Finite Group Databasebeta

← #21422622

Subgroups — #21422622

Order 7552.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#16837936C211yesmaximal, characteristic
2C4×C4⋊Dic59C211yesmaximal, characteristic, complemented
3#16837140C212yesmaximal, complemented
4#16837137C212yesmaximal
5C59×#432C211yesmaximal, characteristic, complemented
6#14273721—21no—
7#14273719C411yescharacteristic, complemented
8#14273715C411yescharacteristic, complemented
9#14273710—21no—
10#14273706C2211yescharacteristic
11#14273701C2211yescharacteristic
12C4×Dic118C411yescharacteristic, complemented
13C4×D236C411yescharacteristic, complemented
14C4×C22⋊D59—21no—
15#14273684—21no—
16C2×C4⋊Dic59—21no—
17C2×C4×Dic59—21no—
18C59⋊#95C2212yes—
19C2×C42×C59C2211yescharacteristic
20C4⋊C8×C59—21no—
21C22⋊C8×C59C2212yes—
22#97×C59—21no—
23C22×C4×C59D411yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59C2311yescharacteristic
26C2×C22⋊D59—21no—
27C22×Dic59—22no—
28C2×D236C2×C411yescharacteristic
29C2×C4×D59—21no—
30C2×Dic118C2×C411yescharacteristic
31C2×C8×C59—22no—
32C42×C59C2×C411yescharacteristic
33C42×C59C2×C411yescharacteristic
34C42×C59D411yescharacteristic
35C42×C59D411yescharacteristic
36C22⋊Dic59—21no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—21no—
39(C2×D59)⋊C4—21no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59—24no—
42C4⋊Dic59C2×C411yescharacteristic
43C4⋊Dic59C2×C411yescharacteristic
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C4×Dic59—42no—
50C23×C59C2×D411yescharacteristic
51C22×D59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—22no—
55C2×C4×C59—41no—
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22⋊C411yescharacteristic
58C2×C4×C59C22⋊C411yescharacteristic
59C2×C4×C59C22⋊C411yescharacteristic
60C2×C4×C59C22×C411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C22⋊D59—41no—
63C22⋊D59—41no—
64C2×Dic59—24no—
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—42no—
69C2×Dic59—42no—
70D236—41no—
71C4×D59—42no—
72Dic118—41no—
73C8×C59—42no—
74C22×C59—21no—
75C22×C59—21no—
76C22×C59C2×C22⋊C411yescharacteristic
77C22×C59AGL(1,ℤ/8)11yescharacteristic
78C22×C59#13711yescharacteristic
79C2×D59—41no—
80C2×D59—41no—
81C2×D59—41no—
82C4×C59—21no—
83C4×C59—21no—
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—21no—
87C4×C59#10412yes—
88Dic59—44no—
89Dic59—41no—
90Dic59—41no—
91Dic59—41no—
92#1509—591nomaximal, Sylow
93C2×C59—21no—
94C2×C59—21no—
95C2×C59#41011yescharacteristic
96C2×C59#41711yescharacteristic
97C2×C59C2×#10411yescharacteristic
98D59—81no—
99#529—591no—
100#432D5911yescharacteristic, complemented
101C4×C4⋊C4—591no—
102#328—592no—
103#327—592no—
104C59#150911yescharacteristic, complemented, Sylow
105#126—1181no—
106#125—591no—
107#124—591no—
108#123—1181no—
109C22⋊Q8—591no—
110#121—591no—
111C4×Q8—591no—
112C4×D4—591no—
113C4×D4—1181no—
114#117—1181no—
115C2×C4⋊C4—1181no—
116C2×C42—1181no—
117C2×C42C2×D5911yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C2×D5912yes—
120#97—21no—
121#95—592no—
122C2×Q8—591no—
123C2×D4—591no—
124C2×D4—1181no—
125C22×C4—1182no—
126C22×C4—1181no—
127C22×C4D23611yescharacteristic
128C22×C4D23611yescharacteristic
129C22×C4C22×D5911yescharacteristic
130C2×C8—22no—
131C4⋊C4—591no—
132C4⋊C4—591no—
133C4⋊C4—1184no—
134C4⋊C4—1181no—
135C4⋊C4—1181no—
136C4⋊C4—1181no—
137C4⋊C4—1181no—
138C22⋊C4—1181no—
139C22⋊C4—1181no—
140C22⋊C4—1181no—
141C22⋊C4—1181no—
142C22⋊C4—1181no—
143C42—1181no—
144C42—2362no—
145C42C4×D5911yescharacteristic
146C42C4×D5911yescharacteristic
147C42C22⋊D5911yescharacteristic
148C42C22⋊D5911yescharacteristic
149C23—1181no—
150C23C2×D23611yescharacteristic
151Q8—2361no—
152D4—2361no—
153D4—2361no—
154D4—2361no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—1184no—
160C2×C4—1181no—
161C2×C4—1181no—
162C2×C4—1181no—
163C2×C4—2362no—
164C2×C4—2362no—
165C2×C4—2362no—
166C2×C4(C2×D59)⋊C411yescharacteristic
167C2×C4(C2×D59)⋊C411yescharacteristic
168C2×C4(C2×D59)⋊C411yescharacteristic
169C2×C4(C2×D59)⋊C411yescharacteristic
170C2×C4C2×C4×D5911yescharacteristic
171C2×C4C2×C22⋊D5911yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—2361no—
176C22—2361no—
177C22—2361no—
178C22C2×(C2×D59)⋊C411yescharacteristic
179C22#1427375511yescharacteristic
180C22#1427376011yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—2364no—
187C4—2361no—
188C4—2361no—
189C4—2361no—
190C4#1427365312yes—
191C2—21no—
192C2—21no—
193C2—4721no—
194C2#1683737511yescharacteristic
195C2#1683740411yescharacteristic
196C2C2×#1427365311yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#432C2
socleC22×C59C2×C22⋊C4
hypercenter#432D59
hypocenterC59#1509
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic59C2semidirect
3. #16837140C2semidirect
5. C59×#432C2semidirect
7. #14273719C4semidirect
8. #14273715C4semidirect
12. C4×Dic118C4semidirect
13. C4×D236C4semidirect
100. #432D59semidirect
104. C59#1509semidirect