Finite Group Databasebeta

← #31824047

Subgroups — #31824047

Order 17984.

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
1#22582873C211yesmaximal, characteristic, complemented
2#22582872C211yesmaximal, characteristic, complemented
3#22582868C211yesmaximal, characteristic, complemented
4#22582863C211yesmaximal, characteristic, complemented
5#22582861C211yesmaximal, characteristic, complemented
6#22582855C211yesmaximal, characteristic, complemented
7#22582852C211yesmaximal, characteristic, complemented
8#22582852C211yesmaximal, characteristic, complemented
9#22582851C211yesmaximal, characteristic, complemented
10#22582849C211yesmaximal, characteristic, complemented
11#22582847C211yesmaximal, characteristic, complemented
12C4×D1124C211yesmaximal, characteristic, complemented
13#22582839C211yesmaximal, characteristic, complemented
14C22⋊C4×D281C211yesmaximal, characteristic, complemented
15#124×C281C211yesmaximal, characteristic, complemented
16C23×D281C2211yescharacteristic
17C2×D1124C2211yescharacteristic
18C2×D1124C2211yescharacteristic
19C2×C22⋊D281C2211yescharacteristic
20C2×C22⋊D281C2211yescharacteristic
21C2×C22⋊D281C2211yescharacteristic
22C2×C22⋊D281C2211yescharacteristic, complemented
23C22×Dic281C2211yescharacteristic, complemented
24C2×C4×D281C2211yescharacteristic
25C2×C4×D281C2211yescharacteristic
26C2×C4×D281C2211yescharacteristic, complemented
27C4⋊Dic281C2211yescharacteristic, complemented
28C4⋊Dic281C2211yescharacteristic, complemented
29#17985117C2211yescharacteristic, complemented
30#17985117C2211yescharacteristic, complemented
31#17985117C2211yescharacteristic, complemented
32#17985117C2211yescharacteristic, complemented
33C22⋊Dic281C2211yescharacteristic
34C22⋊Dic281C2211yescharacteristic
35#17985115C2211yescharacteristic
36#17985115C2211yescharacteristic
37#17985115C2211yescharacteristic
38#17985115C2211yescharacteristic
39#17985115C2211yescharacteristic
40#17985115C2211yescharacteristic
41#17985115C2211yescharacteristic, complemented
42#17985115C2211yescharacteristic, complemented
43C4×Dic281C2211yescharacteristic, complemented
44C2×Q8×C281C2211yescharacteristic, complemented
45C2×D4×C281C2211yescharacteristic
46C22⋊C4×C281C2211yescharacteristic
47C22⋊C4×C281C2211yescharacteristic
48C22⋊C4×C281C2211yescharacteristic, complemented
49C22⋊C4×C281C2211yescharacteristic, complemented
50C42×C281C2211yescharacteristic, complemented
51C22×D281—22no—
52C22×D281—41no—
53C22×D281—41no—
54C22×D281C2311yescharacteristic
55C22×D281C2311yescharacteristic
56C22×D281C2311yescharacteristic
57D1124—22no—
58D1124—41no—
59C22⋊D281—22no—
60C22⋊D281—41no—
61C22⋊D281—41no—
62C22⋊D281—41no—
63C2×Dic281—41no—
64C2×Dic281C2311yescharacteristic
65C2×Dic281C2311yescharacteristic
66C2×Dic281C2311yescharacteristic
67C2×Dic281C2311yescharacteristic
68C2×Dic281C2311yescharacteristic
69C4×D281—41no—
70C4×D281—41no—
71C4×D281—41no—
72C23×C281C2311yescharacteristic
73C23×C281C2311yescharacteristic
74Q8×C281—41no—
75D4×C281—41no—
76C2×C4×C281C2311yescharacteristic
77C2×C4×C281C2311yescharacteristic
78C2×C4×C281C2311yescharacteristic
79C2×C4×C281C2311yescharacteristic
80C2×C4×C281C2311yescharacteristic
81C22×C281—21no—
82C22×C281—21no—
83C22×C281—21no—
84C22×C281—21no—
85C22×C281—21no—
86C22×C281—21no—
87C22×C281C2411yescharacteristic
88C2×D281—21no—
89C2×D281—21no—
90C2×D281—21no—
91C2×D281—21no—
92C2×D281—21no—
93C2×D281—21no—
94C2×D281—21no—
95C2×D281—21no—
96C2×D281—44no—
97C2×D281#4112yes—
98C4×C281—21no—
99C4×C281—21no—
100C4×C281—21no—
101C4×C281—21no—
102C4×C281—21no—
103Dic281—21no—
104Dic281—21no—
105Dic281—21no—
106Dic281—21no—
107Dic281—21no—
108C2×C281—41no—
109C2×C281—41no—
110C2×C281C2×#4111yescharacteristic
111C2×C281H(5,𝔽2)11yescharacteristic
