Finite Group Databasebeta

← #21427331

Subgroups — #21427331

Order 7552.

696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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×D4×Dic59C212yesmaximal, complemented
2C2×D4×Dic59C211yesmaximal, characteristic, complemented
3C2×#14273683C211yesmaximal, characteristic, complemented
4#16837334C211yesmaximal, characteristic, complemented
5#16837327C211yesmaximal, characteristic, complemented
6#16837325C212yesmaximal, complemented
7#16837316C212yesmaximal, complemented
8#16837316C211yesmaximal, characteristic, complemented
9#16837253C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic59C212yesmaximal, complemented
11C59×#392C211yesmaximal, characteristic
12C23×Dic59C2212yes—
13C23×Dic59C2211yescharacteristic
14D4×Dic59—28no—
15D4×Dic59—24no—
16#14273683—24no—
17C2×C4⋊Dic59C2212yes—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×C22⋊Dic59C2212yes—
23C2×C22⋊Dic59C2211yescharacteristic
24C2×C22⋊Dic59C2212yes—
25C2×C22⋊Dic59C2212yes—
26C2×C22⋊Dic59C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2212yes—
29C2×C4×Dic59C2211yescharacteristic
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2211yescharacteristic
33C22×D4×C59C2211yescharacteristic
34C22×D4×C59C2212yes—
35C2×C22⋊C4×C59C2212yes—
36C2×C22⋊C4×C59C2211yescharacteristic
37#95×C59C2211yescharacteristic
38C24×C59C2311yescharacteristic
39C24×C59C2312yes—
40C2×D4×C59—24no—
41C2×D4×C59—24no—
42C2×D4×C59—24no—
43C2×D4×C59—22no—
44C2×D4×C59—24no—
45C22×C4×C59C2311yescharacteristic
46C22×C4×C59C2311yescharacteristic
47C22×C4×C59C2312yes—
48C22×Dic59—22no—
49C22×Dic59—22no—
50C22×Dic59—24no—
51C22×Dic59—24no—
52C22×Dic59—24no—
53C22×Dic59D414yescomplemented
54C22×Dic59C2311yescharacteristic
55C22×Dic59C2312yes—
56C22×Dic59C2312yes—
57C22×Dic59C2311yescharacteristic
58C22×Dic59C2311yescharacteristic
59C22×Dic59C2311yescharacteristic
60C22⋊C4×C59—22no—
61C22⋊C4×C59—24no—
62C22⋊Dic59—24no—
63C22⋊Dic59—24no—
64C22⋊Dic59—22no—
65C22⋊Dic59—24no—
66C22⋊Dic59—24no—
67C4⋊Dic59—22no—
68C4⋊Dic59—24no—
69Dic59⋊C4—22no—
70Dic59⋊C4—24no—
71Dic59⋊C4—22no—
72C4×Dic59—22no—
73C4×Dic59—24no—
74C4×Dic59D414yescomplemented
75C23×C59—21no—
76C23×C59—22no—
77C23×C59—22no—
78C23×C59—22no—
79C23×C59—21no—
80C23×C59—22no—
81C23×C59—22no—
82C23×C59—22no—
83C23×C59—22no—
84C23×C59—22no—
85C23×C59C2×D412yes—
86C23×C59#4114yes—
87C23×C59C2411yescharacteristic
88D4×C59—28no—
89D4×C59—216no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—22no—
95C2×C4×C59C2×D412yes—
96C2×C4×C59#4114yes—
97C2×Dic59—21no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—28no—
101C2×Dic59—21no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59—22no—
108C2×Dic59—22no—
109C2×Dic59—48no—
110C2×Dic59C2×D412yes—
111C2×Dic59C2×D412yes—
112C2×Dic59C2×D412yes—
113C2×Dic59C2×D412yes—
114C2×Dic59#4112yes—
115C22×C59—22no—
116C22×C59—24no—
117C22×C59—24no—
118C22×C59—24no—
119C22×C59—24no—
120C22×C59—42no—
121C22×C59—41no—
122C22×C59—42no—
123C22×C59—42no—
124C22×C59—42no—
125C22×C59—41no—
126C22×C59—42no—
127C22×C59C22×D411yescharacteristic
128C22×C59C22×D411yescharacteristic
129C22×C59C2×#4111yescharacteristic
130C22×C59C2×#4112yes—
131C22×C59C2×#4112yes—
132C4×C59—22no—
133C4×C59—24no—
134C4×C59—41no—
135Dic59—22no—
136Dic59—22no—
137Dic59—42no—
