Finite Group Databasebeta

← #18006202

Subgroups — #18006202

Order 4736.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924563C211yesmaximal, characteristic, complemented
2C2×#11924560C211yesmaximal, characteristic, complemented
3#14558178C211yesmaximal, characteristic, complemented
4#14558176C211yesmaximal, characteristic, complemented
5#14557915C211yesmaximal, characteristic, complemented
6#14557782C211yesmaximal, characteristic, complemented
7#14557778C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557698C211yesmaximal, characteristic, complemented
10#14557692C211yesmaximal, characteristic, complemented
11#14557668C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557610C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic, complemented
19C2×D4×D37C2211yescharacteristic, complemented
20#11924563—24no—
21#11924560—24no—
22C2×#10596942C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic, complemented
25C2×#10596941C2211yescharacteristic, complemented
26C2×D296C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596929C2211yescharacteristic, complemented
30C2×#10596929C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic, complemented
32#11924520—21no—
33#11924518—21no—
34#11924516C2211yescharacteristic, complemented
35#11924512C2211yescharacteristic, complemented
36#11924511C2211yescharacteristic
37#11924510—21no—
38#11924509—21no—
39#11924507C2211yescharacteristic
40#11924506—21no—
41#11924506—21no—
42C4×D148C2211yescharacteristic
43C4×D148C2211yescharacteristic, complemented
44C2×#10596938—21no—
45C22⋊C4×D37—21no—
46#11924469C2211yescharacteristic, complemented
47#11924461C2211yescharacteristic, complemented
48#11924458C2211yescharacteristic, complemented
49#11924457C2211yescharacteristic, complemented
50#11924456C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53C4×#64436C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C22×Dic37—21no—
72#10596966—22no—
73#10596966—41no—
74#10596964—22no—
75#10596964—41no—
76D4×D37—22no—
77D4×D37—22no—
78D4×D37—41no—
79D4×D37—41no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148D411yescharacteristic
83C2×D148C2311yescharacteristic
84C2×D148C2311yescharacteristic
85C2×C4×D37—21no—
86C2×C4×D37—21no—
87C2×C4×D37C2311yescharacteristic
88C2×C4×D37C2311yescharacteristic
89C2×Dic74C2311yescharacteristic
90SD16×C37—22no—
91D8×C37—22no—
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C42×C37C2311yescharacteristic
99C22⋊Dic37—21no—
100#10596942—41no—
101#10596941—22no—
102#10596940—22no—
103#10596939—41no—
104#10596939D414yescomplemented
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938D411yescharacteristic
112#10596938D411yescharacteristic
113C4⋊Dic37—21no—
114C4⋊Dic37D411yescharacteristic
115C4⋊Dic37C2311yescharacteristic
116#10596936—21no—
117C2×#64436C2311yescharacteristic
118C2×#64436C2311yescharacteristic
119D296—22no—
120#10596930—22no—
121#10596929—22no—
122#10596929—22no—
123C23×C37—21no—
124C23×C37—21no—
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—81no—
132C22×D37—81no—
133C22×D37C2×D411yescharacteristic
134C22×D37C2×D411yescharacteristic
135Q8×C37—21no—
136Q8×C37—21no—
137D4×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37C2×D412yes—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—81no—
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—42no—
150C22⋊D37—81no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—42no—
154C2×Dic37C2×D411yescharacteristic
155C2×Dic37C2×D411yescharacteristic
156D148—21no—
157D148—21no—
158D148—21no—
159D148—41no—
160D148—42no—
161D148—81no—
162D148C2×D412yes—
163C4×D37—21no—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—21no—
167C4×D37—42no—
168C4×D37—81no—
169Dic74—21no—
170Dic74—21no—
171C8×C37—21no—
172C8×C37—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—22no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37C22×D411yescharacteristic
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—22no—
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—21no—
188C2×D37—21no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C2×D37—84no—
196C4×C37—21no—
197C4×C37—21no—
198C4×C37—41no—
199C4×C37—41no—
200C4×C37C22×D411yescharacteristic
201C4×C37H(5,𝔽2)11yescharacteristic
202Dic37—21no—
203Dic37—21no—
204Dic37—41no—
205Dic37—41no—
206#3273—371nomaximal, Sylow
207C2×C37—42no—
208C2×C37—81no—
209C2×C37D4211yescharacteristic
210C2×C37#57511yescharacteristic
211C2×C37#57611yescharacteristic
212D37—41no—
213D37—41no—
214D37—42no—
215D37—81no—
216C2×AGL(1,ℤ/8)—371no—
217C2×AGL(1,ℤ/8)—371no—
218#546—371no—
219#546—371no—
220#495—371no—
221#468—371no—
222#468—371no—
223#463—371no—
224#463D3711yescharacteristic, complemented
225#452—371no—
226#452—371no—
227#447—371no—
228#447—371no—
229C4×D8—371no—
230#436—371no—
231C37#327311yescharacteristic, complemented, Sylow
232C2×#41—371no—
233C2×#41—371no—
234C22×D4—371no—
235C22×D4—371no—
