Subgroups — #27156899

Order 12416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261663	C₂	1	2	yes	maximal
2	C₃₂×D₉₇	C₂	1	1	yes	maximal, characteristic
3	#15690881	—	2	2	no	—
4	C₁₆×D₉₇	C₂²	1	1	yes	characteristic
5	#15690716	C₄	1	1	yes	characteristic
6	C₃₂×C₉₇	C₄	1	1	yes	characteristic
7	#13095521	—	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	C₄×D₉₇	D₈	1	1	yes	characteristic
12	#11715897	—	8	2	no	—
13	C₈×C₉₇	C₄⋊C₄	1	1	yes	characteristic
14	#11715895	Q₁₆	1	1	yes	characteristic
15	C₂×D₉₇	Q₃₂	1	1	yes	characteristic
16	C₄×C₉₇	#107	1	1	yes	characteristic
17	Dic₉₇	D₁₆	1	1	yes	characteristic
18	C₂×C₉₇	#366	1	1	yes	characteristic
19	D₉₇	—	2	1	no	—
20	#1425	—	97	1	no	maximal, Sylow
21	C₉₇	#1425	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	—	97	1	no	—
23	#368	—	97	2	no	—
24	C₂×C₁₆	—	97	1	no	—
25	#108	—	194	2	no	—
26	C₃₂	—	97	1	no	—
27	C₃₂	#87604	1	1	yes	characteristic
28	M₁₆	—	388	2	no	—
29	C₂×C₈	—	97	1	no	—
30	C₁₆	—	97	1	no	—
31	C₁₆	C₂×#87604	1	1	yes	characteristic
32	C₂×C₄	—	97	1	no	—
33	C₈	—	776	2	no	—
34	C₈	—	97	1	no	—
35	C₈	C₄⋊#87604	1	1	yes	characteristic
36	C₂²	—	97	1	no	—
37	C₄	—	97	1	no	—
38	C₄	#15690879	1	1	yes	characteristic
39	C₂	—	194	1	no	—
40	C₂	#20261661	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₉₇	#1425	semidirect

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