Finite Group Databasebeta

← #21433375

Subgroups — #21433375

Order 7552.

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

normal subgroups only

This group has 752 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×#14273773C211yesmaximal, characteristic
2C2×#14273760C211yesmaximal, characteristic, complemented
3C22×#11745660C211yesmaximal, characteristic, complemented
4#16837973C211yesmaximal, characteristic, complemented
5#16837566C214yesmaximal, complemented
6#16837555C214yesmaximal, complemented
7#16837408C211yesmaximal, characteristic, complemented
8#16837399C211yesmaximal, characteristic, complemented
9C59×#408C211yesmaximal, characteristic, complemented
10#14273773—24no—
11#14273773—24no—
12C2×#11745689—21no—
13C2×#11745685C2212yes—
14C2×#11745685C2211yescharacteristic
15C22×Dic118C2211yescharacteristic, complemented
16C22×D236C2212yes—
17C22×D236C2211yescharacteristic
18C2×D4×D59—22no—
19C2×D4×D59—21no—
20#14273760—24no—
21C2×Dic236C2212yescomplemented
22C2×#11745660—24no—
23C2×#11745660C2214yescomplemented
24C2×#11745660C2212yescomplemented
25#14273725—21no—
26#14273714—21no—
27#14273708—22no—
28#14273706C2214yescomplemented
29#14273686C2211yescharacteristic, complemented
30#14273652C2212yescomplemented
31#14273649C2212yescomplemented
32#14273649C2214yescomplemented
33C2×#41×C59C2211yescharacteristic
34C2×M16×C59C2211yescharacteristic, complemented
35C22×C8×C59C2211yescharacteristic, complemented
36C22⋊C8×C59C2214yescomplemented
37C23×D59—22no—
38C23×D59—21no—
39#41×C59—22no—
40#41×C59—22no—
41C2×Q8×C59D411yescharacteristic
42C2×D4×C59D412yes—
43C2×D4×C59D411yescharacteristic
44C22×C4×C59C2312yes—
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—22no—
47C2×C22⋊D59—21no—
48C22×Dic59—21no—
49#11745689—28no—
50D4×D59—216no—
51D4×D59—28no—
52#11745685—22no—
53#11745685—24no—
54#11745685—24no—
55#11745685D414yes—
56C2×D236—22no—
57C2×D236—21no—
58C2×D236—22no—
59C2×D236—24no—
60C2×D236—24no—
61C2×D236D414yes—
62C2×D236C2311yescharacteristic
63C2×D236C2312yes—
64C2×C4×D59—22no—
65C2×C4×D59—21no—
66C2×Dic118—22no—
67C2×Dic118—22no—
68C2×Dic118—21no—
69C2×Dic118C2312yes—
70C2×Dic118C2311yescharacteristic
71M16×C59—22no—
72C2×C8×C59—22no—
73C2×C8×C59C2312yes—
74C2×C8×C59C2312yes—
75C22⋊Dic59—21no—
76C22⋊Dic59—24no—
77C4⋊Dic59C2312yes—
78Dic59⋊C4—24no—
79C4×Dic59—21no—
80Dic236—24no—
81#11745660—28no—
82#11745660—24no—
83C23×C59C2×D412yes—
84C23×C59C2×D411yescharacteristic
85C22×D59—22no—
86C22×D59—21no—
87C22×D59—28no—
88C22×D59—24no—
89C22×D59—82no—
90C22×D59—84no—
91Q8×C59—22no—
92D4×C59—24no—
93D4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59C2×D412yes—
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2×D412yes—
99C2×C4×C59C2×D412yes—
100C2×C4×C59C2411yescharacteristic
101C22⋊D59—28no—
102C22⋊D59—24no—
103C2×Dic59—21no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—42no—
107D236—28no—
108D236—24no—
109D236—21no—
110D236—22no—
111D236C2×D412yes—
112D236C2×D414yes—
113C4×D59—28no—
114C4×D59—24no—
115Dic118—21no—
116Dic118—22no—
117Dic118—22no—
118Dic118—42no—
119Dic118C2×D412yes—
120C8×C59—22no—
121C8×C59—22no—
122C22×C59—22no—
123C22×C59—22no—
124C22×C59—24no—
125C22×C59#12012yes—
126C22×C59C22×D411yescharacteristic
127C2×D59—24no—
128C2×D59—22no—
129C2×D59—44no—
130C2×D59—42no—
131C2×D59—84no—
132C2×D59—88no—
133C4×C59—22no—
134C4×C59#12012yes—
135C4×C59C22×D411yescharacteristic
136C4×C59C22×D411yescharacteristic
137Dic59—22no—
138Dic59—42no—
139Dic59—42no—
140#3009—591nomaximal, Sylow
141C2×C59—22no—
142C2×C59—42no—
143C2×C59C2×#12011yescharacteristic
