Finite Group Databasebeta

← #20256168

Subgroups — #20256168

Order 6016.

340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689851C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic
3#15689490C212yesmaximal, complemented
4#15689475C211yesmaximal, characteristic, complemented
5#15689429C212yesmaximal, complemented
6#15689329C211yesmaximal, characteristic
7#15689327C212yesmaximal
8#15689250C211yesmaximal, characteristic, complemented
9#15689222C212yesmaximal
10C4×#10625336C211yesmaximal, characteristic
11C47×#477C211yesmaximal, characteristic, complemented
12C2×#10625325C2212yes—
13C2×#10625336C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094022C2212yes—
16#13094016—21no—
17#13094015C2212yes—
18#13094014—22no—
19#13094004—21no—
20#13094000—22no—
21C4×Dic94—21no—
22C4×Dic94C2211yescharacteristic
23#13093989C2212yes—
24C4×D188C2211yescharacteristic
25#13093986C2212yes—
26C4⋊C4×D47—21no—
27#13093955C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093948C2211yescharacteristic
31#13093947C2212yes—
32#13093947C2212yes—
33#13093944C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#107×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×C4×D47—22no—
46C2×Dic94D411yescharacteristic
47C2×Dic94C2312yes—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2312yes—
52C4⋊C4×C47C2311yescharacteristic
53C42×C47—21no—
54C42×C47C2311yescharacteristic
55#10625336—22no—
56(C2×D47)⋊C4—21no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47—22no—
61C4⋊Dic47D411yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72#10625325—24no—
73C22×D47—21no—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47—81no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87D188—21no—
88D188#4112yes—
89C4×D47—42no—
90C4×D47—82no—
91Dic94—22no—
92Dic94—22no—
93Dic94—22no—
94C8×C47—22no—
95C47⋊C8—21no—
96C47⋊C8—21no—
97C22×C47C22×D411yescharacteristic
98C2×D47—22no—
99C2×D47—41no—
100C2×D47—41no—
101C4×C47—21no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47#13712yes—
106C4×C47C2×#4111yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—22no—
110Dic47—42no—
111Dic47—41no—
112#3372—471nomaximal, Sylow
113C2×C47#54811yescharacteristic
114C2×C47C2×#13711yescharacteristic
115C2×C47#57711yescharacteristic
116D47—42no—
117#557—471no—
118#554—471no—
119#491—472no—
120#487—471no—
121#479—472no—
122#477D4711yescharacteristic, complemented
123#461—471no—
124#461—472no—
125#446—471no—
126#440—472no—
127C4×SD16—471no—
128C47#337211yescharacteristic, complemented, Sylow
129C2×SD16—471no—
130C2×SD16—472no—
131C4⋊Q8—472no—
132C4⋊Q8—471no—
133C4⋊Q8C2×D4711yescharacteristic
134#125—472no—
135#125—941no—
136#125—942no—
137C22⋊Q8—941no—
138C22⋊Q8—942no—
139C4×Q8—471no—
140C4×Q8—472no—
141C4×Q8—941no—
142C4×Q8C2×D4711yescharacteristic
143C4×D4—472no—
144C4×D4—471no—
145C2×C4⋊C4—941no—
146#107C2×D4712yes—
147#106—471no—
148C4⋊C8—472no—
149C4⋊C8C2×D4711yescharacteristic
150#103—471no—
151#103—472no—
152#103—472no—
153#103—472no—
154#103C2×D4712yes—
155#102—471no—
156#97—472no—
157C4×C8—471no—
158C2×Q8—21no—
159C2×Q8—471no—
160C2×Q8—472no—
161C2×Q8C22×D4711yescharacteristic
162C2×D4—471no—
163C22×C4—942no—
164C22×C4—941no—
165SD16—944no—
166SD16—942no—
167C2×C8—471no—
168C2×C8—471no—
169C2×C8C22×D4712yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—472no—
173C4⋊C4—471no—
174C4⋊C4—471no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—941no—
181C4⋊C4—941no—
182C4⋊C4C22×D4711yescharacteristic
183C4⋊C4C22×D4712yes—
184C22⋊C4—942no—
185C22⋊C4—941no—
186C42—21no—
187C42—472no—
188C42—942no—
189C42C22×D4711yescharacteristic
190C23—941no—
191Q8—21no—
192Q8—21no—
193Q8—81no—
194Q8—942no—
195Q8—942no—
196Q8—942no—
197D4—472no—
198D4—941no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—472no—
203C2×C4—472no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—3762no—
207C2×C4—1882no—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—941no—
213C8—941no—
214C22—942no—
215C22—1881no—
216C22—1881no—
217C22C2×D4×D4711yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—41no—
222C4—942no—
223C4—942no—
224C4—1882no—
225C4—1881no—
226C4#1309405612yes—
227C4#41×D4711yescharacteristic
228C4#1309407211yescharacteristic
229C2—1882no—
230C2#1568978311yescharacteristic
231C2C2×#1309405611yescharacteristic
232C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#477C2
socleC22×C47C22×D4
hypercenter#477D47
hypocenterC47#3372
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
3. #15689490C2semidirect
4. #15689475C2semidirect
5. #15689429C2semidirect
8. #15689250C2semidirect
11. C47×#477C2semidirect
122. #477D47semidirect
128. C47#3372semidirect