Finite Group Databasebeta

← #21424039

Subgroups — #21424039

Order 7552.

618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#11745685C211yesmaximal, characteristic
2C2×#14273653C214yesmaximal, complemented
3C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
4C59×#407C211yesmaximal, characteristic, complemented
5C2×#11745685—21no—
6C2×#11745685—21no—
7C2×#11745685—28no—
8C2×#11745685C412yescomplemented
9C2×#11745685C2212yes—
10C22×Dic118C411yescharacteristic, complemented
11C22×D236C411yescharacteristic, complemented
12C22×C22⋊D59—21no—
13C22×C4×D59—21no—
14C2×C22⋊Dic59—21no—
15C2×C4×Dic59C2212yescomplemented
16#14273653—28no—
17C59⋊#95—21no—
18C23×C4×C59C2211yescharacteristic
19C2×M16×C59C2212yescomplemented
20C22⋊C8×C59—21no—
21C22⋊C8×C59—21no—
22C24×C59D411yescharacteristic
23C23×D59—21no—
24C22×C4×C59—24no—
25C22×C4×C59C2×C411yescharacteristic
26C22×C4×C59C2×C411yescharacteristic
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D411yescharacteristic
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—28no—
32C2×C22⋊D59—22no—
33C2×C22⋊D59—22no—
34C22×Dic59—21no—
35C22×Dic59—22no—
36#11745685—28no—
37#11745685—28no—
38#11745685—24no—
39#11745685—24no—
40#11745685—24no—
41#11745685D418yes—
42C2×D236—21no—
43C2×D236—24no—
44C2×D236C2×C412yes—
45C2×C4×D59—28no—
46C2×C4×D59—22no—
47C2×C4×D59—22no—
48C2×Dic118—21no—
49C2×Dic118—24no—
50C2×Dic118C2×C412yes—
51M16×C59—24no—
52C2×C8×C59—22no—
53C22⋊Dic59—24no—
54C4×Dic59—24no—
55C23×C59—22no—
56C23×C59—22no—
57C23×C59—41no—
58C23×C59C22⋊C411yescharacteristic
59C23×C59C22⋊C411yescharacteristic
60C23×C59C2×D411yescharacteristic
61C22×D59—24no—
62C22×D59—22no—
63C22×D59—42no—
64C22×D59—42no—
65C2×C4×C59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59C22⋊C411yescharacteristic
71C2×C4×C59C22⋊C411yescharacteristic
72C2×C4×C59C22×C411yescharacteristic
73C2×C4×C59C2×D414yes—
74C2×C4×C59C2×D411yescharacteristic
75C22⋊D59—28no—
76C22⋊D59—28no—
77C2×Dic59—24no—
78C2×Dic59—22no—
79C2×Dic59—24no—
80C2×Dic59—42no—
81C2×Dic59—42no—
82D236—24no—
83D236—22no—
84D236C22⋊C414yescomplemented
85C4×D59—28no—
86C4×D59—28no—
87Dic118—24no—
88Dic118—22no—
89Dic118C22⋊C414yescomplemented
90C8×C59—42no—
91C22×C59—21no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59—21no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59—21no—
98C22×C59—44no—
99C22×C59#10412yescomplemented
100C22×C59C2×C22⋊C411yescharacteristic
101C22×C59#12012yes—
102C2×D59—24no—
103C2×D59—48no—
104C2×D59—42no—
105C2×D59—42no—
106C4×C59—21no—
107C4×C59—21no—
108C4×C59C2×C22⋊C412yes—
109C4×C59#12012yes—
110Dic59—24no—
111Dic59—44no—
112#1789—591nomaximal, Sylow
113C2×C59—22no—
114C2×C59—22no—
115C2×C59—41no—
116C2×C59#37911yescharacteristic
117C2×C59C2×#10411yescharacteristic
118C2×C59#42111yescharacteristic
119D59—44no—
120C22×#41—591no—
