Subgroups — #31771530

Order 17216.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575523	C₂	1	1	yes	maximal, characteristic
2	#22575521	C₂	1	1	yes	maximal, characteristic
3	#22575392	C₂	1	1	yes	maximal, characteristic
4	#16864412	—	2	1	no	—
5	C₄⋊#11761640	—	2	1	no	—
6	C₈×D₂₆₉	C₂²	1	1	yes	characteristic
7	#16864377	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
9	C₂×#11761640	—	4	1	no	—
10	#14524137	—	4	1	no	—
11	C₄×D₂₆₉	D₄	1	1	yes	characteristic
12	#14524130	Q₈	1	1	yes	characteristic
13	C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₂₆₉	SD₁₆	1	1	yes	characteristic
15	#11761640	—	8	1	no	—
16	C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
17	Dic₂₆₉	SD₁₆	1	1	yes	characteristic
18	C₂×C₂₆₉	#106	1	1	yes	characteristic
19	D₂₆₉	—	2	1	no	—
20	C₂₆₉	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	269	1	no	maximal, Sylow
22	M₃₂	—	269	1	no	—
23	#108	—	269	1	no	—
24	#106	—	269	1	no	—
25	M₁₆	—	538	1	no	—
26	C₂×C₈	—	269	1	no	—
27	C₄⋊C₄	—	538	1	no	—
28	C₁₆	—	269	1	no	—
29	C₁₆	#11761640	1	1	yes	characteristic, complemented
30	C₂×C₄	—	269	1	no	—
31	C₂×C₄	—	1076	1	no	—
32	C₈	—	269	1	no	—
33	C₈	—	1076	1	no	—
34	C₈	C₂×#11761640	1	1	yes	characteristic
35	C₂²	—	269	1	no	—
36	C₄	—	269	1	no	—
37	C₄	—	2152	1	no	—
38	C₄	C₄⋊#11761640	1	1	yes	characteristic
39	C₂	—	538	1	no	—
40	C₂	#22575521	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.