Finite Group Databasebeta

← #18006097

Subgroups — #18006097

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×#11924560C211yesmaximal, characteristic, complemented
2C2×SD16×D37C211yesmaximal, characteristic, complemented
3#14558191C211yesmaximal, characteristic, complemented
4D4×D148C211yesmaximal, characteristic, complemented
5#14557923C211yesmaximal, characteristic, complemented
6#14557782C211yesmaximal, characteristic, complemented
7#14557768C211yesmaximal, characteristic, complemented
8#14557734C211yesmaximal, characteristic, complemented
9#14557682C211yesmaximal, characteristic, complemented
10#14557679C211yesmaximal, characteristic, complemented
11#14557673C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13#14557633C211yesmaximal, characteristic, complemented
14#14557603C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic, complemented
17C2×Q8×D37C2211yescharacteristic, complemented
18C22×D148—21no—
19C2×D4×D37C2211yescharacteristic
20C2×D4×D37C2211yescharacteristic
21#11924560—24no—
22C2×#10596930C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic
25C2×#10596941C2211yescharacteristic, complemented
26C2×#10596941C2211yescharacteristic, complemented
27SD16×D37—24no—
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596939C2211yescharacteristic, complemented
30C2×#10596929C2211yescharacteristic, complemented
31C2×C8×D37C2211yescharacteristic, complemented
32#11924533C2211yescharacteristic
33#11924522—21no—
34#11924513—21no—
35#11924512C2211yescharacteristic, complemented
36#11924511C2211yescharacteristic
37#11924511C2211yescharacteristic
38#11924510—21no—
39#11924509—21no—
40#11924507C2211yescharacteristic, complemented
41#11924506—21no—
42#11924506—21no—
43C4×Dic74C2211yescharacteristic, complemented
44C4×D148C2211yescharacteristic
45#11924496—21no—
46#11924469C2211yescharacteristic, complemented
47#11924459C2211yescharacteristic, complemented
48#11924458C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic, complemented
50#11924457C2211yescharacteristic
51#11924448C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924447C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic
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—
72Q8×D37—22no—
73Q8×D37—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×D148—21no—
83C2×D148—21no—
84C2×D148—44no—
85C2×D148D411yescharacteristic
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37C2311yescharacteristic
90C2×C4×D37C2311yescharacteristic
91C2×Dic74—21no—
92C2×Dic74C2311yescharacteristic
93SD16×C37—22no—
94D8×C37—22no—
95C2×C8×C37C2311yescharacteristic
96C2×C8×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C42×C37C2311yescharacteristic
102C22⋊Dic37—21no—
103#10596941—22no—
104#10596941—41no—
105#10596940D414yescomplemented
106#10596939—22no—
107#10596939—41no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938D411yescharacteristic
112#10596938D411yescharacteristic
113C4⋊Dic37D411yescharacteristic
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936—21no—
117C4×Dic37—21no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120#10596930—22no—
121#10596930—22no—
122#10596929—22no—
123C8×D37—22no—
124C23×C37—21no—
125C23×C37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—42no—
132C22×D37—81no—
133C22×D37—81no—
134C22×D37C2×D411yescharacteristic
135C22×D37C2×D411yescharacteristic
136Q8×C37—21no—
137Q8×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—21no—
141D4×C37C2×D412yes—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—42no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2×D411yescharacteristic
147C2×C4×C37C2411yescharacteristic
148C22⋊D37—42no—
149C22⋊D37—42no—
150C22⋊D37—42no—
151C22⋊D37—42no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—42no—
155C2×Dic37C2×D411yescharacteristic
156C2×Dic37C2×D411yescharacteristic
157D148—22no—
158D148—21no—
159D148—21no—
160D148—21no—
161D148—21no—
162D148—42no—
163D148—42no—
164D148—42no—
165D148—81no—
166C4×D37—21no—
167C4×D37—21no—
168C4×D37—21no—
169C4×D37—21no—
170C4×D37—42no—
171Dic74—21no—
172Dic74—42no—
173Dic74C2×D412yescomplemented
174C8×C37—21no—
175C8×C37—21no—
176#64436—21no—
177#64436C2×D412yescomplemented
178C22×C37—22no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37C22×D411yescharacteristic
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—21no—
188C2×D37—21no—
189C2×D37—21no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C2×D37—41no—
196C2×D37—84no—
197C2×D37—84no—
198C2×D37AGL(1,ℤ/8)12yescomplemented
199C4×C37—21no—
200C4×C37—21no—
201C4×C37—41no—
202C4×C37—41no—
203C4×C37C22×D411yescharacteristic
204C4×C37H(5,𝔽2)11yescharacteristic
205Dic37—22no—
206Dic37—21no—
207Dic37—21no—
208Dic37—41no—
209#3265—371nomaximal, Sylow
210C2×C37—42no—
211C2×C37—81no—
212C2×C37D4211yescharacteristic
213C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C37#57711yescharacteristic
215D37—22no—
216D37—41no—
