Subgroups — #38740662

Order 25216.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161102	C₂	1	1	yes	maximal, characteristic
2	#27160861	C₂	1	1	yes	maximal, characteristic
3	#349×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691342	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₉₇	C₄	1	1	yes	characteristic
6	#20263266	—	2	1	no	—
7	#20263255	—	2	1	no	—
8	#20263255	—	2	1	no	—
9	C₂×M₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
10	M₃₂×C₁₉₇	—	2	1	no	—
11	C₂²×Dic₁₉₇	—	2	1	no	—
12	#15691342	—	4	1	no	—
13	C₂×#13096802	—	2	1	no	—
14	C₄×Dic₁₉₇	—	2	1	no	—
15	C₄×Dic₁₉₇	C₈	1	1	yes	characteristic
16	C₄×Dic₁₉₇	C₈	1	1	yes	characteristic
17	#15691333	—	4	1	no	—
18	C₂²×C₄×C₁₉₇	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₁₉₇	—	4	1	no	—
20	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
22	C₁₆×C₁₉₇	—	4	1	no	—
23	C₂×Dic₁₉₇	—	2	1	no	—
24	C₂×Dic₁₉₇	—	2	1	no	—
25	C₂×Dic₁₉₇	—	4	2	no	—
26	#13096802	—	4	1	no	—
27	C₂³×C₁₉₇	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₉₇	—	2	1	no	—
29	C₂×C₄×C₁₉₇	—	2	1	no	—
30	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₉₇	—	2	1	no	—
33	C₈×C₁₉₇	—	2	1	no	—
34	C₂²×C₁₉₇	—	2	1	no	—
35	C₂²×C₁₉₇	—	4	1	no	—
36	C₂²×C₁₉₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₉₇	—	2	1	no	—
38	C₄×C₁₉₇	#99	1	1	yes	characteristic
39	C₄×C₁₉₇	#101	1	1	yes	characteristic
40	Dic₁₉₇	—	2	2	no	—
41	Dic₁₉₇	—	4	1	no	—
42	C₂×C₁₉₇	—	2	1	no	—
43	C₂×C₁₉₇	—	4	1	no	—
44	C₂×C₁₉₇	#324	1	1	yes	characteristic
45	C₁₉₇	#1327	1	1	yes	characteristic, complemented, Sylow
46	#1327	—	197	1	no	maximal, Sylow
47	#423	—	197	1	no	—
48	#349	—	197	1	no	—
49	#349	D₁₉₇	1	1	yes	characteristic
50	C₂×M₁₆	—	197	1	no	—
51	C₂×M₁₆	C₂×D₁₉₇	1	1	yes	characteristic
52	C₂×C₄²	—	197	1	no	—
53	M₃₂	—	2	1	no	—
54	M₃₂	—	394	1	no	—
55	C₄⋊C₈	—	394	1	no	—
56	C₄⋊C₈	—	394	1	no	—
57	C₂²×C₄	—	394	1	no	—
58	C₂²×C₄	C₄×D₁₉₇	1	1	yes	characteristic
59	M₁₆	—	4	1	no	—
60	M₁₆	—	788	1	no	—
61	C₂×C₈	—	394	1	no	—
62	C₂×C₈	C₂²⋊D₁₉₇	1	1	yes	characteristic
63	C₂×C₈	D₇₈₈	1	1	yes	characteristic
64	C₄²	—	394	1	no	—
65	C₄²	—	197	1	no	—
66	C₄²	—	197	1	no	—
67	C₁₆	—	4	1	no	—
68	C₁₆	—	788	1	no	—
69	C₂³	#15691341	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	788	2	no	—
73	C₂×C₄	—	394	1	no	—
74	C₂×C₄	—	394	1	no	—
75	C₂×C₄	#15691335	1	1	yes	characteristic
76	C₂×C₄	C₈×D₁₉₇	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	788	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	#20263238	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	788	1	no	—
85	C₄	—	394	2	no	—
86	C₄	#20263240	1	1	yes	characteristic
87	C₄	#20263244	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	4	1	no	—
90	C₂	#27160804	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#20263240
commutator	C₂×C₄×C₁₉₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₁₉₇
Fitting	#349×C₁₉₇	C₂
socle	C₂×C₁₉₇	#324
prime radical	C₂³×C₁₉₇	M₁₆
cosocle	C₂×M₁₆×C₁₉₇	C₂²
hypercenter	#349	D₁₉₇
hypocenter	C₁₉₇	#1327
LCS	G ▷ C₂×C₄×C₁₉₇ ▷ C₂²×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
45. C₁₉₇	#1327	semidirect

Maximal subgroups

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

subgroup	index
#27161102	2
#27160861	2
#349×C₁₉₇	2
#1327	197