121C2×#104—594no—
122#407D5911yescharacteristic, complemented
123C4×C22⋊C4—591no—
124C59#178911yescharacteristic, complemented, Sylow
125C2×#41—592no—
126C2×#41—592no—
127C2×#41—1188no—
128C2×#41—1181no—
129C2×#41—1181no—
130C22×Q8—591no—
131C22×D4—591no—
132C22×D4—1181no—
133C23×C4—1181no—
134C23×C4C2×D5911yescharacteristic
135C2×M16C2×D5912yescomplemented
136C2×C22⋊C4—1181no—
137C2×C42—592no—
138#104—1188no—
139C22⋊C8—21no—
140C22⋊C8—21no—
141#95—1181no—
142C24—1181no—
143C24D23611yescharacteristic
144#41—598no—
145#41—1184no—
146#41—1184no—
147#41—1188no—
148#41—1188no—
149#41—1184no—
150C2×Q8—592no—
151C2×Q8—1184no—
152C2×Q8—1181no—
153C2×D4—592no—
154C2×D4—1184no—
155C2×D4—1188no—
156C2×D4—1182no—
157C2×D4—1182no—
158C2×D4—1181no—
159C22×C4—24no—
160C22×C4—1188no—
161C22×C4—1181no—
162C22×C4—1182no—
163C22×C4—1182no—
164C22×C4—1182no—
165C22×C4C4×D5911yescharacteristic
166C22×C4C4×D5911yescharacteristic
167C22×C4D23611yescharacteristic
168C22×C4C22⋊D5911yescharacteristic
169C22×C4C22⋊D5911yescharacteristic
170C22×C4C22×D5911yescharacteristic
171M16—24no—
172C2×C8—22no—
173C22⋊C4—1184no—
174C42—1184no—
175C23—22no—
176C23—22no—
177C23—41no—
178C23—1184no—
179C23—1182no—
180C23—2362no—
181C23—2362no—
182C23(C2×D59)⋊C411yescharacteristic
183C23(C2×D59)⋊C411yescharacteristic
184C23C2×D23611yescharacteristic
185Q8—594no—
186Q8—1184no—
187Q8—1182no—
188D4—594no—
189D4—1184no—
190D4—1188no—
191D4—1188no—
192D4—1182no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—1188no—
199C2×C4—1184no—
200C2×C4—1182no—
201C2×C4—1188no—
202C2×C4—1184no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4(C2×D59)⋊C411yescharacteristic
206C2×C4(C2×D59)⋊C411yescharacteristic
207C2×C4C2×C4×D5911yescharacteristic
208C2×C4D4×D5914yes—
209C2×C4C2×C22⋊D5911yescharacteristic
210C8—42no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—44no—
219C22—1184no—
220C22—2368no—
221C22—2362no—
222C22—2362no—
223C22#1427365312yescomplemented
224C22C2×(C2×D59)⋊C411yescharacteristic
225C22#1427369712yes—
226C4—21no—
227C4—21no—
228C4—1184no—
229C4—2364no—
230C4C22⋊C4×D5912yes—
231C4#1427369512yes—
232C2—22no—
233C2—22no—
234C2—41no—
235C2—2364no—
236C2#1683725711yescharacteristic
237C2C2×#1427365311yescharacteristic
238C2#1683741811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#407C2
socleC22×C59C2×C22⋊C4
hypercenter#407D59
hypocenterC59#1789
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#14273653C2semidirect
3. C4×C22⋊Dic59C2semidirect
4. C59×#407C2semidirect
8. C2×#11745685C4semidirect
10. C22×Dic118C4semidirect
11. C22×D236C4semidirect
15. C2×C4×Dic59C22semidirect
19. C2×M16×C59C22semidirect
84. D236C22⋊C4semidirect
89. Dic118C22⋊C4semidirect
99. C22×C59#104semidirect
122. #407D59semidirect
124. C59#1789semidirect
135. C2×M16C2×D59semidirect
223. C22#14273653semidirect