Subgroups — #27156897

Order 12416.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261661	C₂	1	2	yes	maximal
2	C₃₂×D₉₇	C₂	1	1	yes	maximal, characteristic
3	#15690879	—	2	2	no	—
4	C₁₆×D₉₇	C₂²	1	1	yes	characteristic
5	#15690716	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₉₇	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#87604	—	4	2	no	—
8	C₈×D₉₇	D₄	1	1	yes	characteristic
9	#13095486	Q₈	1	1	yes	characteristic
10	C₁₆×C₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×#87604	—	8	2	no	—
12	C₄×D₉₇	D₈	1	1	yes	characteristic
13	C₈×C₉₇	C₄⋊C₄	1	1	yes	characteristic
14	#11715895	Q₁₆	1	1	yes	characteristic
15	C₂×D₉₇	D₁₆	1	1	yes	characteristic
16	#87604	—	16	2	no	—
17	C₄×C₉₇	#107	1	1	yes	characteristic
18	Dic₉₇	Q₃₂	1	1	yes	characteristic
19	C₂×C₉₇	#366	1	1	yes	characteristic
20	D₉₇	D₃₂	1	1	yes	characteristic
21	D₉₇	Q₆₄	1	1	yes	characteristic
22	#1423	—	97	1	no	maximal, Sylow
23	C₉₇	#1423	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	—	97	1	no	—
25	#366	—	97	2	no	—
26	C₂×C₁₆	—	97	1	no	—
27	#107	—	194	2	no	—
28	C₃₂	—	97	1	no	—
29	C₃₂	#87604	1	1	yes	characteristic, complemented
30	C₂×C₈	—	97	1	no	—
31	C₄⋊C₄	—	388	2	no	—
32	C₁₆	—	97	1	no	—
33	C₁₆	C₂×#87604	1	1	yes	characteristic
34	C₂×C₄	—	776	2	no	—
35	C₂×C₄	—	97	1	no	—
36	C₈	—	97	1	no	—
37	C₈	C₄⋊#87604	1	1	yes	characteristic
38	C₂²	—	97	1	no	—
39	C₄	—	1552	2	no	—
40	C₄	—	97	1	no	—
41	C₄	#15690879	1	1	yes	characteristic
42	C₂	—	97	1	no	—
43	C₂	—	97	1	no	—
44	C₂	#20261661	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.