Finite Group Databasebeta

← #20256078

Subgroups — #20256078

Order 6016.

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

normal subgroups only

This group has 336 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#15689848C211yesmaximal, characteristic, complemented
2#15689847C211yesmaximal, characteristic
3#15689479C212yesmaximal
4#15689428C212yesmaximal, complemented
5#15689400C211yesmaximal, characteristic
6#15689348C212yesmaximal
7#15689330C211yesmaximal, characteristic, complemented
8C8×Dic94C211yesmaximal, characteristic, complemented
9#15689215C212yesmaximal, complemented
10C4×#10625325C211yesmaximal, characteristic
11C47×#487C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625325C2211yescharacteristic
14#13094022—21no—
15#13094019—22no—
16#13094015C2212yes—
17#13094014—22no—
18#13094013C2212yes—
19#13094004—21no—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24#13093989C2212yes—
25C4×D188C2211yescharacteristic
26#13093982—21no—
27#13093957C2212yes—
28#13093956C2211yescharacteristic
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093948C2212yes—
33#13093946C2211yescharacteristic
34#13093944C2212yes—
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#103×C47C2212yes—
39#103×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47C2312yes—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C42×C47C2311yescharacteristic
54#10625337—24no—
55(C2×D47)⋊C4—21no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47D411yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63Dic47⋊C4—21no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72#10625325—22no—
73C22×D47—21no—
74Q8×C47—22no—
75Q8×C47—22no—
76Q8×C47—42no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87D188—21no—
88D188—21no—
89C4×D47—42no—
90Dic94—22no—
91Dic94—21no—
92Dic94#4112yes—
93C8×C47—21no—
94C8×C47—21no—
95C47⋊C8—22no—
96C22×C47C22×D411yescharacteristic
97C2×D47—41no—
98C2×D47—41no—
99C2×D47—41no—
100C4×C47—21no—
101C4×C47—42no—
102C4×C47—42no—
103C4×C47#13512yes—
104C4×C47C2×#4111yescharacteristic
105C4×C472−1+411yescharacteristic
106Dic47—22no—
107Dic47—22no—
108Dic47—22no—
109Dic47—41no—
110Dic47—41no—
111#3364—471nomaximal, Sylow
112C2×C47#54811yescharacteristic
113C2×C47C2×#13511yescharacteristic
114C2×C47#57811yescharacteristic
115D47—81no—
116#557—471no—
117#556—471no—
118#488—472no—
119#487D4711yescharacteristic, complemented
120#479—472no—
121#474—471no—
122#464—472no—
123#462—471no—
124C8×Q8—471no—
125C4×Q16—472no—
126C4×SD16—471no—
127C47#336411yescharacteristic, complemented, Sylow
128C2×Q16—472no—
129C2×SD16—471no—
130C4⋊Q8—941no—
131C4⋊Q8C2×D4711yescharacteristic
132C4⋊Q8C2×D4711yescharacteristic
133#126—942no—
134#125—472no—
135#125—942no—
136#124—472no—
137C22⋊Q8—941no—
138C4×Q8—471no—
139C4×Q8—472no—
140C4×Q8—472no—
141C4×Q8—471no—
142C4×Q8—941no—
143C4×D4—471no—
144#117—941no—
145#107—472no—
146#106—471no—
147C4⋊C8—472no—
148C4⋊C8—471no—
149#103—472no—
150#103—471no—
151#103C2×D4712yes—
152#103C2×D4712yes—
153#102—471no—
154#102—472no—
155C4×C8—472no—
156C4×C8C2×D4711yescharacteristic
157C2×Q8—21no—
158C2×Q8—471no—
159C2×Q8—471no—
160C2×Q8C22×D4712yes—
161C2×D4—471no—
162C22×C4—941no—
163Q16—944no—
164SD16—942no—
165C2×C8—472no—
166C2×C8C22×D4711yescharacteristic
167C2×C8C22×D4711yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—471no—
174C4⋊C4—471no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4C22×D4712yes—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—941no—
184C42—472no—
185C42—942no—
186C42—942no—
187C42—941no—
188C42C22×D4711yescharacteristic
189C23—941no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—472no—
194Q8—942no—
195Q8—941no—
196D4—941no—
197D4—941no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—472no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—21no—
210C8—21no—
211C8—942no—
212C22—1881no—
213C22—1881no—
214C22—1881no—
215C22C2×D4×D4711yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—942no—
220C4—942no—
221C4—942no—
222C4—1881no—
223C4—1881no—
224C4#1309404512yes—
225C4#41×D4711yescharacteristic
226C4#1309407111yescharacteristic
227C2—3761no—
228C2#1568978111yescharacteristic
229C2C2×#1309404511yescharacteristic
230C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3364
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
4. #15689428C2semidirect
7. #15689330C2semidirect
8. C8×Dic94C2semidirect
9. #15689215C2semidirect
11. C47×#487C2semidirect
119. #487D47semidirect
127. C47#3364semidirect