Finite Group Databasebeta

← #21433369

Subgroups — #21433369

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×#14273772C211yesmaximal, characteristic
2C2×#14273758C211yesmaximal, characteristic, complemented
3#16837976C211yesmaximal, characteristic, complemented
4#16837561C214yesmaximal, complemented
5#16837551C214yesmaximal, complemented
6#16837407C211yesmaximal, characteristic, complemented
7#16837399C211yesmaximal, characteristic, complemented
8#16837368C211yesmaximal, characteristic, complemented
9C22×SD16×C59C211yesmaximal, characteristic, complemented
10#14273772—24no—
11#14273772—24no—
12C2×#11745685C2211yescharacteristic
13C2×#11745685C2211yescharacteristic
14C2×#11745687—21no—
15C2×#11745687C2212yes—
16C22×C22⋊D59—22no—
17C2×D4×D59—21no—
18C2×D4×D59C2212yes—
19#14273758—24no—
20C2×#11745672C2212yescomplemented
21C2×#11745671C2212yescomplemented
22C2×#11745664C2211yescharacteristic, complemented
23#14273725—21no—
24#14273716—21no—
25#14273710—22no—
26#14273703C2214yescomplemented
27#14273686C2211yescharacteristic, complemented
28#14273652C2212yescomplemented
29#14273649C2212yescomplemented
30#14273648C2214yescomplemented
31(C2×D59)⋊C8C2214yescomplemented
32C22×Q8×C59C2211yescharacteristic, complemented
33C22×D4×C59C2211yescharacteristic
34C2×SD16×C59—24no—
35C2×SD16×C59C2214yescomplemented
36C22×C8×C59C2211yescharacteristic, complemented
37C24×C59—21no—
38C23×D59—22no—
39C2×Q8×C59—21no—
40C2×Q8×C59—22no—
41C2×Q8×C59—22no—
42C2×Q8×C59C2312yes—
43C2×D4×C59—21no—
44C2×D4×C59—22no—
45C2×D4×C59D414yes—
46C2×D4×C59C2312yes—
47C22×C4×C59—21no—
48C22×C4×C59C2311yescharacteristic
49C2×C22⋊D59—216no—
50C2×C22⋊D59—21no—
51C2×C22⋊D59—22no—
52C2×C22⋊D59—22no—
53C2×C22⋊D59D412yes—
54C22×Dic59—22no—
55#11745687—28no—
56#11745687—24no—
57#11745687—24no—
58D4×D59—28no—
59D4×D59—24no—
60D4×D59—24no—
61#11745685—22no—
62#11745685—22no—
63#11745685—22no—
64#11745685D414yes—
65C2×D236D411yescharacteristic
66C2×D236C2311yescharacteristic
67C2×C4×D59—21no—
68C2×C4×D59C2312yes—
69C2×Dic118D411yescharacteristic
70C2×Dic118C2311yescharacteristic
71SD16×C59—28no—
72C2×C8×C59—22no—
73C2×C8×C59C2312yes—
74C22⋊Dic59—21no—
75#11745672—24no—
76#11745671—24no—
77(C2×D59)⋊C4—24no—
78C4⋊Dic59C2312yes—
79Dic59⋊C4—24no—
80C4×Dic59—21no—
81#11745664—22no—
82C2×C59⋊C8C2312yes—
83C23×C59—22no—
84C23×C59—24no—
85C23×C59—82no—
86C23×C59C2×D411yescharacteristic
87C22×D59—21no—
88C22×D59—28no—
89C22×D59—84no—
90C22×D59C2×D412yes—
91Q8×C59—22no—
92Q8×C59—22no—
93Q8×C59—42no—
94D4×C59—24no—
95D4×C59—22no—
96D4×C59C2×D414yes—
97C2×C4×C59—22no—
98C2×C4×C59—42no—
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2×D412yes—
101C2×C4×C59C2×D412yes—
102C2×C4×C59C2411yescharacteristic
103C22⋊D59—28no—
104C22⋊D59—28no—
105C22⋊D59—24no—
106C22⋊D59—24no—
107C2×Dic59—28no—
108C2×Dic59—21no—
109C2×Dic59—22no—
110C2×Dic59C2×D412yes—
111D236—22no—
112D236—21no—
113D236C2×D412yes—
114C4×D59—24no—
115C4×D59—22no—
116C4×D59—22no—
117Dic118—22no—
118Dic118—21no—
119Dic118C2×D412yes—
120C8×C59—22no—
121C59⋊C8—22no—
122C22×C59—22no—
123C22×C59—24no—
124C22×C59—44no—
125C22×C59—84no—
126C22×C59#12012yes—
127C22×C59C22×D411yescharacteristic
128C2×D59—22no—
129C2×D59—22no—
130C2×D59—24no—
131C2×D59—42no—
132C2×D59—88no—
133C4×C59—42no—
134C4×C59#12012yes—
135C4×C59C22×D411yescharacteristic
136C4×C59C22×D411yescharacteristic
137Dic59—22no—
138Dic59—22no—
139Dic59—42no—
140#3009—591nomaximal, Sylow
141C2×C59—22no—
142C2×C59—44no—
143C2×C59C2×#12011yescharacteristic
144C2×C59#57712yes—
145D59—42no—
