Finite Group Databasebeta

← #37527029

Subgroups — #37527029

Order 22976.

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#26040010C211yesmaximal, characteristic, complemented
2#26040008C211yesmaximal, characteristic, complemented
3#26040001C211yesmaximal, characteristic, complemented
4#26040001C211yesmaximal, characteristic, complemented
5#26040000C211yesmaximal, characteristic, complemented
6#26039995C211yesmaximal, characteristic, complemented
7#26039989C211yesmaximal, characteristic, complemented
8#26039988C211yesmaximal, characteristic, complemented
9#26039986C211yesmaximal, characteristic, complemented
10#26039985C211yesmaximal, characteristic, complemented
11#26039983C211yesmaximal, characteristic, complemented
12#26039977C211yesmaximal, characteristic, complemented
13C4×C22⋊D359C211yesmaximal, characteristic, complemented
14C22⋊C4×D359C211yesmaximal, characteristic, complemented
15#123×C359C211yesmaximal, characteristic, complemented
16C23×D359C2211yescharacteristic
17C2×Dic718C2211yescharacteristic, complemented
18C2×D1436C2211yescharacteristic
19C2×D1436C2211yescharacteristic
20C2×C22⋊D359C2211yescharacteristic
21C2×C22⋊D359C2211yescharacteristic
22C2×C22⋊D359C2211yescharacteristic
23C2×C22⋊D359C2211yescharacteristic, complemented
24C2×C4×D359C2211yescharacteristic
25C2×C4×D359C2211yescharacteristic
26C2×C4×D359C2211yescharacteristic, complemented
27C4⋊Dic359C2211yescharacteristic, complemented
28C4⋊Dic359C2211yescharacteristic, complemented
29Dic359⋊C4C2211yescharacteristic, complemented
30Dic359⋊C4C2211yescharacteristic, complemented
31C22⋊Dic359C2211yescharacteristic
32C22⋊Dic359C2211yescharacteristic
33C22⋊Dic359C2211yescharacteristic, complemented
34(C2×D359)⋊C4C2211yescharacteristic
35(C2×D359)⋊C4C2211yescharacteristic
36(C2×D359)⋊C4C2211yescharacteristic
37(C2×D359)⋊C4C2211yescharacteristic
38(C2×D359)⋊C4C2211yescharacteristic
39(C2×D359)⋊C4C2211yescharacteristic
40(C2×D359)⋊C4C2211yescharacteristic, complemented
41(C2×D359)⋊C4C2211yescharacteristic, complemented
42C4×Dic359C2211yescharacteristic, complemented
43C4×Dic359C2211yescharacteristic, complemented
44C2×D4×C359C2211yescharacteristic
45C22×C4×C359C2211yescharacteristic, complemented
46C4⋊C4×C359C2211yescharacteristic, complemented
47C4⋊C4×C359C2211yescharacteristic, complemented
48C22⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C22⋊C4×C359C2211yescharacteristic, complemented
51C22×D359—22no—
52C22×D359—41no—
53C22×D359—41no—
54C22×D359C2311yescharacteristic
55C22×D359C2311yescharacteristic
56C22×D359C2311yescharacteristic
57Dic718—41no—
58D1436—22no—
59D1436—41no—
60C22⋊D359—22no—
61C22⋊D359—41no—
62C22⋊D359—41no—
63C22⋊D359—41no—
64C2×Dic359C2311yescharacteristic
65C2×Dic359C2311yescharacteristic
66C2×Dic359C2311yescharacteristic
67C2×Dic359C2311yescharacteristic
68C2×Dic359C2311yescharacteristic
69C4×D359—41no—
70C4×D359—41no—
71C4×D359—41no—
72C23×C359C2311yescharacteristic
73C23×C359C2311yescharacteristic
74D4×C359—41no—
75C2×C4×C359—41no—
76C2×C4×C359C2311yescharacteristic
77C2×C4×C359C2311yescharacteristic
78C2×C4×C359C2311yescharacteristic
79C2×C4×C359C2311yescharacteristic
80C2×C4×C359C2311yescharacteristic
81C22×C359—21no—
82C22×C359—21no—
83C22×C359—21no—
84C22×C359—21no—
85C22×C359—21no—
86C22×C359—21no—
87C22×C359C2411yescharacteristic
88C2×D359—21no—
89C2×D359—21no—
90C2×D359—21no—
91C2×D359—21no—
92C2×D359—21no—
93C2×D359—21no—
94C2×D359—21no—
95C2×D359—21no—
96C2×D359—44no—
97C2×D359#4112yes—
98C4×C359—21no—
99C4×C359—21no—
100C4×C359—21no—
101C4×C359—21no—
102C4×C359—21no—
103Dic359—21no—
104Dic359—21no—
105Dic359—21no—
106Dic359—21no—
107Dic359—21no—
108C2×C359—41no—
109C2×C359—41no—
110C2×C359C2×#4111yescharacteristic
111C2×C359H(5,𝔽2)11yescharacteristic
