Finite Group Databasebeta

← #20295705

Subgroups — #20295705

Order 6976.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#16812694C211yesmaximal, characteristic, complemented
2#16812693C211yesmaximal, characteristic, complemented
3#16812685C211yesmaximal, characteristic, complemented
4#16812682C211yesmaximal, characteristic, complemented
5#16812681C211yesmaximal, characteristic, complemented
6#16812680C211yesmaximal, characteristic, complemented
7#16812678C211yesmaximal, characteristic, complemented
8#16812677C211yesmaximal, characteristic, complemented
9#16812667C211yesmaximal, characteristic
10C4×C22⋊D109C211yesmaximal, characteristic, complemented
11#16812656C211yesmaximal, characteristic, complemented
12#16812655C211yesmaximal, characteristic, complemented
13C2×#13182006C211yesmaximal, characteristic, complemented
14C22⋊C4×D109C211yesmaximal, characteristic, complemented
15C4×D4×C109C211yesmaximal, characteristic, complemented
16C23×D109C2211yescharacteristic
17C2×Dic218C2211yescharacteristic, complemented
18C2×C22⋊D109C2211yescharacteristic
19C2×C22⋊D109C2211yescharacteristic
20C22×Dic109C2211yescharacteristic
21C2×C4×D109C2211yescharacteristic
22C2×C4×D109C2211yescharacteristic
23C4⋊Dic109C2211yescharacteristic, complemented
24#13182008C2211yescharacteristic, complemented
25#13182008C2211yescharacteristic, complemented
26#13182008C2211yescharacteristic, complemented
27#13182008C2211yescharacteristic, complemented
28#13182008C2211yescharacteristic, complemented
29#13182008C2211yescharacteristic, complemented
30C22⋊Dic109C2211yescharacteristic
31C22⋊Dic109C2211yescharacteristic
32C22⋊Dic109C2211yescharacteristic, complemented
33C22⋊Dic109C2211yescharacteristic, complemented
34#13182006C2211yescharacteristic
35#13182006C2211yescharacteristic
36#13182006C2211yescharacteristic
37#13182006C2211yescharacteristic
38#13182006C2211yescharacteristic
39#13182006C2211yescharacteristic
40#13182006C2211yescharacteristic
41#13182006C2211yescharacteristic
42C4×Dic109C2211yescharacteristic, complemented
43C4×Dic109C2211yescharacteristic, complemented
44C2×D4×C109C2211yescharacteristic
45C22×C4×C109C2211yescharacteristic
46C22×C4×C109C2211yescharacteristic, complemented
47C4⋊C4×C109C2211yescharacteristic, complemented
48C22⋊C4×C109C2211yescharacteristic
49C22⋊C4×C109C2211yescharacteristic, complemented
50C42×C109C2211yescharacteristic, complemented
51C23×C109C2311yescharacteristic
52C23×C109C2311yescharacteristic
53C22×D109—22no—
54C22×D109—22no—
55C22×D109—41no—
56C22×D109C2311yescharacteristic
57C22×D109C2311yescharacteristic
58D4×C109—22no—
59C2×C4×C109—41no—
60C2×C4×C109—41no—
61C2×C4×C109C2311yescharacteristic
62C2×C4×C109C2311yescharacteristic
63C2×C4×C109C2311yescharacteristic
64C2×C4×C109C2311yescharacteristic
65C2×C4×C109C2311yescharacteristic
66C22⋊D109—22no—
67C22⋊D109—41no—
68C2×Dic109—22no—
69C2×Dic109C2311yescharacteristic
70C2×Dic109C2311yescharacteristic
71C2×Dic109C2311yescharacteristic
72C2×Dic109C2311yescharacteristic
73C2×Dic109C2311yescharacteristic
74C2×Dic109C2311yescharacteristic
75C4×D109—22no—
76C4×D109—41no—
77Dic218—41no—
78C22×C109—21no—
79C22×C109—21no—
80C22×C109—21no—
81C22×C109—21no—
82C22×C109—21no—
83C22×C109#4112yes—
84C22×C109C2411yescharacteristic
85C2×D109—21no—
86C2×D109—21no—
87C2×D109—21no—
88C2×D109—21no—
89C2×D109—21no—
