Finite Group Databasebeta

← #21429717

Subgroups — #21429717

Order 7552.

582 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273721C211yesmaximal, characteristic, complemented
2#16837333C211yesmaximal, characteristic, complemented
3#16837328C211yesmaximal, characteristic, complemented
4#16837316C211yesmaximal, characteristic, complemented
5#16837310C211yesmaximal, characteristic
6#16837302C212yesmaximal, complemented
7#16837296C212yesmaximal, complemented
8#16837281C212yesmaximal, complemented
9#16837275C212yesmaximal, complemented
10#16837248C211yesmaximal, characteristic, complemented
11C2×C4×D4×C59C211yesmaximal, characteristic, complemented
12C22×C22⋊D59C2212yes—
13#14273721—24no—
14C2×Dic59⋊C4C2211yescharacteristic
15C2×Dic59⋊C4C2211yescharacteristic
16C2×Dic59⋊C4C2211yescharacteristic
17C2×Dic59⋊C4C2212yes—
18C2×C22⋊Dic59C2212yes—
19C2×C22⋊Dic59C2212yes—
20C2×C22⋊Dic59C2212yes—
21C2×(C2×D59)⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2212yes—
25C2×C4×Dic59C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C22×D4×C59C2211yescharacteristic
32C23×C4×C59C2212yes—
33C4×D4×C59—24no—
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C22⋊C4×C59C2212yes—
36C2×C42×C59C2211yescharacteristic
37C24×C59C2312yes—
38C23×D59C2311yescharacteristic
39C2×D4×C59—24no—
40C2×D4×C59—22no—
41C22×C4×C59—24no—
42C22×C4×C59—42no—
43C22×C4×C59—42no—
44C22×C4×C59C2312yes—
45C22×C4×C59C2311yescharacteristic
46C22×C4×C59C2311yescharacteristic
47C22×C4×C59C2311yescharacteristic
48C2×C22⋊D59—24no—
49C2×C22⋊D59—24no—
50C2×C22⋊D59—42no—
51C22×Dic59C2312yes—
52C22×Dic59C2311yescharacteristic
53C22×Dic59C2311yescharacteristic
54C22×Dic59C2311yescharacteristic
55C22×Dic59C2312yes—
56C4⋊C4×C59—22no—
57C22⋊C4×C59—24no—
58C42×C59D414yescomplemented
59C22⋊Dic59—24no—
60C22⋊Dic59—24no—
61C22⋊Dic59—42no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4—42no—
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4—42no—
70C4×Dic59—24no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59—22no—
76C23×C59—22no—
77C23×C59#4114yes—
78C23×C59C2411yescharacteristic
79C22×D59—21no—
80C22×D59—22no—
81C22×D59—22no—
82C22×D59—21no—
83C22×D59—21no—
84D4×C59—28no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—48no—
93C2×C4×C59C2×D412yes—
94C2×C4×C59C2×D412yes—
95C2×C4×C59C2×D412yes—
96C22⋊D59—48no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—21no—
101C2×Dic59—21no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—21no—
107C2×Dic59—22no—
108C2×Dic59—21no—
109C2×Dic59#4114yes—
110C22×C59—24no—
111C22×C59—24no—
112C22×C59—24no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59—42no—
117C22×C59C22×D411yescharacteristic
118C22×C59C2×#4112yes—
119C22×C59C2×#4112yes—
120C22×C59H(5,𝔽2)11yescharacteristic
121C22×C59H(5,𝔽2)11yescharacteristic
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—41no—
125C2×D59—42no—
126C2×D59—42no—
127C4×C59—22no—
128C4×C59—22no—
129C4×C59—22no—
130C4×C59—42no—
131Dic59—24no—
132Dic59—41no—
133Dic59—41no—
134Dic59—41no—
135Dic59—42no—
136#2603—591nomaximal, Sylow
137C2×C59—44no—
138C2×C59#52511yescharacteristic
139C2×C59#53211yescharacteristic
