Finite Group Databasebeta

← #18006539

Subgroups — #18006539

Order 4736.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558247C211yesmaximal, characteristic, complemented
2#14558202C211yesmaximal, characteristic, complemented
3#14557878C211yesmaximal, characteristic, complemented
4#14557858C211yesmaximal, characteristic, complemented
5#14557856C211yesmaximal, characteristic, complemented
6#14557826C211yesmaximal, characteristic, complemented
7#14557767C211yesmaximal, characteristic, complemented
8#14557766C211yesmaximal, characteristic, complemented
9#14557726C211yesmaximal, characteristic, complemented
10#14557677C211yesmaximal, characteristic, complemented
11SD16×Dic37C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14#14557528C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596939C2211yescharacteristic
18C22×#64436C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924535C2211yescharacteristic
21#11924532—21no—
22#11924532C2211yescharacteristic
23#11924523—21no—
24#11924522—21no—
25#11924510—21no—
26#11924510C2211yescharacteristic
27#11924508—21no—
28#11924507—21no—
29#11924507C2211yescharacteristic
30#11924507C2211yescharacteristic
31Q8×Dic37C2211yescharacteristic
32D4×Dic37C2211yescharacteristic
33C4×C22⋊D37—21no—
34C4×C22⋊D37C2211yescharacteristic
35#11924495C2211yescharacteristic
36#11924494C2211yescharacteristic
37#11924492—21no—
38#11924470C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924468C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37D411yescharacteristic
74C22×Dic37—21no—
75#10596966—22no—
76#10596966—41no—
77C2×D148—21no—
78C2×D148C2311yescharacteristic
79C2×C4×D37—21no—
80C2×C4×D37C2311yescharacteristic
81C2×Dic74—21no—
82SD16×C37—22no—
83D8×C37—41no—
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C22⋊C4×C37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37D411yescharacteristic
93#10596939—41no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936D411yescharacteristic
103C4×Dic37—21no—
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115C22×D37C2×D411yescharacteristic
116Q8×C37—21no—
117Q8×C37#4112yes—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—42no—
123D4×C37—81no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—42no—
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—22no—
132C22⋊D37—42no—
133C22⋊D37—81no—
134C22⋊D37—81no—
135C22⋊D37—81no—
136C22⋊D37—81no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—42no—
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144D148—21no—
145D148—21no—
146D148—42no—
147C4×D37—21no—
148C4×D37—21no—
149C4×D37—42no—
150Dic74—81no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37C22×D411yescharacteristic
165C2×D37—21no—
166C2×D37—21no—
167C2×D37—21no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C4×C37—22no—
172C4×C37—21no—
173C4×C37—41no—
174C4×C37C2×#4111yescharacteristic
175C4×C37H(5,𝔽2)11yescharacteristic
176Dic37—21no—
177Dic37—21no—
178Dic37—41no—
179Dic37—41no—
180Dic37—41no—
181Dic37#13512yes—
182#3305—371nomaximal, Sylow
183C2×C37—41no—
184C2×C37—81no—
185C2×C37—81no—
186C2×C37#54611yescharacteristic
187C2×C37C2×#13511yescharacteristic
188C2×C37#57611yescharacteristic
189D37—41no—
190D37—81no—
191#555—371no—
192#550—371no—
193#486—371no—
194#482—371no—
195#482—371no—
196#477—371no—
197#466—371no—
198#466—371no—
199#459—371no—
200#449—371no—
201#449D3711yescharacteristic, complemented
202C4×SD16—371no—
203C8×D4—371no—
204#416—371no—
205#416—371no—
206C37#330511yescharacteristic, complemented, Sylow
207C2×#41—371no—
208C2×#41C2×D3711yescharacteristic
209C2×SD16C2×D3711yescharacteristic
210C2×D8—371no—
211C2×D8C2×D3711yescharacteristic
212C22×C8—371no—
213C22×C8—371no—
214C4⋊Q8—371no—
215#127—371no—
216#127—741no—
217#124—741no—
218#124—741no—
219#121—371no—
220#121—371no—
221#121—371no—
222#121—741no—
223#121—741no—
224#121—741no—
225#121C2×D3711yescharacteristic
226C4×Q8—371no—
227C4×D4—371no—
228C4×D4—371no—
229C4×D4—741no—
230#117—371no—
231#117—371no—
232#117—741no—
233#107—371no—
234#107—371no—
235#106—371no—
236C4⋊C8—371no—
237#103—371no—
238#103—371no—
239#103C2×D3711yescharacteristic
240#102—371no—
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102C2×D3711yescharacteristic
247C22⋊C8—371no—
248C22⋊C8C2×D3711yescharacteristic
249C4×C8—371no—
250#41—22no—
251#41—41no—
252#41—742no—
253#41—1481no—
254C2×Q8—741no—
255C2×Q8C22×D3711yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—371no—
259C2×D4—371no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4—741no—
264C2×D4—741no—
265C2×D4—741no—
266C2×D4C22×D3711yescharacteristic
267C2×D4C22×D3711yescharacteristic
268C22×C4—21no—
269C22×C4—371no—
270C22×C4—741no—
271C22×C4—741no—
272C22×C4C22×D3711yescharacteristic
273SD16—22no—
274D8—41no—
275D8—1481no—
276C2×C8—371no—
277C2×C8—371no—
278C2×C8—1481no—
279C2×C8—1481no—
280C2×C8C22×D3711yescharacteristic
281C2×C8C22×D3711yescharacteristic
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—371no—
285C4⋊C4—371no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4C22×D3711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—371no—
291C22⋊C4—371no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C42—371no—
299C42—741no—
300C42—741no—
301C42—741no—
302C23—21no—
303C23—21no—
304C23—371no—
305C23—741no—
306C23D4×D3711yescharacteristic
307Q8—21no—
308Q8—2961no—
309Q8#1059696412yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—2961no—
317D4—2961no—
318D4—2961no—
319D4—2961no—
320D4—742no—
321D4—741no—
322D4—741no—
323D4—1482no—
324D4—1482no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—371no—
331C2×C4—371no—
332C2×C4—371no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—1482no—
339C2×C4—1482no—
340C2×C4D4×D3711yescharacteristic
341C2×C4C23×D3711yescharacteristic
342C8—21no—
343C8—21no—
344C8—741no—
345C8—741no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—741no—
356C22—741no—
357C22—741no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22C2×D4×D3711yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—372no—
366C4—741no—
367C4—741no—
368C4—1481no—
369C4—1481no—
370C4—1481no—
371C4C2×#1059696411yescharacteristic
372C4#1192458111yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—2961no—
377C2—1481no—
378C2#1455817011yescharacteristic
379C2#135×D3711yescharacteristic
380C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3305
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14558247C2semidirect
2. #14558202C2semidirect
3. #14557878C2semidirect
4. #14557858C2semidirect
5. #14557856C2semidirect
6. #14557826C2semidirect
7. #14557767C2semidirect
8. #14557766C2semidirect
9. #14557726C2semidirect
10. #14557677C2semidirect
11. SD16×Dic37C2semidirect
12. #14557596C2semidirect
13. #14557529C2semidirect
14. #14557528C2semidirect
15. C37×#449C2semidirect
201. #449D37semidirect
206. C37#3305semidirect

Maximal subgroups

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

subgroupindex
#145582472
#145582022
#145578782
#145578582
#145578562
#145578262
#145577672
#145577662
#145577262
#145576772
SD16×Dic372
#145575962
#145575292
#145575282
C37×#4492
#330537