Finite Group Databasebeta

← #18004960

Subgroups — #18004960

Order 4736.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558163C211yesmaximal, characteristic, complemented
2#14558103C211yesmaximal, characteristic
3#14557903C211yesmaximal, characteristic, complemented
4#14557900C211yesmaximal, characteristic, complemented
5#14557892C211yesmaximal, characteristic, complemented
6#14557891C211yesmaximal, characteristic, complemented
7#14557886C211yesmaximal, characteristic, complemented
8#14557884C211yesmaximal, characteristic, complemented
9#14557882C211yesmaximal, characteristic, complemented
10#14557540C211yesmaximal, characteristic, complemented
11#14557531C211yesmaximal, characteristic
12#14557526C211yesmaximal, characteristic
13#103×D37C211yesmaximal, characteristic, complemented
14#14557487C211yesmaximal, characteristic, complemented
15C37×#488C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×#10596929C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924536C2211yescharacteristic
21#11924536C2211yescharacteristic
22#11924535—21no—
23#11924535C2211yescharacteristic
24#11924534C2211yescharacteristic
25#11924527C2211yescharacteristic
26#11924526—21no—
27#11924523C2211yescharacteristic
28#11924518—21no—
29#11924518—21no—
30#11924516—21no—
31#11924514—21no—
32#11924513—21no—
33#11924513—21no—
34#11924494C2211yescharacteristic
35#11924493C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic
37#11924461C2211yescharacteristic
38#11924461C2211yescharacteristic
39#11924461C2211yescharacteristic
40#11924461C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924447C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#125×C37C2211yescharacteristic
53#124×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C2×C22⋊D37—21no—
62C22×Dic37—21no—
63Q8×D37—22no—
64Q8×D37—22no—
65#10596964—22no—
66#10596964—22no—
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37C2311yescharacteristic
70C2×Dic74—21no—
71C2×Dic74—21no—
72C2×Dic74—21no—
73C2×Dic74C2311yescharacteristic
74C2×Dic74C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C42×C37C2311yescharacteristic
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86#10596938—21no—
87#10596938D411yescharacteristic
88#10596938D411yescharacteristic
89C4⋊Dic37—21no—
90C4⋊Dic37—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596929—22no—
107C8×D37—22no—
108C23×C37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37—21no—
112D4×C37—21no—
113D4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C22⋊D37—42no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—42no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C4×D37—42no—
130C4×D37—81no—
131C4×D37#4112yes—
132C4×D37#4112yes—
133Dic74—21no—
134Dic74—21no—
135Dic74—21no—
136Dic74—21no—
137Dic74—42no—
138Dic74—81no—
139Dic74—81no—
140C8×C37—21no—
141C8×C37—21no—
142#64436—21no—
143#64436—21no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37C22×D411yescharacteristic
148C2×D37—21no—
149C2×D37—21no—
150C2×D37#12412yes—
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37—41no—
156C4×C37C2×#4111yescharacteristic
157C4×C37C2×#4111yescharacteristic
158Dic37—21no—
159Dic37—21no—
160Dic37—41no—
161Dic37—41no—
162Dic37—41no—
163Dic37—41no—
164Dic37#12412yes—
165#3137—371nomaximal, Sylow
166C2×C37—81no—
167C2×C37C2×#12411yescharacteristic
168C2×C37#57711yescharacteristic
169C2×C37#57811yescharacteristic
170D37—22no—
171#544—371no—
172#536—371no—
173#491—371no—
174#491—371no—
