Finite Group Databasebeta

← #18004319

Subgroups — #18004319

Order 4736.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558332C211yesmaximal, characteristic, complemented
2C2×#11924563C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D37C211yesmaximal, characteristic, complemented
4#14558298C211yesmaximal, characteristic, complemented
5#14557804C211yesmaximal, characteristic, complemented
6#14557803C211yesmaximal, characteristic, complemented
7#14557802C211yesmaximal, characteristic, complemented
8#14557801C211yesmaximal, characteristic, complemented
9#14557799C211yesmaximal, characteristic, complemented
10#14557798C211yesmaximal, characteristic, complemented
11#14557793C211yesmaximal, characteristic, complemented
12#14557580C211yesmaximal, characteristic, complemented
13#14557516C211yesmaximal, characteristic, complemented
14#100×D37C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17#41×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924568—21no—
20#11924567C2211yescharacteristic, complemented
21#11924564C2211yescharacteristic
22#11924564C2211yescharacteristic, complemented
23#11924563—21no—
24#11924563—21no—
25#11924563—21no—
26#11924563—21no—
27#11924563—21no—
28#11924563—21no—
29#11924562C2211yescharacteristic
30#11924561C2211yescharacteristic
31#11924561C2211yescharacteristic, complemented
32#11924560—21no—
33#11924559—21no—
34#11924557—21no—
35C2×#10596941C2211yescharacteristic, complemented
36SD16×D37—21no—
37C2×D296C2211yescharacteristic, complemented
38C2×#10596939C2211yescharacteristic, complemented
39D8×D37—21no—
40#11924544—21no—
41#11924544C2211yescharacteristic, complemented
42#11924543C2211yescharacteristic, complemented
43#11924542—21no—
44#11924542C2211yescharacteristic, complemented
45C2×#10596929—21no—
46C2×#10596929C2211yescharacteristic
47M16×D37—21no—
48M16×D37C2211yescharacteristic
49M16×D37C2211yescharacteristic
50M16×D37C2211yescharacteristic
51#11924472C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924455C2211yescharacteristic, complemented
55#11924453C2211yescharacteristic, complemented
56#11924452C2211yescharacteristic, complemented
57#11924452C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924452C2211yescharacteristic, complemented
60#137×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62C2×SD16×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic, complemented
64#108×C37C2211yescharacteristic, complemented
65#101×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67C23×D37—21no—
68#41×C37C2311yescharacteristic
69C2×Q8×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C2×C22⋊D37—21no—
72#10596966—21no—
73#10596966—21no—
74#10596966—21no—
75#10596966—21no—
76#10596966D411yescharacteristic
77Q8×D37D411yescharacteristic
78#10596964—21no—
79#10596964D411yescharacteristic
80D4×D37—21no—
81D4×D37—21no—
82D4×D37—21no—
83D4×D37—21no—
84D4×D37—21no—
85D4×D37D411yescharacteristic
86#10596962—21no—
87#10596962C2311yescharacteristic
88C2×D148—21no—
89C2×D148C2311yescharacteristic
90C2×D148C2311yescharacteristic
91C2×C4×D37—21no—
92C2×C4×D37—21no—
93C2×C4×D37C2311yescharacteristic
94Q16×C37—21no—
95SD16×C37—21no—
96SD16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99D8×C37—21no—
100M16×C37—21no—
101M16×C37C2311yescharacteristic
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104C2×C8×C37—21no—
105C2×C8×C37C2311yescharacteristic
106#10596942—21no—
107#10596941—21no—
108#10596941—21no—
109#10596941—21no—
110#10596941—21no—
111#10596941—21no—
112#10596940—21no—
113#10596939—21no—
114#10596939—21no—
115#10596939—21no—
116#10596939—21no—
117#10596939—21no—
118#10596934—21no—
119#10596934C2311yescharacteristic
120#10596934C2311yescharacteristic
121#10596934C2311yescharacteristic
122C2×#64436—21no—
123C2×#64436C2311yescharacteristic
124D296—21no—
