Finite Group Databasebeta

← #26012074

Subgroups — #26012074

Order 11072.

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#19149674C211yesmaximal, characteristic, complemented
2#19149673C211yesmaximal, characteristic, complemented
3#19149667C211yesmaximal, characteristic, complemented
4#19149665C211yesmaximal, characteristic, complemented
5#19149664C211yesmaximal, characteristic, complemented
6#19149662C211yesmaximal, characteristic, complemented
7#19149656C211yesmaximal, characteristic, complemented
8#19149653C211yesmaximal, characteristic, complemented
9#19149652C211yesmaximal, characteristic, complemented
10#19149651C211yesmaximal, characteristic, complemented
11#19149649C211yesmaximal, characteristic, complemented
12#19149647C211yesmaximal, characteristic, complemented
13C4×C22⋊D173C211yesmaximal, characteristic, complemented
14C2×#14583803C211yesmaximal, characteristic, complemented
15C4×D4×C173C211yesmaximal, characteristic, complemented
16C23×D173C2211yescharacteristic
17C2×Dic346C2211yescharacteristic, complemented
18C2×D692C2211yescharacteristic
19C2×D692C2211yescharacteristic
20C2×C22⋊D173C2211yescharacteristic
21C2×C22⋊D173C2211yescharacteristic
22C2×C22⋊D173C2211yescharacteristic
23C2×C22⋊D173C2211yescharacteristic, complemented
24C22×Dic173C2211yescharacteristic
25C2×C4×D173C2211yescharacteristic, complemented
26C4⋊Dic173C2211yescharacteristic, complemented
27#14583805C2211yescharacteristic, complemented
28#14583805C2211yescharacteristic, complemented
29#14583805C2211yescharacteristic, complemented
30#14583805C2211yescharacteristic, complemented
31C22⋊Dic173C2211yescharacteristic
32C22⋊Dic173C2211yescharacteristic, complemented
33#14583803C2211yescharacteristic
34#14583803C2211yescharacteristic
35#14583803C2211yescharacteristic
36#14583803C2211yescharacteristic
37#14583803C2211yescharacteristic
38#14583803C2211yescharacteristic
39#14583803C2211yescharacteristic
40#14583803C2211yescharacteristic
41#14583803C2211yescharacteristic, complemented
42#14583803C2211yescharacteristic, complemented
43C4×Dic173C2211yescharacteristic, complemented
44C2×D4×C173C2211yescharacteristic
45C22×C4×C173C2211yescharacteristic
46C22×C4×C173C2211yescharacteristic, complemented
47C4⋊C4×C173C2211yescharacteristic, complemented
48C22⋊C4×C173C2211yescharacteristic
49C22⋊C4×C173C2211yescharacteristic, complemented
50C42×C173C2211yescharacteristic, complemented
51C22×D173—22no—
52C22×D173—41no—
53C22×D173—41no—
54C22×D173C2311yescharacteristic
55C22×D173C2311yescharacteristic
56C22×D173C2311yescharacteristic
57Dic346—41no—
58D692—41no—
59D692—41no—
60C22⋊D173—22no—
61C22⋊D173—41no—
62C22⋊D173—41no—
63C22⋊D173—41no—
64C2×Dic173—41no—
65C2×Dic173C2311yescharacteristic
66C2×Dic173C2311yescharacteristic
67C2×Dic173C2311yescharacteristic
68C2×Dic173C2311yescharacteristic
69C2×Dic173C2311yescharacteristic
70C4×D173—41no—
71C23×C173C2311yescharacteristic
72C23×C173C2311yescharacteristic
73D4×C173—22no—
74C2×C4×C173—41no—
75C2×C4×C173—41no—
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×C173—21no—
85C22×C173—21no—
86C22×C173#4112yes—
87C22×C173C2411yescharacteristic
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—21no—
97C2×D173—44no—
98C4×C173—21no—
99C4×C173—21no—
100C4×C173—21no—
101C4×C173—21no—
102C4×C173—21no—
103Dic173—21no—
104Dic173—21no—
105Dic173—21no—
106Dic173—21no—
107Dic173—21no—