138Dic59—41no—
139Dic59—42no—
140Dic59#12114yes—
141#2392—591nomaximal, Sylow
142C2×C59—42no—
143C2×C59—44no—
144C2×C59C2×#12111yescharacteristic
145C2×C59#52511yescharacteristic
146C2×C59#52512yes—
147C2×C59#52912yes—
148C2×C59#53211yescharacteristic
149C2×C4×D4—591no—
150C2×C4×D4—592no—
151C2×#117—591no—
152#398—591no—
153#397—591no—
154#396—592no—
155#394—592no—
156#394—591no—
157#392D5911yescharacteristic
158C4×C4⋊C4—591no—
159C4×C22⋊C4—592no—
160C59#239211yescharacteristic, complemented, Sylow
161C22×D4C2×D5911yescharacteristic
162C22×D4C2×D5912yes—
163C23×C4—591no—
164C23×C4—592no—
165C4×D4—1184no—
166C4×D4—1188no—
167#117—1184no—
168C2×C4⋊C4—591no—
169C2×C4⋊C4—591no—
170C2×C4⋊C4—592no—
171C2×C4⋊C4—591no—
172C2×C4⋊C4—592no—
173C2×C22⋊C4—591no—
174C2×C22⋊C4—592no—
175C2×C22⋊C4—592no—
176C2×C22⋊C4—592no—
177C2×C22⋊C4—592no—
178C2×C22⋊C4C2×D5911yescharacteristic
179C2×C22⋊C4C2×D5912yes—
180C2×C42—591no—
181C2×C42—591no—
182C2×C42—592no—
183#95—592no—
184#95—592no—
185#95—591no—
186#95C2×D5911yescharacteristic
187C24C22×D5911yescharacteristic
188C24C22×D5912yes—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—22no—
193C2×D4—24no—
194C22×C4—591no—
195C22×C4—594no—
196C22×C4—591no—
197C22×C4—591no—
198C22×C4—592no—
199C22×C4—591no—
200C22×C4—592no—
201C22×C4—1182no—
202C22×C4—1182no—
203C22×C4—1184no—
204C22×C4—1184no—
205C22×C4—1184no—
206C22×C4C22×D5911yescharacteristic
207C22×C4C22×D5911yescharacteristic
208C22×C4C22×D5912yes—
209C4⋊C4—1182no—
210C4⋊C4—1184no—
211C4⋊C4—1182no—
212C4⋊C4—1182no—
213C4⋊C4—1184no—
214C22⋊C4—22no—
215C22⋊C4—24no—
216C22⋊C4—1182no—
217C22⋊C4—1184no—
218C22⋊C4—1184no—
219C22⋊C4—1184no—
220C22⋊C4—1184no—
221C42—594no—
222C42—1182no—
223C42—1184no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23D4×D5912yes—
235C23#1174568714yes—
236C23C23×D5911yescharacteristic
237D4—28no—
238D4—216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—592no—
245C2×C4—592no—
246C2×C4—592no—
247C2×C4—592no—
248C2×C4—592no—
249C2×C4—1188no—
250C2×C4—1181no—
251C2×C4—1181no—
252C2×C4—1182no—
253C2×C4—1182no—
254C2×C4—1181no—
255C2×C4—1182no—
256C2×C4—1182no—
257C2×C4—1182no—
258C2×C4—1182no—
259C2×C4—1182no—
260C2×C4—1182no—
261C2×C4—2368no—
262C2×C4D4×D5912yes—
263C2×C4#1174568714yes—
264C22—22no—
265C22—24no—
266C22—24no—
267C22—24no—
268C22—24no—
269C22—42no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—42no—
276C22C2×D4×D5911yescharacteristic
277C22C2×D4×D5911yescharacteristic
278C22#41×D5911yescharacteristic
279C22C2×#1174568712yes—
280C22C2×#1174568712yes—
281C4—22no—
282C4—24no—
283C4—41no—
284C4—594no—
285C4—1182no—
286C4—1182no—
287C4—2362no—
288C4—2362no—
289C4—2361no—
290C2—42no—
291C2—44no—
292C2#121×D5911yescharacteristic
293C2#1683790811yescharacteristic
294C2#1683790812yes—
295C2#1683793312yes—
296C2#1683795011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#392C2
hypercenter#392D59
hypocenterC59#2392
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic59C2semidirect
2. C2×D4×Dic59C2semidirect
3. C2×#14273683C2semidirect
4. #16837334C2semidirect
5. #16837327C2semidirect
6. #16837325C2semidirect
7. #16837316C2semidirect
8. #16837316C2semidirect
9. #16837253C2semidirect
10. C22⋊C4×Dic59C2semidirect
53. C22×Dic59D4semidirect
74. C4×Dic59D4semidirect
160. C59#2392semidirect