90C2×D109—44no—
91C2×D109#4112yes—
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—21no—
97Dic109—21no—
98Dic109—21no—
99Dic109—21no—
100Dic109—21no—
101Dic109—21no—
102Dic109—21no—
103C2×C109—22no—
104C2×C109—41no—
105C2×C109C2×#4111yescharacteristic
106C2×C109C2×#4111yescharacteristic
107C2×C109H(5,𝔽2)11yescharacteristic
108D109—22no—
109D109—41no—
110C109#55111yescharacteristic, complemented, Sylow
111#551—1091nomaximal, Sylow
112#126—1091no—
113#126—1091no—
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×D4D10911yescharacteristic, complemented
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×D4C2×D10911yescharacteristic
132C22×C4—1091no—
133C22×C4—1091no—
134C22×C4—1091no—
135C22×C4C2×D10911yescharacteristic
136C22×C4C2×D10911yescharacteristic, complemented
137C4⋊C4—1091no—
138C4⋊C4—1091no—
139C4⋊C4—1091no—
140C4⋊C4—1091no—
141C4⋊C4—1091no—
142C4⋊C4—1091no—
143C4⋊C4—1091no—
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⋊C4—1091no—
157C22⋊C4C2×D10911yescharacteristic
158C22⋊C4C2×D10911yescharacteristic, complemented
159C42—1091no—
160C42—1091no—
161C42C2×D10911yescharacteristic, complemented
162C23—1091no—
163C23—1091no—
164C23—4361no—
165C23—2182no—
166C23—2182no—
167C23C22×D10911yescharacteristic
168C23C22×D10911yescharacteristic
169Q8—4361no—
170D4—22no—
171D4—4361no—
172D4—2182no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—1091no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—1091no—
180C2×C4—1091no—
181C2×C4—4361no—
182C2×C4—2182no—
183C2×C4—2182no—
184C2×C4C22×D10911yescharacteristic
185C2×C4C22×D10911yescharacteristic
186C2×C4C22×D10911yescharacteristic
187C2×C4C22×D10911yescharacteristic
188C2×C4C22×D10911yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—1092no—
195C22—4364no—
196C22—2181no—
197C22—2181no—
198C22—2181no—
199C22—2181no—
200C22—2181no—
201C22#1318202912yes—
202C22C23×D10911yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—2181no—
209C4—2181no—
210C4—2181no—
211C4—2181no—
212C4—2181no—
213C4—2181no—
214C2—22no—
215C2—41no—
216C2—4361no—
217C2—2182no—
218C2#41×D10911yescharacteristic
219C2C2×#1318202911yescharacteristic
220C2#1681274411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D109
commutator, socleC22×C109C24
FittingC4×D4×C109C2
hypercenterC4×D4D109
hypocenterC109#551
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16812694C2semidirect
2. #16812693C2semidirect
3. #16812685C2semidirect
4. #16812682C2semidirect
5. #16812681C2semidirect
6. #16812680C2semidirect
7. #16812678C2semidirect
8. #16812677C2semidirect
10. C4×C22⋊D109C2semidirect
11. #16812656C2semidirect
12. #16812655C2semidirect
13. C2×#13182006C2semidirect
14. C22⋊C4×D109C2semidirect
15. C4×D4×C109C2semidirect
17. C2×Dic218C22semidirect
23. C4⋊Dic109C22semidirect
24. #13182008C22semidirect
25. #13182008C22semidirect
26. #13182008C22semidirect
27. #13182008C22semidirect
28. #13182008C22semidirect
29. #13182008C22semidirect
32. C22⋊Dic109C22semidirect
33. C22⋊Dic109C22semidirect
42. C4×Dic109C22semidirect
43. C4×Dic109C22semidirect
46. C22×C4×C109C22semidirect
47. C4⋊C4×C109C22semidirect
49. C22⋊C4×C109C22semidirect
50. C42×C109C22semidirect
110. C109#551semidirect
122. C4×D4D109semidirect
136. C22×C4C2×D109semidirect
144. C4⋊C4C2×D109semidirect
158. C22⋊C4C2×D109semidirect
161. C42C2×D109semidirect