Subgroups — #38740868

Order 25216.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161469	C₂	1	1	yes	maximal, characteristic
2	#27160876	C₂	1	1	yes	maximal, characteristic, complemented
3	#354×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15691345	—	2	1	no	—
5	C₂×#15691343	—	2	1	no	—
6	#20263323	C₄	1	1	yes	characteristic, complemented
7	#20263245	—	2	1	no	—
8	#20263237	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₉₇	C₂²	1	1	yes	characteristic
10	#99×C₁₉₇	—	2	1	no	—
11	C₂×D₇₈₈	—	2	1	no	—
12	C₂×D₇₈₈	—	4	1	no	—
13	#15691345	—	4	2	no	—
14	#15691343	—	4	2	no	—
15	#15691342	—	4	1	no	—
16	C₂×#13096802	—	2	1	no	—
17	C₂×Q₈×C₁₉₇	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₉₇	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×C₁₉₇	—	4	1	no	—
20	C₂²⋊C₄×C₁₉₇	—	4	1	no	—
21	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₉₇	—	4	1	no	—
23	D₇₈₈	—	4	1	no	—
24	D₇₈₈	—	4	1	no	—
25	D₇₈₈	—	8	2	no	—
26	#13096802	—	2	2	no	—
27	#13096802	—	8	1	no	—
28	C₂³×C₁₉₇	—	2	1	no	—
29	Q₈×C₁₉₇	—	4	1	no	—
30	D₄×C₁₉₇	—	4	1	no	—
31	C₂×C₄×C₁₉₇	—	2	1	no	—
32	C₂×C₄×C₁₉₇	—	2	1	no	—
33	C₂×C₄×C₁₉₇	—	8	1	no	—
34	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₁₉₇	—	4	1	no	—
36	C₂²×C₁₉₇	—	8	1	no	—
37	C₂²×C₁₉₇	#99	1	1	yes	characteristic
38	C₂×D₁₉₇	—	8	2	no	—
39	C₂×D₁₉₇	—	8	1	no	—
40	C₄×C₁₉₇	—	2	1	no	—
41	C₄×C₁₉₇	—	4	1	no	—
42	C₄×C₁₉₇	—	4	1	no	—
43	C₄×C₁₉₇	—	16	1	no	—
44	C₂×C₁₉₇	—	2	1	no	—
45	C₂×C₁₉₇	—	8	1	no	—
46	C₂×C₁₉₇	#353	1	1	yes	characteristic
47	D₁₉₇	—	16	1	no	—
48	C₁₉₇	#1406	1	1	yes	characteristic, complemented, Sylow
49	#1406	—	197	1	no	maximal, Sylow
50	#496	—	197	1	no	—
51	#355	—	197	1	no	—
52	#354	D₁₉₇	1	1	yes	characteristic, complemented
53	C₂×SD₁₆	—	394	1	no	—
54	C₂×D₈	—	394	1	no	—
55	#127	—	197	1	no	—
56	#124	C₂×D₁₉₇	1	1	yes	characteristic
57	#101	—	394	1	no	—
58	#99	—	2	1	no	—
59	#97	—	197	1	no	—
60	C₂×Q₈	D₇₈₈	1	1	yes	characteristic
61	C₂×D₄	—	788	1	no	—
62	C₂×D₄	—	394	1	no	—
63	C₂×D₄	C₂²⋊D₁₉₇	1	1	yes	characteristic
64	SD₁₆	—	788	2	no	—
65	D₈	—	788	2	no	—
66	M₁₆	—	788	1	no	—
67	C₂×C₈	—	394	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₁₉₇	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	788	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	788	1	no	—
76	D₄	—	788	1	no	—
77	D₄	—	1576	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	#15691335	1	1	yes	characteristic
82	C₈	—	1576	1	no	—
83	C₈	—	394	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	1576	2	no	—
87	C₂²	—	1576	1	no	—
88	C₂²	#20263240	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	3152	1	no	—
96	C₂	#27160871	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27160871
commutator	C₄²×C₁₉₇	C₂×C₄
Frattini	#124	C₂×D₁₉₇
Fitting	#354×C₁₉₇	C₂
socle	C₂×C₁₉₇	#353
prime radical	#27161469	C₂
cosocle	#124×C₁₉₇	C₂²
hypercenter	#354	D₁₉₇
hypocenter	C₁₉₇	#1406
LCS	G ▷ C₄²×C₁₉₇ ▷ C₂×C₄×C₁₉₇ ▷ C₂²×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #27160876	C₂	semidirect
3. #354×C₁₉₇	C₂	semidirect
6. #20263323	C₄	semidirect
8. #20263237	C₄	semidirect
48. C₁₉₇	#1406	semidirect
52. #354	D₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#27161469	2
#27160876	2
#354×C₁₉₇	2
#1406	197