Finite Group Databasebeta

← #18006451

Subgroups — #18006451

Order 4736.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558233C211yesmaximal, characteristic, complemented
2#14558178C211yesmaximal, characteristic, complemented
3#14557888C211yesmaximal, characteristic, complemented
4#14557870C211yesmaximal, characteristic, complemented
5#14557860C211yesmaximal, characteristic, complemented
6#14557833C211yesmaximal, characteristic, complemented
7#14557768C211yesmaximal, characteristic, complemented
8#14557761C211yesmaximal, characteristic, complemented
9#14557748C211yesmaximal, characteristic, complemented
10#14557675C211yesmaximal, characteristic, complemented
11#14557665C211yesmaximal, characteristic, complemented
12C8×D148C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C4×D8×C37C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596940C2211yescharacteristic, complemented
19C2×#10596939C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic, complemented
22#11924529—21no—
23#11924528C2211yescharacteristic, complemented
24#11924524C2211yescharacteristic
25#11924520—21no—
26#11924519—21no—
27#11924516C2211yescharacteristic
28#11924511C2211yescharacteristic
29#11924510—21no—
30#11924509—21no—
31#11924507C2211yescharacteristic
32#11924507C2211yescharacteristic, complemented
33#11924506—21no—
34C4×D148C2211yescharacteristic
35C4×C22⋊D37—21no—
36#11924494C2211yescharacteristic, complemented
37C4⋊C4×D37C2211yescharacteristic
38C2×#10596938—21no—
39#11924469C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41C4⋊#64436C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic, complemented
52C2×D8×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic, complemented
55#107×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic, complemented
58C4×C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37—21no—
63C22×C4×C37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C22×Dic37—21no—
69#10596964—22no—
70#10596964—41no—
71D4×D37—22no—
72D4×D37—41no—
73C2×D148—21no—
74C2×D148D411yescharacteristic
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37C2311yescharacteristic
78C2×C4×D37C2311yescharacteristic
79C2×Dic74C2311yescharacteristic
80D8×C37—22no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C42×C37C2311yescharacteristic
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90#10596940—41no—
91#10596939—41no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938D411yescharacteristic
98#10596938D411yescharacteristic
99C4⋊Dic37—21no—
100C4⋊Dic37D411yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106C4×Dic37—21no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C8×D37—41no—
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C22×D37—21no—
114C22×D37—42no—
115C22×D37—42no—
116C22×D37—81no—
117C22×D37C2×D411yescharacteristic
118C22×D37C2×D411yescharacteristic
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37#4112yes—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—81no—
126C2×C4×C37—81no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—42no—
131C22⋊D37—42no—
132C22⋊D37—42no—
133C22⋊D37—81no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—42no—
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140D148—22no—
141D148—21no—
142D148—21no—
143D148—81no—
144C4×D37—21no—
145C4×D37—21no—
146C4×D37—21no—
147C4×D37—21no—
148C4×D37—81no—
149Dic74—21no—
150Dic74—21no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—22no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37C22×D411yescharacteristic
162C2×D37—21no—
163C2×D37—21no—
164C2×D37—21no—
165C2×D37—21no—
166C2×D37—21no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—84no—
171C2×D37#13512yes—
172C4×C37—21no—
173C4×C37—21no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37C2×#4111yescharacteristic
177C4×C37H(5,𝔽2)11yescharacteristic
178Dic37—21no—
179Dic37—21no—
180Dic37—41no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—42no—
185C2×C37—81no—
186C2×C37#54611yescharacteristic
187C2×C37C2×#13511yescharacteristic
188C2×C37#57611yescharacteristic
189D37—22no—
190D37—41no—
191D37—81no—
192#553—371no—
193#546—371no—
194#488—371no—
195#484—371no—
196#482—371no—
197#478—371no—
198#466—371no—
199#465—371no—
200#463—371no—
201#449—371no—
202#447—371no—
203C4×D8D3711yescharacteristic, complemented
