Finite Group Databasebeta

← #26012080

Subgroups — #26012080

Order 11072.

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#19149674C211yesmaximal, characteristic, complemented
2#19149667C211yesmaximal, characteristic, complemented
3#19149665C211yesmaximal, characteristic, complemented
4#19149664C211yesmaximal, characteristic, complemented
5#19149661C211yesmaximal, characteristic, complemented
6#19149657C211yesmaximal, characteristic, complemented
7#19149654C211yesmaximal, characteristic, complemented
8#19149654C211yesmaximal, characteristic, complemented
9#19149652C211yesmaximal, characteristic, complemented
10#19149649C211yesmaximal, characteristic, complemented
11#19149649C211yesmaximal, characteristic, complemented
12C4×D692C211yesmaximal, characteristic, complemented
13#19149641C211yesmaximal, characteristic, complemented
14C22⋊C4×D173C211yesmaximal, characteristic, complemented
15#126×C173C211yesmaximal, characteristic, complemented
16C23×D173C2211yescharacteristic
17C2×Dic346C2211yescharacteristic, complemented
18C2×D692C2211yescharacteristic
19C2×D692C2211yescharacteristic
20C2×D692C2211yescharacteristic
21C2×D692C2211yescharacteristic
22C2×D692C2211yescharacteristic, complemented
23C2×C22⋊D173C2211yescharacteristic
24C2×C22⋊D173C2211yescharacteristic
25C2×C4×D173C2211yescharacteristic
26C2×C4×D173C2211yescharacteristic
27C2×C4×D173C2211yescharacteristic, complemented
28C2×C4×D173C2211yescharacteristic, complemented
29C4⋊Dic173C2211yescharacteristic, complemented
30#14583805C2211yescharacteristic, complemented
31#14583805C2211yescharacteristic, complemented
32C22⋊Dic173C2211yescharacteristic
33#14583803C2211yescharacteristic
34#14583803C2211yescharacteristic
35#14583803C2211yescharacteristic
36#14583803C2211yescharacteristic
37#14583803C2211yescharacteristic
38#14583803C2211yescharacteristic
39#14583803C2211yescharacteristic, complemented
40#14583803C2211yescharacteristic, complemented
41#14583803C2211yescharacteristic, complemented
42#14583803C2211yescharacteristic, complemented
43C4×Dic173C2211yescharacteristic, complemented
44C4⋊C4×C173C2211yescharacteristic, complemented
45C4⋊C4×C173C2211yescharacteristic, complemented
46C4⋊C4×C173C2211yescharacteristic, complemented
47C22⋊C4×C173C2211yescharacteristic
48C22⋊C4×C173C2211yescharacteristic
49C22⋊C4×C173C2211yescharacteristic
50C42×C173C2211yescharacteristic, complemented
51C22×D173—22no—
52C22×D173—41no—
53C22×D173—41no—
54C22×D173C2311yescharacteristic
55C22×D173C2311yescharacteristic
56C22×D173C2311yescharacteristic
57C22×D173C2311yescharacteristic
58Dic346—41no—
59D692—22no—
60D692—22no—
61D692—41no—
62D692—41no—
63D692—41no—
64C22⋊D173—41no—
65C22⋊D173—41no—
66C2×Dic173C2311yescharacteristic
67C2×Dic173C2311yescharacteristic
68C2×Dic173C2311yescharacteristic
69C2×Dic173C2311yescharacteristic
70C4×D173—41no—
71C4×D173—41no—
72C4×D173—41no—
73C4×D173—41no—
74C23×C173C2311yescharacteristic
75C2×C4×C173C2311yescharacteristic
76C2×C4×C173C2311yescharacteristic
77C2×C4×C173C2311yescharacteristic
78C2×C4×C173C2311yescharacteristic
79C2×C4×C173C2311yescharacteristic
80C2×C4×C173C2311yescharacteristic
81C22×C173—21no—
82C22×C173—21no—
83C22×C173—21no—
84C22×C173C2411yescharacteristic
85C2×D173—21no—
86C2×D173—21no—
87C2×D173—21no—
88C2×D173—21no—
89C2×D173—21no—
90C2×D173—21no—
91C2×D173—21no—
92C2×D173—21no—
93C2×D173—21no—
94C2×D173—21no—
95C2×D173—21no—
96C2×D173—44no—
97C2×D173#4112yes—
98C4×C173—21no—
99C4×C173—21no—
100C4×C173—21no—
101C4×C173—21no—
102C4×C173—21no—
103C4×C173—21no—
104Dic173—21no—
105Dic173—21no—
106Dic173—21no—
107Dic173—21no—
108C2×C173—41no—
109C2×C173C2×#4111yescharacteristic
110C2×C173H(5,𝔽2)11yescharacteristic
