Finite Group Databasebeta

← #21429864

Subgroups — #21429864

Order 7552.

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×#14273726C211yesmaximal, characteristic, complemented
2C2×#14273705C212yesmaximal
3C2×#14273685C211yesmaximal, characteristic
4#16837335C212yesmaximal, complemented
5#16837332C211yesmaximal, characteristic, complemented
6#16837331C212yesmaximal
7#16837329C211yesmaximal, characteristic
8#16837328C211yesmaximal, characteristic
9#16837306C212yesmaximal, complemented
10#16837266C211yesmaximal, characteristic, complemented
11C59×#398C211yesmaximal, characteristic, complemented
12C22×Dic118C2212yes—
13C22×C4×D59C2211yescharacteristic
14#14273726—24no—
15#14273705—28no—
16#14273685—24no—
17C2×C4⋊Dic59C2211yescharacteristic
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×C4×Dic59C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2212yes—
33C2×C4⋊C4×C59C2212yes—
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C4⋊C4×C59C2211yescharacteristic
36#95×C59C2211yescharacteristic
37#95×C59C2212yes—
38C23×D59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2311yescharacteristic
49C2×C4×D59—22no—
50C2×C4×D59—22no—
51C2×C4×D59D414yes—
52C2×Dic118—24no—
53C2×Dic118—24no—
54C2×Dic118—24no—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—24no—
57C4⋊C4×C59—22no—
58(C2×D59)⋊C4—24no—
59(C2×D59)⋊C4—24no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59—22no—
63C4⋊Dic59—22no—
64Dic59⋊C4—24no—
65Dic59⋊C4—24no—
66Dic59⋊C4—24no—
67C4×Dic59—22no—
68C4×Dic59D414yes—
69C23×C59C2411yescharacteristic
70C22×D59—21no—
71C22×D59—21no—
72C22×D59—22no—
73C22×D59—22no—
74C22×D59C2×D412yes—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59C2×D412yes—
87C2×C4×C59C2×D412yes—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59C2×D412yes—
98C2×Dic59C2×D412yes—
99C2×Dic59C2×D412yes—
100C2×Dic59#4112yes—
101C4×D59—28no—
102Dic118—48no—
103C22×C59C22×D411yescharacteristic
104C22×C59C22×D411yescharacteristic
105C22×C59C2×#4111yescharacteristic
106C22×C592−1+412yes—
107C22×C592−1+412yes—
108C2×D59—22no—
109C2×D59—24no—
110C2×D59—41no—
111C2×D59—41no—
112C2×D59—42no—
113C4×C59—22no—
114C4×C59—22no—
115C4×C59—42no—
116C4×C59—41no—
117C4×C59—42no—
118Dic59—22no—
119Dic59—42no—
120Dic59—42no—
121Dic59—41no—
122Dic59#12114yes—
123#2621—591nomaximal, Sylow
124C2×C59C2×#12111yescharacteristic
125C2×C59#53611yescharacteristic
126C2×C59#53612yes—
127C2×C59#53611yescharacteristic
128C2×C59#54112yes—
129D59—42no—
130C2×C4⋊Q8—591no—
131C2×C22⋊Q8—592no—
132C2×#117—591no—
133#398—591no—
134#398—592no—
135#398D5911yescharacteristic, complemented
136#397—591no—
137#397—591no—
138#397—592no—
139#391—592no—
140#382—591no—
141C59#262111yescharacteristic, complemented, Sylow
142C22×Q8—592no—
143C23×C4—591no—
144C4⋊Q8—1184no—
145C22⋊Q8—1188no—
146#117—1184no—
147C2×C4⋊C4—591no—
148C2×C4⋊C4—592no—
149C2×C4⋊C4—592no—
150C2×C4⋊C4—592no—
151C2×C4⋊C4—591no—
152C2×C4⋊C4C2×D5911yescharacteristic
153C2×C4⋊C4C2×D5912yes—
154C2×C4⋊C4C2×D5911yescharacteristic
155C2×C22⋊C4—591no—
156C2×C22⋊C4—591no—
157C2×C22⋊C4—592no—
158C2×C22⋊C4—592no—
159C2×C42—591no—
160C2×C42—591no—
161#95—592no—
162#95—591no—
163#95—592no—
164#95—592no—
165#95—592no—
166#95C2×D5911yescharacteristic
167#95C2×D5912yes—
168C24—591no—
169C2×Q8—1184no—
170C2×Q8—1184no—
171C2×Q8—1184no—
172C22×C4—591no—
173C22×C4—591no—
174C22×C4—594no—
175C22×C4—591no—
176C22×C4—592no—
177C22×C4—592no—
178C22×C4—1182no—
179C22×C4—1182no—
180C22×C4C22×D5911yescharacteristic
181C22×C4C22×D5912yes—
182C22×C4C22×D5912yes—
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—1182no—
189C4⋊C4—1184no—
190C4⋊C4—1184no—
191C4⋊C4—1184no—
192C4⋊C4—1182no—
193C22⋊C4—1182no—
194C22⋊C4—1184no—
195C22⋊C4—1184no—
196C22⋊C4—1182no—
197C42—594no—
198C42—1182no—
199C23—592no—
200C23—1181no—
201C23—1181no—
202C23—1182no—
203C23—1182no—
204C23C23×D5911yescharacteristic
205Q8—2368no—
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—592no—
218C2×C4—592no—
219C2×C4—592no—
220C2×C4—592no—
221C2×C4—1188no—
222C2×C4—1182no—
223C2×C4—1181no—
224C2×C4—1182no—
225C2×C4—1182no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1182no—
229C2×C4—1182no—
230C2×C4—1182no—
231C2×C4D4×D5912yes—
232C2×C4D4×D5912yes—
233C22—1182no—
234C22—1184no—
235C22—2361no—
236C22—2361no—
237C22—2362no—
238C22C2×D4×D5911yescharacteristic
239C22C2×D4×D5911yescharacteristic
240C22#41×D5911yescharacteristic
241C22#1427377412yes—
242C22#1427377512yes—
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—42no—
248C4—594no—
249C4—1182no—
250C4—2362no—
251C4—2362no—
252C4—2361no—
253C2—2362no—
254C2#121×D5911yescharacteristic
255C2#1683797411yescharacteristic
256C2#1683797512yes—
257C2#1683797711yescharacteristic
258C2#1683801112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2621
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273726C2semidirect
4. #16837335C2semidirect
5. #16837332C2semidirect
9. #16837306C2semidirect
10. #16837266C2semidirect
11. C59×#398C2semidirect
135. #398D59semidirect
141. C59#2621semidirect