Finite Group Databasebeta

← #20253616

Subgroups — #20253616

Order 6016.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689742C211yesmaximal, characteristic
2#15689599C211yesmaximal, characteristic, complemented
3#15689463C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic
5#15689419C211yesmaximal, characteristic, complemented
6#15689408C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689277C211yesmaximal, characteristic, complemented
9#15689260C211yesmaximal, characteristic
10#15689227C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12Q16×Dic47C211yesmaximal, characteristic, complemented
13#15689214C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094017—21no—
21#13094010—21no—
22#13094008—21no—
23#13094001—21no—
24#13094000C2211yescharacteristic
25#13093995C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic
28C4×Dic94—21no—
29C4×Dic94C2211yescharacteristic
30#13093989—21no—
31#13093989C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093982—21no—
34#13093982C2211yescharacteristic
35#13093981—21no—
36#13093981C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64Q8×D47—22no—
65Q8×D47—22no—
66C2×C4×D47—21no—
67C2×C4×D47C2311yescharacteristic
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71Q16×C47—22no—
72SD16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83#10625337—22no—
84#10625335—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114D4×C47—21no—
115D4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—81no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C4×D47—24no—
132C4×D47—21no—
133C4×D47—21no—
134Dic94—24no—
135Dic94—21no—
136Dic94—81no—
137Dic94#4112yes—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C22×D411yescharacteristic
146C2×D47—21no—
147C2×D47—21no—
148C2×D47—21no—
149C4×C47—22no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47C2×#4111yescharacteristic
155C4×C47C2×#4111yescharacteristic
156Dic47—21no—
157Dic47—22no—
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3121—471nomaximal, Sylow
164C2×C47—81no—
165C2×C47#52511yescharacteristic
166C2×C47#57711yescharacteristic
167C2×C47#57811yescharacteristic
168D47—41no—
169#542—471no—
170#519—471no—
171#485—471no—
172#482—471no—
173#477—471no—
174#475—471no—
175#464—471no—
176#464D4711yescharacteristic, complemented
177#451—471no—
178#448—471no—
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312111yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C2×Q16—471no—
187C2×Q16C2×D4711yescharacteristic
188C2×SD16—471no—
189C2×SD16C2×D4711yescharacteristic
190C4⋊Q8—471no—
191#126—941no—
192#124—941no—
193#124C2×D4711yescharacteristic
194#123—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197#121—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×Q8—941no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—471no—
206#117—471no—
207#117—471no—
208#117—941no—
209#117—941no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8C2×D4711yescharacteristic
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103C2×D4711yescharacteristic
222#102—471no—
223#102C2×D4711yescharacteristic
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C4×C8—471no—
228C2×Q8—471no—
229C2×Q8—941no—
230C2×Q8—942no—
231C2×Q8—942no—
232C2×Q8—941no—
233C2×Q8C22×D4711yescharacteristic
234C2×Q8C22×D4711yescharacteristic
235C2×D4—941no—
236C2×D4C22×D4711yescharacteristic
237C22×C4—471no—
238C22×C4—941no—
239C22×C4—941no—
240Q16—22no—
241Q16—942no—
242SD16—22no—
243SD16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—21no—
270C42—471no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—21no—
278C23—471no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—472no—
283Q8—944no—
284Q8—941no—
285Q8—3761no—
286Q8#1062535212yes—
287D4—21no—
288D4—21no—
289D4—3761no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—944no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—3761no—
304C2×C4D4×D4711yescharacteristic
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—941no—
315C22—941no—
316C22—941no—
317C22C2×D4×D4711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—941no—
324C4—942no—
325C4—941no—
326C4—941no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4C2×#1062535211yescharacteristic
332C2—81no—
333C2—1881no—
334C2#1568963311yescharacteristic
335C2#1568993211yescharacteristic
336C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #15689599C2semidirect
3. #15689463C2semidirect
5. #15689419C2semidirect
6. #15689408C2semidirect
7. #15689342C2semidirect
8. #15689277C2semidirect
10. #15689227C2semidirect
11. #15689224C2semidirect
12. Q16×Dic47C2semidirect
13. #15689214C2semidirect
14. #15689183C2semidirect
15. C47×#464C2semidirect
176. #464D47semidirect
184. C47#3121semidirect