Finite Group Databasebeta

← #20255989

Subgroups — #20255989

Order 6016.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689825C211yesmaximal, characteristic, complemented
2#15689820C211yesmaximal, characteristic, complemented
3#15689523C211yesmaximal, characteristic, complemented
4#15689446C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689434C211yesmaximal, characteristic, complemented
8#15689425C211yesmaximal, characteristic, complemented
9#15689421C211yesmaximal, characteristic, complemented
10#15689373C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#469C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17#13094017—21no—
18#13094017—21no—
19#13094015C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094008—21no—
22#13094005—21no—
23#13093996—21no—
24#13093995—21no—
25#13093995C2211yescharacteristic
26#13093995C2211yescharacteristic
27D4×Dic47—21no—
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30C4×C22⋊D47C2211yescharacteristic
31(C22⋊D47)⋊C4—21no—
32#13093983C2211yescharacteristic
33#13093982C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47D411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C2×C4×D47—21no—
71C2×C4×D47C2311yescharacteristic
72D8×C47—22no—
73M16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—41no—
122C22⋊D47—42no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—81no—
137C8×C47—21no—
138C8×C47#4112yes—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47C2×#4111yescharacteristic
158C4×C472−1+411yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3355—471nomaximal, Sylow
167C2×C47—41no—
168C2×C47—81no—
169C2×C47—81no—
170C2×C47#54711yescharacteristic
171C2×C47#57511yescharacteristic
172C2×C47#57611yescharacteristic
173D47—41no—
174#553—471no—
175#553—471no—
176#499—471no—
177#482—471no—
178#482—471no—
179#480—471no—
180#480—471no—
181#478—471no—
182#478—471no—
183#469—471no—
184#469D4711yescharacteristic, complemented
185C4×D8—471no—
186#436—471no—
187#428—471no—
188#428—471no—
189C47#335511yescharacteristic, complemented, Sylow
190C2×D8C2×D4711yescharacteristic
191C2×M16—471no—
192C2×M16C2×D4711yescharacteristic
193#126—941no—
194#126—941no—
195#125—471no—
196#125—471no—
197#123—941no—
198#123—941no—
199#121—471no—
200#121—471no—
201#121—941no—
202#121—941no—
203#121C2×D4711yescharacteristic
204#121C2×D4711yescharacteristic
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210#117—471no—
211#117—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#107—471no—
218#107—471no—
219#106—471no—
220#106—471no—
221#106—471no—
222#106C2×D4711yescharacteristic
223C4⋊C8—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102C2×D4711yescharacteristic
229#102C2×D4711yescharacteristic
230C22⋊C8—471no—
231C22⋊C8—471no—
232C4×C8—471no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4—941no—
238C2×D4C22×D4711yescharacteristic
239C2×D4C22×D4711yescharacteristic
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4C22×D4711yescharacteristic
246D8—22no—
247M16—22no—
248M16—942no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—471no—
269C22⋊C4—471no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—471no—
277C42—941no—
278C42—941no—
279C23—21no—
280C23—21no—
281C23—471no—
282C23D4×D4711yescharacteristic
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—3761no—
290D4—1881no—
291D4—1882no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—3761no—
306C2×C4—3761no—
307C2×C4—3761no—
308C2×C4—3761no—
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—941no—
313C8—941no—
314C8#1062535212yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—941no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4C2×#1062535211yescharacteristic
339C4#1309407111yescharacteristic
340C2—41no—
341C2—81no—
342C2—81no—
343C2—1881no—
344C2#1568977311yescharacteristic
345C2#1568991911yescharacteristic
346C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3355
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #15689825C2semidirect
2. #15689820C2semidirect
3. #15689523C2semidirect
4. #15689446C2semidirect
5. #15689444C2semidirect
6. #15689435C2semidirect
7. #15689434C2semidirect
8. #15689425C2semidirect
9. #15689421C2semidirect
10. #15689373C2semidirect
11. D8×Dic47C2semidirect
12. #15689199C2semidirect
13. #15689165C2semidirect
14. #15689162C2semidirect
15. C47×#469C2semidirect
184. #469D47semidirect
189. C47#3355semidirect