Finite Group Databasebeta

← #468×D37 #18004180

Subgroups — #468×D37 #18004180

Order 4736.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D37C211yesmaximal, characteristic, complemented
2C2×M16×D37C211yesmaximal, characteristic, complemented
3C22⋊Q8×D37C211yesmaximal, characteristic, complemented
4#121×D37C211yesmaximal, characteristic
5#14557782C211yesmaximal, characteristic, complemented
6#14557781C211yesmaximal, characteristic, complemented
7#14557780C211yesmaximal, characteristic, complemented
8#14557779C211yesmaximal, characteristic, complemented
9#14557778C211yesmaximal, characteristic, complemented
10#14557777C211yesmaximal, characteristic, complemented
11#14557776C211yesmaximal, characteristic, complemented
12#107×D37C211yesmaximal, characteristic, complemented
13#103×D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×D4×D37—21no—
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C2×#10596930C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596941C2211yescharacteristic, complemented
23SD16×D37—24no—
24C2×#10596934C2211yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic, complemented
26C2×#10596929C2211yescharacteristic, complemented
27M16×D37—24no—
28C2×C8×D37C2211yescharacteristic
29C2×C8×D37C2211yescharacteristic
30#11924516C2211yescharacteristic, complemented
31#11924515C2211yescharacteristic, complemented
32#11924514—21no—
33#11924513—21no—
34#11924512C2211yescharacteristic, complemented
35#11924511C2211yescharacteristic
36#11924510C2211yescharacteristic
37#11924509—21no—
38#11924508—21no—
39#11924507C2211yescharacteristic
40C4⋊C4×D37—21no—
41C4⋊C4×D37C2211yescharacteristic
42C4⋊C4×D37C2211yescharacteristic
43C22⋊C4×D37—21no—
44C22⋊C4×D37—21no—
45#11924470C2211yescharacteristic, complemented
46#11924469C2211yescharacteristic, complemented
47#11924469C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic, complemented
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×M16×C37C2211yescharacteristic, complemented
56C22⋊Q8×C37C2211yescharacteristic, complemented
57#121×C37C2211yescharacteristic
58#107×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37D411yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—21no—
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C22×Dic37D411yescharacteristic
71Q8×D37—22no—
72Q8×D37—22no—
73D4×D37—22no—
74D4×D37—22no—
75D4×D37—44no—
76C2×D148—21no—
77C2×D148C2311yescharacteristic
78C2×C4×D37—22no—
79C2×C4×D37—22no—
80C2×C4×D37—21no—
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37D411yescharacteristic
84C2×C4×D37D411yescharacteristic
85C2×C4×D37C2311yescharacteristic
86C2×C4×D37C2311yescharacteristic
87C2×Dic74—21no—
88C2×Dic74C2311yescharacteristic
89SD16×C37—22no—
90M16×C37—22no—
91C2×C8×C37C2311yescharacteristic
92C2×C8×C37C2311yescharacteristic
93C4⋊C4×C37—21no—
94C4⋊C4×C37C2311yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100#10596941—22no—
101#10596940—22no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106C4⋊Dic37—21no—
107C4⋊Dic37C2311yescharacteristic
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596934—22no—
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116#10596930—22no—
117#10596929—22no—
118#10596929—22no—
119C8×D37—22no—
120C8×D37D414yescomplemented
121C23×C37—21no—
122C23×C37C2×D411yescharacteristic
123C22×D37—22no—
124C22×D37—22no—
125C22×D37—22no—
126C22×D37—21no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37C2×D411yescharacteristic
131C22×D37C2×D411yescharacteristic
132Q8×C37—21no—
133Q8×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—42no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2411yescharacteristic
144C22⋊D37—42no—
145C22⋊D37—42no—
146C22⋊D37—42no—
147C2×Dic37—22no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37C2×D411yescharacteristic
152C2×Dic37C2×D411yescharacteristic
153D148—21no—
154D148—21no—
155D148—42no—
156C4×D37—22no—
157C4×D37—21no—
158C4×D37—21no—
159C4×D37—22no—
160C4×D37—42no—
161C4×D37—42no—
162C4×D37—42no—
163C4×D37C2×D412yes—
164C4×D37#4112yes—
165Dic74—21no—
166Dic74—21no—
167Dic74—42no—
168C8×C37—21no—
169C8×C37C2×D412yescomplemented
170#64436—21no—
171#64436C2×D412yescomplemented
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—21no—
180C2×D37—21no—
181C2×D37—21no—
182C2×D37—44no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—84no—
187C2×D37#12112yes—
188C2×D37AGL(1,ℤ/8)12yes—
189C2×D37#13712yes—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37—41no—
194C4×C37C22×D411yescharacteristic
195C4×C37C2×#4111yescharacteristic
196Dic37—21no—
197Dic37—41no—
198Dic37—41no—
199Dic37—41no—
200Dic37#12112yes—
201C2×#468—371nomaximal, Sylow
202C2×C37—41no—
203C2×C37—81no—
204C2×C37C2×#12111yescharacteristic
205C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C37C2×#13711yescharacteristic
207D37—41no—
208D37—81no—
209D37#46814yesdirect product factor
210C22×SD16—371no—
211C22×M16—371no—
212C2×C22⋊Q8—371no—
213C2×#121—371no—
214#468—371no—
215#468—371no—
216#468—371no—
217#468—371no—
218#468—371no—
219#468—371no—
220#468—371no—