144C2×C59#57712yes—
145D59—44no—
146D59—42no—
147C2×H(5,𝔽2)—591no—
148C2×#137—591no—
149C22×SD16—591no—
150#536—591no—
151#452—594no—
152#450—594no—
153#418—591no—
154#416—591no—
155#408D5911yescharacteristic, complemented
156C59#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1184no—
158H(5,𝔽2)—1184no—
159C2×#41—591no—
160C2×#41—592no—
161C2×#41—1181no—
162C2×#41C2×D5911yescharacteristic
163C22×Q8—591no—
164C22×D4—591no—
165C22×D4—592no—
166C22×D4—1182no—
167C22×D4—1181no—
168#137—1184no—
169C2×Q16—592no—
170C2×SD16—594no—
171C2×SD16—592no—
172C2×SD16—1184no—
173C2×M16C2×D5911yescharacteristic, complemented
174C22×C8C2×D5911yescharacteristic, complemented
175C4⋊Q8—1181no—
176#124—1181no—
177#123—1182no—
178C22⋊Q8—594no—
179#117—591no—
180#103—592no—
181#102—592no—
182#102—594no—
183C22⋊C8C2×D5914yescomplemented
184C24—1182no—
185C24—1181no—
186#41—22no—
187#41—22no—
188#41—594no—
189#41—1184no—
190#41—1184no—
191#41—1188no—
192#41—1182no—
193C2×Q8—591no—
194C2×Q8—592no—
195C2×Q8—1181no—
196C2×Q8—1182no—
197C2×Q8—1182no—
198C2×Q8D23611yescharacteristic
199C2×D4—594no—
200C2×D4—592no—
201C2×D4—591no—
202C2×D4—1184no—
203C2×D4—1184no—
204C2×D4—11816no—
205C2×D4—1188no—
206C2×D4—1182no—
207C2×D4—1181no—
208C2×D4—1182no—
209C2×D4—1181no—
210C2×D4—1182no—
211C2×D4D23612yes—
212C2×D4D23611yescharacteristic
213C22×C4—1182no—
214C22×C4—1181no—
215C22×C4—1181no—
216C22×C4C22×D5912yes—
217C22×C4C22×D5911yescharacteristic
218Q16—1184no—
219SD16—1188no—
220SD16—1184no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D5912yes—
224C2×C8C22×D5912yes—
225C4⋊C4—592no—
226C4⋊C4—1184no—
227C22⋊C4—1181no—
228C22⋊C4—1184no—
229C42—1181no—
230C23—1188no—
231C23—1184no—
232C23—1182no—
233C23—1181no—
234C23—4722no—
235C23—4724no—
236C23C2×D23612yes—
237C23C2×D23611yescharacteristic
238Q8—22no—
239Q8—592no—
240Q8—1181no—
241Q8—1182no—
242Q8—1182no—
243Q8—2362no—
244D4—24no—
245D4—22no—
246D4—594no—
247D4—592no—
248D4—1188no—
249D4—1188no—
250D4—1184no—
251D4—1184no—
252D4—1181no—
253D4—1182no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—1188no—
257C2×C4—1181no—
258C2×C4—1184no—
259C2×C4—1182no—
260C2×C4—1182no—
261C2×C4—2362no—
262C2×C4C2×D23612yes—
263C2×C4C2×D23611yescharacteristic
264C2×C4D4×D5912yes—
265C2×C4D4×D5912yes—
266C2×C4C23×D5911yescharacteristic
267C8—22no—
268C8—22no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—1184no—
273C22—1182no—
274C22—4724no—
275C22—4728no—
276C22—2364no—
277C22—2362no—
278C22#1427369712yes—
279C22C22×D23611yescharacteristic
280C4—22no—
281C4—1182no—
282C4—2362no—
283C4—2362no—
284C4#1427369712yes—
285C4C2×D4×D5911yescharacteristic
286C4C2×D4×D5911yescharacteristic
287C2—22no—
288C2—42no—
289C2—2364no—
290C2—2362no—
291C2C2×#1427369711yescharacteristic
292C2#1683821412yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3009
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#14273760C2semidirect
3. C22×#11745660C2semidirect
4. #16837973C2semidirect
5. #16837566C2semidirect
6. #16837555C2semidirect
7. #16837408C2semidirect
8. #16837399C2semidirect
9. C59×#408C2semidirect
15. C22×Dic118C22semidirect
21. C2×Dic236C22semidirect
23. C2×#11745660C22semidirect
24. C2×#11745660C22semidirect
28. #14273706C22semidirect
29. #14273686C22semidirect
30. #14273652C22semidirect
31. #14273649C22semidirect
32. #14273649C22semidirect
34. C2×M16×C59C22semidirect
35. C22×C8×C59C22semidirect
36. C22⋊C8×C59C22semidirect
155. #408D59semidirect
156. C59#3009semidirect
173. C2×M16C2×D59semidirect
174. C22×C8C2×D59semidirect
183. C22⋊C8C2×D59semidirect