Finite Group Databasebeta

← #18004800

Subgroups — #18004800

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#14558139C211yesmaximal, characteristic, complemented
2#14558012C211yesmaximal, characteristic, complemented
3#14557853C211yesmaximal, characteristic, complemented
4#14557848C211yesmaximal, characteristic, complemented
5#14557837C211yesmaximal, characteristic, complemented
6#14557734C211yesmaximal, characteristic, complemented
7#14557728C211yesmaximal, characteristic, complemented
8#14557679C211yesmaximal, characteristic, complemented
9#14557679C211yesmaximal, characteristic, complemented
10#14557642C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557620C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#478C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924533C2211yescharacteristic
22#11924521—21no—
23#11924521—21no—
24#11924511—21no—
25#11924511—21no—
26#11924511C2211yescharacteristic
27#11924511C2211yescharacteristic
28C4×Dic74C2211yescharacteristic
29#11924501C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31#11924498C2211yescharacteristic
32#11924498C2211yescharacteristic
33C4×C22⋊D37—21no—
34#11924496—21no—
35#11924493C2211yescharacteristic
36#11924492—21no—
37C2×#10596936—21no—
38C4⋊C4×D37C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924459C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#125×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×D4×C37C2311yescharacteristic
60C22×C4×C37—21no—
61C2×C22⋊D37—21no—
62C22×Dic37—21no—
63C22×Dic37—21no—
64#10596964—22no—
65#10596964—22no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148—21no—
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C42×C37C2311yescharacteristic
86C22⋊Dic37—21no—
87#10596939—22no—
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938D411yescharacteristic
94#10596938D411yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936D411yescharacteristic
100#10596936D411yescharacteristic
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596930—22no—
107#10596930—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37C2×D411yescharacteristic
112D4×C37—21no—
113D4×C37#4112yes—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—81no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—24no—
122C2×Dic37—24no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—81no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129D148—21no—
130D148—21no—
131D148—21no—
132D148—21no—
133D148—81no—
134D148—81no—
135D148—81no—
136D148—81no—
137C4×D37—21no—
138C4×D37—21no—
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—22no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37C22×D411yescharacteristic
152C2×D37—21no—
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37C2×#4111yescharacteristic
167C4×C37C2×#4111yescharacteristic
168Dic37—22no—
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—41no—
173#3119—371nomaximal, Sylow
174C2×C37—42no—
175C2×C37#52511yescharacteristic
176C2×C37#57611yescharacteristic
177C2×C37#57711yescharacteristic
178D37—41no—
179D37—81no—
180D37—81no—
181#540—371no—
182#520—371no—
183#481—371no—
184#480—371no—
185#479—371no—
186#478D3711yescharacteristic, complemented
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#125C2×D3711yescharacteristic
204#123—741no—
205#123—741no—
206#121—371no—
207#121—371no—
208#121—741no—
209#121—741no—
210C4×Q8—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—741no—
216C4×D4—741no—
217C4×D4C2×D3711yescharacteristic
218#117—371no—
219#117—741no—
220C2×C4⋊C4—371no—
221C2×C4⋊C4—741no—
222#107—371no—
223#107C2×D3711yescharacteristic
224#106—371no—
225#106C2×D3711yescharacteristic
226C4⋊C8—371no—
227C4⋊C8C2×D3711yescharacteristic
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⋊C8—371no—
238#97—371no—
239C4×C8—371no—
240#41—742no—
241#41—742no—
242C2×Q8—371no—
243C2×D4—371no—
244C2×D4—371no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—371no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
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—21no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—371no—
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—741no—
287C42—741no—
288C42C22×D3711yescharacteristic
289C23—21no—
290C23—371no—
291C23—741no—
292C23—741no—
293Q8—372no—
294Q8—741no—
295D4—21no—
296D4—2961no—
297D4—2961no—
298D4—2961no—
299D4—2961no—
300D4—744no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—741no—
305D4#1059696612yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—371no—
311C2×C4—371no—
312C2×C4—371no—
313C2×C4—2961no—
314C2×C4—2961no—
315C2×C4—2961no—
316C2×C4—2961no—
317C2×C4—744no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4D4×D3711yescharacteristic
323C2×C4D4×D3711yescharacteristic
324C2×C4C23×D3711yescharacteristic
325C8—21no—
326C8—21no—
327C8—741no—
328C8—741no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—741no—
333C22—741no—
334C22—741no—
335C22—1481no—
336C22—1481no—
337C22—1481no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22C2×D4×D3711yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—741no—
348C4—742no—
349C4—741no—
350C4—741no—
351C4—1481no—
352C4#41×D3711yescharacteristic
353C4C2×#1059696611yescharacteristic
354C2—42no—
355C2—2961no—
356C2—2961no—
357C2—1481no—
358C2#1455804611yescharacteristic
359C2#1455833711yescharacteristic
360C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#478C2
socleC22×C37C22×D4
hypercenter#478D37
hypocenterC37#3119
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14558139C2semidirect
2. #14558012C2semidirect
3. #14557853C2semidirect
4. #14557848C2semidirect
5. #14557837C2semidirect
6. #14557734C2semidirect
7. #14557728C2semidirect
8. #14557679C2semidirect
9. #14557679C2semidirect
10. #14557642C2semidirect
11. #14557632C2semidirect
12. #14557620C2semidirect
13. #14557613C2semidirect
14. #14557593C2semidirect
15. C37×#478C2semidirect
186. #478D37semidirect
196. C37#3119semidirect

Maximal subgroups

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

subgroupindex
#145581392
#145580122
#145578532
#145578482
#145578372
#145577342
#145577282
#145576792
#145576422
#145576322
#145576202
#145576132
#145575932
C37×#4782
#311937