Subgroups — C₄×C₇×C₁₁²⋊C₃ #23778997

Order 10164.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₁²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₁²⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₁²⋊C₃	C₂×C₇	1	1	yes	characteristic
8	C₄×C₁₁²	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₁₁²⋊C₃	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₇×C₁₁	—	3	4	no	—
11	C₂×C₁₁²	C₂×C₃×C₇	1	1	yes	characteristic
12	C₂×C₇×C₁₁	—	3	4	no	—
13	C₁₁²	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₄×C₇	—	121	1	no	maximal, Hall
15	C₇×C₁₁	—	3	4	no	—
16	C₄×C₁₁	—	3	4	no	—
17	C₂×C₃×C₇	—	121	1	no	—
18	C₄×C₇	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₁₁	—	3	4	no	—
20	C₃×C₇	—	121	1	no	Hall
21	C₂×C₇	C₂×C₁₁²⋊C₃	1	1	yes	characteristic
22	C₃×C₄	—	121	1	no	Hall
23	C₁₁	—	3	4	no	—
24	C₇	C₄×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	—	121	1	no	—
26	C₄	C₇×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	121	1	no	Sylow
28	C₂	C₂×C₇×C₁₁²⋊C₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.