Finite Group Databasebeta

← #21436456

Subgroups — #21436456

Order 7552.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#16838112C211yesmaximal, characteristic, complemented
2#16838055C211yesmaximal, characteristic
3#16837798C211yesmaximal, characteristic, complemented
4#16837731C212yesmaximal, complemented
5#16837722C212yesmaximal, complemented
6#16837693C211yesmaximal, characteristic, complemented
7#16837634C212yesmaximal, complemented
8C4×#11745671C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic, complemented
10#106×D59C212yesmaximal, complemented
11C59×#475C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×#11745671C2211yescharacteristic
14C2×C8×D59C2212yes—
15#14273727C2211yescharacteristic
16#14273719—21no—
17#14273712—22no—
18#14273705—22no—
19#14273703—21no—
20#14273703C2212yes—
21#14273702C2212yes—
22C4×D236—21no—
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25C4⋊C4×D59C2212yes—
26C4⋊C4×D59C2212yes—
27#14273659C2212yes—
28#14273658C2212yes—
29#14273658C2211yescharacteristic
30#14273658C2212yes—
31#14273651C2211yescharacteristic
32#14273649C2212yes—
33#14273647C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C4⋊Q8×C59C2211yescharacteristic
37C4×Q8×C59C2211yescharacteristic
38#106×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59—21no—
42C2×Q8×C59C2311yescharacteristic
43#11745689—44no—
44C2×D236—22no—
45C2×D236D411yescharacteristic
46C2×D236C2311yescharacteristic
47C2×C4×D59—22no—
48C2×C4×D59—21no—
49C2×C4×D59—22no—
50C2×C4×D59C2312yes—
51C2×Dic118—21no—
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C42×C59—21no—
58C42×C59C2311yescharacteristic
59#11745671—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4D412yes—
64C4⋊Dic59—21no—
65C4⋊Dic59D411yescharacteristic
66C4⋊Dic59C2312yes—
67C4⋊Dic59C2311yescharacteristic
68Dic59⋊C4—22no—
69Dic59⋊C4—22no—
70Dic59⋊C4—22no—
71C2×C59⋊C8C2311yescharacteristic
72C2×C59⋊C8C2311yescharacteristic
73C8×D59—24no—
74C22×D59—21no—
75C22×D59C2×D412yes—
76Q8×C59—21no—
77Q8×C59—21no—
78Q8×C59—42no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59C2×D412yes—
88D236—21no—
89D236—21no—
90D236—44no—
91D236SD1614yescomplemented
92C4×D59—22no—
93C4×D59—22no—
94C4×D59—44no—
95C4×D59—42no—
96C4×D59—82no—
97Dic118—81no—
98C8×C59—22no—
99C59⋊C8—21no—
100C59⋊C8#4112yescomplemented
101C22×C59C22×D411yescharacteristic
102C2×D59—22no—
103C2×D59—22no—
104C2×D59—41no—
105C2×D59—41no—
106C2×D59—41no—
107C2×D59C2×SD1614yes—
108C4×C59—21no—
109C4×C59—41no—
110C4×C59—42no—
111C4×C59—41no—
112C4×C59C2×SD1612yes—
113C4×C59C2×#4111yescharacteristic
114C4×C592−1+411yescharacteristic
115Dic59—22no—
116Dic59—41no—
117Dic59—42no—
118#3335—591nomaximal, Sylow
119C2×C59#54711yescharacteristic
120C2×C59C22×SD1611yescharacteristic
121C2×C59#57711yescharacteristic
122D59—24no—
123D59—81no—
124#554—591no—
125#547—591no—
126#498—591no—
127#483—592no—
128#481—592no—
129#476—591no—
130#475D5911yescharacteristic, complemented
131#465—592no—
132C4×SD16—591no—
133C8×D4—591no—
134C2×#106—592no—
135C59#333511yescharacteristic, complemented, Sylow
136C2×#41—1181no—
137C2×SD16—591no—
138C22×C8—592no—
139C4⋊Q8—591no—
140C4⋊Q8C2×D5911yescharacteristic
141#125—1181no—
142#123—1182no—
143C22⋊Q8—592no—
144C22⋊Q8—1182no—
145C22⋊Q8—1181no—
146#121—592no—
147C4×Q8C2×D5911yescharacteristic
148C4×D4—591no—
149C4×D4—591no—
150C4×D4—1181no—
151C2×C4⋊C4—592no—
152C2×C4⋊C4—592no—
153#106—592no—
154#106—591no—
155#106—592no—
156#106—592no—
157#106C2×D5912yes—
158C4⋊C8C2×D5911yescharacteristic
159#103—591no—
160#103C2×D5912yes—
161#102—592no—
162#102—591no—
163C22⋊C8—592no—
164C4×C8—591no—
165#41—2364no—
166C2×Q8—21no—
167C2×Q8—1181no—
168C2×Q8C22×D5911yescharacteristic
169C2×D4—591no—
170C2×D4—591no—
171C2×D4—1182no—
172C22×C4—592no—
173C22×C4—1182no—
174C22×C4—1182no—
175C22×C4—1181no—
176SD16—1182no—
177C2×C8—591no—
178C2×C8—591no—
179C2×C8—1184no—
180C2×C8C22×D5912yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—591no—
184C4⋊C4—592no—
185C4⋊C4—591no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1181no—
190C4⋊C4C22×D5911yescharacteristic
191C4⋊C4C22×D5912yes—
192C22⋊C4—592no—
193C22⋊C4—1182no—
194C22⋊C4—1182no—
195C22⋊C4—1181no—
196C42—21no—
197C42C22×D5911yescharacteristic
198C23—592no—
199C23—1181no—
200Q8—21no—
201Q8—21no—
202Q8—42no—
203Q8—4721no—
204D4—594no—
205D4—1181no—
206D4—1181no—
207D4—2364no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—592no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1181no—
216C2×C4—4722no—
217C2×C4—2364no—
218C2×C4—2362no—
219C2×C4D4×D5911yescharacteristic
220C2×C4D4×D5911yescharacteristic
221C2×C4C23×D5911yescharacteristic
222C8—22no—
223C8—592no—
224C8—1181no—
225C22—594no—
226C22—1182no—
227C22—1182no—
228C22—2361no—
229C22—2361no—
230C22—2361no—
231C22C2×D4×D5911yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—41no—
236C4—1182no—
237C4—2361no—
238C4—2362no—
239C4SD16×D5912yes—
240C4#41×D5911yescharacteristic
241C4#1427377511yescharacteristic
242C2—1184no—
243C2—4721no—
244C2#1683805411yescharacteristic
245C2C2×SD16×D5911yescharacteristic
246C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#475C2
socleC22×C59C22×D4
hypercenter#475D59
hypocenterC59#3335
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16838112C2semidirect
3. #16837798C2semidirect
4. #16837731C2semidirect
5. #16837722C2semidirect
6. #16837693C2semidirect
7. #16837634C2semidirect
8. C4×#11745671C2semidirect
9. #16837467C2semidirect
10. #106×D59C2semidirect
11. C59×#475C2semidirect
91. D236SD16semidirect
100. C59⋊C8#41semidirect
130. #475D59semidirect
135. C59#3335semidirect