Finite Group Databasebeta

← #21433456

Subgroups — #21433456

Order 7552.

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

normal subgroups only

This group has 762 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×#14273772C211yesmaximal, characteristic, complemented
2#16838202C212yesmaximal, complemented
3#16837969C211yesmaximal, characteristic, complemented
4#16837582C214yesmaximal, complemented
5#16837572C214yesmaximal, complemented
6#16837418C212yesmaximal, complemented
7C2×#100×C59C211yesmaximal, characteristic, complemented
8#14273772—22no—
9#14273772—24no—
10#14273772C2214yes—
11C2×#11745685C2212yes—
12C2×#11745685C2211yescharacteristic, complemented
13C2×#11745687—22no—
14C22×C22⋊D59—22no—
15C2×D4×D59—22no—
16#14273760—22no—
17#14273760C2214yescomplemented
18#14273755—22no—
19#14273755C2214yescomplemented
20#14273749—24no—
21#14273723C2212yescomplemented
22#14273714C2212yescomplemented
23#14273698—22no—
24#14273696—22no—
25#14273686C2211yescharacteristic, complemented
26#14273653C2218yescomplemented
27C22×D4×C59C2211yescharacteristic
28C2×M16×C59C2212yescomplemented
29#100×C59C2214yescomplemented
30C24×C59D412yes—
31C23×D59—22no—
32C2×D4×C59—22no—
33C2×D4×C59—22no—
34C2×D4×C59D412yes—
35C2×D4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C2×C22⋊D59—24no—
38C2×C22⋊D59—28no—
39C2×C22⋊D59—22no—
40C2×C22⋊D59—28no—
41C2×C22⋊D59—21no—
42C2×C22⋊D59—24no—
43C22×Dic59—22no—
44#11745687—28no—
45#11745687—28no—
46D4×D59—28no—
47D4×D59—28no—
48#11745685—22no—
49#11745685—22no—
50#11745685—22no—
51#11745685—22no—
52#11745685D414yescomplemented
53#11745685C2314yes—
54C2×D236D412yescomplemented
55C2×D236C2311yescharacteristic, complemented
56C2×C4×D59—22no—
57C2×C4×D59—21no—
58C2×Dic118D412yescomplemented
59C2×Dic118C2311yescharacteristic, complemented
60M16×C59—22no—
61M16×C59C2314yescomplemented
62C2×C8×C59—22no—
63C22⋊Dic59—21no—
64C22⋊Dic59—24no—
65C4⋊Dic59—21no—
66C4×Dic59C2312yescomplemented
67Dic236—24no—
68D472—24no—
69#11745660—24no—
70#11745660—24no—
71C23×C59—22no—
72C23×C59—22no—
73C23×C59—82no—
74C23×C59C2×D414yes—
75C23×C59C2×D411yescharacteristic
76C22×D59—22no—
77C22×D59—28no—
78C22×D59—21no—
79C22×D59—84no—
80D4×C59—24no—
81D4×C59—24no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D412yes—
84C2×C4×C59C2×D412yes—
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—216no—
87C22⋊D59—24no—
88C22⋊D59—24no—
89C22⋊D59—41no—
90C22⋊D59—41no—
91C22⋊D59—84no—
92C2×Dic59—28no—
93C2×Dic59—22no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96D236—22no—
97D236—22no—
98D236C2×D414yes—
99C4×D59—24no—
100C4×D59—24no—
101C4×D59—42no—
102Dic118—22no—
103Dic118—22no—
104Dic118C2×D414yes—
105C8×C59—24no—
106C22×C59—24no—
107C22×C59—41no—
108C22×C59—44no—
109C22×C59—44no—
110C22×C59—82no—
111C22×C59#12011yescharacteristic
112C22×C59#12011yescharacteristic
113C22×C59C22×D411yescharacteristic
114C2×D59—24no—
115C2×D59—44no—
116C2×D59—42no—
117C2×D59—41no—
118C2×D59—88no—
119C4×C59#12012yes—
120C4×C59C22×D412yes—
121Dic59—24no—
122Dic59—42no—
123Dic59—41no—
124#3019—591nomaximal, Sylow
125C2×C59—21no—
126C2×C59—21no—
127C2×C59—21no—
128C2×C59—44no—
129C2×C59C2×#12011yescharacteristic
130D59—44no—
131D59—81no—
132C2×H(5,𝔽2)—591no—
133#575—592no—
