Finite Group Databasebeta

← #21432140

Subgroups — #21432140

Order 7552.

580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273713C212yesmaximal, complemented
2#16837319C211yesmaximal, characteristic, complemented
3#16837318C212yesmaximal, complemented
4#16837315C212yesmaximal, complemented
5#16837314C212yesmaximal, complemented
6#16837311C212yesmaximal, complemented
7#16837310C212yesmaximal, complemented
8#16837267C211yesmaximal, characteristic, complemented
9C59×#394C211yesmaximal, characteristic, complemented
10C22×Dic118C2212yes—
11C22×D236C2211yescharacteristic
12C22×C22⋊D59C2212yes—
13C22×C22⋊D59C2212yes—
14#14273713—28no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C2×C4×Dic59C2211yescharacteristic
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2212yes—
27C22×D4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2212yes—
31#95×C59C2211yescharacteristic
32C24×C59C2312yes—
33C23×D59C2312yes—
34C2×D4×C59—42no—
35C2×D4×C59—41no—
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—24no—
41C2×C22⋊D59—42no—
42C2×C22⋊D59—42no—
43C2×C22⋊D59—42no—
44C2×C22⋊D59—42no—
45C2×C22⋊D59—42no—
46C22×Dic59C2312yes—
47C22×Dic59C2312yes—
48C22×Dic59C2312yes—
49C2×D236—42no—
50C2×D236—41no—
51C2×Dic118—24no—
52C2×Dic118—42no—
53C2×Dic118—42no—
54C4⋊C4×C59—41no—
55C22⋊C4×C59—24no—
56C22⋊C4×C59—42no—
57C22⋊Dic59—24no—
58C22⋊Dic59—42no—
59(C2×D59)⋊C4—24no—
60(C2×D59)⋊C4—24no—
61(C2×D59)⋊C4—42no—
62(C2×D59)⋊C4—42no—
63C4⋊Dic59—41no—
64C4×Dic59D414yescomplemented
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—22no—
68C23×C59—22no—
69C23×C59—22no—
70C23×C59—22no—
71C23×C59—22no—
72C23×C59C2411yescharacteristic
73C22×D59—22no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—22no—
77C22×D59—22no—
78C22×D59—22no—
79C22×D59—22no—
80D4×C59—44no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59C2×D412yes—
91C22⋊D59—48no—
92C22⋊D59—48no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59C2×D414yes—
102D236—44no—
103Dic118—48no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—42no—
109C22×C59—42no—
110C22×C59—42no—
111C22×C59C22×D411yescharacteristic
112C22×C59H(5,𝔽2)12yes—
113C22×C59H(5,𝔽2)11yescharacteristic
114C22×C59H(5,𝔽2)12yes—
115C22×C592−1+411yescharacteristic
116C2×D59—42no—
117C2×D59—42no—
118C2×D59—42no—
119C2×D59—42no—
120C2×D59—42no—
121C2×D59—42no—
122C2×D59—42no—
123C4×C59—22no—
124C4×C59—42no—
125C4×C59—41no—
126C4×C59—41no—
127Dic59—24no—
128Dic59—42no—
129Dic59—42no—
130#2819—591nomaximal, Sylow
131C2×C59—82no—
132C2×C59#53512yes—
133C2×C59#53711yescharacteristic
134C2×C59H(3,𝔽4)11yescharacteristic
135C2×C59H(3,𝔽4)11yescharacteristic
136C2×C59#56212yes—
137D59—82no—
138C2×#124—592no—
139#394—591no—
140#394—592no—
141#394D5911yescharacteristic, complemented
142#393—592no—
143#393—592no—
144#392—592no—
145#392—592no—
146#382—591no—
147C59#281911yescharacteristic, complemented, Sylow
148C22×Q8—592no—
149C22×D4—592no—
150C22×D4—592no—
151C22×D4—591no—
152C22×D4C2×D5911yescharacteristic
153#124—1188no—
154C2×C4⋊C4—591no—
155C2×C4⋊C4C2×D5911yescharacteristic
156C2×C22⋊C4—592no—
157C2×C22⋊C4—592no—
158C2×C22⋊C4—592no—
159C2×C22⋊C4—592no—
160C2×C22⋊C4—592no—
161C2×C22⋊C4—592no—
162C2×C22⋊C4C2×D5912yes—
163C2×C22⋊C4C2×D5912yes—
164C2×C42—591no—
165#95—592no—
166#95—592no—
167#95—592no—
168#95—591no—
169#95C2×D5911yescharacteristic
170C24—592no—
171C24C22×D5912yes—
172C2×Q8—1184no—
173C2×Q8—2362no—
174C2×Q8—2362no—
175C2×D4—42no—
176C2×D4—41no—
177C2×D4—1184no—
178C2×D4—2362no—
179C2×D4—2361no—
180C2×D4—2362no—
181C2×D4—2362no—
182C2×D4—2362no—
183C2×D4—2362no—
184C2×D4—2362no—
185C22×C4—592no—
186C22×C4—592no—
187C22×C4—592no—
188C22×C4C22×D5911yescharacteristic
189C22×C4C22×D5911yescharacteristic
190C22×C4C22×D5912yes—
191C22×C4C22×D5911yescharacteristic
192C4⋊C4—41no—
193C4⋊C4—2361no—
194C22⋊C4—24no—
195C22⋊C4—42no—
196C22⋊C4—1184no—
197C22⋊C4—1184no—
198C22⋊C4—1184no—
199C22⋊C4—2362no—
200C22⋊C4—2362no—
201C22⋊C4—2362no—
202C42—594no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—1182no—
211C23—1182no—
212C23—1182no—
213C23—1182no—
214C23—1182no—
215C23—1182no—
216C23—1182no—
217C23C23×D5911yescharacteristic
218Q8—2368no—
219D4—44no—
220D4—2364no—
221D4—2368no—
222D4—2368no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—594no—
233C2×C4—1182no—
234C2×C4—1182no—
235C2×C4—1182no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1182no—
241C2×C4D4×D5912yes—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—2362no—
250C22—2362no—
251C22—2362no—
252C22—2362no—
253C22—2362no—
254C22—2362no—
255C22—2362no—
256C22C2×D4×D5911yescharacteristic
257C22#1427377211yescharacteristic
258C22#1427377212yes—
259C22#1427377312yes—
260C22#1427377411yescharacteristic
261C4—22no—
262C4—41no—
263C4—41no—
264C4—42no—
265C4—1184no—
266C4—2362no—
267C4—2362no—
268C2—82no—
269C2—4722no—
270C2#1683796812yes—
271C2#1683797911yescharacteristic
272C2#1683814411yescharacteristic
273C2#1683814511yescharacteristic
274C2#1683814912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2819
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273713C2semidirect
2. #16837319C2semidirect
3. #16837318C2semidirect
4. #16837315C2semidirect
5. #16837314C2semidirect
6. #16837311C2semidirect
7. #16837310C2semidirect
8. #16837267C2semidirect
9. C59×#394C2semidirect
64. C4×Dic59D4semidirect
141. #394D59semidirect
147. C59#2819semidirect