Subgroups — #38740792

Order 25216.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263266	C₂	1	2	yes	maximal
2	C₂×#97×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	#20263266	—	2	2	no	—
4	#20263266	—	2	2	no	—
5	C₂×#15691333	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₉₇	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉₇	C₄	1	1	yes	characteristic
9	#97×C₁₉₇	—	2	2	no	—
10	#15691333	—	2	4	no	—
11	C₂²×C₄×C₁₉₇	—	2	1	no	—
12	C₂²×C₄×C₁₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉₇	—	2	1	no	—
14	C₂×C₈×C₁₉₇	—	2	1	no	—
15	C₂×C₈×C₁₉₇	C₈	1	2	yes	—
16	C₂×C₈×C₁₉₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₉₇	D₄	1	2	yes	—
18	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉₇	Q₈	1	1	yes	characteristic
20	C₄²×C₁₉₇	—	2	1	no	—
21	C₄²×C₁₉₇	C₈	1	2	yes	—
22	C₂³×C₁₉₇	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₉₇	—	2	2	no	—
24	C₂×C₄×C₁₉₇	—	4	2	no	—
25	C₂×C₄×C₁₉₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉₇	M₁₆	1	1	yes	characteristic
31	C₈×C₁₉₇	—	2	2	no	—
32	C₈×C₁₉₇	C₂²⋊C₄	1	2	yes	—
33	C₈×C₁₉₇	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₉₇	—	2	2	no	—
35	C₂²×C₁₉₇	#97	1	1	yes	characteristic
36	C₂²×C₁₉₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₉₇	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₉₇	—	4	2	no	—
39	C₄×C₁₉₇	#95	1	1	yes	characteristic
40	C₄×C₁₉₇	C₄×C₈	1	1	yes	characteristic
41	C₄×C₁₉₇	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₉₇	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₁₉₇	—	2	1	no	—
44	C₂×C₁₉₇	—	2	1	no	—
45	C₂×C₁₉₇	#336	1	1	yes	characteristic
46	C₂×C₁₉₇	#347	1	2	yes	—
47	C₁₉₇	#1375	1	1	yes	characteristic, complemented, Sylow
48	#1375	—	197	1	no	maximal, Sylow
49	C₂×M₃₂	—	197	2	no	—
50	C₂×#97	D₁₉₇	1	1	yes	characteristic
51	C₂²×C₈	Dic₁₉₇	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₁₉₇	1	1	yes	characteristic
53	C₂×C₄²	Dic₁₉₇	1	1	yes	characteristic
54	M₃₂	—	394	2	no	—
55	M₃₂	—	394	2	no	—
56	C₂×C₁₆	—	197	4	no	—
57	#97	—	2	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×Dic₁₉₇	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	#13096802	1	2	yes	—
63	C₂×C₈	C₄×D₁₉₇	1	2	yes	—
64	C₂×C₈	C₂²⋊D₁₉₇	1	2	yes	—
65	C₂×C₈	D₇₈₈	1	1	yes	characteristic
66	C₂×C₈	Dic₃₉₄	1	1	yes	characteristic
67	C₄²	—	2	1	no	—
68	C₄²	#13096802	1	2	yes	—
69	C₁₆	—	394	4	no	—
70	C₂³	#15691342	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄×Dic₁₉₇	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊Dic₁₉₇	1	1	yes	characteristic
75	C₂×C₄	C₄⋊Dic₁₉₇	1	1	yes	characteristic
76	C₂×C₄	C₂×#13096802	1	1	yes	characteristic
77	C₂×C₄	C₂×#13096802	1	1	yes	characteristic
78	C₂×C₄	#15691342	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	#15691335	1	2	yes	—
81	C₈	#15691337	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#20263237	1	1	yes	characteristic
84	C₂²	C₂²⋊#13096802	1	1	yes	characteristic
85	C₂²	C₄⋊#13096802	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	#20263233	1	1	yes	characteristic
88	C₄	C₄×#13096802	1	1	yes	characteristic
89	C₄	C₂²⋊#13096802	1	1	yes	characteristic
90	C₄	C₄⋊#13096802	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#27160834	1	1	yes	characteristic
94	C₂	#27160857	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₁₉₇
commutator	C₄×C₁₉₇	C₄×C₈
Frattini	C₂²×C₈	C₂×D₁₉₇
Fitting	C₂×#97×C₁₉₇	C₂
socle	C₂²×C₁₉₇	#97
prime radical	C₂³×C₁₉₇	M₁₆
cosocle	C₂²×C₈×C₁₉₇	C₂²
hypercenter	C₂×#97	D₁₉₇
hypocenter	C₁₉₇	#1375
LCS	G ▷ C₄×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
5. C₂×#15691333	C₄	semidirect
47. C₁₉₇	#1375	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263266	2
C₂×#97×C₁₉₇	2
#1375	197