Subgroups — C₂×#27134382 #37589943

Order 24608.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134382	C₂	1	8	yes	maximal, direct product factor
2	C₂×D₃₀₇₆	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×D₇₆₉	C₂	1	3	yes	maximal, complemented
4	C₂×Q₈×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆₉	C₂²	1	3	yes	—
6	D₃₀₇₆	C₂²	1	12	yes	complemented
7	C₂×Dic₇₆₉	C₂²	1	1	yes	characteristic
8	C₄×D₇₆₉	C₂²	1	12	yes	complemented
9	Q₈×C₇₆₉	C₂²	1	4	yes	complemented
10	C₂×C₄×C₇₆₉	C₂²	1	3	yes	—
11	C₂²×C₇₆₉	C₂³	1	1	yes	characteristic
12	C₂×D₇₆₉	—	2	6	no	—
13	C₂×D₇₆₉	C₂³	1	6	yes	—
14	C₄×C₇₆₉	C₂³	1	6	yes	—
15	Dic₇₆₉	C₂³	1	2	yes	—
16	C₂×C₇₆₉	#41	1	2	yes	complemented
17	C₂×C₇₆₉	C₂⁴	1	1	yes	characteristic
18	D₇₆₉	—	2	6	no	—
19	C₇₆₉	C₂×#41	1	1	yes	characteristic, complemented, Sylow
20	C₂×#41	—	769	1	no	maximal, Sylow
21	#41	—	769	8	no	—
22	C₂×Q₈	D₇₆₉	1	1	yes	characteristic, complemented
23	C₂×D₄	—	769	3	no	—
24	C₂²×C₄	—	769	3	no	—
25	C₂³	—	769	3	no	—
26	Q₈	C₂×D₇₆₉	1	4	yes	complemented
27	D₄	—	769	12	no	—
28	C₂×C₄	—	769	1	no	—
29	C₂×C₄	—	769	12	no	—
30	C₂×C₄	C₂×D₇₆₉	1	3	yes	—
31	C₂²	—	769	6	no	—
32	C₂²	—	1538	6	no	—
33	C₂²	C₂²×D₇₆₉	1	1	yes	characteristic
34	C₄	—	769	2	no	—
35	C₄	C₂²×D₇₆₉	1	6	yes	—
36	C₂	—	1538	6	no	—
37	C₂	#27134382	1	2	yes	direct product factor
38	C₂	C₂³×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.