Finite Group Databasebeta

← #21433366

Subgroups — #21433366

Order 7552.

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

normal subgroups only

This group has 784 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, complemented
2C2×#14273755C211yesmaximal, characteristic, complemented
3C22×D472C211yesmaximal, characteristic, complemented
4#16837966C211yesmaximal, characteristic, complemented
5#16837549C214yesmaximal, complemented
6#16837538C214yesmaximal, complemented
7#16837408C211yesmaximal, characteristic, complemented
8#16837399C211yesmaximal, characteristic, complemented
9C59×#408C211yesmaximal, characteristic, complemented
10#14273773—24no—
11#14273773—24no—
12C2×#11745689—21no—
13C2×#11745685C2211yescharacteristic
14C2×#11745685C2212yescomplemented
15C22×D236C2211yescharacteristic
16C22×D236C2211yescharacteristic, complemented
17C22×D236C2212yescomplemented
18C2×D4×D59—21no—
19C2×D4×D59—22no—
20#14273755—24no—
21C2×#11745660C2212yescomplemented
22C2×D472—24no—
23C2×D472C2214yescomplemented
24C2×D472C2212yescomplemented
25#14273723—21no—
26#14273716—21no—
27#14273701C2214yescomplemented
28#14273695—22no—
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—21no—
38C23×D59—22no—
39C23×D59—21no—
40#41×C59—22no—
41#41×C59—22no—
42C2×Q8×C59D411yescharacteristic
43C2×D4×C59D412yes—
44C2×D4×C59D411yescharacteristic
45C22×C4×C59C2312yes—
46C22×C4×C59C2311yescharacteristic
47C2×C22⋊D59—21no—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—24no—
50#11745689—28no—
51D4×D59—216no—
52D4×D59—28no—
53#11745685—22no—
54#11745685—24no—
55#11745685—24no—
56#11745685D414yescomplemented
57C2×D236—21no—
58C2×D236—22no—
59C2×D236—22no—
60C2×D236—24no—
61C2×D236—24no—
62C2×D236—22no—
63C2×D236—22no—
64C2×D236—21no—
65C2×D236D414yescomplemented
66C2×D236C2312yes—
67C2×D236C2312yes—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—22no—
71C2×Dic118C2311yescharacteristic
72M16×C59—22no—
73C2×C8×C59—22no—
74C2×C8×C59C2312yes—
75C2×C8×C59C2312yes—
76C22⋊Dic59—21no—
77(C2×D59)⋊C4—24no—
78C4⋊Dic59C2312yes—
79C4×Dic59—21no—
80D472—28no—
81D472—24no—
82#11745660—24no—
83C23×C59C2×D412yes—
84C23×C59C2×D411yescharacteristic
85C22×D59—21no—
86C22×D59—22no—
87C22×D59—28no—
88C22×D59—24no—
89C22×D59—22no—
90C22×D59—42no—
91C22×D59—82no—
92C22×D59—84no—
93C22×D59—82no—
94Q8×C59—22no—
95D4×C59—24no—
96D4×C59—22no—
97C2×C4×C59—22no—
98C2×C4×C59—22no—
99C2×C4×C59C2×D412yes—
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2×D412yes—
102C2×C4×C59C2×D412yes—
103C2×C4×C59C2411yescharacteristic
104C22⋊D59—28no—
105C22⋊D59—24no—
106C22⋊D59—84no—
107C2×Dic59—21no—
108C2×Dic59—22no—
109D236—28no—
110D236—24no—
111D236—21no—
112D236—22no—
113D236—22no—
114D236—22no—
115D236—42no—
116D236C2×D412yes—
117D236C2×D414yes—
118C4×D59—28no—
119C4×D59—24no—
120Dic118—21no—
121Dic118C2×D412yes—
122C8×C59—22no—
123C8×C59—22no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—24no—
127C22×C59#12012yes—
128C22×C59C22×D411yescharacteristic
129C2×D59—24no—
130C2×D59—22no—
131C2×D59—44no—
132C2×D59—42no—
133C2×D59—42no—
134C2×D59—44no—
135C2×D59—84no—
136C2×D59—88no—
137C2×D59—84no—
138C4×C59—22no—
139C4×C59#12012yes—
140C4×C59C22×D411yescharacteristic
141C4×C59C22×D411yescharacteristic
142Dic59—22no—
143Dic59—42no—
144#3008—591nomaximal, Sylow
145C2×C59—22no—
146C2×C59—42no—
147C2×C59C2×#12011yescharacteristic
148C2×C59#57612yes—
149D59—44no—
150D59—42no—
151D59—82no—
152C2×H(5,𝔽2)—591no—
153C2×AGL(1,ℤ/8)—591no—
154C22×D8—591no—
155#535—591no—
156#449—594no—
157#447—594no—
158#418—591no—