175#489—371no—
176#489—371no—
177#488—371no—
178#488D3711yescharacteristic, complemented
179#487—371no—
180#487—371no—
181#419—371no—
182#417—371no—
183#416—371no—
184C2×#103—371no—
185#405—371no—
186C37#313711yescharacteristic, complemented, Sylow
187C2×#41—371no—
188C22×Q8—371no—
189C2×M16—371no—
190C22×C8—371no—
191C4⋊Q8—371no—
192C4⋊Q8—371no—
193C4⋊Q8—371no—
194C4⋊Q8—371no—
195C4⋊Q8—741no—
196#125—371no—
197#125—741no—
198#125C2×D3711yescharacteristic
199#124—371no—
200#124C2×D3711yescharacteristic
201#123—741no—
202#123—741no—
203C22⋊Q8—741no—
204C22⋊Q8—741no—
205C22⋊Q8—741no—
206C22⋊Q8—741no—
207#117—371no—
208#117—371no—
209C2×C4⋊C4—371no—
210#103—371no—
211#103—371no—
212#103—371no—
213#103—371no—
214#103—371no—
215#103—371no—
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#103C2×D3711yescharacteristic
222#102—371no—
223#102—371no—
224#102C2×D3711yescharacteristic
225#102C2×D3711yescharacteristic
226#97—371no—
227#97—371no—
228C4×C8—371no—
229C4×C8C2×D3711yescharacteristic
230#41—742no—
231#41—742no—
232C2×Q8—371no—
233C2×Q8—371no—
234C2×Q8—741no—
235C2×Q8—741no—
236C2×Q8—742no—
237C2×Q8—742no—
238C2×Q8—741no—
239C2×Q8C22×D3711yescharacteristic
240C2×D4—741no—
241C2×D4C22×D3711yescharacteristic
242C22×C4—371no—
243C22×C4—741no—
244C22×C4—741no—
245C22×C4—741no—
246M16—742no—
247C2×C8—371no—
248C2×C8—371no—
249C2×C8—742no—
250C2×C8C22×D3711yescharacteristic
251C2×C8C22×D3711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—371no—
255C4⋊C4—371no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—371no—
272C22⋊C4—371no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C42—371no—
277C42—741no—
278C42C22×D3711yescharacteristic
279C23—21no—
280C23—371no—
281Q8—21no—
282Q8—21no—
283Q8—2961no—
284Q8—2961no—
285Q8—741no—
286Q8—741no—
287Q8—741no—
288Q8—741no—
289Q8—1482no—
290D4—21no—
291D4—21no—
292D4—1482no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—371no—
297C2×C4—372no—
298C2×C4—372no—
299C2×C4—371no—
300C2×C4—371no—
301C2×C4—2961no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—1482no—
307C2×C4—1482no—
308C2×C4D4×D3711yescharacteristic
309C2×C4D4×D3711yescharacteristic
310C2×C4C23×D3711yescharacteristic
311C8—21no—
312C8—21no—
313C8—741no—
314C8—741no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—372no—
319C22—741no—
320C22—741no—
321C22C2×D4×D3711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—372no—
328C4—741no—
329C4—741no—
330C4—1481no—
331C4—1481no—
332C4—1481no—
333C4—1481no—
334C4#41×D3711yescharacteristic
335C4#41×D3711yescharacteristic
336C2—81no—
337C2—742no—
338C2#124×D3711yescharacteristic
339C2#1455834011yescharacteristic
340C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#488C2
socleC22×C37C22×D4
prime radicalC2×#10596964C22
hypercenter#488D37
hypocenterC37#3137
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14558163C2semidirect
3. #14557903C2semidirect
4. #14557900C2semidirect
5. #14557892C2semidirect
6. #14557891C2semidirect
7. #14557886C2semidirect
8. #14557884C2semidirect
9. #14557882C2semidirect
10. #14557540C2semidirect
13. #103×D37C2semidirect
14. #14557487C2semidirect
15. C37×#488C2semidirect
178. #488D37semidirect
186. C37#3137semidirect

Maximal subgroups

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

subgroupindex
#145581632
#145581032
#145579032
#145579002
#145578922
#145578912
#145578862
#145578842
#145578822
#145575402
#145575312
#145575262
#103×D372
#145574872
C37×#4882
#313737