Finite Group Databasebeta

← #18006440

Subgroups — #18006440

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#14558179C211yesmaximal, characteristic, complemented
2#14557890C211yesmaximal, characteristic, complemented
3#14557868C211yesmaximal, characteristic, complemented
4#14557857C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557760C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557666C211yesmaximal, characteristic, complemented
11C4×#10596939C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557527C211yesmaximal, characteristic, complemented
14C2×#11924456C211yesmaximal, characteristic, complemented
15C37×#553C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C2×#10596940C2211yescharacteristic, complemented
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C22×#64436C2211yescharacteristic, complemented
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924515C2211yescharacteristic
26#11924510C2211yescharacteristic
27#11924509—21no—
28#11924504—21no—
29C4×D148C2211yescharacteristic
30C22⋊C4×D37—21no—
31#11924469C2211yescharacteristic, complemented
32#11924469C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35#11924459C2211yescharacteristic, complemented
36#11924459C2211yescharacteristic, complemented
37#11924459C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic, complemented
39#11924456C2211yescharacteristic
40#11924456C2211yescharacteristic
41#11924456C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic, complemented
47C4×#64436C2211yescharacteristic, complemented
48#126×C37—21no—
49#125×C37C2211yescharacteristic, complemented
50#123×C37—21no—
51#121×C37—21no—
52#121×C37C2211yescharacteristic
53#121×C37C2211yescharacteristic, complemented
54C4×D4×C37—21no—
55C4×D4×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic, complemented
57#117×C37C2211yescharacteristic, complemented
58C2×C4⋊C4×C37C2211yescharacteristic
59C23×D37—21no—
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37D411yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70#10596962—22no—
71#10596962—41no—
72C2×D148—22no—
73C2×D148—21no—
74C2×D148—41no—
75C2×D148C2311yescharacteristic
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×Dic74C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37D411yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C22⋊C4×C37—21no—
88C22⋊C4×C37—21no—
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C22⋊C4×C37D411yescharacteristic
92C22⋊C4×C37D411yescharacteristic
93C42×C37—21no—
94C42×C37C2311yescharacteristic
95C22⋊Dic37—21no—
96#10596940—41no—
97#10596939—22no—
98#10596939—41no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103C4⋊Dic37C2311yescharacteristic
104#10596936—21no—
105C2×#64436—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—81no—
119D4×C37—22no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—42no—
123D4×C37—81no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—81no—
132C2×C4×C37—81no—
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2411yescharacteristic
138C22⋊D37—42no—
139C22⋊D37—81no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142D148—21no—
143D148—21no—
144D148—21no—
145D148—42no—
146D148#4112yes—
147C4×D37—42no—
148C4×D37—81no—
149Dic74—21no—
150Dic74—21no—
151#64436—21no—
152#64436—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37#13512yes—
164C22×C37C22×D411yescharacteristic
165C2×D37—22no—
166C2×D37—41no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—84no—
172C4×C37—21no—
173C4×C37—21no—
174C4×C37—21no—
175C4×C37—21no—
176C4×C37—41no—
177C4×C37—41no—
178C4×C37—41no—
179C4×C37C2×#4111yescharacteristic
180C4×C37H(5,𝔽2)11yescharacteristic
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—22no—
185C2×C37—41no—
186C2×C37—81no—
187C2×C37#54611yescharacteristic
188C2×C37C2×#13511yescharacteristic
189C2×C37#57611yescharacteristic
190D37—42no—
191D37—81no—
192#553D3711yescharacteristic, complemented
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×D8—371no—
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×D8—371no—
