Subgroups — #28417276

Order 14912.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14272345	C₂	1	2	yes	maximal
2	C₈×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14272345	C₄	1	4	yes	—
4	C₂×#14272338	C₄	1	1	yes	characteristic
5	C₄×Dic₂₃₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₃₃	C₄	1	1	yes	characteristic
7	#14272345	—	2	4	no	—
8	C₂×Dic₂₃₃	C₂×C₄	1	2	yes	—
9	#14272338	C₈	1	2	yes	complemented
10	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₂₃₃	C₈	1	2	yes	complemented
12	C₂²×C₂₃₃	C₄²	1	1	yes	characteristic
13	C₄×C₂₃₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₃₃	C₂×C₈	1	1	yes	characteristic
15	Dic₂₃₃	M₁₆	1	4	yes	—
16	C₂×C₂₃₃	C₄×C₈	1	1	yes	characteristic
17	C₂×C₂₃₃	#97	1	2	yes	—
18	C₂₃₃	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	233	1	no	maximal, Sylow
20	C₄×C₈	—	233	2	no	—
21	C₄×C₈	—	233	1	no	—
22	C₂×C₈	—	233	4	no	—
23	C₂×C₈	—	233	1	no	—
24	C₂×C₈	#11745400	1	1	yes	characteristic
25	C₄²	—	233	1	no	—
26	C₂×C₄	—	233	2	no	—
27	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
28	C₈	—	466	4	no	—
29	C₈	—	233	2	no	—
30	C₈	#14272345	1	2	yes	complemented
31	C₂²	C₄×#11745400	1	1	yes	characteristic
32	C₄	—	233	4	no	—
33	C₄	C₂×#14272345	1	1	yes	characteristic
34	C₄	#16836602	1	1	yes	characteristic
35	C₂	C₄×#14272345	1	1	yes	characteristic
36	C₂	#21418589	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.