111C2×C173H(5,𝔽2)11yescharacteristic
112D173—22no—
113D173—41no—
114D173—41no—
115D173—41no—
116C173#53811yescharacteristic, complemented, Sylow
117#538—1731nomaximal, Sylow
118#126—1731no—
119#126D17311yescharacteristic, complemented
120#124—1731no—
121#124—1731no—
122#123—1731no—
123#123—1731no—
124C22⋊Q8—1731no—
125#121—1731no—
126#121—1731no—
127#121—1731no—
128#120—1731no—
129#120—1731no—
130C4×D4—1731no—
131C4×D4—1731no—
132C2×C22⋊C4—1731no—
133C24—1731no—
134C2×Q8—1731no—
135C2×D4—1731no—
136C2×D4—1731no—
137C2×D4—1731no—
138C2×D4—1731no—
139C2×D4—1731no—
140C2×D4—1731no—
141C2×D4—1731no—
142C22×C4—1731no—
143C22×C4—1731no—
144C22×C4—1731no—
145C22×C4—1731no—
146C4⋊C4—1731no—
147C4⋊C4—1731no—
148C4⋊C4—1731no—
149C4⋊C4C2×D17311yescharacteristic, complemented
150C4⋊C4C2×D17311yescharacteristic, complemented
151C4⋊C4C2×D17311yescharacteristic, complemented
152C22⋊C4—1731no—
153C22⋊C4—1731no—
154C22⋊C4—1731no—
155C22⋊C4—1731no—
156C22⋊C4—1731no—
157C22⋊C4—1731no—
158C22⋊C4—1731no—
159C22⋊C4—1731no—
160C22⋊C4—1731no—
161C22⋊C4—1731no—
162C22⋊C4—1731no—
163C22⋊C4C2×D17311yescharacteristic
164C22⋊C4C2×D17311yescharacteristic
165C22⋊C4C2×D17311yescharacteristic
166C42—1731no—
167C42C2×D17311yescharacteristic, complemented
168C23—3462no—
169C23—1731no—
170C23—1731no—
171C23—1731no—
172C23—1731no—
173C23—6921no—
174C23—6921no—
175C23C22×D17311yescharacteristic
176Q8—6921no—
177D4—3462no—
178D4—3462no—
179D4—6921no—
180D4—6921no—
181D4—6921no—
182D4—6921no—
183D4—6921no—
184C2×C4—1731no—
185C2×C4—1731no—
186C2×C4—1731no—
187C2×C4—1731no—
188C2×C4—6921no—
189C2×C4—6921no—
190C2×C4—6921no—
191C2×C4—6921no—
192C2×C4C22×D17311yescharacteristic
193C2×C4C22×D17311yescharacteristic
194C2×C4C22×D17311yescharacteristic
195C2×C4C22×D17311yescharacteristic
196C2×C4C22×D17311yescharacteristic
197C2×C4C22×D17311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—3461no—
202C22—3461no—
203C22—3461no—
204C22—3461no—
205C22—3461no—
206C22—3461no—
207C22—3461no—
208C22—3461no—
209C22—3461no—
210C22—3461no—
211C22—3461no—
212C22—1732no—
213C22—6924no—
214C22C23×D17311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—3461no—
222C4—3461no—
223C4—3461no—
224C4—3461no—
225C2—41no—
226C2—3462no—
227C2—6921no—
228C2—6921no—
229C2—6921no—
230C2#41×D17311yescharacteristic
231C2#1914972511yescharacteristic
232C2#1914972511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutator, socle, cosocleC22×C173C24
Fitting#126×C173C2
hypercenter#126D173
hypocenterC173#538
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #19149674C2semidirect
2. #19149667C2semidirect
3. #19149665C2semidirect
4. #19149664C2semidirect
5. #19149661C2semidirect
6. #19149657C2semidirect
7. #19149654C2semidirect
8. #19149654C2semidirect
9. #19149652C2semidirect
10. #19149649C2semidirect
11. #19149649C2semidirect
12. C4×D692C2semidirect
13. #19149641C2semidirect
14. C22⋊C4×D173C2semidirect
15. #126×C173C2semidirect
17. C2×Dic346C22semidirect
22. C2×D692C22semidirect
27. C2×C4×D173C22semidirect
28. C2×C4×D173C22semidirect
29. C4⋊Dic173C22semidirect
30. #14583805C22semidirect
31. #14583805C22semidirect
39. #14583803C22semidirect
40. #14583803C22semidirect
41. #14583803C22semidirect
42. #14583803C22semidirect
43. C4×Dic173C22semidirect
44. C4⋊C4×C173C22semidirect
45. C4⋊C4×C173C22semidirect
46. C4⋊C4×C173C22semidirect
50. C42×C173C22semidirect
116. C173#538semidirect
119. #126D173semidirect
149. C4⋊C4C2×D173semidirect
150. C4⋊C4C2×D173semidirect
151. C4⋊C4C2×D173semidirect
167. C42C2×D173semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191496742
#191496672
#191496652
#191496642
#191496612
#191496572
#191496542
#191496522
#191496492
C4×D6922
#191496412
C22⋊C4×D1732
#126×C1732
#538173