Finite Group Databasebeta

← #20254497

Subgroups — #20254497

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic, complemented
2#15689515C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689330C211yesmaximal, characteristic, complemented
9#15689325C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689279C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic
13#15689262C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#536C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24#13094024C2211yescharacteristic
25#13094019—21no—
26#13094012C2211yescharacteristic
27#13094010—21no—
28#13094006—21no—
29#13094003C2211yescharacteristic
30#13094002—21no—
31#13093998C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×D188C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50C4⋊Q8×C47C2211yescharacteristic
51C4⋊Q8×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#123×C47—21no—
55#123×C47—21no—
56C22⋊Q8×C47—21no—
57C22⋊Q8×C47—21no—
58#117×C47C2211yescharacteristic
59#41×C47—41no—
60#41×C47—41no—
61C2×Q8×C47—21no—
62C2×Q8×C47—41no—
63C2×Q8×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—21no—
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C2311yescharacteristic
72C2×C22⋊D47—21no—
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47D411yescharacteristic
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
91C22⋊Dic47—21no—
92#10625337—41no—
93#10625337—41no—
94#10625337—41no—
95#10625336—41no—
96#10625336—41no—
97#10625336—41no—
98#10625335—41no—
99#10625334—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C22×D47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47—21no—
122Q8×C47—21no—
123Q8×C47—42no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—42no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144D188—21no—
145D188—21no—
146C4×D47—81no—
147Dic94—21no—
148Dic94—21no—
149Dic94—81no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47H(5,𝔽2)11yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177#3225—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—81no—
180C2×C47#53511yescharacteristic
181C2×C47#57711yescharacteristic
182C2×C47#57811yescharacteristic
183D47—81no—
184#542—471no—
185#536D4711yescharacteristic, complemented
186#497—471no—
187#495—471no—
188#489—471no—
189#487—471no—
190#464—471no—
191#463—471no—
192#462—471no—
193#461—471no—
194#452—471no—
195#451—471no—
196#449—471no—
197#448—471no—
198#433—471no—
199C47#322511yescharacteristic, complemented, Sylow
200C2×#41C2×D4711yescharacteristic
201C22×Q8C2×D4711yescharacteristic
202C2×Q16—471no—
203C2×Q16—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×D8—471no—
210C4⋊Q8—471no—
211C4⋊Q8C2×D4711yescharacteristic
212C4⋊Q8C2×D4711yescharacteristic
213#126—941no—
214#124—471no—
215#124—941no—
216#124C2×D4711yescharacteristic
217#124C2×D4711yescharacteristic
218#123—21no—
219#123—21no—
220#123—941no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—471no—
224C22⋊Q8—941no—
225#121—471no—
226C4×Q8—471no—
227C4×D4—471no—
228#117C2×D4711yescharacteristic
229C4⋊C8—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#102—471no—
238#102—471no—
239C22⋊C8—471no—
240C22⋊C8—471no—
241#97—471no—
242C4×C8—471no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—471no—
249C2×Q8—941no—
250C2×Q8C22×D4711yescharacteristic
251C2×Q8C22×D4711yescharacteristic
252C2×Q8C22×D4711yescharacteristic
253C2×D4—21no—
254C2×D4—471no—
255C2×D4—941no—
256C2×D4C22×D4711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—941no—
260C22×C4C22×D4711yescharacteristic
261Q16—1881no—
262Q16—1881no—
263Q16—1881no—
264SD16—1881no—
265SD16—1881no—
266SD16—1881no—
267SD16—1881no—
268D8—1881no—
269C2×C8—471no—
270C2×C8—471no—
271C2×C8—471no—
272C2×C8—471no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22⋊D4711yescharacteristic
283C4⋊C4C22⋊D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4C22⋊D4711yescharacteristic
294C22⋊C4C22⋊D4711yescharacteristic
295C42—941no—
296C42C22×D4711yescharacteristic
297C42C22×D4711yescharacteristic
298C23—21no—
299C23—941no—
300C23C2×C22⋊D4711yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—941no—
315D4—941no—
316D4—3761no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—3761no—
328C2×C4C2×C22⋊D4711yescharacteristic
329C2×C4C2×C22⋊D4711yescharacteristic
330C2×C4C2×C22⋊D4711yescharacteristic
331C2×C4C2×C22⋊D4711yescharacteristic
332C2×C4C2×C22⋊D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—941no—
335C8—941no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22C22×C22⋊D4711yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4#1309406911yescharacteristic
360C4#1309406911yescharacteristic
361C2—41no—
362C2—81no—
363C2—3761no—
364C2#1568969011yescharacteristic
365C2#1568993111yescharacteristic
366C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3225
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689515C2semidirect
3. #15689505C2semidirect
4. #15689482C2semidirect
5. #15689473C2semidirect
6. #15689342C2semidirect
7. #15689335C2semidirect
8. #15689330C2semidirect
9. #15689325C2semidirect
10. #15689285C2semidirect
11. #15689279C2semidirect
13. #15689262C2semidirect
14. #15689184C2semidirect
15. C47×#536C2semidirect
185. #536D47semidirect
199. C47#3225semidirect