236AGL(1,ℤ/8)—744no—
237AGL(1,ℤ/8)—744no—
238C2×Q16—371no—
239C2×SD16—371no—
240C2×SD16—371no—
241C2×SD16—371no—
242C2×SD16C2×D3711yescharacteristic, complemented
243C2×D8—371no—
244C2×D8—371no—
245C2×D8—371no—
246C2×D8C2×D3711yescharacteristic
247C2×M16—371no—
248C2×M16—371no—
249#124—371no—
250#124C2×D3711yescharacteristic, complemented
251#123—741no—
252#123—741no—
253C22⋊Q8—371no—
254C22⋊Q8—371no—
255#121—371no—
256#121—371no—
257#121—741no—
258#121—741no—
259#120—741no—
260#120—741no—
261C4×D4—371no—
262C4×D4—371no—
263C4×D4C2×D3711yescharacteristic, complemented
264C2×C22⋊C4—741no—
265C2×C22⋊C4—741no—
266#107—371no—
267C4⋊C8C2×D3711yescharacteristic, complemented
268#103—371no—
269#103C2×D3711yescharacteristic, complemented
270#102—371no—
271#102—371no—
272#102—371no—
273#102C2×D3711yescharacteristic, complemented
274C22⋊C8—371no—
275C22⋊C8—371no—
276C4×C8—371no—
277C24—741no—
278C24—741no—
279#41—742no—
280#41—742no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—371no—
286C2×D4—371no—
287C2×D4—371no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4—742no—
293C2×D4—741no—
294C2×D4—742no—
295C2×D4—741no—
296C2×D4—1481no—
297C2×D4—1481no—
298C2×D4C22×D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C22×C4—21no—
301C22×C4—371no—
302C22×C4—371no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4—741no—
306Q16—1481no—
307SD16—22no—
308SD16—742no—
309SD16—742no—
310SD16—742no—
311D8—22no—
312D8—374no—
313D8—742no—
314D8—1481no—
315M16—742no—
316M16—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8C22×D3711yescharacteristic
320C2×C8C22×D3711yescharacteristic
321C4⋊C4—371no—
322C4⋊C4—371no—
323C4⋊C4—741no—
324C4⋊C4—741no—
325C4⋊C4C22×D3711yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—371no—
330C22⋊C4—371no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C22⋊C4—741no—
337C22⋊C4—741no—
338C42C22×D3711yescharacteristic
339C23—21no—
340C23—21no—
341C23—371no—
342C23—371no—
343C23—2961no—
344C23—2961no—
345C23—741no—
346C23—741no—
347C23—1482no—
348C23—1482no—
349C23—1482no—
350C23—1482no—
351Q8—21no—
352Q8—21no—
353Q8—741no—
354Q8—741no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—372no—
359D4—2961no—
360D4—2961no—
361D4—741no—
362D4—741no—
363D4—741no—
364D4—1481no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4—1482no—
369D4D4×D3712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—371no—
374C2×C4—371no—
375C2×C4—2961no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—741no—
382C2×C4—1482no—
383C2×C4—1482no—
384C2×C4D4×D3711yescharacteristic
385C2×C4D4×D3711yescharacteristic
386C2×C4C23×D3711yescharacteristic
387C8—21no—
388C8—21no—
389C8—372no—
390C8—741no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—2964no—
398C22—2964no—
399C22—741no—
400C22—741no—
401C22—741no—
402C22—741no—
403C22—741no—
404C22—741no—
405C22—742no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22—1481no—
410C22—1481no—
411C22C2×D4×D3711yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—741no—
417C4—741no—
418C4—1481no—
419C4—1481no—
420C4C2×D4×D3711yescharacteristic
421C4#1192458211yescharacteristic
422C2—42no—
423C2—81no—
424C2—2961no—
425C2—1481no—
426C2—1481no—
427C2—1482no—
428C2#1455816711yescharacteristic
429C2#1455833011yescharacteristic
430C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
hypercenter#463D37
hypocenterC37#3273
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. C2×#11924563C2semidirect
2. C2×#11924560C2semidirect
3. #14558178C2semidirect
4. #14558176C2semidirect
5. #14557915C2semidirect
6. #14557782C2semidirect
7. #14557778C2semidirect
8. #14557749C2semidirect
9. #14557698C2semidirect
10. #14557692C2semidirect
11. #14557668C2semidirect
12. #14557665C2semidirect
13. C4×#10596939C2semidirect
14. #14557610C2semidirect
15. C37×#463C2semidirect
18. C2×D4×D37C22semidirect
19. C2×D4×D37C22semidirect
22. C2×#10596942C22semidirect
23. C2×#10596930C22semidirect
24. C2×#10596940C22semidirect
25. C2×#10596941C22semidirect
29. C2×#10596929C22semidirect
30. C2×#10596929C22semidirect
31. #11924524C22semidirect
34. #11924516C22semidirect
35. #11924512C22semidirect
43. C4×D148C22semidirect
46. #11924469C22semidirect
47. #11924461C22semidirect
48. #11924458C22semidirect
49. #11924457C22semidirect
50. #11924456C22semidirect
51. #11924448C22semidirect
52. #11924448C22semidirect
53. C4×#64436C22semidirect
54. C2×SD16×C37C22semidirect
56. #124×C37C22semidirect
57. C4×D4×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
104. #10596939D4semidirect
224. #463D37semidirect
231. C37#3273semidirect
242. C2×SD16C2×D37semidirect
250. #124C2×D37semidirect
263. C4×D4C2×D37semidirect
267. C4⋊C8C2×D37semidirect
269. #103C2×D37semidirect
273. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×#119245602
#145581782
#145581762
#145579152
#145577822
#145577782
#145577492
#145576982
#145576922
#145576682
#145576652
C4×#105969392
#145576102
C37×#4632
#327337