Finite Group Databasebeta

← #20254792

Subgroups — #20254792

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689740C211yesmaximal, characteristic, complemented
2#15689726C211yesmaximal, characteristic, complemented
3#15689429C211yesmaximal, characteristic, complemented
4#15689425C211yesmaximal, characteristic, complemented
5#15689411C211yesmaximal, characteristic, complemented
6#15689402C211yesmaximal, characteristic, complemented
7#15689374C211yesmaximal, characteristic, complemented
8#15689367C211yesmaximal, characteristic, complemented
9#15689352C211yesmaximal, characteristic, complemented
10#15689337C211yesmaximal, characteristic, complemented
11#15689336C211yesmaximal, characteristic, complemented
12#15689322C211yesmaximal, characteristic, complemented
13#15689316C211yesmaximal, characteristic, complemented
14#15689149C211yesmaximal, characteristic, complemented
15C47×#466C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094020C2211yescharacteristic
22#13094017—21no—
23#13094015C2211yescharacteristic
24#13094011—21no—
25#13094011C2211yescharacteristic
26#13094008—21no—
27#13094006—21no—
28#13094005—21no—
29#13094003C2211yescharacteristic
30#13094001—21no—
31#13093998C2211yescharacteristic
32#13093996—21no—
33#13093995—21no—
34#13093989C2211yescharacteristic
35D4×Dic47C2211yescharacteristic
36D4×Dic47C2211yescharacteristic
37#13093986C2211yescharacteristic
38#13093983C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093944C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73D8×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47D411yescharacteristic
87C22⋊Dic47D411yescharacteristic
88#10625335—41no—
89#10625334—41no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47D411yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—41no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
117D4×C47—81no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—81no—
125C22⋊D47—81no—
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131C2×Dic47—81no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188—21no—
138C4×D47—81no—
139Dic94—21no—
140Dic94—21no—
141Dic94—81no—
142C8×C47—21no—
143C8×C47—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47H(5,𝔽2)11yescharacteristic
163C4×C472−1+411yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—21no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3257—471nomaximal, Sylow
172C2×C47—41no—
173C2×C47—81no—
174C2×C47—81no—
175C2×C47#53711yescharacteristic
176C2×C47#57611yescharacteristic
177C2×C47#57711yescharacteristic
178D47—81no—
179#542—471no—
180#540—471no—
181#479—471no—
182#478—471no—
183#476—471no—
184#474—471no—
185#469—471no—
186#468—471no—
187#466D4711yescharacteristic, complemented
188#465—471no—
189#463—471no—
190#463—471no—
191#460—471no—
192#459—471no—
193#424—471no—
194C47#325711yescharacteristic, complemented, Sylow
195C2×SD16—471no—
196C2×SD16—471no—
197C2×D8—471no—
198C2×D8C2×D4711yescharacteristic
199C2×M16—471no—
200C22×C8C2×D4711yescharacteristic
201C4⋊Q8—471no—
202#127—471no—
203#126—941no—
204#125—471no—
205#124—471no—
206#124—941no—
207#123—941no—
208#123—941no—
209#123—941no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—941no—
214#121—941no—
215#121C2×D4711yescharacteristic
216#121C2×D4711yescharacteristic
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221#117—471no—
222#107—471no—
223#107C2×D4711yescharacteristic
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229C4⋊C8—471no—
230#103—471no—
231#103—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237#102C2×D4711yescharacteristic
238C2×Q8—471no—
239C2×Q8—941no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—471no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4C22×D4711yescharacteristic
247C2×D4C22×D4711yescharacteristic
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252SD16—1881no—
253SD16—1881no—
254D8—41no—
255D8—1881no—
256M16—1881no—
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22×D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—471no—
285C42—471no—
286C42—941no—
287C23—21no—
288C23—21no—
289C23—941no—
290C23D4×D4711yescharacteristic
291Q8—941no—
292Q8—941no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—941no—
301D4—941no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—21no—
323C8—941no—
324C8—941no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—941no—
342C4—941no—
343C4—941no—
344C4—941no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4#1309406911yescharacteristic
349C4#1309407111yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—3761no—
354C2#1568970011yescharacteristic
355C2#1568992411yescharacteristic
356C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3257
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #15689740C2semidirect
2. #15689726C2semidirect
3. #15689429C2semidirect
4. #15689425C2semidirect
5. #15689411C2semidirect
6. #15689402C2semidirect
7. #15689374C2semidirect
8. #15689367C2semidirect
9. #15689352C2semidirect
10. #15689337C2semidirect
11. #15689336C2semidirect
12. #15689322C2semidirect
13. #15689316C2semidirect
14. #15689149C2semidirect
15. C47×#466C2semidirect
187. #466D47semidirect
194. C47#3257semidirect