Finite Group Databasebeta

← #21436400

Subgroups — #21436400

Order 7552.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838055C211yesmaximal, characteristic, complemented
2#16838055C211yesmaximal, characteristic, complemented
3#16837736C212yesmaximal, complemented
4#16837679C211yesmaximal, characteristic, complemented
5#16837651C212yesmaximal, complemented
6#16837604C211yesmaximal, characteristic, complemented
7#16837550C212yesmaximal, complemented
8C4×D472C211yesmaximal, characteristic, complemented
9#16837481C211yesmaximal, characteristic, complemented
10#16837402C212yesmaximal, complemented
11C59×#487C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×#11745689C2212yes—
14C2×#11745671C2212yes—
15C2×D472C2211yescharacteristic
16C2×#11745659C2212yes—
17#14273712—22no—
18#14273712—22no—
19#14273703—21no—
20#14273703C2212yes—
21#14273702—21no—
22#14273702C2212yes—
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25C4×D236C2211yescharacteristic
26C4⋊C4×D59—21no—
27C4⋊C4×D59C2212yes—
28#14273661C2211yescharacteristic
29#14273660C2212yes—
30C4⋊(C59⋊C8)C2211yescharacteristic
31#14273651C2212yes—
32#14273649C2211yescharacteristic
33#14273649C2211yescharacteristic
34#14273647C2212yes—
35(C2×D59)⋊C8C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4⋊Q8×C59C2211yescharacteristic
38#103×C59C2212yes—
39#103×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59C2312yes—
43#11745689—24no—
44#11745689—42no—
45#11745689—44no—
46C2×D236—22no—
47C2×D236—22no—
48C2×D236D411yescharacteristic
49C2×D236C2311yescharacteristic
50C2×D236C2311yescharacteristic
51C2×C4×D59—22no—
52C2×C4×D59—21no—
53C2×C4×D59—21no—
54C2×C4×D59—22no—
55C2×C4×D59C2312yes—
56C2×C8×C59C2311yescharacteristic
57C2×C8×C59C2311yescharacteristic
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59—21no—
61C4⋊C4×C59C2312yes—
62C42×C59C2311yescharacteristic
63#11745671—42no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67(C2×D59)⋊C4—22no—
68(C2×D59)⋊C4D412yes—
69C4⋊Dic59D411yescharacteristic
70C4⋊Dic59C2311yescharacteristic
71C4⋊Dic59C2311yescharacteristic
72Dic59⋊C4—22no—
73Dic59⋊C4—22no—
74C2×C59⋊C8C2312yes—
75D472—22no—
76#11745659—42no—
77C22×D59—21no—
78C22×D59—21no—
79C22×D59C2×D412yes—
80Q8×C59—22no—
81Q8×C59—22no—
82Q8×C59—42no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2411yescharacteristic
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59C2×D412yes—
91D236—22no—
92D236—21no—
93D236—21no—
94D236—21no—
95D236—44no—
96D236—44no—
97D236#4112yescomplemented
98C4×D59—22no—
99C4×D59—22no—
100C4×D59—44no—
101C4×D59—44no—
102C4×D59—42no—
103C4×D59—42no—
104C8×C59—21no—
105C8×C59—21no—
106C59⋊C8—22no—
107C22×C59C22×D411yescharacteristic
108C2×D59—22no—
109C2×D59—22no—
110C2×D59—22no—
111C2×D59—22no—
112C2×D59—41no—
113C2×D59—41no—
114C2×D59—41no—
115C2×D59—41no—
116C2×D59—41no—
117C4×C59—21no—
118C4×C59—42no—
119C4×C59—42no—
120C4×C59AGL(1,ℤ/8)12yes—
121C4×C59C2×#4111yescharacteristic
122C4×C59H(5,𝔽2)11yescharacteristic
123Dic59—22no—
124Dic59—41no—
125Dic59—41no—
126#3330—591nomaximal, Sylow
