Finite Group Databasebeta

← #20255589

Subgroups — #20255589

Order 6016.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic, complemented
2#15689477C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689434C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689257C211yesmaximal, characteristic, complemented
11C4×#10625334C211yesmaximal, characteristic, complemented
12#15689201C211yesmaximal, characteristic, complemented
13#15689128C211yesmaximal, characteristic, complemented
14#15689124C211yesmaximal, characteristic, complemented
15C47×#546C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic, complemented
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C2×#10625329C2211yescharacteristic, complemented
21#13094019—21no—
22#13094016C2211yescharacteristic, complemented
23#13094006—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic, complemented
26#13093996—21no—
27C4×D188C2211yescharacteristic, complemented
28(C22⋊D47)⋊C4—21no—
29#13093983C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093957C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093948C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic, complemented
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50#124×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#120×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58C2×C22⋊C4×C47—21no—
59C24×C47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—41no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C22×Dic47—21no—
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47D411yescharacteristic
89C22⋊C4×C47D411yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625336—41no—
93#10625334—22no—
94#10625334—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—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×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C23×C47C2×D411yescharacteristic
118C22×D47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—41no—
125D4×C47—42no—
126D4×C47—42no—
127D4×C47—81no—
128D4×C47#4112yes—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—42no—
136C2×C4×C47—81no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—81no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—81no—
148D188—21no—
149D188—21no—
150C4×D47—81no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—22no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—84no—
168C22×C47C22×D411yescharacteristic
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47C2×#4111yescharacteristic
179C4×C47H(5,𝔽2)11yescharacteristic
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3322—471nomaximal, Sylow
184C2×C47—41no—
185C2×C47—41no—
186C2×C47—42no—
187C2×C47—81no—
188C2×C47#54611yescharacteristic
189C2×C47#57511yescharacteristic
190C2×C47#57611yescharacteristic
191D47—81no—
192#553—471no—
193#546D4711yescharacteristic, complemented
194#488—471no—
195#485—471no—
196#480—471no—
197#478—471no—
198#469—471no—
199#468—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203C4×D8—471no—
204#436—471no—
205#418—471no—
206#417—471no—
207C47#332211yescharacteristic, complemented, Sylow
208C2×#41C2×D4711yescharacteristic
209C22×D4C2×D4711yescharacteristic
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C2×M16—471no—
214C2×M16—471no—
215#126—941no—
216#125—471no—
217#124C2×D4711yescharacteristic
218#123—21no—
219#123—941no—
220C22⋊Q8C2×D4711yescharacteristic
221#121—21no—
222#121—471no—
223#121—471no—
224#121—941no—
225#121C2×D4711yescharacteristic
226#120—21no—
227C4×D4—471no—
228C4×D4—941no—
229C4×D4C2×D4711yescharacteristic
230C4×D4C2×D4711yescharacteristic
231#117—471no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—21no—
234#107—471no—
235#107—471no—
236#106—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248C22⋊C8—471no—
249C22⋊C8—471no—
250C4×C8—471no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—471no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4C22⋊D4711yescharacteristic
264C2×D4C22×D4711yescharacteristic
265C2×D4C22×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272SD16—1881no—
273D8—942no—
274D8—1881no—
275M16—1881no—
276M16—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—471no—
281C4⋊C4—21no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4C22⋊D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4C22⋊D4711yescharacteristic
300C22⋊C4C22⋊D4711yescharacteristic
301C42—941no—
302C42C22×D4711yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—941no—
309C23C2×C22⋊D4711yescharacteristic
310C23C2×C22⋊D4711yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—941no—
321D4—941no—
322D4—3761no—
323D4—1882no—
324D4#1062535212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—3761no—
337C2×C4—3761no—
338C2×C4C2×C22⋊D4711yescharacteristic
339C2×C4C2×C22⋊D4711yescharacteristic
340C2×C4C2×C22⋊D4711yescharacteristic
341C2×C4C2×C22⋊D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—941no—
344C8—941no—
345C8—941no—
346C8—941no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C22×C22⋊D4711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—1881no—
371C4—1881no—
372C4—1881no—
373C4C2×#1062535211yescharacteristic
374C4#1309406911yescharacteristic
375C2—41no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—3761no—
380C2#1568976711yescharacteristic
381C2#1568992111yescharacteristic
382C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#546C2
socleC22×C47C22×D4
hypercenter#546D47
hypocenterC47#3322
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689477C2semidirect
3. #15689461C2semidirect
4. #15689434C2semidirect
5. #15689423C2semidirect
6. #15689374C2semidirect
7. #15689371C2semidirect
8. #15689335C2semidirect
9. #15689268C2semidirect
10. #15689257C2semidirect
11. C4×#10625334C2semidirect
12. #15689201C2semidirect
13. #15689128C2semidirect
14. #15689124C2semidirect
15. C47×#546C2semidirect
16. C2×#10625336C22semidirect
20. C2×#10625329C22semidirect
22. #13094016C22semidirect
25. #13093998C22semidirect
27. C4×D188C22semidirect
30. C2×C4⋊Dic47C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093948C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
44. #13093944C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. C4×C47⋊C8C22semidirect
193. #546D47semidirect
207. C47#3322semidirect