Subgroups — #27141351

Order 12416.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261112	C₂	1	6	yes	maximal, complemented
2	C₈²×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₇₆	—	2	12	no	—
4	#15690807	C₂²	1	4	yes	—
5	C₄×C₈×C₉₇	C₂²	1	3	yes	—
6	C₂×D₃₈₈	—	2	12	no	—
7	D₇₇₆	—	4	24	no	—
8	C₂×C₈×C₉₇	D₄	1	6	yes	—
9	C₄²×C₉₇	C₂³	1	1	yes	characteristic
10	C₂²×D₉₇	—	4	4	no	—
11	C₂×C₄×C₉₇	C₂×D₄	1	3	yes	—
12	D₃₈₈	—	4	24	no	—
13	C₈×C₉₇	D₈	1	12	yes	complemented
14	C₂²×C₉₇	#127	1	1	yes	characteristic
15	C₂×D₉₇	—	8	12	no	—
16	C₄×C₉₇	C₂×D₈	1	6	yes	—
17	C₂×C₉₇	#493	1	3	yes	—
18	D₉₇	—	16	4	no	—
19	#1712	—	97	1	no	maximal, Sylow
20	C₉₇	#1712	1	1	yes	characteristic, complemented, Sylow
21	#493	—	97	6	no	—
22	C₈²	D₉₇	1	1	yes	characteristic, complemented
23	C₂×D₈	—	194	12	no	—
24	#127	—	97	4	no	—
25	C₄×C₈	C₂×D₉₇	1	3	yes	—
26	C₂×D₄	—	194	12	no	—
27	D₈	—	388	24	no	—
28	C₂×C₈	D₃₈₈	1	6	yes	—
29	C₄²	C₂²×D₉₇	1	1	yes	characteristic
30	C₂³	—	388	4	no	—
31	D₄	—	388	24	no	—
32	C₂×C₄	C₂×D₃₈₈	1	3	yes	—
33	C₈	D₇₇₆	1	12	yes	complemented
34	C₂²	—	776	12	no	—
35	C₂²	#15690807	1	1	yes	characteristic
36	C₄	C₂×D₇₇₆	1	6	yes	—
37	C₂	—	1552	4	no	—
38	C₂	#20261112	1	3	yes	—

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.