Subgroups — #31799826

Order 17728.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579820	C₂	1	1	yes	maximal, characteristic
2	#22579812	C₂	1	1	yes	maximal, characteristic
3	#108×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₂₇₇	—	2	1	no	—
5	#17984538	C₄	1	2	yes	complemented
6	M₁₆×C₂₇₇	—	2	1	no	—
7	C₂×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₇₇	—	4	1	no	—
9	C₂×C₄×C₂₇₇	D₄	1	1	yes	characteristic
10	C₈×C₂₇₇	—	4	1	no	—
11	C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₇₇	Q₈	1	1	yes	characteristic
13	C₂²×C₂₇₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₇₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₇₇	SD₁₆	1	1	yes	characteristic
16	Dic₂₇₇	—	8	1	no	—
17	C₂×C₂₇₇	—	2	1	no	—
18	C₂×C₂₇₇	#106	1	1	yes	characteristic
19	C₂₇₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	277	1	no	maximal, Sylow
21	M₃₂	—	277	1	no	—
22	#108	D₂₇₇	1	1	yes	characteristic
23	#106	—	277	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₂₇₇	1	1	yes	characteristic
26	C₄⋊C₄	—	554	1	no	—
27	C₁₆	—	277	2	no	—
28	C₂×C₄	—	1108	1	no	—
29	C₂×C₄	C₂²⋊D₂₇₇	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₄×D₂₇₇	1	1	yes	characteristic
32	C₈	Dic₅₅₄	1	1	yes	characteristic
33	C₂²	#17984550	1	1	yes	characteristic
34	C₄	—	2216	1	no	—
35	C₄	#17984542	1	1	yes	characteristic
36	C₄	#17984551	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#22579811	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #17984538	C₄	semidirect
19. C₂₇₇	#365	semidirect

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