Finite Group Databasebeta

← #18006486

Subgroups — #18006486

Order 4736.

386 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#14558222C211yesmaximal, characteristic, complemented
2#14558193C211yesmaximal, characteristic
3#14557889C211yesmaximal, characteristic, complemented
4#14557848C211yesmaximal, characteristic, complemented
5#14557843C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557758C211yesmaximal, characteristic, complemented
9#14557697C211yesmaximal, characteristic, complemented
10#14557690C211yesmaximal, characteristic, complemented
11#14557627C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557527C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#485C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×Dic148C2211yescharacteristic
19C2×#10596942C2211yescharacteristic
20C2×#10596930C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic
23#11924529—21no—
24#11924528—21no—
25#11924527C2211yescharacteristic
26#11924525C2211yescharacteristic
27#11924522—21no—
28#11924518—21no—
29#11924516C2211yescharacteristic
30#11924515C2211yescharacteristic
31#11924514—21no—
32#11924511C2211yescharacteristic
33#11924509—21no—
34#11924501C2211yescharacteristic
35#11924501C2211yescharacteristic
36#11924498—21no—
37C4×C22⋊D37C2211yescharacteristic
38#11924493—21no—
39C4⋊C4×D37C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C22⋊Q8×C37C2211yescharacteristic
53#117×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C2×C22⋊D37—21no—
62C2×C22⋊D37D411yescharacteristic
63Q8×D37—22no—
64Q8×D37—41no—
65#10596962—22no—
66#10596962—41no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37C2311yescharacteristic
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C22⋊C4×C37—21no—
83C22⋊C4×C37—21no—
84C42×C37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596942—41no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436—41no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108Dic148—22no—
109#10596930—41no—
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37—21no—
113C22×D37C2×D411yescharacteristic
114Q8×C37—21no—
115Q8×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37—22no—
125C22⋊D37—42no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132D148—21no—
133D148—21no—
134D148—42no—
135C4×D37—21no—
136C4×D37—21no—
137C4×D37—42no—
138C4×D37—42no—
139C4×D37—42no—
140Dic74—21no—
141Dic74—21no—
142Dic74—21no—
143Dic74—42no—
144Dic74#4112yes—
145C8×C37—21no—
146C8×C37—21no—
147#64436—21no—
148#64436—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37C22×D411yescharacteristic
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37#13512yes—
159C4×C37—21no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37—41no—
164C4×C37C2×#4111yescharacteristic
165C4×C37H(5,𝔽2)11yescharacteristic
166Dic37—22no—
167Dic37—21no—
168Dic37—21no—
169Dic37—21no—
170Dic37—41no—
171Dic37—41no—
172#3300—371nomaximal, Sylow
173C2×C37—41no—
174C2×C37#54611yescharacteristic
175C2×C37C2×#13511yescharacteristic
176C2×C37#57811yescharacteristic
177D37—22no—
178D37—81no—
179#552—371no—
180#548—371no—
181#488—371no—
182#485D3711yescharacteristic, complemented
183#480—371no—
184#479—371no—
185#467—371no—
186#465—371no—
187#464—371no—
188#452—371no—
189#451—371no—
190C4×Q16—371no—
191C8×D4—371no—
192#416—371no—
193C2×#103—371no—
194C37#330011yescharacteristic, complemented, Sylow
195C2×#41—371no—
196C22×Q8—371no—
197C2×Q16—371no—
198C2×Q16—371no—
199C2×SD16—371no—
200C22×C8—371no—
201C22×C8—371no—
202#126—741no—
203#125—371no—
204#125—741no—
205#124—371no—
206#124—741no—
207#123—741no—
208C22⋊Q8—371no—
209C22⋊Q8—371no—
210C22⋊Q8—741no—
211C22⋊Q8C2×D3711yescharacteristic
212#121—371no—
213#121—741no—
214C4×Q8—371no—
215C4×Q8—371no—
216C4×D4—371no—
217C4×D4—741no—
218#117—741no—
219#117C2×D3711yescharacteristic
220C2×C4⋊C4—371no—
221#107—371no—
222#107C2×D3711yescharacteristic
223#106C2×D3711yescharacteristic
224C4⋊C8—371no—
225#103—371no—
226#103—371no—
227#103—371no—
228#103—371no—
229#103—371no—
230#103C2×D3711yescharacteristic
231#103C2×D3711yescharacteristic
232#102—371no—
233#102—371no—
234#102—371no—
235C22⋊C8—371no—
236C22⋊C8C2×D3711yescharacteristic
237C4×C8—371no—
238#41—742no—
239#41—1481no—
240C2×Q8—371no—
241C2×Q8—371no—
242C2×Q8—741no—
243C2×Q8—742no—
244C2×Q8—1481no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—371no—
247C2×D4—371no—
248C2×D4—741no—
249C2×D4—741no—
250C22×C4—371no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4C22×D3711yescharacteristic
255Q16—742no—
256Q16—1481no—
257SD16—1481no—
258C2×C8—371no—
259C2×C8—371no—
260C2×C8—1481no—
261C2×C8—1481no—
262C2×C8C22×D3711yescharacteristic
263C2×C8C22×D3711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
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—21no—
279C22⋊C4—371no—
280C22⋊C4—371no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C42—21no—
287C42—371no—
288C42—741no—
289C42—741no—
290C23—371no—
291C23—741no—
292C23D4×D3711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—372no—
296Q8—741no—
297Q8—741no—
298Q8—741no—
299Q8—1482no—
300D4—742no—
301D4—741no—
302D4—741no—
303D4—1482no—
304D4—1482no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—371no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—1482no—
320C2×C4—1482no—
321C2×C4—1482no—
322C2×C4D4×D3711yescharacteristic
323C2×C4C23×D3711yescharacteristic
324C8—21no—
325C8—21no—
326C8—741no—
327C8—741no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—372no—
332C22—741no—
333C22—741no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22C2×D4×D3711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—741no—
344C4—741no—
345C4—741no—
346C4—742no—
347C4—1481no—
348C4—1481no—
349C4#41×D3711yescharacteristic
350C4#1192458211yescharacteristic
351C2—41no—
352C2—2961no—
353C2—742no—
354C2#1455817511yescharacteristic
355C2#135×D3711yescharacteristic
356C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#485C2
socleC22×C37C22×D4
prime radical#14558193C2
hypercenter#485D37
hypocenterC37#3300
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14558222C2semidirect
3. #14557889C2semidirect
4. #14557848C2semidirect
5. #14557843C2semidirect
6. #14557772C2semidirect
7. #14557763C2semidirect
8. #14557758C2semidirect
9. #14557697C2semidirect
10. #14557690C2semidirect
11. #14557627C2semidirect
12. #14557596C2semidirect
13. #14557527C2semidirect
14. #103×D37C2semidirect
15. C37×#485C2semidirect
182. #485D37semidirect
194. C37#3300semidirect

Maximal subgroups

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

subgroupindex
#145582222
#145581932
#145578892
#145578482
#145578432
#145577722
#145577632
#145577582
#145576972
#145576902
#145576272
#145575962
#145575272
#103×D372
C37×#4852
#330037