140C2×C59#53511yescharacteristic
141C2×C59#55112yes—
142C2×C59#55312yes—
143D59—81no—
144C2×#126—591no—
145C2×C4×D4D5911yescharacteristic, complemented
146#398—591no—
147#397—591no—
148#394—591no—
149#392—591no—
150#390—592no—
151#388—592no—
152#386—592no—
153#385—592no—
154#376—591no—
155C59#260311yescharacteristic, complemented, Sylow
156C22×D4—592no—
157C22×D4C2×D5911yescharacteristic
158C23×C4C2×D5912yes—
159#126—1184no—
160C4×D4—24no—
161C2×C4⋊C4—591no—
162C2×C4⋊C4—591no—
163C2×C4⋊C4—591no—
164C2×C4⋊C4—592no—
165C2×C4⋊C4C2×D5911yescharacteristic
166C2×C22⋊C4—592no—
167C2×C22⋊C4—592no—
168C2×C22⋊C4—591no—
169C2×C22⋊C4—591no—
170C2×C22⋊C4—591no—
171C2×C22⋊C4—592no—
172C2×C22⋊C4—592no—
173C2×C22⋊C4C2×D5912yes—
174C2×C42—592no—
175C2×C42C2×D5911yescharacteristic
176#95—592no—
177#95—591no—
178#95—591no—
179#95—592no—
180#95—592no—
181C24—591no—
182C24C22×D5912yes—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—1184no—
186C2×D4—1184no—
187C2×D4—2362no—
188C22×C4—24no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—592no—
192C22×C4—592no—
193C22×C4—591no—
194C22×C4—591no—
195C22×C4—591no—
196C22×C4C22×D5912yes—
197C22×C4C22×D5911yescharacteristic
198C22×C4C22×D5911yescharacteristic
199C22×C4C22×D5911yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—1182no—
202C4⋊C4—1182no—
203C4⋊C4—1182no—
204C4⋊C4—2362no—
205C22⋊C4—24no—
206C22⋊C4—1184no—
207C22⋊C4—1184no—
208C22⋊C4—1182no—
209C22⋊C4—1182no—
210C22⋊C4—1182no—
211C22⋊C4—2362no—
212C22⋊C4—2362no—
213C42—1184no—
214C42C22⋊D5914yescomplemented
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—1181no—
222C23—1182no—
223C23—1182no—
224C23—1181no—
225C23—1181no—
226C23#1174568514yes—
227C23C23×D5911yescharacteristic
228D4—28no—
229D4—2368no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—48no—
238C2×C4—594no—
239C2×C4—1182no—
240C2×C4—1182no—
241C2×C4—1181no—
242C2×C4—1181no—
243C2×C4—1181no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1182no—
247C2×C4—1182no—
248C2×C4—1181no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4C2×C22⋊D5912yes—
252C2×C4C2×C22⋊D5912yes—
253C2×C4C2×C22⋊D5912yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—2361no—
262C22—2361no—
263C22—2361no—
264C22—2362no—
265C22—2362no—
266C22C22×C22⋊D5911yescharacteristic
267C22#41×D5912yes—
268C22C2×#1174568512yes—
269C22#1427377211yescharacteristic
270C22#1427377211yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—1184no—
276C4—2361no—
277C4—2361no—
278C4—2361no—
279C4—2362no—
280C2—44no—
281C2—4721no—
282C2#1683791311yescharacteristic
283C2#1683794811yescharacteristic
284C2#1683796911yescharacteristic
285C2#1683808112yes—
286C2#1683810112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×C4×D4×C59C2
hypercenterC2×C4×D4D59
hypocenterC59#2603
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14273721C2semidirect
2. #16837333C2semidirect
3. #16837328C2semidirect
4. #16837316C2semidirect
6. #16837302C2semidirect
7. #16837296C2semidirect
8. #16837281C2semidirect
9. #16837275C2semidirect
10. #16837248C2semidirect
11. C2×C4×D4×C59C2semidirect
58. C42×C59D4semidirect
145. C2×C4×D4D59semidirect
155. C59#2603semidirect
214. C42C22⋊D59semidirect