Subgroups — #27139653

Order 12416.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13095486	C₂	1	2	yes	maximal
2	C₈²×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#13095486	C₄	1	4	yes	—
4	C₄×C₈×C₉₇	C₄	1	2	yes	—
5	C₄×C₈×C₉₇	C₂²	1	1	yes	characteristic
6	#13095486	C₈	1	8	yes	complemented
7	C₂×C₈×C₉₇	C₈	1	4	yes	—
8	C₂×C₈×C₉₇	C₂×C₄	1	2	yes	—
9	C₄²×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₉₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₉₇	C₂×C₈	1	2	yes	—
12	C₈×C₉₇	—	2	4	no	—
13	C₈×C₉₇	C₂×C₈	1	4	yes	—
14	C₂²×C₉₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₉₇	C₄×C₈	1	2	yes	—
16	C₄×C₉₇	M₃₂	1	4	yes	—
17	C₂×C₉₇	C₈²	1	1	yes	characteristic
18	C₂×C₉₇	#346	1	2	yes	—
19	#1311	—	97	1	no	maximal, Sylow
20	C₉₇	#1311	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	97	2	no	—
22	C₈²	D₉₇	1	1	yes	characteristic
23	C₂×C₁₆	—	97	4	no	—
24	C₄×C₈	Dic₉₇	1	2	yes	—
25	C₄×C₈	C₂×D₉₇	1	1	yes	characteristic
26	C₂×C₈	#11715895	1	4	yes	—
27	C₂×C₈	C₄×D₉₇	1	2	yes	—
28	C₄²	C₂×Dic₉₇	1	1	yes	characteristic
29	C₁₆	—	97	8	no	—
30	C₂×C₄	C₄×Dic₉₇	1	1	yes	characteristic
31	C₂×C₄	C₂×#11715895	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₈×D₉₇	1	4	yes	—
34	C₂²	C₄×#11715895	1	1	yes	characteristic
35	C₄	C₈×Dic₉₇	1	2	yes	—
36	C₄	#15690750	1	4	yes	—
37	C₂	C₈×#11715895	1	1	yes	characteristic
38	C₂	#20260511	1	2	yes	—

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

N	H ≅ G/N	type
6. #13095486	C₈	semidirect
20. C₉₇	#1311	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.