Finite Group Databasebeta

← #20253363

Subgroups — #20253363

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689702C211yesmaximal, characteristic
2#15689603C211yesmaximal, characteristic, complemented
3#15689467C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689460C211yesmaximal, characteristic, complemented
6#15689459C211yesmaximal, characteristic, complemented
7#15689445C211yesmaximal, characteristic, complemented
8#15689435C211yesmaximal, characteristic, complemented
9#15689434C211yesmaximal, characteristic, complemented
10#15689162C211yesmaximal, characteristic, complemented
11#107×D47C211yesmaximal, characteristic, complemented
12#15689121C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094004C2211yescharacteristic
21#13094003C2211yescharacteristic
22#13094001—21no—
23#13093997—21no—
24#13093996—21no—
25#13093995—21no—
26#13093995C2211yescharacteristic
27C4×Dic94—21no—
28C4×D188—21no—
29(C22⋊D47)⋊C4—21no—
30(C22⋊D47)⋊C4—21no—
31#13093982C2211yescharacteristic
32#13093982C2211yescharacteristic
33C2×C4⋊Dic47C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C2×C22⋊D47D411yescharacteristic
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—22no—
69#10625352—22no—
70#10625350—22no—
71#10625350—22no—
72C2×D188D411yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×Dic94D411yescharacteristic
79C2×Dic94C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47C2×D411yescharacteristic
111C22×D47C2×D411yescharacteristic
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—22no—
123C22⋊D47—22no—
124C22⋊D47—42no—
125C22⋊D47—81no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131C2×Dic47—81no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—22no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—81no—
138C4×D47—81no—
139C4×D47—81no—
140C4×D47#4112yes—
141C4×D47#4112yes—
142Dic94—22no—
143Dic94—21no—
144Dic94—21no—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47#12312yes—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47#12312yes—
174#3098—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—81no—
177C2×C47C2×#12311yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57811yescharacteristic
180D47—22no—
181D47—41no—
182#537—471no—
183#520—471no—
184#485—471no—
185#485—471no—
186#484—471no—
187#484—471no—
188#482—471no—
189#482D4711yescharacteristic, complemented
190#480—471no—
191#480—471no—
192#428—471no—
193C2×#107—471no—
194#417—471no—
195#416—471no—
196#408—471no—
197C47#309811yescharacteristic, complemented, Sylow
198C2×#41—471no—
199C2×#41—471no—
200C2×M16—471no—
201C22×C8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—471no—
204C22⋊Q8—941no—
205#121—471no—
206#121—941no—
207#121—941no—
208#121—941no—
209#121C2×D4711yescharacteristic
210C4×Q8—941no—
211C4×D4—941no—
212C4×D4—941no—
213C4×D4—941no—
214#117—471no—
215#117—471no—
216#117C2×D4711yescharacteristic
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221#107—471no—
222#107—471no—
223#107—471no—
224#107—471no—
225#107—471no—
226#107C2×D4711yescharacteristic
227#106—471no—
228#106C2×D4711yescharacteristic
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#102—471no—
234#102—471no—
235#102C2×D4711yescharacteristic
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8—471no—
239C22⋊C8—471no—
240C22⋊C8C2×D4711yescharacteristic
241#41—942no—
242#41—942no—
243#41—942no—
244#41—942no—
245C2×Q8—471no—
246C2×Q8—471no—
247C2×D4—21no—
248C2×D4—471no—
249C2×D4—471no—
250C2×D4—471no—
251C2×D4—941no—
252C2×D4—941no—
253C2×D4C22×D4711yescharacteristic
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4C22×D4711yescharacteristic
262M16—942no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—942no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C42—21no—
288C42—941no—
289C42—941no—
290C23—21no—
291C23—471no—
292C23—471no—
293C23D4×D4711yescharacteristic
294Q8—942no—
295Q8—941no—
296Q8—941no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—942no—
301D4—942no—
302D4—942no—
303D4—3761no—
304D4—1882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—471no—
311C2×C4—472no—
312C2×C4—472no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4—3761no—
324C2×C4—1882no—
325C2×C4D4×D4711yescharacteristic
326C2×C4C23×D4711yescharacteristic
327C8—21no—
328C8—21no—
329C8—941no—
330C8—941no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—472no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22—941no—
342C22—941no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—472no—
349C4—941no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4#41×D4711yescharacteristic
356C2—41no—
357C2—81no—
358C2—942no—
359C2—1881no—
360C2#123×D4711yescharacteristic
361C2#1568992711yescharacteristic
362C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3098
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #15689603C2semidirect
3. #15689467C2semidirect
4. #15689464C2semidirect
5. #15689460C2semidirect
6. #15689459C2semidirect
7. #15689445C2semidirect
8. #15689435C2semidirect
9. #15689434C2semidirect
10. #15689162C2semidirect
11. #107×D47C2semidirect
12. #15689121C2semidirect
13. #15689116C2semidirect
14. #15689088C2semidirect
15. C47×#482C2semidirect
189. #482D47semidirect
197. C47#3098semidirect