146D59—42no—
147C2×H(5,𝔽2)—591no—
148C2×#137—591no—
149C22×SD16D5911yescharacteristic, complemented
150#536—591no—
151#452—594no—
152#450—594no—
153#418—591no—
154#416—591no—
155#408—591no—
156C59#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1184no—
158H(5,𝔽2)—1184no—
159C2×#41—591no—
160C2×#41—592no—
161C2×#41—591no—
162C2×#41—1181no—
163C22×Q8C2×D5911yescharacteristic, complemented
164C22×D4—592no—
165C22×D4—1181no—
166C22×D4—1182no—
167C22×D4C2×D5911yescharacteristic
168#137—1184no—
169C2×Q16—592no—
170C2×SD16—24no—
171C2×SD16—592no—
172C2×SD16C2×D5914yescomplemented
173C2×M16—591no—
174C22×C8C2×D5911yescharacteristic, complemented
175C4⋊Q8—1181no—
176#124—1181no—
177#123—1182no—
178C22⋊Q8—594no—
179#117—591no—
180#103—592no—
181#102—594no—
182#102—592no—
183C22⋊C8—594no—
184C24—21no—
185C24—1182no—
186#41—594no—
187#41—1184no—
188#41—1188no—
189#41—1184no—
190#41—1182no—
191#41—1182no—
192#41—1182no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—591no—
197C2×Q8—591no—
198C2×Q8C22×D5912yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—592no—
202C2×D4—591no—
203C2×D4—591no—
204C2×D4—1182no—
205C2×D4—1184no—
206C2×D4—1188no—
207C2×D4—1182no—
208C2×D4—11816no—
209C2×D4—1181no—
210C2×D4—1184no—
211C2×D4C22⋊D5914yes—
212C2×D4C22×D5912yes—
213C22×C4—21no—
214C22×C4—592no—
215C22×C4—1182no—
216C22×C4—1181no—
217C22×C4C22×D5911yescharacteristic
218Q16—1184no—
219SD16—28no—
220SD16—1184no—
221M16—1182no—
222C2×C8—22no—
223C2×C8—592no—
224C2×C8C22×D5912yes—
225C4⋊C4—592no—
226C4⋊C4—1184no—
227C22⋊C4—1184no—
228C22⋊C4—1181no—
229C42—1181no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—592no—
234C23—1188no—
235C23—1181no—
236C23—4724no—
237C23D4×D5911yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—592no—
242Q8—1182no—
243Q8—1181no—
244D4—24no—
245D4—22no—
246D4—592no—
247D4—1188no—
248D4—1188no—
249D4—1184no—
250D4—1184no—
251D4—1182no—
252D4—1181no—
253D4C2×C22⋊D5914yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—592no—
257C2×C4—1188no—
258C2×C4—1181no—
259C2×C4—1184no—
260C2×C4—1182no—
261C2×C4—1182no—
262C2×C4—1182no—
263C2×C4D4×D5911yescharacteristic
264C2×C4D4×D5912yes—
265C2×C4C2×C22⋊D5912yes—
266C2×C4C23×D5911yescharacteristic
267C8—22no—
268C8—1182no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—1184no—
274C22—1182no—
275C22—1182no—
276C22—4728no—
277C22—2362no—
278C22#1427369512yes—
279C22C2×D4×D5911yescharacteristic
280C4—42no—
281C4—1182no—
282C4—1182no—
283C4—2362no—
284C4#1427369512yes—
285C4C2×D4×D5911yescharacteristic
286C4C22×C22⋊D5911yescharacteristic
287C2—22no—
288C2—44no—
289C2—2362no—
290C2—2362no—
291C2C2×#1427369511yescharacteristic
292C2#1683820812yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC22×SD16×C59C2
socleC22×C59C22×D4
hypercenterC22×SD16D59
hypocenterC59#3009
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14273758C2semidirect
3. #16837976C2semidirect
4. #16837561C2semidirect
5. #16837551C2semidirect
6. #16837407C2semidirect
7. #16837399C2semidirect
8. #16837368C2semidirect
9. C22×SD16×C59C2semidirect
20. C2×#11745672C22semidirect
21. C2×#11745671C22semidirect
22. C2×#11745664C22semidirect
26. #14273703C22semidirect
27. #14273686C22semidirect
28. #14273652C22semidirect
29. #14273649C22semidirect
30. #14273648C22semidirect
31. (C2×D59)⋊C8C22semidirect
32. C22×Q8×C59C22semidirect
35. C2×SD16×C59C22semidirect
36. C22×C8×C59C22semidirect
149. C22×SD16D59semidirect
156. C59#3009semidirect
163. C22×Q8C2×D59semidirect
172. C2×SD16C2×D59semidirect
174. C22×C8C2×D59semidirect