Finite Group Databasebeta

← #20293365

Subgroups — #20293365

Order 6848.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#16812105C211yesmaximal, characteristic, complemented
2#16812104C211yesmaximal, characteristic, complemented
3#16812102C211yesmaximal, characteristic, complemented
4#16812094C211yesmaximal, characteristic, complemented
5#16812093C211yesmaximal, characteristic, complemented
6#16812092C211yesmaximal, characteristic, complemented
7#16812083C211yesmaximal, characteristic, complemented
8#16812082C211yesmaximal, characteristic, complemented
9#16812081C211yesmaximal, characteristic, complemented
10#16812081C211yesmaximal, characteristic, complemented
11#16812080C211yesmaximal, characteristic, complemented
12#16812079C211yesmaximal, characteristic, complemented
13#16812077C211yesmaximal, characteristic, complemented
14#16812077C211yesmaximal, characteristic, complemented
15#121×C107C211yesmaximal, characteristic, complemented
16C23×D107C2211yescharacteristic
17C2×D428C2211yescharacteristic
18C2×D428C2211yescharacteristic
19C2×C22⋊D107C2211yescharacteristic
20C2×C22⋊D107C2211yescharacteristic
21C2×C22⋊D107C2211yescharacteristic
22C2×C22⋊D107C2211yescharacteristic
23C2×C22⋊D107C2211yescharacteristic
24C2×C22⋊D107C2211yescharacteristic, complemented
25C2×C22⋊D107C2211yescharacteristic, complemented
26C22×Dic107C2211yescharacteristic, complemented
27C2×C4×D107C2211yescharacteristic, complemented
28C4⋊Dic107C2211yescharacteristic, complemented
29C4⋊Dic107C2211yescharacteristic, complemented
30Dic107⋊C4C2211yescharacteristic, complemented
31Dic107⋊C4C2211yescharacteristic, complemented
32Dic107⋊C4C2211yescharacteristic, complemented
33C22⋊Dic107C2211yescharacteristic
34C22⋊Dic107C2211yescharacteristic
35C22⋊Dic107C2211yescharacteristic, complemented
36(C2×D107)⋊C4C2211yescharacteristic
37(C2×D107)⋊C4C2211yescharacteristic
38(C2×D107)⋊C4C2211yescharacteristic
39(C2×D107)⋊C4C2211yescharacteristic
40(C2×D107)⋊C4C2211yescharacteristic
41(C2×D107)⋊C4C2211yescharacteristic
42(C2×D107)⋊C4C2211yescharacteristic, complemented
43C4×Dic107C2211yescharacteristic, complemented
44C2×D4×C107C2211yescharacteristic
45C2×D4×C107C2211yescharacteristic
46C2×D4×C107C2211yescharacteristic, complemented
47C22×C4×C107C2211yescharacteristic, complemented
48C4⋊C4×C107C2211yescharacteristic, complemented
49C22⋊C4×C107C2211yescharacteristic
50C22⋊C4×C107C2211yescharacteristic, complemented
51C23×C107C2311yescharacteristic
52C23×C107C2311yescharacteristic
53C23×C107C2311yescharacteristic
54C22×D107—41no—
55C22×D107—41no—
56C22×D107—41no—
57C22×D107C2311yescharacteristic
58C22×D107C2311yescharacteristic
59C22×D107C2311yescharacteristic
60D4×C107—41no—
61D4×C107—41no—
62D4×C107—41no—
63C2×C4×C107—41no—
64C2×C4×C107C2311yescharacteristic
65C2×C4×C107C2311yescharacteristic
66C2×C4×C107C2311yescharacteristic
67C2×C4×C107C2311yescharacteristic
68C22⋊D107—41no—
69C22⋊D107—41no—
70C22⋊D107—41no—
71C22⋊D107—41no—
72C22⋊D107—41no—
73C22⋊D107—41no—
74C22⋊D107—41no—
75C2×Dic107—41no—
76C2×Dic107C2311yescharacteristic
77C2×Dic107C2311yescharacteristic
78C2×Dic107C2311yescharacteristic
79C2×Dic107C2311yescharacteristic
80C2×Dic107C2311yescharacteristic
81D428—41no—
82D428—41no—
83C4×D107—41no—
84C22×C107—21no—
85C22×C107—21no—
86C22×C107—21no—
87C22×C107—21no—
88C22×C107—21no—
89C22×C107—21no—
90C22×C107—21no—
91C22×C107—21no—
92C22×C107—21no—
93C22×C107C2411yescharacteristic
94C2×D107—21no—
95C2×D107—21no—
96C2×D107—21no—
97C2×D107—21no—
98C2×D107—21no—
99C2×D107—21no—
100C2×D107—21no—
101C2×D107—21no—
102C2×D107—21no—
103C2×D107—44no—
104C4×C107—21no—
105C4×C107—21no—
106C4×C107—21no—
107C4×C107—21no—
108Dic107—21no—
109Dic107—21no—
