Finite Group Databasebeta

← #20295609

Subgroups — #20295609

Order 6976.

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

normal subgroups only

This group has 250 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#16812694C211yesmaximal, characteristic, complemented
2#16812693C211yesmaximal, characteristic, complemented
3#16812687C211yesmaximal, characteristic, complemented
4#16812685C211yesmaximal, characteristic, complemented
5#16812684C211yesmaximal, characteristic, complemented
6#16812682C211yesmaximal, characteristic, complemented
7#16812676C211yesmaximal, characteristic, complemented
8#16812673C211yesmaximal, characteristic, complemented
9#16812672C211yesmaximal, characteristic, complemented
10#16812671C211yesmaximal, characteristic, complemented
11#16812669C211yesmaximal, characteristic, complemented
12#16812667C211yesmaximal, characteristic, complemented
13C4×C22⋊D109C211yesmaximal, characteristic, complemented
14C2×#13182006C211yesmaximal, characteristic, complemented
15C4×D4×C109C211yesmaximal, characteristic, complemented
16C23×D109C2211yescharacteristic
17C2×Dic218C2211yescharacteristic, complemented
18C2×D436C2211yescharacteristic
19C2×D436C2211yescharacteristic
20C2×C22⋊D109C2211yescharacteristic
21C2×C22⋊D109C2211yescharacteristic
22C2×C22⋊D109C2211yescharacteristic
23C2×C22⋊D109C2211yescharacteristic, complemented
24C22×Dic109C2211yescharacteristic
25C2×C4×D109C2211yescharacteristic, complemented
26C4⋊Dic109C2211yescharacteristic, complemented
27#13182008C2211yescharacteristic, complemented
28#13182008C2211yescharacteristic, complemented
29#13182008C2211yescharacteristic, complemented
30#13182008C2211yescharacteristic, complemented
31C22⋊Dic109C2211yescharacteristic
32C22⋊Dic109C2211yescharacteristic, complemented
33#13182006C2211yescharacteristic
34#13182006C2211yescharacteristic
35#13182006C2211yescharacteristic
36#13182006C2211yescharacteristic
37#13182006C2211yescharacteristic
38#13182006C2211yescharacteristic
39#13182006C2211yescharacteristic
40#13182006C2211yescharacteristic
41#13182006C2211yescharacteristic, complemented
42#13182006C2211yescharacteristic, 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—41no—
55C22×D109—41no—
56C22×D109C2311yescharacteristic
57C22×D109C2311yescharacteristic
58C22×D109C2311yescharacteristic
59D4×C109—22no—
60C2×C4×C109—41no—
61C2×C4×C109—41no—
62C2×C4×C109C2311yescharacteristic
63C2×C4×C109C2311yescharacteristic
64C2×C4×C109C2311yescharacteristic
65C2×C4×C109C2311yescharacteristic
66C2×C4×C109C2311yescharacteristic
67C22⋊D109—22no—
68C22⋊D109—41no—
69C22⋊D109—41no—
70C22⋊D109—41no—
71C2×Dic109—41no—
72C2×Dic109C2311yescharacteristic
73C2×Dic109C2311yescharacteristic
74C2×Dic109C2311yescharacteristic
75C2×Dic109C2311yescharacteristic
76C2×Dic109C2311yescharacteristic
77D436—41no—
78D436—41no—
79C4×D109—41no—
80Dic218—41no—
81C22×C109—21no—
82C22×C109—21no—
83C22×C109—21no—
84C22×C109—21no—
85C22×C109—21no—
86C22×C109#4112yes—
87C22×C109C2411yescharacteristic
88C2×D109—21no—
89C2×D109—21no—
90C2×D109—21no—
91C2×D109—21no—
92C2×D109—21no—
93C2×D109—21no—
94C2×D109—21no—
95C2×D109—21no—
96C2×D109—21no—
97C2×D109—44no—
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—21no—
101C4×C109—21no—
102C4×C109—21no—
103Dic109—21no—
104Dic109—21no—
105Dic109—21no—
106Dic109—21no—
107Dic109—21no—
108C2×C109—22no—
109C2×C109—41no—
110C2×C109C2×#4111yescharacteristic
111C2×C109H(5,𝔽2)11yescharacteristic
