Finite Group Databasebeta

← #18006089

Subgroups — #18006089

Order 4736.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924562C211yesmaximal, characteristic, complemented
2C2×SD16×D37C211yesmaximal, characteristic, complemented
3#14558193C211yesmaximal, characteristic, complemented
4D4×C22⋊D37C211yesmaximal, characteristic, complemented
5#14557919C211yesmaximal, characteristic, complemented
6#14557781C211yesmaximal, characteristic, complemented
7#14557768C211yesmaximal, characteristic, complemented
8#14557750C211yesmaximal, characteristic, complemented
9#14557732C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557670C211yesmaximal, characteristic, complemented
12#14557668C211yesmaximal, characteristic, complemented
13#14557630C211yesmaximal, characteristic, complemented
14#14557607C211yesmaximal, characteristic, complemented
15C37×#450C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic, complemented
17C2×Q8×D37C2211yescharacteristic, complemented
18C22×C22⋊D37—21no—
19C2×D4×D37C2211yescharacteristic
20#11924562—24no—
21C2×#10596930C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic
23C2×#10596940C2211yescharacteristic, complemented
24C2×#10596941C2211yescharacteristic, complemented
25SD16×D37—24no—
26C2×D296C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596934C2211yescharacteristic, complemented
30C2×C8×D37C2211yescharacteristic, complemented
31#11924532C2211yescharacteristic
32#11924525C2211yescharacteristic, complemented
33#11924522—21no—
34#11924514—21no—
35#11924511C2211yescharacteristic, complemented
36#11924510C2211yescharacteristic
37#11924509—21no—
38#11924508—21no—
39#11924507C2211yescharacteristic
40#11924505—21no—
41#11924504—21no—
42#11924501C2211yescharacteristic, complemented
43D4×Dic37C2211yescharacteristic
44#11924498—21no—
45C4×C22⋊D37C2211yescharacteristic
46#11924469C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic, complemented
51#11924456C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C22×D4×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic
56C2×SD16×C37C2211yescharacteristic, complemented
57C22⋊Q8×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic, complemented
60C22⋊C8×C37C2211yescharacteristic, complemented
61C24×C37—21no—
62C23×D37—21no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—22no—
65C2×D4×C37—21no—
66C2×D4×C37—41no—
67C2×D4×C37C2311yescharacteristic
68C2×D4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—44no—
77C2×C22⋊D37D411yescharacteristic
78C22×Dic37—21no—
79Q8×D37—22no—
80Q8×D37—41no—
81D4×D37—22no—
82D4×D37—41no—
83#10596962—22no—
84#10596962—41no—
85C2×D148—21no—
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×C4×D37C2311yescharacteristic
91C2×Dic74—21no—
92C2×Dic74C2311yescharacteristic
93SD16×C37—22no—
94SD16×C37—41no—
95C2×C8×C37C2311yescharacteristic
96C2×C8×C37C2311yescharacteristic
97C4⋊C4×C37—21no—
98C4⋊C4×C37C2311yescharacteristic
99C22⋊C4×C37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102C22⋊Dic37D411yescharacteristic
103#10596941—22no—
104#10596940—22no—
105#10596940D414yescomplemented
106#10596939—22no—
107#10596939—22no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112#10596938D411yescharacteristic
113C4⋊Dic37C2311yescharacteristic
114#10596936—21no—
115#10596936D411yescharacteristic
116C4×Dic37—21no—
117C4×Dic37C2311yescharacteristic
118#10596934—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121D296—41no—
122#10596930—22no—
123C8×D37—22no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—81no—
