Finite Group Databasebeta

← #14534552

Subgroups — #14534552

Order 2176.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#10587574C211yesmaximal, characteristic, complemented
2C2×#10587582C212yesmaximal
3C2×#10587578C211yesmaximal, characteristic
4#11762742C212yesmaximal, complemented
5#11762739C211yesmaximal, characteristic, complemented
6#11762738C212yesmaximal
7#11762736C211yesmaximal, characteristic
8#11762735C211yesmaximal, characteristic
9#11762713C212yesmaximal, complemented
10#11762673C211yesmaximal, characteristic, complemented
11C17×#398C211yesmaximal, characteristic, complemented
12C22×C4×D17C2211yescharacteristic
13C22×Dic34C2212yes—
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C4⋊C4×C17C2211yescharacteristic
16C2×C4⋊C4×C17C2212yes—
17C2×#63227C2211yescharacteristic
18C2×#63227C2212yes—
19C2×#63227C2212yes—
20C2×#63227C2211yescharacteristic
21C2×C4⋊Dic17C2211yescharacteristic
22C2×C4⋊Dic17C2211yescharacteristic
23C2×#63225C2212yes—
24C2×#63225C2212yes—
25C2×#63225C2212yes—
26C2×C4×Dic17C2211yescharacteristic
27C2×C4×Dic17C2211yescharacteristic
28#10587582—28no—
29#10587578—24no—
30#10587574—24no—
31C17×#95C2212yes—
32C17×#95C2211yescharacteristic
33#10587502C2212yes—
34#10587502C2212yes—
35#10587502C2212yes—
36#10587502C2211yescharacteristic
37#10587502C2212yes—
38C23×D17C2311yescharacteristic
39C22×C4×C17C2312yes—
40C22×C4×C17C2311yescharacteristic
41C22×C4×C17C2312yes—
42C22×C4×C17C2311yescharacteristic
43C22×C4×C17C2311yescharacteristic
44C22×Dic17C2312yes—
45C22×Dic17C2311yescharacteristic
46C22×Dic17C2312yes—
47C22×Dic17C2311yescharacteristic
48C22×Dic17C2311yescharacteristic
49C2×C4×D17—22no—
50C2×C4×D17—22no—
51C2×C4×D17D414yes—
52C2×Dic34—24no—
53C2×Dic34—24no—
54C2×Dic34—24no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C4⋊C4×C17—24no—
58#63227—24no—
59#63227—24no—
60#63227—22no—
61#63227—22no—
62C4⋊Dic17—22no—
63C4⋊Dic17—22no—
64#63225—24no—
65#63225—24no—
66#63225—24no—
67C4×Dic17—22no—
68C4×Dic17D414yes—
69C23×C17C2411yescharacteristic
70C22×D17—21no—
71C22×D17—21no—
72C22×D17—22no—
73C22×D17—22no—
74C22×D17C2×D412yes—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—22no—
78C2×C4×C17—22no—
79C2×C4×C17—22no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—22no—
86C2×C4×C17C2×D412yes—
87C2×C4×C17C2×D412yes—
88C2×Dic17—22no—
89C2×Dic17—22no—
90C2×Dic17—22no—
91C2×Dic17—21no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17C2×D412yes—
98C2×Dic17C2×D412yes—
99C2×Dic17C2×D412yes—
100C2×Dic17#4112yes—
101C4×D17—28no—
102Dic34—48no—
103#2621—171nomaximal, Sylow
104C22×C17C22×D411yescharacteristic
105C22×C17C22×D411yescharacteristic
106C22×C17C2×#4111yescharacteristic
107C22×C172−1+412yes—
108C22×C172−1+412yes—
109C2×D17—22no—
110C2×D17—24no—
111C2×D17—41no—
112C2×D17—41no—
113C2×D17—42no—
114C4×C17—22no—
115C4×C17—22no—
116C4×C17—42no—
117C4×C17—41no—
118C4×C17—42no—
119Dic17—22no—
120Dic17—42no—
121Dic17—42no—
122Dic17—41no—
123Dic17#12114yes—
124C2×C4⋊Q8—171no—
125C2×C22⋊Q8—172no—