127C2×C59#54611yescharacteristic
128C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C59#57811yescharacteristic
130D59—42no—
131D59—42no—
132D59—81no—
133#547—591no—
134#547—591no—
135#487D5911yescharacteristic, complemented
136#484—592no—
137#474—591no—
138#468—592no—
139#461—591no—
140#449—592no—
141C4×D8—591no—
142#436—591no—
143#417—592no—
144C59#333011yescharacteristic, complemented, Sylow
145C2×#41—592no—
146C2×#41—1181no—
147C2×SD16—592no—
148C2×D8—591no—
149C2×M16—592no—
150C4⋊Q8C2×D5911yescharacteristic
151C4⋊Q8C2×D5911yescharacteristic
152#123—1182no—
153#123—1182no—
154C22⋊Q8—592no—
155C22⋊Q8—1181no—
156#121—592no—
157#121—1181no—
158C4×D4—591no—
159C4×D4—591no—
160C4×D4—591no—
161C2×C4⋊C4—592no—
162C2×C4⋊C4—1181no—
163#107—591no—
164#107—592no—
165C4⋊C8—591no—
166#103—592no—
167#103C2×D5912yes—
168#103C2×D5912yes—
169#102—591no—
170#102—591no—
171#102—592no—
172C22⋊C8—592no—
173C4×C8C2×D5911yescharacteristic
174#41—1184no—
175#41—2362no—
176#41—2364no—
177C2×Q8—21no—
178C2×Q8C22×D5912yes—
179C2×D4—591no—
180C2×D4—591no—
181C2×D4—591no—
182C2×D4—1182no—
183C2×D4—1182no—
184C22×C4—592no—
185C22×C4—1182no—
186C22×C4—1182no—
187C22×C4—1181no—
188C22×C4—1181no—
189SD16—2362no—
190D8—1182no—
191M16—2362no—
192C2×C8—592no—
193C2×C8C22×D5911yescharacteristic
194C2×C8C22×D5911yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—591no—
199C4⋊C4—591no—
200C4⋊C4—591no—
201C4⋊C4—1182no—
202C4⋊C4—1182no—
203C4⋊C4C22×D5912yes—
204C22⋊C4—592no—
205C22⋊C4—1182no—
206C22⋊C4—1182no—
207C22⋊C4—1181no—
208C22⋊C4—1181no—
209C42C22×D5911yescharacteristic
210C23—592no—
211C23—1181no—
212C23—1181no—
213Q8—22no—
214Q8—22no—
215Q8—42no—
216D4—592no—
217D4—1182no—
218D4—1181no—
219D4—1181no—
220D4—1181no—
221D4—2364no—
222D4—2364no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—592no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1181no—
229C2×C4—1181no—
230C2×C4—2364no—
231C2×C4—2364no—
232C2×C4—2362no—
233C2×C4—2362no—
234C2×C4D4×D5911yescharacteristic
235C2×C4D4×D5911yescharacteristic
236C2×C4C23×D5911yescharacteristic
237C8—21no—
238C8—21no—
239C8—1182no—
240C22—1182no—
241C22—1182no—
242C22—1182no—
243C22—1182no—
244C22—2361no—
245C22—2361no—
246C22—2361no—
247C22—2361no—
248C22—2361no—
249C22C2×D4×D5911yescharacteristic
250C4—21no—
251C4—42no—
252C4—42no—
253C4—1182no—
254C4—2361no—
255C4—2361no—
256C4#1427375412yes—
257C4#41×D5911yescharacteristic
258C4#1427377311yescharacteristic
259C2—4721no—
260C2—2362no—
261C2—2362no—
262C2#1683804511yescharacteristic
263C2C2×#1427375411yescharacteristic
264C2#1683821511yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3330
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16838055C2semidirect
2. #16838055C2semidirect
3. #16837736C2semidirect
4. #16837679C2semidirect
5. #16837651C2semidirect
6. #16837604C2semidirect
7. #16837550C2semidirect
8. C4×D472C2semidirect
9. #16837481C2semidirect
10. #16837402C2semidirect
11. C59×#487C2semidirect
97. D236#41semidirect
135. #487D59semidirect
144. C59#3330semidirect