Finite Group Databasebeta

← #18006203

Subgroups — #18006203

Order 4736.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924561C211yesmaximal, characteristic, complemented
3#14558179C211yesmaximal, characteristic, complemented
4#14557915C211yesmaximal, characteristic, complemented
5#14557781C211yesmaximal, characteristic, complemented
6#14557777C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557693C211yesmaximal, characteristic, complemented
11#14557667C211yesmaximal, characteristic, complemented
12#14557666C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557611C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×D148C2211yescharacteristic, complemented
18#11924562—24no—
19#11924561—24no—
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic, complemented
23C2×#10596941C2211yescharacteristic, complemented
24C2×#10596941C2211yescharacteristic, complemented
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic, complemented
30C2×#10596934C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic, complemented
32#11924521—21no—
33#11924515C2211yescharacteristic, complemented
34#11924510C2211yescharacteristic
35#11924509—21no—
36#11924504—21no—
37C4×D148C2211yescharacteristic, complemented
38C22⋊C4×D37—21no—
39#11924469C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924460C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic, complemented
44#11924457C2211yescharacteristic, complemented
45#11924456C2211yescharacteristic, complemented
46#11924456C2211yescharacteristic, complemented
47C22⋊#64436C2211yescharacteristic, complemented
48C22⋊#64436C2211yescharacteristic, complemented
49C4×#64436C2211yescharacteristic, complemented
50C2×#41×C37C2211yescharacteristic
51C22×D4×C37C2211yescharacteristic, complemented
52#124×C37C2211yescharacteristic, complemented
53#123×C37—21no—
54C22⋊Q8×C37C2211yescharacteristic, complemented
55#121×C37—21no—
56#121×C37C2211yescharacteristic
57#120×C37—21no—
58C4×D4×C37C2211yescharacteristic
59C4×D4×C37C2211yescharacteristic, complemented
60C2×C22⋊C4×C37—21no—
61C24×C37—21no—
62C23×D37—21no—
63#41×C37—22no—
64#41×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×D4×C37—22no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37—41no—
71C2×D4×C37D411yescharacteristic
72C2×D4×C37C2311yescharacteristic
73C2×D4×C37C2311yescharacteristic
74C22×C4×C37—21no—
75C22×C4×C37—21no—
76C22×C4×C37C2311yescharacteristic
77C22×C4×C37C2311yescharacteristic
78C2×C22⋊D37—21no—
79C2×C22⋊D37—21no—
80#10596962—22no—
81#10596962—41no—
82C2×D148—22no—
83C2×D148—21no—
84C2×D148—41no—
85C2×D148C2311yescharacteristic
86C2×D148C2311yescharacteristic
87C2×C4×D37—21no—
88C2×C4×D37—21no—
89C2×Dic74C2311yescharacteristic
90C4⋊C4×C37—21no—
91C4⋊C4×C37D411yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37D411yescharacteristic
99C22⋊C4×C37D411yescharacteristic
100C42×C37C2311yescharacteristic
101C22⋊Dic37—21no—
102#10596942—41no—
103#10596941—22no—
104#10596941—22no—
105#10596940—22no—
106#10596940—22no—
107#10596939—22no—
108#10596939—22no—
109#10596939—41no—
110#10596939D414yescomplemented
111#10596938—21no—
112#10596938—21no—
113#10596938—21no—
114#10596938—21no—
115C4⋊Dic37C2311yescharacteristic
116#10596936—21no—
117#10596934—22no—
118#10596934—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—42no—
126C23×C37—42no—
127C23×C37—81no—
128C23×C37C2×D411yescharacteristic
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131C22×D37—21no—
132C22×D37—42no—
133C22×D37—42no—
134C22×D37—81no—
135Q8×C37—21no—
136Q8×C37—21no—
137D4×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—41no—
141D4×C37—42no—
142D4×C37—42no—
143D4×C37—81no—
144D4×C37C2×D412yes—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—42no—
152C2×C4×C37—81no—
153C2×C4×C37C2×D411yescharacteristic
154C2×C4×C37C2×D411yescharacteristic
155C2×C4×C37C2×D411yescharacteristic
156C2×C4×C37C2×D411yescharacteristic
157C2×C4×C37C2411yescharacteristic
158C22⋊D37—42no—
159C22⋊D37—81no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162D148—21no—
163D148—21no—
164D148—21no—
165D148—42no—
166D148C2×D412yes—
167C4×D37—42no—
168C4×D37—81no—
169Dic74—21no—
170Dic74—21no—
171#64436—21no—
172#64436—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—22no—
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—84no—
188C22×C37C22×D411yescharacteristic
189C2×D37—22no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C2×D37—84no—
196C4×C37—21no—
197C4×C37—21no—
198C4×C37—21no—
199C4×C37—21no—
200C4×C37—41no—
201C4×C37—41no—
202C4×C37C22×D411yescharacteristic
203C4×C37H(5,𝔽2)11yescharacteristic
204Dic37—41no—
205Dic37—41no—
206#3273—371nomaximal, Sylow
207C2×C37—41no—
208C2×C37—41no—
209C2×C37—42no—
210C2×C37—81no—
211C2×C37D4211yescharacteristic
212C2×C37#57511yescharacteristic
213C2×C37#57611yescharacteristic
214D37—42no—
215D37—81no—
216C2×AGL(1,ℤ/8)—371no—
217C2×AGL(1,ℤ/8)—371no—
218#546—371no—