108C2×C173—22no—
109C2×C173—41no—
110C2×C173C2×#4111yescharacteristic
111C2×C173H(5,𝔽2)11yescharacteristic
112C2×C173H(5,𝔽2)11yescharacteristic
113D173—41no—
114D173—41no—
115D173—41no—
116C173#53811yescharacteristic, complemented, Sylow
117#538—1731nomaximal, Sylow
118#126—1731no—
119#126—1731no—
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×D4D17311yescharacteristic, complemented
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×D4C2×D17311yescharacteristic
142C22×C4—1731no—
143C22×C4—1731no—
144C22×C4C2×D17311yescharacteristic
145C22×C4C2×D17311yescharacteristic, complemented
146C4⋊C4—1731no—
147C4⋊C4—1731no—
148C4⋊C4—1731no—
149C4⋊C4—1731no—
150C4⋊C4—1731no—
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⋊C4—1731no—
164C22⋊C4C2×D17311yescharacteristic
165C22⋊C4C2×D17311yescharacteristic, complemented
166C42—1731no—
167C42C2×D17311yescharacteristic, complemented
168C23—3462no—
169C23—1731no—
170C23—1731no—
171C23—1731no—
172C23—6921no—
173C23—6921no—
174C23C22×D17311yescharacteristic
175C23C22×D17311yescharacteristic
176Q8—6921no—
177D4—22no—
178D4—3462no—
179D4—6921no—
180D4—6921no—
181D4—6921no—
182D4—6921no—
183D4—6921no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1731no—
187C2×C4—1731no—
188C2×C4—1731no—
189C2×C4—1731no—
190C2×C4—1731no—
191C2×C4—6921no—
192C2×C4—6921no—
193C2×C4C22×D17311yescharacteristic
194C2×C4C22×D17311yescharacteristic
195C2×C4C22×D17311yescharacteristic
196C2×C4C22×D17311yescharacteristic
197C2×C4C22×D17311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—3461no—
204C22—3461no—
205C22—3461no—
206C22—3461no—
207C22—3461no—
208C22—3461no—
209C22—3461no—
210C22—3461no—
211C22—3461no—
212C22—6924no—
213C22#1458382612yes—
214C22C23×D17311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—3461no—
221C4—3461no—
222C4—3461no—
223C4—3461no—
224C4—3461no—
225C2—22no—
226C2—41no—
227C2—6921no—
228C2—6921no—
229C2—6921no—
230C2C2×#1458382611yescharacteristic
231C2#1914972411yescharacteristic
232C2#1914972511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutator, socle, cosocleC22×C173C24
FittingC4×D4×C173C2
hypercenterC4×D4D173
hypocenterC173#538
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #19149674C2semidirect
2. #19149673C2semidirect
3. #19149667C2semidirect
4. #19149665C2semidirect
5. #19149664C2semidirect
6. #19149662C2semidirect
7. #19149656C2semidirect
8. #19149653C2semidirect
9. #19149652C2semidirect
10. #19149651C2semidirect
11. #19149649C2semidirect
12. #19149647C2semidirect
13. C4×C22⋊D173C2semidirect
14. C2×#14583803C2semidirect
15. C4×D4×C173C2semidirect
17. C2×Dic346C22semidirect
23. C2×C22⋊D173C22semidirect
25. C2×C4×D173C22semidirect
26. C4⋊Dic173C22semidirect
27. #14583805C22semidirect
28. #14583805C22semidirect
29. #14583805C22semidirect
30. #14583805C22semidirect
32. C22⋊Dic173C22semidirect
41. #14583803C22semidirect
42. #14583803C22semidirect
43. C4×Dic173C22semidirect
46. C22×C4×C173C22semidirect
47. C4⋊C4×C173C22semidirect
49. C22⋊C4×C173C22semidirect
50. C42×C173C22semidirect
116. C173#538semidirect
131. C4×D4D173semidirect
145. C22×C4C2×D173semidirect
151. C4⋊C4C2×D173semidirect
165. C22⋊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
#191496732
#191496672
#191496652
#191496642
#191496622
#191496562
#191496532
#191496522
#191496512
#191496492
#191496472
C4×C22⋊D1732
C2×#145838032
C4×D4×C1732
#538173