Subgroups — C₂³×#11715895 #20261492

Order 6208.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715895	C₂	1	14	yes	maximal, direct product factor
2	C₂³×C₄×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715895	C₂²	1	28	yes	direct product factor
4	C₂⁴×C₉₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₉₇	C₄	1	7	yes	—
6	C₂²×C₄×C₉₇	C₂²	1	7	yes	—
7	C₂³×C₉₇	C₈	1	8	yes	complemented
8	C₂³×C₉₇	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₉₇	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₉₇	C₂³	1	7	yes	—
11	#11715895	C₂³	1	8	yes	direct product factor
12	C₂²×C₉₇	C₂×C₈	1	28	yes	complemented
13	C₂²×C₉₇	C₂²×C₄	1	7	yes	—
14	C₄×C₉₇	C₂²×C₄	1	7	yes	—
15	C₄×C₉₇	C₂⁴	1	1	yes	characteristic
16	C₂×C₉₇	C₂²×C₈	1	14	yes	complemented
17	C₂×C₉₇	C₂³×C₄	1	1	yes	characteristic
18	C₉₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	97	1	no	maximal, Sylow
20	C₂³×C₄	D₉₇	1	1	yes	characteristic
21	C₂²×C₈	—	97	14	no	—
22	C₂⁴	Dic₉₇	1	1	yes	characteristic
23	C₂²×C₄	Dic₉₇	1	7	yes	—
24	C₂²×C₄	C₂×D₉₇	1	7	yes	—
25	C₂×C₈	—	97	28	no	—
26	C₂³	#11715895	1	8	yes	direct product factor
27	C₂³	C₂×Dic₉₇	1	7	yes	—
28	C₂×C₄	C₂×Dic₉₇	1	21	yes	—
29	C₂×C₄	C₂²×D₉₇	1	7	yes	—
30	C₈	—	97	8	no	—
31	C₂²	C₂×#11715895	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₉₇	1	7	yes	—
33	C₄	C₂²×Dic₉₇	1	7	yes	—
34	C₄	C₂³×D₉₇	1	1	yes	characteristic
35	C₂	C₂²×#11715895	1	14	yes	direct product factor
36	C₂	C₂³×Dic₉₇	1	1	yes	characteristic

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