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131C22×D37—21no—
132C22×D37—42no—
133C22×D37—42no—
134C22×D37—81no—
135C22×D37C2×D411yescharacteristic
136Q8×C37—21no—
137Q8×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—21no—
141D4×C37—42no—
142D4×C37C2×D412yes—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2411yescharacteristic
149C22⋊D37—22no—
150C22⋊D37—42no—
151C22⋊D37—42no—
152C22⋊D37—42no—
153C22⋊D37—42no—
154C22⋊D37—42no—
155C22⋊D37—81no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158C2×Dic37—42no—
159C2×Dic37C2×D411yescharacteristic
160C2×Dic37C2×D411yescharacteristic
161C2×Dic37C2×D411yescharacteristic
162D148—21no—
163D148—21no—
164D148—21no—
165D148—21no—
166D148—42no—
167C4×D37—21no—
168C4×D37—21no—
169C4×D37—42no—
170C4×D37—42no—
171Dic74—21no—
172Dic74—42no—
173Dic74C2×D412yescomplemented
174C8×C37—21no—
175C8×C37—21no—
176#64436—21no—
177#64436C2×D412yescomplemented
178C22×C37—21no—
179C22×C37—22no—
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—84no—
188C22×C37C22×D411yescharacteristic
189C2×D37—21no—
190C2×D37—21no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C2×D37—41no—
196C2×D37—41no—
197C2×D37—84no—
198C2×D37AGL(1,ℤ/8)12yescomplemented
199C4×C37—21no—
200C4×C37—41no—
201C4×C37—41no—
202C4×C37C22×D411yescharacteristic
203C4×C37H(5,𝔽2)11yescharacteristic
204Dic37—22no—
205Dic37—21no—
206Dic37—21no—
207Dic37—21no—
208Dic37—41no—
209#3265—371nomaximal, Sylow
210C2×C37—42no—
211C2×C37—41no—
212C2×C37—81no—
213C2×C37D4211yescharacteristic
214C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C37#57711yescharacteristic
216D37—22no—
217D37—81no—
218D37—81no—
219C2×AGL(1,ℤ/8)—371no—
220C22×SD16—371no—
221#548—371no—
222D42—371no—
223#496—371no—
224#468—371no—
225#466—371no—
226#463—371no—
227#460—371no—
228#450D3711yescharacteristic, complemented
229#449—371no—
230#448—371no—
231#447—371no—
232#440—371no—
233#435—371no—
234C37#326511yescharacteristic, complemented, Sylow
235C2×#41—371no—
236C22×Q8—371no—
237C22×D4—371no—
238C22×D4—741no—
239C22×D4C2×D3711yescharacteristic
240AGL(1,ℤ/8)—744no—
241C2×SD16—371no—
242C2×SD16—371no—
243C2×SD16—371no—
244C2×SD16—371no—
245C2×SD16—744no—
246C2×SD16C2×D3711yescharacteristic
247C2×SD16C2×D3711yescharacteristic, complemented
248C2×D8—371no—
249C2×D8—371no—
250C2×D8—371no—
251C2×M16—371no—
252C22×C8—371no—
253#127—371no—
254#124—371no—
255#124—741no—
256C22⋊Q8—741no—
257C22⋊Q8C2×D3711yescharacteristic, complemented
258#121—371no—
259#121—371no—
260#121—371no—
261#121—741no—
262#121—741no—
263#120—741no—
264#120—741no—
265C4×Q8—371no—
266C4×D4—371no—
267C4×D4—371no—
268C4×D4—741no—
269#107—371no—
270C4⋊C8—371no—
271#103—371no—
272#103—371no—
273#102—371no—
274#102—371no—
275#102C2×D3711yescharacteristic
276#102C2×D3711yescharacteristic, complemented
277C22⋊C8—371no—
278C22⋊C8C2×D3711yescharacteristic, complemented
279#97—371no—
280C24—21no—
281C24—741no—
282#41—742no—
283#41—1481no—
284C2×Q8—371no—
285C2×Q8—741no—
286C2×Q8—742no—
287C2×Q8—1481no—
288C2×Q8C22×D3711yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—371no—
293C2×D4—371no—
294C2×D4—371no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4—741no—
299C2×D4—742no—
300C2×D4—741no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—1481no—
304C2×D4—1484no—
305C2×D4C22×D3711yescharacteristic
306C2×D4C22×D3711yescharacteristic
307C22×C4—371no—
308C22×C4—741no—
309C22×C4—741no—
310C22×C4—741no—
311C22×C4C22×D3711yescharacteristic
312SD16—22no—
