Finite Group Databasebeta

← #11763547

Subgroups — #11763547

Order 1088.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C17×#121C211yesmaximal, characteristic, complemented
2#10587626C211yesmaximal, characteristic, complemented
3#10587625C211yesmaximal, characteristic, complemented
4#10587625C211yesmaximal, characteristic, complemented
5#10587624C211yesmaximal, characteristic, complemented
6#10587623C211yesmaximal, characteristic, complemented
7#10587623C211yesmaximal, characteristic, complemented
8#10587616C211yesmaximal, characteristic, complemented
9#10587615C211yesmaximal, characteristic, complemented
10#10587584C211yesmaximal, characteristic, complemented
11#10587580C211yesmaximal, characteristic, complemented
12#10587572C211yesmaximal, characteristic, complemented
13#10587570C211yesmaximal, characteristic, complemented
14#10587568C211yesmaximal, characteristic, complemented
15#10587565C211yesmaximal, characteristic, complemented
16C23×D17C2211yescharacteristic
17C2×D4×C17C2211yescharacteristic
18C2×D4×C17C2211yescharacteristic
19C2×D4×C17C2211yescharacteristic, complemented
20C22×C4×C17C2211yescharacteristic, complemented
21C2×C22⋊D17C2211yescharacteristic
22C2×C22⋊D17C2211yescharacteristic
23C2×C22⋊D17C2211yescharacteristic
24C2×C22⋊D17C2211yescharacteristic
25C2×C22⋊D17C2211yescharacteristic
26C2×C22⋊D17C2211yescharacteristic, complemented
27C2×C22⋊D17C2211yescharacteristic, complemented
28C22×Dic17C2211yescharacteristic, complemented
29C2×D68C2211yescharacteristic
30C2×D68C2211yescharacteristic
31C2×C4×D17C2211yescharacteristic, complemented
32C4⋊C4×C17C2211yescharacteristic, complemented
33C22⋊C4×C17C2211yescharacteristic
34C22⋊C4×C17C2211yescharacteristic, complemented
35C22⋊Dic17C2211yescharacteristic
36C22⋊Dic17C2211yescharacteristic
37C22⋊Dic17C2211yescharacteristic, complemented
38#63227C2211yescharacteristic
39#63227C2211yescharacteristic
40#63227C2211yescharacteristic
41#63227C2211yescharacteristic
42#63227C2211yescharacteristic
43#63227C2211yescharacteristic
44#63227C2211yescharacteristic, complemented
45C4⋊Dic17C2211yescharacteristic, complemented
46C4⋊Dic17C2211yescharacteristic, complemented
47#63225C2211yescharacteristic, complemented
48#63225C2211yescharacteristic, complemented
49#63225C2211yescharacteristic, complemented
50C4×Dic17C2211yescharacteristic, complemented
51C23×C17C2311yescharacteristic
52C23×C17C2311yescharacteristic
53C23×C17C2311yescharacteristic
54C22×D17—41no—
55C22×D17—41no—
56C22×D17—41no—
57C22×D17C2311yescharacteristic
58C22×D17C2311yescharacteristic
59C22×D17C2311yescharacteristic
60D4×C17—41no—
61D4×C17—41no—
62D4×C17—41no—
63C2×C4×C17—41no—
64C2×C4×C17C2311yescharacteristic
65C2×C4×C17C2311yescharacteristic
66C2×C4×C17C2311yescharacteristic
67C2×C4×C17C2311yescharacteristic
68C22⋊D17—41no—
69C22⋊D17—41no—
70C22⋊D17—41no—
71C22⋊D17—41no—
72C22⋊D17—41no—
73C22⋊D17—41no—
74C22⋊D17—41no—
75C2×Dic17—41no—
76C2×Dic17C2311yescharacteristic
77C2×Dic17C2311yescharacteristic
78C2×Dic17C2311yescharacteristic
79C2×Dic17C2311yescharacteristic
80C2×Dic17C2311yescharacteristic
81D68—41no—
82D68—41no—
83C4×D17—41no—
84C22×C17—21no—
85C22×C17—21no—
86C22×C17—21no—
87C22×C17—21no—
88C22×C17—21no—
89C22×C17—21no—
90C22×C17—21no—
91C22×C17—21no—
92C22×C17—21no—
93C22×C17C2411yescharacteristic
94C2×D17—21no—
95C2×D17—21no—
96C2×D17—21no—
97C2×D17—21no—
98C2×D17—21no—
99C2×D17—21no—
100C2×D17—21no—
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—44no—
104C4×C17—21no—
105C4×C17—21no—
106C4×C17—21no—
107C4×C17—21no—
108Dic17—21no—
109Dic17—21no—
110Dic17—21no—
111Dic17—21no—
112Dic17—21no—
113#560—171nomaximal, Sylow
114C2×C17—41no—
115C2×C17—41no—
116C2×C17—41no—
