Finite Group Databasebeta

← #19152182

Subgroups — #19152182

Order 5696.

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#15668006C211yesmaximal, characteristic, complemented
2#15668005C211yesmaximal, characteristic, complemented
3#15668001C211yesmaximal, characteristic, complemented
4#15667996C211yesmaximal, characteristic, complemented
5#15667994C211yesmaximal, characteristic, complemented
6#15667988C211yesmaximal, characteristic, complemented
7#15667985C211yesmaximal, characteristic, complemented
8#15667985C211yesmaximal, characteristic, complemented
9#15667984C211yesmaximal, characteristic, complemented
10#15667982C211yesmaximal, characteristic, complemented
11#15667980C211yesmaximal, characteristic, complemented
12C4×D356C211yesmaximal, characteristic, complemented
13#15667972C211yesmaximal, characteristic, complemented
14C22⋊C4×D89C211yesmaximal, characteristic, complemented
15#124×C89C211yesmaximal, characteristic, complemented
16C23×D89C2211yescharacteristic
17C2×D356C2211yescharacteristic
18C2×D356C2211yescharacteristic
19C2×C22⋊D89C2211yescharacteristic
20C2×C22⋊D89C2211yescharacteristic
21C2×C22⋊D89C2211yescharacteristic
22C2×C22⋊D89C2211yescharacteristic, complemented
23C22×Dic89C2211yescharacteristic, complemented
24C2×C4×D89C2211yescharacteristic
25C2×C4×D89C2211yescharacteristic
26C2×C4×D89C2211yescharacteristic, complemented
27C4⋊Dic89C2211yescharacteristic, complemented
28C4⋊Dic89C2211yescharacteristic, complemented
29#13083553C2211yescharacteristic, complemented
30#13083553C2211yescharacteristic, complemented
31#13083553C2211yescharacteristic, complemented
32#13083553C2211yescharacteristic, complemented
33C22⋊Dic89C2211yescharacteristic
34C22⋊Dic89C2211yescharacteristic
35#13083551C2211yescharacteristic
36#13083551C2211yescharacteristic
37#13083551C2211yescharacteristic
38#13083551C2211yescharacteristic
39#13083551C2211yescharacteristic
40#13083551C2211yescharacteristic
41#13083551C2211yescharacteristic, complemented
42#13083551C2211yescharacteristic, complemented
43C4×Dic89C2211yescharacteristic, complemented
44C2×Q8×C89C2211yescharacteristic, complemented
45C2×D4×C89C2211yescharacteristic
46C22⋊C4×C89C2211yescharacteristic
47C22⋊C4×C89C2211yescharacteristic
48C22⋊C4×C89C2211yescharacteristic, complemented
49C22⋊C4×C89C2211yescharacteristic, complemented
50C42×C89C2211yescharacteristic, complemented
51C23×C89C2311yescharacteristic
52C23×C89C2311yescharacteristic
53C22×D89—22no—
54C22×D89—41no—
55C22×D89—41no—
56C22×D89C2311yescharacteristic
57C22×D89C2311yescharacteristic
58C22×D89C2311yescharacteristic
59Q8×C89—41no—
60D4×C89—41no—
61C2×C4×C89C2311yescharacteristic
62C2×C4×C89C2311yescharacteristic
63C2×C4×C89C2311yescharacteristic
64C2×C4×C89C2311yescharacteristic
65C2×C4×C89C2311yescharacteristic
66C22⋊D89—22no—
67C22⋊D89—41no—
68C22⋊D89—41no—
69C22⋊D89—41no—
70C2×Dic89—41no—
71C2×Dic89C2311yescharacteristic
72C2×Dic89C2311yescharacteristic
73C2×Dic89C2311yescharacteristic
74C2×Dic89C2311yescharacteristic
75C2×Dic89C2311yescharacteristic
76D356—22no—
77D356—41no—
78C4×D89—41no—
79C4×D89—41no—
80C4×D89—41no—
81C22×C89—21no—
82C22×C89—21no—
83C22×C89—21no—
84C22×C89—21no—
85C22×C89—21no—
86C22×C89—21no—
87C22×C89C2411yescharacteristic
88C2×D89—21no—
89C2×D89—21no—
90C2×D89—21no—
91C2×D89—21no—
92C2×D89—21no—
93C2×D89—21no—
94C2×D89—21no—
95C2×D89—21no—
96C2×D89—44no—
97C2×D89#4112yes—
98C4×C89—21no—
99C4×C89—21no—
100C4×C89—21no—
101C4×C89—21no—
102C4×C89—21no—
103Dic89—21no—
104Dic89—21no—
105Dic89—21no—
