Finite Group Databasebeta

← #21436450

Subgroups — #21436450

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#16838113C211yesmaximal, characteristic, complemented
2#16838057C211yesmaximal, characteristic
3#16837798C211yesmaximal, characteristic, complemented
4#16837734C212yesmaximal, complemented
5#16837719C212yesmaximal, complemented
6#16837688C211yesmaximal, characteristic, complemented
7#16837630C212yesmaximal, complemented
8C4×#11745670C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic, complemented
10#106×D59C212yesmaximal, complemented
11C59×#476C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×#11745670C2211yescharacteristic
14C2×C8×D59C2212yes—
15#14273727C2211yescharacteristic
16#14273718—21no—
17#14273709—22no—
18#14273707C2212yes—
19#14273706—21no—
20#14273703—22no—
21#14273698C2212yes—
22C4×Dic118C2211yescharacteristic
23C4×D236C2211yescharacteristic
24#14273689—21no—
25C4⋊C4×D59C2212yes—
26C4⋊C4×D59C2212yes—
27#14273659C2212yes—
28#14273658C2211yescharacteristic
29#14273658C2212yes—
30#14273658C2212yes—
31#14273652C2212yes—
32#14273650C2211yescharacteristic
33#14273648C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C4⋊Q8×C59C2211yescharacteristic
37C4×D4×C59C2211yescharacteristic
38#106×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#102×C59C2212yes—
41C2×Q8×C59—21no—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C2×C22⋊D59—22no—
45#11745685—44no—
46C2×D236D411yescharacteristic
47C2×C4×D59—22no—
48C2×C4×D59—22no—
49C2×C4×D59C2312yes—
50C2×Dic118—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2312yes—
55C4⋊C4×C59C2311yescharacteristic
56C22⋊C4×C59—21no—
57C42×C59C2311yescharacteristic
58C22⋊Dic59—22no—
59#11745670—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4D412yes—
62C4⋊Dic59—21no—
63C4⋊Dic59—22no—
64C4⋊Dic59D411yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66C4⋊Dic59C2312yes—
67Dic59⋊C4—21no—
68Dic59⋊C4—22no—
69Dic59⋊C4—22no—
70C4×Dic59—21no—
71C2×C59⋊C8C2311yescharacteristic
72C2×C59⋊C8C2311yescharacteristic
73C8×D59—24no—
74C23×C59—21no—
75C22×D59C2×D412yes—
76Q8×C59—81no—
77D4×C59—21no—
78D4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—42no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—44no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—22no—
89C2×Dic59C2×D412yes—
90D236SD1614yescomplemented
91C4×D59—22no—
92C4×D59—22no—
93C4×D59—44no—
94C4×D59—82no—
95Dic118—21no—
96Dic118—21no—
97Dic118—42no—
98C8×C59—22no—
99C59⋊C8—21no—
100C59⋊C8#4112yescomplemented
101C22×C59—41no—
102C22×C59—41no—
103C22×C59—41no—
104C22×C59C22×D411yescharacteristic
105C2×D59—22no—
106C2×D59—22no—
107C2×D59C2×SD1614yes—
108C4×C59—21no—
109C4×C59—41no—
110C4×C59—42no—
111C4×C59C2×SD1612yes—
112C4×C59C2×#4111yescharacteristic
113C4×C592−1+411yescharacteristic
114Dic59—22no—
115Dic59—41no—
116Dic59—42no—
117Dic59—41no—
118#3335—591nomaximal, Sylow
119C2×C59—81no—
120C2×C59#54711yescharacteristic
121C2×C59C22×SD1611yescharacteristic
122C2×C59#57711yescharacteristic
123D59—24no—
124#554—591no—
125#547—591no—
126#498—591no—
127#483—592no—
128#481—592no—
129#476D5911yescharacteristic, complemented
130#475—591no—
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×Q8—591no—
148C4×D4—591no—
149C4×D4—1181no—
150C4×D4C2×D5911yescharacteristic
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—592no—
160#103—591no—
161#102—591no—
162#102C2×D5912yes—
163C22⋊C8—592no—
164C4×C8—591no—
165#41—2364no—
166C2×Q8—21no—
167C2×Q8—591no—
168C2×Q8—1181no—
169C2×D4—591no—
170C2×D4—1182no—
171C2×D4C22×D5911yescharacteristic
172C22×C4—21no—
173C22×C4—592no—
174C22×C4—1182no—
175C22×C4—1182no—
176SD16—1182no—
177C2×C8—591no—
178C2×C8—591no—
179C2×C8—1184no—
180C2×C8C22×D5912yes—
181C4⋊C4—21no—
182C4⋊C4—591no—
183C4⋊C4—591no—
184C4⋊C4—592no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1181no—
189C4⋊C4—1181no—
190C4⋊C4C22×D5912yes—
191C4⋊C4C22×D5911yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—592no—
194C22⋊C4—1182no—
195C22⋊C4—1182no—
196C42—1181no—
197C42C22×D5911yescharacteristic
198C23—21no—
199C23—592no—
200Q8—81no—
201Q8—1181no—
202Q8—1181no—
203Q8—2362no—
204D4—21no—
205D4—21no—
206D4—594no—
207D4—2364no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—592no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1181no—
215C2×C4—1181no—
216C2×C4—1182no—
217C2×C4—4722no—
218C2×C4—2364no—
219C2×C4D4×D5911yescharacteristic
220C2×C4D4×D5911yescharacteristic
221C2×C4C23×D5911yescharacteristic
222C8—22no—
223C8—592no—
224C8—1181no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—594no—
229C22—1182no—
230C22—1182no—
231C22C2×D4×D5911yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—1182no—
236C4—2362no—
237C4—2361no—
238C4—2361no—
239C4SD16×D5912yes—
240C4#41×D5911yescharacteristic
241C4#1427377511yescharacteristic
242C2—81no—
243C2—1184no—
244C2#1683805411yescharacteristic
245C2C2×SD16×D5911yescharacteristic
246C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#476C2
socleC22×C59C22×D4
hypercenter#476D59
hypocenterC59#3335
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16838113C2semidirect
3. #16837798C2semidirect
4. #16837734C2semidirect
5. #16837719C2semidirect
6. #16837688C2semidirect
7. #16837630C2semidirect
8. C4×#11745670C2semidirect
9. #16837467C2semidirect
10. #106×D59C2semidirect
11. C59×#476C2semidirect
90. D236SD16semidirect
100. C59⋊C8#41semidirect
129. #476D59semidirect
135. C59#3335semidirect