204C8×D4—371no—
205#416—371no—
206C2×#102—371no—
207C37#329711yescharacteristic, complemented, Sylow
208C2×#41—371no—
209C22×D4—371no—
210C2×SD16—371no—
211C2×D8—371no—
212C2×D8C2×D3711yescharacteristic
213C22×C8—371no—
214C22×C8—371no—
215#126—741no—
216#125—371no—
217#124—371no—
218#123—741no—
219#123—741no—
220C22⋊Q8—371no—
221#121—371no—
222#121—371no—
223#121—371no—
224#121—741no—
225#121—741no—
226#120—741no—
227C4×D4—371no—
228C4×D4—741no—
229C4×D4C2×D3711yescharacteristic
230C4×D4C2×D3711yescharacteristic, complemented
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107C2×D3711yescharacteristic, complemented
236#106—371no—
237C4⋊C8—371no—
238#103—371no—
239#103—371no—
240#103—371no—
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102C2×D3711yescharacteristic
247#102C2×D3711yescharacteristic, complemented
248C22⋊C8—371no—
249C22⋊C8—371no—
250C4×C8C2×D3711yescharacteristic, complemented
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8—371no—
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—741no—
258C2×D4—741no—
259C2×D4—741no—
260C2×D4—742no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4—1481no—
264C2×D4C22×D3711yescharacteristic
265C2×D4C22×D3711yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—371no—
269C22×C4—371no—
270C22×C4—741no—
271C22×C4—741no—
272SD16—1481no—
273D8—22no—
274D8—1481no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—1481no—
278C2×C8—1481no—
279C2×C8C22×D3711yescharacteristic
280C2×C8C22×D3711yescharacteristic
281C4⋊C4—371no—
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—741no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4C22×D3711yescharacteristic
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—371no—
293C22⋊C4—371no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C42—741no—
302C42C22×D3711yescharacteristic
303C23—21no—
304C23—21no—
305C23—371no—
306C23—371no—
307C23—2961no—
308C23—741no—
309C23—1482no—
310C23—1482no—
311Q8—741no—
312Q8—741no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2961no—
317D4—2961no—
318D4—742no—
319D4—741no—
320D4—741no—
321D4—1482no—
322D4—1482no—
323D4—1482no—
324D4#1059696212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—371no—
330C2×C4—371no—
331C2×C4—2961no—
332C2×C4—741no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—1482no—
340C2×C4D4×D3711yescharacteristic
341C2×C4D4×D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—21no—
344C8—21no—
345C8—741no—
346C8—741no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—372no—
354C22—2964no—
355C22—741no—
356C22—741no—
357C22—741no—
358C22—741no—
359C22—741no—
360C22—1481no—
361C22—1481no—
362C22—1481no—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—741no—
369C4—741no—
370C4—1481no—
371C4—1481no—
372C4—1481no—
373C4C2×#1059696211yescharacteristic
374C4#1192458211yescharacteristic
375C2—42no—
376C2—81no—
377C2—2961no—
378C2—742no—
379C2—1481no—
380C2#1455817911yescharacteristic
381C2#135×D3711yescharacteristic
382C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×D8×C37C2
socleC22×C37C22×D4
hypercenterC4×D8D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14558233C2semidirect
2. #14558178C2semidirect
3. #14557888C2semidirect
4. #14557870C2semidirect
5. #14557860C2semidirect
6. #14557833C2semidirect
7. #14557768C2semidirect
8. #14557761C2semidirect
9. #14557748C2semidirect
10. #14557675C2semidirect
11. #14557665C2semidirect
12. C8×D148C2semidirect
13. #14557526C2semidirect
14. #102×D37C2semidirect
15. C4×D8×C37C2semidirect
18. C2×#10596940C22semidirect
21. C2×C8×D37C22semidirect
23. #11924528C22semidirect
32. #11924507C22semidirect
36. #11924494C22semidirect
39. #11924469C22semidirect
40. #11924467C22semidirect
41. C4⋊#64436C22semidirect
42. #11924461C22semidirect
43. #11924461C22semidirect
44. #11924459C22semidirect
51. #11924448C22semidirect
54. C4×D4×C37C22semidirect
55. #107×C37C22semidirect
57. #102×C37C22semidirect
58. C4×C8×C37C22semidirect
203. C4×D8D37semidirect
207. C37#3297semidirect
230. C4×D4C2×D37semidirect
235. #107C2×D37semidirect
247. #102C2×D37semidirect
250. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582332
#145581782
#145578882
#145578702
#145578602
#145578332
#145577682
#145577612
#145577482
#145576752
#145576652
C8×D1482
#145575262
#102×D372
C4×D8×C372
#329737