Finite Group Databasebeta

← #21434704

Subgroups — #21434704

Order 7552.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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
2#16837937C211yesmaximal, characteristic
3#16837796C211yesmaximal, characteristic, complemented
4#16837772C211yesmaximal, characteristic, complemented
5#16837764C211yesmaximal, characteristic, complemented
6#16837661C212yesmaximal, complemented
7#16837649C212yesmaximal
8#16837496C212yesmaximal, complemented
9#16837489C212yesmaximal, complemented
10#16837354C211yesmaximal, characteristic, complemented
11C59×#501C211yesmaximal, characteristic, complemented
12C2×Dic236C2212yes—
13C2×#11745660C2212yes—
14C2×#11745659C2212yes—
15#14273727C2211yescharacteristic
16#14273722—21no—
17#14273718—21no—
18#14273715C2211yescharacteristic
19#14273712—21no—
20#14273707C2212yes—
21#14273707C2211yescharacteristic
22#14273703—21no—
23#14273702C2211yescharacteristic
24Q8×Dic59—21no—
25#14273692C2211yescharacteristic
26#14273692C2212yes—
27#14273689—21no—
28#14273689C2211yescharacteristic
29#14273685—21no—
30#14273685—21no—
31C42×D59C2211yescharacteristic
32#14273650C2212yes—
33#14273650C2212yes—
34#14273650C2212yes—
35#14273647C2212yes—
36#14273638C2211yescharacteristic
37C8×Dic59C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44C2×D236—21no—
45C2×D236C2311yescharacteristic
46C2×C4×D59—21no—
47C2×C4×D59D411yescharacteristic
48C2×C4×D59D411yescharacteristic
49C2×C4×D59C2311yescharacteristic
50C2×Dic118C2311yescharacteristic
51C2×Dic118C2312yes—
52C2×C8×C59C2312yes—
53C4⋊C4×C59—21no—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2311yescharacteristic
57C4⋊C4×C59C2312yes—
58C4⋊C4×C59C2311yescharacteristic
59C42×C59C2311yescharacteristic
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—21no—
65(C2×D59)⋊C4—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59—22no—
70Dic59⋊C4—22no—
71Dic59⋊C4—21no—
72C4×Dic59—21no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78Dic236—24no—
79#11745660—24no—
80#11745659—24no—
81C22×D59—21no—
82C22×D59C2×D411yescharacteristic
83Q8×C59—42no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2411yescharacteristic
90C2×Dic59—22no—
91C2×Dic59—21no—
92C2×Dic59C2×D411yescharacteristic
93C2×Dic59C2×D411yescharacteristic
94C2×Dic59C2×D411yescharacteristic
95D236—22no—
96D236—42no—
97C4×D59—22no—
98C4×D59—22no—
99C4×D59—41no—
100C4×D59—42no—
101Dic118—22no—
102Dic118—22no—
103Dic118—22no—
104C8×C59#4114yes—
105C59⋊C8—22no—
106C22×C59C22×D411yescharacteristic
107C2×D59—21no—
108C2×D59—21no—
109C2×D59—21no—
110C2×D59—41no—
111C2×D59—41no—
112C2×D59—41no—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—41no—
116C4×C59—41no—
117C4×C59—42no—
118C4×C59C2×#4112yes—
119Dic59—21no—
120Dic59—21no—
121Dic59—42no—
122Dic59—41no—
123Dic59#13712yes—
124#3172—591nomaximal, Sylow
125C2×C59#53211yescharacteristic
126C2×C59C2×#13711yescharacteristic
127C2×C59#57511yescharacteristic
128D59—41no—
129D59—81no—
130#533—591no—
131#529—591no—
132#501D5911yescharacteristic, complemented
133#497—591no—
134#491—591no—
135#489—591no—
136#470—592no—
137#468—592no—
138C4×Q16—592no—
139C4×SD16—592no—
140C4×M16—591no—
141C59#317211yescharacteristic, complemented, Sylow
142C2×Q16—592no—
143C2×SD16—592no—
144C2×M16—592no—
145C4⋊Q8—591no—
146C4⋊Q8C2×D5911yescharacteristic
147#126—1181no—
148#125—1181no—
149#125C2×D5911yescharacteristic
150#124—591no—
151#123—1181no—
152C22⋊Q8—591no—
153C22⋊Q8—592no—
154C22⋊Q8—1181no—
155#121—591no—
156C4×Q8—591no—
157C4×Q8—592no—
158C4×Q8—1181no—
159C4×D4—591no—
160C4×D4—1181no—
161#117—1181no—
162#117—1181no—
163C2×C42—591no—
164#107C2×D5912yes—
165#106C2×D5912yes—
166#103—592no—
167#103—592no—
168#103—592no—
169#102—592no—
170#97—591no—
171#97C2×D5911yescharacteristic
172C4×C8—592no—
173C2×Q8—21no—
174C2×Q8—591no—
175C2×Q8—592no—
176C2×D4—591no—
177C2×D4—1181no—
178C22×C4—591no—
179C22×C4—591no—
180C22×C4—591no—
181C22×C4—1181no—
182Q16—1184no—
183SD16—1184no—
184M16—1184no—
185C2×C8—592no—
186C2×C8C22×D5912yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—1181no—
191C4⋊C4—1182no—
192C4⋊C4—1181no—
193C4⋊C4—1182no—
194C4⋊C4—1181no—
195C4⋊C4—1181no—
196C4⋊C4C22×D5912yes—
197C4⋊C4C22×D5911yescharacteristic
198C4⋊C4C22×D5911yescharacteristic
199C22⋊C4—1181no—
200C22⋊C4—1181no—
201C22⋊C4—1182no—
202C22⋊C4—1181no—
203C22⋊C4—1181no—
204C22⋊C4—1181no—
205C42—591no—
206C42—591no—
207C42—591no—
208C42—1181no—
209C42—1182no—
210C42C22×D5911yescharacteristic
211C23—591no—
212C23—1181no—
213Q8—42no—
214Q8—1182no—
215Q8—1182no—
216Q8—1182no—
217D4—1182no—
218D4—2362no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—591no—
223C2×C4—591no—
224C2×C4—591no—
225C2×C4—1182no—
226C2×C4—1182no—
227C2×C4—1181no—
228C2×C4—1182no—
229C2×C4—2361no—
230C2×C4—2362no—
231C2×C4D4×D5911yescharacteristic
232C2×C4D4×D5911yescharacteristic
233C2×C4C23×D5911yescharacteristic
234C8—1182no—
235C8#1174568914yes—
236C22—1181no—
237C22—1181no—
238C22—1181no—
239C22—2361no—
240C22—2361no—
241C22—2361no—
242C22C2×D4×D5911yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—592no—
249C4—1181no—
250C4—1181no—
251C4—2361no—
252C4—2362no—
253C4C2×#1174568912yes—
254C2—4721no—
255C2—2361no—
256C2#1683795311yescharacteristic
257C2#137×D5911yescharacteristic
258C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3172
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837796C2semidirect
4. #16837772C2semidirect
5. #16837764C2semidirect
6. #16837661C2semidirect
8. #16837496C2semidirect
9. #16837489C2semidirect
10. #16837354C2semidirect
11. C59×#501C2semidirect
132. #501D59semidirect
141. C59#3172semidirect