Finite Group Databasebeta

← #20253581

Subgroups — #20253581

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#15689603C211yesmaximal, characteristic, complemented
2#15689439C211yesmaximal, characteristic, complemented
3#15689434C211yesmaximal, characteristic, complemented
4#15689427C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689320C211yesmaximal, characteristic, complemented
7#15689315C211yesmaximal, characteristic, complemented
8#15689266C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689233C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12C4×#10625335C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#540C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25(C22⋊D47)⋊C4—21no—
26(C22⋊D47)⋊C4—21no—
27#13093982—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29C4⋊C4×D47—21no—
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#127×C47C2211yescharacteristic
49#125×C47C2211yescharacteristic
50#123×C47—21no—
51#123×C47—21no—
52#121×C47—21no—
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C22×Dic47—21no—
70#10625350—22no—
71#10625350—22no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91#10625335—22no—
92#10625335—22no—
93#10625334—22no—
94#10625334—22no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
117D4×C47—81no—
118D4×C47—81no—
119D4×C47—81no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—24no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—81no—
137D188—21no—
138D188#4112yes—
139C4×D47—24no—
140C4×D47—81no—
141C4×D47—81no—
142Dic94—21no—
143Dic94#4112yes—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—22no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C2×#4111yescharacteristic
169C4×C47C2×#4111yescharacteristic
170Dic47—22no—
171Dic47—41no—
172Dic47—41no—
173#3119—471nomaximal, Sylow
174C2×C47—41no—
175C2×C47—81no—
176C2×C47—81no—
177C2×C47#52511yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57711yescharacteristic
180D47—42no—
181#540D4711yescharacteristic, complemented
182#520—471no—
183#481—471no—
184#480—471no—
185#479—471no—
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#127C2×D4711yescharacteristic
203#125C2×D4711yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D4711yescharacteristic
209#121C2×D4711yescharacteristic
210C4×Q8—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—941no—
215C4×D4—941no—
216C4×D4C2×D4711yescharacteristic
217C4×D4C2×D4711yescharacteristic
218#117—941no—
219#117C2×D4711yescharacteristic
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228#103—471no—
229#103—471no—
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×Q8—471no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—942no—
259SD16—942no—
260D8—942no—
261D8—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22⋊D4711yescharacteristic
274C4⋊C4C22⋊D4711yescharacteristic
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4C22⋊D4711yescharacteristic
284C22⋊C4C22⋊D4711yescharacteristic
285C42—941no—
286C42—941no—
287C42C22×D4711yescharacteristic
288C42C22×D4711yescharacteristic
289C23—21no—
290C23—21no—
291C23—941no—
292C23C2×C22⋊D4711yescharacteristic
293Q8—472no—
294Q8—941no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—472no—
304D4—944no—
305D4—941no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—944no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4C2×C22⋊D4711yescharacteristic
320C2×C4C2×C22⋊D4711yescharacteristic
321C2×C4C2×C22⋊D4711yescharacteristic
322C2×C4C2×C22⋊D4711yescharacteristic
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—941no—
326C8—941no—
327C8—941no—
328C8—941no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—942no—
339C22—1881no—
340C22—1881no—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—942no—
350C4—1881no—
351C4—1881no—
352C4#41×D4711yescharacteristic
353C4#41×D4711yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—1882no—
358C2#1568963011yescharacteristic
359C2#1568992611yescharacteristic
360C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#540C2
socleC22×C47C22×D4
hypercenter#540D47
hypocenterC47#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #15689603C2semidirect
2. #15689439C2semidirect
3. #15689434C2semidirect
4. #15689427C2semidirect
5. #15689420C2semidirect
6. #15689320C2semidirect
7. #15689315C2semidirect
8. #15689266C2semidirect
9. #15689266C2semidirect
10. #15689233C2semidirect
11. #15689223C2semidirect
12. C4×#10625335C2semidirect
13. C4×#10625334C2semidirect
14. #15689184C2semidirect
15. C47×#540C2semidirect
181. #540D47semidirect
196. C47#3119semidirect