Subgroups — #36378876

Order 22592.

54 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	—	2	2	no	—
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	—	4	2	no	—
8	C₂×#13083443	D₄	1	1	yes	characteristic
9	C₂×#13083443	Q₈	1	1	yes	characteristic
10	#15667732	—	2	1	no	—
11	C₄×D₃₅₃	C₂×C₄	1	1	yes	characteristic
12	#15667725	C₈	1	1	yes	characteristic, complemented
13	C₈×C₃₅₃	C₈	1	1	yes	characteristic, complemented
14	C₂×D₃₅₃	C₄⋊C₄	1	1	yes	characteristic
15	#13083443	—	2	1	no	—
16	#13083443	SD₁₆	1	2	yes	—
17	C₄×C₃₅₃	C₂×C₈	1	1	yes	characteristic
18	Dic₃₅₃	M₁₆	1	1	yes	characteristic
19	C₂×C₃₅₃	C₄⋊C₈	1	1	yes	characteristic
20	D₃₅₃	#106	1	1	yes	characteristic
21	D₃₅₃	#108	1	1	yes	characteristic
22	C₃₅₃	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	353	1	no	maximal, Sylow
24	C₄⋊C₈	—	353	2	no	—
25	C₄×C₈	—	353	1	no	—
26	C₂×C₈	—	353	1	no	—
27	C₂×C₈	—	353	1	no	—
28	C₂×C₈	—	706	2	no	—
29	C₄²	—	353	1	no	—
30	C₂×C₄	—	353	1	no	—
31	C₂×C₄	—	353	1	no	—
32	C₂×C₄	—	353	1	no	—
33	C₈	—	353	1	no	—
34	C₈	—	1412	2	no	—
35	C₈	—	706	1	no	—
36	C₈	#15667734	1	1	yes	characteristic, complemented
37	C₂²	—	353	1	no	—
38	C₄	—	353	2	no	—
39	C₄	—	353	1	no	—
40	C₄	—	706	1	no	—
41	C₄	C₂×#15667734	1	1	yes	characteristic
42	C₂	—	353	1	no	—
43	C₂	—	353	1	no	—
44	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.