Finite Group Databasebeta

← #21435289

Subgroups — #21435289

Order 7552.

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

normal subgroups only

This group has 366 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#16837958C211yesmaximal, characteristic, complemented
2#16837950C211yesmaximal, characteristic
3#16837812C211yesmaximal, characteristic, complemented
4#16837811C211yesmaximal, characteristic, complemented
5#16837766C211yesmaximal, characteristic, complemented
6#16837725C212yesmaximal, complemented
7#16837724C212yesmaximal, complemented
8#16837690C212yesmaximal, complemented
9#16837680C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#490C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13#14273727C2211yescharacteristic
14#14273726C2211yescharacteristic
15#14273726C2211yescharacteristic
16#14273719C2211yescharacteristic
17#14273714—21no—
18#14273705—21no—
19#14273705—21no—
20#14273698—21no—
21#14273698C2212yes—
22#14273692—21no—
23#14273692—21no—
24D4×Dic59—21no—
25D4×Dic59C2212yes—
26#14273685C2211yescharacteristic
27#14273685C2211yescharacteristic
28C42×D59C2211yescharacteristic
29#14273661C2212yes—
30#14273660C2212yes—
31#14273659C2212yes—
32#14273658C2212yes—
33Dic59⋊C8C2212yes—
34#14273648C2212yes—
35#14273648C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic
38#127×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#102×C59C2212yes—
41#102×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×D4×C59—21no—
44C2×D4×C59—21no—
45C2×D4×C59C2312yes—
46C2×C22⋊D59—22no—
47C22×Dic59—22no—
48#11745687—44no—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53C2×Dic118—21no—
54C2×Dic118—21no—
55C2×C8×C59C2312yes—
56C4⋊C4×C59—21no—
57C4⋊C4×C59—21no—
58C4⋊C4×C59C2311yescharacteristic
59C4⋊C4×C59C2311yescharacteristic
60C42×C59C2311yescharacteristic
61C22⋊Dic59—22no—
62C22⋊Dic59—22no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59C2311yescharacteristic
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2312yes—
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73C4×Dic59—21no—
74C4×Dic59—21no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79C23×C59—22no—
80C22×D59C2×D411yescharacteristic
81D4×C59—24no—
82D4×C59—42no—
83D4×C59—42no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2411yescharacteristic
89C22⋊D59—44no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93C2×Dic59—44no—
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C4×D59—22no—
98C4×D59—22no—
99C4×D59—41no—
100Dic118—42no—
101Dic118—42no—
102Dic118—42no—
103C8×C59—22no—
104C59⋊C8—22no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59C22×D411yescharacteristic
109C2×D59—21no—
110C2×D59—21no—
111C2×D59—21no—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—41no—
115C4×C59—41no—
116C4×C592−1+412yes—
117Dic59—21no—
118Dic59—21no—
119Dic59—41no—
120Dic59—42no—
121Dic59—41no—
122Dic59AGL(1,ℤ/8)12yes—
123#3235—591nomaximal, Sylow
124C2×C59—82no—
125C2×C59#53611yescharacteristic
126C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C59#57511yescharacteristic
128D59—41no—
129#533—591no—
130#532—591no—
131#501—591no—
132#501—591no—
133#490—591no—
134#490D5911yescharacteristic, complemented
135#482—592no—
136#482—592no—
137#476—592no—
138#474—592no—
139#432—591no—
140C59#323511yescharacteristic, complemented, Sylow
141C2×#41—1181no—
142C4⋊Q8—591no—
143C4⋊Q8—591no—
144C4⋊Q8—591no—
145#127C2×D5911yescharacteristic
146#125—591no—
147#125C2×D5911yescharacteristic
148#124—1181no—
149C22⋊Q8—1181no—
150C22⋊Q8—1181no—
151#121—592no—
152#121—1181no—
153C4×Q8—1181no—
154C4×Q8—1181no—
155C4×D4—592no—
156C4×D4—1181no—
157#117—591no—
158#117—591no—
159C2×C42—591no—
160#107—592no—
161#107—592no—
162#106—592no—
163#106—592no—
164C4⋊C8—592no—
165#102—592no—
166#102—592no—
167#102C2×D5912yes—
168#102C2×D5912yes—
169C22⋊C8—592no—
170#97—591no—
171#97C2×D5911yescharacteristic
172#41—2364no—
173C2×Q8—1181no—
174C2×Q8—1181no—
175C2×Q8—1181no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—1182no—
179C2×D4C22×D5912yes—
180C22×C4—591no—
181C22×C4—591no—
182C22×C4—591no—
183C22×C4—1182no—
184C2×C8—592no—
185C2×C8C22×D5912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—591no—
189C4⋊C4—591no—
190C4⋊C4—592no—
191C4⋊C4—1181no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C4⋊C4C22×D5911yescharacteristic
197C4⋊C4C22×D5911yescharacteristic
198C22⋊C4—1181no—
199C22⋊C4—1181no—
200C22⋊C4—1182no—
201C22⋊C4—1182no—
202C42—591no—
203C42—591no—
204C42—591no—
205C42—1181no—
206C42—1181no—
207C42C22×D5911yescharacteristic
208C23—22no—
209C23—591no—
210Q8—2362no—
211Q8—2362no—
212Q8—2362no—
213D4—24no—
214D4—42no—
215D4—42no—
216D4—2364no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—591no—
220C2×C4—591no—
221C2×C4—591no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—1182no—
227C2×C4—2361no—
228C2×C4—2364no—
229C2×C4D4×D5911yescharacteristic
230C2×C4D4×D5911yescharacteristic
231C2×C4C23×D5911yescharacteristic
232C8—22no—
233C8—1182no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—1181no—
238C22—1181no—
239C22—1181no—
240C22C2×D4×D5911yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—41no—
245C4—592no—
246C4—1181no—
247C4—1181no—
248C4—2362no—
249C4—2361no—
250C4—2361no—
251C4#1427377412yes—
252C2—82no—
253C2—2361no—
254C2#1683797211yescharacteristic
255C2AGL(1,ℤ/8)×D5911yescharacteristic
256C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#490C2
socleC22×C59C22×D4
hypercenter#490D59
hypocenterC59#3235
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16837958C2semidirect
3. #16837812C2semidirect
4. #16837811C2semidirect
5. #16837766C2semidirect
6. #16837725C2semidirect
7. #16837724C2semidirect
8. #16837690C2semidirect
9. #16837680C2semidirect
10. #16837457C2semidirect
11. C59×#490C2semidirect
134. #490D59semidirect
140. C59#3235semidirect