Finite Group Databasebeta

← #20253196

Subgroups — #20253196

Order 6016.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
2C4×#10625352C211yesmaximal, characteristic
3#15689417C212yesmaximal, complemented
4#15689411C212yesmaximal, complemented
5#15689409C211yesmaximal, characteristic, complemented
6#15689405C211yesmaximal, characteristic, complemented
7#15689403C211yesmaximal, characteristic, complemented
8#15689164C212yesmaximal, complemented
9#15689145C211yesmaximal, characteristic, complemented
10#15689121C212yesmaximal
11C47×#474C211yesmaximal, characteristic, complemented
12C2×#10625352C2211yescharacteristic
13C2×Q8×D47—21no—
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic
16#13094023—21no—
17#13094023C2212yes—
18#13094022—21no—
19C4×Dic94C2211yescharacteristic
20#13093989C2211yescharacteristic
21D4×Dic47C2211yescharacteristic
22C4×C22⋊D47—21no—
23(C22⋊D47)⋊C4—21no—
24#13093982C2211yescharacteristic
25#13093980—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47C2212yes—
28C2×C4×Dic47—21no—
29C42×D47C2211yescharacteristic
30#13093957C2212yes—
31#13093956C2212yes—
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093949C2212yes—
36#13093947C2212yes—
37#13093945C2212yes—
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—
47C22×Dic47—21no—
48C22×Dic47—21no—
49Q8×D47—44no—
50#10625352—22no—
51#10625352Q814yescomplemented
52C2×C4×D47—22no—
53C2×C4×D47D411yescharacteristic
54C2×C4×D47D411yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×Dic94—21no—
57C2×Dic94—22no—
58C2×Dic94C2311yescharacteristic
59C2×C8×C47C2312yes—
60C4⋊C4×C47—21no—
61C4⋊C4×C47C2311yescharacteristic
62C4⋊C4×C47C2312yes—
63C22⋊C4×C47—21no—
64C42×C47C2311yescharacteristic
65C22⋊Dic47—21no—
66(C2×D47)⋊C4—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47C2312yes—
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—21no—
74C4×Dic47—21no—
75C4×Dic47—21no—
76C4×Dic47—21no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81#10625324—24no—
82C23×C47—21no—
83C22×D47C2×D411yescharacteristic
84Q8×C47—42no—
85D4×C47—21no—
86D4×C47C2×Q812yescomplemented
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47—42no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—24no—
94C2×Dic47—21no—
95C2×Dic47—24no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—42no—
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C4×D47—22no—
103C4×D47—22no—
104C4×D47—44no—
105C4×D47C2×Q812yes—
106C4×D47#4112yes—
107Dic94—21no—
108Dic94—44no—
109Dic94—42no—
110Dic94C2×Q812yescomplemented
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47—22no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47C22×D411yescharacteristic
117C2×D47—21no—
118C2×D47—21no—
119C2×D47C22⋊Q812yes—
120C4×C47—21no—
121C4×C47—42no—
122C4×C47—41no—
123C4×C47AGL(1,ℤ/8)12yes—
124C4×C47C22×Q811yescharacteristic
125C4×C47C2×#4111yescharacteristic
126Dic47—22no—
127Dic47—21no—
128Dic47—42no—
129Dic47—41no—
130Dic47C22⋊Q812yes—
131Dic47#13712yes—
132#3079—471nomaximal, Sylow
133C2×C47—42no—
134C2×C47C2×C22⋊Q811yescharacteristic
135C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C47C2×#13711yescharacteristic
137D47—22no—
138C2×C4⋊Q8—471no—
139C4×#41—471no—
140#477—472no—
141#476—472no—
142#475—471no—
143#475—471no—
144#474—471no—
145#474D4711yescharacteristic, complemented
146#428—472no—
147#423—471no—
148#417—472no—
149C47#307911yescharacteristic, complemented, Sylow
150C2×#41—471no—
151C22×Q8—941no—
152C2×M16—472no—
153C4⋊Q8—472no—
154C4⋊Q8—471no—
155C4⋊Q8—941no—
156C4⋊Q8—941no—
157C4⋊Q8C2×D4711yescharacteristic
158C4×Q8—471no—
159C4×Q8—471no—
160C4×D4—471no—
161C4×D4—941no—
162C4×D4—941no—
163C4×D4C2×D4711yescharacteristic
164#117—471no—
165#117—941no—
166C2×C4⋊C4—472no—
167C2×C4⋊C4—941no—
168C2×C42—471no—
169C2×C42—941no—
170#107—472no—
171#107C2×D4712yes—
172#106—472no—
173#106—472no—
174C4⋊C8—472no—
175C4⋊C8—471no—
176C4⋊C8C2×D4711yescharacteristic
177#103—472no—
178#103—472no—
179#102—472no—
180#102C2×D4712yes—
181#41—474no—
182#41—942no—
183C2×Q8—21no—
184C2×Q8—471no—
185C2×Q8—942no—
186C2×Q8—941no—
187C2×Q8—1884no—
188C2×D4—941no—
189C2×D4C22×D4711yescharacteristic
190C22×C4—21no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—942no—
195C22×C4—941no—
196C22×C4—941no—
197M16—944no—
198C2×C8—472no—
199C2×C8C22×D4712yes—
200C4⋊C4—21no—
201C4⋊C4—472no—
202C4⋊C4—471no—
203C4⋊C4—942no—
204C4⋊C4—942no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4C22×D4712yes—
209C4⋊C4C22×D4711yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—941no—
212C22⋊C4—941no—
213C42—471no—
214C42—471no—
215C42—471no—
216C42—941no—
217C42—941no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—21no—
221C23—471no—
222Q8—42no—
223Q8—472no—
224Q8—941no—
225Q8—1884no—
226Q8—1882no—
227D4—21no—
228D4—944no—
229D4Q8×D4712yescomplemented
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—471no—
234C2×C4—471no—
235C2×C4—472no—
236C2×C4—472no—
237C2×C4—471no—
238C2×C4—942no—
239C2×C4—944no—
240C2×C4—941no—
241C2×C4—942no—
242C2×C4—941no—
243C2×C4—942no—
244C2×C4—1884no—
245C2×C4—1882no—
246C2×C4D4×D4711yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—22no—
250C8—942no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—472no—
255C22—941no—
256C22—941no—
257C22C2×D4×D4711yescharacteristic
258C4—21no—
259C4—41no—
260C4—42no—
261C4—472no—
262C4—472no—
263C4—942no—
264C4—941no—
265C4—1882no—
266C4—1881no—
267C4#1309404812yes—
268C4C2×Q8×D4711yescharacteristic
269C4#41×D4711yescharacteristic
270C2—42no—
271C2—942no—
272C2C22⋊Q8×D4711yescharacteristic
273C2C2×#1309404811yescharacteristic
274C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3079
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. C4⋊Q8×D47C2semidirect
3. #15689417C2semidirect
4. #15689411C2semidirect
5. #15689409C2semidirect
6. #15689405C2semidirect
7. #15689403C2semidirect
8. #15689164C2semidirect
9. #15689145C2semidirect
11. C47×#474C2semidirect
51. #10625352Q8semidirect
86. D4×C47C2×Q8semidirect
110. Dic94C2×Q8semidirect
145. #474D47semidirect
149. C47#3079semidirect
229. D4Q8×D47semidirect