Finite Group Databasebeta

← #18006369

Subgroups — #18006369

Order 4736.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558348C211yesmaximal, characteristic, complemented
2#14558347C211yesmaximal, characteristic, complemented
3#14558344C211yesmaximal, characteristic, complemented
4#14557924C211yesmaximal, characteristic, complemented
5#14557808C211yesmaximal, characteristic, complemented
6#14557806C211yesmaximal, characteristic, complemented
7#14557794C211yesmaximal, characteristic, complemented
8#14557793C211yesmaximal, characteristic, complemented
9#14557716C211yesmaximal, characteristic, complemented
10#14557714C211yesmaximal, characteristic, complemented
11#14557711C211yesmaximal, characteristic, complemented
12#14557704C211yesmaximal, characteristic, complemented
13#14557655C211yesmaximal, characteristic, complemented
14#14557653C211yesmaximal, characteristic, complemented
15C37×#577C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic
17#11924583C2211yescharacteristic, complemented
18#11924567—21no—
19#11924567C2211yescharacteristic, complemented
20#11924566—21no—
21#11924566—21no—
22#11924566C2211yescharacteristic
23#11924566C2211yescharacteristic
24#11924566C2211yescharacteristic
25#11924566C2211yescharacteristic, complemented
26#11924565—21no—
27#11924565—21no—
28#11924562—21no—
29#11924562C2211yescharacteristic
30#11924556—21no—
31#11924556—21no—
32#11924556C2211yescharacteristic
33#11924555—21no—
34C2×Dic148C2211yescharacteristic, complemented
35C2×#10596942—21no—
36C2×#10596942C2211yescharacteristic, complemented
37Q16×D37—21no—
38C2×#10596940—21no—
39C2×#10596940C2211yescharacteristic
40#11924543C2211yescharacteristic
41#11924543C2211yescharacteristic, complemented
42#11924542C2211yescharacteristic, complemented
43#11924534C2211yescharacteristic, complemented
44#11924523C2211yescharacteristic
45#11924472C2211yescharacteristic, complemented
46#11924471C2211yescharacteristic, complemented
47#11924463C2211yescharacteristic
48#11924463C2211yescharacteristic
49#11924463C2211yescharacteristic, complemented
50#11924462C2211yescharacteristic, complemented
51#11924455C2211yescharacteristic, complemented
52#11924454C2211yescharacteristic, complemented
53#11924454C2211yescharacteristic, complemented
54#11924453C2211yescharacteristic
55#11924446C2211yescharacteristic, complemented
562−1+4×C37C2211yescharacteristic
57H(5,𝔽2)×C37C2211yescharacteristic
58#137×C37—21no—
59#137×C37C2211yescharacteristic
60AGL(1,ℤ/8)×C37—21no—
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62#135×C37—21no—
63#135×C37C2211yescharacteristic
64C2×SD16×C37—21no—
65C2×SD16×C37C2211yescharacteristic
66#131×C37C2211yescharacteristic
67#41×C37—21no—
68#41×C37—21no—
69#41×C37—21no—
70#41×C37—21no—
71#41×C37—41no—
72#41×C37C2311yescharacteristic
73#41×C37C2311yescharacteristic
74#41×C37C2311yescharacteristic
75C2×Q8×C37—21no—
76C2×Q8×C37—21no—
77C2×Q8×C37C2311yescharacteristic
78C2×D4×C37—21no—
79C2×D4×C37—21no—
80C2×D4×C37—41no—
81C2×D4×C37C2311yescharacteristic
82Q8×D37—21no—
83Q8×D37—21no—
84#10596964—21no—
85#10596964—21no—
86#10596964—41no—
87#10596964—41no—
88#10596962—21no—
89#10596962—21no—
90#10596962C2311yescharacteristic
91C2×Dic74—21no—
92C2×Dic74—21no—
93C2×Dic74C2311yescharacteristic
94C2×Dic74C2311yescharacteristic
95Q16×C37—21no—
96Q16×C37D411yescharacteristic
97SD16×C37—21no—
98SD16×C37—21no—
99SD16×C37—21no—
100SD16×C37—21no—
101SD16×C37D411yescharacteristic
102SD16×C37D411yescharacteristic
103D8×C37—21no—
104D8×C37D411yescharacteristic
105M16×C37—21no—
106M16×C37C2311yescharacteristic
107C2×C8×C37—21no—
108C2×C8×C37C2311yescharacteristic