219#546D3711yescharacteristic, complemented
220#495—371no—
221#468—371no—
222#468—371no—
223#463—371no—
224#463—371no—
225#452—371no—
226#452—371no—
227#447—371no—
228#447—371no—
229C4×D8—371no—
230#436—371no—
231C37#327311yescharacteristic, complemented, Sylow
232C2×#41—371no—
233C2×#41C2×D3711yescharacteristic
234C22×D4—371no—
235C22×D4C2×D3711yescharacteristic, complemented
236AGL(1,ℤ/8)—744no—
237AGL(1,ℤ/8)—744no—
238C2×Q16—371no—
239C2×SD16—371no—
240C2×SD16—371no—
241C2×SD16—371no—
242C2×SD16—371no—
243C2×D8—371no—
244C2×D8—371no—
245C2×D8—371no—
246C2×D8—371no—
247C2×M16—371no—
248C2×M16—371no—
249#124—371no—
250#124C2×D3711yescharacteristic, complemented
251#123—21no—
252#123—741no—
253C22⋊Q8—371no—
254C22⋊Q8C2×D3711yescharacteristic, complemented
255#121—21no—
256#121—371no—
257#121—741no—
258#121C2×D3711yescharacteristic
259#120—21no—
260#120—741no—
261C4×D4—371no—
262C4×D4C2×D3711yescharacteristic
263C4×D4C2×D3711yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—741no—
266#107—371no—
267C4⋊C8—371no—
268#103—371no—
269#103—371no—
270#102—371no—
271#102—371no—
272#102—371no—
273#102—371no—
274C22⋊C8—371no—
275C22⋊C8—371no—
276C4×C8—371no—
277C24—21no—
278C24—741no—
279#41—22no—
280#41—41no—
281#41—742no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—371no—
291C2×D4—371no—
292C2×D4—742no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—1481no—
297C2×D4C22⋊D3711yescharacteristic
298C2×D4C22×D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—741no—
303C22×C4—741no—
304C22×C4C22×D3711yescharacteristic
305C22×C4C22×D3711yescharacteristic
306Q16—1481no—
307SD16—742no—
308SD16—742no—
309SD16—742no—
310SD16—742no—
311D8—374no—
312D8—742no—
313D8—742no—
314D8—1481no—
315M16—742no—
316M16—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—371no—
320C2×C8—371no—
321C4⋊C4—21no—
322C4⋊C4—371no—
323C4⋊C4—741no—
324C4⋊C4C22⋊D3711yescharacteristic
325C4⋊C4C22×D3711yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C22⋊C4C22⋊D3711yescharacteristic
337C22⋊C4C22⋊D3711yescharacteristic
338C42C22×D3711yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—2961no—
345C23—741no—
346C23—741no—
347C23—1482no—
348C23—1482no—
349C23C2×C22⋊D3711yescharacteristic
350C23C2×C22⋊D3711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—741no—
354Q8—741no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—372no—
363D4—2961no—
364D4—741no—
365D4—741no—
366D4—741no—
367D4—1482no—
368D4—1482no—
369D4D4×D3712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—2961no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—1482no—
382C2×C4C2×C22⋊D3711yescharacteristic
383C2×C4C2×C22⋊D3711yescharacteristic
384C2×C4C2×C22⋊D3711yescharacteristic
385C2×C4C2×C22⋊D3711yescharacteristic
386C2×C4C23×D3711yescharacteristic
387C8—372no—
388C8—741no—
389C8—741no—
390C8—741no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—2964no—
405C22—742no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22—1481no—
410C22—1481no—
411C22C22×C22⋊D3711yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—1481no—
419C4—1481no—
420C4C2×D4×D3711yescharacteristic
421C4#1192458111yescharacteristic
422C2—41no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—2961no—
427C2—1482no—
428C2D4×C22⋊D3711yescharacteristic
429C2#1455833111yescharacteristic
430C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3273
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. C2×#11924562C2semidirect
2. C2×#11924561C2semidirect
3. #14558179C2semidirect
4. #14557915C2semidirect
5. #14557781C2semidirect
6. #14557777C2semidirect
7. #14557748C2semidirect
8. #14557745C2semidirect
9. #14557695C2semidirect
10. #14557693C2semidirect
11. #14557667C2semidirect
12. #14557666C2semidirect
13. C4×#10596939C2semidirect
14. #14557611C2semidirect
15. C37×#546C2semidirect
17. C22×D148C22semidirect
20. C2×#10596942C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596940C22semidirect
23. C2×#10596941C22semidirect
24. C2×#10596941C22semidirect
29. C2×#10596934C22semidirect
30. C2×#10596934C22semidirect
31. #11924524C22semidirect
33. #11924515C22semidirect
37. C4×D148C22semidirect
39. #11924469C22semidirect
40. C4⋊#64436C22semidirect
41. #11924460C22semidirect
42. #11924459C22semidirect
43. #11924457C22semidirect
44. #11924457C22semidirect
45. #11924456C22semidirect
46. #11924456C22semidirect
47. C22⋊#64436C22semidirect
48. C22⋊#64436C22semidirect
49. C4×#64436C22semidirect
51. C22×D4×C37C22semidirect
52. #124×C37C22semidirect
54. C22⋊Q8×C37C22semidirect
59. C4×D4×C37C22semidirect
110. #10596939D4semidirect
219. #546D37semidirect
231. C37#3273semidirect
235. C22×D4C2×D37semidirect
250. #124C2×D37semidirect
254. C22⋊Q8C2×D37semidirect
263. C4×D4C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245612
#145581792
#145579152
#145577812
#145577772
#145577482
#145577452
#145576952
#145576932
#145576672
#145576662
C4×#105969392
#145576112
C37×#5462
#327337