112C2×C359H(5,𝔽2)11yescharacteristic
113D359—22no—
114D359—41no—
115D359—41no—
116C359#53811yescharacteristic, complemented, Sylow
117#538—3591nomaximal, Sylow
118#126—3591no—
119#126—3591no—
120#124—3591no—
121#124—3591no—
122#123—3591no—
123#123D35911yescharacteristic, complemented
124C22⋊Q8—3591no—
125#121—3591no—
126#121—3591no—
127#121—3591no—
128#120—3591no—
129#120—3591no—
130C4×D4—3591no—
131C4×D4—3591no—
132C2×C22⋊C4—3591no—
133C24—3591no—
134C2×Q8—3591no—
135C2×D4—3591no—
136C2×D4—3591no—
137C2×D4—3591no—
138C2×D4—3591no—
139C2×D4—3591no—
140C2×D4—3591no—
141C2×D4C2×D35911yescharacteristic
142C22×C4—3591no—
143C22×C4—3591no—
144C22×C4—3591no—
145C22×C4C2×D35911yescharacteristic, complemented
146C4⋊C4—3591no—
147C4⋊C4—3591no—
148C4⋊C4—3591no—
149C4⋊C4—3591no—
150C4⋊C4C2×D35911yescharacteristic, complemented
151C4⋊C4C2×D35911yescharacteristic, complemented
152C22⋊C4—3591no—
153C22⋊C4—3591no—
154C22⋊C4—3591no—
155C22⋊C4—3591no—
156C22⋊C4—3591no—
157C22⋊C4—3591no—
158C22⋊C4—3591no—
159C22⋊C4—3591no—
160C22⋊C4—3591no—
161C22⋊C4—3591no—
162C22⋊C4—3591no—
163C22⋊C4C2×D35911yescharacteristic
164C22⋊C4C2×D35911yescharacteristic
165C22⋊C4C2×D35911yescharacteristic, complemented
166C42—3591no—
167C42—3591no—
168C23—3591no—
169C23—3591no—
170C23—3591no—
171C23—14361no—
172C23—14361no—
173C23—7182no—
174C23C22×D35911yescharacteristic
175C23C22×D35911yescharacteristic
176Q8—14361no—
177D4—41no—
178D4—14361no—
179D4—14361no—
180D4—14361no—
181D4—14361no—
182D4—7182no—
183D4—7182no—
184C2×C4—41no—
185C2×C4—3591no—
186C2×C4—3591no—
187C2×C4—3591no—
188C2×C4—3591no—
189C2×C4—3591no—
190C2×C4—14361no—
191C2×C4—14361no—
192C2×C4—14361no—
193C2×C4C22×D35911yescharacteristic
194C2×C4C22×D35911yescharacteristic
195C2×C4C22×D35911yescharacteristic
196C2×C4C22×D35911yescharacteristic
197C2×C4C22×D35911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—3592no—
205C22—14364no—
206C22—7181no—
207C22—7181no—
208C22—7181no—
209C22—7181no—
210C22—7181no—
211C22—7181no—
212C22—7181no—
213C22—7181no—
214C22C23×D35911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—7181no—
221C4—7181no—
222C4—7181no—
223C4—7181no—
224C4—7181no—
225C2—41no—
226C2—41no—
227C2—14361no—
228C2—14361no—
229C2—7182no—
230C2#41×D35911yescharacteristic
231C2#2604006011yescharacteristic
232C2#2604006111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#123×C359C2
hypercenter#123D359
hypocenterC359#538
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #26040010C2semidirect
2. #26040008C2semidirect
3. #26040001C2semidirect
4. #26040001C2semidirect
5. #26040000C2semidirect
6. #26039995C2semidirect
7. #26039989C2semidirect
8. #26039988C2semidirect
9. #26039986C2semidirect
10. #26039985C2semidirect
11. #26039983C2semidirect
12. #26039977C2semidirect
13. C4×C22⋊D359C2semidirect
14. C22⋊C4×D359C2semidirect
15. #123×C359C2semidirect
17. C2×Dic718C22semidirect
23. C2×C22⋊D359C22semidirect
26. C2×C4×D359C22semidirect
27. C4⋊Dic359C22semidirect
28. C4⋊Dic359C22semidirect
29. Dic359⋊C4C22semidirect
30. Dic359⋊C4C22semidirect
33. C22⋊Dic359C22semidirect
40. (C2×D359)⋊C4C22semidirect
41. (C2×D359)⋊C4C22semidirect
42. C4×Dic359C22semidirect
43. C4×Dic359C22semidirect
45. C22×C4×C359C22semidirect
46. C4⋊C4×C359C22semidirect
47. C4⋊C4×C359C22semidirect
50. C22⋊C4×C359C22semidirect
116. C359#538semidirect
123. #123D359semidirect
145. C22×C4C2×D359semidirect
150. C4⋊C4C2×D359semidirect
151. C4⋊C4C2×D359semidirect
165. C22⋊C4C2×D359semidirect

Maximal subgroups

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

subgroupindex
#260400102
#260400082
#260400012
#260400002
#260399952
#260399892
#260399882
#260399862
#260399852
#260399832
#260399772
C4×C22⋊D3592
C22⋊C4×D3592
#123×C3592
#538359