Finite Group Databasebeta

← #18006450

Subgroups — #18006450

Order 4736.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558235C211yesmaximal, characteristic, complemented
2#14558177C211yesmaximal, characteristic, complemented
3#14557886C211yesmaximal, characteristic, complemented
4#14557869C211yesmaximal, characteristic, complemented
5#14557855C211yesmaximal, characteristic, complemented
6#14557831C211yesmaximal, characteristic, complemented
7#14557766C211yesmaximal, characteristic, complemented
8#14557760C211yesmaximal, characteristic, complemented
9#14557746C211yesmaximal, characteristic, complemented
10#14557675C211yesmaximal, characteristic, complemented
11D8×Dic37C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14C2×#11924457C211yesmaximal, characteristic, complemented
15C37×#447C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596940C2211yescharacteristic, complemented
18C22×#64436C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic, complemented
20#11924529—21no—
21#11924527C2211yescharacteristic, complemented
22#11924523C2211yescharacteristic
23#11924520—21no—
24#11924517—21no—
25#11924515C2211yescharacteristic
26#11924508—21no—
27#11924508—21no—
28#11924507C2211yescharacteristic
29#11924507C2211yescharacteristic, complemented
30#11924505—21no—
31D4×Dic37—21no—
32D4×Dic37C2211yescharacteristic
33D4×Dic37C2211yescharacteristic, complemented
34C4×C22⋊D37C2211yescharacteristic
35#11924494C2211yescharacteristic, complemented
36C2×C4⋊Dic37C2211yescharacteristic
37C2×C22⋊Dic37—21no—
38#11924470C2211yescharacteristic, complemented
39#11924470C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C2×D8×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C24×C37—21no—
60C2×D4×C37—22no—
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37—41no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37D411yescharacteristic
72C22×Dic37—21no—
73C22×Dic37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76#10596964—22no—
77#10596964—41no—
78C2×C4×D37C2311yescharacteristic
79C2×Dic74C2311yescharacteristic
80D8×C37—22no—
81D8×C37—41no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37—21no—
93C22⋊Dic37D411yescharacteristic
94#10596940—41no—
95#10596938—21no—
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104#10596936D411yescharacteristic
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—42no—
115C23×C37—42no—
116C23×C37—81no—
117C23×C37C2×D411yescharacteristic
118C22×D37C2×D411yescharacteristic
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—42no—
125D4×C37—42no—
126D4×C37#4112yes—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2411yescharacteristic
132C22⋊D37—22no—
133C22⋊D37—42no—
134C22⋊D37—81no—
135C22⋊D37—81no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—42no—
141C2×Dic37—81no—
142C2×Dic37—81no—
143C2×Dic37—81no—
144C2×Dic37C2×D411yescharacteristic
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147C4×D37—21no—
148C4×D37—21no—
149Dic74—21no—
150Dic74—21no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—22no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—84no—
167C22×C37#13512yes—
168C22×C37C22×D411yescharacteristic
169C2×D37—21no—
170C2×D37—21no—
171C2×D37—21no—
172C4×C37—21no—
173C4×C37—41no—
174C4×C37C2×#4111yescharacteristic
175C4×C37H(5,𝔽2)11yescharacteristic
176Dic37—21no—
177Dic37—21no—
178Dic37—21no—
179Dic37—41no—
180Dic37—41no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—22no—
185C2×C37—42no—
186C2×C37—81no—
187C2×C37—81no—
188C2×C37#54611yescharacteristic
189C2×C37C2×#13511yescharacteristic
190C2×C37#57611yescharacteristic
191D37—41no—
192#553—371no—
193#546—371no—
194#488—371no—
195#484—371no—
196#482—371no—
197#478—371no—
198#466—371no—
199#465—371no—
200#463—371no—
201#449—371no—
202#447D3711yescharacteristic, complemented
203C4×D8—371no—
204C8×D4—371no—
205#416—371no—
206C2×#102—371no—
207C37#329711yescharacteristic, complemented, Sylow
