Finite Group Databasebeta

← #21433452

Subgroups — #21433452

Order 7552.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273772C211yesmaximal, characteristic, complemented
2#16838200C212yesmaximal, complemented
3#16837579C214yesmaximal, complemented
4#16837569C214yesmaximal, complemented
5#16837420C212yesmaximal, complemented
6C2×#14273644C211yesmaximal, characteristic, complemented
7C59×#535C211yesmaximal, characteristic, complemented
8#14273772—22no—
9#14273772—24no—
10#14273772C2214yes—
11C2×#11745685C2212yes—
12C2×#11745687—22no—
13C22×C22⋊D59—22no—
14C2×D4×D59—22no—
15#14273758C2214yescomplemented
16#14273757—22no—
17#14273753C2214yescomplemented
18#14273752—22no—
19#14273747—24no—
20C2×#11745664C2212yescomplemented
21#14273655C2218yescomplemented
22#14273644C2214yescomplemented
23C2×#41×C59C2211yescharacteristic, complemented
24C22×D4×C59C2211yescharacteristic
25#127×C59C2212yescomplemented
26#124×C59C2212yescomplemented
27#121×C59—22no—
28#120×C59—22no—
29#117×C59C2211yescharacteristic, complemented
30C24×C59D412yes—
31C23×D59—22no—
32#41×C59—22no—
33#41×C59—22no—
34C2×Q8×C59C2311yescharacteristic, complemented
35C2×D4×C59—21no—
36C2×D4×C59—24no—
37C2×D4×C59—22no—
38C2×D4×C59—22no—
39C2×D4×C59D412yes—
40C2×D4×C59C2312yes—
41C2×D4×C59C2311yescharacteristic, complemented
42C22×C4×C59—21no—
43C22×C4×C59C2311yescharacteristic
44C2×C22⋊D59—24no—
45C2×C22⋊D59—28no—
46C2×C22⋊D59—22no—
47C2×C22⋊D59—28no—
48C22×Dic59—22no—
49#11745687—28no—
50#11745687—28no—
51D4×D59—28no—
52D4×D59—28no—
53#11745685—22no—
54#11745685—22no—
55#11745685D414yescomplemented
56#11745685C2314yes—
57C2×D236D412yescomplemented
58C2×C4×D59—22no—
59C2×Dic118D412yescomplemented
60C4⋊C4×C59—21no—
61C22⋊C4×C59—21no—
62C22⋊C4×C59—24no—
63C42×C59C2312yescomplemented
64#11745672—24no—
65#11745671—24no—
66#11745670—24no—
67#11745669—24no—
68#11745664—22no—
69#11745664C2314yescomplemented
70C2×C59⋊C8—22no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—21no—
74C23×C59—82no—
75C23×C59C2×D414yes—
76C23×C59C2×D411yescharacteristic
77C22×D59—22no—
78C22×D59—28no—
79C22×D59—84no—
80Q8×C59—22no—
81D4×C59—24no—
82D4×C59—24no—
83D4×C59—22no—
84D4×C59—41no—
85D4×C59—41no—
86D4×C59—84no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—42no—
90C2×C4×C59C2×D412yes—
91C2×C4×C59C2×D412yes—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2411yescharacteristic
94C22⋊D59—216no—
95C22⋊D59—24no—
96C22⋊D59—24no—
97C2×Dic59—28no—
98C2×Dic59—22no—
99D236—22no—
100D236C2×D414yes—
101C4×D59—24no—
102C4×D59—24no—
103Dic118—22no—
104Dic118C2×D414yes—
105C59⋊C8—24no—
106C22×C59—24no—
107C22×C59—41no—
108C22×C59—44no—
109C22×C59—44no—
110C22×C59—42no—
111C22×C59—41no—
112C22×C59—82no—
113C22×C59#12011yescharacteristic
114C22×C59#12011yescharacteristic
115C22×C59C22×D411yescharacteristic
116C2×D59—24no—
117C2×D59—44no—
118C2×D59—88no—
119C4×C59—42no—
120C4×C59—41no—
121C4×C59#12012yes—
122C4×C59C22×D412yes—
123Dic59—24no—
124#3019—591nomaximal, Sylow
125C2×C59—21no—
126C2×C59—21no—
127C2×C59—21no—
128C2×C59—44no—
129C2×C59—81no—
130C2×C59C2×#12011yescharacteristic
131D59—44no—
132C2×H(5,𝔽2)—591no—
133#575—592no—
134#535D5911yescharacteristic, complemented
135#455—594no—
136#453—594no—
