Finite Group Databasebeta

← #20253594

Subgroups — #20253594

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689729C211yesmaximal, characteristic, complemented
2#15689605C211yesmaximal, characteristic, complemented
3#15689443C211yesmaximal, characteristic, complemented
4#15689438C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689323C211yesmaximal, characteristic, complemented
7#15689319C211yesmaximal, characteristic, complemented
8#15689271C211yesmaximal, characteristic, complemented
9#15689271C211yesmaximal, characteristic, complemented
10#15689234C211yesmaximal, characteristic, complemented
11#15689226C211yesmaximal, characteristic, complemented
12#15689208C211yesmaximal, characteristic, complemented
13#15689205C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094021C2211yescharacteristic
22#13094009—21no—
23#13094009—21no—
24#13093999—21no—
25#13093999—21no—
26#13093999C2211yescharacteristic
27#13093999C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29C4×D188—21no—
30C4×D188C2211yescharacteristic
31#13093986—21no—
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093981—21no—
36#13093981C2211yescharacteristic
37C4⋊C4×D47—21no—
38C4⋊C4×D47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60#10625354—22no—
61#10625354—22no—
62C2×D188—21no—
63C2×D188—21no—
64C2×D188—21no—
65C2×D188—21no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×D188C2311yescharacteristic
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87#10625336—22no—
88#10625336—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106D376—22no—
107D376—22no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—21no—
113Q8×C47#4112yes—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125D188—24no—
126D188—21no—
127D188—21no—
128D188—21no—
129D188—21no—
130D188—21no—
131D188—81no—
132D188—81no—
133D188—81no—
134D188—81no—
135D188#4112yes—
136C4×D47—24no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—81no—
140C4×D47—81no—
141C4×D47—81no—
142C4×D47—81no—
143C4×D47—81no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—22no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—22no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47C2×#4111yescharacteristic
168C4×C47C2×#4111yescharacteristic
169Dic47—21no—
170Dic47—21no—
171Dic47—21no—
172Dic47—41no—
173#3119—471nomaximal, Sylow
174C2×C47#52511yescharacteristic
175C2×C47#57611yescharacteristic
176C2×C47#57711yescharacteristic
177D47—41no—
178D47—42no—
179D47—81no—
180D47—81no—
181#540—471no—
182#520—471no—
183#481—471no—
184#480—471no—
185#479D4711yescharacteristic, complemented
186#478—471no—
187#460—471no—
188#459—471no—
189#449—471no—
190#449—471no—
191#442—471no—
192#440—471no—
193C4×SD16—471no—
194C4×D8—471no—
195#433—471no—
196C47#311911yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C2×SD16—471no—
199C2×SD16—471no—
200C2×D8—471no—
201C2×D8—471no—
202#127—471no—
203#125C2×D4711yescharacteristic
204#123—941no—
205#123—941no—
206#121—471no—
207#121—471no—
208#121—941no—
209#121—941no—
210C4×Q8—471no—
211C4×Q8C2×D4711yescharacteristic
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—941no—
217C4×D4—941no—
218#117—471no—
219#117—941no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222#107—471no—
223#107C2×D4711yescharacteristic
224#106—471no—
225#106C2×D4711yescharacteristic
226C4⋊C8—471no—
227C4⋊C8C2×D4711yescharacteristic
228#103C2×D4711yescharacteristic
229#103C2×D4711yescharacteristic
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236C22⋊C8—471no—
237C22⋊C8—471no—
238#97—471no—
239C4×C8—471no—
240#41—942no—
241#41—942no—
242C2×Q8C22×D4711yescharacteristic
243C2×D4—471no—
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—941no—
251C22×C4—471no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258SD16—942no—
259SD16—942no—
260D8—942no—
261D8—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4C22×D4711yescharacteristic
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—471no—
278C22⋊C4—471no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C42—21no—
286C42—471no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C23—471no—
290C23—941no—
291C23—941no—
292C23—941no—
293Q8—21no—
294Q8#1062535412yes—
295D4—472no—
296D4—944no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—941no—
301D4—941no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305D4—3761no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—944no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4D4×D4711yescharacteristic
323C2×C4D4×D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—21no—
326C8—21no—
327C8—941no—
328C8—941no—
329C22—942no—
330C22—941no—
331C22—941no—
332C22—941no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22C2×D4×D4711yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—941no—
349C4—941no—
350C4—941no—
351C4—1881no—
352C4#41×D4711yescharacteristic
353C4C2×#1062535411yescharacteristic
354C2—3761no—
355C2—3761no—
356C2—1881no—
357C2—1882no—
358C2#1568963611yescharacteristic
359C2#1568992511yescharacteristic
360C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #15689729C2semidirect
2. #15689605C2semidirect
3. #15689443C2semidirect
4. #15689438C2semidirect
5. #15689420C2semidirect
6. #15689323C2semidirect
7. #15689319C2semidirect
8. #15689271C2semidirect
9. #15689271C2semidirect
10. #15689234C2semidirect
11. #15689226C2semidirect
12. #15689208C2semidirect
13. #15689205C2semidirect
14. #15689183C2semidirect
15. C47×#479C2semidirect
185. #479D47semidirect
196. C47#3119semidirect