Finite Group Databasebeta

← #20253442

Subgroups — #20253442

Order 6016.

434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10625350C211yesmaximal, characteristic, complemented
2#15689444C212yesmaximal, complemented
3#15689415C211yesmaximal, characteristic, complemented
4#15689410C211yesmaximal, characteristic, complemented
5#15689320C211yesmaximal, characteristic, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689266C212yesmaximal, complemented
8C4×#10625335C212yesmaximal, complemented
9C4×#10625334C212yesmaximal, complemented
10#15689176C211yesmaximal, characteristic, complemented
11C47×#532C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625335C2212yes—
14C2×#10625334C2212yes—
15C4×Dic94C2211yescharacteristic
16C4×Dic94C2211yescharacteristic
17C4×D188C2211yescharacteristic
18C4×D188C2211yescharacteristic
19C4×C22⋊D47—21no—
20C4×C22⋊D47—21no—
21#13093983C2211yescharacteristic
22#13093981—21no—
23C42×D47—21no—
24#13093957C2212yes—
25#13093955C2212yes—
26C4⋊(C47⋊C8)C2211yescharacteristic
27C4⋊(C47⋊C8)C2211yescharacteristic
28#13093947C2212yes—
29#13093945C2212yes—
30#13093945C2212yes—
31#13093944C2212yes—
32C22⋊(C47⋊C8)C2212yes—
33C4×C47⋊C8C2212yes—
34C2×#41×C47—21no—
35C4⋊Q8×C47C2211yescharacteristic
36#127×C47C2211yescharacteristic
37#124×C47—21no—
38#121×C47—21no—
39#121×C47C2212yes—
40C4×D4×C47—21no—
41C4×D4×C47C2212yes—
42C2×C42×C47C2211yescharacteristic
43#41×C47—44no—
44C2×Q8×C47—21no—
45C2×D4×C47—22no—
46C2×D4×C47—21no—
47C2×D4×C47—21no—
48C2×D4×C47C2312yes—
49C22×C4×C47—22no—
50C22×C4×C47D411yescharacteristic
51C22×C4×C47D411yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—21no—
54#10625350—22no—
55#10625350—22no—
56C2×D188C2311yescharacteristic
57C2×C4×D47—21no—
58C2×C4×D47—21no—
59C2×C4×D47—21no—
60C2×Dic94C2311yescharacteristic
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2312yes—
63C22⋊C4×C47—22no—
64C22⋊C4×C47—22no—
65C42×C47D411yescharacteristic
66C42×C47D411yescharacteristic
67C42×C47C2311yescharacteristic
68C42×C47C2311yescharacteristic
69C22⋊Dic47—21no—
70#10625335—24no—
71#10625334—24no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74C4⋊Dic47C2311yescharacteristic
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—21no—
77Dic47⋊C4—21no—
78C4×Dic47—21no—
79C4×Dic47—21no—
80C4×Dic47—21no—
81C2×C47⋊C8C2312yes—
82C2×C47⋊C8C2312yes—
83C23×C47—22no—
84C23×C47C2×D411yescharacteristic
85C22×D47—21no—
86Q8×C47—42no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—42no—
90D4×C47—44no—
91D4×C47—42no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—22no—
97C2×C4×C47—44no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—24no—
105C2×Dic47—21no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108D188—21no—
109D188#4112yescomplemented
110C4×D47—24no—
111C4×D47—42no—
112C4×D47—42no—
113Dic94—21no—
114Dic94#4112yescomplemented
115C47⋊C8—22no—
116C47⋊C8—22no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47C22×D411yescharacteristic
124C2×D47—22no—
125C2×D47—41no—
126C2×D47—41no—
127C4×C47—21no—
128C4×C47—21no—
129C4×C47—21no—
130C4×C47—42no—
131C4×C47#13512yes—
132C4×C47AGL(1,ℤ/8)12yes—
133C4×C47C2×#4111yescharacteristic
134C4×C47C2×#4111yescharacteristic
135Dic47—22no—
136Dic47—41no—
137Dic47—41no—
138#3106—471nomaximal, Sylow
139C2×C47—41no—
