Finite Group Databasebeta

← #20253638

Subgroups — #20253638

Order 6016.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689734C211yesmaximal, characteristic, complemented
2#15689595C211yesmaximal, characteristic
3#15689463C211yesmaximal, characteristic, complemented
4#15689462C211yesmaximal, characteristic, complemented
5#15689424C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689325C211yesmaximal, characteristic, complemented
8#15689272C211yesmaximal, characteristic
9#15689272C211yesmaximal, characteristic
10#15689226C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#461C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19#13094019—21no—
20#13094019—21no—
21#13094016C2211yescharacteristic, complemented
22#13094014—21no—
23#13094014—21no—
24#13094000C2211yescharacteristic
25#13094000C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic, complemented
27Q8×Dic47C2211yescharacteristic, complemented
28C4×D188C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30#13093986C2211yescharacteristic
31C4×C22⋊D47—21no—
32(C22⋊D47)⋊C4—21no—
33#13093982C2211yescharacteristic
34#13093981C2211yescharacteristic
35C2×(C2×D47)⋊C4—21no—
36C22⋊C4×D47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66D4×D47—22no—
67D4×D47—22no—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47C2311yescharacteristic
72SD16×C47—22no—
73SD16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82#10625336—22no—
83#10625336—22no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C22×D47—21no—
110C22×D47—24no—
111C22×D47—81no—
112C22×D47—81no—
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118D4×C47—21no—
119D4×C47#4112yes—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—81no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—24no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—81no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—21no—
136D188#4112yes—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—81no—
140C4×D47—81no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—22no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—84no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—21no—
164Dic47—21no—
165Dic47—21no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3123—471nomaximal, Sylow
170C2×C47—42no—
171C2×C47#52511yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57711yescharacteristic
174D47—41no—
175D47—42no—
176#541—471no—
177#518—471no—
178#485—471no—
179#485—471no—
180#478—471no—
181#478—471no—
182#461—471no—
183#461D4711yescharacteristic, complemented
184#450—471no—
185#450—471no—
186#440—471no—
187#440—471no—
188C4×SD16—471no—
189C4×SD16—471no—
190#433—471no—
191C47#312311yescharacteristic, complemented, Sylow
192C22×D4—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×SD16C2×D4711yescharacteristic
196C2×SD16C2×D4711yescharacteristic
197C4⋊Q8C2×D4711yescharacteristic, complemented
198#126—941no—
199#126—941no—
200#125—471no—
201#125—941no—
202#125—941no—
203C22⋊Q8—471no—
204C22⋊Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—471no—
210C4×D4—941no—
211C4×D4—941no—
212C4×D4C2×D4711yescharacteristic
213#117—471no—
214#117—471no—
215C2×C22⋊C4—941no—
216C2×C22⋊C4—941no—
217#107—471no—
218#107—471no—
219#106—471no—
220#106—471no—
221C4⋊C8—471no—
222C4⋊C8C2×D4711yescharacteristic, complemented
223#103—471no—
224#103—471no—
225#103C2×D4711yescharacteristic, complemented
226#103C2×D4711yescharacteristic, complemented
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231C22⋊C8—471no—
232C22⋊C8—471no—
233#97—471no—
234C4×C8—471no—
235C24—941no—
236C2×Q8C22×D4711yescharacteristic
237C2×Q8C22×D4711yescharacteristic
238C2×D4—471no—
239C2×D4—941no—
240C2×D4—942no—
241C2×D4—942no—
242C2×D4C22×D4711yescharacteristic
243C22×C4—21no—
244C22×C4—471no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248SD16—22no—
249SD16—22no—
250SD16—942no—
251SD16—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C42—471no—
280C42—941no—
281C42—941no—
282C42—941no—
283C42C22×D4711yescharacteristic
284C23—21no—
285C23—471no—
286C23—944no—
287C23—941no—
288C23—3761no—
289C23—3761no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—472no—
296D4—944no—
297D4—941no—
298D4#1062535212yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—471no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—3761no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4D4×D4711yescharacteristic
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—941no—
320C8—941no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—941no—
325C22—942no—
326C22—941no—
327C22—941no—
328C22—3764no—
329C22—1881no—
330C22—1881no—
331C22C2×D4×D4711yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—941no—
338C4—941no—
339C4—941no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4#41×D4711yescharacteristic
344C4C2×#1062535211yescharacteristic
345C2—42no—
346C2—1881no—
347C2—1882no—
348C2#1568963311yescharacteristic
349C2#1568992911yescharacteristic
350C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689734C2semidirect
3. #15689463C2semidirect
4. #15689462C2semidirect
5. #15689424C2semidirect
6. #15689423C2semidirect
7. #15689325C2semidirect
10. #15689226C2semidirect
11. #15689224C2semidirect
12. SD16×Dic47C2semidirect
13. #15689208C2semidirect
14. #15689183C2semidirect
15. C47×#461C2semidirect
21. #13094016C22semidirect
26. Q8×Dic47C22semidirect
27. Q8×Dic47C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093948C22semidirect
43. #13093948C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
54. C4⋊Q8×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
58. #103×C47C22semidirect
183. #461D47semidirect
191. C47#3123semidirect
197. C4⋊Q8C2×D47semidirect
222. C4⋊C8C2×D47semidirect
225. #103C2×D47semidirect
226. #103C2×D47semidirect