Finite Group Databasebeta

← #21429002

Subgroups — #21429002

Order 7552.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14273705C212yesmaximal, complemented
2C2×#14273692C211yesmaximal, characteristic, complemented
3C2×#14273689C211yesmaximal, characteristic
4#16837333C211yesmaximal, characteristic, complemented
5#16837320C211yesmaximal, characteristic
6#16837319C211yesmaximal, characteristic
7#16837292C212yesmaximal, complemented
8#16837291C212yesmaximal, complemented
9#16837266C211yesmaximal, characteristic, complemented
10#16837261C212yesmaximal, complemented
11C59×#398C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×D236C2211yescharacteristic
14C22×C4×D59C2212yes—
15#14273705—28no—
16#14273692—24no—
17#14273689—24no—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2211yescharacteristic
29C2×C4×Dic59C2211yescharacteristic
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2211yescharacteristic
33C2×C4⋊C4×C59C2212yes—
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C4⋊C4×C59C2211yescharacteristic
36#95×C59C2212yes—
37#95×C59C2211yescharacteristic
38C23×D59C2312yes—
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2311yescharacteristic
49C2×D236—24no—
50C2×D236—22no—
51C2×C4×D59—24no—
52C2×C4×D59—24no—
53C2×C4×D59—24no—
54C2×Dic118—22no—
55C2×Dic118—22no—
56C2×Dic118D414yescomplemented
57C4⋊C4×C59—22no—
58C4⋊C4×C59—22no—
59C4⋊C4×C59—24no—
60(C2×D59)⋊C4—24no—
61(C2×D59)⋊C4—24no—
62(C2×D59)⋊C4—24no—
63(C2×D59)⋊C4—24no—
64(C2×D59)⋊C4—24no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4—24no—
68Dic59⋊C4—24no—
69C4×Dic59—22no—
70C4×Dic59—22no—
71C4×Dic59D414yes—
72C23×C59C2411yescharacteristic
73C22×D59—22no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—22no—
77C22×D59—22no—
78C22×D59—22no—
79C22×D59#4114yes—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59C2×D412yes—
92C2×C4×C59C2×D412yes—
93C2×Dic59—21no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59C2×D412yes—
102C2×Dic59C2×D412yes—
103C2×Dic59C2×D412yes—
104C2×Dic59C2×D412yes—
105C2×Dic59#4112yes—
106D236—28no—
107C4×D59—48no—
108Dic118—28no—
109C22×C59C22×D411yescharacteristic
110C22×C59C22×D411yescharacteristic
111C22×C59C2×#4111yescharacteristic
112C22×C59C2×#4112yes—
113C22×C592−1+412yes—
114C2×D59—24no—
115C2×D59—24no—
116C2×D59—24no—
117C2×D59—42no—
118C2×D59—42no—
119C2×D59—42no—
120C2×D59—42no—
121C4×C59—22no—
122C4×C59—22no—
123C4×C59—42no—
124C4×C59—41no—
125C4×C59—42no—
126Dic59—22no—
127Dic59—22no—
128Dic59—41no—
129Dic59—42no—
130Dic59#12114yes—
131#2536—591nomaximal, Sylow
132C2×C59C2×#12111yescharacteristic
133C2×C59#52511yescharacteristic
134C2×C59#53611yescharacteristic
135C2×C59#54812yes—
136C2×C59#55212yes—
137D59—44no—
138C2×C22⋊Q8—592no—
139C2×C4×Q8—591no—
140C2×C4×D4—591no—
141#398—591no—
142#398D5911yescharacteristic, complemented
143#394—591no—
144#394—591no—
145#388—592no—
146#388—592no—
147#382—591no—
148#380—592no—
149C59#253611yescharacteristic, complemented, Sylow
150C22×Q8—591no—
151C22×D4—591no—
152C23×C4—592no—
153C22⋊Q8—1188no—
154C4×Q8—1184no—
155C4×D4—1184no—
156C2×C4⋊C4—591no—
157C2×C4⋊C4—591no—
158C2×C4⋊C4—592no—
159C2×C4⋊C4—592no—
160C2×C4⋊C4C2×D5911yescharacteristic
161C2×C4⋊C4C2×D5911yescharacteristic
162C2×C4⋊C4C2×D5912yes—
163C2×C22⋊C4—592no—
164C2×C22⋊C4—592no—
165C2×C22⋊C4—592no—
166C2×C22⋊C4—592no—
167C2×C22⋊C4—592no—
168C2×C42—591no—
169C2×C42—591no—
170C2×C42—591no—
171#95—592no—
172#95—592no—
173#95—591no—
174#95C2×D5912yes—
175#95C2×D5911yescharacteristic
176C24—592no—
177C2×Q8—594no—
178C2×Q8—1182no—
179C2×Q8—1182no—
180C2×D4—1184no—
181C2×D4—1182no—
182C22×C4—591no—
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—592no—
186C22×C4—591no—
187C22×C4—1184no—
188C22×C4—1184no—
189C22×C4—1184no—
190C22×C4C22×D5912yes—
191C22×C4C22×D5912yes—
192C22×C4C22×D5911yescharacteristic
193C22×C4C22×D5911yescharacteristic
194C22×C4C22×D5911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—1182no—
199C4⋊C4—1184no—
200C4⋊C4—1184no—
201C4⋊C4—1182no—
202C22⋊C4—1184no—
203C22⋊C4—1184no—
204C22⋊C4—1184no—
205C22⋊C4—1184no—
206C22⋊C4—1184no—
207C42—594no—
208C42—1182no—
209C42—1182no—
210C23—594no—
211C23—1182no—
212C23—1182no—
213C23—1182no—
214C23—1182no—
215C23—1182no—
216C23—1182no—
217C23C23×D5911yescharacteristic
218Q8—1188no—
219D4—1188no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—592no—
232C2×C4—592no—
233C2×C4—592no—
234C2×C4—592no—
235C2×C4—592no—
236C2×C4—1181no—
237C2×C4—1181no—
238C2×C4—1182no—
239C2×C4—1181no—
240C2×C4—1182no—
241C2×C4—1182no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—2368no—
245C2×C4D4×D5912yes—
246C2×C4D4×D5912yes—
247C22—1184no—
248C22—1184no—
249C22—1184no—
250C22—2362no—
251C22—2362no—
252C22—2362no—
253C22—2362no—
254C22C2×D4×D5911yescharacteristic
255C22C2×D4×D5911yescharacteristic
256C22#41×D5911yescharacteristic
257C22#41×D5912yes—
258C22#1427377512yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—41no—
263C4—42no—
264C4—594no—
265C4—1182no—
266C4—1182no—
267C4—2361no—
268C4—2362no—
269C2—2364no—
270C2#121×D5911yescharacteristic
271C2#1683791011yescharacteristic
272C2#1683797711yescharacteristic
273C2#1683806212yes—
274C2#1683808412yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2536
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273705C2semidirect
2. C2×#14273692C2semidirect
4. #16837333C2semidirect
7. #16837292C2semidirect
8. #16837291C2semidirect
9. #16837266C2semidirect
10. #16837261C2semidirect
11. C59×#398C2semidirect
56. C2×Dic118D4semidirect
142. #398D59semidirect
149. C59#2536semidirect