Finite Group Databasebeta

← #21435308

Subgroups — #21435308

Order 7552.

322 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 113 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#16837957C211yesmaximal, characteristic
2#16837956C211yesmaximal, characteristic
3#16837810C212yesmaximal, complemented
4#16837769C212yesmaximal, complemented
5#16837745C212yesmaximal
6#16837741C212yesmaximal
7#16837694C211yesmaximal, characteristic, complemented
8#16837688C211yesmaximal, characteristic, complemented
9#16837687C211yesmaximal, characteristic, complemented
10#16837458C211yesmaximal, characteristic
11C59×#477C211yesmaximal, characteristic, complemented
12#14273727C2211yescharacteristic
13#14273726C2211yescharacteristic
14#14273725C2211yescharacteristic
15#14273718C2212yes—
16#14273717—21no—
17#14273707—21no—
18#14273707C2211yescharacteristic
19#14273705—21no—
20#14273703—21no—
21#14273703C2211yescharacteristic
22Q8×Dic59—21no—
23C4×Dic118—21no—
24C4×Dic118C2211yescharacteristic
25#14273692—21no—
26#14273685C2212yes—
27#14273684—21no—
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273659C2212yes—
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273651C2212yes—
35#14273650C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273637C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45C2×C4×D59D411yescharacteristic
46C2×C4×D59D411yescharacteristic
47C2×C4×D59C2311yescharacteristic
48C2×Dic118—21no—
49C2×Dic118—21no—
50C2×Dic118C2311yescharacteristic
51C2×C8×C59C2312yes—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2312yes—
55C4⋊C4×C59C2311yescharacteristic
56C42×C59—21no—
57C42×C59C2311yescharacteristic
58(C2×D59)⋊C4—21no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—22no—
61C4⋊Dic59—21no—
62C4⋊Dic59—21no—
63C4⋊Dic59—22no—
64C4⋊Dic59C2312yes—
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—21no—
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—22no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72C4×Dic59—21no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78C22×D59C2×D411yescharacteristic
79Q8×C59—21no—
80Q8×C59—21no—
81Q8×C59—42no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2411yescharacteristic
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59C2×D411yescharacteristic
92C2×Dic59C2×D411yescharacteristic
93C2×Dic59C2×D411yescharacteristic
94C4×D59—22no—
95C4×D59—21no—
96C4×D59—21no—
97C4×D59—41no—
98Dic118—21no—
99Dic118—21no—
100Dic118—42no—
101Dic118—42no—
102C8×C59—22no—
103C59⋊C8—22no—
104C22×C59C22×D411yescharacteristic
105C2×D59—21no—
106C2×D59—21no—
107C2×D59—21no—
108C4×C59—21no—
109C4×C59—41no—
110C4×C59—41no—
111C4×C59—42no—
112C4×C59#13712yes—
113C4×C592−1+411yescharacteristic
114C4×C592−1+411yescharacteristic
115Dic59—21no—
116Dic59—21no—
117Dic59—21no—
118Dic59—41no—
119Dic59—42no—
120Dic59—41no—
121#3237—591nomaximal, Sylow
122C2×C59#53611yescharacteristic
123C2×C59C2×#13711yescharacteristic
124C2×C59#57511yescharacteristic
125D59—41no—
126#533—591no—
127#533—591no—
128#501—592no—
129#491—592no—
130#485—592no—
131#485—592no—
132#477—591no—
133#477D5911yescharacteristic, complemented
134#475—591no—
135#475—591no—
136#432—591no—
137C59#323711yescharacteristic, complemented, Sylow
138C4⋊Q8—591no—
139C4⋊Q8—591no—
140C4⋊Q8—591no—
141C4⋊Q8C2×D5911yescharacteristic
142#125—592no—
143#125—1181no—
144C22⋊Q8—591no—
145C22⋊Q8—591no—
146C22⋊Q8—1181no—
147C22⋊Q8—1181no—
148C22⋊Q8—1181no—
149C4×Q8—591no—
150C4×Q8—1181no—
151C4×Q8—1181no—
152C4×Q8—1181no—
153C4×Q8C2×D5911yescharacteristic
154#117—592no—
155#117—1181no—
156C2×C42—591no—
157#107—592no—
158#107C2×D5912yes—
159#106—592no—
160#106—592no—
161C4⋊C8—591no—
162C4⋊C8C2×D5911yescharacteristic
163#103—592no—
164#103—592no—
165#103—592no—
166#103C2×D5912yes—
167C22⋊C8—592no—
168#97—592no—
169C2×Q8—21no—
170C2×Q8—591no—
171C2×Q8—1181no—
172C2×Q8—1181no—
173C2×Q8C22×D5911yescharacteristic
174C22×C4—591no—
175C22×C4—591no—
176C22×C4—591no—
177C2×C8—592no—
178C2×C8C22×D5912yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—592no—
182C4⋊C4—591no—
183C4⋊C4—1181no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1181no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4C22×D5912yes—
193C4⋊C4C22×D5911yescharacteristic
194C22⋊C4—1182no—
195C22⋊C4—1181no—
196C22⋊C4—1181no—
197C42—21no—
198C42—591no—
199C42—591no—
200C42—591no—
201C42—1182no—
202C42—1181no—
203C42C22×D5911yescharacteristic
204C23—591no—
205Q8—21no—
206Q8—21no—
207Q8—42no—
208Q8—1181no—
209Q8—1181no—
210Q8—2362no—
211Q8—2362no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—591no—
216C2×C4—591no—
217C2×C4—591no—
218C2×C4—1182no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—1182no—
222C2×C4—1181no—
223C2×C4—1181no—
224C2×C4—2361no—
225C2×C4D4×D5911yescharacteristic
226C2×C4D4×D5911yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—22no—
229C8—1182no—
230C22—1181no—
231C22—1181no—
232C22—1181no—
233C22C2×D4×D5911yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—1181no—
239C4—1181no—
240C4—1181no—
241C4—2362no—
242C4—2361no—
243C4—2361no—
244C4#1427375912yes—
245C4#1427377411yescharacteristic
246C4#1427377511yescharacteristic
247C2—2361no—
248C2#1683797511yescharacteristic
249C2C2×#1427375911yescharacteristic
250C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3237
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16837810C2semidirect
4. #16837769C2semidirect
7. #16837694C2semidirect
8. #16837688C2semidirect
9. #16837687C2semidirect
11. C59×#477C2semidirect
133. #477D59semidirect
137. C59#3237semidirect