Finite Group Databasebeta

← #18004273

Subgroups — #18004273

Order 4736.

504 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×#11924560C211yesmaximal, characteristic, complemented
2C2×#11924544C211yesmaximal, characteristic, complemented
3#14558112C211yesmaximal, characteristic, complemented
4#14558099C211yesmaximal, characteristic, complemented
5#14557785C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557778C211yesmaximal, characteristic, complemented
8#14557767C211yesmaximal, characteristic, complemented
9#14557766C211yesmaximal, characteristic, complemented
10#14557763C211yesmaximal, characteristic, complemented
11#14557760C211yesmaximal, characteristic, complemented
12#14557572C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#469C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924560—24no—
20C2×#10596930C2211yescharacteristic
21C2×#10596940C2211yescharacteristic
22C2×#10596939C2211yescharacteristic
23#11924544—24no—
24C2×#10596929C2211yescharacteristic
25C2×#10596929C2211yescharacteristic, complemented
26C22×#64436C2211yescharacteristic, complemented
27C2×C8×D37C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic, complemented
29#11924532—21no—
30#11924522—21no—
31#11924516C2211yescharacteristic, complemented
32#11924515C2211yescharacteristic, complemented
33#11924513—21no—
34#11924511C2211yescharacteristic
35#11924510C2211yescharacteristic
36#11924509—21no—
37#11924508—21no—
38#11924507—21no—
39#11924507C2211yescharacteristic
40#11924507C2211yescharacteristic, complemented
41#11924506—21no—
42#11924504—21no—
43#11924494C2211yescharacteristic
44C4⋊C4×D37C2211yescharacteristic
45#11924470C2211yescharacteristic, complemented
46#11924469C2211yescharacteristic, complemented
47#11924467C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic
51#11924457C2211yescharacteristic
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55C2×M16×C37C2211yescharacteristic, complemented
56#121×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic, complemented
58#106×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37D411yescharacteristic
73C2×C22⋊D37D411yescharacteristic
74C22×Dic37—21no—
75#10596964—22no—
76#10596964—22no—
77D4×D37—22no—
78D4×D37—22no—
79#10596962—22no—
80#10596962—22no—
81C2×D148—21no—
82C2×D148D411yescharacteristic
83C2×D148C2311yescharacteristic
84C2×C4×D37—21no—
85C2×C4×D37C2311yescharacteristic
86C2×C4×D37C2311yescharacteristic
87C2×Dic74D411yescharacteristic
88C2×Dic74C2311yescharacteristic
89D8×C37—22no—
90M16×C37—22no—
91C2×C8×C37C2311yescharacteristic
92C2×C8×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100#10596940—22no—
101#10596939—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—
111C4×Dic37—21no—
112C2×#64436—22no—
113C2×#64436C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115#10596930—22no—
116#10596929—22no—
117#10596929D414yescomplemented
118C8×D37—22no—
119C8×D37—22no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37C2×D411yescharacteristic
123C22×D37—21no—
124C22×D37—42no—
125C22×D37—81no—
126C22×D37—81no—
127C22×D37C2×D411yescharacteristic
128C22×D37C2×D411yescharacteristic
129D4×C37—21no—
130D4×C37—21no—
131D4×C37—21no—
132D4×C37—21no—
133D4×C37—81no—
134D4×C37—81no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C22⋊D37—22no—
142C22⋊D37—22no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C22⋊D37—81no—
146C22⋊D37—81no—
147C22⋊D37—81no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37—42no—
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154D148—22no—
155D148—21no—
156D148—21no—
157D148—81no—
158C4×D37—21no—
159C4×D37—21no—
160C4×D37—81no—
161C4×D37C2×D412yes—
162C4×D37#4112yes—
163Dic74—22no—
164Dic74—21no—
165Dic74—21no—
166C8×C37—21no—
167C8×C37C2×D412yes—
168#64436—21no—
169#64436C2×D412yes—
170C22×C37—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37C22×D411yescharacteristic
180C2×D37—21no—
181C2×D37—21no—
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—21no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C2×D37—84no—
189C2×D37#12112yes—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37C22×D411yescharacteristic
194C4×C37C2×#4111yescharacteristic
195Dic37—21no—
196Dic37—41no—
197Dic37—41no—
198Dic37—41no—
199Dic37#12112yes—
200#3062—371nomaximal, Sylow
201C2×C37—41no—
202C2×C37—81no—
203C2×C37—81no—
204C2×C37C2×#12111yescharacteristic
205C2×C37#57611yescharacteristic
206C2×C37#57711yescharacteristic
207D37—22no—
208D37—41no—
209D37—81no—
210C2×AGL(1,ℤ/8)—371no—
211C2×#131—371no—
212#537—371no—
213#535—371no—