134#535—591no—
135#455—594no—
136#453—594no—
137#421—592no—
138C2×#100D5911yescharacteristic, complemented
139C59#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—594no—
141H(5,𝔽2)—1184no—
142H(5,𝔽2)—1182no—
143C2×#41—592no—
144C2×#41—591no—
145C2×#41—1182no—
146C22×D4—1182no—
147C22×D4—1182no—
148C22×D4C2×D5911yescharacteristic
149#137—594no—
150#137—1182no—
151AGL(1,ℤ/8)—594no—
152AGL(1,ℤ/8)—1182no—
153#135—1184no—
154C2×M16C2×D5912yescomplemented
155#127—592no—
156#124—592no—
157#121—1182no—
158#120—1182no—
159#117—591no—
160#104—598no—
161#100C2×D5914yescomplemented
162C24—1182no—
163C24D23612yes—
164#41—594no—
165#41—594no—
166#41—1188no—
167#41—1188no—
168#41—1182no—
169#41—1182no—
170#41—1182no—
171#41—1182no—
172C2×Q8—592no—
173C2×Q8—591no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—592no—
177C2×D4—591no—
178C2×D4—1188no—
179C2×D4—1188no—
180C2×D4—1184no—
181C2×D4—1188no—
182C2×D4—1182no—
183C2×D4—1188no—
184C2×D4—1184no—
185C2×D4—1181no—
186C2×D4D23612yes—
187C2×D4C22×D5912yes—
188C22×C4—1182no—
189C22×C4—1182no—
190C22×C4—1181no—
191C22×C4C22×D5911yescharacteristic
192Q16—1184no—
193SD16—1184no—
194SD16—1184no—
195D8—1184no—
196M16—22no—
197M16C22×D5914yescomplemented
198C2×C8—22no—
199C4⋊C4—1181no—
200C22⋊C4—1181no—
201C22⋊C4—1184no—
202C42—592no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—1188no—
207C23—1182no—
208C23—1181no—
209C23—4724no—
210C23C2×D23614yes—
211C23C2×D23611yescharacteristic
212Q8—594no—
213Q8—1182no—
214Q8—1182no—
215D4—24no—
216D4—24no—
217D4—594no—
218D4—11816no—
219D4—1184no—
220D4—1184no—
221D4—1182no—
222D4—1182no—
223D4—4724no—
224D4—2361no—
225D4—2361no—
226C2×C4—1188no—
227C2×C4—1182no—
228C2×C4—1184no—
229C2×C4—1184no—
230C2×C4—1182no—
231C2×C4—1181no—
232C2×C4—2362no—
233C2×C4C2×D23611yescharacteristic
234C2×C4D4×D5912yes—
235C2×C4D4×D5912yes—
236C2×C4C23×D5911yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—1184no—
244C22—4728no—
245C22—2362no—
246C22—2364no—
247C22—2361no—
248C22#1427369711yescharacteristic
249C22#1427369711yescharacteristic
250C22C22×D23611yescharacteristic
251C4—1184no—
252C4—2362no—
253C4—2361no—
254C4#1427369712yes—
255C4C2×D4×D5912yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—4721no—
261C2—2364no—
262C2C2×#1427369711yescharacteristic
subgroupG/H
centerC2C2×#14273697
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#100×C59C2
socleC2×C59C2×#120
hypercenterC2×#100D59
hypocenterC59#3019
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#14273772C2semidirect
2. #16838202C2semidirect
3. #16837969C2semidirect
4. #16837582C2semidirect
5. #16837572C2semidirect
6. #16837418C2semidirect
7. C2×#100×C59C2semidirect
12. C2×#11745685C22semidirect
17. #14273760C22semidirect
19. #14273755C22semidirect
21. #14273723C22semidirect
22. #14273714C22semidirect
25. #14273686C22semidirect
26. #14273653C22semidirect
28. C2×M16×C59C22semidirect
29. #100×C59C22semidirect
52. #11745685D4semidirect
54. C2×D236D4semidirect
55. C2×D236C23semidirect
58. C2×Dic118D4semidirect
59. C2×Dic118C23semidirect
61. M16×C59C23semidirect
66. C4×Dic59C23semidirect
138. C2×#100D59semidirect
139. C59#3019semidirect
154. C2×M16C2×D59semidirect
161. #100C2×D59semidirect
197. M16C22×D59semidirect