Finite Group Databasebeta

← #18006093

Subgroups — #18006093

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×#11924563C211yesmaximal, characteristic, complemented
2C2×SD16×D37C211yesmaximal, characteristic, complemented
3#14558195C211yesmaximal, characteristic, complemented
4D4×D148C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557780C211yesmaximal, characteristic, complemented
7#14557770C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557733C211yesmaximal, characteristic, complemented
10#14557685C211yesmaximal, characteristic, complemented
11#14557681C211yesmaximal, characteristic, complemented
12#14557673C211yesmaximal, characteristic, complemented
13#14557668C211yesmaximal, characteristic, complemented
14#14557606C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic, complemented
17C2×Q8×D37C2211yescharacteristic, complemented
18C22×D148—21no—
19C2×D4×D37C2211yescharacteristic
20C2×D4×D37C2211yescharacteristic
21#11924563—24no—
22C2×#10596930C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic
25C2×#10596941C2211yescharacteristic, complemented
26C2×#10596941C2211yescharacteristic, complemented
27SD16×D37—24no—
28C2×D296C2211yescharacteristic, complemented
29C2×D296C2211yescharacteristic, complemented
30C2×#10596939C2211yescharacteristic
31C2×#10596929C2211yescharacteristic, complemented
32C2×C8×D37C2211yescharacteristic, complemented
33#11924533C2211yescharacteristic
34#11924524—21no—
35#11924524C2211yescharacteristic, complemented
36#11924516—21no—
37#11924516C2211yescharacteristic, complemented
38#11924511—21no—
39#11924511C2211yescharacteristic
40#11924511C2211yescharacteristic
41#11924511C2211yescharacteristic, complemented
42#11924510—21no—
43#11924506—21no—
44#11924506—21no—
45C4×D148—21no—
46C4×D148C2211yescharacteristic
47C4⋊#64436C2211yescharacteristic, complemented
48#11924459C2211yescharacteristic, complemented
49#11924456C2211yescharacteristic, complemented
50#11924456C2211yescharacteristic, complemented
51#11924456C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924448C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic
55C4×Q8×C37C2211yescharacteristic, complemented
56C4×D4×C37C2211yescharacteristic
57#107×C37C2211yescharacteristic, complemented
58#103×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68#10596966—22no—
69#10596966—41no—
70Q8×D37—22no—
71Q8×D37—41no—
72D4×D37—22no—
73D4×D37—22no—
74D4×D37—41no—
75D4×D37—41no—
76C2×D148—21no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148—21no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148—44no—
83C2×D148D411yescharacteristic
84C2×D148C2311yescharacteristic
85C2×D148C2311yescharacteristic
86C2×D148C2311yescharacteristic
87C2×C4×D37—21no—
88C2×C4×D37—21no—
89C2×C4×D37C2311yescharacteristic
90C2×C4×D37C2311yescharacteristic
91C2×Dic74—21no—
92C2×Dic74C2311yescharacteristic
93SD16×C37D414yescomplemented
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C4⋊C4×C37—21no—
97C4⋊C4×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C22⋊C4×C37—21no—
100C42×C37—21no—
101C42×C37C2311yescharacteristic
102#10596941—22no—
103#10596941—22no—
104#10596940—22no—
105#10596939—22no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112#10596938D411yescharacteristic
113#10596938D411yescharacteristic
114C4⋊Dic37—21no—
115C4⋊Dic37D411yescharacteristic
116C2×#64436C2311yescharacteristic
117C2×#64436C2311yescharacteristic
118D296—22no—
119D296—41no—
120#10596930—22no—
121#10596930—41no—
122#10596929—22no—
123C8×D37—22no—
124C23×C37—21no—
125C22×D37—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×C37C2×D412yescomplemented
138D4×C37—21no—
139D4×C37C2×D412yes—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—42no—
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C22⋊D37—42no—
148C22⋊D37—42no—
149C2×Dic37—21no—
150C2×Dic37C2×D411yescharacteristic
151C2×Dic37C2×D411yescharacteristic
152D148—22no—
153D148—21no—
154D148—21no—
155D148—21no—
156D148—21no—
157D148—21no—
158D148—21no—
159D148—42no—
160D148—42no—
161D148—42no—
162D148—42no—
163D148—42no—
164D148—81no—
165C4×D37—21no—
166C4×D37—21no—
167C4×D37—21no—
168C4×D37—21no—
169C4×D37—42no—
170C4×D37—42no—
171Dic74—21no—
172Dic74—21no—
173Dic74—42no—
174C8×C37—21no—
175C8×C37C2×D412yescomplemented
176#64436—21no—
177#64436—21no—
178C22×C37—22no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37C22×D411yescharacteristic
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—21no—
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—41no—
188C2×D37—41no—
189C2×D37—41no—
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—22no—
200C4×C37—21no—
201C4×C37—21no—
202C4×C37—41no—
203C4×C37—41no—
204C4×C37C22×D411yescharacteristic
