Subgroups — C₄×#19150751 #36378912

Order 22592.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150751	C₂	1	2	yes	maximal
2	C₄×#15667734	C₂	1	1	yes	maximal, characteristic
3	#19150751	C₄	1	4	yes	direct product factor
4	C₂×#15667734	C₄	1	1	yes	characteristic
5	C₂×#15667734	C₂²	1	1	yes	characteristic
6	C₄×#13083443	C₄	1	1	yes	characteristic
7	#15667734	C₈	1	2	yes	—
8	#15667734	C₂×C₄	1	2	yes	—
9	C₂×#13083443	C₈	1	1	yes	characteristic
10	C₂×#13083443	C₂×C₄	1	1	yes	characteristic
11	C₄×D₃₅₃	C₈	1	1	yes	characteristic
12	C₂×D₃₅₃	C₂×C₈	1	1	yes	characteristic
13	#13083443	C₁₆	1	2	yes	complemented
14	#13083443	C₄²	1	1	yes	characteristic
15	#13083443	C₂×C₈	1	1	yes	characteristic
16	C₄×C₃₅₃	C₁₆	1	1	yes	characteristic, complemented
17	Dic₃₅₃	C₁₆	1	1	yes	characteristic, complemented
18	C₂×C₃₅₃	C₂×C₁₆	1	1	yes	characteristic
19	D₃₅₃	C₄×C₈	1	1	yes	characteristic
20	D₃₅₃	C₂×C₁₆	1	1	yes	characteristic
21	C₃₅₃	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	353	1	no	maximal, Sylow
23	C₂×C₁₆	—	353	2	no	—
24	C₄×C₈	—	353	1	no	—
25	C₂×C₈	—	353	1	no	—
26	C₂×C₈	—	353	1	no	—
27	C₄²	—	353	1	no	—
28	C₁₆	—	353	4	no	—
29	C₂×C₄	—	353	1	no	—
30	C₂×C₄	—	353	1	no	—
31	C₂×C₄	—	353	1	no	—
32	C₈	—	353	2	no	—
33	C₈	—	353	2	no	—
34	C₂²	—	353	1	no	—
35	C₄	—	353	1	no	—
36	C₄	—	353	1	no	—
37	C₄	—	353	2	no	—
38	C₄	—	353	1	no	—
39	C₄	#19150751	1	1	yes	characteristic, direct product factor
40	C₂	—	353	1	no	—
41	C₂	—	353	1	no	—
42	C₂	C₂×#19150751	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.