Finite Group Databasebeta

← #21433460

Subgroups — #21433460

Order 7552.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#16838200C212yesmaximal, complemented
2#16837976C211yesmaximal, characteristic, complemented
3#16837585C214yesmaximal, complemented
4#16837575C214yesmaximal, complemented
5#16837419C212yesmaximal, complemented
6C2×#14273646C211yesmaximal, characteristic, complemented
7C2×2−1+4×C59C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273758—22no—
10#14273757C2214yescomplemented
11#14273753—22no—
12#14273752C2214yescomplemented
13#14273747—24no—
14C2×#11745664C2212yes—
15#14273725C2212yescomplemented
16#14273716C2212yescomplemented
17#14273710—22no—
18#14273703—22no—
19#14273686C2211yescharacteristic
20#14273654C2218yescomplemented
21#14273646C2214yescomplemented
222−1+4×C59—24no—
232−1+4×C59—22no—
242−1+4×C59C2214yes—
25C2×#41×C59—22no—
26C2×#41×C59—22no—
27C2×#41×C59C2212yes—
28C22×Q8×C59—22no—
29C22×Q8×C59C2211yescharacteristic
30#41×C59—28no—
31#41×C59—28no—
32#41×C59—28no—
33#41×C59—28no—
34#41×C59—22no—
35#41×C59—22no—
36#41×C59D414yes—
37#41×C59C2314yes—
38C2×Q8×C59—22no—
39C2×Q8×C59—28no—
40C2×Q8×C59—28no—
41C2×Q8×C59—22no—
42C2×Q8×C59—22no—
43C2×Q8×C59D412yes—
44C2×Q8×C59D412yes—
45C2×Q8×C59C2312yes—
46C2×D4×C59—22no—
47C2×D4×C59—22no—
48C2×D4×C59D412yes—
49C22×C4×C59—24no—
50C22×C4×C59—22no—
51C22×C4×C59D412yes—
52C22×C4×C59C2311yescharacteristic
53C2×C22⋊D59—21no—
54#11745685—22no—
55#11745685—22no—
56C2×D236C2311yescharacteristic
57C2×C4×D59—21no—
58C2×Dic118C2311yescharacteristic
59C22⋊Dic59—21no—
60#11745672—24no—
61#11745671—24no—
62#11745670—24no—
63#11745669—24no—
64(C2×D59)⋊C4—24no—
65C4⋊Dic59—21no—
66Dic59⋊C4—24no—
67C4×Dic59C2312yes—
68#11745664—22no—
69#11745664C2314yes—
70C2×C59⋊C8—22no—
71C23×C59—22no—
72C23×C59C2×D411yescharacteristic
73C22×D59—21no—
74Q8×C59—28no—
75Q8×C59—22no—
76Q8×C59—24no—
77Q8×C59—24no—
78Q8×C59C2×D414yes—
79D4×C59—28no—
80D4×C59—24no—
81D4×C59—24no—
82D4×C59—22no—
83D4×C59C2×D414yes—
84C2×C4×C59—216no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—24no—
89C2×C4×C59—24no—
90C2×C4×C59C2×D414yes—
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D412yes—
93C2×C4×C59C2×D412yes—
94C2×C4×C59C2411yescharacteristic
95C22⋊D59—41no—
96C22⋊D59—41no—
97C2×Dic59—22no—
98C2×Dic59—21no—
99D236—22no—
100C4×D59—42no—
101Dic118—22no—
102C59⋊C8—24no—
103C22×C59—24no—
104C22×C59—41no—
105C22×C59—44no—
106C22×C59#12011yescharacteristic
107C22×C59#12011yescharacteristic
108C22×C59C22×D411yescharacteristic
109C2×D59—42no—
110C2×D59—41no—
111C4×C59—24no—
112C4×C59—24no—
113C4×C59#12012yes—
114C4×C59C22×D412yes—
115Dic59—42no—
116Dic59—41no—
117#3020—591nomaximal, Sylow
118C2×C59—21no—
119C2×C59—21no—
120C2×C59—21no—
121C2×C59—44no—
122C2×C59C2×#12011yescharacteristic
123D59—81no—
124C2×2−1+4D5911yescharacteristic, complemented
125#575—592no—
126#536—591no—
127#456—594no—
128#454—594no—
129#421—592no—
130C2×#101—591no—
131C59#302011yescharacteristic, complemented, Sylow
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D5914yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—591no—
138C2×#41C2×D5912yes—
139C22×Q8—22no—
140C22×Q8C2×D5911yescharacteristic
141#137—594no—
142#137—1182no—
143AGL(1,ℤ/8)—594no—
144AGL(1,ℤ/8)—1182no—
145#135—1184no—
146C2×M16—592no—
147C4⋊Q8—592no—
148#124—592no—
149#123—1182no—
150C22⋊Q8—1182no—
151#117—591no—
152#104—598no—
153#101—594no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—1182no—
161#41—1182no—
162#41C22⋊D5914yes—
163#41C22×D5914yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—591no—
170C2×Q8C22⋊D5912yes—
171C2×Q8C22⋊D5912yes—
172C2×Q8C22×D5912yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—591no—
176C2×D4—1181no—
177C2×D4C22⋊D5912yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—1181no—
181C22×C4C22⋊D5912yes—
182C22×C4C22×D5911yescharacteristic
183Q16—1184no—
184SD16—1184no—
185SD16—1184no—
186D8—1184no—
187M16—594no—
188M16—1182no—
189C2×C8—1182no—
190C4⋊C4—1181no—
191C4⋊C4—1184no—
192C22⋊C4—1181no—
193C22⋊C4—1184no—
194C42—592no—
195C23—22no—
196C23—1181no—
197C23C2×C22⋊D5911yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—1182no—
203Q8C2×C22⋊D5914yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—1182no—
209D4—2361no—
210D4—2361no—
211D4C2×C22⋊D5914yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—1182no—
219C2×C4—1181no—
220C2×C4—2362no—
221C2×C4C2×C22⋊D5914yes—
222C2×C4C2×C22⋊D5911yescharacteristic
223C2×C4C2×C22⋊D5912yes—
224C2×C4C2×C22⋊D5912yes—
225C2×C4C23×D5911yescharacteristic
226C8—1184no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—2362no—
231C22—2361no—
232C22#1427369611yescharacteristic
233C22#1427369611yescharacteristic
234C22C22×C22⋊D5911yescharacteristic
235C4—24no—
236C4—24no—
237C4—2362no—
238C4—2361no—
239C4#1427369612yes—
240C4C22×C22⋊D5912yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—4721no—
246C2C2×#1427369611yescharacteristic
subgroupG/H
centerC2C2×#14273696
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×2−1+4×C59C2
socleC2×C59C2×#120
hypercenterC2×2−1+4D59
hypocenterC59#3020
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #16838200C2semidirect
2. #16837976C2semidirect
3. #16837585C2semidirect
4. #16837575C2semidirect
5. #16837419C2semidirect
6. C2×#14273646C2semidirect
7. C2×2−1+4×C59C2semidirect
10. #14273757C22semidirect
12. #14273752C22semidirect
15. #14273725C22semidirect
16. #14273716C22semidirect
20. #14273654C22semidirect
21. #14273646C22semidirect
124. C2×2−1+4D59semidirect
131. C59#3020semidirect