Finite Group Databasebeta

← #17002073

Subgroups — #17002073

Order 4352.

1202 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 355 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#14542555C211yesmaximal, characteristic
2#14531705C211yesmaximal, characteristic, complemented
3#14527345C216yesmaximal, complemented
4#14527280C216yesmaximal, complemented
5C17×#2982C211yesmaximal, characteristic, complemented
6C2×#10587694—21no—
7#11763481C414yescomplemented
8Q8×D68C414yescomplemented
9#11763471—24no—
10#11763390—23no—
11#11763359C2216yes—
12C2×Q8×Dic17—21no—
13#11762708—23no—
14#11762675C2213yes—
15C4×C4⋊Dic17C2213yes—
16#11762544C2214yes—
17#11762544C22112yes—
18C2×C4×Q8×C17C2211yescharacteristic
19C8×Q8×C17—24no—
20C17×#431C2216yes—
21C22×Q8×C17D411yescharacteristic
22#10587694—44no—
23#10587694—44no—
24C2×#63256—24no—
25C2×Q8×D17—24no—
26C2×#63252—26no—
27C4×Q8×C17C2×C414yes—
28C4×Q8×C17D414yes—
29C2×C4⋊C4×C17D413yes—
30C2×C42×C17C2313yes—
31Q8×Dic17—44no—
32#10587616—26no—
33#10587616C2314yes—
34C2×C4⋊Dic17—23no—
35C2×C4⋊Dic17—23no—
36C2×C4×Dic17—23no—
37#10587583—212no—
38#10587581—212no—
39#10587561—26no—
40#10587560C2×C416yes—
41C4×D68—26no—
42C4×D68C2×C4112yes—
43#10587555C2×C416yes—
44C17×C4⋊C8—26no—
45C17×C22⋊C8C2314yes—
46C4×C8×C17—26no—
47#10587502—23no—
48#10587502C2311yescharacteristic
49#10587502C2313yes—
50C2×Q8×C17C22⋊C414yes—
51C2×Q8×C17D814yes—
52C2×Q8×C17SD1614yes—
53C22×C4×C17C2×D413yes—
54C22×C4×C17C2×D413yes—
55C22×C4×C17C2411yescharacteristic
56C2×C22⋊D17—24no—
57C22×Dic17—21no—
58C22×Dic17—23no—
59#63256—416no—
60Q8×D17—416no—
61#63252—412no—
62#63252—412no—
63C2×D68—26no—
64C2×D68—26no—
65C2×D68C22×C414yes—
66C2×C4×D17—212no—
67C2×Dic34—26no—
68C2×C8×C17—24no—
69C4⋊C4×C17C22⋊C4112yes—
70C42×C17C22×C416yes—
71C42×C17C2×D416yes—
72#63227—212no—
73#63227—24no—
74C4⋊Dic17—26no—
75C4⋊Dic17—46no—
76C4⋊Dic17—46no—
77C4⋊Dic17C22×C414yes—
78C4×Dic17—46no—
79#17618—171nomaximal, Sylow
80C23×C17C22×D411yescharacteristic
81C22×D17—24no—
82Q8×C17#102116yes—
83C2×C4×C17—43no—
84C2×C4×C17—41no—
85C2×C4×C17C2×C22⋊C416yes—
86C2×C4×C17C2×C22⋊C416yes—
87C2×C4×C17C2×D816yes—
88C2×C4×C17C2×SD1616yes—
89C2×C4×C17C23×C411yescharacteristic
90C2×C4×C17C22×D411yescharacteristic
91C22⋊D17—44no—
92C22⋊D17—44no—
93C2×Dic17—22no—
94C2×Dic17—24no—
95C2×Dic17—41no—
96C2×Dic17—41no—
97C2×Dic17—43no—
98C2×Dic17—43no—
99C2×Dic17—43no—
100D68—44no—
101D68—412no—
102D68—86no—
103C4×D17—424no—
104Dic34—412no—
105C8×C17—44no—
106#3497—171no—
107#2982D1711yescharacteristic, complemented
108#2351—171no—
109#1517—176no—
110#1502—176no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17C22×C22⋊C411yescharacteristic
114C22×C17C22×D811yescharacteristic
115C22×C17C22×SD1611yescharacteristic
116C2×D17—44no—
117C2×D17—44no—
118C2×D17—44no—
119C4×C17—21no—
120C4×C17—21no—
121C4×C17—26no—
122C4×C17C2×#102112yes—
123Dic17—42no—
124Dic17—44no—
125Dic17—83no—
126C2×2−1+4—341no—
127#550—174no—
128D4×Q8—174no—
