Finite Group Databasebeta

← #18004230

Subgroups — #18004230

Order 4736.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D37C211yesmaximal, characteristic, complemented
2C2×#11924542C211yesmaximal, characteristic, complemented
3#14558106C211yesmaximal, characteristic, complemented
4#14558099C211yesmaximal, characteristic
5#14557782C211yesmaximal, characteristic, complemented
6#14557781C211yesmaximal, characteristic, complemented
7#14557778C211yesmaximal, characteristic, complemented
8#14557777C211yesmaximal, characteristic, complemented
9#14557763C211yesmaximal, characteristic, complemented
10#14557762C211yesmaximal, characteristic, complemented
11#14557759C211yesmaximal, characteristic, complemented
12#14557568C211yesmaximal, characteristic, complemented
13#14557540C211yesmaximal, characteristic, complemented
14#14557536C211yesmaximal, characteristic, complemented
15C37×#465C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×#10596940C2211yescharacteristic
21C2×#10596941C2211yescharacteristic
22SD16×D37—24no—
23#11924542—24no—
24C2×#10596934C2211yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×#10596929C2211yescharacteristic, complemented
27C2×C8×D37C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic, complemented
29#11924535—21no—
30#11924532—21no—
31#11924522—21no—
32#11924522—21no—
33#11924521—21no—
34#11924518—21no—
35#11924516C2211yescharacteristic, complemented
36#11924515C2211yescharacteristic, complemented
37#11924512C2211yescharacteristic, complemented
38#11924511C2211yescharacteristic
39#11924510C2211yescharacteristic
40#11924507C2211yescharacteristic
41#11924506—21no—
42#11924504—21no—
43#11924494C2211yescharacteristic
44#11924494C2211yescharacteristic
45#11924469C2211yescharacteristic, complemented
46#11924469C2211yescharacteristic, complemented
47#11924468C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic
52#11924457C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×SD16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic, complemented
56C22⋊Q8×C37C2211yescharacteristic, complemented
57#121×C37C2211yescharacteristic
58#106×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37D411yescharacteristic
70C2×C22⋊D37D411yescharacteristic
71Q8×D37—22no—
72Q8×D37—22no—
73D4×D37—22no—
74D4×D37—22no—
75#10596962—22no—
76#10596962—22no—
77C2×D148—21no—
78C2×D148D411yescharacteristic
79C2×D148C2311yescharacteristic
80C2×C4×D37—21no—
81C2×C4×D37C2311yescharacteristic
82C2×C4×D37C2311yescharacteristic
83C2×Dic74—21no—
84C2×Dic74D411yescharacteristic
85C2×Dic74C2311yescharacteristic
86SD16×C37—22no—
87C2×C8×C37—22no—
88C2×C8×C37C2311yescharacteristic
89C2×C8×C37C2311yescharacteristic
90C4⋊C4×C37—21no—
91C4⋊C4×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97#10596941—22no—
98#10596940—22no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37C2311yescharacteristic
107C4⋊Dic37C2311yescharacteristic
108#10596936—21no—
109#10596936—21no—
110C4×Dic37—21no—
111C4×Dic37—21no—
112#10596934—22no—
113C2×#64436C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115#10596930—22no—
116#10596929—22no—
117#10596929—22no—
118C8×D37—22no—
119C8×D37D414yescomplemented
120C23×C37—21no—
121C23×C37C2×D411yescharacteristic
122C22×D37—21no—
123C22×D37—42no—
124C22×D37—81no—
125C22×D37—81no—
126C22×D37C2×D411yescharacteristic
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130D4×C37—21no—
131D4×C37—21no—
132D4×C37—81no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2411yescharacteristic
140C22⋊D37—22no—
141C22⋊D37—22no—
142C22⋊D37—42no—
143C22⋊D37—81no—
144C22⋊D37—81no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37C2×D411yescharacteristic
149C2×Dic37C2×D411yescharacteristic
150D148—22no—
151D148—21no—
152D148—21no—
153D148—81no—
154C4×D37—21no—
155C4×D37—21no—
156C4×D37—42no—
157C4×D37C2×D412yes—
158C4×D37#4112yes—
159Dic74—22no—
160Dic74—21no—
161Dic74—21no—
162Dic74—42no—
163C8×C37—21no—
164C8×C37C2×D412yes—
165#64436—21no—
166#64436C2×D412yes—
167C22×C37—21no—
168C22×C37—21no—
169C22×C37—21no—
170C22×C37—41no—
171C22×C37—41no—
172C22×C37—41no—
173C22×C37C22×D411yescharacteristic
174C2×D37—21no—
175C2×D37—21no—
176C2×D37—21no—
177C2×D37—21no—
178C2×D37—21no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—84no—
183C2×D37#12112yes—
184C4×C37—21no—
185C4×C37—41no—
186C4×C37—41no—
187C4×C37—41no—
188C4×C37C22×D411yescharacteristic
189C4×C37C2×#4111yescharacteristic
190Dic37—21no—
191Dic37—41no—
192Dic37—41no—
193Dic37—41no—
194Dic37#12112yes—
195#3057—371nomaximal, Sylow
196C2×C37—41no—
197C2×C37—81no—
198C2×C37C2×#12111yescharacteristic
199C2×C37#57711yescharacteristic
200C2×C37#57711yescharacteristic
201D37—22no—
202D37—41no—
203D37—81no—
204C22×SD16—371no—
