Finite Group Databasebeta

← #21422463

Subgroups — #21422463

Order 7552.

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

normal subgroups only

This group has 214 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
1C2×#14273721C211yesmaximal, characteristic
2#16837459C211yesmaximal, characteristic, complemented
3#16837127C212yesmaximal, complemented
4#16837125C212yesmaximal
5C59×#431C211yesmaximal, characteristic, complemented
6#14273721—21no—
7#14273721—21no—
8#14273721—21no—
9#14273721—21no—
10C2×Dic59⋊C4C411yescharacteristic
11C2×Dic59⋊C4C411yescharacteristic
12C2×Dic59⋊C4C2211yescharacteristic
13C2×(C2×D59)⋊C4C411yescharacteristic
14C2×(C2×D59)⋊C4C411yescharacteristic
15C2×(C2×D59)⋊C4C2211yescharacteristic
16C4⋊(C59⋊C8)—21no—
17C22⋊(C59⋊C8)C2212yes—
18#14273638—21no—
19C2×C42×C59C2211yescharacteristic
20C4⋊C8×C59—21no—
21C22⋊C8×C59C2212yes—
22C4×C8×C59—21no—
23C23×D59C2×C411yescharacteristic
24C22×C4×C59C2×C411yescharacteristic
25C22×C4×C59C2×C411yescharacteristic
26C22×C4×C59C2311yescharacteristic
27C22×Dic59C2×C411yescharacteristic
28C22×Dic59C2×C411yescharacteristic
29C22×Dic59C2×C411yescharacteristic
30C2×C8×C59—22no—
31C42×C59D411yescharacteristic
32C42×C59D411yescharacteristic
33C42×C59D411yescharacteristic
34C42×C59D411yescharacteristic
35(C2×D59)⋊C4—21no—
36(C2×D59)⋊C4—21no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—21no—
39(C2×D59)⋊C4—21no—
40(C2×D59)⋊C4—21no—
41Dic59⋊C4—21no—
42Dic59⋊C4—21no—
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47C2×C59⋊C8—22no—
48C23×C59C22×C411yescharacteristic
49C22×D59—21no—
50C22×D59—22no—
51C22×D59—41no—
52C22×D59—41no—
53C2×C4×C59—22no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22⋊C411yescharacteristic
58C2×C4×C59C22⋊C411yescharacteristic
59C2×C4×C59C22⋊C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—22no—
66C2×Dic59—41no—
67C2×Dic59—41no—
68C8×C59—42no—
69C59⋊C8—42no—
70C22×C59—21no—
71C22×C59—21no—
72C22×C59C2×C22⋊C411yescharacteristic
73C22×C59#13112yes—
74C2×D59—41no—
75C2×D59—41no—
76C2×D59—41no—
77C2×D59—82no—
78C4×C59—21no—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—21no—
83C4×C59—21no—
84Dic59—41no—
85Dic59—41no—
86Dic59—41no—
87#1473—591nomaximal, Sylow
88C2×C59—22no—
89C2×C59#40811yescharacteristic
90C2×C59#41011yescharacteristic
91C2×C59#41311yescharacteristic
92D59—81no—
93C2×#126—591no—
94#432—591no—
95#431D5911yescharacteristic, complemented
96#324—592no—
97#323—592no—
98C59#147311yescharacteristic, complemented, Sylow
99#126—1181no—
100#126—1181no—
101#126—1181no—
102#126—1181no—
103C2×C4⋊C4—591no—
104C2×C4⋊C4—591no—
105C2×C4⋊C4—591no—
106C2×C22⋊C4—591no—
107C2×C22⋊C4—591no—
108C2×C22⋊C4—591no—
109C2×C42C2×D5911yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—1181no—
112C22⋊C8—592no—
113C22⋊C8C2×D5912yes—
114#97—1181no—
115C4×C8—21no—
116C24—591no—
117C22×C4—591no—
118C22×C4—591no—
119C22×C4—591no—
120C22×C4C4×D5911yescharacteristic
121C22×C4C4×D5911yescharacteristic
122C22×C4C22×D5911yescharacteristic
123C2×C8—22no—
124C2×C8—1182no—
125C4⋊C4—1181no—
126C4⋊C4—1181no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C22⋊C4—1181no—
132C22⋊C4—1181no—
133C22⋊C4—1181no—
134C22⋊C4—1181no—
135C22⋊C4—1181no—
136C22⋊C4—1181no—
137C42D23611yescharacteristic
138C42D23611yescharacteristic
139C42C22⋊D5911yescharacteristic
140C42C22⋊D5911yescharacteristic
141C23—1182no—
142C23—1181no—
143C23—2361no—
144C23—2361no—
145C23C2×C4×D5911yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—1181no—
150C2×C4—1181no—
151C2×C4—1181no—
152C2×C4—1182no—
153C2×C4—2361no—
154C2×C4—2361no—
155C2×C4(C2×D59)⋊C411yescharacteristic
156C2×C4(C2×D59)⋊C411yescharacteristic
157C2×C4(C2×D59)⋊C411yescharacteristic
158C2×C4(C2×D59)⋊C411yescharacteristic
159C2×C4C2×D23611yescharacteristic
160C2×C4C2×C22⋊D5911yescharacteristic
161C8—42no—
162C8—2362no—
163C22—21no—
164C22—21no—
165C22—4722no—
166C22—2361no—
167C22—2361no—
168C22—2361no—
169C22C2×(C2×D59)⋊C411yescharacteristic
170C22#1427373312yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—2361no—
178C4—2361no—
179C4—2361no—
180C2—22no—
181C2—4721no—
182C2#1683736811yescharacteristic
183C2#1683737511yescharacteristic
184C2#1683738411yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#431C2
socleC22×C59C2×C22⋊C4
hypercenter#431D59
hypocenterC59#1473
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16837459C2semidirect
3. #16837127C2semidirect
5. C59×#431C2semidirect
95. #431D59semidirect
98. C59#1473semidirect