Finite Group Databasebeta

← #18006453

Subgroups — #18006453

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#14558176C211yesmaximal, characteristic, complemented
3#14557887C211yesmaximal, characteristic, complemented
4#14557867C211yesmaximal, characteristic, complemented
5#14557856C211yesmaximal, characteristic, complemented
6#14557834C211yesmaximal, characteristic, complemented
7#14557766C211yesmaximal, characteristic, complemented
8#14557759C211yesmaximal, characteristic, complemented
9#14557677C211yesmaximal, characteristic, complemented
10#14557665C211yesmaximal, characteristic, complemented
11C4×#10596939C211yesmaximal, characteristic, complemented
12#14557598C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic, complemented
21#11924529—21no—
22#11924528C2211yescharacteristic, complemented
23#11924519—21no—
24#11924518—21no—
25#11924512C2211yescharacteristic
26#11924509—21no—
27#11924509—21no—
28#11924507C2211yescharacteristic
29#11924507C2211yescharacteristic
30#11924507C2211yescharacteristic, complemented
31#11924506—21no—
32C4×D148C2211yescharacteristic
33C4×D148C2211yescharacteristic
34C4×C22⋊D37—21no—
35#11924494C2211yescharacteristic, complemented
36C4⋊C4×D37C2211yescharacteristic
37C22⋊C4×D37—21no—
38#11924470C2211yescharacteristic, complemented
39#11924469C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924460C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51C4×#64436C2211yescharacteristic, complemented
52C2×SD16×C37C2211yescharacteristic, complemented
53C2×D8×C37C2211yescharacteristic
54#124×C37C2211yescharacteristic
55C4×D4×C37C2211yescharacteristic, complemented
56C4⋊C8×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68#10596966—22no—
69#10596966—41no—
70D4×D37—22no—
71D4×D37—41no—
72C2×D148—21no—
73C2×D148D411yescharacteristic
74C2×D148C2311yescharacteristic
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×C4×D37C2311yescharacteristic
80SD16×C37—41no—
81D8×C37—41no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92#10596939—22no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
97#10596938D411yescharacteristic
98C4⋊Dic37D411yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
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
119Q8×C37—21no—
120Q8×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—42no—
132C22⋊D37—42no—
133C22⋊D37—81no—
134C22⋊D37—81no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140D148—22no—
141D148—21no—
142D148—42no—
143D148#4112yes—
144C4×D37—21no—
145C4×D37—21no—
146C4×D37—21no—
147C4×D37—21no—
148C4×D37—42no—
149C4×D37—81no—
150C4×D37—81no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—41no—
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—22no—
166C2×D37—21no—
167C2×D37—21no—
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—81no—
185C2×C37—81no—
186C2×C37#54611yescharacteristic
187C2×C37C2×#13511yescharacteristic
188C2×C37#57611yescharacteristic
189D37—22no—
190D37—41no—
191D37—42no—
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#463D3711yescharacteristic, complemented
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×SD16C2×D3711yescharacteristic, complemented
211C2×D8—371no—
212C2×D8C2×D3711yescharacteristic
213C22×C8—371no—
214C22×C8—371no—
215#126—741no—
216#125—371no—
217#124C2×D3711yescharacteristic
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—371no—
229C4×D4—741no—
230C4×D4C2×D3711yescharacteristic, complemented
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107—371no—
236#106—371no—
237C4⋊C8C2×D3711yescharacteristic, complemented
238#103—371no—
239#103—371no—
240#103C2×D3711yescharacteristic, complemented
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102C2×D3711yescharacteristic
248C22⋊C8—371no—
249C22⋊C8—371no—
250C4×C8—371no—
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8C22×D3711yescharacteristic
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—741no—
258C2×D4—741no—
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—371no—
268C22×C4—371no—
269C22×C4—741no—
270C22×C4—741no—
271C22×C4—741no—
272SD16—41no—
273D8—41no—
274D8—742no—
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—371no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4—741no—
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—371no—
294C22⋊C4—371no—
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—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—372no—
318D4—2961no—
319D4—2961no—
320D4—742no—
321D4—741no—
322D4—1482no—
323D4—1482no—
324D4—1482no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—371no—
329C2×C4—371no—
330C2×C4—2961no—
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—41no—
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—742no—
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—
373C4#41×D3711yescharacteristic
374C4#1192458111yescharacteristic
375C2—81no—
376C2—81no—
377C2—742no—
378C2—1482no—
379C2—1481no—
380C2#1455818011yescharacteristic
381C2#135×D3711yescharacteristic
382C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
hypercenter#463D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14558233C2semidirect
2. #14558176C2semidirect
3. #14557887C2semidirect
4. #14557867C2semidirect
5. #14557856C2semidirect
6. #14557834C2semidirect
7. #14557766C2semidirect
8. #14557759C2semidirect
9. #14557677C2semidirect
10. #14557665C2semidirect
11. C4×#10596939C2semidirect
12. #14557598C2semidirect
13. #14557528C2semidirect
14. #102×D37C2semidirect
15. C37×#463C2semidirect
20. C2×C8×D37C22semidirect
22. #11924528C22semidirect
30. #11924507C22semidirect
35. #11924494C22semidirect
38. #11924470C22semidirect
39. #11924469C22semidirect
40. #11924468C22semidirect
41. #11924460C22semidirect
42. #11924460C22semidirect
47. #11924457C22semidirect
50. #11924448C22semidirect
51. C4×#64436C22semidirect
52. C2×SD16×C37C22semidirect
55. C4×D4×C37C22semidirect
56. C4⋊C8×C37C22semidirect
57. #103×C37C22semidirect
200. #463D37semidirect
207. C37#3297semidirect
210. C2×SD16C2×D37semidirect
230. C4×D4C2×D37semidirect
237. C4⋊C8C2×D37semidirect
240. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582332
#145581762
#145578872
#145578672
#145578562
#145578342
#145577662
#145577592
#145576772
#145576652
C4×#105969392
#145575982
#145575282
#102×D372
C37×#4632
#329737