Finite Group Databasebeta

← #37527122

Subgroups — #37527122

Order 22976.

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#26040010C211yesmaximal, characteristic, complemented
2#26040009C211yesmaximal, characteristic, complemented
3#26040001C211yesmaximal, characteristic, complemented
4#26039998C211yesmaximal, characteristic, complemented
5#26039997C211yesmaximal, characteristic, complemented
6#26039996C211yesmaximal, characteristic, complemented
7#26039994C211yesmaximal, characteristic, complemented
8#26039993C211yesmaximal, characteristic, complemented
9#26039983C211yesmaximal, characteristic
10C4×C22⋊D359C211yesmaximal, characteristic, complemented
11#26039972C211yesmaximal, characteristic, complemented
12#26039971C211yesmaximal, characteristic, complemented
13C2×(C2×D359)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D359C211yesmaximal, characteristic, complemented
15C4×D4×C359C211yesmaximal, characteristic, complemented
16C23×D359C2211yescharacteristic
17C2×Dic718C2211yescharacteristic, complemented
18C2×C22⋊D359C2211yescharacteristic
19C2×C22⋊D359C2211yescharacteristic
20C22×Dic359C2211yescharacteristic
21C2×C4×D359C2211yescharacteristic
22C2×C4×D359C2211yescharacteristic
23C4⋊Dic359C2211yescharacteristic, complemented
24Dic359⋊C4C2211yescharacteristic, complemented
25Dic359⋊C4C2211yescharacteristic, complemented
26Dic359⋊C4C2211yescharacteristic, complemented
27Dic359⋊C4C2211yescharacteristic, complemented
28Dic359⋊C4C2211yescharacteristic, complemented
29Dic359⋊C4C2211yescharacteristic, complemented
30C22⋊Dic359C2211yescharacteristic
31C22⋊Dic359C2211yescharacteristic
32C22⋊Dic359C2211yescharacteristic, complemented
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
41(C2×D359)⋊C4C2211yescharacteristic
42C4×Dic359C2211yescharacteristic, complemented
43C4×Dic359C2211yescharacteristic, complemented
44C2×D4×C359C2211yescharacteristic
45C22×C4×C359C2211yescharacteristic
46C22×C4×C359C2211yescharacteristic, complemented
47C4⋊C4×C359C2211yescharacteristic, complemented
48C22⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic, complemented
50C42×C359C2211yescharacteristic, complemented
51C22×D359—22no—
52C22×D359—22no—
53C22×D359—41no—
54C22×D359C2311yescharacteristic
55C22×D359C2311yescharacteristic
56Dic718—41no—
57C22⋊D359—22no—
58C22⋊D359—41no—
59C2×Dic359—22no—
60C2×Dic359C2311yescharacteristic
61C2×Dic359C2311yescharacteristic
62C2×Dic359C2311yescharacteristic
63C2×Dic359C2311yescharacteristic
64C2×Dic359C2311yescharacteristic
65C2×Dic359C2311yescharacteristic
66C4×D359—22no—
67C4×D359—41no—
68C23×C359C2311yescharacteristic
69C23×C359C2311yescharacteristic
70D4×C359—22no—
71C2×C4×C359—41no—
72C2×C4×C359—41no—
73C2×C4×C359C2311yescharacteristic
74C2×C4×C359C2311yescharacteristic
75C2×C4×C359C2311yescharacteristic
76C2×C4×C359C2311yescharacteristic
77C2×C4×C359C2311yescharacteristic
78C22×C359—21no—
79C22×C359—21no—
80C22×C359—21no—
81C22×C359—21no—
82C22×C359—21no—
83C22×C359#4112yes—
84C22×C359C2411yescharacteristic
85C2×D359—21no—
86C2×D359—21no—
87C2×D359—21no—
88C2×D359—21no—
89C2×D359—21no—
90C2×D359—44no—
91C2×D359#4112yes—
92C4×C359—21no—
93C4×C359—21no—
94C4×C359—21no—
95C4×C359—21no—
96C4×C359—21no—
97Dic359—21no—
98Dic359—21no—
99Dic359—21no—
100Dic359—21no—
101Dic359—21no—
102Dic359—21no—
103C2×C359—22no—
104C2×C359—41no—
105C2×C359C2×#4111yescharacteristic
106C2×C359C2×#4111yescharacteristic
107C2×C359H(5,𝔽2)11yescharacteristic
108D359—22no—
109D359—41no—
110C359#55111yescharacteristic, complemented, Sylow
111#551—3591nomaximal, Sylow
