Finite Group Databasebeta

← #18006087

Subgroups — #18006087

Order 4736.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924562C211yesmaximal, characteristic, complemented
2C22×#10596940C211yesmaximal, characteristic, complemented
3#14558192C211yesmaximal, characteristic, complemented
4#14557920C211yesmaximal, characteristic, complemented
5#14557777C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557730C211yesmaximal, characteristic, complemented
9#14557684C211yesmaximal, characteristic, complemented
10#14557676C211yesmaximal, characteristic, complemented
11#14557671C211yesmaximal, characteristic, complemented
12#14557667C211yesmaximal, characteristic, complemented
13#14557633C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15D42×C37C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic, complemented
17C22×Dic74C2211yescharacteristic, complemented
18#11924562—24no—
19C2×#10596940—24no—
20C2×#10596940C2211yescharacteristic
21C2×#10596940C2211yescharacteristic
22C2×#10596940C2211yescharacteristic, complemented
23C2×#10596940C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic, complemented
25C2×#10596940C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic, complemented
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596934C2211yescharacteristic, complemented
30C22×#64436C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic, complemented
32#11924522—21no—
33#11924515C2211yescharacteristic, complemented
34#11924514—21no—
35#11924510C2211yescharacteristic, complemented
36#11924508—21no—
37C4×Dic74C2211yescharacteristic, complemented
38#11924496—21no—
39#11924469C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924459C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic
44#11924457C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic, complemented
46#11924456C2211yescharacteristic, complemented
47C22⋊#64436C2211yescharacteristic, complemented
48C22⋊#64436C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50C22×D4×C37—21no—
51C22×D4×C37C2211yescharacteristic
52C22×D4×C37C2211yescharacteristic
53#127×C37C2211yescharacteristic
54#121×C37—21no—
55#121×C37C2211yescharacteristic
56#121×C37C2211yescharacteristic
57#120×C37—21no—
58#120×C37—21no—
59C4×D4×C37C2211yescharacteristic
60C4×D4×C37C2211yescharacteristic
61C24×C37—21no—
62C24×C37—21no—
63C2×D4×C37—22no—
64C2×D4×C37—22no—
65C2×D4×C37—21no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37—21no—
71C2×D4×C37—41no—
72C2×D4×C37—41no—
73C2×D4×C37—44no—
74C2×D4×C37D411yescharacteristic
75C2×D4×C37C2311yescharacteristic
76C2×D4×C37C2311yescharacteristic
77C2×D4×C37C2311yescharacteristic
78C22×C4×C37—21no—
79C22×C4×C37C2311yescharacteristic
80C22×C4×C37C2311yescharacteristic
81C2×C22⋊D37—21no—
82C2×C22⋊D37—21no—
83C22×Dic37—21no—
84#10596962—22no—
85#10596962—41no—
86C2×D148C2311yescharacteristic
87C2×C4×D37—21no—
88C2×Dic74—22no—
89C2×Dic74—21no—
90C2×Dic74—41no—
91C2×Dic74C2311yescharacteristic
92C2×Dic74C2311yescharacteristic
93C4⋊C4×C37D411yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37D411yescharacteristic
99C22⋊C4×C37D411yescharacteristic
100C42×C37C2311yescharacteristic
101C22⋊Dic37—21no—
102#10596940—22no—
103#10596940—22no—
104#10596940—22no—
105#10596940—22no—
106#10596940—41no—
107#10596940D414yescomplemented
108#10596939—22no—
109#10596939—22no—
110#10596939—41no—
111#10596938—21no—
112#10596938—21no—
113#10596938—21no—
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936—21no—
