Finite Group Databasebeta

← #18004798

Subgroups — #18004798

Order 4736.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558136C211yesmaximal, characteristic, complemented
2#14558014C211yesmaximal, characteristic, complemented
3#14557851C211yesmaximal, characteristic, complemented
4#14557839C211yesmaximal, characteristic, complemented
5#14557836C211yesmaximal, characteristic, complemented
6#14557732C211yesmaximal, characteristic, complemented
7#14557727C211yesmaximal, characteristic, complemented
8#14557680C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557642C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13#14557615C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#480C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924532C2211yescharacteristic
22#11924527C2211yescharacteristic
23#11924520—21no—
24#11924518—21no—
25#11924510C2211yescharacteristic
26#11924508—21no—
27#11924507—21no—
28#11924501C2211yescharacteristic
29#11924501C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31#11924498C2211yescharacteristic
32#11924498C2211yescharacteristic
33#11924498C2211yescharacteristic
34C4×C22⋊D37—21no—
35C4×C22⋊D37—21no—
36#11924495C2211yescharacteristic
37#11924494—21no—
38C4⋊C4×D37—21no—
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#121×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68#10596962—22no—
69#10596962—22no—
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37D411yescharacteristic
86C22⋊Dic37D411yescharacteristic
87#10596940—22no—
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37D411yescharacteristic
95C4⋊Dic37D411yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107#10596930—22no—
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111C22×D37—21no—
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—81no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—81no—
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2411yescharacteristic
123C22⋊D37—24no—
124C22⋊D37—81no—
125C22⋊D37—81no—
126C22⋊D37—81no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—81no—
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134D148—21no—
135D148—21no—
136D148—21no—
137D148#4112yes—
138C4×D37—24no—
139C4×D37—81no—
140C4×D37—81no—
141C4×D37—81no—
142Dic74—21no—
143Dic74#4112yes—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C2×D37—22no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C4×C37—21no—
162C4×C37—41no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37C2×#4111yescharacteristic
166C4×C37C2×#4111yescharacteristic
167Dic37—22no—
168Dic37—21no—
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—41no—
173#3119—371nomaximal, Sylow
174C2×C37—41no—
175C2×C37—81no—
176C2×C37#52511yescharacteristic
177C2×C37#57611yescharacteristic
178C2×C37#57711yescharacteristic
179D37—42no—
180D37—81no—
181#540—371no—
182#520—371no—
183#481—371no—
184#480D3711yescharacteristic, complemented
185#479—371no—
186#478—371no—
187#460—371no—
188#459—371no—
189#449—371no—
190#449—371no—
191#442—371no—
192#440—371no—
193C4×SD16—371no—
194C4×D8—371no—
195#433—371no—
196C37#311911yescharacteristic, complemented, Sylow
197C2×#41—371no—
198C2×SD16—371no—
199C2×SD16—371no—
200C2×D8—371no—
201C2×D8—371no—
202#127—371no—
203#125—371no—
204#123—741no—
205#123—741no—
206#121—371no—
207#121—741no—
208#121—741no—
209#121C2×D3711yescharacteristic
210C4×Q8—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—741no—
217C4×D4—741no—
218#117—371no—
219#117—741no—
220C2×C4⋊C4—741no—
221C2×C4⋊C4C2×D3711yescharacteristic
222#107C2×D3711yescharacteristic
223#107C2×D3711yescharacteristic
224#106—371no—
225#106—371no—
226C4⋊C8—371no—
227C4⋊C8—371no—
228#103—371no—
229#103—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102C2×D3711yescharacteristic
235#102C2×D3711yescharacteristic
236C22⋊C8—371no—
237C22⋊C8C2×D3711yescharacteristic
238#97—371no—
239C4×C8—371no—
240#41—742no—
241#41—742no—
242C2×Q8—371no—
243C2×D4—21no—
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4C22×D3711yescharacteristic
258SD16—742no—
259SD16—742no—
260D8—742no—
261D8—742no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8C22×D3711yescharacteristic
265C2×C8C22×D3711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4C22×D3711yescharacteristic
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—371no—
279C22⋊C4—371no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C42—371no—
286C42—371no—
287C42—741no—
288C42—741no—
289C23—21no—
290C23—741no—
291C23—741no—
292C23D4×D3711yescharacteristic
293Q8—372no—
294Q8—741no—
295D4—21no—
296D4—21no—
297D4—81no—
298D4—372no—
299D4—2961no—
300D4—2961no—
301D4—2961no—
302D4—744no—
303D4—741no—
304D4—741no—
305D4—741no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—371no—
315C2×C4—371no—
316C2×C4—2961no—
317C2×C4—2961no—
318C2×C4—2961no—
319C2×C4—2961no—
320C2×C4—744no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4D4×D3711yescharacteristic
324C2×C4C23×D3711yescharacteristic
325C8—21no—
326C8—21no—
327C8—741no—
328C8—741no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—742no—
336C22—1481no—
337C22—1481no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22C2×D4×D3711yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—742no—
347C4—741no—
348C4—741no—
349C4—741no—
350C4—741no—
351C4—1481no—
352C4#41×D3711yescharacteristic
353C4#41×D3711yescharacteristic
354C2—41no—
355C2—81no—
356C2—2961no—
357C2—1482no—
358C2#1455804111yescharacteristic
359C2#1455833411yescharacteristic
360C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#480C2
socleC22×C37C22×D4
hypercenter#480D37
hypocenterC37#3119
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14558136C2semidirect
2. #14558014C2semidirect
3. #14557851C2semidirect
4. #14557839C2semidirect
5. #14557836C2semidirect
6. #14557732C2semidirect
7. #14557727C2semidirect
8. #14557680C2semidirect
9. #14557676C2semidirect
10. #14557642C2semidirect
11. #14557632C2semidirect
12. #14557624C2semidirect
13. #14557615C2semidirect
14. #14557591C2semidirect
15. C37×#480C2semidirect
184. #480D37semidirect
196. C37#3119semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145581362
#145580142
#145578512
#145578392
#145578362
#145577322
#145577272
#145576802
#145576762
#145576422
#145576322
#145576242
#145576152
#145575912
C37×#4802
#311937