221#468D3711yescharacteristic, direct product factor
222C2×#107—371no—
223C2×#103—371no—
224C2×#102—371no—
225C37C2×#46811yescharacteristic, complemented, Sylow
226C22×Q8—371no—
227C22×D4—371no—
228C22×D4—741no—
229C23×C4—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16—744no—
234C2×SD16C2×D3711yescharacteristic, complemented
235C2×M16—371no—
236C2×M16—371no—
237C2×M16—371no—
238C2×M16—744no—
239C2×M16C2×D3711yescharacteristic, complemented
240C22×C8—371no—
241C22×C8—371no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246C22⋊Q8—741no—
247C22⋊Q8C2×D3711yescharacteristic, complemented
248#121—371no—
249#121—371no—
250#121—371no—
251#121—741no—
252#121—741no—
253#121C2×D3711yescharacteristic
254C2×C4⋊C4—371no—
255C2×C4⋊C4—371no—
256C2×C4⋊C4—741no—
257C2×C22⋊C4—741no—
258C2×C22⋊C4—741no—
259#107—371no—
260#107—371no—
261#107—371no—
262#107C2×D3711yescharacteristic, complemented
263#103—371no—
264#103—371no—
265#103—371no—
266#103C2×D3711yescharacteristic, complemented
267#102—371no—
268#102—371no—
269#102—371no—
270#102C2×D3711yescharacteristic, complemented
271C24—371no—
272C24—741no—
273C2×Q8—371no—
274C2×Q8—741no—
275C2×Q8—742no—
276C2×Q8—742no—
277C2×Q8C22×D3711yescharacteristic
278C2×D4—21no—
279C2×D4—371no—
280C2×D4—741no—
281C2×D4—742no—
282C2×D4—742no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4—741no—
286C2×D4—1484no—
287C2×D4C22×D3711yescharacteristic
288C22×C4—371no—
289C22×C4—371no—
290C22×C4—371no—
291C22×C4—371no—
292C22×C4—371no—
293C22×C4—742no—
294C22×C4—742no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4C22×D3711yescharacteristic
299SD16—22no—
300SD16—742no—
301SD16—742no—
302SD16—742no—
303M16—22no—
304M16—742no—
305M16—742no—
306M16—742no—
307C2×C8—371no—
308C2×C8—374no—
309C2×C8—371no—
310C2×C8—742no—
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—371no—
315C4⋊C4—371no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4—741no—
320C4⋊C4—741no—
321C4⋊C4C22×D3711yescharacteristic
322C4⋊C4C22×D3711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C23—21no—
332C23—371no—
333C23—371no—
334C23—742no—
335C23—742no—
336C23—742no—
337C23—741no—
338C23—1482no—
339C23—1482no—
340C23—1482no—
341C23D4×D3711yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—741no—
345Q8—741no—
346Q8—1482no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—741no—
351D4—741no—
352D4—1482no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—371no—
362C2×C4—372no—
363C2×C4—372no—
364C2×C4—371no—
365C2×C4—742no—
366C2×C4—742no—
367C2×C4—742no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—741no—
372C2×C4—741no—
373C2×C4—1482no—
374C2×C4—1482no—
375C2×C4—1482no—
376C2×C4D4×D3711yescharacteristic
377C2×C4C23×D3711yescharacteristic
378C8—21no—
379C8—372no—
380C8—741no—
381C8D4×D3712yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—372no—
389C22—372no—
390C22—372no—
391C22—2964no—
392C22—741no—
393C22—741no—
394C22—741no—
395C22—1484no—
396C22—1481no—
397C22—1481no—
398C22—1481no—
399C22C2×D4×D3711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—372no—
405C4—741no—
406C4—1481no—
407C4—1481no—
408C4—1481no—
409C4C2×D4×D3711yescharacteristic
410C4#41×D3711yescharacteristic
411C2—41no—
412C2—81no—
413C2—374no—
414C2—2961no—
415C2—1481no—
416C2#121×D3711yescharacteristic
417C2AGL(1,ℤ/8)×D3711yescharacteristic
418C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#468C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#468D37
hypocenterC37C2×#468
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D37C2semidirect
2. C2×M16×D37C2semidirect
3. C22⋊Q8×D37C2semidirect
5. #14557782C2semidirect
6. #14557781C2semidirect
7. #14557780C2semidirect
8. #14557779C2semidirect
9. #14557778C2semidirect
10. #14557777C2semidirect
11. #14557776C2semidirect
12. #107×D37C2semidirect
13. #103×D37C2semidirect
14. #102×D37C2semidirect
15. C37×#468C2semidirect
20. C2×#10596930C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596941C22semidirect
24. C2×#10596934C22semidirect
25. C2×#10596929C22semidirect
26. C2×#10596929C22semidirect
30. #11924516C22semidirect
31. #11924515C22semidirect
34. #11924512C22semidirect
45. #11924470C22semidirect
46. #11924469C22semidirect
47. #11924469C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
51. #11924458C22semidirect
52. #11924457C22semidirect
53. #11924456C22semidirect
54. C2×SD16×C37C22semidirect
55. C2×M16×C37C22semidirect
56. C22⋊Q8×C37C22semidirect
58. #107×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
120. C8×D37D4semidirect
169. C8×C37C2×D4semidirect
171. #64436C2×D4semidirect
209. D37#468direct (N × H)
221. #468D37direct (N × H)
225. C37C2×#468semidirect
234. C2×SD16C2×D37semidirect
239. C2×M16C2×D37semidirect
247. C22⋊Q8C2×D37semidirect
262. #107C2×D37semidirect
266. #103C2×D37semidirect
270. #102C2×D37semidirect
381. C8D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D372
C2×M16×D372
C22⋊Q8×D372
#121×D372
#145577822
#145577812
#145577802
#145577792
#145577782
#145577772
#145577762
#107×D372
#103×D372
#102×D372
C37×#4682
C2×#46837