112#126—3591no—
113#126—3591no—
114#124—3591no—
115#123—3591no—
116#123—3591no—
117#123—3591no—
118C22⋊Q8—3591no—
119C22⋊Q8—3591no—
120#120—3591no—
121C4×D4—3591no—
122C4×D4D35911yescharacteristic, complemented
123#117—3591no—
124#117—3591no—
125C2×C22⋊C4—3591no—
126C2×C22⋊C4—3591no—
127C24—3591no—
128C2×Q8—3591no—
129C2×D4—3591no—
130C2×D4—3591no—
131C2×D4C2×D35911yescharacteristic
132C22×C4—3591no—
133C22×C4—3591no—
134C22×C4—3591no—
135C22×C4C2×D35911yescharacteristic
136C22×C4C2×D35911yescharacteristic, complemented
137C4⋊C4—3591no—
138C4⋊C4—3591no—
139C4⋊C4—3591no—
140C4⋊C4—3591no—
141C4⋊C4—3591no—
142C4⋊C4—3591no—
143C4⋊C4—3591no—
144C4⋊C4C2×D35911yescharacteristic, complemented
145C22⋊C4—3591no—
146C22⋊C4—3591no—
147C22⋊C4—3591no—
148C22⋊C4—3591no—
149C22⋊C4—3591no—
150C22⋊C4—3591no—
151C22⋊C4—3591no—
152C22⋊C4—3591no—
153C22⋊C4—3591no—
154C22⋊C4—3591no—
155C22⋊C4—3591no—
156C22⋊C4—3591no—
157C22⋊C4C2×D35911yescharacteristic
158C22⋊C4C2×D35911yescharacteristic, complemented
159C42—3591no—
160C42—3591no—
161C42C2×D35911yescharacteristic, complemented
162C23—3591no—
163C23—3591no—
164C23—14361no—
165C23—7182no—
166C23—7182no—
167C23C22×D35911yescharacteristic
168C23C22×D35911yescharacteristic
169Q8—14361no—
170D4—22no—
171D4—14361no—
172D4—7182no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3591no—
176C2×C4—3591no—
177C2×C4—3591no—
178C2×C4—3591no—
179C2×C4—3591no—
180C2×C4—3591no—
181C2×C4—14361no—
182C2×C4—7182no—
183C2×C4—7182no—
184C2×C4C22×D35911yescharacteristic
185C2×C4C22×D35911yescharacteristic
186C2×C4C22×D35911yescharacteristic
187C2×C4C22×D35911yescharacteristic
188C2×C4C22×D35911yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—3592no—
195C22—14364no—
196C22—7181no—
197C22—7181no—
198C22—7181no—
199C22—7181no—
200C22—7181no—
201C22#1915334112yes—
202C22C23×D35911yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—7181no—
209C4—7181no—
210C4—7181no—
211C4—7181no—
212C4—7181no—
213C4—7181no—
214C2—22no—
215C2—41no—
216C2—14361no—
217C2—7182no—
218C2#41×D35911yescharacteristic
219C2C2×#1915334111yescharacteristic
220C2#2604006011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
FittingC4×D4×C359C2
prime radical#26039983C2
hypercenterC4×D4D359
hypocenterC359#551
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26040010C2semidirect
2. #26040009C2semidirect
3. #26040001C2semidirect
4. #26039998C2semidirect
5. #26039997C2semidirect
6. #26039996C2semidirect
7. #26039994C2semidirect
8. #26039993C2semidirect
10. C4×C22⋊D359C2semidirect
11. #26039972C2semidirect
12. #26039971C2semidirect
13. C2×(C2×D359)⋊C4C2semidirect
14. C22⋊C4×D359C2semidirect
15. C4×D4×C359C2semidirect
17. C2×Dic718C22semidirect
23. C4⋊Dic359C22semidirect
24. Dic359⋊C4C22semidirect
25. Dic359⋊C4C22semidirect
26. Dic359⋊C4C22semidirect
27. Dic359⋊C4C22semidirect
28. Dic359⋊C4C22semidirect
29. Dic359⋊C4C22semidirect
32. C22⋊Dic359C22semidirect
33. C22⋊Dic359C22semidirect
42. C4×Dic359C22semidirect
43. C4×Dic359C22semidirect
46. C22×C4×C359C22semidirect
47. C4⋊C4×C359C22semidirect
49. C22⋊C4×C359C22semidirect
50. C42×C359C22semidirect
110. C359#551semidirect
122. C4×D4D359semidirect
136. C22×C4C2×D359semidirect
144. C4⋊C4C2×D359semidirect
158. C22⋊C4C2×D359semidirect
161. C42C2×D359semidirect

Maximal subgroups

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

subgroupindex
#260400102
#260400092
#260400012
#260399982
#260399972
#260399962
#260399942
#260399932
#260399832
C4×C22⋊D3592
#260399722
#260399712
C2×(C2×D359)⋊C42
C22⋊C4×D3592
C4×D4×C3592
#551359