Finite Group Databasebeta

← #20253639

Subgroups — #20253639

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#15689731C211yesmaximal, characteristic, complemented
2#15689595C211yesmaximal, characteristic
3#15689466C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689327C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic
10#15689272C211yesmaximal, characteristic
11#15689225C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20#13094022C2211yescharacteristic, complemented
21#13094019—21no—
22#13094018—21no—
23#13094016—21no—
24#13094015C2211yescharacteristic, complemented
25#13094014—21no—
26#13094004C2211yescharacteristic
27#13094000C2211yescharacteristic
28C4×Dic94C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982C2211yescharacteristic
35#13093981C2211yescharacteristic
36C2×(C2×D47)⋊C4—21no—
37C22⋊C4×D47—21no—
38#13093958C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65D4×D47—22no—
66D4×D47—22no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94C2311yescharacteristic
72SD16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82#10625336—22no—
83#10625335—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
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—22no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47—24no—
111C22×D47—81no—
112C22×D47—81no—
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—21no—
117D4×C47#4112yes—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—24no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188#4112yes—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—81no—
138C4×D47—81no—
139Dic94—21no—
140Dic94—21no—
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#461—471no—
184#450—471no—
185#450—471no—
186#440—471no—
187#440D4711yescharacteristic, complemented
188C4×SD16—471no—
189C4×SD16—471no—
190#433—471no—
191C47#312311yescharacteristic, complemented, Sylow
192C22×D4—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×SD16—471no—
196C2×SD16C2×D4711yescharacteristic
197C4⋊Q8—471no—
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×Q8C2×D4711yescharacteristic, complemented
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#107C2×D4711yescharacteristic, complemented
219#106—471no—
220#106—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103C2×D4711yescharacteristic, complemented
227#102—471no—
228#102—471no—
229#102—471no—
230#102C2×D4711yescharacteristic
231C22⋊C8—471no—
232C22⋊C8—471no—
233#97C2×D4711yescharacteristic, complemented
234C4×C8—471no—
235C24—941no—
236C2×Q8—471no—
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—942no—
250SD16—942no—
251SD16—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
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—21no—
280C42—471no—
281C42—941no—
282C42—941no—
283C42C22×D4711yescharacteristic
284C23—21no—
285C23—471no—
286C23—944no—
287C23—941no—
288C23—3761no—
289C23—3761no—
290Q8—21no—
291Q8—21no—
292Q8—941no—
293Q8—941no—
294D4—21no—
295D4—472no—
296D4—944no—
297D4—941no—
298D4#1062535012yes—
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×#1062535011yescharacteristic
345C2—42no—
346C2—1881no—
347C2—1882no—
348C2#1568963211yescharacteristic
349C2#1568993211yescharacteristic
350C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689731C2semidirect
3. #15689466C2semidirect
4. #15689463C2semidirect
5. #15689426C2semidirect
6. #15689421C2semidirect
7. #15689327C2semidirect
8. #15689326C2semidirect
11. #15689225C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625335C2semidirect
14. #15689185C2semidirect
15. C47×#440C2semidirect
20. #13094022C22semidirect
24. #13094015C22semidirect
28. C4×Dic94C22semidirect
38. #13093958C22semidirect
39. #13093955C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
45. #13093947C22semidirect
51. C4×C47⋊C8C22semidirect
53. C4×Q8×C47C22semidirect
55. #107×C47C22semidirect
56. #103×C47C22semidirect
58. #97×C47C22semidirect
187. #440D47semidirect
191. C47#3123semidirect
206. C4×Q8C2×D47semidirect
218. #107C2×D47semidirect
226. #103C2×D47semidirect
233. #97C2×D47semidirect