Finite Group Databasebeta

← #21433459

Subgroups — #21433459

Order 7552.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273775C211yesmaximal, characteristic, complemented
2#16838200C212yesmaximal, complemented
3#16837584C214yesmaximal, complemented
4#16837574C214yesmaximal, complemented
5#16837420C212yesmaximal, complemented
6C2×#14273646C211yesmaximal, characteristic, complemented
7C59×#536C211yesmaximal, characteristic, complemented
8#14273775—22no—
9#14273775—24no—
10#14273775C2214yes—
11C2×#11745689—22no—
12C2×#11745685—22no—
13C2×#11745685C2212yes—
14C2×Q8×D59—22no—
15#14273758C2214yescomplemented
16#14273757—22no—
17#14273753C2214yescomplemented
18#14273752—22no—
19#14273747—24no—
20C2×#11745664C2212yes—
21#14273655C2218yescomplemented
22#14273646C2214yescomplemented
23C2×#41×C59C2211yescharacteristic
24C22×Q8×C59C2211yescharacteristic
25C4⋊Q8×C59C2212yescomplemented
26#124×C59C2212yescomplemented
27#123×C59—22no—
28C22⋊Q8×C59—22no—
29#117×C59C2211yescharacteristic
30#41×C59—22no—
31#41×C59—22no—
32C2×Q8×C59—22no—
33C2×Q8×C59—22no—
34C2×Q8×C59D412yes—
35C2×Q8×C59C2311yescharacteristic
36C2×Q8×C59C2312yes—
37C2×D4×C59—21no—
38C2×D4×C59C2311yescharacteristic
39C22×C4×C59—21no—
40C22×C4×C59D412yes—
41C22×C4×C59C2311yescharacteristic
42C2×C22⋊D59—22no—
43#11745689—28no—
44#11745689—28no—
45Q8×D59—28no—
46Q8×D59—28no—
47#11745685—28no—
48#11745685—28no—
49#11745685—22no—
50#11745685—22no—
51#11745685D414yes—
52#11745685C2314yes—
53C2×D236—22no—
54C2×D236D412yes—
55C2×C4×D59—24no—
56C2×C4×D59—22no—
57C2×Dic118—22no—
58C2×Dic118D412yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59—24no—
61C22⋊C4×C59—21no—
62C22⋊C4×C59—24no—
63C42×C59C2312yes—
64#11745672—24no—
65#11745671—24no—
66#11745670—24no—
67#11745669—24no—
68#11745664—22no—
69#11745664C2314yes—
70C2×C59⋊C8—22no—
71C23×C59—21no—
72C23×C59C2×D411yescharacteristic
73C22×D59—22no—
74Q8×C59—24no—
75Q8×C59—24no—
76Q8×C59—22no—
77D4×C59—22no—
78D4×C59—41no—
79D4×C59—41no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—42no—
85C2×C4×C59C2×D412yes—
86C2×C4×C59C2×D412yes—
87C2×C4×C59C2×D414yes—
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2411yescharacteristic
90C22⋊D59—24no—
91C22⋊D59—24no—
92C2×Dic59—22no—
93D236—28no—
94D236—22no—
95D236C2×D414yes—
96C4×D59—216no—
97C4×D59—24no—
98C4×D59—24no—
99Dic118—28no—
100Dic118—22no—
101Dic118C2×D414yes—
102C59⋊C8—24no—
103C22×C59—41no—
104C22×C59—42no—
105C22×C59—41no—
106C22×C59#12011yescharacteristic
107C22×C59#12011yescharacteristic
108C22×C59C22×D411yescharacteristic
109C2×D59—24no—
110C2×D59—44no—
111C4×C59—24no—
112C4×C59—42no—
113C4×C59—41no—
114C4×C59#12012yes—
115C4×C59C22×D412yes—
116Dic59—24no—
117#3020—591nomaximal, Sylow
118C2×C59—21no—
119C2×C59—21no—
120C2×C59—21no—
121C2×C59—81no—
122C2×C59C2×#12011yescharacteristic
123D59—44no—
124C2×2−1+4—591no—
125#575—592no—
126#536D5911yescharacteristic, complemented
127#456—594no—
128#454—594no—
129#421—592no—
130C2×#101—591no—
131C59#302011yescharacteristic, complemented, Sylow
1322−1+4—594no—
1332−1+4—1184no—
1342−1+4—1182no—
135C2×#41—592no—
136C2×#41—1182no—
137C2×#41—1182no—
138C2×#41C2×D5911yescharacteristic
139C22×Q8—1182no—
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⋊Q8C2×D5912yescomplemented
148#124C2×D5912yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D5911yescharacteristic
152#104—598no—
153#101—594no—
154#41—22no—
155#41—22no—
156#41—594no—
157#41—594no—
158#41—1188no—
159#41—1188no—
160#41—1188no—
161#41—1182no—
162#41—1182no—
163#41—1188no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—592no—
167C2×Q8—1182no—
168C2×Q8—1188no—
169C2×Q8—1188no—
170C2×Q8C22⋊D5912yes—
171C2×Q8C22×D5911yescharacteristic
172C2×Q8C22×D5912yes—
173C2×D4—21no—
174C2×D4—592no—
175C2×D4—1182no—
176C2×D4—1182no—
177C2×D4C22×D5911yescharacteristic
178C22×C4—21no—
179C22×C4—1184no—
180C22×C4—1182no—
181C22×C4C22⋊D5912yes—
182C22×C4C22×D5911yescharacteristic
183Q16—1184no—
184SD16—1184no—
185SD16—1184no—
186D8—1184no—
187M16—594no—
188M16—1182no—
189C2×C8—1182no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D5912yes—
195C23—21no—
196C23—1182no—
197C23C2×C22⋊D5911yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—594no—
202Q8—1188no—
203Q8—1182no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—594no—
208D4—1188no—
209D4—1184no—
210D4—1184no—
211D4—1182no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—11816no—
218C2×C4—1182no—
219C2×C4—1184no—
220C2×C4—1184no—
221C2×C4D4×D5912yes—
222C2×C4D4×D5912yes—
223C2×C4C2×C22⋊D5914yes—
224C2×C4C2×C22⋊D5911yescharacteristic
225C2×C4C23×D5911yescharacteristic
226C8—1184no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—1184no—
231C22—2364no—
232C22#1427369511yescharacteristic
233C22#1427369511yescharacteristic
234C22C22×C22⋊D5911yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—1184no—
239C4#1427369512yes—
240C4C2×D4×D5912yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—2364no—
246C2C2×#1427369511yescharacteristic
subgroupG/H
centerC2C2×#14273695
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#536C2
socleC2×C59C2×#120
hypercenter#536D59
hypocenterC59#3020
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#14273775C2semidirect
2. #16838200C2semidirect
3. #16837584C2semidirect
4. #16837574C2semidirect
5. #16837420C2semidirect
6. C2×#14273646C2semidirect
7. C59×#536C2semidirect
15. #14273758C22semidirect
17. #14273753C22semidirect
21. #14273655C22semidirect
22. #14273646C22semidirect
25. C4⋊Q8×C59C22semidirect
26. #124×C59C22semidirect
126. #536D59semidirect
131. C59#3020semidirect
147. C4⋊Q8C2×D59semidirect
148. #124C2×D59semidirect