Finite Group Databasebeta

← #21433894

Subgroups — #21433894

Order 7552.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#16837957C211yesmaximal, characteristic, complemented
2C4×D4×D59C211yesmaximal, characteristic
3#16837701C212yesmaximal, complemented
4#16837700C212yesmaximal, complemented
5#16837689C211yesmaximal, characteristic, complemented
6#16837683C211yesmaximal, characteristic, complemented
7#16837682C211yesmaximal, characteristic, complemented
8#16837441C212yesmaximal, complemented
9#16837424C211yesmaximal, characteristic, complemented
10#16837405C212yesmaximal
11C59×#476C211yesmaximal, characteristic, complemented
12C2×D4×D59C2211yescharacteristic
13C22×C4×D59—21no—
14C2×#11745659C2212yes—
15#14273727C2211yescharacteristic, complemented
16#14273718C2212yescomplemented
17#14273707—21no—
18#14273703—21no—
19Q8×Dic59—21no—
20#14273692—21no—
21C4×D236C2211yescharacteristic
22D4×Dic59C2211yescharacteristic
23#14273689C2211yescharacteristic
24C4×C22⋊D59—21no—
25(C22⋊D59)⋊C4—21no—
26#14273685C2212yes—
27C4⋊C4×D59C2211yescharacteristic
28C22⋊C4×D59—21no—
29C42×D59C2211yescharacteristic
30#14273661C2212yescomplemented
31#14273660C2212yescomplemented
32#14273658C2212yescomplemented
33C4⋊(C59⋊C8)C2211yescharacteristic, complemented
34Dic59⋊C8C2212yescomplemented
35#14273649C2212yes—
36#14273648C2212yes—
37#14273647C2212yes—
38C4⋊Q8×C59C2211yescharacteristic, complemented
39C4×D4×C59C2211yescharacteristic
40#106×C59C2212yescomplemented
41C4⋊C8×C59C2211yescharacteristic, complemented
42#102×C59C2212yes—
43C23×D59—21no—
44C2×Q8×C59—21no—
45C2×D4×C59C2311yescharacteristic
46C22×C4×C59—21no—
47C2×C22⋊D59—21no—
48C22×Dic59—21no—
49D4×D59—22no—
50D4×D59Q814yescomplemented
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×C4×D59—21no—
54C2×C4×D59—21no—
55C2×C4×D59—44no—
56C2×C4×D59D411yescharacteristic
57C2×C4×D59D411yescharacteristic
58C2×C4×D59C2311yescharacteristic
59C2×Dic118—21no—
60C2×C8×C59C2312yes—
61C4⋊C4×C59—21no—
62C4⋊C4×C59C2312yes—
63C4⋊C4×C59C2311yescharacteristic
64C22⋊C4×C59—21no—
65C42×C59C2311yescharacteristic
66C22⋊Dic59—21no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4—21no—
70C4⋊Dic59—21no—
71C4⋊Dic59—22no—
72C4⋊Dic59C2312yes—
73C4⋊Dic59C2311yescharacteristic
74Dic59⋊C4—21no—
75Dic59⋊C4—22no—
76C4×Dic59—22no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81#11745659—24no—
82C23×C59—21no—
83C22×D59—21no—
84C22×D59—24no—
85C22×D59—42no—
86C22×D59—42no—
87C22×D59C2×D411yescharacteristic
88Q8×C59—42no—
89D4×C59—21no—
90D4×C59C2×Q812yes—
91C2×C4×C59—22no—
92C2×C4×C59—21no—
93C2×C4×C59—42no—
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2411yescharacteristic
97C22⋊D59—24no—
98C2×Dic59—22no—
99C2×Dic59—21no—
100C2×Dic59—42no—
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D411yescharacteristic
104D236—21no—
105D236C2×Q812yes—
106C4×D59—22no—
107C4×D59—41no—
108C4×D59—42no—
109C4×D59—42no—
110C4×D59—42no—
111C4×D59C2×Q812yes—
112C4×D59#4112yes—
113Dic118—42no—
114C8×C59—22no—
115C59⋊C8—22no—
116C22×C59—22no—
117C22×C59—41no—
118C22×C59—41no—
119C22×C59C22×D411yescharacteristic
120C2×D59—21no—
121C2×D59—21no—
122C2×D59—22no—
123C2×D59—48no—
124C2×D59—41no—
125C2×D59—41no—
126C2×D59C22⋊Q812yes—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59—42no—
130C4×C59AGL(1,ℤ/8)12yes—
131C4×C59C22×Q811yescharacteristic
132C4×C59C2×#4111yescharacteristic
133Dic59—21no—
134Dic59—21no—
135Dic59—42no—
136Dic59—41no—
137Dic59C22⋊Q812yes—
138#3077—591nomaximal, Sylow
139C2×C59—42no—
140C2×C59C2×C22⋊Q811yescharacteristic
