Subgroups — #31799825

Order 17728.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579816	C₂	1	1	yes	maximal, characteristic
2	#22579812	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	#17984547	—	2	1	no	—
5	C₄⋊Dic₂₇₇	—	2	1	no	—
6	C₂×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₂₇₇	C₄	1	2	yes	complemented
8	C₂×Dic₂₇₇	—	4	1	no	—
9	#14555660	—	4	1	no	—
10	C₂×C₄×C₂₇₇	D₄	1	1	yes	characteristic
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	D₂₇₇	1	1	yes	characteristic
22	#108	—	277	1	no	—
23	#106	—	277	1	no	—
24	M₁₆	—	554	1	no	—
25	C₂×C₈	C₂×D₂₇₇	1	1	yes	characteristic
26	C₄⋊C₄	—	554	1	no	—
27	C₁₆	Dic₂₇₇	1	2	yes	complemented
28	C₂×C₄	—	1108	1	no	—
29	C₂×C₄	D₁₁₀₈	1	1	yes	characteristic
30	C₈	—	1108	1	no	—
31	C₈	C₂×Dic₂₇₇	1	1	yes	characteristic
32	C₈	Dic₅₅₄	1	1	yes	characteristic
33	C₂²	#17984552	1	1	yes	characteristic
34	C₄	—	2216	1	no	—
35	C₄	C₄⋊Dic₂₇₇	1	1	yes	characteristic
36	C₄	#17984552	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#22579812	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.