117C2×C17H(5,𝔽2)11yescharacteristic
118C2×C17H(5,𝔽2)11yescharacteristic
119C2×C17H(5,𝔽2)11yescharacteristic
120D17—41no—
121D17—41no—
122D17—41no—
123#127—171no—
124#126—171no—
125#126—171no—
126#123—171no—
127#123—171no—
128#123—171no—
129#121—171no—
130#121—171no—
131#121—171no—
132#121—171no—
133#121—171no—
134#121D1711yescharacteristic, complemented
135#120—171no—
136#120—171no—
137#120—171no—
138C17#56011yescharacteristic, complemented, Sylow
139C24—171no—
140C2×D4—171no—
141C2×D4—171no—
142C2×D4—171no—
143C2×D4—171no—
144C2×D4—171no—
145C2×D4—171no—
146C2×D4—171no—
147C2×D4—171no—
148C2×D4—171no—
149C2×D4C2×D1711yescharacteristic
150C2×D4C2×D1711yescharacteristic
151C2×D4C2×D1711yescharacteristic, complemented
152C22×C4—171no—
153C22×C4—171no—
154C22×C4C2×D1711yescharacteristic, complemented
155C4⋊C4—171no—
156C4⋊C4—171no—
157C4⋊C4—171no—
158C4⋊C4—171no—
159C4⋊C4—171no—
160C4⋊C4C2×D1711yescharacteristic, complemented
161C22⋊C4—171no—
162C22⋊C4—171no—
163C22⋊C4—171no—
164C22⋊C4—171no—
165C22⋊C4—171no—
166C22⋊C4—171no—
167C22⋊C4—171no—
168C22⋊C4—171no—
169C22⋊C4—171no—
170C22⋊C4—171no—
171C22⋊C4C2×D1711yescharacteristic
172C22⋊C4C2×D1711yescharacteristic, complemented
173C42—171no—
174C23—171no—
175C23—171no—
176C23—171no—
177C23—681no—
178C23—681no—
179C23—681no—
180C23C22×D1711yescharacteristic
181C23C22×D1711yescharacteristic
182C23C22×D1711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—681no—
187D4—681no—
188D4—681no—
189D4—681no—
190D4—681no—
191D4—681no—
192D4—681no—
193D4—681no—
194D4—681no—
195C2×C4—41no—
196C2×C4—171no—
197C2×C4—171no—
198C2×C4—171no—
199C2×C4—171no—
200C2×C4—171no—
201C2×C4—681no—
202C2×C4—681no—
203C2×C4C22×D1711yescharacteristic
204C2×C4C22×D1711yescharacteristic
205C2×C4C22×D1711yescharacteristic
206C2×C4C22×D1711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—341no—
217C22—341no—
218C22—341no—
219C22—341no—
220C22—341no—
221C22—341no—
222C22—341no—
223C22—341no—
224C22—341no—
225C22—684no—
226C22C23×D1711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—341no—
232C4—341no—
233C4—341no—
234C4—341no—
235C4—341no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—681no—
240C2—681no—
241C2—681no—
242C2#1058769111yescharacteristic
243C2#1058769111yescharacteristic
244C2#1058769611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D17
commutator, socle, cosocleC22×C17C24
FittingC17×#121C2
hypercenter#121D17
hypocenterC17#560
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C17×#121C2semidirect
2. #10587626C2semidirect
3. #10587625C2semidirect
4. #10587625C2semidirect
5. #10587624C2semidirect
6. #10587623C2semidirect
7. #10587623C2semidirect
8. #10587616C2semidirect
9. #10587615C2semidirect
10. #10587584C2semidirect
11. #10587580C2semidirect
12. #10587572C2semidirect
13. #10587570C2semidirect
14. #10587568C2semidirect
15. #10587565C2semidirect
19. C2×D4×C17C22semidirect
20. C22×C4×C17C22semidirect
26. C2×C22⋊D17C22semidirect
27. C2×C22⋊D17C22semidirect
28. C22×Dic17C22semidirect
31. C2×C4×D17C22semidirect
32. C4⋊C4×C17C22semidirect
34. C22⋊C4×C17C22semidirect
37. C22⋊Dic17C22semidirect
44. #63227C22semidirect
45. C4⋊Dic17C22semidirect
46. C4⋊Dic17C22semidirect
47. #63225C22semidirect
48. #63225C22semidirect
49. #63225C22semidirect
50. C4×Dic17C22semidirect
134. #121D17semidirect
138. C17#560semidirect
151. C2×D4C2×D17semidirect
154. C22×C4C2×D17semidirect
160. C4⋊C4C2×D17semidirect
172. C22⋊C4C2×D17semidirect

Maximal subgroups

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

subgroupindex
C17×#1212
#105876262
#105876252
#105876242
#105876232
#105876162
#105876152
#105875842
#105875802
#105875722
#105875702
#105875682
#105875652
#56017