110Dic107—21no—
111Dic107—21no—
112Dic107—21no—
113C2×C107—41no—
114C2×C107—41no—
115C2×C107—41no—
116C2×C107H(5,𝔽2)11yescharacteristic
117C2×C107H(5,𝔽2)11yescharacteristic
118C2×C107H(5,𝔽2)11yescharacteristic
119D107—41no—
120D107—41no—
121D107—41no—
122C107#56011yescharacteristic, complemented, Sylow
123#560—1071nomaximal, Sylow
124#127—1071no—
125#126—1071no—
126#126—1071no—
127#123—1071no—
128#123—1071no—
129#123—1071no—
130#121—1071no—
131#121—1071no—
132#121—1071no—
133#121—1071no—
134#121—1071no—
135#121D10711yescharacteristic, complemented
136#120—1071no—
137#120—1071no—
138#120—1071no—
139C24—1071no—
140C2×D4—1071no—
141C2×D4—1071no—
142C2×D4—1071no—
143C2×D4—1071no—
144C2×D4—1071no—
145C2×D4—1071no—
146C2×D4—1071no—
147C2×D4—1071no—
148C2×D4—1071no—
149C2×D4C2×D10711yescharacteristic
150C2×D4C2×D10711yescharacteristic
151C2×D4C2×D10711yescharacteristic, complemented
152C22×C4—1071no—
153C22×C4—1071no—
154C22×C4C2×D10711yescharacteristic, complemented
155C4⋊C4—1071no—
156C4⋊C4—1071no—
157C4⋊C4—1071no—
158C4⋊C4—1071no—
159C4⋊C4—1071no—
160C4⋊C4C2×D10711yescharacteristic, complemented
161C22⋊C4—1071no—
162C22⋊C4—1071no—
163C22⋊C4—1071no—
164C22⋊C4—1071no—
165C22⋊C4—1071no—
166C22⋊C4—1071no—
167C22⋊C4—1071no—
168C22⋊C4—1071no—
169C22⋊C4—1071no—
170C22⋊C4—1071no—
171C22⋊C4C2×D10711yescharacteristic
172C22⋊C4C2×D10711yescharacteristic, complemented
173C42—1071no—
174C23—1071no—
175C23—1071no—
176C23—1071no—
177C23—4281no—
178C23—4281no—
179C23—4281no—
180C23C22×D10711yescharacteristic
181C23C22×D10711yescharacteristic
182C23C22×D10711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—4281no—
187D4—4281no—
188D4—4281no—
189D4—4281no—
190D4—4281no—
191D4—4281no—
192D4—4281no—
193D4—4281no—
194D4—4281no—
195C2×C4—41no—
196C2×C4—1071no—
197C2×C4—1071no—
198C2×C4—1071no—
199C2×C4—1071no—
200C2×C4—1071no—
201C2×C4—4281no—
202C2×C4—4281no—
203C2×C4C22×D10711yescharacteristic
204C2×C4C22×D10711yescharacteristic
205C2×C4C22×D10711yescharacteristic
206C2×C4C22×D10711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—4284no—
217C22—2141no—
218C22—2141no—
219C22—2141no—
220C22—2141no—
221C22—2141no—
222C22—2141no—
223C22—2141no—
224C22—2141no—
225C22—2141no—
226C22C23×D10711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—2141no—
232C4—2141no—
233C4—2141no—
234C4—2141no—
235C4—2141no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—4281no—
240C2—4281no—
241C2—4281no—
242C2#1681215411yescharacteristic
243C2#1681215411yescharacteristic
244C2#1681215511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D107
commutator, socleC22×C107C24
Fitting#121×C107C2
hypercenter#121D107
hypocenterC107#560
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #16812105C2semidirect
2. #16812104C2semidirect
3. #16812102C2semidirect
4. #16812094C2semidirect
5. #16812093C2semidirect
6. #16812092C2semidirect
7. #16812083C2semidirect
8. #16812082C2semidirect
9. #16812081C2semidirect
10. #16812081C2semidirect
11. #16812080C2semidirect
12. #16812079C2semidirect
13. #16812077C2semidirect
14. #16812077C2semidirect
15. #121×C107C2semidirect
24. C2×C22⋊D107C22semidirect
25. C2×C22⋊D107C22semidirect
26. C22×Dic107C22semidirect
27. C2×C4×D107C22semidirect
28. C4⋊Dic107C22semidirect
29. C4⋊Dic107C22semidirect
30. Dic107⋊C4C22semidirect
31. Dic107⋊C4C22semidirect
32. Dic107⋊C4C22semidirect
35. C22⋊Dic107C22semidirect
42. (C2×D107)⋊C4C22semidirect
43. C4×Dic107C22semidirect
46. C2×D4×C107C22semidirect
47. C22×C4×C107C22semidirect
48. C4⋊C4×C107C22semidirect
50. C22⋊C4×C107C22semidirect
122. C107#560semidirect
135. #121D107semidirect
151. C2×D4C2×D107semidirect
154. C22×C4C2×D107semidirect
160. C4⋊C4C2×D107semidirect
172. C22⋊C4C2×D107semidirect