Subgroups — C₂×#27134371 #37589916

Order 24608.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₃₈	C₂	1	1	yes	maximal, characteristic
2	#27134371	C₂	1	4	yes	maximal, direct product factor
3	C₂×#20259670	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₇₆₉	C₂	1	1	yes	maximal, characteristic
5	Dic₁₅₃₈	—	2	1	no	—
6	Dic₁₅₃₈	C₂²	1	2	yes	—
7	C₂×Dic₇₆₉	—	2	1	no	—
8	#20259670	C₂²	1	2	yes	—
9	Q₈×C₇₆₉	—	2	1	no	—
10	Q₈×C₇₆₉	C₂²	1	2	yes	—
11	C₂×C₄×C₇₆₉	—	2	1	no	—
12	C₂×C₄×C₇₆₉	C₂²	1	1	yes	characteristic
13	C₂²×C₇₆₉	D₄	1	1	yes	characteristic
14	C₄×C₇₆₉	—	2	2	no	—
15	C₄×C₇₆₉	D₄	1	1	yes	characteristic
16	C₄×C₇₆₉	C₂³	1	1	yes	characteristic
17	Dic₇₆₉	—	2	2	no	—
18	C₂×C₇₆₉	Q₁₆	1	2	yes	complemented
19	C₂×C₇₆₉	C₂×D₄	1	1	yes	characteristic
20	C₇₆₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	769	1	no	maximal, Sylow
22	C₂×Q₈	—	769	1	no	—
23	C₂×Q₈	D₇₆₉	1	1	yes	characteristic
24	Q₁₆	—	769	4	no	—
25	C₂×C₈	—	769	1	no	—
26	Q₈	—	769	2	no	—
27	Q₈	—	2	1	no	—
28	Q₈	—	1538	1	no	—
29	Q₈	C₂×D₇₆₉	1	2	yes	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	1538	1	no	—
32	C₂×C₄	C₂×D₇₆₉	1	1	yes	characteristic
33	C₈	—	769	2	no	—
34	C₂²	C₂²⋊D₇₆₉	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	1538	2	no	—
37	C₄	C₂²⋊D₇₆₉	1	1	yes	characteristic
38	C₄	C₂²×D₇₆₉	1	1	yes	characteristic
39	C₂	#27134371	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊D₇₆₉	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.