106Dic89—21no—
107Dic89—21no—
108C2×C89—41no—
109C2×C89—41no—
110C2×C89C2×#4111yescharacteristic
111C2×C89H(5,𝔽2)11yescharacteristic
112C2×C89H(5,𝔽2)11yescharacteristic
113D89—22no—
114D89—41no—
115D89—41no—
116C89#53811yescharacteristic, complemented, Sylow
117#538—891nomaximal, Sylow
118#126—891no—
119#126—891no—
120#124—891no—
121#124D8911yescharacteristic, complemented
122#123—891no—
123#123—891no—
124C22⋊Q8—891no—
125#121—891no—
126#121—891no—
127#121—891no—
128#120—891no—
129#120—891no—
130C4×D4—891no—
131C4×D4—891no—
132C2×C22⋊C4—891no—
133C24—891no—
134C2×Q8C2×D8911yescharacteristic, complemented
135C2×D4—891no—
136C2×D4—891no—
137C2×D4—891no—
138C2×D4—891no—
139C2×D4—891no—
140C2×D4—891no—
141C2×D4C2×D8911yescharacteristic
142C22×C4—891no—
143C22×C4—891no—
144C22×C4—891no—
145C22×C4—891no—
146C4⋊C4—891no—
147C4⋊C4—891no—
148C4⋊C4—891no—
149C4⋊C4—891no—
150C4⋊C4—891no—
151C4⋊C4—891no—
152C22⋊C4—891no—
153C22⋊C4—891no—
154C22⋊C4—891no—
155C22⋊C4—891no—
156C22⋊C4—891no—
157C22⋊C4—891no—
158C22⋊C4—891no—
159C22⋊C4—891no—
160C22⋊C4—891no—
161C22⋊C4—891no—
162C22⋊C4C2×D8911yescharacteristic
163C22⋊C4C2×D8911yescharacteristic
164C22⋊C4C2×D8911yescharacteristic, complemented
165C22⋊C4C2×D8911yescharacteristic, complemented
166C42—891no—
167C42C2×D8911yescharacteristic, complemented
168C23—891no—
169C23—891no—
170C23—891no—
171C23—3561no—
172C23—3561no—
173C23—1782no—
174C23C22×D8911yescharacteristic
175C23C22×D8911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—3561no—
179D4—3561no—
180D4—3561no—
181D4—3561no—
182D4—1782no—
183D4—1782no—
184C2×C4—891no—
185C2×C4—891no—
186C2×C4—891no—
187C2×C4—891no—
188C2×C4—891no—
189C2×C4—3561no—
190C2×C4—3561no—
191C2×C4—3561no—
192C2×C4—3561no—
193C2×C4C22×D8911yescharacteristic
194C2×C4C22×D8911yescharacteristic
195C2×C4C22×D8911yescharacteristic
196C2×C4C22×D8911yescharacteristic
197C2×C4C22×D8911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—892no—
205C22—3564no—
206C22—1781no—
207C22—1781no—
208C22—1781no—
209C22—1781no—
210C22—1781no—
211C22—1781no—
212C22—1781no—
213C22—1781no—
214C22C23×D8911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—1781no—
221C4—1781no—
222C4—1781no—
223C4—1781no—
224C4—1781no—
225C2—41no—
226C2—41no—
227C2—3561no—
228C2—3561no—
229C2—1782no—
230C2#41×D8911yescharacteristic
231C2#1566805711yescharacteristic
232C2#1566805811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D89
commutator, socleC22×C89C24
Fitting#124×C89C2
hypercenter#124D89
hypocenterC89#538
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #15668006C2semidirect
2. #15668005C2semidirect
3. #15668001C2semidirect
4. #15667996C2semidirect
5. #15667994C2semidirect
6. #15667988C2semidirect
7. #15667985C2semidirect
8. #15667985C2semidirect
9. #15667984C2semidirect
10. #15667982C2semidirect
11. #15667980C2semidirect
12. C4×D356C2semidirect
13. #15667972C2semidirect
14. C22⋊C4×D89C2semidirect
15. #124×C89C2semidirect
22. C2×C22⋊D89C22semidirect
23. C22×Dic89C22semidirect
26. C2×C4×D89C22semidirect
27. C4⋊Dic89C22semidirect
28. C4⋊Dic89C22semidirect
29. #13083553C22semidirect
30. #13083553C22semidirect
31. #13083553C22semidirect
32. #13083553C22semidirect
41. #13083551C22semidirect
42. #13083551C22semidirect
43. C4×Dic89C22semidirect
44. C2×Q8×C89C22semidirect
48. C22⋊C4×C89C22semidirect
49. C22⋊C4×C89C22semidirect
50. C42×C89C22semidirect
116. C89#538semidirect
121. #124D89semidirect
134. C2×Q8C2×D89semidirect
164. C22⋊C4C2×D89semidirect
165. C22⋊C4C2×D89semidirect
167. C42C2×D89semidirect