Finite Group Databasebeta

← #20254703

Subgroups — #20254703

Order 6016.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689677C211yesmaximal, characteristic, complemented
2#15689674C211yesmaximal, characteristic
3#15689412C212yesmaximal, complemented
4#15689405C211yesmaximal, characteristic, complemented
5#15689355C212yesmaximal, complemented
6#15689353C212yesmaximal, complemented
7#15689327C212yesmaximal, complemented
8#15689324C211yesmaximal, characteristic, complemented
9#15689323C211yesmaximal, characteristic, complemented
10C4⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13C2×#10625325C2212yes—
14C2×#10625336C2212yes—
15C2×C8×D47C2212yes—
16#13094023C2211yescharacteristic
17#13094022C2211yescharacteristic
18#13094021C2211yescharacteristic
19#13094014—21no—
20#13094013—21no—
21#13094004C2211yescharacteristic
22#13094002—21no—
23#13094000C2211yescharacteristic
24#13093999—21no—
25#13093999C2212yes—
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic
28#13093986—21no—
29#13093986C2212yes—
30#13093981—21no—
31C42×D47C2211yescharacteristic
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093947C2212yes—
36#13093946C2212yes—
37#13093944C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×Q8×C47C2211yescharacteristic
40#106×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#103×C47C2212yes—
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45#10625354—44no—
46C2×D188—22no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188C2312yes—
50C2×C4×D47—22no—
51C2×C4×D47D411yescharacteristic
52C2×C4×D47D411yescharacteristic
53C2×C4×D47C2311yescharacteristic
54C2×Dic94—21no—
55C2×Dic94C2311yescharacteristic
56C2×C8×C47C2312yes—
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2312yes—
60C4⋊C4×C47C2311yescharacteristic
61C42×C47—21no—
62C42×C47C2311yescharacteristic
63#10625336—42no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68C4⋊Dic47—21no—
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75C4×Dic47—21no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80#10625325—42no—
81C8×D47—42no—
82C22×D47—22no—
83C22×D47C2×D411yescharacteristic
84Q8×C47—21no—
85Q8×C47—21no—
86Q8×C47—42no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98D188—22no—
99D188—22no—
100D188—42no—
101D188—44no—
102D188—42no—
103C4×D47—21no—
104C4×D47—21no—
105C4×D47—41no—
106C4×D47—44no—
107C4×D47SD1614yescomplemented
108Dic94—21no—
109Dic94—21no—
110Dic94—42no—
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47C22×D411yescharacteristic
114C2×D47—21no—
115C2×D47—21no—
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47C2×SD1612yes—
120C4×C47—21no—
121C4×C47—41no—
122C4×C47—42no—
123C4×C47—41no—
124C4×C47C2×SD1612yes—
125C4×C47H(5,𝔽2)11yescharacteristic
126C4×C472−1+411yescharacteristic
127Dic47—21no—
128Dic47—21no—
129Dic47—41no—
130Dic47—41no—
131Dic47C2×SD1612yes—
132#3246—471nomaximal, Sylow
133C2×C47#53711yescharacteristic
134C2×C47C22×SD1611yescharacteristic
135C2×C47#57511yescharacteristic
136D47—22no—
137D47—82no—
138#533—471no—
139#532—471no—
140#476—472no—
141#475—471no—
142#475D4711yescharacteristic, complemented
143#465—472no—
144#465—472no—
145#461—472no—
146#460—471no—
147#460—471no—
148C2×C4⋊C8—471no—
149C47#324611yescharacteristic, complemented, Sylow
150C2×#41—941no—
151C2×SD16—472no—
152C2×SD16—472no—
153C22×C8—472no—
154C4⋊Q8—471no—
155C4⋊Q8—471no—
156C4⋊Q8C2×D4711yescharacteristic
157#127—471no—
158#125—941no—
159#124—941no—
160C22⋊Q8—471no—
161C22⋊Q8—471no—
162C22⋊Q8—941no—
163#121—472no—
164#121—941no—
165C4×Q8—471no—
166C4×Q8—941no—
167C4×Q8C2×D4711yescharacteristic
168C4×D4—472no—
169C4×D4—941no—
170#117—941no—
171C2×C42—471no—
172#106—472no—
173#106C2×D4712yes—
174C4⋊C8—472no—
175C4⋊C8—471no—
176C4⋊C8C2×D4711yescharacteristic
177#103—472no—
178#103C2×D4712yes—
179#102—472no—
180#102—472no—
181#41—1884no—
182C2×Q8—21no—
183C2×Q8—471no—
184C2×Q8—941no—
185C2×Q8C22×D4711yescharacteristic
186C2×D4—472no—
187C2×D4—942no—
188C2×D4—941no—
189C2×D4—941no—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—942no—
194SD16—1882no—
195SD16—1882no—
196C2×C8—472no—
197C2×C8—1882no—
198C2×C8C22×D4712yes—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—471no—
202C4⋊C4—941no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4C22×D4711yescharacteristic
209C4⋊C4C22×D4712yes—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C42—21no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—471no—
221C23—942no—
222Q8—21no—
223Q8—21no—
224Q8—42no—
225Q8—941no—
226Q8—941no—
227Q8—1882no—
228D4—942no—
229D4—942no—
230D4—1882no—
231D4—1884no—
232D4—1882no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—471no—
237C2×C4—474no—
238C2×C4—471no—
239C2×C4—471no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—941no—
244C2×C4—1881no—
245C2×C4—1884no—
246C2×C4D4×D4711yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—22no—
250C8—942no—
251C22—472no—
252C22—941no—
253C22—941no—
254C22—1882no—
255C22—1882no—
256C22—1882no—
257C22C2×D4×D4711yescharacteristic
258C4—21no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—472no—
263C4—941no—
264C4—941no—
265C4—1881no—
266C4—1881no—
267C4SD16×D4712yes—
268C4#1309407011yescharacteristic
269C4#1309407211yescharacteristic
270C2—942no—
271C2—3762no—
272C2#1568970311yescharacteristic
273C2C2×SD16×D4711yescharacteristic
274C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3246
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689412C2semidirect
4. #15689405C2semidirect
5. #15689355C2semidirect
6. #15689353C2semidirect
7. #15689327C2semidirect
8. #15689324C2semidirect
9. #15689323C2semidirect
10. C4⋊C8×D47C2semidirect
11. C47×#475C2semidirect
107. C4×D47SD16semidirect
142. #475D47semidirect
149. C47#3246semidirect