Finite Group Databasebeta

← #20256127

Subgroups — #20256127

Order 6016.

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

normal subgroups only

This group has 338 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#15689853C211yesmaximal, characteristic, complemented
2#15689843C211yesmaximal, characteristic
3#15689481C212yesmaximal
4#15689475C211yesmaximal, characteristic, complemented
5#15689407C212yesmaximal, complemented
6#15689344C212yesmaximal
7#15689334C211yesmaximal, characteristic, complemented
8#15689250C211yesmaximal, characteristic, complemented
9#15689229C212yesmaximal, complemented
10C4×#10625335C211yesmaximal, characteristic
11C47×#476C211yesmaximal, characteristic
12C2×Dic188C2212yes—
13C2×#10625335C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094023—21no—
16#13094023C2212yes—
17#13094022—22no—
18#13094017—22no—
19#13094011C2212yes—
20#13094003—21no—
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23#13093989—21no—
24#13093989C2212yes—
25#13093989C2212yes—
26#13093983—21no—
27#13093955C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093947C2212yes—
31#13093947C2212yes—
32#13093947C2211yescharacteristic
33#13093945C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×D4×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#102×C47C2212yes—
41C2×Q8×C47—21no—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C2×Dic94—22no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2312yes—
47C2×Dic94C2311yescharacteristic
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47C2311yescharacteristic
51C4⋊C4×C47C2312yes—
52C22⋊C4×C47—21no—
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56#10625335—22no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47D411yescharacteristic
60C4⋊Dic47C2311yescharacteristic
61Dic47⋊C4—21no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4D412yes—
66C4×Dic47—21no—
67C4×Dic47—22no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72Dic188—24no—
73C23×C47—21no—
74Q8×C47—81no—
75D4×C47—21no—
76D4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—42no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88Dic94—22no—
89Dic94—21no—
90Dic94—22no—
91Dic94—22no—
92Dic94—82no—
93Dic94#4112yes—
94C8×C47—22no—
95C47⋊C8—21no—
96C47⋊C8—21no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47C22×D411yescharacteristic
101C4×C47—21no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47#13712yes—
105C4×C47C2×#4111yescharacteristic
106C4×C472−1+411yescharacteristic
107Dic47—22no—
108Dic47—22no—
109Dic47—22no—
110Dic47—42no—
111Dic47—41no—
112#3369—471nomaximal, Sylow
113C2×C47—81no—
114C2×C47#54811yescharacteristic
115C2×C47C2×#13711yescharacteristic
116C2×C47#57711yescharacteristic
117Q82—471no—
118#556—471no—
119#489—472no—
120#487—471no—
121#476D4711yescharacteristic
122#475—472no—
123#464—472no—
124#462—471no—
125#446—471no—
126#441—472no—
127C4×SD16—471no—
128C47#336911yescharacteristic, complemented, Sylow
129C2×Q16—472no—
130C2×SD16—471no—
131C4⋊Q8—472no—
132C4⋊Q8—471no—
133C4⋊Q8—941no—
134C4⋊Q8—942no—
135C4⋊Q8C2×D4711yescharacteristic
136#126—942no—
137#124—472no—
138C22⋊Q8—941no—
139C4×Q8—471no—
140C4×Q8—472no—
141C4×Q8—472no—
142C4×Q8—471no—
143C4×Q8—941no—
144C4×D4C2×D4711yescharacteristic
145#117—941no—
146#106—471no—
147#106C2×D4712yes—
148C4⋊C8—472no—
149C4⋊C8C2×D4711yescharacteristic
150#103—472no—
151#103—471no—
152#103—472no—
153#103—472no—
154#102—471no—
155#102C2×D4712yes—
156#97—472no—
157C4×C8—471no—
158C2×Q8—21no—
159C2×Q8—471no—
160C2×Q8—471no—
161C2×Q8—472no—
162C2×Q8—942no—
163C2×D4C22×D4711yescharacteristic
164C22×C4—21no—
165Q16—944no—
166SD16—942no—
167C2×C8—471no—
168C2×C8—471no—
169C2×C8C22×D4712yes—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—471no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—941no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4C22×D4712yes—
181C4⋊C4C22×D4711yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C42—472no—
186C42—942no—
187C42—942no—
188C42—941no—
189C42C22×D4711yescharacteristic
190C23—21no—
191Q8—81no—
192Q8—472no—
193Q8—942no—
194Q8—941no—
195Q8—942no—
196Q8—942no—
197Q8—3762no—
198D4—21no—
199D4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—472no—
204C2×C4—472no—
205C2×C4—941no—
206C2×C4—942no—
207C2×C4—941no—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—941no—
213C8—941no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×D4×D4711yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—942no—
222C4—942no—
223C4—942no—
224C4—1882no—
225C4—1881no—
226C4#1309405312yes—
227C4#41×D4711yescharacteristic
228C4#1309407211yescharacteristic
229C2—81no—
230C2#1568978311yescharacteristic
231C2C2×#1309405311yescharacteristic
232C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3369
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #15689853C2semidirect
4. #15689475C2semidirect
5. #15689407C2semidirect
7. #15689334C2semidirect
8. #15689250C2semidirect
9. #15689229C2semidirect
128. C47#3369semidirect