Finite Group Databasebeta

← #20254727

Subgroups — #20254727

Order 6016.

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

normal subgroups only

This group has 354 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#15689678C211yesmaximal, characteristic, complemented
2#15689655C211yesmaximal, characteristic
3#15689429C212yesmaximal, complemented
4#15689405C211yesmaximal, characteristic, complemented
5#15689365C212yesmaximal, complemented
6#15689351C212yesmaximal
7#15689344C212yesmaximal, complemented
8#15689334C211yesmaximal, characteristic, complemented
9#15689328C211yesmaximal, characteristic, complemented
10C4⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#474C211yesmaximal, characteristic, complemented
12C2×Dic188C2212yes—
13C2×#10625335C2212yes—
14C2×C8×D47C2212yes—
15#13094024C2211yescharacteristic
16#13094017—21no—
17#13094015—21no—
18#13094015C2211yescharacteristic
19#13094011C2211yescharacteristic
20#13094006—21no—
21#13094004C2212yes—
22#13094004C2211yescharacteristic
23#13094000—21no—
24#13093995C2211yescharacteristic
25Q8×Dic47—21no—
26C4×Dic94C2211yescharacteristic
27#13093989C2212yes—
28C4×C22⋊D47—21no—
29#13093983—21no—
30#13093982—21no—
31C42×D47C2211yescharacteristic
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093949C2212yes—
36#13093947C2212yes—
37#13093947C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×D4×C47C2211yescharacteristic
40#107×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#102×C47C2212yes—
43C2×Q8×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—21no—
47C2×C4×D47D411yescharacteristic
48C2×C4×D47D411yescharacteristic
49C2×C4×D47C2311yescharacteristic
50C2×Dic94C2311yescharacteristic
51C2×Dic94C2312yes—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2311yescharacteristic
55C4⋊C4×C47C2312yes—
56C22⋊C4×C47—21no—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—21no—
59C22⋊Dic47—21no—
60C22⋊Dic47—21no—
61#10625335—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47—22no—
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—22no—
73C4×Dic47—21no—
74C4×Dic47—22no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79Dic188—42no—
80C8×D47—42no—
81C23×C47—21no—
82C22×D47C2×D411yescharacteristic
83Q8×C47—42no—
84D4×C47—21no—
85D4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—42no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—42no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C4×D47—22no—
100C4×D47—22no—
101C4×D47—21no—
102C4×D47—21no—
103Dic94—21no—
104Dic94—22no—
105Dic94—21no—
106Dic94—22no—
107C8×C47—22no—
108C47⋊C8—22no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47C22×D411yescharacteristic
113C2×D47—21no—
114C2×D47—21no—
115C2×D47#13712yes—
116C4×C47—21no—
117C4×C47—41no—
118C4×C47—42no—
119C4×C47#13512yes—
120C4×C47H(5,𝔽2)11yescharacteristic
121C4×C472−1+411yescharacteristic
122Dic47—21no—
123Dic47—21no—
124Dic47—21no—
125Dic47—41no—
126Dic47—42no—
127Dic47—41no—
128#3248—471nomaximal, Sylow
129C2×C47—81no—
130C2×C47#53711yescharacteristic
131C2×C47C2×#13511yescharacteristic
132C2×C47C2×#13711yescharacteristic
133D47—22no—
134#533—471no—
135#529—471no—
136#479—472no—
137#475—471no—
138#474D4711yescharacteristic, complemented
139#467—472no—
140#465—472no—
141#464—472no—
142#462—471no—
143#461—471no—
144C2×C4⋊C8—471no—
145C47#324811yescharacteristic, complemented, Sylow
146C2×Q16—472no—
147C2×SD16—472no—
148C22×C8—472no—
149C4⋊Q8—471no—
150C4⋊Q8C2×D4711yescharacteristic
151#126—941no—
152#125—471no—
153#125—941no—
154#124—471no—
155#123—941no—
156C22⋊Q8—471no—
157C22⋊Q8—472no—
158C22⋊Q8—941no—
159#121—471no—
160C4×Q8—472no—
161C4×Q8—471no—
162C4×Q8—941no—
163C4×D4—941no—
164C4×D4C2×D4711yescharacteristic
165#117—941no—
166#117—941no—
167C2×C42—471no—
168#107C2×D4712yes—
169#106—472no—
170C4⋊C8—472no—
171C4⋊C8—471no—
172C4⋊C8C2×D4711yescharacteristic
173#103—472no—
174#103—472no—
175#103—472no—
176#102C2×D4712yes—
177C2×Q8—21no—
178C2×Q8—471no—
179C2×Q8—472no—
180C2×D4—941no—
181C2×D4C22×D4711yescharacteristic
182C22×C4—21no—
183C22×C4—471no—
184C22×C4—471no—
185C22×C4—471no—
186Q16—1882no—
187SD16—1882no—
188C2×C8—472no—
189C2×C8—1882no—
190C2×C8C22×D4712yes—
191C4⋊C4—21no—
192C4⋊C4—471no—
193C4⋊C4—941no—
194C4⋊C4—942no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4—942no—
198C4⋊C4—941no—
199C4⋊C4—941no—
200C4⋊C4—941no—
201C4⋊C4C22×D4712yes—
202C4⋊C4C22×D4711yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—942no—
205C22⋊C4—941no—
206C22⋊C4—941no—
207C22⋊C4—941no—
208C22⋊C4—941no—
209C42—471no—
210C42—471no—
211C42—471no—
212C42—942no—
213C42—941no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—471no—
217Q8—42no—
218Q8—942no—
219Q8—941no—
220Q8—941no—
221Q8—942no—
222D4—21no—
223D4—21no—
224D4—1882no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—471no—
229C2×C4—471no—
230C2×C4—471no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—941no—
234C2×C4—941no—
235C2×C4—941no—
236C2×C4—941no—
237C2×C4—942no—
238C2×C4D4×D4711yescharacteristic
239C2×C4D4×D4711yescharacteristic
240C2×C4C23×D4711yescharacteristic
241C8—22no—
242C8—942no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—472no—
247C22—941no—
248C22—941no—
249C22C2×D4×D4711yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—941no—
254C4—941no—
255C4—941no—
256C4—1881no—
257C4—1881no—
258C4—1882no—
259C4#1309404312yes—
260C4#1309407011yescharacteristic
261C4#1309407211yescharacteristic
262C2—81no—
263C2—942no—
264C2#1568970311yescharacteristic
265C2C2×#1309404311yescharacteristic
266C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3248
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689429C2semidirect
4. #15689405C2semidirect
5. #15689365C2semidirect
7. #15689344C2semidirect
8. #15689334C2semidirect
9. #15689328C2semidirect
10. C4⋊C8×D47C2semidirect
11. C47×#474C2semidirect
138. #474D47semidirect
145. C47#3248semidirect