Finite Group Databasebeta

← #21433371

Subgroups — #21433371

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×#14273758C211yesmaximal, characteristic, complemented
3C22×#11745671C211yesmaximal, characteristic, complemented
4#16837562C214yesmaximal, complemented
5#16837552C214yesmaximal, complemented
6#16837406C211yesmaximal, characteristic, complemented
7#16837396C211yesmaximal, characteristic, complemented
8#16837369C211yesmaximal, characteristic, complemented
9C59×#536C211yesmaximal, characteristic, complemented
10#14273773—24no—
11#14273773—24no—
12C2×#11745689—21no—
13C2×#11745685C2212yes—
14C2×#11745685C2211yescharacteristic
15C22×D236C2212yes—
16C22×D236C2211yescharacteristic
17C2×D4×D59—22no—
18C2×D4×D59—21no—
19#14273758—24no—
20C2×#11745672C2212yescomplemented
21C2×#11745671—24no—
22C2×#11745671C2214yescomplemented
23C2×#11745671C2212yescomplemented
24C2×#11745664C2211yescharacteristic, complemented
25C22×C59⋊C8C2211yescharacteristic, complemented
26#14273650C2212yescomplemented
27#14273647C2212yescomplemented
28#14273647C2214yescomplemented
29C22⋊(C59⋊C8)C2214yescomplemented
30C2×#41×C59C2211yescharacteristic
31C22×Q8×C59C2211yescharacteristic, complemented
32C4⋊Q8×C59—21no—
33#124×C59—21no—
34#123×C59—22no—
35C22⋊Q8×C59C2214yescomplemented
36#117×C59C2211yescharacteristic, complemented
37C23×D59—22no—
38C23×D59—21no—
39#41×C59—22no—
40#41×C59—22no—
41C2×Q8×C59—21no—
42C2×Q8×C59—22no—
43C2×Q8×C59—22no—
44C2×Q8×C59D411yescharacteristic
45C2×Q8×C59C2312yes—
46C2×D4×C59D412yes—
47C2×D4×C59D411yescharacteristic
48C22×C4×C59—21no—
49C22×C4×C59C2312yes—
50C22×C4×C59C2311yescharacteristic
51C2×C22⋊D59—22no—
52C2×C22⋊D59—21no—
53#11745689—28no—
54D4×D59—216no—
55D4×D59—28no—
56#11745685—22no—
57#11745685—24no—
58#11745685—24no—
59#11745685D414yes—
60C2×D236—22no—
61C2×D236—21no—
62C2×D236—22no—
63C2×D236—24no—
64C2×D236—24no—
65C2×D236D414yes—
66C2×D236C2311yescharacteristic
67C2×D236C2312yes—
68C2×C4×D59—22no—
69C2×C4×D59—21no—
70C2×Dic118C2311yescharacteristic
71C4⋊C4×C59—24no—
72C4⋊C4×C59C2312yes—
73C22⋊C4×C59—21no—
74C22⋊C4×C59—24no—
75C42×C59—21no—
76#11745672—24no—
77#11745671—28no—
78#11745671—24no—
79#11745664—22no—
80C2×C59⋊C8—22no—
81C2×C59⋊C8C2312yes—
82C2×C59⋊C8C2312yes—
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—
92Q8×C59—22no—
93Q8×C59—22no—
94Q8×C59—42no—
95D4×C59—24no—
96D4×C59—22no—
97C2×C4×C59—22no—
98C2×C4×C59—22no—
99C2×C4×C59—22no—
100C2×C4×C59—22no—
101C2×C4×C59—42no—
102C2×C4×C59C2×D412yes—
103C2×C4×C59C2×D412yes—
104C2×C4×C59C2×D412yes—
105C2×C4×C59C2×D411yescharacteristic
106C2×C4×C59C2411yescharacteristic
107C22⋊D59—28no—
108C22⋊D59—24no—
109C2×Dic59—21no—
110D236—28no—
111D236—24no—
112D236—21no—
113D236—22no—
114D236C2×D412yes—
115D236C2×D414yes—
116C4×D59—28no—
117C4×D59—24no—
118Dic118—21no—
119Dic118C2×D412yes—
120C59⋊C8—22no—
121C59⋊C8—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—42no—
135C4×C59—42no—
136C4×C59#12012yes—
137C4×C59C22×D411yescharacteristic