117C4×Dic37—21no—
118#10596934—22no—
119C2×#64436—22no—
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C2×#64436C2311yescharacteristic
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—21no—
127C23×C37—42no—
128C23×C37—42no—
129C23×C37—42no—
130C23×C37—42no—
131C23×C37—81no—
132C23×C37—81no—
133C23×C37C2×D411yescharacteristic
134C23×C37C2×D411yescharacteristic
135C22×D37—21no—
136D4×C37—22no—
137D4×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—21no—
141D4×C37—21no—
142D4×C37—42no—
143D4×C37—42no—
144D4×C37—42no—
145D4×C37—42no—
146D4×C37—42no—
147D4×C37—81no—
148D4×C37C2×D412yes—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—42no—
155C2×C4×C37C2×D411yescharacteristic
156C2×C4×C37C2×D411yescharacteristic
157C2×C4×C37C2×D411yescharacteristic
158C2×C4×C37C2×D411yescharacteristic
159C2×C4×C37C2411yescharacteristic
160C22⋊D37—42no—
161C22⋊D37—42no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—42no—
166D148—21no—
167D148—21no—
168C4×D37—42no—
169Dic74—21no—
170Dic74—21no—
171Dic74—21no—
172Dic74—42no—
173Dic74C2×D412yescomplemented
174#64436—21no—
175#64436—21no—
176#64436—21no—
177#64436C2×D412yescomplemented
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—22no—
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—41no—
190C22×C37—41no—
191C22×C37—41no—
192C22×C37—84no—
193C22×C37—84no—
194C22×C37AGL(1,ℤ/8)12yescomplemented
195C22×C37C22×D411yescharacteristic
196C2×D37—41no—
197C2×D37—41no—
198C2×D37—41no—
199C4×C37—21no—
200C4×C37—21no—
201C4×C37—21no—
202C4×C37—21no—
203C4×C37—41no—
204C4×C37C22×D411yescharacteristic
205C4×C37H(5,𝔽2)11yescharacteristic
206Dic37—22no—
207Dic37—41no—
208Dic37—41no—
209#3265—371nomaximal, Sylow
210C2×C37—22no—
211C2×C37—41no—
212C2×C37—42no—
213C2×C37—81no—
214C2×C37—81no—
215C2×C37D4211yescharacteristic
216C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
217C2×C37#57711yescharacteristic
218D37—81no—
219C2×AGL(1,ℤ/8)—371no—
220C22×SD16—371no—
221#548—371no—
222D42D3711yescharacteristic, complemented
223#496—371no—
224#468—371no—
225#466—371no—
226#463—371no—
227#460—371no—
228#450—371no—
229#449—371no—
230#448—371no—
231#447—371no—
232#440—371no—
233#435—371no—
234C37#326511yescharacteristic, complemented, Sylow
235C2×#41—371no—
236C22×Q8—371no—
237C22×D4—21no—
238C22×D4C2×D3711yescharacteristic
239C22×D4C2×D3711yescharacteristic
240AGL(1,ℤ/8)—744no—
241C2×SD16—371no—
242C2×SD16—371no—
243C2×SD16—371no—
244C2×SD16—371no—
245C2×SD16—371no—
246C2×SD16—371no—
247C2×SD16—744no—
248C2×D8—371no—
249C2×D8—371no—
250C2×D8—371no—
251C2×M16—371no—
252C22×C8—371no—
253#127C2×D3711yescharacteristic
254#124—371no—
255#124—741no—
256C22⋊Q8—371no—
257C22⋊Q8—741no—
258#121—21no—
259#121—371no—
260#121—741no—
261#121C2×D3711yescharacteristic
262#121C2×D3711yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—371no—
266C4×D4—741no—
267C4×D4C2×D3711yescharacteristic
268C4×D4C2×D3711yescharacteristic
269#107—371no—
270C4⋊C8—371no—
271#103—371no—
272#103—371no—
273#102—371no—
274#102—371no—
275#102—371no—
276#102—371no—
277C22⋊C8—371no—
278C22⋊C8—371no—
279#97—371no—
280C24—21no—
281C24—21no—
282#41—742no—
283#41—1481no—
284C2×Q8—371no—
285C2×Q8—371no—
286C2×Q8—742no—
287C2×Q8—741no—
288C2×Q8—1481no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—371no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4C22⋊D3711yescharacteristic
304C2×D4C22×D3711yescharacteristic
