Subgroups — #38740632

Order 25216.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27160855	C₂	1	1	yes	maximal, characteristic
2	#27160800	C₂	1	1	yes	maximal, characteristic
3	#346×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691333	C₄	1	2	yes	—
5	C₄×#13096802	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₉₇	C₄	1	2	yes	—
7	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
8	C₂×#13096802	—	2	2	no	—
9	#15691333	—	2	2	no	—
10	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₉₇	C₈	1	4	yes	complemented
14	#13096802	—	4	2	no	—
15	C₂×C₄×C₁₉₇	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₁₉₇	M₁₆	1	2	yes	—
17	C₈×C₁₉₇	C₂×C₈	1	2	yes	—
18	C₈×C₁₉₇	M₁₆	1	2	yes	—
19	C₂²×C₁₉₇	#97	1	1	yes	characteristic
20	C₄×C₁₉₇	—	2	2	no	—
21	C₄×C₁₉₇	C₄×C₈	1	1	yes	characteristic
22	C₄×C₁₉₇	#97	1	1	yes	characteristic
23	C₂×C₁₉₇	#322	1	1	yes	characteristic
24	C₂×C₁₉₇	#347	1	2	yes	—
25	C₁₉₇	#1313	1	1	yes	characteristic, complemented, Sylow
26	#1313	—	197	1	no	maximal, Sylow
27	#346	—	197	1	no	—
28	#346	D₁₉₇	1	1	yes	characteristic
29	#322	—	197	1	no	—
30	C₂×C₁₆	—	197	2	no	—
31	C₂×C₁₆	Dic₁₉₇	1	2	yes	—
32	C₄×C₈	—	197	2	no	—
33	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
34	C₂×C₈	—	394	2	no	—
35	C₂×C₈	C₄×D₁₉₇	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₁₉₇	1	1	yes	characteristic
37	C₄²	C₄×D₁₉₇	1	1	yes	characteristic
38	C₁₆	—	394	2	no	—
39	C₁₆	#13096802	1	4	yes	complemented
40	C₂×C₄	C₄×Dic₁₉₇	1	1	yes	characteristic
41	C₂×C₄	#15691341	1	2	yes	—
42	C₈	—	788	2	no	—
43	C₈	C₂×#13096802	1	2	yes	—
44	C₈	#15691341	1	2	yes	—
45	C₂²	#20263236	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄×#13096802	1	1	yes	characteristic
48	C₄	#20263236	1	1	yes	characteristic
49	C₂	#27160800	1	1	yes	characteristic
50	C₂	#27160856	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₁₉₇
commutator	C₄×C₁₉₇	C₄×C₈
Frattini	C₄×C₈	C₂×D₁₉₇
Fitting	#346×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	#97
cosocle	C₄×C₈×C₁₉₇	C₂²
hypercenter	#346	D₁₉₇
hypocenter	C₁₉₇	#1313
LCS	G ▷ C₄×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ #346

Complements

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

N	H ≅ G/N	type
13. C₁₆×C₁₉₇	C₈	semidirect
25. C₁₉₇	#1313	semidirect
39. C₁₆	#13096802	semidirect

Maximal subgroups

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

subgroup	index
#27160855	2
#27160800	2
#346×C₁₉₇	2
#1313	197