126C2×#117—171no—
127#398—171no—
128#398—172no—
129#398D1711yescharacteristic, complemented
130#397—171no—
131#397—171no—
132#397—172no—
133#391—172no—
134#382—171no—
135C2×C17C2×#12111yescharacteristic
136C2×C17#53611yescharacteristic
137C2×C17#53612yes—
138C2×C17#53611yescharacteristic
139C2×C17#54112yes—
140D17—42no—
141C22×Q8—172no—
142C23×C4—171no—
143C4⋊Q8—344no—
144C22⋊Q8—348no—
145#117—344no—
146C2×C4⋊C4—171no—
147C2×C4⋊C4—172no—
148C2×C4⋊C4—172no—
149C2×C4⋊C4—172no—
150C2×C4⋊C4—171no—
151C2×C4⋊C4C2×D1711yescharacteristic
152C2×C4⋊C4C2×D1712yes—
153C2×C4⋊C4C2×D1711yescharacteristic
154C2×C22⋊C4—171no—
155C2×C22⋊C4—171no—
156C2×C22⋊C4—172no—
157C2×C22⋊C4—172no—
158C2×C42—171no—
159C2×C42—171no—
160#95—172no—
161#95—171no—
162#95—172no—
163#95—172no—
164#95—172no—
165#95C2×D1711yescharacteristic
166#95C2×D1712yes—
167C17#262111yescharacteristic, complemented, Sylow
168C24—171no—
169C2×Q8—344no—
170C2×Q8—344no—
171C2×Q8—344no—
172C22×C4—171no—
173C22×C4—171no—
174C22×C4—174no—
175C22×C4—171no—
176C22×C4—172no—
177C22×C4—172no—
178C22×C4—342no—
179C22×C4—342no—
180C22×C4C22×D1711yescharacteristic
181C22×C4C22×D1712yes—
182C22×C4C22×D1712yes—
183C22×C4C22×D1711yescharacteristic
184C22×C4C22×D1711yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—342no—
189C4⋊C4—344no—
190C4⋊C4—344no—
191C4⋊C4—344no—
192C4⋊C4—342no—
193C22⋊C4—342no—
194C22⋊C4—344no—
195C22⋊C4—344no—
196C22⋊C4—342no—
197C42—174no—
198C42—342no—
199C23—172no—
200C23—341no—
201C23—342no—
202C23—341no—
203C23—342no—
204C23C23×D1711yescharacteristic
205Q8—688no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—172no—
218C2×C4—172no—
219C2×C4—172no—
220C2×C4—172no—
221C2×C4—348no—
222C2×C4—342no—
223C2×C4—341no—
224C2×C4—342no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—342no—
228C2×C4—342no—
229C2×C4—342no—
230C2×C4—342no—
231C2×C4D4×D1712yes—
232C2×C4D4×D1712yes—
233C22—342no—
234C22—344no—
235C22—681no—
236C22—681no—
237C22—682no—
238C22C2×D4×D1711yescharacteristic
239C22C2×D4×D1711yescharacteristic
240C22#1058769412yes—
241C22#41×D1711yescharacteristic
242C22#1058769712yes—
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—42no—
248C4—174no—
249C4—342no—
250C4—682no—
251C4—682no—
252C4—681no—
253C2—682no—
254C2#121×D1711yescharacteristic
255C2#1176338111yescharacteristic
256C2#1176338212yes—
257C2#1176338411yescharacteristic
258C2#1176341812yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, cosocleC23×C17C24
FittingC17×#398C2
prime radicalC23×D17C23
hypercenter#398D17
hypocenterC17#2621
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#10587574C2semidirect
4. #11762742C2semidirect
5. #11762739C2semidirect
9. #11762713C2semidirect
10. #11762673C2semidirect
11. C17×#398C2semidirect
129. #398D17semidirect
167. C17#2621semidirect

Maximal subgroups

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

subgroupindex
C2×#105875742
C2×#105875822
C2×#105875782
#117627422
#117627392
#117627382
#117627362
#117627352
#117627132
#117626732
C17×#3982
#262117