Finite Group Databasebeta

← #20254491

Subgroups — #20254491

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#15689699C211yesmaximal, characteristic, complemented
2#15689518C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689475C211yesmaximal, characteristic, complemented
6#15689345C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689333C211yesmaximal, characteristic, complemented
9#15689328C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689278C211yesmaximal, characteristic, complemented
12#15689266C211yesmaximal, characteristic
13#15689261C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625335C2211yescharacteristic
23C2×#10625335C2211yescharacteristic
24C2×#10625336C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26#13094024C2211yescharacteristic
27#13094024C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094012C2211yescharacteristic
30#13094008—21no—
31#13094008—21no—
32#13094004—21no—
33#13094004—21no—
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67#10625350—41no—
68#10625350—41no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94—41no—
73C2×Dic94—41no—
74C2×Dic94C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C42×C47—21no—
92C42×C47C2311yescharacteristic
93C42×C47C2311yescharacteristic
94#10625337—41no—
95#10625337—41no—
96#10625337—41no—
97#10625336—41no—
98#10625335—41no—
99#10625335—41no—
100#10625335—41no—
101#10625334—41no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—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—81no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—81no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—81no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—42no—
140D188—21no—
141D188—21no—
142C4×D47—42no—
143Dic94—21no—
144Dic94—21no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—42no—
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#542D4711yescharacteristic, complemented
185#536—471no—
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×#41—471no—
201C22×Q8—471no—
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⋊Q8—471no—
212C4⋊Q8C2×D4711yescharacteristic
213#126—21no—
214#124—21no—
215#124—471no—
216#124—471no—
217#124C2×D4711yescharacteristic
218#123—21no—
219#123—941no—
220#123—941no—
221C22⋊Q8—21no—
222C22⋊Q8—941no—
223C22⋊Q8—941no—
224C22⋊Q8C2×D4711yescharacteristic
225#121C2×D4711yescharacteristic
226C4×Q8C2×D4711yescharacteristic
227C4×D4C2×D4711yescharacteristic
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—1881no—
244#41—1881no—
245C2×Q8—21no—
246C2×Q8—471no—
247C2×Q8—471no—
248C2×Q8—471no—
249C2×Q8—941no—
250C2×Q8—1881no—
251C2×Q8—1881no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—21no—
254C2×D4—471no—
255C2×D4—941no—
256C2×D4C22×D4711yescharacteristic
257C22×C4—21no—
258C22×C4—941no—
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—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4C22⋊D4711yescharacteristic
281C4⋊C4C22⋊D4711yescharacteristic
282C4⋊C4C22×D4711yescharacteristic
283C4⋊C4C22×D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4C22⋊D4711yescharacteristic
294C22⋊C4C22⋊D4711yescharacteristic
295C42—21no—
296C42C22×D4711yescharacteristic
297C42C22×D4711yescharacteristic
298C23—21no—
299C23—941no—
300C23C2×C22⋊D4711yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—81no—
304Q8—941no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308Q8—941no—
309Q8—941no—
310Q8—1882no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—941no—
315D4—941no—
316D4—1882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—1882no—
327C2×C4—1882no—
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#1309407011yescharacteristic
360C4#1309407011yescharacteristic
361C2—41no—
362C2—81no—
363C2—3761no—
364C2#1568968711yescharacteristic
365C2#1568993411yescharacteristic
366C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3225
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689699C2semidirect
2. #15689518C2semidirect
3. #15689505C2semidirect
4. #15689485C2semidirect
5. #15689475C2semidirect
6. #15689345C2semidirect
7. #15689338C2semidirect
8. #15689333C2semidirect
9. #15689328C2semidirect
10. #15689283C2semidirect
11. #15689278C2semidirect
13. #15689261C2semidirect
14. #15689184C2semidirect
15. C47×#542C2semidirect
184. #542D47semidirect
199. C47#3225semidirect