Finite Group Databasebeta

← #18006432

Subgroups — #18006432

Order 4736.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558222C211yesmaximal, characteristic, complemented
2#14558171C211yesmaximal, characteristic
3#14557889C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557857C211yesmaximal, characteristic, complemented
6#14557835C211yesmaximal, characteristic, complemented
7#14557773C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557758C211yesmaximal, characteristic, complemented
10#14557695C211yesmaximal, characteristic, complemented
11#14557685C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×#10596942C2211yescharacteristic, complemented
18C2×#10596930C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924529—21no—
22#11924528—21no—
23#11924527C2211yescharacteristic, complemented
24#11924525C2211yescharacteristic
25#11924519—21no—
26#11924518—21no—
27#11924516C2211yescharacteristic
28#11924515C2211yescharacteristic, complemented
29#11924512C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924508—21no—
32#11924504—21no—
33#11924501C2211yescharacteristic, complemented
34D4×Dic37C2211yescharacteristic
35C4×C22⋊D37C2211yescharacteristic
36#11924493—21no—
37C4⋊C4×D37C2211yescharacteristic
38C2×#10596938—21no—
39#11924469C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic, complemented
52C2×#41×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic, complemented
54#117×C37C2211yescharacteristic, complemented
55#103×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37D411yescharacteristic
70C22×Dic37—21no—
71D4×D37—22no—
72D4×D37—41no—
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37—41no—
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C22⋊C4×C37—21no—
83C42×C37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596942—41no—
88#10596940—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936—21no—
104#10596936D411yescharacteristic
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109#10596930—41no—
110C8×D37—41no—
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—42no—
115C22×D37—42no—
116C22×D37—81no—
117C22×D37C2×D411yescharacteristic
118Q8×C37—21no—
119Q8×C37—21no—
120D4×C37—21no—
121D4×C37—42no—
122D4×C37#4112yes—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—42no—
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—22no—
132C22⋊D37—42no—
133C22⋊D37—81no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—81no—
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140C2×Dic37C2×D411yescharacteristic
141D148—21no—
142D148—21no—
143C4×D37—21no—
144C4×D37—21no—
145C4×D37—42no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—22no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—84no—
165C2×D37#13512yes—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37H(5,𝔽2)11yescharacteristic
172Dic37—21no—
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—42no—
180C2×C37—41no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—22no—
185D37—81no—
186#552—371no—
187#546—371no—
188#488—371no—
189#483—371no—
190#482—371no—
191#478—371no—
192#467—371no—
193#465—371no—
194#464—371no—
195#452—371no—
196#450—371no—
197C4×SD16—371no—
198C8×D4—371no—
199#416D3711yescharacteristic, complemented
200C2×#102—371no—
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41C2×D3711yescharacteristic
203C22×D4—371no—
204C2×Q16—371no—
205C2×SD16—371no—
206C2×SD16—371no—
207C22×C8—371no—
208C22×C8C2×D3711yescharacteristic, complemented
209#126—741no—
210#125—371no—
211#125—741no—
212#124—371no—
213#123—741no—
214#123—741no—
215C22⋊Q8—371no—
216C22⋊Q8—371no—
217C22⋊Q8—371no—
218#121—371no—
219#121—741no—
220#120—741no—
221C4×Q8—371no—
222C4×D4—371no—
223C4×D4—371no—
224#117—741no—
225#117C2×D3711yescharacteristic, complemented
226C2×C4⋊C4—371no—
227C2×C22⋊C4—741no—
228#107—371no—
229#106—371no—
230#106—371no—
231C4⋊C8—371no—
232#103—371no—
233#103—371no—
234#103C2×D3711yescharacteristic, complemented
235#103C2×D3711yescharacteristic, complemented
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102C2×D3711yescharacteristic
241#102C2×D3711yescharacteristic
242C22⋊C8—371no—
243C22⋊C8—371no—
244C4×C8—371no—
245C24—741no—
246#41—22no—
247#41—41no—
248C2×Q8—371no—
249C2×Q8C22×D3711yescharacteristic
250C2×D4—21no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—742no—
256C2×D4—1481no—
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263Q16—1481no—
264SD16—742no—
265SD16—1481no—
266C2×C8—41no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—1481no—
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C4⋊C4—371no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—741no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—371no—
286C22⋊C4—371no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—21no—
295C42—371no—
296C42—741no—
297C23—21no—
298C23—371no—
299C23—2961no—
300C23—741no—
301C23—1482no—
302C23—1482no—
303C23D4×D3711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—741no—
307Q8—741no—
308D4—21no—
309D4—42no—
310D4—2961no—
311D4—742no—
312D4—741no—
313D4—741no—
314D4—1482no—
315D4#1059696212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—371no—
325C2×C4—2961no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—741no—
331C2×C4—1482no—
332C2×C4D4×D3711yescharacteristic
333C2×C4C23×D3711yescharacteristic
334C8—21no—
335C8—21no—
336C8—741no—
337C8—741no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—372no—
345C22—2964no—
346C22—741no—
347C22—741no—
348C22—1481no—
349C22—1481no—
350C22—1481no—
351C22C2×D4×D3711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—741no—
357C4—741no—
358C4—741no—
359C4—1481no—
360C4—1481no—
361C4—1481no—
362C4C2×#1059696211yescharacteristic
363C4#1192458111yescharacteristic
364C2—41no—
365C2—42no—
366C2—2961no—
367C2—742no—
368C2#1455817311yescharacteristic
369C2#135×D3711yescharacteristic
370C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radical#14558171C2
hypercenter#416D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14558222C2semidirect
3. #14557889C2semidirect
4. #14557862C2semidirect
5. #14557857C2semidirect
6. #14557835C2semidirect
7. #14557773C2semidirect
8. #14557762C2semidirect
9. #14557758C2semidirect
10. #14557695C2semidirect
11. #14557685C2semidirect
12. #14557624C2semidirect
13. C8×C22⋊D37C2semidirect
14. #102×D37C2semidirect
15. C37×#416C2semidirect
17. C2×#10596942C22semidirect
23. #11924527C22semidirect
28. #11924515C22semidirect
33. #11924501C22semidirect
39. #11924469C22semidirect
40. #11924468C22semidirect
41. #11924467C22semidirect
42. #11924465C22semidirect
43. #11924461C22semidirect
44. #11924460C22semidirect
49. C22⋊#64436C22semidirect
51. C8×Dic37C22semidirect
53. C22×C8×C37C22semidirect
54. #117×C37C22semidirect
55. #103×C37C22semidirect
56. #103×C37C22semidirect
199. #416D37semidirect
201. C37#3296semidirect
208. C22×C8C2×D37semidirect
225. #117C2×D37semidirect
234. #103C2×D37semidirect
235. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582222
#145581712
#145578892
#145578622
#145578572
#145578352
#145577732
#145577622
#145577582
#145576952
#145576852
#145576242
C8×C22⋊D372
#102×D372
C37×#4162
#329637