Finite Group Databasebeta

← #18006557

Subgroups — #18006557

Order 4736.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558187C211yesmaximal, characteristic, complemented
2#14557892C211yesmaximal, characteristic, complemented
3#14557861C211yesmaximal, characteristic, complemented
4#14557849C211yesmaximal, characteristic, complemented
5#14557823C211yesmaximal, characteristic, complemented
6#14557784C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557678C211yesmaximal, characteristic, complemented
10#14557667C211yesmaximal, characteristic, complemented
11#14557643C211yesmaximal, characteristic, complemented
12#14557605C211yesmaximal, characteristic, complemented
13#14557534C211yesmaximal, characteristic, complemented
14C2×#11924457C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic, complemented
16C2×#10596964—21no—
17C2×#10596941C2211yescharacteristic, complemented
18C2×#10596939C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596934C2211yescharacteristic, complemented
21C22×#64436C2211yescharacteristic
22#11924536C2211yescharacteristic, complemented
23#11924520—21no—
24#11924520—21no—
25#11924516—21no—
26#11924510C2211yescharacteristic
27#11924510C2211yescharacteristic, complemented
28C4×D148C2211yescharacteristic, complemented
29C2×C4⋊Dic37C2211yescharacteristic
30C2×C4⋊Dic37C2211yescharacteristic, complemented
31#11924467C2211yescharacteristic, complemented
32#11924467C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35#11924460C2211yescharacteristic, complemented
36#11924460C2211yescharacteristic, complemented
37#11924460C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924456C2211yescharacteristic, complemented
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic, complemented
47#11924447C2211yescharacteristic, complemented
48C2×#41×C37C2211yescharacteristic
49C22×D4×C37C2211yescharacteristic
50#124×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53#121×C37—21no—
54#121×C37C2211yescharacteristic
55#120×C37—21no—
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58C2×C22⋊C4×C37—21no—
59C24×C37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—22no—
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37—21no—
67C2×D4×C37—41no—
68C2×D4×C37D411yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C22×C4×C37C2311yescharacteristic
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C22×Dic37—21no—
78C22×Dic37—21no—
79#10596964—44no—
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×Dic74—21no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37D411yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C22⋊C4×C37—21no—
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C22⋊C4×C37D411yescharacteristic
92C22⋊C4×C37D411yescharacteristic
93C42×C37C2311yescharacteristic
94#10596941—41no—
95#10596939—22no—
96#10596939—41no—
97#10596938—21no—
98#10596938—21no—
99#10596938—21no—
100C4⋊Dic37—21no—
101C4⋊Dic37—21no—
102C4⋊Dic37—21no—
103C4⋊Dic37C2311yescharacteristic
104C4⋊Dic37C2311yescharacteristic
105C4⋊Dic37C2311yescharacteristic
106#10596934—41no—
107C2×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C2×#64436C2311yescharacteristic
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—42no—
115C23×C37—42no—
116C23×C37—81no—
117C23×C37C2×D411yescharacteristic
118C23×C37C2×D411yescharacteristic
119C22×D37—21no—
120Q8×C37—21no—
121Q8×C37—21no—
122D4×C37—22no—
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—21no—
126D4×C37—42no—
127D4×C37—42no—
128D4×C37—81no—
129D4×C37#4112yescomplemented
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—42no—
137C2×C4×C37—81no—
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2×D411yescharacteristic
142C2×C4×C37C2411yescharacteristic
143C22⋊D37—42no—
144C22⋊D37—42no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—42no—
149C2×Dic37—42no—
150D148—21no—
151D148—21no—
152C4×D37—42no—
153Dic74—42no—
154#64436—21no—
155#64436—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—22no—
162C22×C37—21no—
163C22×C37—21no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—84no—
170C22×C37AGL(1,ℤ/8)12yes—
171C22×C37C22×D411yescharacteristic
172C2×D37—41no—
173C2×D37—41no—
174C2×D37—41no—
175C4×C37—21no—
176C4×C37—21no—
177C4×C37—21no—
178C4×C37—21no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37C2×#4111yescharacteristic
182C4×C37H(5,𝔽2)11yescharacteristic
183Dic37—41no—
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—22no—
