Finite Group Databasebeta

← #21433608

Subgroups — #21433608

Order 7552.

494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14273753C211yesmaximal, characteristic
2C22×#11745670C211yesmaximal, characteristic, complemented
3#16837978C211yesmaximal, characteristic, complemented
4#16837617C214yesmaximal, complemented
5#16837607C214yesmaximal, complemented
6#16837429C211yesmaximal, characteristic, complemented
7#16837410C211yesmaximal, characteristic, complemented
8#16837396C211yesmaximal, characteristic, complemented
9C59×#518C211yesmaximal, characteristic, complemented
10C2×#11745685C2211yescharacteristic
11C22×Dic118C2211yescharacteristic
12#14273753—24no—
13C2×#11745670—24no—
14C2×#11745670C2214yes—
15C2×#11745670C2212yes—
16C2×#11745669C2212yes—
17C2×#11745664C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19#14273727C2212yescomplemented
20#14273715C2212yescomplemented
21#14273711—22no—
22#14273707—22no—
23C4⋊(C59⋊C8)C2214yescomplemented
24#14273650C2212yescomplemented
25#14273650C2214yescomplemented
26#14273647C2212yescomplemented
27C22×D4×C59C2211yescharacteristic
28C4×D4×C59—22no—
29C4×D4×C59C2214yes—
30#117×C59C2211yescharacteristic
31#117×C59C2211yescharacteristic
32C2×C22⋊C4×C59—22no—
33C24×C59—21no—
34C2×D4×C59—21no—
35C2×D4×C59—22no—
36C2×D4×C59D414yes—
37C2×D4×C59C2312yes—
38C22×C4×C59—24no—
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—21no—
41C22×Dic59—21no—
42#11745685—22no—
43#11745685—22no—
44C2×D236C2311yescharacteristic
45C2×C4×D59—21no—
46C2×Dic118—22no—
47C2×Dic118—22no—
48C2×Dic118—21no—
49C2×Dic118C2312yes—
50C2×Dic118C2311yescharacteristic
51C4⋊C4×C59D412yes—
52C4⋊C4×C59C2312yes—
53C22⋊C4×C59—21no—
54C22⋊C4×C59—24no—
55C22⋊C4×C59D412yes—
56C42×C59—21no—
57C42×C59C2312yes—
58#11745670—28no—
59#11745670—24no—
60#11745669—24no—
61(C2×D59)⋊C4—24no—
62C4⋊Dic59—24no—
63#11745664—22no—
64C2×C59⋊C8—22no—
65C2×C59⋊C8C2312yes—
66C2×C59⋊C8C2312yes—
67C23×C59—22no—
68C23×C59—24no—
69C23×C59—82no—
70C23×C59C2×D411yescharacteristic
71C22×D59—21no—
72D4×C59—24no—
73D4×C59—22no—
74D4×C59C2×D414yes—
75C2×C4×C59—22no—
76C2×C4×C59—84no—
77C2×C4×C59C2×D412yes—
78C2×C4×C59C2×D414yes—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59#4112yes—
81C2×C4×C59C2411yescharacteristic
82C22⋊D59—42no—
83C2×Dic59—21no—
84C2×Dic59—22no—
85C2×Dic59—42no—
86D236—21no—
87D236—21no—
88C4×D59—42no—
89Dic118—22no—
90Dic118—21no—
91Dic118—22no—
92Dic118—21no—
93Dic118—42no—
94C59⋊C8—22no—
95C59⋊C8—22no—
96C22×C59—22no—
97C22×C59—24no—
98C22×C59—44no—
99C22×C59—84no—
100C22×C59#12112yes—
101C22×C59C22×D411yescharacteristic
102C2×D59—41no—
103C2×D59—42no—
104C4×C59—24no—
105C4×C59—42no—
106C4×C59#12112yes—
107C4×C59C22×D411yescharacteristic
108C4×C59C2×#4111yescharacteristic
109Dic59—42no—
110Dic59—41no—
111#3042—591nomaximal, Sylow
112C2×C59—22no—
113C2×C59—44no—