125D296—21no—
126D296—21no—
127D296—21no—
128#10596930—21no—
129#10596930—21no—
130#10596929—21no—
131#10596929—21no—
132#10596929—21no—
133#10596929—21no—
134#10596929—21no—
135#10596929D411yescharacteristic
136#10596929D411yescharacteristic
137#10596929D411yescharacteristic
138#10596929D411yescharacteristic
139C8×D37—21no—
140C8×D37—21no—
141C8×D37—21no—
142C8×D37—21no—
143C8×D37—21no—
144C23×C37—21no—
145C22×D37—21no—
146C22×D37—21no—
147C22×D37—21no—
148C22×D37—41no—
149C22×D37—41no—
150C22×D37—82no—
151C22×D37#4111yescharacteristic
152Q8×C37—21no—
153Q8×C37—21no—
154Q8×C37C2×D411yescharacteristic
155D4×C37—21no—
156D4×C37—21no—
157D4×C37—21no—
158D4×C37C2×D411yescharacteristic
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37C2411yescharacteristic
162C22⋊D37—21no—
163C22⋊D37—21no—
164C22⋊D37—21no—
165C22⋊D37—41no—
166C22⋊D37—41no—
167C2×Dic37—21no—
168C2×Dic37#4111yescharacteristic
169D148—21no—
170D148—21no—
171D148—21no—
172D148—21no—
173D148—21no—
174D148—41no—
175D148—41no—
176D148C2×D411yescharacteristic
177C4×D37—21no—
178C4×D37—21no—
179C4×D37—21no—
180C4×D37—41no—
181C4×D37—41no—
182C4×D37C2×D411yescharacteristic
183C4×D37C2×D411yescharacteristic
184C4×D37C2×D411yescharacteristic
185C4×D37C2×D411yescharacteristic
186Dic74—21no—
187Dic74C2×D411yescharacteristic
188C8×C37—21no—
189C8×C37—21no—
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—41no—
200C22×C37—81no—
201C22×C37C2×#4111yescharacteristic
202C2×D37—21no—
203C2×D37—41no—
204C2×D37—41no—
205C2×D37—41no—
206C2×D37—81no—
207C2×D37—82no—
208C2×D37—82no—
209C2×D37—81no—
210C2×D37—81no—
211C2×D37#12111yescharacteristic
212C2×D37#12111yescharacteristic
213C4×C37—21no—
214C4×C37—41no—
215C4×C37C22×D411yescharacteristic
216C4×C37C22×D411yescharacteristic
217Dic37—21no—
218Dic37#12111yescharacteristic
219Dic37#12111yescharacteristic
220#3068—371nomaximal, Sylow
221C2×C37—21no—
222C2×C37—41no—
223C2×C37—81no—
224C2×C37C2×#12111yescharacteristic
225D37—21no—
226D37—21no—
227D37—41no—
228D37—81no—
229D37—81no—
230#575—371no—
231C2×AGL(1,ℤ/8)—371no—
232C2×AGL(1,ℤ/8)—371no—
233#568—371no—
234#472—371no—
235#472—371no—
236#472—371no—
237#472—371no—
238#471—371no—
239#471—371no—
240#471—371no—
241#471D3711yescharacteristic, complemented
242#430—371no—
243#413—371no—
244C2×#100—371no—
245C37#306811yescharacteristic, complemented, Sylow
246C2×#41—371no—
247C2×#41—371no—
248C22×D4—371no—
249#137—371no—
250#137—741no—
251#137C2×D3711yescharacteristic, complemented
252AGL(1,ℤ/8)—371no—
253AGL(1,ℤ/8)—371no—
254AGL(1,ℤ/8)—371no—
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—741no—
258AGL(1,ℤ/8)—741no—
259AGL(1,ℤ/8)—741no—
260AGL(1,ℤ/8)—741no—
261AGL(1,ℤ/8)—741no—
262AGL(1,ℤ/8)—741no—
263AGL(1,ℤ/8)—741no—
264AGL(1,ℤ/8)C2×D3711yescharacteristic
265#135—741no—
266#135—741no—
267C2×SD16—371no—
268C2×SD16—741no—
269C2×SD16C2×D3711yescharacteristic, complemented
270C2×D8—371no—
271C2×D8—371no—
272C2×D8—741no—
273#131—371no—
274#131—371no—
275#131—371no—
276#131—741no—
277#131—741no—
278#131C2×D3711yescharacteristic, complemented
279C2×M16—371no—
280C2×M16—371no—
281C2×M16—371no—
282C2×M16—371no—
283C2×M16—741no—
284C2×M16—741no—
285#108—371no—
286#108—371no—
287#108—371no—
288#108C2×D3711yescharacteristic, complemented
289#101—371no—
290#101C2×D3711yescharacteristic, complemented
291#100—371no—
292#100—371no—
293#100—371no—
294#100—371no—
295#100—371no—
296#100C2×D3711yescharacteristic, complemented
297C24—741no—
298#41—371no—
299#41—371no—
300#41—371no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—741no—
306#41—741no—
307#41C22×D3711yescharacteristic
308C2×Q8—371no—
309C2×Q8C22×D3711yescharacteristic
310C2×D4—371no—
311C2×D4—371no—
312C2×D4—371no—
313C2×D4—741no—
314C2×D4—741no—
315C2×D4—741no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—741no—
