Finite Group Databasebeta

← #20295701

Subgroups — #20295701

Order 6976.

248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 248 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#16812692C211yesmaximal, characteristic, complemented
2#16812685C211yesmaximal, characteristic, complemented
3#16812684C211yesmaximal, characteristic, complemented
4#16812684C211yesmaximal, characteristic, complemented
5#16812681C211yesmaximal, characteristic, complemented
6#16812679C211yesmaximal, characteristic, complemented
7#16812677C211yesmaximal, characteristic, complemented
8#16812669C211yesmaximal, characteristic
9C4×D436C211yesmaximal, characteristic, complemented
10#16812661C211yesmaximal, characteristic, complemented
11#16812657C211yesmaximal, characteristic, complemented
12#16812656C211yesmaximal, characteristic, complemented
13C22⋊C4×D109C211yesmaximal, characteristic, complemented
14C22⋊C4×D109C211yesmaximal, characteristic, complemented
15#126×C109C211yesmaximal, characteristic, complemented
16C23×D109C2211yescharacteristic
17C2×Dic218C2211yescharacteristic, complemented
18C2×D436C2211yescharacteristic
19C2×D436C2211yescharacteristic
20C2×C22⋊D109C2211yescharacteristic
21C2×C4×D109C2211yescharacteristic
22C2×C4×D109C2211yescharacteristic
23C2×C4×D109C2211yescharacteristic
24C2×C4×D109C2211yescharacteristic
25C2×C4×D109C2211yescharacteristic, complemented
26C4⋊Dic109C2211yescharacteristic, complemented
27C4⋊Dic109C2211yescharacteristic, complemented
28#13182008C2211yescharacteristic, complemented
29#13182008C2211yescharacteristic, complemented
30#13182008C2211yescharacteristic, complemented
31C22⋊Dic109C2211yescharacteristic
32C22⋊Dic109C2211yescharacteristic
33#13182006C2211yescharacteristic
34#13182006C2211yescharacteristic
35#13182006C2211yescharacteristic
36#13182006C2211yescharacteristic
37#13182006C2211yescharacteristic
38#13182006C2211yescharacteristic
39#13182006C2211yescharacteristic, complemented
40#13182006C2211yescharacteristic, complemented
41#13182006C2211yescharacteristic, complemented
42C4×Dic109C2211yescharacteristic, complemented
43C4×Dic109C2211yescharacteristic, complemented
44C4⋊C4×C109C2211yescharacteristic, complemented
45C4⋊C4×C109C2211yescharacteristic, complemented
46C4⋊C4×C109C2211yescharacteristic, complemented
47C22⋊C4×C109C2211yescharacteristic
48C22⋊C4×C109C2211yescharacteristic
49C22⋊C4×C109C2211yescharacteristic
50C42×C109C2211yescharacteristic, complemented
51C23×C109C2311yescharacteristic
52C22×D109—22no—
53C22×D109—22no—
54C22×D109—41no—
55C22×D109C2311yescharacteristic
56C22×D109C2311yescharacteristic
57C22×D109C2311yescharacteristic
58C2×C4×C109C2311yescharacteristic
59C2×C4×C109C2311yescharacteristic
60C2×C4×C109C2311yescharacteristic
61C2×C4×C109C2311yescharacteristic
62C2×C4×C109C2311yescharacteristic
63C2×C4×C109C2311yescharacteristic
64C22⋊D109—41no—
65C2×Dic109C2311yescharacteristic
66C2×Dic109C2311yescharacteristic
67C2×Dic109C2311yescharacteristic
68C2×Dic109C2311yescharacteristic
69C2×Dic109C2311yescharacteristic
70D436—22no—
71D436—22no—
72C4×D109—22no—
73C4×D109—22no—
74C4×D109—41no—
75C4×D109—41no—
76C4×D109—41no—
77Dic218—41no—
78C22×C109—21no—
79C22×C109—21no—
80C22×C109—21no—
81C22×C109C2411yescharacteristic
82C2×D109—21no—
83C2×D109—21no—
84C2×D109—21no—
85C2×D109—21no—
86C2×D109—21no—
87C2×D109—21no—
88C2×D109—21no—
89C2×D109—44no—
90C2×D109#4112yes—
91C2×D109#4112yes—
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—21no—
97C4×C109—21no—
98Dic109—21no—
99Dic109—21no—
100Dic109—21no—
101Dic109—21no—
