Finite Group Databasebeta

← #20254334

Subgroups — #20254334

Order 6016.

384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689675C211yesmaximal, characteristic
2C2×#13094022C211yesmaximal, characteristic
3#15689501C212yesmaximal, complemented
4#15689472C212yesmaximal, complemented
5#15689332C212yesmaximal, complemented
6#15689331C212yesmaximal, complemented
7#15689281C211yesmaximal, characteristic
8#15689279C211yesmaximal, characteristic
9#15689278C211yesmaximal, characteristic
10#15689173C211yesmaximal, characteristic
11C47×#451C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C2×Dic188C2212yes—
14C2×#10625337C2212yes—
15C2×#10625337C2212yes—
16#13094023C2211yescharacteristic
17#13094022—21no—
18#13094022—21no—
19#13094022C2212yes—
20#13094022C2211yescharacteristic
21#13094022C2212yes—
22#13094014—21no—
23#13094003C2211yescharacteristic
24#13094001—21no—
25Q8×Dic47C2211yescharacteristic
26#13093989—21no—
27#13093989C2211yescharacteristic
28#13093980—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×C4×Dic47C2211yescharacteristic
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093948C2212yes—
35#13093947C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37C8×Dic47C2212yes—
38C22×Q8×C47C2211yescharacteristic
39C2×Q16×C47C2212yes—
40C22⋊Q8×C47C2211yescharacteristic
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47—42no—
45C2×Q8×C47C2312yes—
46C2×Q8×C47C2311yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C22×Dic47—21no—
50C22×Dic47D411yescharacteristic
51C22×Dic47D411yescharacteristic
52C2×Dic94—21no—
53C2×Dic94—21no—
54C2×Dic94—42no—
55C2×Dic94C2312yes—
56C2×Dic94C2311yescharacteristic
57Q16×C47—42no—
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2311yescharacteristic
61C22⋊C4×C47—21no—
62C22⋊Dic47—21no—
63#10625337—42no—
64#10625337—42no—
65C4⋊Dic47—21no—
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—21no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—22no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76C4×Dic47—21no—
77C4×Dic47—21no—
78C4×Dic47D411yescharacteristic
79C4×Dic47D411yescharacteristic
80C4×Dic47C2311yescharacteristic
81C4×Dic47C2311yescharacteristic
82C2×C47⋊C8C2312yes—
83Dic188—42no—
84C23×C47C2×D411yescharacteristic
85Q8×C47—22no—
86Q8×C47—22no—
87Q8×C47—22no—
88Q8×C47—42no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—42no—
101C2×Dic47Q1614yescomplemented
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C2×Dic47C2×D411yescharacteristic
106Dic94—22no—
107Dic94—22no—
108Dic94—22no—
109Dic94—42no—
110Dic94—42no—
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47—21no—
114C22×C47—21no—
115C22×C47C2×Q1612yes—
116C22×C47C22×D411yescharacteristic
117C4×C47—21no—
118C4×C47—42no—
119C4×C47—41no—
120C4×C47—41no—
121C4×C47H(5,𝔽2)12yes—
122Dic47—21no—
123Dic47—42no—
124Dic47—41no—
125Dic47—41no—
126Dic47C2×Q1612yes—
127Dic47C2×Q1612yes—
128Dic47#13712yes—
129#3209—471nomaximal, Sylow
130C2×C47—22no—
131C2×C47#53511yescharacteristic
132C2×C47C22×Q1611yescharacteristic
133C2×C47C2×#13711yescharacteristic
134#533—471no—
135C2×C4⋊Q8—471no—
136#494—472no—
137#487—472no—
138#462—472no—
139#462—472no—
140#451—471no—
141#451—471no—
142#451—471no—
143#451D4711yescharacteristic
144#431—471no—
145C47#320911yescharacteristic, complemented, Sylow
146C22×Q8—471no—
147C22×Q8C2×D4711yescharacteristic
148C2×Q16—472no—
149C2×Q16—472no—
150C2×Q16—472no—
151C2×Q16C2×D4712yes—
152C4⋊Q8—471no—
153C4⋊Q8—472no—
154C4⋊Q8—472no—
155C4⋊Q8—471no—
156C4⋊Q8—941no—
157C4⋊Q8—941no—
158#125—941no—
159C22⋊Q8—471no—
160C22⋊Q8—941no—
161C22⋊Q8C2×D4711yescharacteristic
162C4×Q8—471no—
163C4×Q8—471no—
164C4×Q8—941no—
165#117—941no—
166C2×C4⋊C4—941no—
167C2×C4⋊C4—941no—
168C2×C42—471no—
169C4⋊C8—472no—
170#103—472no—
171#103—472no—
172#103—472no—
173#103C2×D4712yes—
174C22⋊C8—471no—
175C22⋊C8C2×D4711yescharacteristic
176C4×C8—472no—
177C2×Q8—21no—
178C2×Q8—42no—
179C2×Q8—472no—
180C2×Q8—471no—
181C2×Q8—941no—
182C2×Q8—941no—
183C2×Q8—1882no—
184C2×Q8C22×D4712yes—
185C2×Q8C22×D4711yescharacteristic
186C22×C4—21no—
187C22×C4—471no—
188C22×C4—471no—
189C22×C4—941no—
190C22×C4C22×D4711yescharacteristic
191Q16—42no—
192Q16—1882no—
193Q16—1882no—
194Q16—1882no—
195C2×C8—472no—
196C2×C8C22×D4712yes—
197C4⋊C4—21no—
198C4⋊C4—471no—
199C4⋊C4—942no—
200C4⋊C4—942no—
201C4⋊C4—942no—
202C4⋊C4—942no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4—941no—
209C4⋊C4C22×D4711yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—941no—
212C42—471no—
213C42—471no—
214C42—471no—
215C42—471no—
216C42—941no—
217C42—941no—
218C23D4×D4711yescharacteristic
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—42no—
223Q8—942no—
224Q8—942no—
225Q8—942no—
226Q8—1882no—
227Q8—1882no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—474no—
234C2×C4—471no—
235C2×C4—471no—
236C2×C4—471no—
237C2×C4—471no—
238C2×C4—942no—
239C2×C4—941no—
240C2×C4—941no—
241C2×C4—942no—
242C2×C4—1882no—
243C2×C4D4×D4711yescharacteristic
244C2×C4C23×D4711yescharacteristic
245C8—22no—
246C8—942no—
247C22—21no—
248C22—21no—
249C22Q16×D4712yes—
250C22C2×D4×D4711yescharacteristic
251C4—21no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—472no—
256C4—472no—
257C4—472no—
258C4—941no—
259C4—1881no—
260C4—1882no—
261C4—1881no—
262C4#1309406912yes—
263C2—22no—
264C2#1568968811yescharacteristic
265C2C2×Q16×D4711yescharacteristic
266C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3209
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #15689501C2semidirect
4. #15689472C2semidirect
5. #15689332C2semidirect
6. #15689331C2semidirect
101. C2×Dic47Q16semidirect
145. C47#3209semidirect