112C2×C109H(5,𝔽2)11yescharacteristic
113D109—41no—
114D109—41no—
115D109—41no—
116C109#53811yescharacteristic, complemented, Sylow
117#538—1091nomaximal, Sylow
118#126—1091no—
119#126—1091no—
120#124—1091no—
121#124—1091no—
122#123—1091no—
123#123—1091no—
124C22⋊Q8—1091no—
125#121—1091no—
126#121—1091no—
127#121—1091no—
128#120—1091no—
129#120—1091no—
130C4×D4—1091no—
131C4×D4D10911yescharacteristic, complemented
132C2×C22⋊C4—1091no—
133C24—1091no—
134C2×Q8—1091no—
135C2×D4—1091no—
136C2×D4—1091no—
137C2×D4—1091no—
138C2×D4—1091no—
139C2×D4—1091no—
140C2×D4—1091no—
141C2×D4C2×D10911yescharacteristic
142C22×C4—1091no—
143C22×C4—1091no—
144C22×C4C2×D10911yescharacteristic
145C22×C4C2×D10911yescharacteristic, complemented
146C4⋊C4—1091no—
147C4⋊C4—1091no—
148C4⋊C4—1091no—
149C4⋊C4—1091no—
150C4⋊C4—1091no—
151C4⋊C4C2×D10911yescharacteristic, complemented
152C22⋊C4—1091no—
153C22⋊C4—1091no—
154C22⋊C4—1091no—
155C22⋊C4—1091no—
156C22⋊C4—1091no—
157C22⋊C4—1091no—
158C22⋊C4—1091no—
159C22⋊C4—1091no—
160C22⋊C4—1091no—
161C22⋊C4—1091no—
162C22⋊C4—1091no—
163C22⋊C4—1091no—
164C22⋊C4C2×D10911yescharacteristic
165C22⋊C4C2×D10911yescharacteristic, complemented
166C42—1091no—
167C42C2×D10911yescharacteristic, complemented
168C23—1091no—
169C23—1091no—
170C23—1091no—
171C23—4361no—
172C23—4361no—
173C23—2182no—
174C23C22×D10911yescharacteristic
175C23C22×D10911yescharacteristic
176Q8—4361no—
177D4—22no—
178D4—4361no—
179D4—4361no—
180D4—4361no—
181D4—4361no—
182D4—4361no—
183D4—2182no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1091no—
187C2×C4—1091no—
188C2×C4—1091no—
189C2×C4—1091no—
190C2×C4—1091no—
191C2×C4—4361no—
192C2×C4—4361no—
193C2×C4C22×D10911yescharacteristic
194C2×C4C22×D10911yescharacteristic
195C2×C4C22×D10911yescharacteristic
196C2×C4C22×D10911yescharacteristic
197C2×C4C22×D10911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—4364no—
204C22—2181no—
205C22—2181no—
206C22—2181no—
207C22—2181no—
208C22—2181no—
209C22—2181no—
210C22—2181no—
211C22—2181no—
212C22—2181no—
213C22#1318202912yes—
214C22C23×D10911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—2181no—
221C4—2181no—
222C4—2181no—
223C4—2181no—
224C4—2181no—
225C2—22no—
226C2—41no—
227C2—4361no—
228C2—4361no—
229C2—4361no—
230C2C2×#1318202911yescharacteristic
231C2#1681274411yescharacteristic
232C2#1681274511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D109
commutator, socleC22×C109C24
FittingC4×D4×C109C2
hypercenterC4×D4D109
hypocenterC109#538
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. #16812687C2semidirect
4. #16812685C2semidirect
5. #16812684C2semidirect
6. #16812682C2semidirect
7. #16812676C2semidirect
8. #16812673C2semidirect
9. #16812672C2semidirect
10. #16812671C2semidirect
11. #16812669C2semidirect
12. #16812667C2semidirect
13. C4×C22⋊D109C2semidirect
14. C2×#13182006C2semidirect
15. C4×D4×C109C2semidirect
17. C2×Dic218C22semidirect
23. C2×C22⋊D109C22semidirect
25. C2×C4×D109C22semidirect
26. C4⋊Dic109C22semidirect
27. #13182008C22semidirect
28. #13182008C22semidirect
29. #13182008C22semidirect
30. #13182008C22semidirect
32. C22⋊Dic109C22semidirect
41. #13182006C22semidirect
42. #13182006C22semidirect
43. C4×Dic109C22semidirect
46. C22×C4×C109C22semidirect
47. C4⋊C4×C109C22semidirect
49. C22⋊C4×C109C22semidirect
50. C42×C109C22semidirect
116. C109#538semidirect
131. C4×D4D109semidirect
145. C22×C4C2×D109semidirect
151. C4⋊C4C2×D109semidirect
165. C22⋊C4C2×D109semidirect
167. C42C2×D109semidirect