319C2×D4—741no—
320C2×D4C22×D3711yescharacteristic
321C22×C4—371no—
322C22×C4—741no—
323C22×C4—741no—
324Q16—21no—
325Q16—741no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—741no—
331SD16—741no—
332SD16—741no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337SD16—741no—
338D8—21no—
339D8—741no—
340D8—741no—
341D8—741no—
342D8—741no—
343D8—741no—
344D8—741no—
345D8—741no—
346D8—741no—
347D8—741no—
348M16—21no—
349M16—371no—
350M16—371no—
351M16—371no—
352M16—371no—
353M16—371no—
354M16—371no—
355M16—371no—
356M16—741no—
357M16—741no—
358M16—741no—
359M16—741no—
360M16—741no—
361M16—741no—
362M16C22×D3711yescharacteristic
363M16C22×D3711yescharacteristic
364M16C22×D3711yescharacteristic
365C2×C8—21no—
366C2×C8—371no—
367C2×C8—741no—
368C2×C8—741no—
369C2×C8—741no—
370C2×C8—741no—
371C2×C8—741no—
372C2×C8—741no—
373C2×C8C22×D3711yescharacteristic
374C23—21no—
375C23—371no—
376C23—2962no—
377C23—741no—
378C23—741no—
379C23—741no—
380C23—1481no—
381C23—1481no—
382Q8—21no—
383Q8—21no—
384Q8—371no—
385Q8—741no—
386Q8D4×D3711yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—371no—
391D4—741no—
392D4—741no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—741no—
398D4—741no—
399D4—1481no—
400D4—1481no—
401D4—1481no—
402D4—1481no—
403D4D4×D3711yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—371no—
407C2×C4—371no—
408C2×C4—371no—
409C2×C4—371no—
410C2×C4—371no—
411C2×C4—741no—
412C2×C4—741no—
413C2×C4—741no—
414C2×C4—741no—
415C2×C4—1481no—
416C2×C4—1481no—
417C2×C4C23×D3711yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—371no—
422C8—371no—
423C8—741no—
424C8—741no—
425C8—741no—
426C8D4×D3711yescharacteristic
427C8D4×D3711yescharacteristic
428C22—21no—
429C22—41no—
430C22—81no—
431C22—371no—
432C22—371no—
433C22—2961no—
434C22—2961no—
435C22—2961no—
436C22—2962no—
437C22—2962no—
438C22—741no—
439C22—1481no—
440C22—1481no—
441C22—1481no—
442C22#41×D3711yescharacteristic
443C4—21no—
444C4—41no—
445C4—371no—
446C4—371no—
447C4—741no—
448C4C2×D4×D3711yescharacteristic
449C4C2×D4×D3711yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—2961no—
454C2—2961no—
455C2—741no—
456C2—741no—
457C2—1481no—
458C2#121×D3711yescharacteristic
subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37C2×#121
hypercenter#471D37
hypocenterC37#3068
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14558332C2semidirect
2. C2×#11924563C2semidirect
3. AGL(1,ℤ/8)×D37C2semidirect
4. #14558298C2semidirect
5. #14557804C2semidirect
6. #14557803C2semidirect
7. #14557802C2semidirect
8. #14557801C2semidirect
9. #14557799C2semidirect
10. #14557798C2semidirect
11. #14557793C2semidirect
12. #14557580C2semidirect
13. #14557516C2semidirect
14. #100×D37C2semidirect
15. C37×#471C2semidirect
20. #11924567C22semidirect
22. #11924564C22semidirect
31. #11924561C22semidirect
35. C2×#10596941C22semidirect
37. C2×D296C22semidirect
38. C2×#10596939C22semidirect
41. #11924544C22semidirect
42. #11924543C22semidirect
44. #11924542C22semidirect
51. #11924472C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924455C22semidirect
55. #11924453C22semidirect
56. #11924452C22semidirect
57. #11924452C22semidirect
58. #11924452C22semidirect
59. #11924452C22semidirect
60. #137×C37C22semidirect
62. C2×SD16×C37C22semidirect
63. #131×C37C22semidirect
64. #108×C37C22semidirect
65. #101×C37C22semidirect
66. #100×C37C22semidirect
241. #471D37semidirect
245. C37#3068semidirect
251. #137C2×D37semidirect
269. C2×SD16C2×D37semidirect
278. #131C2×D37semidirect
288. #108C2×D37semidirect
290. #101C2×D37semidirect
296. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583322
C2×#119245632
AGL(1,ℤ/8)×D372
#145582982
#145578042
#145578032
#145578022
#145578012
#145577992
#145577982
#145577932
#145575802
#145575162
#100×D372
C37×#4712
#306837