205C2×#131—371no—
206#536—371no—
207#535—371no—
208#468—371no—
209#468—371no—
210#468—371no—
211#468—371no—
212#465—371no—
213#465—371no—
214#465—371no—
215#465D3711yescharacteristic, complemented
216#427—371no—
217#419—371no—
218#418—371no—
219C37#305711yescharacteristic, complemented, Sylow
220C2×#41—371no—
221C22×Q8—371no—
222C22×D4—371no—
223C2×SD16—371no—
224C2×SD16—371no—
225C2×SD16—371no—
226C2×SD16—744no—
227C2×SD16C2×D3711yescharacteristic
228#131—744no—
229C2×M16—371no—
230C2×M16—371no—
231C2×M16—371no—
232C22×C8—371no—
233C22×C8—371no—
234C22×C8C2×D3711yescharacteristic, complemented
235C4⋊Q8—741no—
236#127—741no—
237#124—741no—
238#124—741no—
239#123—741no—
240#123—741no—
241C22⋊Q8—371no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8C2×D3711yescharacteristic, complemented
245#121—371no—
246#121—371no—
247#121—371no—
248#121C2×D3711yescharacteristic
249#120—741no—
250#120—741no—
251#117—371no—
252#117—371no—
253#107—371no—
254#107—371no—
255#106—371no—
256#106C2×D3711yescharacteristic, complemented
257#103—371no—
258#103—371no—
259#103—371no—
260#103C2×D3711yescharacteristic, complemented
261#102—371no—
262#102—371no—
263#102—371no—
264#102C2×D3711yescharacteristic
265C24—741no—
266#41—742no—
267#41—742no—
268C2×Q8—371no—
269C2×Q8—371no—
270C2×Q8—741no—
271C2×Q8—742no—
272C2×Q8—742no—
273C2×Q8C22×D3711yescharacteristic
274C2×D4—21no—
275C2×D4—371no—
276C2×D4—371no—
277C2×D4—371no—
278C2×D4—371no—
279C2×D4—741no—
280C2×D4—742no—
281C2×D4—742no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4C22×D3711yescharacteristic
286C22×C4—371no—
287C22×C4—371no—
288C22×C4—741no—
289C22×C4C22×D3711yescharacteristic
290SD16—22no—
291SD16—742no—
292SD16—742no—
293SD16—742no—
294M16—742no—
295M16—742no—
296M16—742no—
297C2×C8—22no—
298C2×C8—371no—
299C2×C8—374no—
300C2×C8—371no—
301C2×C8—742no—
302C2×C8C22×D3711yescharacteristic
303C2×C8C22×D3711yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—371no—
306C4⋊C4—371no—
307C4⋊C4—741no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4C22×D3711yescharacteristic
311C4⋊C4C22×D3711yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C42—741no—
323C42—741no—
324C23—21no—
325C23—371no—
326C23—371no—
327C23—2961no—
328C23—2961no—
329C23—741no—
330C23—1482no—
331C23D4×D3711yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—742no—
335Q8—741no—
336Q8—741no—
337Q8—1482no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—2961no—
342D4—2961no—
343D4—2961no—
344D4—742no—
345D4—742no—
346D4—742no—
347D4—741no—
348D4—741no—
349D4—1482no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—371no—
356C2×C4—372no—
357C2×C4—372no—
358C2×C4—371no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—1482no—
365C2×C4D4×D3711yescharacteristic
366C2×C4C23×D3711yescharacteristic
367C8—21no—
368C8—372no—
369C8—741no—
370C8D4×D3712yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—372no—
378C22—2964no—
379C22—741no—
380C22—741no—
381C22—741no—
382C22—741no—
383C22—741no—
384C22—1481no—
385C22—1481no—
386C22—1481no—
387C22C2×D4×D3711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—372no—
393C4—741no—
394C4—1481no—
395C4—1481no—
396C4—1481no—
397C4C2×D4×D3711yescharacteristic
398C4#41×D3711yescharacteristic
399C2—41no—
400C2—81no—
401C2—2961no—
402C2—742no—
403C2—1481no—
404C2#121×D3711yescharacteristic
405C2#1455833911yescharacteristic
406C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#465C2
socleC22×C37C22×D4
prime radical#14558099C2
hypercenter#465D37
hypocenterC37#3057
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D37C2semidirect
2. C2×#11924542C2semidirect
3. #14558106C2semidirect
5. #14557782C2semidirect
6. #14557781C2semidirect
7. #14557778C2semidirect
8. #14557777C2semidirect
9. #14557763C2semidirect
10. #14557762C2semidirect
11. #14557759C2semidirect
12. #14557568C2semidirect
13. #14557540C2semidirect
14. #14557536C2semidirect
15. C37×#465C2semidirect
24. C2×#10596934C22semidirect
26. C2×#10596929C22semidirect
28. C2×C8×D37C22semidirect
35. #11924516C22semidirect
36. #11924515C22semidirect
37. #11924512C22semidirect
45. #11924469C22semidirect
46. #11924469C22semidirect
47. #11924468C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
55. C22×C8×C37C22semidirect
56. C22⋊Q8×C37C22semidirect
58. #106×C37C22semidirect
59. #103×C37C22semidirect
119. C8×D37D4semidirect
215. #465D37semidirect
219. C37#3057semidirect
234. C22×C8C2×D37semidirect
244. C22⋊Q8C2×D37semidirect
256. #106C2×D37semidirect
260. #103C2×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×#119245422
#145581062
#145580992
#145577822
#145577812
#145577782
#145577772
#145577632
#145577622
#145577592
#145575682
#145575402
#145575362
C37×#4652
#305737