137#421—592no—
138C2×#100—591no—
139C59#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—594no—
141H(5,𝔽2)—1184no—
142H(5,𝔽2)—1182no—
143C2×#41—592no—
144C2×#41—1182no—
145C2×#41C2×D5911yescharacteristic, complemented
146C22×D4—1182no—
147C22×D4—1182no—
148C22×D4C2×D5911yescharacteristic
149#137—594no—
150#137—1182no—
151AGL(1,ℤ/8)—594no—
152AGL(1,ℤ/8)—1182no—
153#135—1184no—
154C2×M16—592no—
155#127C2×D5912yescomplemented
156#124C2×D5912yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D5911yescharacteristic, complemented
160#104—598no—
161#100—594no—
162C24—1182no—
163C24C22⋊D5912yes—
164#41—22no—
165#41—22no—
166#41—594no—
167#41—594no—
168#41—1188no—
169#41—1188no—
170#41—1182no—
171#41—1182no—
172C2×Q8—592no—
173C2×Q8C22×D5911yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—592no—
179C2×D4—1188no—
180C2×D4—1188no—
181C2×D4—1184no—
182C2×D4—1188no—
183C2×D4—1182no—
184C2×D4—1188no—
185C2×D4C22⋊D5912yes—
186C2×D4C22×D5912yes—
187C2×D4C22×D5911yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—1182no—
190C22×C4—1182no—
191C22×C4C22×D5911yescharacteristic
192Q16—1184no—
193SD16—1184no—
194SD16—1184no—
195D8—1184no—
196M16—594no—
197M16—1182no—
198C2×C8—1182no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D5912yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—1188no—
208C23—1182no—
209C23—4724no—
210C23C2×C22⋊D5914yes—
211C23C2×C22⋊D5911yescharacteristic
212Q8—22no—
213Q8—594no—
214Q8—1182no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—594no—
222D4—11816no—
223D4—1184no—
224D4—1184no—
225D4—1182no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—1188no—
230C2×C4—1182no—
231C2×C4—1184no—
232C2×C4—1184no—
233C2×C4D4×D5912yes—
234C2×C4D4×D5912yes—
235C2×C4C2×C22⋊D5911yescharacteristic
236C2×C4C23×D5911yescharacteristic
237C8—1184no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—1184no—
246C22—4728no—
247C22—2364no—
248C22#1427369511yescharacteristic
249C22#1427369511yescharacteristic
250C22C22×C22⋊D5911yescharacteristic
251C4—42no—
252C4—41no—
253C4—1184no—
254C4#1427369512yes—
255C4C2×D4×D5912yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—2364no—
262C2C2×#1427369511yescharacteristic
subgroupG/H
centerC2C2×#14273695
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#535C2
socleC2×C59C2×#120
hypercenter#535D59
hypocenterC59#3019
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14273772C2semidirect
2. #16838200C2semidirect
3. #16837579C2semidirect
4. #16837569C2semidirect
5. #16837420C2semidirect
6. C2×#14273644C2semidirect
7. C59×#535C2semidirect
15. #14273758C22semidirect
17. #14273753C22semidirect
20. C2×#11745664C22semidirect
21. #14273655C22semidirect
22. #14273644C22semidirect
23. C2×#41×C59C22semidirect
25. #127×C59C22semidirect
26. #124×C59C22semidirect
29. #117×C59C22semidirect
34. C2×Q8×C59C23semidirect
41. C2×D4×C59C23semidirect
55. #11745685D4semidirect
57. C2×D236D4semidirect
59. C2×Dic118D4semidirect
63. C42×C59C23semidirect
69. #11745664C23semidirect
134. #535D59semidirect
139. C59#3019semidirect
145. C2×#41C2×D59semidirect
155. #127C2×D59semidirect
156. #124C2×D59semidirect
159. #117C2×D59semidirect
173. C2×Q8C22×D59semidirect
187. C2×D4C22×D59semidirect
202. C42C22×D59semidirect