Subgroups — C₈×#15688419 #37560262

Order 23872.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15688419	C₂	1	2	yes	maximal
2	C₈×Dic₃₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688419	C₄	1	4	yes	—
4	C₂×#15688412	C₄	1	1	yes	characteristic
5	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₇₃	C₄	1	1	yes	characteristic
7	#15688419	C₈	1	8	yes	direct product factor
8	C₂×Dic₃₇₃	C₂×C₄	1	2	yes	—
9	#15688412	C₈	1	2	yes	complemented
10	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₃₇₃	C₈	1	2	yes	complemented
12	C₂²×C₃₇₃	C₄²	1	1	yes	characteristic
13	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
15	Dic₃₇₃	C₂×C₈	1	4	yes	—
16	C₂×C₃₇₃	C₄×C₈	1	2	yes	—
17	C₂×C₃₇₃	C₄×C₈	1	1	yes	characteristic
18	C₃₇₃	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	373	1	no	maximal, Sylow
20	C₄×C₈	—	373	2	no	—
21	C₄×C₈	—	373	1	no	—
22	C₂×C₈	—	373	4	no	—
23	C₂×C₈	—	373	1	no	—
24	C₂×C₈	#13093637	1	1	yes	characteristic
25	C₄²	—	373	1	no	—
26	C₂×C₄	—	373	2	no	—
27	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
28	C₈	—	373	8	no	—
29	C₈	—	373	2	no	—
30	C₈	#15688419	1	2	yes	direct product factor
31	C₂²	C₄×#13093637	1	1	yes	characteristic
32	C₄	—	373	4	no	—
33	C₄	C₂×#15688419	1	1	yes	characteristic
34	C₄	D₃₇₃⋊C₈	1	1	yes	characteristic
35	C₂	C₈×#13093637	1	2	yes	—
36	C₂	C₄×#15688419	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.