Finite Group Databasebeta

← #20254610

Subgroups — #20254610

Order 6016.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C4⋊Q8×D47C211yesmaximal, characteristic, complemented
2#15689658C211yesmaximal, characteristic
3#15689533C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689455C212yesmaximal, complemented
7#15689438C212yesmaximal
8#15689417C212yesmaximal, complemented
9#15689412C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#501C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094022—21no—
17#13094019—21no—
18#13094012C2211yescharacteristic
19#13094009—21no—
20#13094004C2211yescharacteristic
21#13093999C2211yescharacteristic
22#13093989C2211yescharacteristic
23#13093986—21no—
24#13093986C2211yescharacteristic
25#13093982—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47C2212yes—
28C42×D47C2211yescharacteristic
29#13093957C2212yes—
30#13093955C2212yes—
31Dic47⋊C8C2212yes—
32#13093949C2212yes—
33#13093947C2212yes—
34#13093946C2212yes—
35#13093944C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#107×C47C2212yes—
41#106×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44Q8×D47—44no—
45C2×D188—21no—
46C2×D188C2311yescharacteristic
47C2×C4×D47—22no—
48C2×C4×D47—21no—
49C2×C4×D47D411yescharacteristic
50C2×C4×D47D411yescharacteristic
51C2×C4×D47C2311yescharacteristic
52C2×Dic94—21no—
53C2×Dic94—22no—
54C2×Dic94C2311yescharacteristic
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2311yescharacteristic
60C4⋊C4×C47C2312yes—
61C4⋊C4×C47C2311yescharacteristic
62C42×C47C2311yescharacteristic
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68C4⋊Dic47—21no—
69C4⋊Dic47—21no—
70C4⋊Dic47C2312yes—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—21no—
74C4×Dic47—21no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79C22×D47—21no—
80C22×D47C2×D411yescharacteristic
81Q8×C47—42no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47C2×D411yescharacteristic
91C2×Dic47C2×D411yescharacteristic
92C2×Dic47C2×D411yescharacteristic
93D188—22no—
94D188—42no—
95C4×D47—22no—
96C4×D47—22no—
97C4×D47—22no—
98C4×D47—44no—
99C4×D47—42no—
100Dic94—22no—
101Dic94—44no—
102Dic94—42no—
103C8×C47—22no—
104C47⋊C8—22no—
105C22×C47C22×D411yescharacteristic
106C2×D47—21no—
107C2×D47—21no—
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47AGL(1,ℤ/8)12yes—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47—41no—
116C4×C47—41no—
117C4×C472−1+412yes—
118Dic47—21no—
119Dic47—21no—
120Dic47—41no—
121Dic47—42no—
122Dic47#13712yes—
123#3238—471nomaximal, Sylow
124C2×C47#53611yescharacteristic
125C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C47C2×#13711yescharacteristic
127D47—22no—
128D47—81no—
129C2×C4⋊Q8—471no—
130#529—471no—
131#501—471no—
132#501D4711yescharacteristic, complemented
133#489—471no—
134#489—471no—
135#483—472no—
136#480—472no—
137#477—472no—
138#476—472no—
139#432—471no—
140C47#323811yescharacteristic, complemented, Sylow
141C22×Q8—941no—
142C4⋊Q8—472no—
143C4⋊Q8—471no—
144C4⋊Q8—941no—
145C4⋊Q8—941no—
146C4⋊Q8C2×D4711yescharacteristic
147#126—941no—
148#125C2×D4711yescharacteristic
149#124—471no—
150#123—941no—
151C22⋊Q8—471no—
152#121—471no—
153C4×Q8—471no—
154C4×D4—471no—
155C4×D4—941no—
156#117—941no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—941no—
159C2×C42—471no—
160#107—472no—
161#107C2×D4712yes—
162#106—472no—
163#106C2×D4712yes—
164C4⋊C8—472no—
165#103—472no—
166#103—472no—
167#102—472no—
168#102—472no—
169C22⋊C8—472no—
170#97—471no—
171#97C2×D4711yescharacteristic
172C2×Q8—21no—
173C2×Q8—471no—
174C2×Q8—942no—
175C2×Q8—941no—
176C2×Q8—1884no—
177C2×D4—471no—
178C2×D4—941no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—941no—
183C22×C4—942no—
184C2×C8—472no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—472no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4C22×D4712yes—
196C4⋊C4C22×D4711yescharacteristic
197C4⋊C4C22×D4711yescharacteristic
198C22⋊C4—941no—
199C22⋊C4—941no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C22⋊C4—941no—
203C42—471no—
204C42—471no—
205C42—471no—
206C42—941no—
207C42C22×D4711yescharacteristic
208C23—471no—
209C23—941no—
210Q8—42no—
211Q8—942no—
212Q8—1882no—
213Q8—1884no—
214D4—942no—
215D4—1882no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—471no—
220C2×C4—471no—
221C2×C4—471no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—1882no—
228C2×C4—1884no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—22no—
233C8—942no—
234C22—472no—
235C22—941no—
236C22—941no—
237C22—1881no—
238C22—1881no—
239C22—1881no—
240C22C2×D4×D4711yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—472no—
247C4—941no—
248C4—941no—
249C4—1882no—
250C4—1881no—
251C4#1309407212yes—
252C2—942no—
253C2—3761no—
254C2#1568969811yescharacteristic
255C2AGL(1,ℤ/8)×D4711yescharacteristic
256C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3238
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D47C2semidirect
3. #15689533C2semidirect
4. #15689485C2semidirect
5. #15689483C2semidirect
6. #15689455C2semidirect
8. #15689417C2semidirect
9. #15689412C2semidirect
10. #15689178C2semidirect
11. C47×#501C2semidirect
132. #501D47semidirect
140. C47#3238semidirect