Finite Group Databasebeta

← #21422635

Subgroups — #21422635

Order 7552.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#16837268C211yesmaximal, 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—
17C59⋊#95—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—42no—
42C4⋊Dic59C2×C411yescharacteristic
43C4⋊Dic59C2×C411yescharacteristic
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C23×C59C2×D411yescharacteristic
50C22×D59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59C22⋊C411yescharacteristic
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22⋊C411yescharacteristic
58C2×C4×C59C22⋊C411yescharacteristic
59C2×C4×C59C22×C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C22⋊D59—41no—
62C22⋊D59—41no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—21no—
66C2×Dic59—42no—
67C2×Dic59—42no—
68C2×Dic59—42no—
69D236—41no—
70C4×D59—42no—
71Dic118—41no—
72C8×C59—42no—
73C22×C59—21no—
74C22×C59—21no—
75C22×C59C2×C22⋊C411yescharacteristic
76C22×C59AGL(1,ℤ/8)11yescharacteristic
77C22×C59#13711yescharacteristic
78C2×D59—41no—
79C2×D59—41no—
80C2×D59—41no—
81C4×C59—21no—
82C4×C59—21no—
83C4×C59—21no—
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—21no—
87Dic59—41no—
88Dic59—41no—
89Dic59—41no—
90Dic59—82no—
91#1512—591nomaximal, Sylow
92C2×C59—21no—
93C2×C59—21no—
94C2×C59#41011yescharacteristic
95C2×C59#41711yescharacteristic
96C2×C59#42111yescharacteristic
97D59—81no—
98#529—591no—
99#432D5911yescharacteristic, complemented
100#382—591no—
101#328—592no—
102#327—592no—
103C59#151211yescharacteristic, complemented, Sylow
104#126—1181no—
105#125—591no—
106#124—591no—
107#123—1181no—
108C22⋊Q8—591no—
109#121—591no—
110C4×Q8—591no—
111C4×D4—591no—
112C4×D4—1181no—
113#117—1181no—
114C2×C4⋊C4—1181no—
115C2×C42C2×D5911yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D5912yes—
118#97—21no—
119#95—592no—
120#95—1181no—
121C2×Q8—591no—
122C2×D4—591no—
123C2×D4—1181no—
124C22×C4—1181no—
125C22×C4—1182no—
126C22×C4D23611yescharacteristic
127C22×C4D23611yescharacteristic
128C22×C4C22×D5911yescharacteristic
129C2×C8—22no—
130C4⋊C4—591no—
131C4⋊C4—591no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C4⋊C4—1181no—
136C4⋊C4—2362no—
137C22⋊C4—1181no—
138C22⋊C4—1181no—
139C22⋊C4—1181no—
140C22⋊C4—1181no—
141C22⋊C4—1181no—
142C42—1181no—
143C42C4×D5911yescharacteristic
144C42C4×D5911yescharacteristic
145C42C22⋊D5911yescharacteristic
146C42C22⋊D5911yescharacteristic
147C23—1181no—
148C23C2×D23611yescharacteristic
149Q8—2361no—
150D4—2361no—
151D4—2361no—
152D4—2361no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—1181no—
158C2×C4—1181no—
159C2×C4—1181no—
160C2×C4—2362no—
161C2×C4—2362no—
162C2×C4—2362no—
163C2×C4—2362no—
164C2×C4(C2×D59)⋊C411yescharacteristic
165C2×C4(C2×D59)⋊C411yescharacteristic
166C2×C4(C2×D59)⋊C411yescharacteristic
167C2×C4(C2×D59)⋊C411yescharacteristic
168C2×C4C2×C4×D5911yescharacteristic
169C2×C4C2×C22⋊D5911yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—2361no—
174C22—2361no—
175C22—2361no—
176C22C2×(C2×D59)⋊C411yescharacteristic
177C22#1427375511yescharacteristic
178C22#1427376011yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—4722no—
186C4—2361no—
187C4—2361no—
188C4—2361no—
189C2—21no—
190C2—21no—
191C2—4721no—
192C2#1683737511yescharacteristic
193C2#1683740411yescharacteristic
194C2#1683741811yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#432C2
socleC22×C59C2×C22⋊C4
hypercenter#432D59
hypocenterC59#1512
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. #16837268C2semidirect
3. #16837140C2semidirect
5. C59×#432C2semidirect
7. #14273719C4semidirect
8. #14273715C4semidirect
12. C4×Dic118C4semidirect
13. C4×D236C4semidirect
99. #432D59semidirect
103. C59#1512semidirect