140C2×C47—82no—
141C2×C47#52511yescharacteristic
142C2×C47C2×#13511yescharacteristic
143C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
144D47—42no—
145#532D4711yescharacteristic, complemented
146C4×#41—471no—
147#482—472no—
148#477—471no—
149#476—471no—
150#460—471no—
151#459—471no—
152#449—472no—
153C4×SD16—472no—
154C4×D8—472no—
155#431—471no—
156C47#310611yescharacteristic, complemented, Sylow
157C2×#41—21no—
158C2×#41—471no—
159C2×SD16—472no—
160C2×D8—472no—
161C4⋊Q8C2×D4711yescharacteristic
162#127C2×D4711yescharacteristic
163#124—21no—
164#121—21no—
165#121C2×D4712yes—
166C4×Q8—471no—
167C4×Q8—471no—
168C4×D4—21no—
169C4×D4—471no—
170C4×D4—471no—
171C4×D4—941no—
172C4×D4—941no—
173C4×D4C2×D4712yes—
174#117—471no—
175#117—941no—
176C2×C42—941no—
177C2×C42C2×D4711yescharacteristic
178#107—472no—
179#106—472no—
180C4⋊C8—471no—
181C4⋊C8—471no—
182#103—472no—
183#102—472no—
184#102—472no—
185#102—472no—
186C22⋊C8—472no—
187C4×C8—472no—
188#41—44no—
189#41—942no—
190#41—942no—
191C2×Q8—21no—
192C2×Q8—471no—
193C2×D4—22no—
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—471no—
197C2×D4—941no—
198C2×D4C22×D4712yes—
199C22×C4—22no—
200C22×C4—941no—
201C22×C4—941no—
202C22×C4—941no—
203C22×C4C22⋊D4711yescharacteristic
204C22×C4C22⋊D4711yescharacteristic
205C22×C4C22×D4711yescharacteristic
206SD16—944no—
207D8—944no—
208C2×C8—472no—
209C2×C8—472no—
210C4⋊C4—21no—
211C4⋊C4—471no—
212C4⋊C4—471no—
213C4⋊C4—941no—
214C4⋊C4—941no—
215C4⋊C4C22×D4712yes—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—941no—
219C22⋊C4—941no—
220C22⋊C4—941no—
221C42—941no—
222C42—941no—
223C42—941no—
224C42C22⋊D4711yescharacteristic
225C42C22⋊D4711yescharacteristic
226C42C22×D4711yescharacteristic
227C42C22×D4711yescharacteristic
228C23—22no—
229C23—941no—
230C23C2×C22⋊D4711yescharacteristic
231Q8—42no—
232Q8—472no—
233Q8—941no—
234D4—22no—
235D4—22no—
236D4—42no—
237D4—44no—
238D4—42no—
239D4—472no—
240D4—944no—
241D4—941no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—944no—
249C2×C4—941no—
250C2×C4—941no—
251C2×C4—941no—
252C2×C4—1882no—
253C2×C4—1882no—
254C2×C4C2×C22⋊D4711yescharacteristic
255C2×C4C2×C22⋊D4711yescharacteristic
256C2×C4C2×C22⋊D4711yescharacteristic
257C2×C4C2×C22⋊D4711yescharacteristic
258C2×C4C2×C22⋊D4711yescharacteristic
259C2×C4C23×D4711yescharacteristic
260C8—942no—
261C8—942no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—942no—
269C22—1881no—
270C22—1881no—
271C22C22×C22⋊D4711yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—942no—
277C4—1881no—
278C4—1881no—
279C4#1309404412yes—
280C4#1309405012yes—
281C4#41×D4711yescharacteristic
282C4#41×D4711yescharacteristic
283C2—41no—
284C2—82no—
285C2—1882no—
286C2#1568963011yescharacteristic
287C2C2×#1309404411yescharacteristic
288C2C2×#1309405011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3106
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C4×#10625350C2semidirect
2. #15689444C2semidirect
3. #15689415C2semidirect
4. #15689410C2semidirect
5. #15689320C2semidirect
6. #15689315C2semidirect
7. #15689266C2semidirect
8. C4×#10625335C2semidirect
9. C4×#10625334C2semidirect
10. #15689176C2semidirect
11. C47×#532C2semidirect
109. D188#41semidirect
114. Dic94#41semidirect
145. #532D47semidirect
156. C47#3106semidirect