214#469—371no—
215#469D3711yescharacteristic, complemented
216#468—371no—
217#468—371no—
218#466—371no—
219#466—371no—
220#465—371no—
221#465—371no—
222#428—371no—
223#416—371no—
224C2×#102—371no—
225C37#306211yescharacteristic, complemented, Sylow
226C2×#41—371no—
227C2×#41—371no—
228C22×D4—371no—
229AGL(1,ℤ/8)—744no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×D8—371no—
233C2×D8C2×D3711yescharacteristic
234#131—744no—
235C2×M16—371no—
236C2×M16—371no—
237C2×M16C2×D3711yescharacteristic, complemented
238C22×C8—371no—
239C22×C8—371no—
240C22×C8—371no—
241#127—741no—
242#124—741no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246#121—371no—
247#121—371no—
248#121—371no—
249#121—371no—
250#121—741no—
251#121—741no—
252#121—741no—
253#121C2×D3711yescharacteristic
254#121C2×D3711yescharacteristic, complemented
255#120—741no—
256#120—741no—
257#117—371no—
258C2×C4⋊C4—371no—
259#107—371no—
260#107—371no—
261#106—371no—
262#106C2×D3711yescharacteristic, complemented
263#103—371no—
264#103—371no—
265#102—371no—
266#102—371no—
267#102—371no—
268#102—371no—
269#102C2×D3711yescharacteristic
270#102C2×D3711yescharacteristic, complemented
271C24—741no—
272#41—742no—
273#41—742no—
274#41—742no—
275#41—742no—
276C2×Q8—371no—
277C2×Q8—371no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—371no—
283C2×D4—371no—
284C2×D4—741no—
285C2×D4—742no—
286C2×D4—742no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4C22×D3711yescharacteristic
293C2×D4C22×D3711yescharacteristic
294C22×C4—371no—
295C22×C4—371no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4C22×D3711yescharacteristic
299SD16—742no—
300SD16—742no—
301D8—22no—
302D8—742no—
303M16—22no—
304M16—374no—
305M16—742no—
306C2×C8—371no—
307C2×C8—371no—
308C2×C8—742no—
309C2×C8—742no—
310C2×C8—742no—
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C4⋊C4—371no—
314C4⋊C4—371no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4C22×D3711yescharacteristic
319C4⋊C4C22×D3711yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C42—741no—
330C23—21no—
331C23—21no—
332C23—371no—
333C23—371no—
334C23—2961no—
335C23—2961no—
336C23—741no—
337C23—1482no—
338C23D4×D3711yescharacteristic
339Q8—742no—
340Q8—741no—
341Q8—741no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—2961no—
349D4—2961no—
350D4—2961no—
351D4—2961no—
352D4—742no—
353D4—742no—
354D4—742no—
355D4—741no—
356D4—741no—
357D4—1482no—
358D4—1482no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—371no—
364C2×C4—372no—
365C2×C4—372no—
366C2×C4—371no—
367C2×C4—2961no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—741no—
372C2×C4—741no—
373C2×C4—1482no—
374C2×C4D4×D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—372no—
378C8—741no—
379C8D4×D3712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—372no—
390C22—2964no—
391C22—741no—
392C22—741no—
393C22—741no—
394C22—741no—
395C22—741no—
396C22—1481no—
397C22—1481no—
398C22—1481no—
399C22C2×D4×D3711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—372no—
404C4—741no—
405C4—1481no—
406C4—1481no—
407C4—1481no—
408C4C2×D4×D3711yescharacteristic
409C4#41×D3711yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—2961no—
414C2—742no—
415C2—1481no—
416C2#121×D3711yescharacteristic
417C2#1455833711yescharacteristic
418C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3062
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. C2×#11924544C2semidirect
3. #14558112C2semidirect
4. #14558099C2semidirect
5. #14557785C2semidirect
6. #14557779C2semidirect
7. #14557778C2semidirect
8. #14557767C2semidirect
9. #14557766C2semidirect
10. #14557763C2semidirect
11. #14557760C2semidirect
12. #14557572C2semidirect
13. #14557526C2semidirect
14. #102×D37C2semidirect
15. C37×#469C2semidirect
25. C2×#10596929C22semidirect
26. C22×#64436C22semidirect
28. C2×C8×D37C22semidirect
31. #11924516C22semidirect
32. #11924515C22semidirect
40. #11924507C22semidirect
45. #11924470C22semidirect
46. #11924469C22semidirect
47. #11924467C22semidirect
48. #11924461C22semidirect
49. #11924459C22semidirect
52. #11924457C22semidirect
55. C2×M16×C37C22semidirect
57. #121×C37C22semidirect
58. #106×C37C22semidirect
60. #102×C37C22semidirect
117. #10596929D4semidirect
215. #469D37semidirect
225. C37#3062semidirect
237. C2×M16C2×D37semidirect
254. #121C2×D37semidirect
262. #106C2×D37semidirect
270. #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×#119245442
#145581122
#145580992
#145577852
#145577792
#145577782
#145577672
#145577662
#145577632
#145577602
#145575722
#145575262
#102×D372
C37×#4692
#306237