Finite Group Databasebeta

← #18003879

Subgroups — #18003879

Order 4736.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924583C211yesmaximal, characteristic, complemented
2C2×#11924560C211yesmaximal, characteristic, complemented
3C2×SD16×D37C211yesmaximal, characteristic, complemented
4#14558099C211yesmaximal, characteristic, complemented
5#14557679C211yesmaximal, characteristic, complemented
6#14557678C211yesmaximal, characteristic, complemented
7#14557675C211yesmaximal, characteristic, complemented
8#14557674C211yesmaximal, characteristic, complemented
9#14557673C211yesmaximal, characteristic, complemented
10#14557671C211yesmaximal, characteristic, complemented
11#14557670C211yesmaximal, characteristic, complemented
12#14557540C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14#14557498C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16#11924583—24no—
17#11924583—24no—
18C2×#10596962—21no—
19C2×#10596962C2211yescharacteristic
20C2×#10596964—21no—
21C2×#10596964—21no—
22C2×#10596964C2211yescharacteristic
23C2×#10596964C2211yescharacteristic, complemented
24C22×Dic74—21no—
25C22×Dic74C2211yescharacteristic, complemented
26C2×Q8×D37C2211yescharacteristic
27C2×Q8×D37C2211yescharacteristic, complemented
28C2×D4×D37C2211yescharacteristic
29#11924560—24no—
30C2×#10596930C2211yescharacteristic
31C2×#10596930C2211yescharacteristic
32C2×#10596940C2211yescharacteristic
33C2×#10596940C2211yescharacteristic
34C2×#10596941C2211yescharacteristic
35SD16×D37—24no—
36C2×#10596939C2211yescharacteristic
37C2×#10596929C2211yescharacteristic
38C2×C8×D37C2211yescharacteristic
39#11924532—21no—
40#11924522—21no—
41#11924511C2211yescharacteristic
42#11924510C2211yescharacteristic
43#11924507C2211yescharacteristic
44#11924506—21no—
45#11924504—21no—
46#11924494C2211yescharacteristic
47#11924461C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924459C2211yescharacteristic, complemented
52#11924457C2211yescharacteristic, complemented
53C22⋊#64436C2211yescharacteristic, complemented
54#11924448C2211yescharacteristic, complemented
55#11924448C2211yescharacteristic, complemented
56C2×#41×C37C2211yescharacteristic, complemented
57C2×SD16×C37C2211yescharacteristic
58C2×D8×C37C2211yescharacteristic
59#121×C37C2211yescharacteristic
60#103×C37C2211yescharacteristic, complemented
61#102×C37C2211yescharacteristic, complemented
62C22⋊C8×C37C2211yescharacteristic, complemented
63C23×D37—21no—
64#41×C37—22no—
65#41×C37—22no—
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37C2311yescharacteristic
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37—21no—
78C2×C22⋊D37D411yescharacteristic
79C2×C22⋊D37D411yescharacteristic
80C22×Dic37—21no—
81C22×Dic37—21no—
82C22×Dic37—21no—
83Q8×D37—22no—
84Q8×D37—22no—
85Q8×D37—22no—
86Q8×D37D414yescomplemented
87#10596964—28no—
88#10596964—28no—
89#10596964—22no—
90#10596964—22no—
91#10596964—22no—
92#10596964D414yescomplemented
93D4×D37—22no—
94D4×D37—22no—
95#10596962—28no—
96#10596962—22no—
97#10596962—22no—
98C2×D148—21no—
99C2×D148D411yescharacteristic
100C2×D148C2311yescharacteristic
101C2×C4×D37—21no—
102C2×C4×D37—21no—
103C2×C4×D37C2311yescharacteristic
104C2×C4×D37C2311yescharacteristic
105C2×Dic74—28no—
106C2×Dic74—21no—
107C2×Dic74—21no—
108C2×Dic74—21no—
109C2×Dic74—22no—
110C2×Dic74—22no—
111C2×Dic74D411yescharacteristic
112C2×Dic74C2311yescharacteristic
113C2×Dic74C2311yescharacteristic
114SD16×C37—22no—
115D8×C37—22no—
116C2×C8×C37C2311yescharacteristic
117C2×C8×C37C2311yescharacteristic
118C4⋊C4×C37C2311yescharacteristic
119C22⋊C4×C37—21no—
120C22⋊Dic37—21no—
121#10596941—22no—
122#10596940—22no—
123#10596940—22no—
124#10596939—22no—
125#10596938—21no—
126#10596938—21no—
127#10596938—21no—
