Finite Group Databasebeta

← #20256083

Subgroups — #20256083

Order 6016.

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

normal subgroups only

This group has 348 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#15689858C211yesmaximal, characteristic
2#15689848C211yesmaximal, characteristic, complemented
3#15689479C212yesmaximal, complemented
4#15689471C211yesmaximal, characteristic
5#15689422C212yesmaximal, complemented
6#15689348C212yesmaximal, complemented
7#15689324C211yesmaximal, characteristic
8#15689247C211yesmaximal, characteristic, complemented
9C4×#10625337C211yesmaximal, characteristic, complemented
10#15689210C212yesmaximal, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×#10625337C2211yescharacteristic
13C2×#10625325C2212yes—
14#13094022—21no—
15#13094021C2211yescharacteristic
16#13094015C2212yes—
17#13094014—22no—
18#13094013C2212yes—
19#13094012—21no—
20#13094009—22no—
21Q8×Dic47—21no—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24#13093989C2212yes—
25C4×D188—21no—
26#13093986C2212yes—
27#13093957C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093948C2211yescharacteristic
30#13093947C2211yescharacteristic
31#13093946C2212yes—
32#13093944C2212yes—
33#13093944C2212yes—
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188—21no—
44C2×D188—21no—
45C2×D188C2312yes—
46C2×C4×D47—22no—
47C2×Dic94D411yescharacteristic
48C2×Dic94C2311yescharacteristic
49C2×C8×C47C2312yes—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C4⋊C4×C47C2311yescharacteristic
54C42×C47—21no—
55C42×C47C2311yescharacteristic
56#10625337—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47D411yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63Dic47⋊C4—21no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72#10625325—24no—
73C22×D47—22no—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47—42no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87D188—22no—
88D188—22no—
89D188—42no—
90D188—81no—
91C4×D47—82no—
92Dic94—22no—
93Dic94—21no—
94Dic94#4112yes—
95C8×C47—22no—
96C47⋊C8—21no—
97C47⋊C8—21no—
98C22×C47C22×D411yescharacteristic
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C4×C47—21no—
103C4×C47—41no—
104C4×C47—42no—
105C4×C47—41no—
106C4×C47#13512yes—
107C4×C47C2×#4111yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—22no—
111Dic47—22no—
112Dic47—41no—
113#3365—471nomaximal, Sylow
114C2×C47#54811yescharacteristic
115C2×C47C2×#13511yescharacteristic
116C2×C47#57711yescharacteristic
117D47—82no—
118#559—471no—
119#557—471no—
120#488—472no—
121#486—471no—
122#478—472no—
123#475D4711yescharacteristic, complemented
124#464—472no—
125#460—471no—
126C8×Q8—471no—
127C4×Q16—471no—
128C4×SD16—472no—
129C47#336511yescharacteristic, complemented, Sylow
130C2×Q16—471no—
131C2×SD16—472no—
132C4⋊Q8—941no—
133C4⋊Q8C2×D4711yescharacteristic
134#127—471no—
135#125—472no—
136#125—942no—
137#124—472no—
138#124—941no—
139#123—942no—
140C4×Q8—471no—
141C4×Q8—472no—
142C4×Q8—471no—
143C4×Q8—941no—
144C4×Q8C2×D4711yescharacteristic
145C4×D4—472no—
146C4×D4—941no—
147#107—471no—
148#106C2×D4712yes—
149C4⋊C8—472no—
150C4⋊C8C2×D4711yescharacteristic
151#103—471no—
152#103—471no—
153#103C2×D4712yes—
154#102—472no—
155#102—472no—
156#102—472no—
157C4×C8—472no—
158C4×C8—471no—
159C2×Q8—21no—
160C2×Q8—471no—
161C2×Q8—471no—
162C2×Q8C22×D4711yescharacteristic
163C2×D4—472no—
164C2×D4—941no—
165C2×D4—941no—
166C22×C4—942no—
167Q16—942no—
168SD16—944no—
169C2×C8—471no—
170C2×C8—471no—
171C2×C8C22×D4712yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—472no—
175C4⋊C4—471no—
176C4⋊C4—471no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—941no—
181C4⋊C4C22×D4712yes—
182C4⋊C4C22×D4711yescharacteristic
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—21no—
187C42—472no—
188C42—942no—
189C42—941no—
190C42C22×D4711yescharacteristic
191C23—942no—
192Q8—21no—
193Q8—21no—
194Q8—42no—
195Q8—472no—
196Q8—942no—
197Q8—941no—
198D4—942no—
199D4—942no—
200D4—3761no—
201D4—1882no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—472no—
206C2×C4—472no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—3762no—
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4C23×D4711yescharacteristic
213C8—22no—
214C8—941no—
215C8—941no—
216C22—1882no—
217C22—1882no—
218C22—1882no—
219C22C2×D4×D4711yescharacteristic
220C4—21no—
221C4—41no—
222C4—42no—
223C4—41no—
224C4—942no—
225C4—942no—
226C4—942no—
227C4—1881no—
228C4#1309404512yes—
229C4#41×D4711yescharacteristic
230C4#1309407211yescharacteristic
231C2—3762no—
232C2#1568978311yescharacteristic
233C2C2×#1309404511yescharacteristic
234C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3365
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #15689848C2semidirect
3. #15689479C2semidirect
5. #15689422C2semidirect
6. #15689348C2semidirect
8. #15689247C2semidirect
9. C4×#10625337C2semidirect
10. #15689210C2semidirect
11. C47×#475C2semidirect
123. #475D47semidirect
129. C47#3365semidirect