Subgroups — C₂³×#17987237 #49149019

Order 36928.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#17987237	C₂	1	14	yes	maximal, direct product factor
2	C₂³×Dic₅₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#17987237	C₂²	1	28	yes	direct product factor
4	C₂²×Dic₅₇₇	C₄	1	7	yes	—
5	C₂²×Dic₅₇₇	C₂²	1	7	yes	—
6	C₂⁴×C₅₇₇	C₄	1	1	yes	characteristic
7	#17987237	C₂³	1	8	yes	direct product factor
8	C₂×Dic₅₇₇	C₂×C₄	1	21	yes	—
9	C₂×Dic₅₇₇	C₂³	1	7	yes	—
10	C₂³×C₅₇₇	C₈	1	8	yes	complemented
11	C₂³×C₅₇₇	C₂×C₄	1	7	yes	—
12	C₂²×C₅₇₇	C₂×C₈	1	28	yes	complemented
13	C₂²×C₅₇₇	C₂²×C₄	1	7	yes	—
14	Dic₅₇₇	C₂²×C₄	1	7	yes	—
15	Dic₅₇₇	C₂⁴	1	1	yes	characteristic
16	C₂×C₅₇₇	C₂²×C₈	1	14	yes	complemented
17	C₂×C₅₇₇	C₂³×C₄	1	1	yes	characteristic
18	C₅₇₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	577	1	no	maximal, Sylow
20	C₂³×C₄	—	577	1	no	—
21	C₂²×C₈	—	577	14	no	—
22	C₂⁴	#14556313	1	1	yes	characteristic
23	C₂²×C₄	—	577	7	no	—
24	C₂²×C₄	—	577	7	no	—
25	C₂×C₈	—	577	28	no	—
26	C₂³	#17987237	1	8	yes	direct product factor
27	C₂³	C₂×#14556313	1	7	yes	—
28	C₂×C₄	—	577	7	no	—
29	C₂×C₄	—	577	21	no	—
30	C₈	—	577	8	no	—
31	C₂²	C₂×#17987237	1	28	yes	direct product factor
32	C₂²	C₂²×#14556313	1	7	yes	—
33	C₄	—	577	1	no	—
34	C₄	—	577	7	no	—
35	C₂	C₂²×#17987237	1	14	yes	direct product factor
36	C₂	C₂³×#14556313	1	1	yes	characteristic

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

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