159#416—591no—
160#408D5911yescharacteristic, complemented
161C59#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1184no—
163H(5,𝔽2)—1184no—
164C2×#41—591no—
165C2×#41—592no—
166C2×#41—1181no—
167C2×#41C2×D5911yescharacteristic
168C22×D4—591no—
169C22×D4—591no—
170C22×D4—592no—
171C22×D4—1182no—
172C22×D4—1181no—
173AGL(1,ℤ/8)—1184no—
174C2×SD16—592no—
175C2×D8—594no—
176C2×D8—592no—
177C2×D8—1184no—
178C2×M16C2×D5911yescharacteristic, complemented
179C22×C8C2×D5911yescharacteristic, complemented
180#127—1181no—
181#124—1181no—
182#121—594no—
183#120—1182no—
184#117—591no—
185#103—592no—
186#102—592no—
187#102—594no—
188C22⋊C8C2×D5914yescomplemented
189C24—1182no—
190C24—1181no—
191C24—1181no—
192#41—22no—
193#41—22no—
194#41—594no—
195#41—1184no—
196#41—1184no—
197#41—1188no—
198#41—1182no—
199C2×Q8—591no—
200C2×Q8D23611yescharacteristic
201C2×D4—594no—
202C2×D4—592no—
203C2×D4—591no—
204C2×D4—592no—
205C2×D4—1184no—
206C2×D4—1184no—
207C2×D4—11816no—
208C2×D4—1188no—
209C2×D4—1182no—
210C2×D4—1181no—
211C2×D4—1184no—
212C2×D4—1182no—
213C2×D4—1181no—
214C2×D4—1181no—
215C2×D4—1182no—
216C2×D4—1182no—
217C2×D4—1182no—
218C2×D4D23612yes—
219C2×D4D23611yescharacteristic
220C22×C4—1182no—
221C22×C4—1181no—
222C22×C4C22×D5912yes—
223C22×C4C22×D5911yescharacteristic
224SD16—1184no—
225D8—1188no—
226D8—1184no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D5912yes—
230C2×C8C22×D5912yes—
231C4⋊C4—592no—
232C22⋊C4—1181no—
233C22⋊C4—1184no—
234C42—1181no—
235C23—1188no—
236C23—1184no—
237C23—1182no—
238C23—1181no—
239C23—1182no—
240C23—4722no—
241C23—4722no—
242C23—4724no—
243C23—2362no—
244C23C2×D23612yes—
245C23C2×D23611yescharacteristic
246Q8—22no—
247Q8—592no—
248Q8—1181no—
249D4—24no—
250D4—22no—
251D4—594no—
252D4—592no—
253D4—1188no—
254D4—1188no—
255D4—1184no—
256D4—1184no—
257D4—1181no—
258D4—1182no—
259D4—1182no—
260D4—1182no—
261D4—4724no—
262D4—2362no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—1188no—
266C2×C4—1181no—
267C2×C4—1184no—
268C2×C4—1182no—
269C2×C4C2×D23612yes—
270C2×C4C2×D23611yescharacteristic
271C2×C4D4×D5912yes—
272C2×C4D4×D5912yes—
273C2×C4C23×D5911yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—1184no—
280C22—1182no—
281C22—4724no—
282C22—4724no—
283C22—4728no—
284C22—2362no—
285C22—2364no—
286C22—2364no—
287C22—2362no—
288C22#1427369712yes—
289C22C22×D23611yescharacteristic
290C4—22no—
291C4—1182no—
292C4—2362no—
293C4#1427369712yes—
294C4C2×D4×D5911yescharacteristic
295C4C2×D4×D5911yescharacteristic
296C2—22no—
297C2—42no—
298C2—4722no—
299C2—2364no—
300C2—2362no—
301C2C2×#1427369711yescharacteristic
302C2#1683820712yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3008
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
1. C2×#14273773C2semidirect
2. C2×#14273755C2semidirect
3. C22×D472C2semidirect
4. #16837966C2semidirect
5. #16837549C2semidirect
6. #16837538C2semidirect
7. #16837408C2semidirect
8. #16837399C2semidirect
9. C59×#408C2semidirect
14. C2×#11745685C22semidirect
16. C22×D236C22semidirect
17. C22×D236C22semidirect
21. C2×#11745660C22semidirect
23. C2×D472C22semidirect
24. C2×D472C22semidirect
27. #14273701C22semidirect
29. #14273686C22semidirect
30. #14273652C22semidirect
31. #14273649C22semidirect
32. #14273649C22semidirect
34. C2×M16×C59C22semidirect
35. C22×C8×C59C22semidirect
36. C22⋊C8×C59C22semidirect
56. #11745685D4semidirect
65. C2×D236D4semidirect
160. #408D59semidirect
161. C59#3008semidirect
178. C2×M16C2×D59semidirect
179. C22×C8C2×D59semidirect
188. C22⋊C8C2×D59semidirect