Finite Group Databasebeta

← #22581537

Subgroups — #22581537

Order 8896.

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#17984836C211yesmaximal, characteristic, complemented
2#17984835C211yesmaximal, characteristic, complemented
3#17984831C211yesmaximal, characteristic, complemented
4#17984826C211yesmaximal, characteristic, complemented
5#17984824C211yesmaximal, characteristic, complemented
6#17984818C211yesmaximal, characteristic, complemented
7#17984815C211yesmaximal, characteristic, complemented
8#17984815C211yesmaximal, characteristic, complemented
9#17984814C211yesmaximal, characteristic, complemented
10#17984812C211yesmaximal, characteristic, complemented
11#17984810C211yesmaximal, characteristic, complemented
12C4×D556C211yesmaximal, characteristic, complemented
13(C22⋊D139)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D139C211yesmaximal, characteristic, complemented
15#124×C139C211yesmaximal, characteristic, complemented
16C23×D139C2211yescharacteristic
17C2×D556C2211yescharacteristic
18C2×D556C2211yescharacteristic
19C2×C22⋊D139C2211yescharacteristic
20C2×C22⋊D139C2211yescharacteristic
21C2×C22⋊D139C2211yescharacteristic
22C2×C22⋊D139C2211yescharacteristic, complemented
23C22×Dic139C2211yescharacteristic, complemented
24C2×C4×D139C2211yescharacteristic
25C2×C4×D139C2211yescharacteristic
26C2×C4×D139C2211yescharacteristic, complemented
27C4⋊Dic139C2211yescharacteristic, complemented
28C4⋊Dic139C2211yescharacteristic, complemented
29Dic139⋊C4C2211yescharacteristic, complemented
30Dic139⋊C4C2211yescharacteristic, complemented
31Dic139⋊C4C2211yescharacteristic, complemented
32Dic139⋊C4C2211yescharacteristic, complemented
33C22⋊Dic139C2211yescharacteristic
34C22⋊Dic139C2211yescharacteristic
35(C2×D139)⋊C4C2211yescharacteristic
36(C2×D139)⋊C4C2211yescharacteristic
37(C2×D139)⋊C4C2211yescharacteristic
38(C2×D139)⋊C4C2211yescharacteristic
39(C2×D139)⋊C4C2211yescharacteristic
40(C2×D139)⋊C4C2211yescharacteristic
41(C2×D139)⋊C4C2211yescharacteristic, complemented
42(C2×D139)⋊C4C2211yescharacteristic, complemented
43C4×Dic139C2211yescharacteristic, complemented
44C2×Q8×C139C2211yescharacteristic, complemented
45C2×D4×C139C2211yescharacteristic
46C22⋊C4×C139C2211yescharacteristic
47C22⋊C4×C139C2211yescharacteristic
48C22⋊C4×C139C2211yescharacteristic, complemented
49C22⋊C4×C139C2211yescharacteristic, complemented
50C42×C139C2211yescharacteristic, complemented
51C22×D139—22no—
52C22×D139—41no—
53C22×D139—41no—
54C22×D139C2311yescharacteristic
55C22×D139C2311yescharacteristic
56C22×D139C2311yescharacteristic
57D556—22no—
58D556—41no—
59C22⋊D139—22no—
60C22⋊D139—41no—
61C22⋊D139—41no—
62C22⋊D139—41no—
63C2×Dic139—41no—
64C2×Dic139C2311yescharacteristic
65C2×Dic139C2311yescharacteristic
66C2×Dic139C2311yescharacteristic
67C2×Dic139C2311yescharacteristic
68C2×Dic139C2311yescharacteristic
69C4×D139—41no—
70C4×D139—41no—
71C4×D139—41no—
72C23×C139C2311yescharacteristic
73C23×C139C2311yescharacteristic
74Q8×C139—41no—
75D4×C139—41no—
76C2×C4×C139C2311yescharacteristic
77C2×C4×C139C2311yescharacteristic
78C2×C4×C139C2311yescharacteristic
79C2×C4×C139C2311yescharacteristic
80C2×C4×C139C2311yescharacteristic
81C22×C139—21no—
82C22×C139—21no—
83C22×C139—21no—
84C22×C139—21no—
85C22×C139—21no—
86C22×C139—21no—
87C22×C139C2411yescharacteristic
88C2×D139—21no—
89C2×D139—21no—
90C2×D139—21no—
91C2×D139—21no—
92C2×D139—21no—
93C2×D139—21no—
94C2×D139—21no—
95C2×D139—21no—
96C2×D139—44no—
97C2×D139#4112yes—
98C4×C139—21no—
99C4×C139—21no—
100C4×C139—21no—
101C4×C139—21no—
102C4×C139—21no—
103Dic139—21no—
104Dic139—21no—
105Dic139—21no—
106Dic139—21no—
