Finite Group Databasebeta

← #21424537

Subgroups — #21424537

Order 7552.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#16837913C211yesmaximal, characteristic
2C22×C4×Dic59C211yesmaximal, characteristic, complemented
3C2×#14273653C212yesmaximal, complemented
4#16837163C212yesmaximal, complemented
5C59×#407C211yesmaximal, characteristic, complemented
6C2×#11745685C2211yescharacteristic
7C23×Dic59—21no—
8#14273710—21no—
9#14273706C412yescomplemented
10#14273701C412yescomplemented
11#14273696—21no—
12C4×C22⋊D59—22no—
13#14273686C2211yescharacteristic
14C2×C4×Dic59—21no—
15C2×C4×Dic59—24no—
16C2×C4×Dic59C2212yes—
17#14273653—24no—
18C23×C4×C59C2211yescharacteristic
19C2×M16×C59C2212yes—
20C22⋊C8×C59—22no—
21C24×C59D411yescharacteristic
22C22×C4×C59—22no—
23C22×C4×C59—22no—
24C22×C4×C59C2×C412yes—
25C22×C4×C59D411yescharacteristic
26C22×C4×C59D412yes—
27C22×C4×C59C2311yescharacteristic
28C2×C22⋊D59—22no—
29C2×C22⋊D59—21no—
30C22×Dic59—24no—
31C22×Dic59—28no—
32C22×Dic59—22no—
33#11745685—22no—
34#11745685—22no—
35C2×D236C2×C411yescharacteristic, complemented
36C2×C4×D59—21no—
37C2×Dic118C2×C411yescharacteristic, complemented
38M16×C59—22no—
39M16×C59—22no—
40C2×C8×C59—22no—
41C22⋊Dic59—22no—
42C22⋊Dic59—21no—
43(C2×D59)⋊C4—22no—
44C4⋊Dic59C2×C412yescomplemented
45Dic59⋊C4—22no—
46C4×Dic59—24no—
47C4×Dic59—22no—
48C4×Dic59—21no—
49C4×Dic59D414yescomplemented
50C23×C59—24no—
51C23×C59—21no—
52C23×C59—21no—
53C23×C59C22⋊C412yes—
54C23×C59C2×D411yescharacteristic
55C22×D59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—24no—
59C2×C4×C59—24no—
60C2×C4×C59C22⋊C412yes—
61C2×C4×C59C22×C411yescharacteristic
62C2×C4×C59C2×D412yes—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59#4112yes—
65C22⋊D59—44no—
66C22⋊D59—41no—
67C22⋊D59—41no—
68C2×Dic59—216no—
69C2×Dic59—28no—
70C2×Dic59—24no—
71C2×Dic59—22no—
72C2×Dic59—21no—
73D236—22no—
74C4×D59—42no—
75Dic118—22no—
76C8×C59—42no—
77C22×C59—24no—
78C22×C59—24no—
79C22×C59—22no—
80C22×C59—22no—
81C22×C59—22no—
82C22×C59#10414yescomplemented
83C22×C59C2×C22⋊C411yescharacteristic
84C22×C59#12011yescharacteristic
85C22×C59#12311yescharacteristic
86C2×D59—41no—
87C2×D59—42no—
88C4×C59—22no—
89C4×C59C4×D412yes—
90C4×C59#12112yes—
91Dic59—28no—
92Dic59—41no—
93Dic59—42no—
94#1896—591nomaximal, Sylow
95C2×C59—21no—
96C2×C59—24no—
97C2×C59—21no—
98C2×C59#38611yescharacteristic
99C2×C59C2×#10412yes—
100D59—81no—
101#525—591no—
102C22×C42—591no—
103C2×#104—592no—
104#407D5911yescharacteristic, complemented
105#339—592no—
106C59#189611yescharacteristic, complemented, Sylow
107C2×#41—591no—
108C23×C4—1181no—
109C23×C4C2×D5911yescharacteristic
110C2×M16C2×D5912yes—
111#123—1181no—
112C22⋊Q8—592no—
113#121—592no—
114#120—1181no—
115C4×D4—1182no—
116#117—591no—
117C2×C42—592no—
118C2×C42—1184no—
119C2×C42—1181no—
120#104—1184no—
121C22⋊C8—22no—
122C24D23611yescharacteristic
123#41—1182no—
124#41—1182no—
125C2×Q8—591no—
126C2×D4—591no—
127C2×D4—1182no—
128C2×D4—1181no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—1184no—
132C22×C4—1188no—
133C22×C4—1182no—
134C22×C4—1181no—
135C22×C4C4×D5912yes—
136C22×C4D23611yescharacteristic
137C22×C4C22⋊D5912yes—
138C22×C4C22×D5911yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—592no—
143C4⋊C4—1182no—
144C22⋊C4—1182no—
145C22⋊C4—1181no—
146C22⋊C4—1182no—
147C42—594no—
148C42—1184no—
149C42—1182no—
150C42—1181no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—1181no—
155C23(C2×D59)⋊C412yes—
156C23C2×D23611yescharacteristic
157Q8—1182no—
158D4—1182no—
159D4—2364no—
160D4—2361no—
161D4—2361no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—11816no—
167C2×C4—1188no—
168C2×C4—1184no—
169C2×C4—1182no—
170C2×C4—1181no—
171C2×C4—2362no—
172C2×C4(C2×D59)⋊C412yes—
173C2×C4C2×C4×D5911yescharacteristic
174C2×C4D4×D5912yes—
175C2×C4#1174568712yes—
176C2×C4C2×C22⋊D5911yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—2362no—
184C22—2361no—
185C22#1427365314yescomplemented
186C22C2×(C2×D59)⋊C411yescharacteristic
187C22#1427369711yescharacteristic
188C22#1427371111yescharacteristic
189C4—22no—
190C4—1188no—
191C4—2362no—
192C4—2361no—
193C4(C22⋊D59)⋊C412yes—
194C4#1427369912yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—4721no—
199C2#1683727911yescharacteristic
200C2C2×#1427365312yes—
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#407C2
socleC22×C59C2×C22⋊C4
hypercenter#407D59
hypocenterC59#1896
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. C22×C4×Dic59C2semidirect
3. C2×#14273653C2semidirect
4. #16837163C2semidirect
5. C59×#407C2semidirect
9. #14273706C4semidirect
10. #14273701C4semidirect
35. C2×D236C2×C4semidirect
37. C2×Dic118C2×C4semidirect
44. C4⋊Dic59C2×C4semidirect
49. C4×Dic59D4semidirect
82. C22×C59#104semidirect
104. #407D59semidirect
106. C59#1896semidirect
185. C22#14273653semidirect