Subgroups — #36378871

Order 22592.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15667734	C₂	1	2	yes	maximal
2	C₈×#13083443	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667734	C₄	1	4	yes	—
4	#19150745	C₄	1	1	yes	characteristic
5	C₄×#13083443	C₂²	1	1	yes	characteristic
6	C₈×D₃₅₃	C₄	1	1	yes	characteristic
7	#15667734	—	2	4	no	—
8	C₂×#13083443	C₂×C₄	1	2	yes	—
9	#15667732	C₈	1	2	yes	complemented
10	C₄×D₃₅₃	C₂×C₄	1	1	yes	characteristic
11	#15667725	C₈	1	1	yes	characteristic, complemented
12	C₈×C₃₅₃	C₈	1	1	yes	characteristic, complemented
13	C₂×D₃₅₃	C₄²	1	1	yes	characteristic
14	#13083443	M₁₆	1	4	yes	—
15	C₄×C₃₅₃	C₂×C₈	1	1	yes	characteristic
16	Dic₃₅₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₃₅₃	C₄×C₈	1	1	yes	characteristic
18	D₃₅₃	#97	1	2	yes	—
19	C₃₅₃	#322	1	1	yes	characteristic, complemented, Sylow
20	#322	—	353	1	no	maximal, Sylow
21	C₄×C₈	—	353	1	no	—
22	C₄×C₈	—	353	2	no	—
23	C₂×C₈	—	353	1	no	—
24	C₂×C₈	—	353	1	no	—
25	C₂×C₈	—	353	4	no	—
26	C₄²	—	353	1	no	—
27	C₂×C₄	—	353	2	no	—
28	C₂×C₄	—	353	1	no	—
29	C₈	—	353	2	no	—
30	C₈	—	353	1	no	—
31	C₈	—	706	4	no	—
32	C₈	#15667734	1	1	yes	characteristic, complemented
33	C₂²	—	353	1	no	—
34	C₄	—	353	4	no	—
35	C₄	—	353	1	no	—
36	C₄	C₂×#15667734	1	1	yes	characteristic
37	C₂	—	353	2	no	—
38	C₂	C₄×#15667734	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.