213C22×C8—371no—
214C22×C8—371no—
215#126—21no—
216#125C2×D3711yescharacteristic, complemented
217#124—371no—
218#123—21no—
219#123—741no—
220C22⋊Q8—371no—
221#121—21no—
222#121—371no—
223#121—741no—
224#121C2×D3711yescharacteristic
225#121C2×D3711yescharacteristic, complemented
226#120—741no—
227C4×D4—21no—
228C4×D4—371no—
229C4×D4C2×D3711yescharacteristic
230C4×D4C2×D3711yescharacteristic, complemented
231#117C2×D3711yescharacteristic, complemented
232C2×C4⋊C4C2×D3711yescharacteristic
233C2×C22⋊C4—741no—
234#107—371no—
235#107—371no—
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#102—371no—
247#102—371no—
248C22⋊C8—371no—
249C22⋊C8—371no—
250C4×C8—371no—
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8—371no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—371no—
258C2×D4—371no—
259C2×D4—742no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4—1481no—
264C2×D4C22⋊D3711yescharacteristic
265C2×D4C22×D3711yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4C22×D3711yescharacteristic
271C22×C4C22×D3711yescharacteristic
272SD16—1481no—
273D8—742no—
274D8—1481no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—371no—
278C2×C8—371no—
279C2×C8—1481no—
280C2×C8—1481no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—371no—
285C4⋊C4—741no—
286C4⋊C4C22⋊D3711yescharacteristic
287C4⋊C4C22×D3711yescharacteristic
288C4⋊C4C22×D3711yescharacteristic
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4C22⋊D3711yescharacteristic
300C22⋊C4C22⋊D3711yescharacteristic
301C42—21no—
302C42C22×D3711yescharacteristic
303C23—21no—
304C23—2961no—
305C23—741no—
306C23—741no—
307C23—1482no—
308C23—1482no—
309C23C2×C22⋊D3711yescharacteristic
310C23C2×C22⋊D3711yescharacteristic
311Q8—741no—
312Q8—741no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—372no—
319D4—2961no—
320D4—741no—
321D4—741no—
322D4—741no—
323D4—1482no—
324D4—1482no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—2961no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—1482no—
338C2×C4C2×C22⋊D3711yescharacteristic
339C2×C4C2×C22⋊D3711yescharacteristic
340C2×C4C2×C22⋊D3711yescharacteristic
341C2×C4C2×C22⋊D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—741no—
344C8—741no—
345C8—741no—
346C8—741no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2964no—
356C22—742no—
357C22—1481no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22#1192455612yes—
363C22C22×C22⋊D3711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—1481no—
372C4—1481no—
373C4#41×D3711yescharacteristic
374C4#1192458211yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—2961no—
379C2—1482no—
380C2#1455817111yescharacteristic
381C2C2×#1192455611yescharacteristic
382C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#553C2
socleC22×C37C22×D4
hypercenter#553D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14558179C2semidirect
2. #14557890C2semidirect
3. #14557868C2semidirect
4. #14557857C2semidirect
5. #14557830C2semidirect
6. #14557767C2semidirect
7. #14557760C2semidirect
8. #14557748C2semidirect
9. #14557676C2semidirect
10. #14557666C2semidirect
11. C4×#10596939C2semidirect
12. D4×#64436C2semidirect
13. #14557527C2semidirect
14. C2×#11924456C2semidirect
15. C37×#553C2semidirect
18. C2×#10596940C22semidirect
22. C22×#64436C22semidirect
31. #11924469C22semidirect
32. #11924469C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. #11924459C22semidirect
36. #11924459C22semidirect
37. #11924459C22semidirect
38. #11924457C22semidirect
46. C22⋊#64436C22semidirect
47. C4×#64436C22semidirect
49. #125×C37C22semidirect
53. #121×C37C22semidirect
56. C4×D4×C37C22semidirect
57. #117×C37C22semidirect
192. #553D37semidirect
207. C37#3297semidirect
216. #125C2×D37semidirect
225. #121C2×D37semidirect
230. C4×D4C2×D37semidirect
231. #117C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581792
#145578902
#145578682
#145578572
#145578302
#145577672
#145577602
#145577482
#145576762
#145576662
C4×#105969392
D4×#644362
#145575272
C2×#119244562
C37×#5532
#329737