Subgroups — #28412322

Order 14656.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14270087	C₂	1	2	yes	maximal
2	C₈×Dic₂₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14270087	C₄	1	4	yes	—
4	C₂×#14270080	C₄	1	1	yes	characteristic
5	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₂₉	C₄	1	1	yes	characteristic
7	#14270087	—	2	4	no	—
8	C₂×Dic₂₂₉	C₂×C₄	1	2	yes	—
9	#14270080	C₈	1	2	yes	complemented
10	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₂₂₉	C₈	1	2	yes	complemented
12	C₂²×C₂₂₉	C₄²	1	1	yes	characteristic
13	C₄×C₂₂₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₂₉	C₂×C₈	1	1	yes	characteristic
15	Dic₂₂₉	M₁₆	1	4	yes	—
16	C₂×C₂₂₉	C₄×C₈	1	1	yes	characteristic
17	C₂×C₂₂₉	#97	1	2	yes	—
18	C₂₂₉	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	229	1	no	maximal, Sylow
20	C₄×C₈	—	229	2	no	—
21	C₄×C₈	—	229	1	no	—
22	C₂×C₈	—	229	4	no	—
23	C₂×C₈	—	229	1	no	—
24	C₂×C₈	#11745021	1	1	yes	characteristic
25	C₄²	—	229	1	no	—
26	C₂×C₄	—	229	2	no	—
27	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
28	C₈	—	458	4	no	—
29	C₈	—	229	2	no	—
30	C₈	#14270087	1	2	yes	complemented
31	C₂²	C₄×#11745021	1	1	yes	characteristic
32	C₄	—	229	4	no	—
33	C₄	C₂×#14270087	1	1	yes	characteristic
34	C₄	D₂₂₉⋊C₈	1	1	yes	characteristic
35	C₂	C₄×#14270087	1	1	yes	characteristic
36	C₂	#20301042	1	2	yes	—

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.