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#463D3711yescharacteristic, complemented
227#460—371no—
228#450—371no—
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—371no—
239C22×D4—741no—
240AGL(1,ℤ/8)—744no—
241C2×SD16—371no—
242C2×SD16—371no—
243C2×SD16—371no—
244C2×SD16—371no—
245C2×SD16—371no—
246C2×SD16—744no—
247C2×SD16C2×D3711yescharacteristic
248C2×D8—371no—
249C2×D8—371no—
250C2×D8C2×D3711yescharacteristic
251C2×M16—371no—
252C22×C8—371no—
253#127—371no—
254#124—741no—
255#124C2×D3711yescharacteristic, complemented
256C22⋊Q8—371no—
257C22⋊Q8—741no—
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—741no—
268C4×D4C2×D3711yescharacteristic
269#107—371no—
270C4⋊C8C2×D3711yescharacteristic, complemented
271#103—371no—
272#103C2×D3711yescharacteristic, complemented
273#102—371no—
274#102—371no—
275#102—371no—
276#102C2×D3711yescharacteristic, complemented
277C22⋊C8—371no—
278C22⋊C8—371no—
279#97—371no—
280C24—741no—
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—371no—
290C2×D4—371no—
291C2×D4—371no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—742no—
297C2×D4—742no—
298C2×D4—741no—
299C2×D4—741no—
300C2×D4—741no—
301C2×D4—741no—
302C2×D4—1484no—
303C2×D4—1481no—
304C2×D4—1481no—
305C2×D4C22×D3711yescharacteristic
306C2×D4C22×D3711yescharacteristic
307C22×C4—21no—
308C22×C4—371no—
309C22×C4—371no—
310C22×C4—741no—
311C22×C4—741no—
312SD16—22no—
313SD16—374no—
314SD16—742no—
315SD16—742no—
316SD16—742no—
317SD16—1481no—
318D8—22no—
319D8—742no—
320D8—1481no—
321M16—742no—
322C2×C8—371no—
323C2×C8—371no—
324C2×C8—742no—
325C2×C8C22×D3711yescharacteristic
326C2×C8C22×D3711yescharacteristic
327C4⋊C4—371no—
328C4⋊C4—371no—
329C4⋊C4—741no—
330C4⋊C4—741no—
331C4⋊C4C22×D3711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—371no—
336C22⋊C4—371no—
337C22⋊C4—741no—
338C22⋊C4—741no—
339C22⋊C4—741no—
340C22⋊C4—741no—
341C42—741no—
342C42C22×D3711yescharacteristic
343C23—21no—
344C23—21no—
345C23—371no—
346C23—371no—
347C23—2961no—
348C23—2961no—
349C23—741no—
350C23—741no—
351C23—1482no—
352C23—1482no—
353C23—1482no—
354C23—1482no—
355Q8—21no—
356Q8—21no—
357Q8—372no—
358Q8—741no—
359Q8—1482no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—2961no—
364D4—742no—
365D4—741no—
366D4—741no—
367D4—741no—
368D4—741no—
369D4—1482no—
370D4—1482no—
371D4—1482no—
372D4—1482no—
373D4—1482no—
374D4—1482no—
375D4—1482no—
376D4D4×D3712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—371no—
381C2×C4—371no—
382C2×C4—741no—
383C2×C4—741no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—1482no—
389C2×C4—1482no—
390C2×C4D4×D3711yescharacteristic
391C2×C4D4×D3711yescharacteristic
392C2×C4C23×D3711yescharacteristic
393C8—21no—
394C8—21no—
395C8—372no—
396C8—741no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—372no—
404C22—2964no—
405C22—2964no—
406C22—741no—
407C22—741no—
408C22—741no—
409C22—741no—
410C22—741no—
411C22—1481no—
412C22—1481no—
413C22—1481no—
414C22—1481no—
415C22—1481no—
416C22—1481no—
417C22C2×D4×D3711yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—741no—
423C4—741no—
424C4—742no—
425C4—1481no—
426C4C2×D4×D3711yescharacteristic
427C4#1192458211yescharacteristic
428C2—42no—
429C2—81no—
430C2—2961no—
431C2—2961no—
432C2—742no—
433C2—1481no—
434C2#1455816711yescharacteristic
435C2AGL(1,ℤ/8)×D3711yescharacteristic
436C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
hypercenter#463D37
hypocenterC37#3265
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×#11924560C2semidirect
2. C2×SD16×D37C2semidirect
3. #14558191C2semidirect
4. D4×D148C2semidirect
5. #14557923C2semidirect
6. #14557782C2semidirect
7. #14557768C2semidirect
8. #14557734C2semidirect
9. #14557682C2semidirect
10. #14557679C2semidirect
11. #14557673C2semidirect
12. #14557665C2semidirect
13. #14557633C2semidirect
14. #14557603C2semidirect
15. C37×#463C2semidirect
16. C2×#10596964C22semidirect
17. C2×Q8×D37C22semidirect
22. C2×#10596930C22semidirect
23. C2×#10596930C22semidirect
25. C2×#10596941C22semidirect
26. C2×#10596941C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596939C22semidirect
30. C2×#10596929C22semidirect
31. C2×C8×D37C22semidirect
35. #11924512C22semidirect
40. #11924507C22semidirect
43. C4×Dic74C22semidirect
46. #11924469C22semidirect
47. #11924459C22semidirect
48. #11924458C22semidirect
49. #11924458C22semidirect
51. #11924448C22semidirect
52. #11924448C22semidirect
53. #11924447C22semidirect
56. #124×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
105. #10596940D4semidirect
173. Dic74C2×D4semidirect
177. #64436C2×D4semidirect
198. C2×D37AGL(1,ℤ/8)semidirect
226. #463D37semidirect
234. C37#3265semidirect
255. #124C2×D37semidirect
270. C4⋊C8C2×D37semidirect
272. #103C2×D37semidirect
276. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
C2×SD16×D372
#145581912
D4×D1482
#145579232
#145577822
#145577682
#145577342
#145576822
#145576792
#145576732
#145576652
#145576332
#145576032
C37×#4632
#326537