Subgroups — C₂²×#13095486 #20261147

Order 6208.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095486	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
3	#13095486	C₂²	1	4	yes	direct product factor
4	C₂²×C₄×C₉₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₉₇	C₄	1	3	yes	—
6	C₂×C₈×C₉₇	C₂²	1	3	yes	—
7	C₂³×C₉₇	C₈	1	1	yes	characteristic
8	C₂×C₄×C₉₇	C₈	1	3	yes	—
9	C₂×C₄×C₉₇	C₂×C₄	1	3	yes	—
10	C₈×C₉₇	C₂×C₄	1	3	yes	—
11	C₈×C₉₇	C₂³	1	1	yes	characteristic
12	C₂²×C₉₇	C₁₆	1	4	yes	complemented
13	C₂²×C₉₇	C₂×C₈	1	3	yes	—
14	C₄×C₉₇	C₂×C₈	1	3	yes	—
15	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₉₇	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₉₇	C₂²×C₈	1	1	yes	characteristic
18	C₉₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	97	1	no	maximal, Sylow
20	C₂²×C₈	D₉₇	1	1	yes	characteristic
21	C₂×C₁₆	—	97	6	no	—
22	C₂²×C₄	Dic₉₇	1	1	yes	characteristic
23	C₂×C₈	Dic₉₇	1	3	yes	—
24	C₂×C₈	C₂×D₉₇	1	3	yes	—
25	C₁₆	—	97	4	no	—
26	C₂³	#11715895	1	1	yes	characteristic
27	C₂×C₄	#11715895	1	3	yes	—
28	C₂×C₄	C₂×Dic₉₇	1	3	yes	—
29	C₈	C₂×Dic₉₇	1	3	yes	—
30	C₈	C₂²×D₉₇	1	1	yes	characteristic
31	C₂²	#13095486	1	4	yes	direct product factor
32	C₂²	C₂×#11715895	1	3	yes	—
33	C₄	C₂×#11715895	1	3	yes	—
34	C₄	C₂²×Dic₉₇	1	1	yes	characteristic
35	C₂	C₂×#13095486	1	6	yes	direct product factor
36	C₂	C₂²×#11715895	1	1	yes	characteristic

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