Finite Group Databasebeta

← #21422697

Subgroups — #21422697

Order 7552.

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

normal subgroups only

This group has 212 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
1C2×#14273719C211yesmaximal, characteristic
2#16837459C211yesmaximal, characteristic
3#16837143C214yesmaximal, complemented
4C4×M16×C59C211yesmaximal, characteristic
5#14273719—21no—
6#14273719—21no—
7#14273719C412yes—
8#14273719C2212yes—
9C2×C4⋊Dic59C411yescharacteristic
10C2×C4⋊Dic59C411yescharacteristic
11C2×Dic59⋊C4—21no—
12C2×Dic59⋊C4—21no—
13C4⋊(C59⋊C8)—21no—
14C22⋊(C59⋊C8)—21no—
15#14273638C2212yes—
16C2×M16×C59—21no—
17C2×C42×C59C2211yescharacteristic
18#97×C59C2212yes—
19C4×C8×C59—21no—
20C22×C4×C59C2×C411yescharacteristic
21C22×C4×C59D411yescharacteristic
22C22×C4×C59D411yescharacteristic
23C22×Dic59—21no—
24C22×Dic59—21no—
25M16×C59—24no—
26C2×C8×C59—22no—
27C42×C59C2×C411yescharacteristic
28C42×C59D411yescharacteristic
29C42×C59D411yescharacteristic
30C42×C59C2311yescharacteristic
31C4⋊Dic59—21no—
32C4⋊Dic59—21no—
33C4⋊Dic59C2×C412yes—
34C4⋊Dic59C2×C412yes—
35Dic59⋊C4—22no—
36Dic59⋊C4—22no—
37Dic59⋊C4—22no—
38Dic59⋊C4—22no—
39C2×C59⋊C8—22no—
40C23×C59C22⋊C411yescharacteristic
41C2×C4×C59—22no—
42C2×C4×C59—22no—
43C2×C4×C59—41no—
44C2×C4×C59C22⋊C411yescharacteristic
45C2×C4×C59C22⋊C411yescharacteristic
46C2×C4×C59C22⋊C411yescharacteristic
47C2×C4×C59C22×C411yescharacteristic
48C2×C4×C59C2×D411yescharacteristic
49C2×C4×C59C2×D411yescharacteristic
50C2×Dic59—22no—
51C2×Dic59—22no—
52C2×Dic59—42no—
53C2×Dic59—42no—
54C8×C59—24no—
55C59⋊C8—42no—
56C22×C59—21no—
57C22×C59—21no—
58C22×C59#10412yes—
59C22×C59C2×C22⋊C411yescharacteristic
60C4×C59—21no—
61C4×C59—21no—
62C4×C59—21no—
63C4×C59—21no—
64C4×C59—21no—
65C4×C59#10112yes—
66Dic59—42no—
67Dic59—42no—
68#1528—591nomaximal, Sylow
69C2×C59—22no—
70C2×C59C2×#10111yescharacteristic
71C2×C59C2×#10411yescharacteristic
72C2×C59#42111yescharacteristic
73C2×#125—591no—
74#432—591no—
75C4×M16D5911yescharacteristic
76#330—594no—
77C59#152811yescharacteristic, complemented, Sylow
78C2×M16—21no—
79#125—592no—
80#125—592no—
81#125—1181no—
82#125—1181no—
83C2×C4⋊C4—591no—
84C2×C4⋊C4—591no—
85C2×C4⋊C4—1181no—
86C2×C4⋊C4—1181no—
87C2×C42C2×D5911yescharacteristic
88C4⋊C8—1181no—
89C22⋊C8—1181no—
90#97—592no—
91#97C2×D5912yes—
92C4×C8—21no—
93C22×C4—1181no—
94C22×C4—1181no—
95C22×C4C4×D5911yescharacteristic
96C22×C4D23611yescharacteristic
97C22×C4C22⋊D5911yescharacteristic
98M16—24no—
99C2×C8—22no—
100C2×C8—1182no—
101C4⋊C4—592no—
102C4⋊C4—592no—
103C4⋊C4—1181no—
104C4⋊C4—1181no—
105C4⋊C4—1182no—
106C4⋊C4—1182no—
107C4⋊C4—1182no—
108C4⋊C4—1182no—
109C42C4×D5911yescharacteristic
110C42D23611yescharacteristic
111C42C22⋊D5911yescharacteristic
112C42C22×D5911yescharacteristic
113C23(C2×D59)⋊C411yescharacteristic
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—41no—
117C2×C4—1182no—
118C2×C4—1182no—
119C2×C4—2362no—
120C2×C4—2362no—
121C2×C4(C2×D59)⋊C411yescharacteristic
122C2×C4(C2×D59)⋊C411yescharacteristic
123C2×C4(C2×D59)⋊C411yescharacteristic
124C2×C4C2×C4×D5911yescharacteristic
125C2×C4C2×D23611yescharacteristic
126C2×C4C2×C22⋊D5911yescharacteristic
127C8—24no—
128C8—2362no—
129C22—21no—
130C22—21no—
131C22#1427365512yes—
132C22C2×(C2×D59)⋊C411yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—21no—
138C4—2362no—
139C4—2362no—
140C4#1427364512yes—
141C2—22no—
142C2C2×#1427364511yescharacteristic
143C2C2×#1427365511yescharacteristic
144C2#1683741811yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC4×M16×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC4×M16D59
hypocenterC59#1528
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #16837143C2semidirect
77. C59#1528semidirect