Finite Group Databasebeta

← #20256454

Subgroups — #20256454

Order 6016.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689858C211yesmaximal, characteristic, complemented
2#15689515C211yesmaximal, characteristic, complemented
3#15689513C211yesmaximal, characteristic
4#15689505C211yesmaximal, characteristic, complemented
5#15689345C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689325C211yesmaximal, characteristic, complemented
10#15689323C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic, complemented
13#15689228C211yesmaximal, characteristic, complemented
14C4×#10625336C211yesmaximal, characteristic, complemented
15C47×#556C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25#13094021C2211yescharacteristic
26#13094013—21no—
27#13094012C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094009—21no—
30#13094009—21no—
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093986—21no—
35#13093955C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#124×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53C22⋊Q8×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47—21no—
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×D188—21no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×Dic94C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C42×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C42×C47C2311yescharacteristic
88C42×C47C2311yescharacteristic
89#10625337—22no—
90#10625337—41no—
91#10625336—22no—
92#10625336—41no—
93#10625336—41no—
94#10625336—41no—
95#10625335—41no—
96#10625334—22no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—41no—
119D4×C47—21no—
120D4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—42no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C2×Dic47—21no—
133C2×Dic47—21no—
134D188—21no—
135D188—21no—
136D188—21no—
137D188—21no—
138D188—42no—
139D188—81no—
140C4×D47—81no—
141C4×D47—81no—
142Dic94—21no—
143Dic94—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8#4112yes—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47C2×#4111yescharacteristic
168C4×C47H(5,𝔽2)11yescharacteristic
169Dic47—41no—
170Dic47—41no—
171#3401—471nomaximal, Sylow
172C2×C47—81no—
173C2×C47#55011yescharacteristic
174C2×C47#57511yescharacteristic
175C2×C47#57711yescharacteristic
176D47—81no—
177D47—81no—
178#559—471no—
179#556D4711yescharacteristic, complemented
180#497—471no—
181#496—471no—
182#495—471no—
183#464—471no—
184#464—471no—
185#463—471no—
186#463—471no—
187#461—471no—
188#460—471no—
189#446—471no—
190#442—471no—
191#441—471no—
192C4×SD16—471no—
193C47#340111yescharacteristic, complemented, Sylow
194C2×Q16—471no—
195C2×Q16—471no—
196C2×SD16—471no—
197C2×SD16—471no—
198C2×SD16—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8C2×D4711yescharacteristic
204#127—471no—
205#126—21no—
206#126—21no—
207#124—471no—
208#124—471no—
209#124—941no—
210#124C2×D4711yescharacteristic
211#124C2×D4711yescharacteristic
212#123—941no—
213#123—941no—
214C22⋊Q8—21no—
215C4×Q8—471no—
216C4×Q8C2×D4711yescharacteristic
217C4×Q8C2×D4711yescharacteristic
218C4×Q8C2×D4711yescharacteristic
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—941no—
222C4×D4C2×D4711yescharacteristic
223#117—21no—
224#106—471no—
225C4⋊C8—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#97—471no—
235#97—471no—
236C4×C8—471no—
237C2×Q8—471no—
238C2×Q8C22⋊D4711yescharacteristic
239C2×Q8C22×D4711yescharacteristic
240C2×Q8C22×D4711yescharacteristic
241C2×D4—471no—
242C2×D4—471no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C22×C4—21no—
247C22×C4—941no—
248C22×C4—941no—
249Q16—942no—
250Q16—1881no—
251SD16—942no—
252SD16—1881no—
253SD16—1881no—
254SD16—1881no—
255SD16—1881no—
256D8—942no—
257D8—1881no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—471no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4C22⋊D4711yescharacteristic
269C4⋊C4C22⋊D4711yescharacteristic
270C4⋊C4C22⋊D4711yescharacteristic
271C4⋊C4C22×D4711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C42—21no—
284C42—21no—
285C42—941no—
286C42C22×D4711yescharacteristic
287C42C22×D4711yescharacteristic
288C42C22×D4711yescharacteristic
289C23—21no—
290C23—941no—
291C23—941no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—941no—
298Q8—941no—
299D4—21no—
300D4—21no—
301D4—941no—
302D4—941no—
303D4—941no—
304D4—941no—
305D4—3761no—
306D4—1882no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—3761no—
314C2×C4—3761no—
315C2×C4C2×C22⋊D4711yescharacteristic
316C2×C4C2×C22⋊D4711yescharacteristic
317C2×C4C2×C22⋊D4711yescharacteristic
318C2×C4C2×C22⋊D4711yescharacteristic
319C2×C4C2×C22⋊D4711yescharacteristic
320C2×C4C2×C22⋊D4711yescharacteristic
321C2×C4C23×D4711yescharacteristic
322C8—472no—
323C8—941no—
324C8—941no—
325C8—941no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22C22×C22⋊D4711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—1881no—
346C4—1881no—
347C4#41×D4711yescharacteristic
348C4#1309407011yescharacteristic
349C2—81no—
350C2—3761no—
351C2—3761no—
352C2#1568979211yescharacteristic
353C2#1568992111yescharacteristic
354C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3401
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689515C2semidirect
4. #15689505C2semidirect
5. #15689345C2semidirect
6. #15689342C2semidirect
7. #15689338C2semidirect
8. #15689335C2semidirect
9. #15689325C2semidirect
10. #15689323C2semidirect
11. #15689254C2semidirect
12. #15689233C2semidirect
13. #15689228C2semidirect
14. C4×#10625336C2semidirect
15. C47×#556C2semidirect
179. #556D47semidirect
193. C47#3401semidirect