Finite Group Databasebeta

← #20244911

Subgroups — #20244911

Order 6016.

274 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13093957C211yesmaximal, characteristic, complemented
2C2×#13093956C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15689026C211yesmaximal, characteristic
5#15688988C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C22⋊Dic47—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093957—22no—
14#13093956—22no—
15#13093945—22no—
16C47⋊#95—22no—
17C22×D4×C47C2211yescharacteristic
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20#102×C47—22no—
21C24×C47—21no—
22C2×D4×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47Q812yes—
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47D412yes—
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C2×C8×C47D412yes—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C22⋊Dic47—44no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4×Dic47—21no—
44C4×Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D412yes—
48C23×C47—22no—
49C23×C47—41no—
50C23×C47—41no—
51C23×C47—42no—
52C23×C47—42no—
53C23×C47C2×D411yescharacteristic
54D4×C47—22no—
55D4×C47—22no—
56D4×C47—41no—
57D4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×Q811yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—42no—
72C2×Dic47—42no—
73C8×C47—22no—
74C47⋊C8—22no—
75C22×C47—42no—
76C22×C47—44no—
77C22×C47—82no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47C22⋊Q811yescharacteristic
81C22×C47#12311yescharacteristic
82C22×C47#12711yescharacteristic
83C22×C47#13512yes—
84C22×C47AGL(1,ℤ/8)12yes—
85C4×C47—81no—
86C4×C47C22⋊Q811yescharacteristic
87C4×C47C22⋊Q811yescharacteristic
88C4×C47#12311yescharacteristic
89C4×C47#12311yescharacteristic
90Dic47—42no—
91Dic47—81no—
92Dic47—81no—
93#2092—471nomaximal, Sylow
94C2×C47—82no—
95C2×C47#39911yescharacteristic
96C2×C47#47812yes—
97C2×C47#48212yes—
98C2×C47#49511yescharacteristic
99C2×C47#49611yescharacteristic
100C2×#107—471no—
101C2×#106—471no—
102C2×#102—471no—
103C2×#102D4711yescharacteristic
104#390—471no—
105#382—471no—
106#336—471no—
107C47#209211yescharacteristic, complemented, Sylow
108C22×D4C2×D4711yescharacteristic
109C22×C8—471no—
110C22×C8C2×D4711yescharacteristic
111C2×C4⋊C4—471no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4C2×D4711yescharacteristic
114C2×C22⋊C4—942no—
115C2×C42—471no—
116#107—942no—
117#106—942no—
118#102—22no—
119#102—942no—
120#95—942no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic9412yes—
128C22×C4—21no—
129C22×C4—472no—
130C22×C4—941no—
131C22×C4—941no—
132C22×C4C22×D4711yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—472no—
136C2×C8—941no—
137C2×C8—941no—
138C2×C8C22⋊D4712yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C22⋊C4—1884no—
146C42—941no—
147C42—941no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23D4×D4711yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—942no—
161C2×C4—942no—
162C2×C4—942no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4—1882no—
166C2×C4—1882no—
167C2×C4C2×Dic9411yescharacteristic
168C2×C4#1062535011yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4#1062535211yescharacteristic
171C2×C4#1062535211yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—22no—
174C8—942no—
175C22—42no—
176C22—44no—
177C22—81no—
178C22—81no—
179C22—82no—
180C22#1309400111yescharacteristic
181C22#1309400611yescharacteristic
182C22#1309402011yescharacteristic
183C22#1309404512yes—
184C22#1309404812yes—
185C4—81no—
186C4—3761no—
187C4—3761no—
188C4—1882no—
189C4#1309400111yescharacteristic
190C4#1309400311yescharacteristic
191C4#1309400511yescharacteristic
192C4#1309400611yescharacteristic
193C2—82no—
194C2#1568905911yescharacteristic
195C2#1568942512yes—
196C2#1568944612yes—
197C2#1568950411yescharacteristic
198C2#1568951111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2092
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13093957C2semidirect
2. C2×#13093956C2semidirect
5. #15688988C2semidirect
6. #15688877C2semidirect
107. C47#2092semidirect