Finite Group Databasebeta

← #18006551

Subgroups — #18006551

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#14558179C211yesmaximal, characteristic, complemented
2#14557895C211yesmaximal, characteristic, complemented
3#14557863C211yesmaximal, characteristic, complemented
4#14557851C211yesmaximal, characteristic, complemented
5#14557820C211yesmaximal, characteristic, complemented
6#14557784C211yesmaximal, characteristic, complemented
7#14557760C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557666C211yesmaximal, characteristic, complemented
11#14557643C211yesmaximal, characteristic, complemented
12#14557605C211yesmaximal, characteristic, complemented
13#14557532C211yesmaximal, characteristic, complemented
14C2×#11924456C211yesmaximal, characteristic, complemented
15C37×#547C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C2×#10596940C2211yescharacteristic, complemented
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C2×#10596934C2211yescharacteristic, complemented
22C22×#64436C2211yescharacteristic
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924515C2211yescharacteristic
26#11924510C2211yescharacteristic
27#11924509—21no—
28#11924504—21no—
29C4×D148C2211yescharacteristic
30C22⋊C4×D37—21no—
31#11924467C2211yescharacteristic, complemented
32#11924467C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35#11924459C2211yescharacteristic, complemented
36#11924459C2211yescharacteristic, complemented
37#11924459C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic, complemented
39#11924456C2211yescharacteristic
40#11924456C2211yescharacteristic
41#11924456C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic, complemented
47#11924447C2211yescharacteristic, complemented
48C2×#41×C37—21no—
49C4⋊Q8×C37C2211yescharacteristic, complemented
50#123×C37—21no—
51#123×C37—21no—
52C22⋊Q8×C37—21no—
53#121×C37C2211yescharacteristic
54#121×C37C2211yescharacteristic, complemented
55C4×D4×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic, complemented
57C2×C4⋊C4×C37C2211yescharacteristic
58C2×C4⋊C4×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60#41×C37—44no—
61C2×Q8×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37D411yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73#10596962—22no—
74#10596962—41no—
75C2×D148—22no—
76C2×D148—21no—
77C2×D148—41no—
78C2×D148C2311yescharacteristic
79C2×D148C2311yescharacteristic
80C2×C4×D37—21no—
81C2×C4×D37—21no—
82C2×Dic74C2311yescharacteristic
83C4⋊C4×C37—21no—
84C4⋊C4×C37—21no—
85C4⋊C4×C37—21no—
86C4⋊C4×C37D411yescharacteristic
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C22⋊C4×C37—21no—
91C22⋊C4×C37—21no—
92C22⋊C4×C37—21no—
93C22⋊C4×C37D411yescharacteristic
94C22⋊C4×C37D411yescharacteristic
95C42×C37C2311yescharacteristic
96C22⋊Dic37—21no—
97#10596940—41no—
98#10596939—22no—
99#10596939—41no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104C4⋊Dic37C2311yescharacteristic
105#10596936—21no—
106#10596934—41no—
107C2×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C2×#64436C2311yescharacteristic
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C23×C37C2×D411yescharacteristic
115C22×D37—21no—
116C22×D37—21no—
117C22×D37—42no—
118C22×D37—42no—
119C22×D37—81no—
120Q8×C37—42no—
121D4×C37—22no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—42no—
125D4×C37—42no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—42no—
134C2×C4×C37—42no—
135C2×C4×C37—42no—
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C22⋊D37—42no—
142C22⋊D37—81no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145D148—21no—
146D148—21no—
147D148—21no—
148D148—42no—
149D148#4112yescomplemented
150C4×D37—42no—
151C4×D37—81no—
152Dic74—21no—
153Dic74—21no—
154#64436—21no—
155#64436—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—21no—
162C22×C37—21no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37AGL(1,ℤ/8)12yes—
167C22×C37C22×D411yescharacteristic
168C2×D37—22no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37—41no—
174C2×D37—84no—
175C4×C37—21no—
176C4×C37—21no—
177C4×C37—21no—
