Finite Group Databasebeta

← #20244351

Subgroups — #20244351

Order 6016.

252 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13094015C211yesmaximal, characteristic
2C2×C8×Dic47C211yesmaximal, characteristic
3#15688988C211yesmaximal, characteristic
4#15688886C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9#13094015—22no—
10#13094015C414yescomplemented
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C4×Dic47C2211yescharacteristic
16C8×Dic47—22no—
17C47⋊#95—21no—
18C47⋊#95—21no—
19C22×C8×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47D411yescharacteristic
28C22×Dic47D411yescharacteristic
29C2×C8×C47—21no—
30C2×C8×C47—21no—
31C2×C8×C47Q812yes—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47C2×C412yes—
36C4⋊Dic47—21no—
37C4⋊Dic47—24no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47C2×C412yes—
41Dic47⋊C4—24no—
42C4×Dic47C2×C412yes—
43C4×Dic47D412yes—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8Q812yes—
47C23×C47C2×D411yescharacteristic
48C2×C4×C47—22no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×Q811yescharacteristic
57C2×C4×C47C2×Q811yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—22no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47C22⋊C412yes—
71C2×Dic47C22⋊C412yes—
72C8×C47—22no—
73C47⋊C8—22no—
74C22×C47C2×C22⋊C411yescharacteristic
75C22×C47#12411yescharacteristic
76C22×C47C4⋊Q811yescharacteristic
77C22×C47#13511yescharacteristic
78C22×C47#13511yescharacteristic
79C22×C47#13511yescharacteristic
80C22×C47#13511yescharacteristic
81C4×C47—42no—
82C4×C47—81no—
83C4×C47C4×Q811yescharacteristic
84C4×C47C4×Q811yescharacteristic
85C4×C47C22⋊Q811yescharacteristic
86C4×C47C22⋊Q811yescharacteristic
87Dic47—22no—
88Dic47—22no—
89Dic47—42no—
90Dic47—81no—
91#1991—471nomaximal, Sylow
92C2×C47#39111yescharacteristic
93C2×C47#41611yescharacteristic
94C2×C47#41611yescharacteristic
95C2×C47#48811yescharacteristic
96C2×C47#48811yescharacteristic
97C2×C47#49911yescharacteristic
98C2×C47#49911yescharacteristic
99C2×#125—471no—
100C2×C4×C8—471no—
101#382—471no—
102#340—471no—
103#340—471no—
104#340—471no—
105#340D4711yescharacteristic
106C47#199111yescharacteristic, complemented, Sylow
107C22×C8—471no—
108C22×C8C2×D4711yescharacteristic
109#125—474no—
110#125—942no—
111C2×C4⋊C4—471no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—941no—
114C2×C4⋊C4—941no—
115C2×C4⋊C4C2×D4711yescharacteristic
116C2×C4⋊C4C2×D4711yescharacteristic
117C2×C42—471no—
118C4×C8—942no—
119#95—941no—
120#95—941no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—471no—
124C22×C4—471no—
125C22×C4—941no—
126C22×C4—941no—
127C22×C4C22×D4711yescharacteristic
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—472no—
131C2×C8—941no—
132C2×C8—941no—
133C2×C8Dic9412yes—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—472no—
138C4⋊C4—944no—
139C4⋊C4—944no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4C4×D4712yes—
144C42—472no—
145C42—472no—
146C23D4×D4711yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—472no—
154C2×C4—472no—
155C2×C4—941no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4—941no—
159C2×C4—942no—
160C2×C4—1881no—
161C2×C4—1881no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4C2×Dic9411yescharacteristic
166C2×C4C2×C4×D4711yescharacteristic
167C2×C4#1062535011yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4#1062535211yescharacteristic
170C2×C4Q8×D4711yescharacteristic
171C8—22no—
172C8—942no—
173C22C22⋊C4×D4711yescharacteristic
174C22#1309401011yescharacteristic
175C22#1309402311yescharacteristic
176C22#1309404311yescharacteristic
177C22#1309404511yescharacteristic
178C22#1309404511yescharacteristic
179C22#1309404711yescharacteristic
180C4—42no—
181C4—81no—
182C4—942no—
183C4—942no—
184C4—3761no—
185C4—1882no—
186C4#1309398911yescharacteristic
187C4C4×Dic9411yescharacteristic
188C4#1309400111yescharacteristic
189C4#1309400211yescharacteristic
190C2#1568902711yescharacteristic
191C2#1568911611yescharacteristic
192C2#1568911811yescharacteristic
193C2#1568947611yescharacteristic
194C2#1568947911yescharacteristic
195C2#1568952311yescharacteristic
196C2#1568952411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1991
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
10. #13094015C4semidirect
106. C47#1991semidirect