129#548—344no—
130#537—343no—
131#532—176no—
132C2×C4×Q8—341no—
133C2×C4×Q8C2×D1711yescharacteristic
134C8×Q8—24no—
135#431C2×D1716yes—
136#389—343no—
137#382—173no—
138C4×C4⋊C4—173no—
139#327—174no—
140#327—1712no—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17#288411yescharacteristic
144C2×C17C22×#10211yescharacteristic
145C2×C17#290111yescharacteristic
146D17—84no—
1472−1+4—684no—
1482−1+4—684no—
149C2×#41—344no—
150C2×#41—346no—
151C22×Q8—344no—
152C22×Q8D6811yescharacteristic
153C4⋊Q8—176no—
154#127—176no—
155#124—346no—
156C22⋊Q8—3412no—
157#121—174no—
158#121—346no—
159#121—3412no—
160C4×Q8—684no—
161C4×Q8C4×D1714yes—
162C4×Q8C22⋊D1714yes—
163C4×D4—1712no—
164C4×D4—346no—
165C2×C4⋊C4—343no—
166C2×C4⋊C4—343no—
167C2×C4⋊C4D6813yes—
168C2×C42—343no—
169C2×C42C22×D1713yes—
170C4⋊C8—26no—
171C22⋊C8C22×D1714yes—
172C4×C8—26no—
173#95—171no—
174#95—173no—
175#95—343no—
176C17#1761811yescharacteristic, complemented, Sylow
177#41—6816no—
178#41—6812no—
179#41—6812no—
180C2×Q8—346no—
181C2×Q8—6816no—
182C2×Q8#6321914yes—
183C2×Q8D13614yes—
184C2×Q8#6322714yes—
185C2×D4—174no—
186C2×D4—344no—
187C2×D4—346no—
188C2×D4—346no—
189C22×C4—341no—
190C22×C4—3412no—
191C22×C4—343no—
192C22×C4C2×D6813yes—
193C22×C4C2×D6813yes—
194C22×C4C23×D1711yescharacteristic
195C2×C8—24no—
196C4⋊C4—174no—
197C4⋊C4—346no—
198C4⋊C4—686no—
199C4⋊C4—686no—
200C4⋊C4#63227112yes—
201C22⋊C4—344no—
202C22⋊C4—3412no—
203C42—686no—
204C42C2×C4×D1716yes—
205C42C2×C22⋊D1716yes—
206C23—344no—
207C23C22×D6811yescharacteristic
208Q8—6812no—
209Q8#10587492116yes—
210D4—684no—
211D4—684no—
212D4—684no—
213D4—6812no—
214D4—1366no—
215C2×C4—43no—
216C2×C4—41no—
217C2×C4—342no—
218C2×C4—344no—
219C2×C4—681no—
220C2×C4—681no—
221C2×C4—6824no—
222C2×C4—683no—
223C2×C4—683no—
224C2×C4—683no—
225C2×C4C2×#6321916yes—
226C2×C4C2×D13616yes—
227C2×C4C2×#6322716yes—
228C2×C4C2×#6322716yes—
229C2×C4C22×C4×D1711yescharacteristic
230C2×C4C22×C22⋊D1711yescharacteristic
231C8—44no—
232C22—21no—
233C22—21no—
234C22—684no—
235C22—684no—
236C22—684no—
237C22C22×#6322711yescharacteristic
238C22C22×D13611yescharacteristic
239C22C22×#6321911yescharacteristic
240C4—21no—
241C4—21no—
242C4—26no—
243C4—682no—
244C4—684no—
245C4—1363no—
246C4C2×#10587492112yes—
247C2—21no—
248C2—21no—
249C2—1364no—
250C2#1453724711yescharacteristic
251C2C22×#1058749211yescharacteristic
252C2#1453732911yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2982C2
socleC22×C17C22×C22⋊C4
prime radical#14542555C2
cosocleC22×C4×C17C24
hypercenter#2982D17
hypocenterC17#17618
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #14531705C2semidirect
3. #14527345C2semidirect
4. #14527280C2semidirect
5. C17×#2982C2semidirect
7. #11763481C4semidirect
8. Q8×D68C4semidirect
107. #2982D17semidirect
176. C17#17618semidirect

Maximal subgroups

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

subgroupindex
#145425552
#145317052
#145273452
#145272802
C17×#29822
#1761817