178C4×C37—21no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37C2×#4111yescharacteristic
183C4×C37H(5,𝔽2)11yescharacteristic
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—22no—
188C2×C37—41no—
189C2×C37—81no—
190C2×C37#54611yescharacteristic
191C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C37#57711yescharacteristic
193D37—42no—
194D37—81no—
195#547D3711yescharacteristic, complemented
196#546—371no—
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—21no—
212C2×#41—371no—
213C22×D4—371no—
214C2×SD16—371no—
215C2×D8—371no—
216C2×D8—371no—
217C2×M16—371no—
218C22×C8—371no—
219C4⋊Q8C2×D3711yescharacteristic, complemented
220#124—371no—
221#123—21no—
222#123—21no—
223#123—741no—
224C22⋊Q8—21no—
225C22⋊Q8—371no—
226#121—371no—
227#121—741no—
228#121C2×D3711yescharacteristic
229#121C2×D3711yescharacteristic, complemented
230#120—741no—
231C4×D4—371no—
232C4×D4C2×D3711yescharacteristic
233C4×D4C2×D3711yescharacteristic, complemented
234C2×C4⋊C4C2×D3711yescharacteristic
235C2×C4⋊C4C2×D3711yescharacteristic, complemented
236C2×C22⋊C4—741no—
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—741no—
255#41—44no—
256#41—742no—
257#41—1481no—
258C2×Q8—21no—
259C2×Q8—371no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—371no—
263C2×D4—371no—
264C2×D4—742no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—1481no—
269C2×D4C22⋊D3711yescharacteristic
270C2×D4C22×D3711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
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—21no—
289C4⋊C4—21no—
290C4⋊C4—371no—
291C4⋊C4—741no—
292C4⋊C4C22⋊D3711yescharacteristic
293C4⋊C4C22×D3711yescharacteristic
294C4⋊C4C22×D3711yescharacteristic
295C4⋊C4C22×D3711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4C22⋊D3711yescharacteristic
305C22⋊C4C22⋊D3711yescharacteristic
306C42C22×D3711yescharacteristic
307C23—21no—
308C23—2961no—
309C23—741no—
310C23—741no—
311C23—1482no—
312C23—1482no—
313C23C2×C22⋊D3711yescharacteristic
314C23C2×C22⋊D3711yescharacteristic
315Q8—42no—
316Q8—741no—
317Q8—741no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—372no—
324D4—2961no—
325D4—741no—
326D4—741no—
327D4—741no—
328D4—1482no—
329D4—1482no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—2961no—
341C2×C4—741no—
342C2×C4—741no—
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—41no—
359C22—41no—
360C22—41no—
361C22—2964no—
362C22—742no—
363C22—1481no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22#1192456212yes—
369C22C22×C22⋊D3711yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1481no—
378C4—1481no—
379C4#41×D3711yescharacteristic
380C4#1192458211yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—2961no—
385C2—1482no—
386C2#1455817111yescharacteristic
387C2C2×#1192456211yescharacteristic
388C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#547C2
socleC22×C37C22×D4
hypercenter#547D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14558179C2semidirect
2. #14557895C2semidirect
3. #14557863C2semidirect
4. #14557851C2semidirect
5. #14557820C2semidirect
6. #14557784C2semidirect
7. #14557760C2semidirect
8. #14557748C2semidirect
9. #14557676C2semidirect
10. #14557666C2semidirect
11. #14557643C2semidirect
12. #14557605C2semidirect
13. #14557532C2semidirect
14. C2×#11924456C2semidirect
15. C37×#547C2semidirect
18. C2×#10596940C22semidirect
21. C2×#10596934C22semidirect
31. #11924467C22semidirect
32. #11924467C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. #11924459C22semidirect
36. #11924459C22semidirect
37. #11924459C22semidirect
38. #11924457C22semidirect
46. C22⋊#64436C22semidirect
47. #11924447C22semidirect
49. C4⋊Q8×C37C22semidirect
54. #121×C37C22semidirect
56. C4×D4×C37C22semidirect
58. C2×C4⋊C4×C37C22semidirect
149. D148#41semidirect
195. #547D37semidirect
210. C37#3306semidirect
219. C4⋊Q8C2×D37semidirect
229. #121C2×D37semidirect
233. C4×D4C2×D37semidirect
235. C2×C4⋊C4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581792
#145578952
#145578632
#145578512
#145578202
#145577842
#145577602
#145577482
#145576762
#145576662
#145576432
#145576052
#145575322
C2×#119244562
C37×#5472
#330637