Finite Group Databasebeta

← #18004817

Subgroups — #18004817

Order 4736.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558146C211yesmaximal, characteristic, complemented
2#14558015C211yesmaximal, characteristic
3#14557870C211yesmaximal, characteristic, complemented
4#14557865C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557743C211yesmaximal, characteristic, complemented
7#14557739C211yesmaximal, characteristic, complemented
8#14557698C211yesmaximal, characteristic
9#14557698C211yesmaximal, characteristic
10#14557637C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557625C211yesmaximal, characteristic, complemented
13#14557620C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#479C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×#10596930C2211yescharacteristic
21#11924536C2211yescharacteristic
22#11924531—21no—
23#11924531—21no—
24#11924527—21no—
25#11924527—21no—
26#11924516C2211yescharacteristic
27#11924516C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29#11924501C2211yescharacteristic
30#11924501C2211yescharacteristic
31C4×D148—21no—
32C4×D148C2211yescharacteristic
33#11924498—21no—
34#11924498C2211yescharacteristic
35#11924493—21no—
36#11924493C2211yescharacteristic
37C4⋊C4×D37—21no—
38C4⋊C4×D37C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#125×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60#10596966—22no—
61#10596966—22no—
62C2×D148—21no—
63C2×D148C2311yescharacteristic
64C2×C4×D37—21no—
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37—21no—
68C2×C4×D37C2311yescharacteristic
69C2×Dic74C2311yescharacteristic
70C2×Dic74C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37C2311yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C42×C37—21no—
80C42×C37C2311yescharacteristic
81#10596942—22no—
82#10596942—22no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938D411yescharacteristic
88#10596938D411yescharacteristic
89C4⋊Dic37—21no—
90C4⋊Dic37—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37C2311yescharacteristic
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936D411yescharacteristic
99#10596936D411yescharacteristic
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596930—22no—
107#10596930—22no—
108C22×D37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37#4112yes—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2411yescharacteristic
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37C2×D411yescharacteristic
123C2×Dic37C2×D411yescharacteristic
124C2×Dic37C2×D411yescharacteristic
125D148—24no—
126D148—21no—
127D148#4112yes—
128C4×D37—24no—
129C4×D37—21no—
130C4×D37—21no—
131C4×D37—81no—
132C4×D37—81no—
133C4×D37—81no—
134Dic74—21no—
135Dic74—21no—
136Dic74—21no—
137Dic74—21no—
138C8×C37—21no—
139C8×C37—21no—
140#64436—21no—
141#64436—21no—
142C22×C37C22×D411yescharacteristic
143C2×D37—21no—
144C2×D37—22no—
145C2×D37—21no—
146C2×D37—21no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—22no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37C2×#4111yescharacteristic
156C4×C37C2×#4111yescharacteristic
157Dic37—21no—
158Dic37—21no—
159Dic37—21no—
160Dic37—41no—
161Dic37—41no—
162Dic37—41no—
163#3120—371nomaximal, Sylow
164C2×C37#52511yescharacteristic
165C2×C37#57711yescharacteristic
166C2×C37#57811yescharacteristic
167D37—41no—
168D37—42no—
169#541—371no—
170#520—371no—
171#484—371no—
172#483—371no—
173#479D3711yescharacteristic, complemented
174#478—371no—
175#462—371no—
176#461—371no—
177#452—371no—
178#452—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312011yescharacteristic, complemented, Sylow
185C2×#41—371no—
186C2×Q16—371no—
187C2×Q16—371no—
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8—371no—
191#126—741no—
192#126—741no—
193#125—741no—
194#125—741no—
195#125C2×D3711yescharacteristic
196C22⋊Q8—371no—
197C22⋊Q8—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—371no—
201C4×Q8C2×D3711yescharacteristic
202C4×D4—371no—
203C4×D4—371no—
204C4×D4—741no—
205C4×D4—741no—
206#117—371no—
207#117—741no—
208C2×C4⋊C4—371no—
209C2×C4⋊C4—741no—
210#107—371no—
211#107C2×D3711yescharacteristic
212#106—371no—
213#106C2×D3711yescharacteristic
214C4⋊C8—371no—
215C4⋊C8C2×D3711yescharacteristic
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#103C2×D3711yescharacteristic
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8—371no—
226#97—371no—
227C4×C8—371no—
228#41—742no—
229#41—742no—
230C2×Q8—371no—
231C2×Q8—371no—
232C2×Q8C22×D3711yescharacteristic
233C2×D4—371no—
234C2×D4—741no—
235C22×C4—371no—
236C22×C4—741no—
237C22×C4—741no—
238C22×C4—741no—
239C22×C4—741no—
240Q16—742no—
241Q16—742no—
242SD16—742no—
243SD16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8C22×D3711yescharacteristic
247C2×C8C22×D3711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—371no—
252C4⋊C4—371no—
253C4⋊C4—371no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4C22×D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—371no—
266C22⋊C4—371no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C42—21no—
272C42—371no—
273C42—741no—
274C42—741no—
275C42—741no—
276C42C22×D3711yescharacteristic
277C23—371no—
278C23—741no—
279Q8—21no—
280Q8—741no—
281Q8—741no—
282Q8—741no—
283Q8—741no—
284Q8#1059696612yes—
285D4—372no—
286D4—744no—
287D4—741no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—371no—
293C2×C4—371no—
294C2×C4—371no—
295C2×C4—2961no—
296C2×C4—2961no—
297C2×C4—2961no—
298C2×C4—744no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4D4×D3711yescharacteristic
305C2×C4D4×D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—21no—
308C8—21no—
309C8—741no—
310C8—741no—
311C22—742no—
312C22—741no—
313C22—741no—
314C22—741no—
315C22—1481no—
316C22—1481no—
317C22C2×D4×D3711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—741no—
325C4—741no—
326C4—741no—
327C4—1481no—
328C4—1481no—
329C4—1481no—
330C4#41×D3711yescharacteristic
331C4C2×#1059696611yescharacteristic
332C2—1481no—
333C2—1482no—
334C2#1455804611yescharacteristic
335C2#1455834011yescharacteristic
336C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#479C2
socleC22×C37C22×D4
prime radicalC2×#10596966C22
hypercenter#479D37
hypocenterC37#3120
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14558146C2semidirect
3. #14557870C2semidirect
4. #14557865C2semidirect
5. #14557830C2semidirect
6. #14557743C2semidirect
7. #14557739C2semidirect
10. #14557637C2semidirect
11. #14557632C2semidirect
12. #14557625C2semidirect
13. #14557620C2semidirect
14. #14557593C2semidirect
15. C37×#479C2semidirect
173. #479D37semidirect
184. C37#3120semidirect

Maximal subgroups

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

subgroupindex
#145581462
#145580152
#145578702
#145578652
#145578302
#145577432
#145577392
#145576982
#145576372
#145576322
#145576252
#145576202
#145575932
C37×#4792
#312037