Finite Group Databasebeta

← #21435302

Subgroups — #21435302

Order 7552.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837959C211yesmaximal, characteristic
2#16837812C212yesmaximal, complemented
3#16837772C212yesmaximal, complemented
4#16837737C212yesmaximal
5#16837732C212yesmaximal
6#16837706C214yesmaximal, complemented
7#16837459C211yesmaximal, characteristic
8C2×#125×C59C211yesmaximal, characteristic
9#14273727C2211yescharacteristic
10#14273727C2211yescharacteristic
11#14273719—21no—
12#14273706—21no—
13#14273706C2212yes—
14C4×Dic118—21no—
15C4×Dic118C2212yes—
16#14273686—21no—
17#14273660C2214yes—
18#14273658C2214yes—
19C4⋊(C59⋊C8)C2212yes—
20#14273650C2214yes—
21#14273650C2214yes—
22C22⋊(C59⋊C8)C2212yes—
23#14273638C2212yes—
24#125×C59—21no—
25#125×C59—21no—
26#125×C59C2212yes—
27#125×C59C2212yes—
28C2×C4⋊C4×C59—21no—
29C2×C4⋊C4×C59—21no—
30C2×C4⋊C4×C59C2211yescharacteristic
31C2×C4⋊C4×C59C2211yescharacteristic
32C2×C42×C59C2211yescharacteristic
33C22×C4×C59—21no—
34C22×C4×C59—21no—
35C22×C4×C59D411yescharacteristic
36C22×C4×C59D411yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C2×Dic118—21no—
39C2×Dic118C2312yes—
40C4⋊C4×C59—22no—
41C4⋊C4×C59—22no—
42C4⋊C4×C59—22no—
43C4⋊C4×C59—22no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59C2312yes—
47C4⋊C4×C59C2312yes—
48C42×C59D411yescharacteristic
49C42×C59D411yescharacteristic
50C42×C59C2311yescharacteristic
51C42×C59C2311yescharacteristic
52C22⋊Dic59—22no—
53C4⋊Dic59—21no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59C4×Dic59—22no—
60C2×C59⋊C8C2314yes—
61C23×C59C2×D411yescharacteristic
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—41no—
67C2×C4×C59—42no—
68C2×C4×C59—42no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2411yescharacteristic
75C2×Dic59—22no—
76C2×Dic59—22no—
77Dic118—24no—
78Dic118—42no—
79C59⋊C8—24no—
80C22×C59—21no—
81C22×C59—21no—
82C22×C59#13712yes—
83C22×C59C22×D411yescharacteristic
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—21no—
87C4×C59—21no—
88C4×C59—21no—
89C4×C59—42no—
90C4×C59—42no—
91C4×C592−1+412yes—
92Dic59—42no—
93Dic59—42no—
94#3236—591nomaximal, Sylow
95C2×C59—22no—
96C2×C59#53611yescharacteristic
97C2×C59C2×#13711yescharacteristic
98C2×C59#57511yescharacteristic
99#533—591no—
100C2×#125D5911yescharacteristic
101#501—592no—
102#491—592no—
103#484—592no—
104#483—592no—
105#479—594no—
106#432—591no—
107C59#323611yescharacteristic, complemented, Sylow
108C4⋊Q8—591no—
109C4⋊Q8—591no—
110#125—21no—
111#125—21no—
112#125—1181no—
113#125C2×D5912yes—
114#125C2×D5912yes—
115C22⋊Q8—592no—
116C22⋊Q8—1181no—
117C4×Q8—592no—
118C4×Q8—1181no—
119#117—1181no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D5911yescharacteristic
123C2×C4⋊C4C2×D5911yescharacteristic
124C2×C42C2×D5911yescharacteristic
125#107—594no—
126#106—594no—
127C4⋊C8—592no—
128#103—594no—
129#103—594no—
130C22⋊C8—592no—
131#97—592no—
132C2×Q8—592no—
133C2×Q8—1181no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D5911yescharacteristic
137C22×C4C22⋊D5911yescharacteristic
138C22×C4C22×D5911yescharacteristic
139C2×C8—594no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—592no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C4⋊C4—1182no—
150C4⋊C4—1182no—
151C4⋊C4—1181no—
152C4⋊C4C22×D5912yes—
153C4⋊C4C22×D5912yes—
154C22⋊C4—1182no—
155C42—1182no—
156C42C22⋊D5911yescharacteristic
157C42C22⋊D5911yescharacteristic
158C42C22×D5911yescharacteristic
159C42C22×D5911yescharacteristic
160C23C2×C22⋊D5911yescharacteristic
161Q8—1184no—
162Q8—2362no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—1182no—
171C2×C4—1182no—
172C2×C4C2×C22⋊D5911yescharacteristic
173C2×C4C2×C22⋊D5911yescharacteristic
174C2×C4C2×C22⋊D5911yescharacteristic
175C2×C4C2×C22⋊D5911yescharacteristic
176C2×C4C2×C22⋊D5911yescharacteristic
177C2×C4C23×D5911yescharacteristic
178C8—1184no—
179C22—21no—
180C22—21no—
181C22#1427375712yes—
182C22C22×C22⋊D5911yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—2362no—
191C4—2362no—
192C4#1427377512yes—
193C2—22no—
194C2#1683797611yescharacteristic
195C2C2×#1427375711yescharacteristic
196C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#125×C59C2
socleC22×C59C22×D4
hypercenterC2×#125D59
hypocenterC59#3236
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16837812C2semidirect
3. #16837772C2semidirect
6. #16837706C2semidirect
107. C59#3236semidirect