Finite Group Databasebeta

← #20255656

Subgroups — #20255656

Order 6016.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689813C211yesmaximal, characteristic, complemented
2#15689477C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689444C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11C4×#10625337C211yesmaximal, characteristic, complemented
12#15689201C211yesmaximal, characteristic, complemented
13#15689132C211yesmaximal, characteristic, complemented
14#15689124C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21#13094017—21no—
22#13094016C2211yescharacteristic
23#13094014—21no—
24#13094005—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28#13093983C2211yescharacteristic
29#13093980—21no—
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47C2211yescharacteristic
54#121×C47—21no—
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×Dic47—21no—
75C2×Dic94C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47D411yescharacteristic
85C22⋊C4×C47D411yescharacteristic
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91#10625337—22no—
92#10625337—41no—
93#10625335—41no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105#10625329—41no—
106#10625329—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—42no—
118Q8×C47#4112yes—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—41no—
122D4×C47—42no—
123D4×C47—42no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—42no—
143Dic94—21no—
144Dic94—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—22no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47H(5,𝔽2)11yescharacteristic
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#3327—471nomaximal, Sylow
173C2×C47—41no—
174C2×C47—41no—
175C2×C47—81no—
176C2×C47#54611yescharacteristic
177C2×C47#57511yescharacteristic
178C2×C47#57811yescharacteristic
179#552—471no—
180#548D4711yescharacteristic
181#488—471no—
182#484—471no—
183#482—471no—
184#479—471no—
185#470—471no—
186#468—471no—
187#464—471no—
188#452—471no—
189#451—471no—
190C4×Q16—471no—
191#436—471no—
192#419—471no—
193#417—471no—
194C47#332711yescharacteristic, complemented, Sylow
195C2×#41C2×D4711yescharacteristic
196C22×Q8C2×D4711yescharacteristic
197C2×Q16—471no—
198C2×Q16—471no—
199C2×SD16—471no—
200C2×M16—471no—
201C2×M16—471no—
202#126—941no—
203#125—471no—
204#125—941no—
205#124—21no—
206#124C2×D4711yescharacteristic
207#123—941no—
208C22⋊Q8—21no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8C2×D4711yescharacteristic
212#121—21no—
213#121C2×D4711yescharacteristic
214C4×Q8—471no—
215C4×Q8C2×D4711yescharacteristic
216C4×D4—21no—
217C4×D4C2×D4711yescharacteristic
218#117—471no—
219#117—941no—
220C2×C4⋊C4—471no—
221#107—471no—
222#107—471no—
223#106—471no—
224C4⋊C8—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235C22⋊C8—471no—
236C22⋊C8—471no—
237C4×C8—471no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—471no—
244C2×Q8C22×D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D4711yescharacteristic
249C2×D4C22×D4711yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—941no—
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255Q16—942no—
256Q16—1881no—
257SD16—1881no—
258M16—1881no—
259M16—1881no—
260C2×C8—471no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8—471no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
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⋊C4—941no—
284C22⋊C4C22⋊D4711yescharacteristic
285C22⋊C4C22⋊D4711yescharacteristic
286C42—21no—
287C42—941no—
288C42—941no—
289C42C22×D4711yescharacteristic
290C23—21no—
291C23C2×C22⋊D4711yescharacteristic
292C23C2×C22⋊D4711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—941no—
298Q8—941no—
299Q8#1062535212yes—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—1882no—
319C2×C4C2×C22⋊D4711yescharacteristic
320C2×C4C2×C22⋊D4711yescharacteristic
321C2×C4C2×C22⋊D4711yescharacteristic
322C2×C4C2×C22⋊D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C8—941no—
325C8—941no—
326C8—941no—
327C8—941no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4C2×#1062535211yescharacteristic
350C4#1309406911yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#1568976711yescharacteristic
355C2#1568992111yescharacteristic
356C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#548C2
socleC22×C47C22×D4
hypercenter#548D47
hypocenterC47#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
2. #15689477C2semidirect
3. #15689456C2semidirect
4. #15689444C2semidirect
5. #15689430C2semidirect
6. #15689379C2semidirect
7. #15689367C2semidirect
8. #15689342C2semidirect
9. #15689285C2semidirect
10. #15689279C2semidirect
11. C4×#10625337C2semidirect
12. #15689201C2semidirect
13. #15689132C2semidirect
14. #15689124C2semidirect
194. C47#3327semidirect