114C2×C59C2×#12111yescharacteristic
115C2×C59#57712yes—
116D59—81no—
117C2×AGL(1,ℤ/8)—591no—
118C22×SD16—591no—
119#536—591no—
120#518D5911yescharacteristic, complemented
121#463—594no—
122#461—594no—
123#424—591no—
124#419—591no—
125#416—591no—
126C59#304211yescharacteristic, complemented, Sylow
127C2×#41—591no—
128C22×Q8—591no—
129C22×D4C2×D5911yescharacteristic
130AGL(1,ℤ/8)—1184no—
131C2×SD16—594no—
132C2×SD16—592no—
133C2×SD16—1184no—
134C2×D8—592no—
135C2×M16—591no—
136C22×C8—591no—
137C4⋊Q8—592no—
138#124—592no—
139#123—1182no—
140C22⋊Q8—1182no—
141C4×D4—22no—
142C4×D4C2×D5914yes—
143#117C2×D5911yescharacteristic
144#117C2×D5911yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—594no—
147#103—592no—
148#103—594no—
149#102—592no—
150C24—21no—
151#41—1182no—
152#41—1182no—
153C2×Q8—592no—
154C2×Q8—591no—
155C2×Q8—1181no—
156C2×Q8—1182no—
157C2×Q8—1182no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—591no—
161C2×D4—1181no—
162C2×D4D23614yes—
163C2×D4C22×D5912yes—
164C22×C4—24no—
165C22×C4—1181no—
166C22×C4—1181no—
167C22×C4C22×D5911yescharacteristic
168SD16—1188no—
169SD16—1184no—
170D8—1184no—
171M16—1182no—
172C2×C8—592no—
173C2×C8—592no—
174C2×C8—1182no—
175C4⋊C4—1184no—
176C4⋊C4C22⋊D5912yes—
177C4⋊C4C22×D5912yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—1184no—
181C22⋊C4C22⋊D5912yes—
182C42—21no—
183C42C22×D5912yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1181no—
188C23C2×C22⋊D5911yescharacteristic
189Q8—1182no—
190Q8—1181no—
191Q8—1182no—
192Q8—1181no—
193Q8—2362no—
194D4—24no—
195D4—22no—
196D4—1181no—
197D4—1181no—
198D4—2362no—
199D4C2×D23614yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—1182no—
203C2×C4—1181no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4C2×D23612yes—
207C2×C4#1174568512yes—
208C2×C4C2×C22⋊D5914yes—
209C2×C4C2×C22⋊D5911yescharacteristic
210C2×C4C23×D5911yescharacteristic
211C8—1182no—
212C8—1182no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—2361no—
218C22—2362no—
219C22#1427370112yes—
220C22C22×C22⋊D5911yescharacteristic
221C4—24no—
222C4—42no—
223C4—2361no—
224C4—2362no—
225C4#1427370112yes—
226C4C22×D23611yescharacteristic
227C4C2×#1174568511yescharacteristic
228C2—22no—
229C2—44no—
230C2—4721no—
231C2C2×#1427370111yescharacteristic
232C2#1683821312yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#518C2
socleC22×C59C22×D4
hypercenter#518D59
hypocenterC59#3042
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#11745670C2semidirect
3. #16837978C2semidirect
4. #16837617C2semidirect
5. #16837607C2semidirect
6. #16837429C2semidirect
7. #16837410C2semidirect
8. #16837396C2semidirect
9. C59×#518C2semidirect
19. #14273727C22semidirect
20. #14273715C22semidirect
23. C4⋊(C59⋊C8)C22semidirect
24. #14273650C22semidirect
25. #14273650C22semidirect
26. #14273647C22semidirect
120. #518D59semidirect
126. C59#3042semidirect