109C22⋊Dic37—41no—
110#10596942—21no—
111#10596942—21no—
112#10596942—21no—
113#10596942—21no—
114#10596942—21no—
115#10596942—21no—
116#10596942—21no—
117#10596942D411yescharacteristic
118#10596941—21no—
119#10596941D411yescharacteristic
120#10596940—21no—
121#10596940—21no—
122#10596940—21no—
123#10596940—21no—
124#10596940—21no—
125#10596940—21no—
126#10596940—21no—
127#10596940D411yescharacteristic
128#10596939—21no—
129#10596939D411yescharacteristic
130#10596936—41no—
131C4×Dic37C2311yescharacteristic
132#10596934—21no—
133#10596934—21no—
134#10596934C2311yescharacteristic
135#10596934C2311yescharacteristic
136#10596934C2311yescharacteristic
137C2×#64436—21no—
138C2×#64436—21no—
139C2×#64436C2311yescharacteristic
140Dic148—21no—
141Dic148—21no—
142#10596929—21no—
143C8×D37—21no—
144C23×C37—21no—
145C23×C37—41no—
146Q8×C37—21no—
147Q8×C37—21no—
148Q8×C37—41no—
149Q8×C37C2×D411yescharacteristic
150Q8×C37C2×D411yescharacteristic
151Q8×C37C2×D411yescharacteristic
152D4×C37—21no—
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—21no—
157D4×C37—41no—
158D4×C37—41no—
159D4×C37—41no—
160D4×C37C2×D411yescharacteristic
161D4×C37C2×D411yescharacteristic
162D4×C37C2×D411yescharacteristic
163C2×C4×C37—21no—
164C2×C4×C37—21no—
165C2×C4×C37—21no—
166C2×C4×C37—21no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37C2411yescharacteristic
171C22⋊D37—21no—
172C22⋊D37—41no—
173C22⋊D37—41no—
174C2×Dic37—21no—
175C2×Dic37—21no—
176C2×Dic37—21no—
177C2×Dic37—41no—
178C2×Dic37—41no—
179D148C2×D411yescharacteristic
180C4×D37—21no—
181C4×D37—41no—
182C4×D37—41no—
183Dic74—21no—
184Dic74—21no—
185Dic74—21no—
186Dic74—21no—
187Dic74—41no—
188Dic74—41no—
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37C2×D411yescharacteristic
192C8×C37C2×D411yescharacteristic
193#64436—21no—
194#64436—21no—
195#64436—21no—
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—41no—
202C22×C37—81no—
203C22×C37—161no—
204C22×C37H(5,𝔽2)11yescharacteristic
205C2×D37—21no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—21no—
209C4×C37—41no—
210C4×C37C22×D411yescharacteristic
211C4×C37C22×D411yescharacteristic
212Dic37—21no—
213Dic37—41no—
214Dic37—41no—
215Dic37—41no—
216#3289—371nomaximal, Sylow
217C2×C37—21no—
218C2×C37—41no—
219C2×C37—41no—
220C2×C37—41no—
221C2×C37—81no—
222C2×C37D4211yescharacteristic
223D37—41no—
224#578—371no—
225#578—371no—
226#577—371no—
227#577D3711yescharacteristic, complemented
228#497—371no—
229#473—371no—
230#473—371no—
231#471—371no—
232#471—371no—
233#456—371no—
234#456—371no—
235#455—371no—
236#454—371no—
237#444—371no—
238#444—371no—
239C37#328911yescharacteristic, complemented, Sylow
2402−1+4—371no—
2412−1+4—371no—
2422−1+4C2×D3711yescharacteristic
243H(5,𝔽2)C2×D3711yescharacteristic
244#137—21no—
245#137—371no—
246#137—371no—
247#137—371no—
248#137—371no—
249#137—371no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137—741no—
255#137C2×D3711yescharacteristic
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—741no—
259AGL(1,ℤ/8)C2×D3711yescharacteristic
260#135—21no—
261#135—371no—
262#135—741no—
263#135—741no—
264#135—741no—
265#135C2×D3711yescharacteristic
266C2×Q16—371no—
267C2×Q16—371no—
268C2×Q16—741no—
269C2×Q16—741no—
270C2×SD16—21no—
271C2×SD16—371no—
272C2×SD16—741no—
273C2×SD16C2×D3711yescharacteristic
274#131—371no—
275#131—371no—
276#131—371no—
277#131C2×D3711yescharacteristic
278C4⋊Q8—371no—
279#124—371no—
280#108—371no—
281#108—371no—
282#104—371no—
283#104—371no—
284#104—371no—
285#104—371no—
286#101—371no—
287#101—371no—
288#101—371no—
289#100—371no—
290#97—371no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—371no—
