Subgroups — C₄×#14584116 #26013865

Order 11172.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14584116	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#14584116	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×#87705	—	7	8	no	maximal
6	C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×#87705	—	7	8	no	—
8	C₄×#3861	—	19	1	no	maximal, Hall
9	C₄×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
10	#87705	—	7	8	no	—
11	C₂×#3861	—	19	1	no	—
12	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	—
13	C₄×C₁₉⋊C₃	—	49	1	no	Hall
14	C₄×C₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	#3861	—	19	1	no	Hall
16	C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
17	C₂×C₁₉⋊C₃	—	49	1	no	—
18	C₂×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
19	C₄×ΓL(1,𝔽₈)	—	133	8	no	—
20	C₄×C₁₉	#3861	1	1	yes	characteristic, complemented, Hall
21	C₁₉⋊C₃	—	49	1	no	Hall
22	C₇²	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×ΓL(1,𝔽₈)	—	133	8	no	—
24	C₂×C₁₉	C₂×#3861	1	1	yes	characteristic
25	C₄×C₇	#87705	1	8	yes	complemented
26	ΓL(1,𝔽₈)	—	133	8	no	—
27	C₁₉	C₄×#3861	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₇	C₂×#87705	1	8	yes	—
29	C₃×C₄	—	931	1	no	Hall
30	C₇	C₄×#87705	1	8	yes	complemented
31	C₂×C₃	—	931	1	no	—
32	C₄	#14584116	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	931	1	no	Sylow
34	C₂	C₂×#14584116	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.