313SD16—41no—
314SD16—374no—
315SD16—742no—
316SD16—742no—
317SD16—742no—
318D8—742no—
319D8—742no—
320D8—1481no—
321M16—742no—
322C2×C8—371no—
323C2×C8—371no—
324C2×C8—742no—
325C2×C8C22×D3711yescharacteristic
326C2×C8C22×D3711yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—371no—
329C4⋊C4—371no—
330C4⋊C4—741no—
331C4⋊C4C22×D3711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—371no—
334C22⋊C4—371no—
335C22⋊C4—741no—
336C22⋊C4—741no—
337C22⋊C4—741no—
338C22⋊C4—741no—
339C22⋊C4—741no—
340C22⋊C4—741no—
341C42—371no—
342C42—741no—
343C23—21no—
344C23—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—371no—
349C23—2961no—
350C23—741no—
351C23—741no—
352C23—1482no—
353C23—1482no—
354C23D4×D3711yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—372no—
358Q8—741no—
359Q8—1482no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—2961no—
365D4—742no—
366D4—741no—
367D4—741no—
368D4—741no—
369D4—741no—
370D4—1482no—
371D4—1482no—
372D4—1482no—
373D4—1482no—
374D4—1482no—
375D4—1482no—
376D4D4×D3712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—371no—
382C2×C4—371no—
383C2×C4—371no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—1482no—
389C2×C4—1482no—
390C2×C4—1482no—
391C2×C4D4×D3711yescharacteristic
392C2×C4C23×D3711yescharacteristic
393C8—21no—
394C8—21no—
395C8—372no—
396C8—741no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—84no—
407C22—372no—
408C22—2964no—
409C22—741no—
410C22—741no—
411C22—1481no—
412C22—1481no—
413C22—1481no—
414C22—1481no—
415C22—1481no—
416C22—1481no—
417C22C2×D4×D3711yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—741no—
422C4—741no—
423C4—741no—
424C4—742no—
425C4—1481no—
426C4C2×D4×D3711yescharacteristic
427C4#1192458111yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—2961no—
432C2—2961no—
433C2—742no—
434C2#1455816511yescharacteristic
435C2AGL(1,ℤ/8)×D3711yescharacteristic
436C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#450C2
socleC22×C37C22×D4
hypercenter#450D37
hypocenterC37#3265
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×SD16×D37C2semidirect
3. #14558193C2semidirect
4. D4×C22⋊D37C2semidirect
5. #14557919C2semidirect
6. #14557781C2semidirect
7. #14557768C2semidirect
8. #14557750C2semidirect
9. #14557732C2semidirect
10. #14557680C2semidirect
11. #14557670C2semidirect
12. #14557668C2semidirect
13. #14557630C2semidirect
14. #14557607C2semidirect
15. C37×#450C2semidirect
16. C2×#10596962C22semidirect
17. C2×Q8×D37C22semidirect
21. C2×#10596930C22semidirect
23. C2×#10596940C22semidirect
24. C2×#10596941C22semidirect
26. C2×D296C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596934C22semidirect
30. C2×C8×D37C22semidirect
32. #11924525C22semidirect
35. #11924511C22semidirect
42. #11924501C22semidirect
46. #11924469C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924458C22semidirect
51. #11924456C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
56. C2×SD16×C37C22semidirect
57. C22⋊Q8×C37C22semidirect
59. #102×C37C22semidirect
60. C22⋊C8×C37C22semidirect
105. #10596940D4semidirect
173. Dic74C2×D4semidirect
177. #64436C2×D4semidirect
198. C2×D37AGL(1,ℤ/8)semidirect
228. #450D37semidirect
234. C37#3265semidirect
247. C2×SD16C2×D37semidirect
257. C22⋊Q8C2×D37semidirect
276. #102C2×D37semidirect
278. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×SD16×D372
#145581932
D4×C22⋊D372
#145579192
#145577812
#145577682
#145577502
#145577322
#145576802
#145576702
#145576682
#145576302
#145576072
C37×#4502
#326537