Finite Group Databasebeta

← #18006431

Subgroups — #18006431

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#14558223C211yesmaximal, characteristic, complemented
2#14557887C211yesmaximal, characteristic, complemented
3#14557861C211yesmaximal, characteristic, complemented
4#14557854C211yesmaximal, characteristic, complemented
5#14557833C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557760C211yesmaximal, characteristic, complemented
8#14557752C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557684C211yesmaximal, characteristic, complemented
11C4×#10596940C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14C2×#11924457C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic
16C2×#10596942C2211yescharacteristic, complemented
17C2×#10596940C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C22×#64436C2211yescharacteristic
20C22×#64436C2211yescharacteristic, complemented
21#11924529—21no—
22#11924528C2211yescharacteristic, complemented
23#11924526—21no—
24#11924517—21no—
25#11924515C2211yescharacteristic
26#11924515C2211yescharacteristic, complemented
27C4×Dic74C2211yescharacteristic, complemented
28#11924495C2211yescharacteristic, complemented
29#11924492—21no—
30C2×C4⋊Dic37C2211yescharacteristic
31#11924469C2211yescharacteristic, complemented
32#11924467C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35#11924460C2211yescharacteristic, complemented
36#11924460C2211yescharacteristic, complemented
37#11924460C2211yescharacteristic, complemented
38#11924459C2211yescharacteristic, complemented
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924457C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic, complemented
47C4×#64436C2211yescharacteristic, complemented
48C2×#41×C37C2211yescharacteristic
49C22×D4×C37C2211yescharacteristic
50#124×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53#121×C37—21no—
54#121×C37C2211yescharacteristic
55#120×C37—21no—
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58C2×C22⋊C4×C37—21no—
59C24×C37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—22no—
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37—21no—
67C2×D4×C37—41no—
68C2×D4×C37D411yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C22×C4×C37C2311yescharacteristic
75C22×Dic37—21no—
76C2×Dic74C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37D411yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C22⋊C4×C37D411yescharacteristic
86C22⋊C4×C37D411yescharacteristic
87C42×C37C2311yescharacteristic
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91#10596942—41no—
92#10596940—22no—
93#10596940—41no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C2×#64436—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—42no—
114C23×C37—42no—
115C23×C37—81no—
116C23×C37C2×D411yescharacteristic
117C23×C37C2×D411yescharacteristic
118Q8×C37—21no—
119Q8×C37—21no—
120D4×C37—22no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—42no—
125D4×C37—42no—
126D4×C37—81no—
127D4×C37#4112yes—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—42no—
135C2×C4×C37—81no—
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—42no—
146Dic74—21no—
147Dic74—21no—
148#64436—21no—
149#64436—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—22no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—84no—
164C22×C37#13512yes—
165C22×C37C22×D411yescharacteristic
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—22no—
180C2×C37—41no—
181C2×C37—42no—
182C2×C37—81no—
183C2×C37#54611yescharacteristic
184C2×C37C2×#13511yescharacteristic
185C2×C37#57711yescharacteristic
186#552—371no—
187#546D3711yescharacteristic
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#416—371no—
200C2×#102—371no—
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41C2×D3711yescharacteristic
203C22×D4C2×D3711yescharacteristic
204C2×Q16—371no—
205C2×SD16—371no—
206C2×SD16—371no—
207C22×C8—371no—
208C22×C8—371no—
209#126—741no—
210#125—371no—
211#125—741no—
212#124C2×D3711yescharacteristic
213#123—21no—
214#123—741no—
215C22⋊Q8—371no—
216C22⋊Q8—371no—
217C22⋊Q8C2×D3711yescharacteristic
218#121—21no—
219#121C2×D3711yescharacteristic
220#120—21no—
221C4×Q8—371no—
222C4×D4C2×D3711yescharacteristic
223C4×D4C2×D3711yescharacteristic
224#117—371no—
225#117—741no—
226C2×C4⋊C4—371no—
227C2×C22⋊C4—21no—
228#107—371no—
229#106—371no—
230#106—371no—
231C4⋊C8—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241#102—371no—
242C22⋊C8—371no—
243C22⋊C8—371no—
244C4×C8—371no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—371no—
249C2×Q8C22×D3711yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D3711yescharacteristic
256C2×D4C22×D3711yescharacteristic
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—741no—
261C22×C4C22×D3711yescharacteristic
262C22×C4C22×D3711yescharacteristic
263Q16—1481no—
264SD16—742no—
265SD16—1481no—
266C2×C8—371no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8—1481no—
272C4⋊C4—21no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
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—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4C22⋊D3711yescharacteristic
293C22⋊C4C22⋊D3711yescharacteristic
294C42—741no—
295C42—741no—
296C42C22×D3711yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D3711yescharacteristic
303C23C2×C22⋊D3711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—741no—
307Q8—741no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1059696412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—1482no—
329C2×C4C2×C22⋊D3711yescharacteristic
330C2×C4C2×C22⋊D3711yescharacteristic
331C2×C4C2×C22⋊D3711yescharacteristic
332C2×C4C2×C22⋊D3711yescharacteristic
333C2×C4C23×D3711yescharacteristic
334C8—741no—
335C8—741no—
336C8—741no—
337C8—741no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1192455612yes—
351C22C22×C22⋊D3711yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—1481no—
359C4—1481no—
360C4—1481no—
361C4—1481no—
362C4C2×#1059696411yescharacteristic
363C4#1192458111yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1455817711yescharacteristic
369C2C2×#1192455611yescharacteristic
370C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14558223C2semidirect
2. #14557887C2semidirect
3. #14557861C2semidirect
4. #14557854C2semidirect
5. #14557833C2semidirect
6. #14557772C2semidirect
7. #14557760C2semidirect
8. #14557752C2semidirect
9. #14557695C2semidirect
10. #14557684C2semidirect
11. C4×#10596940C2semidirect
12. D4×#64436C2semidirect
13. #14557529C2semidirect
14. C2×#11924457C2semidirect
16. C2×#10596942C22semidirect
20. C22×#64436C22semidirect
22. #11924528C22semidirect
26. #11924515C22semidirect
27. C4×Dic74C22semidirect
28. #11924495C22semidirect
31. #11924469C22semidirect
32. #11924467C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. #11924460C22semidirect
36. #11924460C22semidirect
37. #11924460C22semidirect
38. #11924459C22semidirect
46. C22⋊#64436C22semidirect
47. C4×#64436C22semidirect
201. C37#3296semidirect

Maximal subgroups

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

subgroupindex
#145582232
#145578872
#145578612
#145578542
#145578332
#145577722
#145577602
#145577522
#145576952
#145576842
C4×#105969402
D4×#644362
#145575292
C2×#119244572
C37×#5462
#329637