102Dic109—21no—
103C2×C109—41no—
104C2×C109C2×#4111yescharacteristic
105C2×C109C2×#4111yescharacteristic
106C2×C109H(5,𝔽2)11yescharacteristic
107D109—22no—
108D109—22no—
109D109—41no—
110C109#55111yescharacteristic, complemented, Sylow
111#551—1091nomaximal, Sylow
112#126—1091no—
113#126D10911yescharacteristic, complemented
114#124—1091no—
115#123—1091no—
116#123—1091no—
117#123—1091no—
118C22⋊Q8—1091no—
119C22⋊Q8—1091no—
120#120—1091no—
121C4×D4—1091no—
122C4×D4—1091no—
123#117—1091no—
124#117—1091no—
125C2×C22⋊C4—1091no—
126C2×C22⋊C4—1091no—
127C24—1091no—
128C2×Q8—1091no—
129C2×D4—1091no—
130C2×D4—1091no—
131C2×D4—1091no—
132C22×C4—1091no—
133C22×C4—1091no—
134C22×C4—1091no—
135C22×C4—1091no—
136C22×C4—1091no—
137C4⋊C4—1091no—
138C4⋊C4—1091no—
139C4⋊C4—1091no—
140C4⋊C4—1091no—
141C4⋊C4—1091no—
142C4⋊C4C2×D10911yescharacteristic, complemented
143C4⋊C4C2×D10911yescharacteristic, complemented
144C4⋊C4C2×D10911yescharacteristic, complemented
145C22⋊C4—1091no—
146C22⋊C4—1091no—
147C22⋊C4—1091no—
148C22⋊C4—1091no—
149C22⋊C4—1091no—
150C22⋊C4—1091no—
151C22⋊C4—1091no—
152C22⋊C4—1091no—
153C22⋊C4—1091no—
154C22⋊C4—1091no—
155C22⋊C4—1091no—
156C22⋊C4C2×D10911yescharacteristic
157C22⋊C4C2×D10911yescharacteristic
158C22⋊C4C2×D10911yescharacteristic
159C42—1091no—
160C42—1091no—
161C42C2×D10911yescharacteristic, complemented
162C23—1091no—
163C23—1091no—
164C23—1091no—
165C23—4361no—
166C23—2182no—
167C23—2182no—
168C23C22×D10911yescharacteristic
169Q8—4361no—
170D4—4361no—
171D4—2182no—
172D4—2182no—
173C2×C4—1091no—
174C2×C4—1091no—
175C2×C4—1091no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—4361no—
179C2×C4—4361no—
180C2×C4—4361no—
181C2×C4—2182no—
182C2×C4—2182no—
183C2×C4C22×D10911yescharacteristic
184C2×C4C22×D10911yescharacteristic
185C2×C4C22×D10911yescharacteristic
186C2×C4C22×D10911yescharacteristic
187C2×C4C22×D10911yescharacteristic
188C2×C4C22×D10911yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—1092no—
193C22—1092no—
194C22—4364no—
195C22—2181no—
196C22—2181no—
197C22—2181no—
198C22—2181no—
199C22—2181no—
200C22—2181no—
201C22—2181no—
202C22C23×D10911yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—2181no—
210C4—2181no—
211C4—2181no—
212C4—2181no—
213C4—2181no—
214C2—41no—
215C2—4361no—
216C2—2182no—
217C2—2182no—
218C2#41×D10911yescharacteristic
219C2#41×D10911yescharacteristic
220C2#1681274511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D109
commutator, socleC22×C109C24
Fitting#126×C109C2
hypercenter#126D109
hypocenterC109#551
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #16812692C2semidirect
2. #16812685C2semidirect
3. #16812684C2semidirect
4. #16812684C2semidirect
5. #16812681C2semidirect
6. #16812679C2semidirect
7. #16812677C2semidirect
9. C4×D436C2semidirect
10. #16812661C2semidirect
11. #16812657C2semidirect
12. #16812656C2semidirect
13. C22⋊C4×D109C2semidirect
14. C22⋊C4×D109C2semidirect
15. #126×C109C2semidirect
17. C2×Dic218C22semidirect
25. C2×C4×D109C22semidirect
26. C4⋊Dic109C22semidirect
27. C4⋊Dic109C22semidirect
28. #13182008C22semidirect
29. #13182008C22semidirect
30. #13182008C22semidirect
39. #13182006C22semidirect
40. #13182006C22semidirect
41. #13182006C22semidirect
42. C4×Dic109C22semidirect
43. C4×Dic109C22semidirect
44. C4⋊C4×C109C22semidirect
45. C4⋊C4×C109C22semidirect
46. C4⋊C4×C109C22semidirect
50. C42×C109C22semidirect
110. C109#551semidirect
113. #126D109semidirect
142. C4⋊C4C2×D109semidirect
143. C4⋊C4C2×D109semidirect
144. C4⋊C4C2×D109semidirect
161. C42C2×D109semidirect