128C4⋊Dic37C2311yescharacteristic
129C4×Dic37—21no—
130C2×#64436C2311yescharacteristic
131C2×#64436C2311yescharacteristic
132#10596930—22no—
133#10596930—22no—
134#10596929—22no—
135C8×D37—22no—
136C23×C37—21no—
137C23×C37—21no—
138C23×C37C2×D411yescharacteristic
139C22×D37—21no—
140C22×D37—42no—
141C22×D37—81no—
142C22×D37—81no—
143C22×D37C2×D411yescharacteristic
144C22×D37C2×D411yescharacteristic
145Q8×C37—21no—
146Q8×C37C2×D412yes—
147D4×C37—24no—
148D4×C37—21no—
149D4×C37—21no—
150D4×C37—21no—
151D4×C37—81no—
152D4×C37C2×D412yes—
153C2×C4×C37—24no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37C2×D411yescharacteristic
159C2×C4×C37C2411yescharacteristic
160C22⋊D37—24no—
161C22⋊D37—22no—
162C22⋊D37—24no—
163C22⋊D37—22no—
164C22⋊D37—42no—
165C22⋊D37—81no—
166C22⋊D37—81no—
167C2×Dic37—24no—
168C2×Dic37—24no—
169C2×Dic37—21no—
170C2×Dic37—21no—
171C2×Dic37—24no—
172C2×Dic37—21no—
173C2×Dic37C2×D411yescharacteristic
174C2×Dic37C2×D411yescharacteristic
175D148—22no—
176D148—21no—
177D148—21no—
178D148—81no—
179C4×D37—24no—
180C4×D37—24no—
181C4×D37—21no—
182C4×D37—21no—
183C4×D37C2×D412yes—
184C4×D37C2×D412yes—
185Dic74—24no—
186Dic74—24no—
187Dic74—21no—
188Dic74—21no—
189Dic74—22no—
190Dic74—24no—
191Dic74C2×D412yes—
192Dic74C2×D412yes—
193C8×C37—21no—
194C8×C37—21no—
195#64436—21no—
196#64436—21no—
197C22×C37—21no—
198C22×C37—22no—
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—41no—
202C22×C37—41no—
203C22×C37—41no—
204C22×C37—41no—
205C22×C37—41no—
206C22×C37C22×D411yescharacteristic
207C2×D37—21no—
208C2×D37—21no—
209C2×D37—21no—
210C2×D37—21no—
211C2×D37—21no—
212C2×D37—41no—
213C2×D37—41no—
214C2×D37—41no—
215C2×D37—84no—
216C2×D37#12012yes—
217C4×C37—21no—
218C4×C37—22no—
219C4×C37—41no—
220C4×C37C22×D411yescharacteristic
221C4×C37C22×D411yescharacteristic
222Dic37—21no—
223Dic37—22no—
224Dic37—22no—
225Dic37—41no—
226Dic37#12012yes—
227#3010—371nomaximal, Sylow
228C2×C37—41no—
229C2×C37—42no—
230C2×C37—81no—
231C2×C37C2×#12011yescharacteristic
232C2×C37#57711yescharacteristic
233C2×C37#57711yescharacteristic
234D37—22no—
235D37—41no—
236D37—81no—
237C2×2−1+4—371no—
238C2×AGL(1,ℤ/8)—371no—
239C22×SD16—371no—
240#535—371no—
241#449—371no—
242#449—371no—
243#449—371no—
244#449D3711yescharacteristic, complemented
245#448—371no—
246#448—371no—
247#448—371no—
248#448—371no—
249#419—371no—
250#416—371no—
251#408—371no—
252C37#301011yescharacteristic, complemented, Sylow
2532−1+4—744no—
2542−1+4—744no—
255C2×#41—371no—
256C2×#41—371no—
257C2×#41—371no—
258C2×#41—741no—
259C2×#41—741no—
260C2×#41—741no—
261C2×#41C2×D3711yescharacteristic, complemented
262C22×Q8—371no—
263C22×Q8—371no—
264C22×Q8—371no—
265C22×Q8—741no—
266C22×D4—371no—
267AGL(1,ℤ/8)—744no—
268C2×SD16—371no—
269C2×SD16—371no—
270C2×SD16—371no—
271C2×SD16—371no—
272C2×SD16—371no—
273C2×SD16—744no—
274C2×SD16C2×D3711yescharacteristic
275C2×D8—371no—
276C2×D8C2×D3711yescharacteristic
277C2×M16—371no—
278C22×C8—371no—
279#127—741no—
280#124—741no—
281#121—371no—
282#121—371no—
283#121—371no—
284#121C2×D3711yescharacteristic
285#120—741no—
286#120—741no—
287#117—371no—
288#103—371no—
289#103—371no—
290#103—371no—
291#103—371no—
292#103—371no—
293#103C2×D3711yescharacteristic, complemented
294#102—371no—
295#102C2×D3711yescharacteristic, complemented
296C22⋊C8—371no—
297C22⋊C8—371no—
298C22⋊C8—371no—
299C22⋊C8C2×D3711yescharacteristic, complemented
300C24—741no—
301#41—22no—
302#41—22no—
303#41—374no—
304#41—742no—
305#41—742no—
306#41—748no—
307#41—742no—
308#41—742no—
309#41—748no—
310#41—748no—
311#41—742no—
312C2×Q8—371no—
313C2×Q8—374no—
314C2×Q8—371no—
315C2×Q8—371no—
316C2×Q8—741no—
317C2×Q8—741no—
318C2×Q8—742no—
319C2×Q8—742no—
320C2×Q8—748no—
321C2×Q8—742no—
