Finite Group Databasebeta

← #21435287

Subgroups — #21435287

Order 7552.

368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#16837953C211yesmaximal, characteristic
2#125×D59C211yesmaximal, characteristic, complemented
3#16837808C211yesmaximal, characteristic, complemented
4#16837768C211yesmaximal, characteristic, complemented
5#16837767C211yesmaximal, characteristic, complemented
6#16837722C212yesmaximal, complemented
7#16837717C212yesmaximal, complemented
8#16837705C212yesmaximal, complemented
9#16837701C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#501C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13#14273724C2211yescharacteristic
14#14273719C2211yescharacteristic
15#14273718C2211yescharacteristic
16#14273718C2211yescharacteristic
17#14273717—21no—
18#14273717—21no—
19#14273716—21no—
20#14273702—21no—
21#14273702C2212yes—
22#14273689—21no—
23#14273689C2212yes—
24C4⋊C4×D59—21no—
25C4⋊C4×D59—21no—
26C4⋊C4×D59C2211yescharacteristic
27C4⋊C4×D59C2211yescharacteristic
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273658C2212yes—
31Dic59⋊C8C2212yes—
32#14273649C2212yes—
33#14273649C2212yes—
34#14273647C2212yes—
35#14273647C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44#11745689—44no—
45C2×D236—22no—
46C2×D236—21no—
47C2×D236—21no—
48C2×D236C2312yes—
49C2×C4×D59—21no—
50C2×C4×D59—21no—
51C2×C4×D59—22no—
52C2×C4×D59D411yescharacteristic
53C2×C4×D59D411yescharacteristic
54C2×C4×D59C2311yescharacteristic
55C2×C8×C59C2312yes—
56C4⋊C4×C59—21no—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59C2311yescharacteristic
60C4⋊C4×C59C2312yes—
61C4⋊C4×C59C2311yescharacteristic
62C42×C59C2311yescharacteristic
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—22no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—21no—
74Dic59⋊C4—21no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79C22×D59—22no—
80C22×D59C2×D411yescharacteristic
81Q8×C59—42no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2411yescharacteristic
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59C2×D411yescharacteristic
91C2×Dic59C2×D411yescharacteristic
92C2×Dic59C2×D411yescharacteristic
93D236—24no—
94D236—42no—
95D236—42no—
96D236—44no—
97C4×D59—22no—
98C4×D59—22no—
99C4×D59—41no—
100C4×D59—44no—
101C4×D59—42no—
102C4×D59—42no—
103C8×C59—22no—
104C59⋊C8—22no—
105C22×C59C22×D411yescharacteristic
106C2×D59—21no—
107C2×D59—21no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—42no—
111C2×D59AGL(1,ℤ/8)12yes—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—42no—
115C4×C59—41no—
116C4×C59—41no—
117C4×C592−1+412yes—
118Dic59—21no—
119Dic59—21no—
120Dic59—21no—
121Dic59—41no—
122Dic59—41no—
123#3234—591nomaximal, Sylow
124C2×C59#53611yescharacteristic
125C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C59#57511yescharacteristic
127D59—22no—
128D59—82no—
129#532—591no—
130C2×#125—591no—
131#501—591no—
132#501D5911yescharacteristic, complemented
133#490—591no—
134#490—591no—
135#481—592no—
136#480—592no—
137#478—592no—
138#478—592no—
139#432—591no—
140C59#323411yescharacteristic, complemented, Sylow
141C2×#41—1181no—
142C4⋊Q8C2×D5911yescharacteristic
143#127—591no—
144#125—591no—
145#125—591no—
146#125—591no—
147#125—1181no—
148#125—1181no—
149#125C2×D5911yescharacteristic
150#124—1181no—
151#121—592no—
152#121—1181no—
153C4×D4—592no—
154C4×D4—1181no—
155C2×C4⋊C4—591no—
156C2×C4⋊C4—591no—
157C2×C4⋊C4—1181no—
158C2×C4⋊C4—1181no—
159C2×C42—591no—
160#107—592no—
161#107C2×D5912yes—
162#106—592no—
163#106C2×D5912yes—
164C4⋊C8—592no—
165#102—592no—
166#102—592no—
167#102—592no—
168#102—592no—
169C22⋊C8—592no—
170#97—591no—
171#97C2×D5911yescharacteristic
172#41—2364no—
173C2×Q8—21no—
174C2×D4—592no—
175C2×D4—1182no—
176C2×D4—1181no—
177C2×D4—1181no—
178C22×C4—591no—
179C22×C4—591no—
180C22×C4—591no—
181C22×C4—1182no—
182C22×C4—1181no—
183C22×C4—1181no—
184C2×C8—592no—
185C2×C8C22×D5912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—591no—
190C4⋊C4—591no—
191C4⋊C4—1181no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4C22×D5911yescharacteristic
200C4⋊C4C22×D5911yescharacteristic
201C4⋊C4C22×D5912yes—
202C22⋊C4—1182no—
203C22⋊C4—1182no—
204C42—591no—
205C42—591no—
206C42—591no—
207C42C22×D5911yescharacteristic
208C23—591no—
209C23—1182no—
210Q8—42no—
211D4—1184no—
212D4—2362no—
213D4—2362no—
214D4—2364no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—591no—
219C2×C4—591no—
220C2×C4—591no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—1181no—
224C2×C4—1181no—
225C2×C4—2361no—
226C2×C4—2364no—
227C2×C4—2362no—
228C2×C4—2362no—
229C2×C4D4×D5911yescharacteristic
230C2×C4D4×D5911yescharacteristic
231C2×C4C23×D5911yescharacteristic
232C8—22no—
233C8—1182no—
234C22—592no—
235C22—1181no—
236C22—1181no—
237C22—2362no—
238C22—2362no—
239C22—2362no—
240C22C2×D4×D5911yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—1181no—
247C4—1181no—
248C4—1181no—
249C4—2361no—
250C4—2361no—
251C4#1427377512yes—
252C2—1182no—
253C2—4722no—
254C2#1683797711yescharacteristic
255C2AGL(1,ℤ/8)×D5911yescharacteristic
256C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3234
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #125×D59C2semidirect
3. #16837808C2semidirect
4. #16837768C2semidirect
5. #16837767C2semidirect
6. #16837722C2semidirect
7. #16837717C2semidirect
8. #16837705C2semidirect
9. #16837701C2semidirect
10. #16837457C2semidirect
11. C59×#501C2semidirect
132. #501D59semidirect
140. C59#3234semidirect