305C2×D4C22×D3711yescharacteristic
306C2×D4C22×D3711yescharacteristic
307C22×C4—21no—
308C22×C4—741no—
309C22×C4—741no—
310C22×C4C22×D3711yescharacteristic
311C22×C4C22×D3711yescharacteristic
312SD16—374no—
313SD16—742no—
314SD16—742no—
315SD16—742no—
316SD16—742no—
317SD16—1481no—
318D8—742no—
319D8—742no—
320D8—1481no—
321M16—742no—
322C2×C8—371no—
323C2×C8—371no—
324C2×C8—371no—
325C2×C8—371no—
326C2×C8—742no—
327C4⋊C4—371no—
328C4⋊C4—741no—
329C4⋊C4—741no—
330C4⋊C4C22⋊D3711yescharacteristic
331C4⋊C4C22×D3711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—741no—
336C22⋊C4—741no—
337C22⋊C4—741no—
338C22⋊C4—741no—
339C22⋊C4C22⋊D3711yescharacteristic
340C22⋊C4C22⋊D3711yescharacteristic
341C42—741no—
342C42C22×D3711yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—741no—
353C23C2×C22⋊D3711yescharacteristic
354C23C2×C22⋊D3711yescharacteristic
355Q8—372no—
356Q8—741no—
357Q8—741no—
358Q8—741no—
359Q8—1482no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—741no—
373D4—741no—
374D4—1482no—
375D4—1482no—
376D4D4×D3712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—741no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—1482no—
387C2×C4—1482no—
388C2×C4C2×C22⋊D3711yescharacteristic
389C2×C4C2×C22⋊D3711yescharacteristic
390C2×C4C2×C22⋊D3711yescharacteristic
391C2×C4C2×C22⋊D3711yescharacteristic
392C2×C4C23×D3711yescharacteristic
393C8—372no—
394C8—741no—
395C8—741no—
396C8—741no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—1481no—
414C22—1481no—
415C22—1481no—
416C22#1192456212yescomplemented
417C22C22×C22⋊D3711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—742no—
424C4—1481no—
425C4—1481no—
426C4C2×D4×D3711yescharacteristic
427C4#1192458111yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—2961no—
434C2D4×C22⋊D3711yescharacteristic
435C2C2×#1192456211yescharacteristic
436C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingD42×C37C2
socleC22×C37C22×D4
hypercenterD42D37
hypocenterC37#3265
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C22×#10596940C2semidirect
3. #14558192C2semidirect
4. #14557920C2semidirect
5. #14557777C2semidirect
6. #14557767C2semidirect
7. #14557748C2semidirect
8. #14557730C2semidirect
9. #14557684C2semidirect
10. #14557676C2semidirect
11. #14557671C2semidirect
12. #14557667C2semidirect
13. #14557633C2semidirect
14. #14557605C2semidirect
15. D42×C37C2semidirect
16. C2×#10596962C22semidirect
17. C22×Dic74C22semidirect
22. C2×#10596940C22semidirect
23. C2×#10596940C22semidirect
24. C2×#10596940C22semidirect
25. C2×#10596940C22semidirect
27. C2×#10596939C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596934C22semidirect
30. C22×#64436C22semidirect
31. #11924524C22semidirect
33. #11924515C22semidirect
35. #11924510C22semidirect
37. C4×Dic74C22semidirect
39. #11924469C22semidirect
40. C4⋊#64436C22semidirect
41. #11924459C22semidirect
42. #11924459C22semidirect
44. #11924457C22semidirect
45. #11924457C22semidirect
46. #11924456C22semidirect
47. C22⋊#64436C22semidirect
48. C22⋊#64436C22semidirect
49. #11924447C22semidirect
107. #10596940D4semidirect
173. Dic74C2×D4semidirect
177. #64436C2×D4semidirect
194. C22×C37AGL(1,ℤ/8)semidirect
222. D42D37semidirect
234. C37#3265semidirect
416. C22#11924562semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C22×#105969402
#145581922
#145579202
#145577772
#145577672
#145577482
#145577302
#145576842
#145576762
#145576712
#145576672
#145576332
#145576052
D42×C372
#326537