Finite Group Databasebeta

← #21433620

Subgroups — #21433620

Order 7552.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273757C211yesmaximal, characteristic, complemented
2C22×#11745660C211yesmaximal, characteristic, complemented
3#16837966C211yesmaximal, characteristic
4#16837879C211yesmaximal, characteristic, complemented
5#16837627C214yesmaximal, complemented
6#16837601C214yesmaximal, complemented
7#16837428C211yesmaximal, characteristic, complemented
8#16837406C211yesmaximal, characteristic, complemented
9C59×#416C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12#14273757—24no—
13C2×#11745672C2212yescomplemented
14C2×#11745660—24no—
15C2×#11745660C2214yes—
16C2×#11745670C2212yescomplemented
17C2×#11745664C2211yescharacteristic
18#14273723C2212yes—
19#14273716C2212yes—
20#14273701—22no—
21#14273695—22no—
22C4×Dic118—22no—
23#14273692C2214yescomplemented
24#14273686C2211yescharacteristic
25#14273683—22no—
26Dic59⋊C8C2214yescomplemented
27#14273647C2214yes—
28C2×#41×C59C2211yescharacteristic
29C22×C8×C59C2211yescharacteristic
30#117×C59C2211yescharacteristic
31#103×C59C2212yescomplemented
32#102×C59C2212yescomplemented
33C23×D59—21no—
34#41×C59—22no—
35#41×C59—22no—
36C2×Q8×C59C2311yescharacteristic
37C2×D4×C59—21no—
38C2×D4×C59C2311yescharacteristic
39C22×C4×C59—21no—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—24no—
42C22×Dic59—21no—
43C2×D236—22no—
44C2×D236—22no—
45C2×D236—21no—
46C2×D236C2312yes—
47C2×Dic118—21no—
48C2×Dic118—22no—
49C2×Dic118D414yescomplemented
50C2×Dic118C2312yes—
51C2×C8×C59—22no—
52C2×C8×C59C2312yes—
53C4⋊C4×C59C2312yes—
54C22⋊C4×C59—21no—
55C42×C59—21no—
56C22⋊Dic59D412yes—
57#11745672—24no—
58#11745670—24no—
59(C2×D59)⋊C4—24no—
60C4⋊Dic59D412yes—
61Dic59⋊C4—24no—
62C4×Dic59—24no—
63C4×Dic59C2312yes—
64#11745664—22no—
65C2×C59⋊C8C2312yes—
66#11745660—28no—
67C23×C59—21no—
68C23×C59C2×D411yescharacteristic
69C22×D59—22no—
70C22×D59—42no—
71C22×D59—82no—
72Q8×C59—21no—
73Q8×C59—21no—
74D4×C59—21no—
75D4×C59—21no—
76D4×C59—42no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—42no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D412yes—
82C2×C4×C59#4112yes—
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—84no—
85C2×Dic59—24no—
86C2×Dic59—22no—
87C2×Dic59C2×D414yes—
88D236—22no—
89D236—22no—
90D236—42no—
91Dic118—24no—
92Dic118—22no—
93Dic118C2×D414yes—
94C8×C59—22no—
95C59⋊C8—22no—
96C22×C59—22no—
97C22×C59—41no—
98C22×C59—42no—
99C22×C59#12112yes—
100C22×C59C22×D411yescharacteristic
101C2×D59—42no—
102C2×D59—44no—
103C2×D59—84no—
104C4×C59—41no—
105C4×C59—42no—
106C4×C59#12112yes—
107C4×C59C22×D411yescharacteristic
108C4×C59C2×#4111yescharacteristic
109Dic59—24no—
110Dic59—24no—
111#3043—591nomaximal, Sylow
112C2×C59—22no—
113C2×C59—81no—
114C2×C59C2×#12111yescharacteristic
115C2×C59#57712yes—
116D59—82no—
117C2×#137—591no—
118C22×SD16—591no—
119#535—591no—
120#519—591no—
121#464—594no—
122#460—594no—
123#424—591no—
124#418—591no—
125#416D5911yescharacteristic, complemented
126C59#304311yescharacteristic, complemented, Sylow
127C2×#41C2×D5911yescharacteristic
128C22×Q8—591no—
129C22×D4—591no—
130#137—1184no—
131C2×Q16—592no—
132C2×SD16—592no—
133C2×SD16—594no—
134C2×SD16—1184no—
135C2×M16—591no—
136C22×C8C2×D5911yescharacteristic
137#127—592no—
138#124—592no—
139#121—1182no—
140#120—1182no—
141C4×Q8—594no—
142C4×Q8—1182no—
143#117—591no—
144#117—1182no—
145#117C2×D5911yescharacteristic
146C4⋊C8—594no—
147#103C2×D5912yescomplemented
148#102—594no—
149#102C2×D5912yescomplemented
150C24—1181no—
151#41—22no—
152#41—22no—
153C2×Q8—594no—
154C2×Q8—592no—
155C2×Q8—1182no—
156C2×Q8—1181no—
157C2×Q8C22×D5911yescharacteristic
158C2×D4—21no—
159C2×D4—592no—
160C2×D4—1184no—
161C2×D4—1182no—
162C2×D4—1182no—
163C2×D4—1181no—
164C2×D4C22×D5911yescharacteristic
165C22×C4—21no—
166C22×C4—1181no—
167C22×C4C22×D5911yescharacteristic
168Q16—1184no—
169SD16—1188no—
170SD16—1184no—
171M16—1182no—
172C2×C8—22no—
173C2×C8—592no—
174C2×C8C22×D5912yes—
175C4⋊C4—592no—
176C4⋊C4—1184no—
177C4⋊C4C22×D5912yes—
178C22⋊C4—21no—
179C22⋊C4—592no—
180C22⋊C4—1184no—
181C42—21no—
182C42—592no—
183C42—1184no—
184C23—21no—
185C23—1182no—
186C23—4722no—
187C23—2362no—
188C23D4×D5911yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—594no—
192Q8—1184no—
193Q8—1182no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—1182no—
198D4—1182no—
199D4—4724no—
200D4—2362no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—594no—
205C2×C4—1184no—
206C2×C4—1182no—
207C2×C4#1174568512yes—
208C2×C4D4×D5911yescharacteristic
209C2×C4D4×D5912yes—
210C2×C4C23×D5911yescharacteristic
211C8—22no—
212C8—1182no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—4724no—
217C22—2362no—
218C22—2364no—
219C22#1427370012yes—
220C22C2×D4×D5911yescharacteristic
221C4—41no—
222C4—42no—
223C4—1184no—
224C4—1184no—
225C4#1427370012yes—
226C4C2×D4×D5911yescharacteristic
227C4C2×#1174568511yescharacteristic
228C2—22no—
229C2—81no—
230C2—4722no—
231C2C2×#1427370011yescharacteristic
232C2#1683820912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#416C2
socleC22×C59C22×D4
hypercenter#416D59
hypocenterC59#3043
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14273757C2semidirect
2. C22×#11745660C2semidirect
4. #16837879C2semidirect
5. #16837627C2semidirect
6. #16837601C2semidirect
7. #16837428C2semidirect
8. #16837406C2semidirect
9. C59×#416C2semidirect
13. C2×#11745672C22semidirect
16. C2×#11745670C22semidirect
23. #14273692C22semidirect
26. Dic59⋊C8C22semidirect
31. #103×C59C22semidirect
32. #102×C59C22semidirect
49. C2×Dic118D4semidirect
125. #416D59semidirect
126. C59#3043semidirect
147. #103C2×D59semidirect
149. #102C2×D59semidirect