205C4×C37H(5,𝔽2)11yescharacteristic
206Dic37—21no—
207Dic37—21no—
208Dic37—41no—
209#3265—371nomaximal, Sylow
210C2×C37—42no—
211C2×C37D4211yescharacteristic
212C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C37#57711yescharacteristic
214D37—22no—
215D37—41no—
216D37—81no—
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#450—371no—
229#449—371no—
230#448—371no—
231#447—371no—
232#440D3711yescharacteristic, complemented
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×D8—371no—
251C2×M16—371no—
252C22×C8—371no—
253#127—371no—
254#124—371no—
255#124—741no—
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×Q8C2×D3711yescharacteristic, complemented
266C4×D4—371no—
267C4×D4—741no—
268C4×D4C2×D3711yescharacteristic
269#107C2×D3711yescharacteristic, complemented
270C4⋊C8—371no—
271#103—371no—
272#103C2×D3711yescharacteristic, complemented
273#102—371no—
274#102—371no—
275#102—371no—
276#102C2×D3711yescharacteristic
277C22⋊C8—371no—
278C22⋊C8—371no—
279#97C2×D3711yescharacteristic, complemented
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—371no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4—741no—
299C2×D4—742no—
300C2×D4—742no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—1484no—
304C2×D4—1481no—
305C2×D4—1481no—
306C2×D4C22×D3711yescharacteristic
307C22×C4—21no—
308C22×C4—371no—
309C22×C4—371no—
310C22×C4—741no—
311C22×C4—741no—
312SD16—742no—
313SD16—742no—
314SD16—742no—
315SD16—742no—
316SD16—1481no—
317SD16D14814yescomplemented
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—741no—
330C4⋊C4C22×D3711yescharacteristic
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—21no—
342C42C22×D3711yescharacteristic
343C23—21no—
344C23—371no—
345C23—371no—
346C23—2961no—
347C23—2961no—
348C23—741no—
349C23—741no—
350C23—741no—
351C23—1482no—
352C23—1482no—
353C23—1482no—
354C23—1482no—
355Q8—21no—
356Q8—741no—
357Q8—741no—
358Q8—1482no—
359Q8C2×D14812yescomplemented
360D4—21no—
361D4—2961no—
362D4—742no—
363D4—741no—
364D4—741no—
365D4—741no—
366D4—741no—
367D4—741no—
368D4—741no—
369D4—1482no—
370D4—1482no—
371D4—1482no—
372D4—1482no—
373D4—1482no—
374D4—1482no—
375D4—1482no—
376D4C2×D14812yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—371no—
382C2×C4—371no—
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—741no—
395C8—741no—
396C8C2×D14812yescomplemented
397C22—22no—
398C22—41no—
399C22—41no—
400C22—372no—
401C22—2964no—
402C22—2964no—
403C22—741no—
404C22—741no—
405C22—741no—
406C22—741no—
407C22—741no—
408C22—1481no—
409C22—1481no—
410C22—1481no—
411C22—1481no—
412C22—1481no—
413C22—1481no—
414C22—1481no—
415C22—1481no—
416C22—1481no—
417C22C2×D4×D3711yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—741no—
424C4—741no—
425C4—1481no—
426C4C22×D14811yescharacteristic
427C4#1192458211yescharacteristic
428C2—42no—
429C2—2961no—
430C2—2961no—
431C2—2961no—
432C2—742no—
433C2—1481no—
434C2D4×D14811yescharacteristic
435C2AGL(1,ℤ/8)×D3711yescharacteristic
436C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
hypercenter#440D37
hypocenterC37#3265
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C2×SD16×D37C2semidirect
3. #14558195C2semidirect
4. D4×D148C2semidirect
5. #14557922C2semidirect
6. #14557780C2semidirect
7. #14557770C2semidirect
8. #14557748C2semidirect
9. #14557733C2semidirect
10. #14557685C2semidirect
11. #14557681C2semidirect
12. #14557673C2semidirect
13. #14557668C2semidirect
14. #14557606C2semidirect
15. C37×#440C2semidirect
16. C2×#10596966C22semidirect
17. C2×Q8×D37C22semidirect
22. C2×#10596930C22semidirect
23. C2×#10596930C22semidirect
25. C2×#10596941C22semidirect
26. C2×#10596941C22semidirect
28. C2×D296C22semidirect
29. C2×D296C22semidirect
31. C2×#10596929C22semidirect
32. C2×C8×D37C22semidirect
35. #11924524C22semidirect
37. #11924516C22semidirect
41. #11924511C22semidirect
47. C4⋊#64436C22semidirect
48. #11924459C22semidirect
49. #11924456C22semidirect
50. #11924456C22semidirect
51. #11924456C22semidirect
52. #11924448C22semidirect
53. #11924448C22semidirect
55. C4×Q8×C37C22semidirect
57. #107×C37C22semidirect
58. #103×C37C22semidirect
60. #97×C37C22semidirect
93. SD16×C37D4semidirect
137. Q8×C37C2×D4semidirect
175. C8×C37C2×D4semidirect
198. C2×D37AGL(1,ℤ/8)semidirect
232. #440D37semidirect
234. C37#3265semidirect
265. C4×Q8C2×D37semidirect
269. #107C2×D37semidirect
272. #103C2×D37semidirect
279. #97C2×D37semidirect
317. SD16D148semidirect
359. Q8C2×D148semidirect
396. C8C2×D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×SD16×D372
#145581952
D4×D1482
#145579222
#145577802
#145577702
#145577482
#145577332
#145576852
#145576812
#145576732
#145576682
#145576062
C37×#4402
#326537