Finite Group Databasebeta

← #18005189

Subgroups — #18005189

Order 4736.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558080C211yesmaximal, characteristic, complemented
2#14558065C211yesmaximal, characteristic, complemented
3#14557941C211yesmaximal, characteristic, complemented
4#14557921C211yesmaximal, characteristic, complemented
5#14557896C211yesmaximal, characteristic, complemented
6#14557891C211yesmaximal, characteristic, complemented
7#14557785C211yesmaximal, characteristic, complemented
8#14557783C211yesmaximal, characteristic, complemented
9#14557780C211yesmaximal, characteristic, complemented
10#14557778C211yesmaximal, characteristic, complemented
11C4×#10596930C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14C4×#10596929C211yesmaximal, characteristic, complemented
15C4×D8×C37C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21C2×#10596929C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924532C2211yescharacteristic
24#11924529—21no—
25#11924527C2211yescharacteristic
26#11924523C2211yescharacteristic
27#11924522—21no—
28#11924518—21no—
29#11924516C2211yescharacteristic
30#11924511C2211yescharacteristic
31#11924509—21no—
32#11924507C2211yescharacteristic
33#11924507C2211yescharacteristic
34C4×Dic74C2211yescharacteristic
35C4×D148C2211yescharacteristic
36C4×C22⋊D37—21no—
37C4×C22⋊D37—21no—
38#11924495—21no—
39C42×D37C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924467C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924446C2211yescharacteristic
50#11924446C2211yescharacteristic
51C4×#64436C2211yescharacteristic
52C2×D8×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×D4×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67#10596962—44no—
68C2×D148—21no—
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37D411yescharacteristic
72C2×C4×D37D411yescharacteristic
73C2×C4×D37C2311yescharacteristic
74C2×Dic74—21no—
75C2×Dic74C2311yescharacteristic
76D8×C37—22no—
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C42×C37C2311yescharacteristic
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88#10596940—22no—
89#10596939—22no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100C4×Dic37—21no—
101C4×Dic37D411yescharacteristic
102C4×Dic37D411yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596930—22no—
107#10596929—22no—
108#10596929—22no—
109C23×C37—21no—
110C23×C37—21no—
111C22×D37—21no—
112C22×D37C2×D411yescharacteristic
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—42no—
120C2×C4×C37—42no—
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37—42no—
125C22⋊D37—42no—
126C22⋊D37—42no—
127C22⋊D37—42no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134D148—21no—
135D148—21no—
136D148—42no—
137C4×D37—22no—
138C4×D37—21no—
139C4×D37—21no—
140C4×D37—41no—
141C4×D37—42no—
142Dic74—21no—
143Dic74—21no—
144Dic74—42no—
145C8×C37—21no—
146C8×C37#4112yescomplemented
147#64436—21no—
148#64436#4112yescomplemented
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C4×C37—21no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37AGL(1,ℤ/8)12yes—
166C4×C37C2×#4111yescharacteristic
167C4×C37C2×#4111yescharacteristic
168Dic37—21no—
169Dic37—21no—
170Dic37—21no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174#3171—371nomaximal, Sylow
175C2×C37—81no—
176C2×C37—81no—
177C2×C37#53211yescharacteristic
178C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C37#57511yescharacteristic
180D37—41no—
181D37—81no—
182#532—371no—
183#529—371no—
184#501—371no—
185#496—371no—
186#490—371no—
187#489—371no—
188#469—371no—
189#469—371no—
190#468—371no—
191#468—371no—
192C4×SD16—371no—
193C4×SD16—371no—
194C4×D8—371no—
195C4×D8D3711yescharacteristic, complemented
196C4×M16—371no—
197C37#317111yescharacteristic, complemented, Sylow
198C2×#41—741no—
199C2×SD16—371no—
200C2×SD16—371no—
201C2×D8—371no—
202C2×D8C2×D3711yescharacteristic
203C2×M16—371no—
204C2×M16—371no—
205C4⋊Q8—371no—
206#127—371no—
207#126—741no—
208#125—371no—
209#124—371no—
210#124—741no—
211#123—741no—
212C22⋊Q8—371no—
213#121—371no—
214#121—371no—
215#121—371no—
216#121—741no—
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4—741no—
220C4×D4—741no—
221C4×D4C2×D3711yescharacteristic
222C4×D4C2×D3711yescharacteristic
223#117—741no—
224C2×C42—371no—
225#107—371no—
226#107C2×D3711yescharacteristic
227#106—371no—
228#106—371no—
229#103—371no—
230#103—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102C2×D3711yescharacteristic
236#102C2×D3711yescharacteristic
237#97—371no—
238#97—371no—
239C4×C8—371no—
240C4×C8C2×D3711yescharacteristic
241#41—1484no—
242C2×Q8—371no—
243C2×Q8—741no—
244C2×D4—371no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C2×D4C22×D3711yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—371no—
255C22×C4—371no—
256C22×C4—371no—
257C22×C4—741no—
258SD16—742no—
259SD16—742no—
260D8—22no—
261D8—742no—
262M16—742no—
263M16—742no—
264C2×C8—371no—
265C2×C8—371no—
266C2×C8C22×D3711yescharacteristic
267C2×C8C22×D3711yescharacteristic
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C42—371no—
287C42—371no—
288C42—371no—
289C42—741no—
290C42C22×D3711yescharacteristic
291C23—21no—
292C23—21no—
293C23—371no—
294C23—741no—
295Q8—741no—
296Q8—741no—
297Q8—1482no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—741no—
303D4—741no—
304D4—1482no—
305D4—1482no—
306D4—1482no—
307D4—1482no—
308D4—1482no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—371no—
314C2×C4—371no—
315C2×C4—371no—
316C2×C4—742no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—1481no—
323C2×C4—1482no—
324C2×C4D4×D3711yescharacteristic
325C2×C4D4×D3711yescharacteristic
326C2×C4C23×D3711yescharacteristic
327C8—21no—
328C8—372no—
329C8—741no—
330C8#1059696212yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—741no—
338C22—741no—
339C22—741no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—741no—
348C4—741no—
349C4—741no—
350C4—1481no—
351C4—1481no—
352C4—1481no—
353C4#1192456012yes—
354C4#41×D3711yescharacteristic
355C4C2×#1059696211yescharacteristic
356C2—81no—
357C2—81no—
358C2—2961no—
359C2—1481no—
360C2#1455808011yescharacteristic
361C2C2×#1192456011yescharacteristic
362C2#1455833011yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×D8×C37C2
socleC22×C37C22×D4
hypercenterC4×D8D37
hypocenterC37#3171
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14558080C2semidirect
2. #14558065C2semidirect
3. #14557941C2semidirect
4. #14557921C2semidirect
5. #14557896C2semidirect
6. #14557891C2semidirect
7. #14557785C2semidirect
8. #14557783C2semidirect
9. #14557780C2semidirect
10. #14557778C2semidirect
11. C4×#10596930C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. C4×#10596929C2semidirect
15. C4×D8×C37C2semidirect
146. C8×C37#41semidirect
148. #64436#41semidirect
195. C4×D8D37semidirect
197. C37#3171semidirect
330. C8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145580802
#145580652
#145579412
#145579212
#145578962
#145578912
#145577852
#145577832
#145577802
#145577782
C4×#105969302
C4×#105969402
C4×#105969392
C4×#105969292
C4×D8×C372
#317137