188C2×C37—41no—
189C2×C37—42no—
190C2×C37—81no—
191C2×C37#54611yescharacteristic
192C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C37#57711yescharacteristic
194D37—81no—
195#547—371no—
196#546D3711yescharacteristic, complemented
197#489—371no—
198#483—371no—
199#481—371no—
200#476—371no—
201#469—371no—
202#465—371no—
203#463—371no—
204#449—371no—
205#447—371no—
206#442—371no—
207#435—371no—
208#417—371no—
209C2×#102—371no—
210C37#330611yescharacteristic, complemented, Sylow
211C2×#41—741no—
212C2×#41C2×D3711yescharacteristic
213C22×D4C2×D3711yescharacteristic
214C2×SD16—371no—
215C2×D8—371no—
216C2×D8—371no—
217C2×M16—371no—
218C22×C8—371no—
219C4⋊Q8—371no—
220#124C2×D3711yescharacteristic
221#123—21no—
222#123—741no—
223#123—741no—
224C22⋊Q8—741no—
225C22⋊Q8C2×D3711yescharacteristic
226#121—21no—
227#121—371no—
228#121—371no—
229#121C2×D3711yescharacteristic
230#120—21no—
231C4×D4—371no—
232C4×D4C2×D3711yescharacteristic
233C4×D4C2×D3711yescharacteristic
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C22⋊C4—21no—
237#106—371no—
238#106—371no—
239#106—371no—
240C4⋊C8—371no—
241#103—371no—
242#103—371no—
243#103—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248#102—371no—
249#102—371no—
250#102—371no—
251C22⋊C8—371no—
252C22⋊C8—371no—
253#97—371no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—1484no—
258C2×Q8—741no—
259C2×Q8C22×D3711yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—371no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4C22⋊D3711yescharacteristic
269C2×D4C22×D3711yescharacteristic
270C2×D4C22×D3711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—741no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4C22×D3711yescharacteristic
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—742no—
280D8—1481no—
281M16—1481no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—371no—
285C2×C8—371no—
286C2×C8—1481no—
287C4⋊C4—21no—
288C4⋊C4—371no—
289C4⋊C4—371no—
290C4⋊C4—371no—
291C4⋊C4—741no—
292C4⋊C4—741no—
293C4⋊C4—741no—
294C4⋊C4C22⋊D3711yescharacteristic
295C4⋊C4C22×D3711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4C22⋊D3711yescharacteristic
305C22⋊C4C22⋊D3711yescharacteristic
306C42C22×D3711yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—741no—
313C23C2×C22⋊D3711yescharacteristic
314C23C2×C22⋊D3711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1482no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—741no—
326D4—741no—
327D4—1482no—
328D4—1482no—
329D4#1059696412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—1482no—
342C2×C4—1482no—
343C2×C4—1482no—
344C2×C4C2×C22⋊D3711yescharacteristic
345C2×C4C2×C22⋊D3711yescharacteristic
346C2×C4C2×C22⋊D3711yescharacteristic
347C2×C4C2×C22⋊D3711yescharacteristic
348C2×C4C23×D3711yescharacteristic
349C8—741no—
350C8—741no—
351C8—741no—
352C8—741no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22#1192456112yes—
369C22C22×C22⋊D3711yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—1481no—
377C4—1481no—
378C4—1481no—
379C4C2×#1059696411yescharacteristic
380C4#1192458111yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—2961no—
386C2#1455817711yescharacteristic
387C2C2×#1192456111yescharacteristic
388C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14558187C2semidirect
2. #14557892C2semidirect
3. #14557861C2semidirect
4. #14557849C2semidirect
5. #14557823C2semidirect
6. #14557784C2semidirect
7. #14557764C2semidirect
8. #14557745C2semidirect
9. #14557678C2semidirect
10. #14557667C2semidirect
11. #14557643C2semidirect
12. #14557605C2semidirect
13. #14557534C2semidirect
14. C2×#11924457C2semidirect
15. C37×#546C2semidirect
17. C2×#10596941C22semidirect
20. C2×#10596934C22semidirect
22. #11924536C22semidirect
27. #11924510C22semidirect
28. C4×D148C22semidirect
30. C2×C4⋊Dic37C22semidirect
31. #11924467C22semidirect
32. #11924467C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. #11924460C22semidirect
36. #11924460C22semidirect
37. #11924460C22semidirect
44. #11924456C22semidirect
46. C22⋊#64436C22semidirect
47. #11924447C22semidirect
129. D4×C37#41semidirect
196. #546D37semidirect
210. C37#3306semidirect
329. D4#10596964semidirect

Maximal subgroups

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

subgroupindex
#145581872
#145578922
#145578612
#145578492
#145578232
#145577842
#145577642
#145577452
#145576782
#145576672
#145576432
#145576052
#145575342
C2×#119244572
C37×#5462
#330637