141C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C59#57511yescharacteristic
143D59—22no—
144D59—42no—
145#533—591no—
146C2×C4×D4—591no—
147#478—592no—
148#478—592no—
149#476—591no—
150#476D5911yescharacteristic, complemented
151#474—591no—
152#474—591no—
153#428—592no—
154#423—591no—
155#418—592no—
156C59#307711yescharacteristic, complemented, Sylow
157C22×D4—591no—
158C23×C4—1181no—
159C2×M16—592no—
160C4⋊Q8—591no—
161C4⋊Q8C2×D5911yescharacteristic, complemented
162#125—592no—
163C22⋊Q8—1181no—
164C22⋊Q8—1181no—
165C4×Q8—1181no—
166C4×Q8—1181no—
167C4×D4—591no—
168C4×D4—591no—
169C4×D4—591no—
170C4×D4—1181no—
171C4×D4—1181no—
172C4×D4C2×D5911yescharacteristic
173#117—592no—
174C2×C4⋊C4—591no—
175C2×C22⋊C4—1181no—
176C2×C42—591no—
177#107—592no—
178#107—592no—
179#106—592no—
180#106C2×D5912yescomplemented
181C4⋊C8—592no—
182C4⋊C8—591no—
183C4⋊C8C2×D5911yescharacteristic, complemented
184#102—592no—
185#102—592no—
186#102—592no—
187#102C2×D5912yes—
188C24—1181no—
189C2×Q8—21no—
190C2×Q8—1181no—
191C2×D4—594no—
192C2×D4—591no—
193C2×D4—1182no—
194C2×D4—1181no—
195C2×D4C22×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—591no—
198C22×C4—591no—
199C22×C4—591no—
200C22×C4—1181no—
201C22×C4—1181no—
202C22×C4—1181no—
203C22×C4—1181no—
204C22×C4—2364no—
205M16—1184no—
206C2×C8—592no—
207C2×C8C22×D5912yes—
208C4⋊C4—21no—
209C4⋊C4—592no—
210C4⋊C4—591no—
211C4⋊C4—1181no—
212C4⋊C4—1182no—
213C4⋊C4—1182no—
214C4⋊C4—1181no—
215C4⋊C4C22×D5912yes—
216C4⋊C4C22×D5911yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—1181no—
219C22⋊C4—1182no—
220C22⋊C4—1181no—
221C22⋊C4—1181no—
222C42—591no—
223C42—591no—
224C42—591no—
225C42—1182no—
226C42C22×D5911yescharacteristic
227C23—21no—
228C23—591no—
229C23—1184no—
230C23—1181no—
231C23—2362no—
232C23—2362no—
233Q8—42no—
234Q8—2362no—
235D4—21no—
236D4—592no—
237D4—1184no—
238D4—1181no—
239D4Q8×D5912yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—591no—
244C2×C4—592no—
245C2×C4—592no—
246C2×C4—591no—
247C2×C4—591no—
248C2×C4—1182no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—2361no—
252C2×C4—2362no—
253C2×C4—2362no—
254C2×C4—2362no—
255C2×C4—2362no—
256C2×C4D4×D5911yescharacteristic
257C2×C4D4×D5911yescharacteristic
258C2×C4C23×D5911yescharacteristic
259C8—22no—
260C8—1182no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—592no—
265C22—1181no—
266C22—1181no—
267C22—1182no—
268C22—2368no—
269C22—2361no—
270C22—2361no—
271C22C2×D4×D5911yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—592no—
276C4—1181no—
277C4—1181no—
278C4—2361no—
279C4—2362no—
280C4#1427375412yes—
281C4C2×Q8×D5911yescharacteristic
282C4#41×D5911yescharacteristic
283C2—42no—
284C2—1182no—
285C2—2362no—
286C2C22⋊Q8×D5911yescharacteristic
287C2C2×#1427375411yescharacteristic
288C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#476C2
socleC22×C59C22×D4
hypercenter#476D59
hypocenterC59#3077
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837701C2semidirect
4. #16837700C2semidirect
5. #16837689C2semidirect
6. #16837683C2semidirect
7. #16837682C2semidirect
8. #16837441C2semidirect
9. #16837424C2semidirect
11. C59×#476C2semidirect
15. #14273727C22semidirect
16. #14273718C22semidirect
30. #14273661C22semidirect
31. #14273660C22semidirect
32. #14273658C22semidirect
33. C4⋊(C59⋊C8)C22semidirect
34. Dic59⋊C8C22semidirect
38. C4⋊Q8×C59C22semidirect
40. #106×C59C22semidirect
41. C4⋊C8×C59C22semidirect
50. D4×D59Q8semidirect
150. #476D59semidirect
156. C59#3077semidirect
161. C4⋊Q8C2×D59semidirect
180. #106C2×D59semidirect
183. C4⋊C8C2×D59semidirect