Subgroups — C₂×#26045271 #37558023

Order 23776.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045271	C₂	1	8	yes	maximal, direct product factor
2	C₂×D₂₉₇₂	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×D₇₄₃	C₂	1	3	yes	maximal, complemented
4	C₂×Q₈×C₇₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₄₃	C₂²	1	3	yes	—
6	D₂₉₇₂	C₂²	1	12	yes	complemented
7	C₂×Dic₇₄₃	C₂²	1	1	yes	characteristic
8	C₄×D₇₄₃	C₂²	1	12	yes	complemented
9	Q₈×C₇₄₃	C₂²	1	4	yes	complemented
10	C₂×C₄×C₇₄₃	C₂²	1	3	yes	—
11	C₂²×C₇₄₃	C₂³	1	1	yes	characteristic
12	C₂×D₇₄₃	—	2	6	no	—
13	C₂×D₇₄₃	C₂³	1	6	yes	—
14	C₄×C₇₄₃	C₂³	1	6	yes	—
15	Dic₇₄₃	C₂³	1	2	yes	—
16	C₂×C₇₄₃	#41	1	2	yes	complemented
17	C₂×C₇₄₃	C₂⁴	1	1	yes	characteristic
18	D₇₄₃	—	2	6	no	—
19	C₇₄₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
20	C₂×#41	—	743	1	no	maximal, Sylow
21	#41	—	743	8	no	—
22	C₂×Q₈	D₇₄₃	1	1	yes	characteristic, complemented
23	C₂×D₄	—	743	3	no	—
24	C₂²×C₄	—	743	3	no	—
25	C₂³	—	743	3	no	—
26	Q₈	C₂×D₇₄₃	1	4	yes	complemented
27	D₄	—	743	12	no	—
28	C₂×C₄	—	743	1	no	—
29	C₂×C₄	—	743	12	no	—
30	C₂×C₄	C₂×D₇₄₃	1	3	yes	—
31	C₂²	—	1486	6	no	—
32	C₂²	—	743	6	no	—
33	C₂²	C₂²×D₇₄₃	1	1	yes	characteristic
34	C₄	—	743	2	no	—
35	C₄	C₂²×D₇₄₃	1	6	yes	—
36	C₂	—	1486	6	no	—
37	C₂	#26045271	1	2	yes	direct product factor
38	C₂	C₂³×D₇₄₃	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.