Finite Group Databasebeta

← #20243595

Subgroups — #20243595

Order 6016.

278 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#10625329C211yesmaximal, characteristic
2C2×#13093960C212yesmaximal, complemented
3#15689087C211yesmaximal, characteristic
4#15688888C212yesmaximal, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic
6C2×#10625329—21no—
7C2×#10625329—24no—
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2212yes—
11C22×C47⋊C8—21no—
12#13093960—24no—
13C22⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)—21no—
15C23×C4×C47C2211yescharacteristic
16C22×C8×C47C2212yes—
17C22⋊C8×C47C412yes—
18C22⋊C8×C47C412yes—
19C24×C47Q811yescharacteristic
20C22×C4×C47—22no—
21C22×C4×C47—22no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47Q811yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C2×C8×C47—22no—
29C2×C8×C47—22no—
30C2×C8×C47C2×C414yes—
31#10625329—24no—
32#10625329—22no—
33#10625329—22no—
34#10625329—22no—
35#10625329D414yes—
36C2×C47⋊C8—24no—
37C2×C47⋊C8—22no—
38C2×C47⋊C8—21no—
39C2×C47⋊C8—21no—
40C23×C47—22no—
41C23×C47—22no—
42C23×C47—41no—
43C23×C47C4⋊C411yescharacteristic
44C23×C47C4⋊C411yescharacteristic
45C23×C47C2×Q811yescharacteristic
46C2×C4×C47—22no—
47C2×C4×C47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—21no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47C4⋊C411yescharacteristic
54C2×C4×C47C4⋊C411yescharacteristic
55C2×C4×C47C22×C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D412yes—
58C2×C4×C47#4112yes—
59C8×C47—24no—
60C47⋊C8—24no—
61C47⋊C8—41no—
62C47⋊C8—41no—
63C22×C47—21no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—44no—
71C22×C47#10812yescomplemented
72C22×C47C2×C4⋊C411yescharacteristic
73C22×C47C22⋊Q812yes—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47C4×D412yes—
77C4×C47#12011yescharacteristic
78C4×C47#12311yescharacteristic
79#1855—471nomaximal, Sylow
80C2×C47—22no—
81C2×C47—22no—
82C2×C47—41no—
83C2×C47#38511yescharacteristic
84C2×C47C2×#10811yescharacteristic
85C2×C47#43011yescharacteristic
86C22×M16—471no—
87C2×#108—472no—
88#407—471no—
89C2×C22⋊C8D4711yescharacteristic
90#341—472no—
91C47#185511yescharacteristic, complemented, Sylow
92C23×C4C2×D4711yescharacteristic
93C2×M16—472no—
94C2×M16—471no—
95C2×M16—471no—
96C2×M16—944no—
97C2×M16—941no—
98C22×C8—941no—
99C22×C8C2×D4712yes—
100#108—944no—
101C22⋊C8—941no—
102C22⋊C8—941no—
103C22⋊C8Dic4712yes—
104C22⋊C8Dic4712yes—
105C24Dic9411yescharacteristic
106C22×C4—22no—
107C22×C4—22no—
108C22×C4Dic9411yescharacteristic
109C22×C4D18811yescharacteristic
110C22×C4D18811yescharacteristic
111C22×C4C2×Dic4711yescharacteristic
112C22×C4C2×Dic4711yescharacteristic
113C22×C4C22×D4711yescharacteristic
114M16—474no—
115M16—944no—
116M16—942no—
117M16—942no—
118M16—942no—
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—944no—
122C2×C8—942no—
123C2×C8—941no—
124C2×C8—941no—
125C2×C8C2×Dic4714yes—
126C23—22no—
127C23—22no—
128C23—41no—
129C23C4⋊Dic4711yescharacteristic
130C23C4⋊Dic4711yescharacteristic
131C23C2×Dic9411yescharacteristic
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4C4⋊Dic4711yescharacteristic
140C2×C4C4⋊Dic4711yescharacteristic
141C2×C4C2×D18811yescharacteristic
142C2×C4D4×D4712yes—
143C2×C4#1062535212yes—
144C2×C4C22×Dic4711yescharacteristic
145C8—24no—
146C8—944no—
147C8—1881no—
148C8—1881no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—21no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22—44no—
157C22#1309396012yescomplemented
158C22C2×C4⋊Dic4711yescharacteristic
159C22#1309400112yes—
160C4—21no—
161C4—21no—
162C4D4×Dic4712yes—
163C4#1309399411yescharacteristic
164C4#1309400811yescharacteristic
165C2—22no—
166C2—22no—
167C2—41no—
168C2#1568899811yescharacteristic
169C2C2×#1309396011yescharacteristic
170C2#1568917211yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C2×C4⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47#1855
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
4. #15688888C2semidirect
71. C22×C47#108semidirect
91. C47#1855semidirect
157. C22#13093960semidirect