Finite Group Databasebeta

← #21433611

Subgroups — #21433611

Order 7552.

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

normal subgroups only

This group has 494 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×#14273752C211yesmaximal, characteristic
2C22×#11745660C211yesmaximal, characteristic, complemented
3#16837973C211yesmaximal, characteristic, complemented
4#16837876C211yesmaximal, characteristic, complemented
5#16837616C214yesmaximal, complemented
6#16837606C214yesmaximal, complemented
7#16837428C211yesmaximal, characteristic, complemented
8#16837410C211yesmaximal, characteristic, complemented
9C59×#416C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12#14273752—24no—
13C2×#11745660—24no—
14C2×#11745660C2214yes—
15C2×#11745671C2212yes—
16C2×#11745669C2212yes—
17C2×#11745664C2211yescharacteristic
18#14273725C2212yescomplemented
19#14273714C2212yescomplemented
20#14273708—22no—
21#14273706—22no—
22C4×D236—22no—
23#14273689C2214yes—
24#14273686C2211yescharacteristic
25C22⋊C4×D59—22no—
26Dic59⋊C8C2214yescomplemented
27#14273650C2214yescomplemented
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
41C22×Dic59—21no—
42C2×D236—21no—
43C2×D236—22no—
44C2×D236D414yes—
45C2×D236C2312yes—
46C2×C4×D59—24no—
47C2×Dic118—22no—
48C2×Dic118—22no—
49C2×Dic118—21no—
50C2×Dic118C2312yes—
51C2×C8×C59—22no—
52C2×C8×C59C2312yes—
53C4⋊C4×C59C2312yes—
54C22⋊C4×C59—21no—
55C42×C59—21no—
56C22⋊Dic59—24no—
57C22⋊Dic59D412yes—
58#11745671—24no—
59#11745669—24no—
60(C2×D59)⋊C4—24no—
61C4⋊Dic59D412yes—
62Dic59⋊C4—24no—
63C4×Dic59C2312yes—
64#11745664—22no—
65C2×C59⋊C8C2312yes—
66#11745660—28no—
67C23×C59—21no—
68C23×C59C2×D411yescharacteristic
69C22×D59—22no—
70C22×D59—24no—
71C22×D59—82no—
72Q8×C59—21no—
73Q8×C59—21no—
74D4×C59—21no—
75D4×C59—21no—
76D4×C59—42no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—42no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D412yes—
82C2×C4×C59#4112yes—
83C2×C4×C59C2411yescharacteristic
84C2×Dic59—22no—
85C2×Dic59—42no—
86C2×Dic59C2×D414yes—
87D236—24no—
88D236—22no—
89D236C2×D414yes—
90C4×D59—84no—
91Dic118—22no—
92Dic118—22no—
93Dic118—42no—
94C8×C59—22no—
95C59⋊C8—22no—
96C22×C59—22no—
97C22×C59—41no—
98C22×C59—42no—
99C22×C59#12112yes—
100C22×C59C22×D411yescharacteristic
101C2×D59—24no—
102C2×D59—44no—
103C2×D59—84no—
104C4×C59—41no—
105C4×C59—42no—
106C4×C59#12112yes—
107C4×C59C22×D411yescharacteristic
108C4×C59C2×#4111yescharacteristic
109Dic59—24no—
110Dic59—42no—
111#3042—591nomaximal, Sylow
112C2×C59—22no—
113C2×C59—81no—
114C2×C59C2×#12111yescharacteristic
115C2×C59#57712yes—
116D59—44no—
117C2×AGL(1,ℤ/8)—591no—
118C22×SD16—591no—
119#536—591no—
120#518—591no—
121#463—594no—
122#461—594no—
123#424—591no—
124#419—591no—
125#416D5911yescharacteristic, complemented
126C59#304211yescharacteristic, complemented, Sylow
127C2×#41C2×D5911yescharacteristic
128C22×Q8—591no—
129C22×D4—591no—
130AGL(1,ℤ/8)—1184no—
131C2×SD16—592no—
132C2×SD16—594no—
133C2×SD16—1184no—
134C2×D8—592no—
135C2×M16—591no—
136C22×C8C2×D5911yescharacteristic
137C4⋊Q8—592no—
138#124—592no—
139#123—1182no—
140C22⋊Q8—1182no—
141C4×D4—594no—
142C4×D4—1182no—
143#117—591no—
144#117C2×D5911yescharacteristic
145C2×C22⋊C4—1182no—
146C4⋊C8—594no—
147#103—594no—
148#103C2×D5912yescomplemented
149#102C2×D5912yescomplemented
150C24—1181no—
151#41—22no—
152#41—22no—
153C2×Q8—592no—
154C2×Q8—1181no—
155C2×Q8—1182no—
156C2×Q8—1182no—
157C2×Q8C22×D5911yescharacteristic
158C2×D4—21no—
159C2×D4—594no—
160C2×D4—592no—
161C2×D4—1182no—
162C2×D4—1181no—
163C2×D4C22×D5911yescharacteristic
164C22×C4—21no—
165C22×C4—1184no—
166C22×C4—1181no—
167C22×C4C22×D5911yescharacteristic
168SD16—1188no—
169SD16—1184no—
170D8—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—
181C22⋊C4—1184no—
182C42—21no—
183C42—592no—
184C23—21no—
185C23—1184no—
186C23—1182no—
187C23—4722no—
188C23D4×D5911yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—1182no—
192Q8—1182no—
193Q8—2362no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—594no—
198D4—1184no—
199D4—1182no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—594no—
204C2×C4—1182no—
205C2×C4—4724no—
206C2×C4—2362no—
207C2×C4#1174568512yes—
208C2×C4D4×D5911yescharacteristic
209C2×C4D4×D5912yes—
210C2×C4C23×D5911yescharacteristic
211C8—22no—
212C8—1182no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—1184no—
217C22—4724no—
218C22—2364no—
219C22#1427370012yes—
220C22C2×D4×D5911yescharacteristic
221C4—41no—
222C4—42no—
223C4—1184no—
224C4—2362no—
225C4#1427370012yes—
226C4C2×D4×D5911yescharacteristic
227C4C2×#1174568511yescharacteristic
228C2—22no—
229C2—81no—
230C2—2364no—
231C2C2×#1427370011yescharacteristic
232C2#1683820912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#416C2
socleC22×C59C22×D4
hypercenter#416D59
hypocenterC59#3042
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
2. C22×#11745660C2semidirect
3. #16837973C2semidirect
4. #16837876C2semidirect
5. #16837616C2semidirect
6. #16837606C2semidirect
7. #16837428C2semidirect
8. #16837410C2semidirect
9. C59×#416C2semidirect
18. #14273725C22semidirect
19. #14273714C22semidirect
26. Dic59⋊C8C22semidirect
27. #14273650C22semidirect
31. #103×C59C22semidirect
32. #102×C59C22semidirect
125. #416D59semidirect
126. C59#3042semidirect
148. #103C2×D59semidirect
149. #102C2×D59semidirect