138C4×C59C22×D411yescharacteristic
139Dic59—22no—
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#536D5911yescharacteristic, complemented
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—1181no—
162C2×#41C2×D5911yescharacteristic
163C22×Q8C2×D5911yescharacteristic, complemented
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×M16—591no—
174C22×C8—591no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D5914yescomplemented
179#117C2×D5911yescharacteristic, complemented
180#103—592no—
181#102—592no—
182#102—594no—
183C22⋊C8—594no—
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—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—591no—
197C2×Q8C22⋊D5911yescharacteristic
198C2×Q8C22×D5912yes—
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—1182no—
210C2×D4—1181no—
211C2×D4C22⋊D5912yes—
212C2×D4C22⋊D5911yescharacteristic
213C22×C4—21no—
214C22×C4—1182no—
215C22×C4—1181no—
216C22×C4C22×D5912yes—
217C22×C4C22×D5911yescharacteristic
218Q16—1184no—
219SD16—1188no—
220SD16—1184no—
221M16—1182no—
222C2×C8—592no—
223C2×C8—592no—
224C2×C8—1182no—
225C4⋊C4—24no—
226C4⋊C4C22×D5912yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—1188no—
231C23—1184no—
232C23—1182no—
233C23—1181no—
234C23—4722no—
235C23—4724no—
236C23C2×C22⋊D5912yes—
237C23C2×C22⋊D5911yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—592no—
243Q8—1181no—
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—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—1188no—
260C2×C4—1181no—
261C2×C4—1184no—
262C2×C4D4×D5912yes—
263C2×C4D4×D5912yes—
264C2×C4C2×C22⋊D5912yes—
265C2×C4C2×C22⋊D5911yescharacteristic
266C2×C4C23×D5911yescharacteristic
267C8—1182no—
268C8—1182no—
269C22—22no—
270C22—24no—
271C22—22no—
272C22—1184no—
273C22—1182no—
274C22—4724no—
275C22—4728no—
276C22—2364no—
277C22—2362no—
278C22#1427369512yes—
279C22C22×C22⋊D5911yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—1182no—
284C4#1427369512yes—
285C4C2×D4×D5911yescharacteristic
286C4C2×D4×D5911yescharacteristic
287C2—22no—
288C2—42no—
289C2—2364no—
290C2—2362no—
291C2C2×#1427369511yescharacteristic
292C2#1683821012yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#536C2
socleC22×C59C22×D4
hypercenter#536D59
hypocenterC59#3009
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#14273758C2semidirect
3. C22×#11745671C2semidirect
4. #16837562C2semidirect
5. #16837552C2semidirect
6. #16837406C2semidirect
7. #16837396C2semidirect
8. #16837369C2semidirect
9. C59×#536C2semidirect
20. C2×#11745672C22semidirect
22. C2×#11745671C22semidirect
23. C2×#11745671C22semidirect
24. C2×#11745664C22semidirect
25. C22×C59⋊C8C22semidirect
26. #14273650C22semidirect
27. #14273647C22semidirect
28. #14273647C22semidirect
29. C22⋊(C59⋊C8)C22semidirect
31. C22×Q8×C59C22semidirect
35. C22⋊Q8×C59C22semidirect
36. #117×C59C22semidirect
150. #536D59semidirect
156. C59#3009semidirect
163. C22×Q8C2×D59semidirect
178. C22⋊Q8C2×D59semidirect
179. #117C2×D59semidirect