322C2×Q8—742no—
323C2×Q8—742no—
324C2×Q8—741no—
325C2×Q8C22×D3711yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—371no—
329C2×D4—371no—
330C2×D4—371no—
331C2×D4—371no—
332C2×D4—741no—
333C2×D4—742no—
334C2×D4—742no—
335C2×D4—741no—
336C2×D4—741no—
337C2×D4—741no—
338C2×D4—741no—
339C2×D4—741no—
340C2×D4C22×D3711yescharacteristic
341C2×D4C22×D3711yescharacteristic
342C22×C4—21no—
343C22×C4—371no—
344C22×C4—371no—
345C22×C4—741no—
346C22×C4—741no—
347C22×C4—741no—
348C22×C4—741no—
349C22×C4—741no—
350C22×C4C22×D3711yescharacteristic
351SD16—22no—
352SD16—742no—
353SD16—742no—
354SD16—742no—
355SD16—742no—
356SD16—742no—
357D8—22no—
358D8—742no—
359M16—742no—
360C2×C8—371no—
361C2×C8—371no—
362C2×C8—742no—
363C2×C8C22×D3711yescharacteristic
364C2×C8C22×D3711yescharacteristic
365C4⋊C4—371no—
366C4⋊C4C22×D3711yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—741no—
369C22⋊C4—741no—
370C22⋊C4—741no—
371C22⋊C4—741no—
372C42—741no—
373C23—21no—
374C23—21no—
375C23—371no—
376C23—371no—
377C23—2961no—
378C23—2961no—
379C23—741no—
380C23—1482no—
381C23D4×D3711yescharacteristic
382Q8—21no—
383Q8—372no—
384Q8—372no—
385Q8—742no—
386Q8—744no—
387Q8—744no—
388Q8—744no—
389Q8—741no—
390Q8—741no—
391Q8D4×D3712yes—
392D4—24no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—81no—
397D4—2961no—
398D4—2961no—
399D4—2961no—
400D4—742no—
401D4—742no—
402D4—742no—
403D4—744no—
404D4—744no—
405D4—741no—
406D4—741no—
407D4—1482no—
408D4D4×D3712yes—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—371no—
415C2×C4—372no—
416C2×C4—372no—
417C2×C4—371no—
418C2×C4—744no—
419C2×C4—744no—
420C2×C4—744no—
421C2×C4—744no—
422C2×C4—744no—
423C2×C4—741no—
424C2×C4—741no—
425C2×C4—741no—
426C2×C4—741no—
427C2×C4—741no—
428C2×C4D4×D3711yescharacteristic
429C2×C4C23×D3711yescharacteristic
430C8—21no—
431C8—21no—
432C8—741no—
433C8—741no—
434C22—21no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—372no—
444C22—2964no—
445C22—741no—
446C22—741no—
447C22—741no—
448C22—741no—
449C22—741no—
450C22—1481no—
451C22—1481no—
452C22—1481no—
453C22C2×D4×D3711yescharacteristic
454C4—21no—
455C4—22no—
456C4—41no—
457C4—372no—
458C4—741no—
459C4—742no—
460C4—742no—
461C4—1481no—
462C4C2×D4×D3711yescharacteristic
463C4C2×D4×D3711yescharacteristic
464C2—41no—
465C2—42no—
466C2—81no—
467C2—2961no—
468C2—742no—
469C2—1481no—
470C2#120×D3711yescharacteristic
471C2#1455834011yescharacteristic
472C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3010
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11924583C2semidirect
2. C2×#11924560C2semidirect
3. C2×SD16×D37C2semidirect
4. #14558099C2semidirect
5. #14557679C2semidirect
6. #14557678C2semidirect
7. #14557675C2semidirect
8. #14557674C2semidirect
9. #14557673C2semidirect
10. #14557671C2semidirect
11. #14557670C2semidirect
12. #14557540C2semidirect
13. #14557526C2semidirect
14. #14557498C2semidirect
15. C37×#449C2semidirect
23. C2×#10596964C22semidirect
25. C22×Dic74C22semidirect
27. C2×Q8×D37C22semidirect
47. #11924461C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
51. #11924459C22semidirect
52. #11924457C22semidirect
53. C22⋊#64436C22semidirect
54. #11924448C22semidirect
55. #11924448C22semidirect
56. C2×#41×C37C22semidirect
60. #103×C37C22semidirect
61. #102×C37C22semidirect
62. C22⋊C8×C37C22semidirect
86. Q8×D37D4semidirect
92. #10596964D4semidirect
244. #449D37semidirect
252. C37#3010semidirect
261. C2×#41C2×D37semidirect
293. #103C2×D37semidirect
295. #102C2×D37semidirect
299. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
C2×#119245602
C2×SD16×D372
#145580992
#145576792
#145576782
#145576752
#145576742
#145576732
#145576712
#145576702
#145575402
#145575262
#145574982
C37×#4492
#301037