297#41—741no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—1481no—
302#41—1481no—
303#41C22×D3711yescharacteristic
304#41C22×D3711yescharacteristic
305#41C22×D3711yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—371no—
309C2×Q8—371no—
310C2×Q8—741no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×Q8C22×D3711yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4C22×D3711yescharacteristic
319Q16—21no—
320Q16—371no—
321Q16—741no—
322Q16—741no—
323Q16—741no—
324Q16—741no—
325Q16—741no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16—741no—
330Q16C22⋊D3711yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—371no—
336SD16—371no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16C22⋊D3711yescharacteristic
346SD16C22⋊D3711yescharacteristic
347D8—21no—
348D8—371no—
349D8—741no—
350D8C22⋊D3711yescharacteristic
351M16—21no—
352M16—371no—
353M16—371no—
354M16—371no—
355M16—741no—
356M16—741no—
357M16—741no—
358M16C22×D3711yescharacteristic
359C2×C8—21no—
360C2×C8—371no—
361C2×C8—741no—
362C2×C8—741no—
363C2×C8—741no—
364C2×C8C22×D3711yescharacteristic
365C4⋊C4—1481no—
366C22⋊C4—1481no—
367C42—371no—
368C23—21no—
369C23—41no—
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—371no—
374Q8—741no—
375Q8—741no—
376Q8—741no—
377Q8—741no—
378Q8—1481no—
379Q8—1481no—
380Q8D4×D3711yescharacteristic
381Q8C2×C22⋊D3711yescharacteristic
382Q8C2×C22⋊D3711yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—21no—
388D4—41no—
389D4—41no—
390D4—41no—
391D4—371no—
392D4—741no—
393D4—1481no—
394D4—1481no—
395D4D4×D3711yescharacteristic
396D4C2×C22⋊D3711yescharacteristic
397D4C2×C22⋊D3711yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—741no—
406C2×C4—741no—
407C2×C4—741no—
408C2×C4—741no—
409C2×C4—1481no—
410C2×C4—1481no—
411C2×C4—1481no—
412C2×C4—1481no—
413C2×C4C23×D3711yescharacteristic
414C8—21no—
415C8—371no—
416C8—371no—
417C8—741no—
418C8—741no—
419C8—741no—
420C8C2×C22⋊D3711yescharacteristic
421C8C2×C22⋊D3711yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—81no—
427C22—161no—
428C22—741no—
429C22#1192458111yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—741no—
435C4—1481no—
436C4—1481no—
437C4—1481no—
438C4C2×D4×D3711yescharacteristic
439C4C22×C22⋊D3711yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—81no—
445C2—1481no—
446C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#577C2
socleC2×C37D42
hypercenter#577D37
hypocenterC37#3289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #14558348C2semidirect
2. #14558347C2semidirect
3. #14558344C2semidirect
4. #14557924C2semidirect
5. #14557808C2semidirect
6. #14557806C2semidirect
7. #14557794C2semidirect
8. #14557793C2semidirect
9. #14557716C2semidirect
10. #14557714C2semidirect
11. #14557711C2semidirect
12. #14557704C2semidirect
13. #14557655C2semidirect
14. #14557653C2semidirect
15. C37×#577C2semidirect
17. #11924583C22semidirect
19. #11924567C22semidirect
25. #11924566C22semidirect
34. C2×Dic148C22semidirect
36. C2×#10596942C22semidirect
41. #11924543C22semidirect
42. #11924542C22semidirect
43. #11924534C22semidirect
45. #11924472C22semidirect
46. #11924471C22semidirect
49. #11924463C22semidirect
50. #11924462C22semidirect
51. #11924455C22semidirect
52. #11924454C22semidirect
53. #11924454C22semidirect
55. #11924446C22semidirect
227. #577D37semidirect
239. C37#3289semidirect

Maximal subgroups

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

subgroupindex
#145583482
#145583472
#145583442
#145579242
#145578082
#145578062
#145577942
#145577932
#145577162
#145577142
#145577112
#145577042
#145576552
#145576532
C37×#5772
#328937