Finite Group Databasebeta

← #18006520

Subgroups — #18006520

Order 4736.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558246C211yesmaximal, characteristic, complemented
2#14558182C211yesmaximal, characteristic, complemented
3#14557882C211yesmaximal, characteristic, complemented
4#14557874C211yesmaximal, characteristic, complemented
5#14557872C211yesmaximal, characteristic, complemented
6#14557821C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557737C211yesmaximal, characteristic, complemented
10#14557679C211yesmaximal, characteristic, complemented
11#14557678C211yesmaximal, characteristic, complemented
12#14557613C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#14557526C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924534C2211yescharacteristic
23#11924524—21no—
24#11924522—21no—
25#11924519—21no—
26#11924517—21no—
27#11924515C2211yescharacteristic
28#11924512C2211yescharacteristic
29#11924511C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924509—21no—
32#11924508—21no—
33D4×Dic37C2211yescharacteristic
34#11924498C2211yescharacteristic
35C4×C22⋊D37C2211yescharacteristic
36#11924494C2211yescharacteristic
37#11924493—21no—
38C2×#10596936—21no—
39#11924469C2211yescharacteristic
40#11924468C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#117×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37D411yescharacteristic
69C22×Dic37—21no—
70C22×Dic37—21no—
71#10596964—22no—
72#10596964—41no—
73C2×D148—21no—
74C2×D148C2311yescharacteristic
75C2×C4×D37—21no—
76C2×C4×D37C2311yescharacteristic
77C2×Dic74—21no—
78C2×Dic74C2311yescharacteristic
79C2×C8×C37—41no—
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C42×C37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37D411yescharacteristic
89#10596941—41no—
90#10596939—22no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
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×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—42no—
119D4×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—42no—
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—22no—
129C22⋊D37—42no—
130C22⋊D37—81no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—42no—
135C2×Dic37—42no—
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138C2×Dic37C2×D411yescharacteristic
139D148—21no—
140D148—21no—
141D148—81no—
142C4×D37—21no—
143C4×D37—21no—
144C4×D37—42no—
145Dic74—21no—
146Dic74—21no—
147Dic74—81no—
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—21no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37#13512yes—
177#3303—371nomaximal, Sylow
178C2×C37—41no—
179C2×C37—42no—
180C2×C37#54611yescharacteristic
181C2×C37C2×#13511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—41no—
184D37—81no—
185#555—371no—
186#547—371no—
187#487—371no—
188#485—371no—
189#485—371no—
190#476—371no—
191#465—371no—
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196C4×D8—371no—
197C8×D4—371no—
198#416—371no—
199#416D3711yescharacteristic, complemented
200C37#330311yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C2×#41C2×D3711yescharacteristic
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C22×C8—371no—
207C22×C8C2×D3711yescharacteristic
208C4⋊Q8—371no—
209C4⋊Q8—371no—
210#124—741no—
211#124—741no—
212#123—741no—
213#123—741no—
214C22⋊Q8—371no—
215C22⋊Q8—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—371no—
223#117—371no—
224#117—741no—
225#117C2×D3711yescharacteristic
226C2×C4⋊C4—741no—
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103C2×D3711yescharacteristic
236#103C2×D3711yescharacteristic
237#102—371no—
238#102—371no—
239#102C2×D3711yescharacteristic
240#102C2×D3711yescharacteristic
241C22⋊C8—371no—
242C22⋊C8—371no—
243C4×C8—371no—
244#41—22no—
245#41—41no—
246#41—742no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8—741no—
250C2×Q8C22×D3711yescharacteristic
251C2×D4—21no—
252C2×D4—371no—
253C2×D4—371no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4C22×D3711yescharacteristic
264SD16—1481no—
265SD16—1481no—
266D8—742no—
267C2×C8—41no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
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⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—371no—
285C22⋊C4—371no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C42—21no—
294C42—371no—
295C42—741no—
296C23—21no—
297C23—371no—
298C23—741no—
299C23D4×D3711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—2961no—
303Q8—741no—
304Q8—741no—
305D4—21no—
306D4—42no—
307D4—2961no—
308D4—2961no—
309D4—742no—
310D4—741no—
311D4—741no—
312D4—1482no—
313D4#1059696212yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—371no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—1482no—
329C2×C4—1482no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—741no—
344C22—741no—
345C22—741no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—372no—
355C4—741no—
356C4—741no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696211yescharacteristic
361C4#1192458111yescharacteristic
362C2—41no—
363C2—42no—
364C2—2961no—
365C2—1481no—
366C2#1455817311yescharacteristic
367C2#135×D3711yescharacteristic
368C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
hypercenter#416D37
hypocenterC37#3303
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. #14558246C2semidirect
2. #14558182C2semidirect
3. #14557882C2semidirect
4. #14557874C2semidirect
5. #14557872C2semidirect
6. #14557821C2semidirect
7. #14557765C2semidirect
8. #14557762C2semidirect
9. #14557737C2semidirect
10. #14557679C2semidirect
11. #14557678C2semidirect
12. #14557613C2semidirect
13. C8×C22⋊D37C2semidirect
14. #14557526C2semidirect
15. C37×#416C2semidirect
199. #416D37semidirect
200. C37#3303semidirect

Maximal subgroups

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

subgroupindex
#145582462
#145581822
#145578822
#145578742
#145578722
#145578212
#145577652
#145577622
#145577372
#145576792
#145576782
#145576132
C8×C22⋊D372
#145575262
C37×#4162
#330337