C227C2311yescharacteristic
81C22×C227—21no—
82C22×C227—21no—
83C22×C227—21no—
84C22×C227—21no—
85C22×C227—21no—
86C22×C227#4112yes—
87C22×C227C2411yescharacteristic
88C2×D227—21no—
89C2×D227—21no—
90C2×D227—21no—
91C2×D227—21no—
92C2×D227—21no—
93C2×D227—21no—
94C2×D227—21no—
95C2×D227—21no—
96C2×D227—21no—
97C2×D227—44no—
98C4×C227—21no—
99C4×C227—21no—
100C4×C227—21no—
101C4×C227—21no—
102C4×C227—21no—
103Dic227—21no—
104Dic227—21no—
105Dic227—21no—
106Dic227—21no—
107Dic227—21no—
108C2×C227—22no—
109C2×C227—41no—
110C2×C227C2×#4111yescharacteristic
111C2×C227H(5,𝔽2)11yescharacteristic
112C2×C227H(5,𝔽2)11yescharacteristic
113D227—41no—
114D227—41no—
115D227—41no—
116C227#53811yescharacteristic, complemented, Sylow
117#538—2271nomaximal, Sylow
118#126—2271no—
119#126—2271no—
120#124—2271no—
121#124—2271no—
122#123—2271no—
123#123—2271no—
124C22⋊Q8—2271no—
125#121—2271no—
126#121—2271no—
127#121—2271no—
128#120—2271no—
129#120—2271no—
130C4×D4—2271no—
131C4×D4D22711yescharacteristic, complemented
132C2×C22⋊C4—2271no—
133C24—2271no—
134C2×Q8—2271no—
135C2×D4—2271no—
136C2×D4—2271no—
137C2×D4—2271no—
138C2×D4—2271no—
139C2×D4—2271no—
140C2×D4—2271no—
141C2×D4C2×D22711yescharacteristic
142C22×C4—2271no—
143C22×C4—2271no—
144C22×C4C2×D22711yescharacteristic
145C22×C4C2×D22711yescharacteristic, complemented
146C4⋊C4—2271no—
147C4⋊C4—2271no—
148C4⋊C4—2271no—
149C4⋊C4—2271no—
150C4⋊C4—2271no—
151C4⋊C4C2×D22711yescharacteristic, complemented
152C22⋊C4—2271no—
153C22⋊C4—2271no—
154C22⋊C4—2271no—
155C22⋊C4—2271no—
156C22⋊C4—2271no—
157C22⋊C4—2271no—
158C22⋊C4—2271no—
159C22⋊C4—2271no—
160C22⋊C4—2271no—
161C22⋊C4—2271no—
162C22⋊C4—2271no—
163C22⋊C4—2271no—
164C22⋊C4C2×D22711yescharacteristic
165C22⋊C4C2×D22711yescharacteristic, complemented
166C42—2271no—
167C42C2×D22711yescharacteristic, complemented
168C23—9081no—
169C23—9081no—
170C23—4542no—
171C23—2271no—
172C23—2271no—
173C23—2271no—
174C23C22×D22711yescharacteristic
175C23C22×D22711yescharacteristic
176Q8—9081no—
177D4—22no—
178D4—9081no—
179D4—9081no—
180D4—9081no—
181D4—9081no—
182D4—9081no—
183D4—4542no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—9081no—
187C2×C4—9081no—
188C2×C4—2271no—
189C2×C4—2271no—
190C2×C4—2271no—
191C2×C4—2271no—
192C2×C4—2271no—
193C2×C4C22×D22711yescharacteristic
194C2×C4C22×D22711yescharacteristic
195C2×C4C22×D22711yescharacteristic
196C2×C4C22×D22711yescharacteristic
197C2×C4C22×D22711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—9084no—
204C22—4541no—
205C22—4541no—
206C22—4541no—
207C22—4541no—
208C22—4541no—
209C22—4541no—
210C22—4541no—
211C22—4541no—
212C22—4541no—
213C22#1681388412yes—
214C22C23×D22711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—4541no—
221C4—4541no—
222C4—4541no—
223C4—4541no—
224C4—4541no—
225C2—22no—
226C2—41no—
227C2—9081no—
228C2—9081no—
229C2—9081no—
230C2C2×#1681388411yescharacteristic
231C2#2030033311yescharacteristic
232C2#2030033411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D227
commutator, socle, cosocleC22×C227C24
FittingC4×D4×C227C2
hypercenterC4×D4D227
hypocenterC227#538
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20300283C2semidirect
2. #20300282C2semidirect
3. #20300276C2semidirect
4. #20300274C2semidirect
5. #20300273C2semidirect
6. #20300271C2semidirect
7. #20300265C2semidirect
8. #20300262C2semidirect
9. #20300261C2semidirect
10. #20300260C2semidirect
11. #20300258C2semidirect
12. #20300256C2semidirect
13. C4×C22⋊D227C2semidirect
14. C2×(C2×D227)⋊C4C2semidirect
15. C4×D4×C227C2semidirect
17. C2×Dic454C22semidirect
23. C2×C22⋊D227C22semidirect
25. C2×C4×D227C22semidirect
26. C4⋊Dic227C22semidirect
27. Dic227⋊C4C22semidirect
28. Dic227⋊C4C22semidirect
29. Dic227⋊C4C22semidirect
30. Dic227⋊C4C22semidirect
32. C22⋊Dic227C22semidirect
41. (C2×D227)⋊C4C22semidirect
42. (C2×D227)⋊C4C22semidirect
43. C4×Dic227C22semidirect
46. C22×C4×C227C22semidirect
47. C4⋊C4×C227C22semidirect
49. C22⋊C4×C227C22semidirect
50. C42×C227C22semidirect
116. C227#538semidirect
131. C4×D4D227semidirect
145. C22×C4C2×D227semidirect
151. C4⋊C4C2×D227semidirect
165. C22⋊C4C2×D227semidirect
167. C42C2×D227semidirect

Maximal subgroups

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

subgroupindex
#203002832
#203002822
#203002762
#203002742
#203002732
#203002712
#203002652
#203002622
#203002612
#203002602
#203002582
#203002562
C4×C22⋊D2272
C2×(C2×D227)⋊C42
C4×D4×C2272
#538227