Subgroups — C₂²×#17984566 #31801055

Order 17728.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984566	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#14555660	C₂	1	1	yes	maximal, characteristic
3	#17984566	C₂²	1	4	yes	direct product factor
4	C₂×#14555660	C₄	1	3	yes	—
5	C₂×#14555660	C₂²	1	3	yes	—
6	C₂²×C₄×C₂₇₇	C₄	1	1	yes	characteristic
7	#14555660	C₂×C₄	1	3	yes	—
8	#14555660	C₂³	1	1	yes	characteristic
9	C₂³×C₂₇₇	C₈	1	1	yes	characteristic
10	C₂×C₄×C₂₇₇	C₈	1	3	yes	—
11	C₂×C₄×C₂₇₇	C₂×C₄	1	3	yes	—
12	C₂²×C₂₇₇	C₁₆	1	4	yes	complemented
13	C₂²×C₂₇₇	C₂×C₈	1	3	yes	—
14	C₄×C₂₇₇	C₂×C₈	1	3	yes	—
15	C₄×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₂₇₇	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₂₇₇	C₂²×C₈	1	1	yes	characteristic
18	C₂₇₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	277	1	no	maximal, Sylow
20	C₂²×C₈	—	277	1	no	—
21	C₂×C₁₆	—	277	6	no	—
22	C₂²×C₄	#11764308	1	1	yes	characteristic
23	C₂×C₈	—	277	3	no	—
24	C₂×C₈	—	277	3	no	—
25	C₁₆	—	277	4	no	—
26	C₂³	#14555667	1	1	yes	characteristic
27	C₂×C₄	#14555667	1	3	yes	—
28	C₂×C₄	C₂×#11764308	1	3	yes	—
29	C₈	—	277	3	no	—
30	C₈	—	277	1	no	—
31	C₂²	#17984566	1	4	yes	direct product factor
32	C₂²	C₂×#14555667	1	3	yes	—
33	C₄	C₂×#14555667	1	3	yes	—
34	C₄	C₂²×#11764308	1	1	yes	characteristic
35	C₂	C₂×#17984566	1	6	yes	direct product factor
36	C₂	C₂²×#14555667	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.