208C2×#41—371no—
209C22×D4C2×D3711yescharacteristic
210C2×SD16—371no—
211C2×D8C2×D3711yescharacteristic
212C2×D8C2×D3711yescharacteristic
213C22×C8—371no—
214C22×C8—371no—
215#126—741no—
216#125—371no—
217#124—371no—
218#123—741no—
219#123—741no—
220C22⋊Q8—371no—
221#121—371no—
222#121—371no—
223#121—741no—
224#121—741no—
225#121C2×D3711yescharacteristic
226#120—741no—
227C4×D4—371no—
228C4×D4—371no—
229C4×D4—371no—
230C4×D4—741no—
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107—371no—
236#106—371no—
237C4⋊C8—371no—
238#103—371no—
239#103—371no—
240#103—371no—
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102C2×D3711yescharacteristic
247#102C2×D3711yescharacteristic
248C22⋊C8—371no—
249C22⋊C8C2×D3711yescharacteristic
250C4×C8—371no—
251C24—21no—
252#41—742no—
253#41—1481no—
254C2×Q8—371no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—371no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4C22×D3711yescharacteristic
264C2×D4C22×D3711yescharacteristic
265C2×D4C22×D3711yescharacteristic
266C22×C4—371no—
267C22×C4—741no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4—741no—
271C22×C4C22×D3711yescharacteristic
272SD16—1481no—
273D8—22no—
274D8—41no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—1481no—
278C2×C8—1481no—
279C2×C8C22×D3711yescharacteristic
280C2×C8C22×D3711yescharacteristic
281C4⋊C4—371no—
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—371no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4—741no—
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—371no—
292C22⋊C4—371no—
293C22⋊C4—741no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C42—371no—
302C42—741no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—371no—
310C23D4×D3711yescharacteristic
311Q8—741no—
312Q8—741no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—2961no—
321D4—2961no—
322D4—742no—
323D4—1482no—
324D4#1059696412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—371no—
329C2×C4—371no—
330C2×C4—371no—
331C2×C4—2961no—
332C2×C4—2961no—
333C2×C4—2961no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—1482no—
341C2×C4D4×D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—21no—
344C8—21no—
345C8—741no—
346C8—741no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—741no—
360C22—741no—
361C22—741no—
362C22#1192455512yes—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—41no—
366C4—741no—
367C4—741no—
368C4—741no—
369C4—1481no—
370C4—1481no—
371C4—1481no—
372C4—1481no—
373C4C2×#1059696411yescharacteristic
374C4#1192458111yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—1481no—
380C2#1455817011yescharacteristic
381C2C2×#1192455511yescharacteristic
382C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#447C2
socleC22×C37C22×D4
hypercenter#447D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14558235C2semidirect
2. #14558177C2semidirect
3. #14557886C2semidirect
4. #14557869C2semidirect
5. #14557855C2semidirect
6. #14557831C2semidirect
7. #14557766C2semidirect
8. #14557760C2semidirect
9. #14557746C2semidirect
10. #14557675C2semidirect
11. D8×Dic37C2semidirect
12. #14557596C2semidirect
13. #14557526C2semidirect
14. C2×#11924457C2semidirect
15. C37×#447C2semidirect
17. C2×#10596940C22semidirect
19. C2×C8×D37C22semidirect
21. #11924527C22semidirect
29. #11924507C22semidirect
33. D4×Dic37C22semidirect
35. #11924494C22semidirect
38. #11924470C22semidirect
39. #11924470C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924461C22semidirect
43. #11924461C22semidirect
44. #11924459C22semidirect
49. #11924457C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
202. #447D37semidirect
207. C37#3297semidirect

Maximal subgroups

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

subgroupindex
#145582352
#145581772
#145578862
#145578692
#145578552
#145578312
#145577662
#145577602
#145577462
#145576752
D8×Dic372
#145575962
#145575262
C2×#119244572
C37×#4472
#329737