Finite Group Databasebeta

← #18005290

Subgroups — #18005290

Order 4736.

410 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#14558070C211yesmaximal, characteristic, complemented
3#14557941C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557896C211yesmaximal, characteristic, complemented
6#14557894C211yesmaximal, characteristic, complemented
7#14557770C211yesmaximal, characteristic, complemented
8#14557768C211yesmaximal, characteristic, complemented
9#14557765C211yesmaximal, characteristic, complemented
10#14557759C211yesmaximal, characteristic, complemented
11#14557646C211yesmaximal, characteristic, complemented
12#14557643C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, characteristic, complemented
14#97×D37C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×#10596941C2211yescharacteristic
18C2×D296C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924532C2211yescharacteristic
24#11924531—21no—
25#11924527C2211yescharacteristic
26#11924525C2211yescharacteristic
27#11924522—21no—
28#11924521—21no—
29#11924512C2211yescharacteristic
30#11924511C2211yescharacteristic
31#11924511C2211yescharacteristic
32#11924509—21no—
33#11924507C2211yescharacteristic
34C4×D148—21no—
35C4×D148C2211yescharacteristic
36C4×D148C2211yescharacteristic
37C4×C22⋊D37—21no—
38#11924493—21no—
39C42×D37C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924467C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924447C2211yescharacteristic
50#11924446C2211yescharacteristic
51#11924446C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65#10596962—44no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37D411yescharacteristic
73C2×C4×D37D411yescharacteristic
74C2×C4×D37C2311yescharacteristic
75C2×Dic74—21no—
76SD16×C37—22no—
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C22⋊C4×C37—21no—
83C42×C37—21no—
84C42×C37C2311yescharacteristic
85C22⋊Dic37—21no—
86#10596941—22no—
87#10596939—22no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37D411yescharacteristic
102C4×Dic37D411yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107C8×D37—22no—
108C8×D37—22no—
109C23×C37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C22×D37C2×D411yescharacteristic
113Q8×C37—21no—
114Q8×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—42no—
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37—42no—
125C22⋊D37—42no—
126C22⋊D37—42no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132D148—21no—
133D148—21no—
134D148—21no—
135D148—21no—
136D148—42no—
137D148—42no—
138C4×D37—22no—
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—41no—
142C4×D37—42no—
143C4×D37—42no—
144Dic74—42no—
145C8×C37—21no—
146C8×C37#4112yescomplemented
147#64436—21no—
148#64436#4112yescomplemented
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37C22×D411yescharacteristic
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37AGL(1,ℤ/8)12yes—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37C2×#4111yescharacteristic
168C4×C37C2×#4111yescharacteristic
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—41no—
173Dic37—41no—
174#3180—371nomaximal, Sylow
175C2×C37—81no—
176C2×C37#53211yescharacteristic
177C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C37#57511yescharacteristic
179D37—22no—
180D37—81no—
181D37—81no—
182#532—371no—
183#529—371no—
184#501—371no—
185#496—371no—
186#490—371no—
187#489—371no—
188#466—371no—
189#466—371no—
190#465—371no—
191#465—371no—
192#442—371no—
193#442—371no—
194#440—371no—
195#440D3711yescharacteristic, complemented
196C2×#97—371no—
197C37#318011yescharacteristic, complemented, Sylow
198C2×#41—741no—
199C2×SD16—371no—
200C2×SD16C2×D3711yescharacteristic
201C2×D8—371no—
202C2×D8—371no—
203C22×C8—371no—
204C22×C8—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×Q8C2×D3711yescharacteristic
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—741no—
221C4×D4—741no—
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#103C2×D3711yescharacteristic
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236#102C2×D3711yescharacteristic
237#97—371no—
238#97—371no—
239#97—371no—
240#97C2×D3711yescharacteristic
241#41—1484no—
242C2×Q8—741no—
243C2×Q8C22×D3711yescharacteristic
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4—741no—
251C2×D4C22×D3711yescharacteristic
252C22×C4—21no—
253C22×C4—371no—
254C22×C4—371no—
255C22×C4—371no—
256C22×C4—741no—
257C22×C4—741no—
258SD16—22no—
259SD16—742no—
260D8—742no—
261D8—742no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8—742no—
265C2×C8—742no—
266C2×C8C22×D3711yescharacteristic
267C2×C8C22×D3711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—371no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C42—21no—
287C42—371no—
288C42—371no—
289C42—371no—
290C42C22×D3711yescharacteristic
291C23—21no—
292C23—371no—
293C23—741no—
294C23—741no—
295Q8—21no—
296Q8—21no—
297Q8—1482no—
298D4—21no—
299D4—21no—
300D4—741no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—1482no—
305D4—1482no—
306D4—1482no—
307D4—1482no—
308D4—1482no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
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—1481no—
322C2×C4—1482no—
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—372no—
335C22—741no—
336C22—741no—
337C22—1481no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—741no—
350C4—741no—
351C4—741no—
352C4—1481no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4C2×#1059696211yescharacteristic
356C2—81no—
357C2—2961no—
358C2—2961no—
359C2—742no—
360C2#1455808011yescharacteristic
361C2AGL(1,ℤ/8)×D3711yescharacteristic
362C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
hypercenter#440D37
hypocenterC37#3180
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14558080C2semidirect
2. #14558070C2semidirect
3. #14557941C2semidirect
4. #14557919C2semidirect
5. #14557896C2semidirect
6. #14557894C2semidirect
7. #14557770C2semidirect
8. #14557768C2semidirect
9. #14557765C2semidirect
10. #14557759C2semidirect
11. #14557646C2semidirect
12. #14557643C2semidirect
13. #14557631C2semidirect
14. #97×D37C2semidirect
15. C37×#440C2semidirect
146. C8×C37#41semidirect
148. #64436#41semidirect
195. #440D37semidirect
197. C37#3180semidirect
330. C8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145580802
#145580702
#145579412
#145579192
#145578962
#145578942
#145577702
#145577682
#145577652
#145577592
#145576462
#145576432
#145576312
#97×D372
C37×#4402
#318037