Subgroups — C₂×Dic₁₃₈ #11764271

Order 1104.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₆₉	C₂	1	2	yes	maximal
3	Dic₁₃₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₄₆	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₂₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₂₃	C₂²	1	2	yes	—
7	Dic₆₉	C₂²	1	4	yes	—
8	C₂×C₄×C₂₃	D₃	1	1	yes	characteristic
9	C₂×Dic₂₃	—	3	2	no	—
10	Dic₄₆	—	3	4	no	—
11	C₂×C₃×C₂₃	Q₈	1	2	yes	complemented
12	C₂×C₃×C₂₃	C₂³	1	1	yes	characteristic
13	C₂²×C₂₃	C₂×D₃	1	1	yes	characteristic
14	C₄×C₂₃	C₂×D₃	1	2	yes	—
15	Dic₂₃	—	3	4	no	—
16	C₃×C₂₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
17	C₂×Dic₆	—	23	1	no	maximal, Hall
18	C₂×C₂₃	Dic₆	1	2	yes	complemented
19	C₂×C₂₃	C₂²×D₃	1	1	yes	characteristic
20	C₂×C₃×C₄	D₂₃	1	1	yes	characteristic
21	C₂×Dic₃	—	23	2	no	—
22	Dic₆	—	23	4	no	—
23	C₂₃	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×Q₈	—	69	1	no	Sylow
25	C₂²×C₃	C₂×D₂₃	1	1	yes	characteristic
26	C₃×C₄	C₂×D₂₃	1	2	yes	—
27	Dic₃	—	23	4	no	—
28	Q₈	—	69	4	no	—
29	C₂×C₄	—	69	2	no	—
30	C₂×C₄	D₆₉	1	1	yes	characteristic
31	C₂×C₃	Dic₄₆	1	2	yes	complemented
32	C₂×C₃	C₂²×D₂₃	1	1	yes	characteristic
33	C₂²	C₂×D₆₉	1	1	yes	characteristic
34	C₄	—	69	4	no	—
35	C₄	C₂×D₆₉	1	2	yes	—
36	C₃	C₂×Dic₄₆	1	1	yes	characteristic, complemented, Sylow
37	C₂	Dic₁₃₈	1	2	yes	direct product factor
38	C₂	C₂²×D₆₉	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.