Finite Group Databasebeta

← #20255304

Subgroups — #20255304

Order 6016.

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

normal subgroups only

This group has 386 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#15689847C211yesmaximal, characteristic, complemented
2#15689776C211yesmaximal, characteristic
3#15689462C212yesmaximal, complemented
4#15689400C211yesmaximal, characteristic, complemented
5#15689363C212yesmaximal, complemented
6#15689330C211yesmaximal, characteristic, complemented
7#15689288C212yesmaximal, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9C8×D188C211yesmaximal, characteristic, complemented
10#15689118C212yesmaximal, complemented
11C47×#487C211yesmaximal, characteristic, complemented
12C2×#10625354C2212yes—
13C2×#10625337C2212yes—
14C2×#10625325C2211yescharacteristic
15C2×C8×D47C2212yes—
16#13094019—22no—
17#13094013—21no—
18#13094009—22no—
19#13094004C2212yes—
20#13094000C2212yes—
21#13093999—21no—
22Q8×Dic47—21no—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26#13093982C2212yes—
27C4⋊C4×D47—21no—
28#13093957C2212yes—
29#13093956C2211yescharacteristic
30C4⋊(C47⋊C8)C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093948C2212yes—
33#13093946C2211yescharacteristic
34#13093944C2212yes—
35(C2×D47)⋊C8C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#103×C47C2212yes—
39#103×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47C2312yes—
43#10625354—24no—
44#10625354—42no—
45C2×D188—22no—
46C2×D188D411yescharacteristic
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×C4×D47—22no—
50C2×C4×D47C2312yes—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2312yes—
58C42×C47C2311yescharacteristic
59#10625337—42no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4D412yes—
65C4⋊Dic47—22no—
66C4⋊Dic47D411yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71C4×Dic47—21no—
72C4×Dic47—22no—
73C2×C47⋊C8C2312yes—
74#10625325—22no—
75C8×D47—42no—
76C22×D47—21no—
77C22×D47C2×D412yes—
78Q8×C47—22no—
79Q8×C47—22no—
80Q8×C47—42no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47C2×D412yes—
90D188—22no—
91D188—21no—
92D188—44no—
93D188#4112yes—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—44no—
97C4×D47—42no—
98Dic94—21no—
99Dic94—21no—
100C8×C47—21no—
101C8×C47—21no—
102C47⋊C8—22no—
103C22×C47C22×D411yescharacteristic
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—41no—
109C2×D47—41no—
110C4×C47—21no—
111C4×C47—42no—
112C4×C47—42no—
113C4×C47#13512yes—
114C4×C47C2×#4111yescharacteristic
115C4×C47H(5,𝔽2)11yescharacteristic
116Dic47—22no—
117Dic47—41no—
118Dic47—41no—
119Dic47—41no—
120#3302—471nomaximal, Sylow
121C2×C47#54611yescharacteristic
122C2×C47C2×#13511yescharacteristic
123C2×C47#57811yescharacteristic
124D47—42no—
125D47—42no—
126#556—471no—
127#547—471no—
128#487D4711yescharacteristic, complemented
129#485—472no—
130#474—471no—
131#467—472no—
132#462—471no—
133#452—472no—
134C4×SD16—471no—
135C8×D4—471no—
136#416—472no—
137C47#330211yescharacteristic, complemented, Sylow
138C2×#41—472no—
139C2×Q16—472no—
140C2×SD16—471no—
141C22×C8—472no—
142C4⋊Q8C2×D4711yescharacteristic
143C4⋊Q8C2×D4711yescharacteristic
144#126—942no—
145#124—941no—
146#123—942no—
147C22⋊Q8—472no—
148C22⋊Q8—472no—
149#121—941no—
150C4×Q8—471no—
151C4×Q8—941no—
152C4×D4—471no—
153C4×D4—471no—
154#117—472no—
155C2×C4⋊C4—941no—
156#107—472no—
157#106—471no—
158C4⋊C8—471no—
159#103—472no—
160#103—471no—
161#103C2×D4712yes—
162#103C2×D4712yes—
163#102—471no—
164#102—472no—
165C22⋊C8—472no—
166C4×C8C2×D4711yescharacteristic
167#41—944no—
168#41—1882no—
169C2×Q8—21no—
170C2×Q8—471no—
171C2×Q8C22×D4712yes—
172C2×D4—471no—
173C2×D4—471no—
174C2×D4—942no—
175C22×C4—472no—
176C22×C4—942no—
177C22×C4—941no—
178Q16—1882no—
179SD16—942no—
180C2×C8—472no—
181C2×C8—1882no—
182C2×C8C22×D4711yescharacteristic
183C2×C8C22×D4711yescharacteristic
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—471no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—941no—
193C4⋊C4C22×D4712yes—
194C22⋊C4—472no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—942no—
198C22⋊C4—941no—
199C42—942no—
200C42—941no—
201C42C22×D4711yescharacteristic
202C23—472no—
203C23—941no—
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—941no—
208Q8—941no—
209D4—472no—
210D4—942no—
211D4—941no—
212D4—1884no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—472no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4—1884no—
222C2×C4—1882no—
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—21no—
227C8—21no—
228C8—942no—
229C22—942no—
230C22—942no—
231C22—942no—
232C22—942no—
233C22—1881no—
234C22—1881no—
235C22C2×D4×D4711yescharacteristic
236C4—21no—
237C4—42no—
238C4—42no—
239C4—942no—
240C4—1881no—
241C4—1881no—
242C4—1881no—
243C4#1309404512yes—
244C4#41×D4711yescharacteristic
245C4#1309407011yescharacteristic
246C2—1882no—
247C2—1882no—
248C2#1568976611yescharacteristic
249C2C2×#1309404511yescharacteristic
250C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3302
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. #15689847C2semidirect
3. #15689462C2semidirect
4. #15689400C2semidirect
5. #15689363C2semidirect
6. #15689330C2semidirect
7. #15689288C2semidirect
8. C4×#10625325C2semidirect
9. C8×D188C2semidirect
10. #15689118C2semidirect
11. C47×#487C2semidirect
128. #487D47semidirect
137. C47#3302semidirect