112C2×C281H(5,𝔽2)11yescharacteristic
113D281—22no—
114D281—41no—
115D281—41no—
116C281#53811yescharacteristic, complemented, Sylow
117#538—2811nomaximal, Sylow
118#126—2811no—
119#126—2811no—
120#124—2811no—
121#124D28111yescharacteristic, complemented
122#123—2811no—
123#123—2811no—
124C22⋊Q8—2811no—
125#121—2811no—
126#121—2811no—
127#121—2811no—
128#120—2811no—
129#120—2811no—
130C4×D4—2811no—
131C4×D4—2811no—
132C2×C22⋊C4—2811no—
133C24—2811no—
134C2×Q8C2×D28111yescharacteristic, complemented
135C2×D4—2811no—
136C2×D4—2811no—
137C2×D4—2811no—
138C2×D4—2811no—
139C2×D4—2811no—
140C2×D4—2811no—
141C2×D4C2×D28111yescharacteristic
142C22×C4—2811no—
143C22×C4—2811no—
144C22×C4—2811no—
145C22×C4—2811no—
146C4⋊C4—2811no—
147C4⋊C4—2811no—
148C4⋊C4—2811no—
149C4⋊C4—2811no—
150C4⋊C4—2811no—
151C4⋊C4—2811no—
152C22⋊C4—2811no—
153C22⋊C4—2811no—
154C22⋊C4—2811no—
155C22⋊C4—2811no—
156C22⋊C4—2811no—
157C22⋊C4—2811no—
158C22⋊C4—2811no—
159C22⋊C4—2811no—
160C22⋊C4—2811no—
161C22⋊C4—2811no—
162C22⋊C4C2×D28111yescharacteristic
163C22⋊C4C2×D28111yescharacteristic
164C22⋊C4C2×D28111yescharacteristic, complemented
165C22⋊C4C2×D28111yescharacteristic, complemented
166C42—2811no—
167C42C2×D28111yescharacteristic, complemented
168C23—2811no—
169C23—2811no—
170C23—2811no—
171C23—5622no—
172C23—11241no—
173C23—11241no—
174C23C22×D28111yescharacteristic
175C23C22×D28111yescharacteristic
176Q8—41no—
177D4—41no—
178D4—5622no—
179D4—5622no—
180D4—11241no—
181D4—11241no—
182D4—11241no—
183D4—11241no—
184C2×C4—2811no—
185C2×C4—2811no—
186C2×C4—2811no—
187C2×C4—2811no—
188C2×C4—2811no—
189C2×C4—11241no—
190C2×C4—11241no—
191C2×C4—11241no—
192C2×C4—11241no—
193C2×C4C22×D28111yescharacteristic
194C2×C4C22×D28111yescharacteristic
195C2×C4C22×D28111yescharacteristic
196C2×C4C22×D28111yescharacteristic
197C2×C4C22×D28111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—2812no—
205C22—5621no—
206C22—5621no—
207C22—5621no—
208C22—5621no—
209C22—5621no—
210C22—5621no—
211C22—5621no—
212C22—5621no—
213C22—11244no—
214C22C23×D28111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—5621no—
221C4—5621no—
222C4—5621no—
223C4—5621no—
224C4—5621no—
225C2—41no—
226C2—41no—
227C2—5622no—
228C2—11241no—
229C2—11241no—
230C2#41×D28111yescharacteristic
231C2#2258292411yescharacteristic
232C2#2258292511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
Fitting#124×C281C2
hypercenter#124D281
hypocenterC281#538
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #22582873C2semidirect
2. #22582872C2semidirect
3. #22582868C2semidirect
4. #22582863C2semidirect
5. #22582861C2semidirect
6. #22582855C2semidirect
7. #22582852C2semidirect
8. #22582852C2semidirect
9. #22582851C2semidirect
10. #22582849C2semidirect
11. #22582847C2semidirect
12. C4×D1124C2semidirect
13. #22582839C2semidirect
14. C22⋊C4×D281C2semidirect
15. #124×C281C2semidirect
22. C2×C22⋊D281C22semidirect
23. C22×Dic281C22semidirect
26. C2×C4×D281C22semidirect
27. C4⋊Dic281C22semidirect
28. C4⋊Dic281C22semidirect
29. #17985117C22semidirect
30. #17985117C22semidirect
31. #17985117C22semidirect
32. #17985117C22semidirect
41. #17985115C22semidirect
42. #17985115C22semidirect
43. C4×Dic281C22semidirect
44. C2×Q8×C281C22semidirect
48. C22⋊C4×C281C22semidirect
49. C22⋊C4×C281C22semidirect
50. C42×C281C22semidirect
116. C281#538semidirect
121. #124D281semidirect
134. C2×Q8C2×D281semidirect
164. C22⋊C4C2×D281semidirect
165. C22⋊C4C2×D281semidirect
167. C42C2×D281semidirect

Maximal subgroups

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

subgroupindex
#225828732
#225828722
#225828682
#225828632
#225828612
#225828552
#225828522
#225828512
#225828492
#225828472
C4×D11242
#225828392
C22⋊C4×D2812
#124×C2812
#538281