107Dic139—21no—
108C2×C139—41no—
109C2×C139—41no—
110C2×C139C2×#4111yescharacteristic
111C2×C139H(5,𝔽2)11yescharacteristic
112C2×C139H(5,𝔽2)11yescharacteristic
113D139—22no—
114D139—41no—
115D139—41no—
116C139#53811yescharacteristic, complemented, Sylow
117#538—1391nomaximal, Sylow
118#126—1391no—
119#126—1391no—
120#124—1391no—
121#124D13911yescharacteristic, complemented
122#123—1391no—
123#123—1391no—
124C22⋊Q8—1391no—
125#121—1391no—
126#121—1391no—
127#121—1391no—
128#120—1391no—
129#120—1391no—
130C4×D4—1391no—
131C4×D4—1391no—
132C2×C22⋊C4—1391no—
133C24—1391no—
134C2×Q8C2×D13911yescharacteristic, complemented
135C2×D4—1391no—
136C2×D4—1391no—
137C2×D4—1391no—
138C2×D4—1391no—
139C2×D4—1391no—
140C2×D4—1391no—
141C2×D4C2×D13911yescharacteristic
142C22×C4—1391no—
143C22×C4—1391no—
144C22×C4—1391no—
145C22×C4—1391no—
146C4⋊C4—1391no—
147C4⋊C4—1391no—
148C4⋊C4—1391no—
149C4⋊C4—1391no—
150C4⋊C4—1391no—
151C4⋊C4—1391no—
152C22⋊C4—1391no—
153C22⋊C4—1391no—
154C22⋊C4—1391no—
155C22⋊C4—1391no—
156C22⋊C4—1391no—
157C22⋊C4—1391no—
158C22⋊C4—1391no—
159C22⋊C4—1391no—
160C22⋊C4—1391no—
161C22⋊C4—1391no—
162C22⋊C4C2×D13911yescharacteristic
163C22⋊C4C2×D13911yescharacteristic
164C22⋊C4C2×D13911yescharacteristic, complemented
165C22⋊C4C2×D13911yescharacteristic, complemented
166C42—1391no—
167C42C2×D13911yescharacteristic, complemented
168C23—2782no—
169C23—5561no—
170C23—5561no—
171C23—1391no—
172C23—1391no—
173C23—1391no—
174C23C22×D13911yescharacteristic
175C23C22×D13911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—2782no—
179D4—2782no—
180D4—5561no—
181D4—5561no—
182D4—5561no—
183D4—5561no—
184C2×C4—5561no—
185C2×C4—5561no—
186C2×C4—5561no—
187C2×C4—5561no—
188C2×C4—1391no—
189C2×C4—1391no—
190C2×C4—1391no—
191C2×C4—1391no—
192C2×C4—1391no—
193C2×C4C22×D13911yescharacteristic
194C2×C4C22×D13911yescharacteristic
195C2×C4C22×D13911yescharacteristic
196C2×C4C22×D13911yescharacteristic
197C2×C4C22×D13911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—2781no—
205C22—2781no—
206C22—2781no—
207C22—2781no—
208C22—2781no—
209C22—2781no—
210C22—2781no—
211C22—2781no—
212C22—5564no—
213C22—1392no—
214C22C23×D13911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—2781no—
221C4—2781no—
222C4—2781no—
223C4—2781no—
224C4—2781no—
225C2—41no—
226C2—41no—
227C2—2782no—
228C2—5561no—
229C2—5561no—
230C2#41×D13911yescharacteristic
231C2#1798488711yescharacteristic
232C2#1798488811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D139
commutator, socleC22×C139C24
Fitting#124×C139C2
hypercenter#124D139
hypocenterC139#538
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17984836C2semidirect
2. #17984835C2semidirect
3. #17984831C2semidirect
4. #17984826C2semidirect
5. #17984824C2semidirect
6. #17984818C2semidirect
7. #17984815C2semidirect
8. #17984815C2semidirect
9. #17984814C2semidirect
10. #17984812C2semidirect
11. #17984810C2semidirect
12. C4×D556C2semidirect
13. (C22⋊D139)⋊C4C2semidirect
14. C22⋊C4×D139C2semidirect
15. #124×C139C2semidirect
22. C2×C22⋊D139C22semidirect
23. C22×Dic139C22semidirect
26. C2×C4×D139C22semidirect
27. C4⋊Dic139C22semidirect
28. C4⋊Dic139C22semidirect
29. Dic139⋊C4C22semidirect
30. Dic139⋊C4C22semidirect
31. Dic139⋊C4C22semidirect
32. Dic139⋊C4C22semidirect
41. (C2×D139)⋊C4C22semidirect
42. (C2×D139)⋊C4C22semidirect
43. C4×Dic139C22semidirect
44. C2×Q8×C139C22semidirect
48. C22⋊C4×C139C22semidirect
49. C22⋊C4×C139C22semidirect
50. C42×C139C22semidirect
116. C139#538semidirect
121. #124D139semidirect
134. C2×Q8C2×D139semidirect
164. C22⋊C4C2×D139semidirect
165. C22⋊C4C2×D139semidirect
167. C42C2×D139semidirect