Subgroups — C₂×#20261793 #27158700

Order 12416.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261793	C₂	1	8	yes	maximal, direct product factor
2	C₂×#15690884	C₂	1	3	yes	maximal, complemented
3	C₂²×#13095514	C₂	1	3	yes	maximal, complemented
4	C₂×#15690817	C₂	1	1	yes	maximal, characteristic
5	#15690884	C₂²	1	12	yes	complemented
6	C₂×#13095514	C₂²	1	1	yes	characteristic
7	C₂×#13095514	C₂²	1	3	yes	—
8	C₂×#13095514	C₂²	1	12	yes	complemented
9	#15690817	C₄	1	4	yes	—
10	#15690817	C₂²	1	4	yes	—
11	C₂×#13095495	C₄	1	3	yes	—
12	C₂²×#11715895	C₂²	1	3	yes	—
13	C₂×#41×C₉₇	C₄	1	1	yes	characteristic
14	#13095514	C₂³	1	2	yes	—
15	#13095514	C₂³	1	6	yes	—
16	#13095495	C₂×C₄	1	12	yes	—
17	C₂×#11715895	C₂×C₄	1	3	yes	—
18	C₂×#11715895	C₂×C₄	1	6	yes	—
19	C₂×#11715895	C₂³	1	1	yes	characteristic
20	C₂×#11715895	C₂³	1	6	yes	—
21	#41×C₉₇	C₈	1	4	yes	—
22	#41×C₉₇	C₂×C₄	1	4	yes	—
23	C₂×Q₈×C₉₇	C₈	1	1	yes	characteristic
24	C₂×D₄×C₉₇	C₈	1	3	yes	—
25	C₂²×C₄×C₉₇	C₂×C₄	1	3	yes	—
26	C₂³×C₉₇	C₂×C₈	1	3	yes	—
27	Q₈×C₉₇	C₂×C₈	1	4	yes	—
28	D₄×C₉₇	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₉₇	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₉₇	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₉₇	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
33	#11715895	C₂²×C₄	1	1	yes	characteristic
34	#11715895	C₂²×C₄	1	6	yes	—
35	#11715895	C₂⁴	1	1	yes	characteristic
36	C₂²×C₉₇	—	2	6	no	—
37	C₂²×C₉₇	C₂²×C₈	1	6	yes	—
38	C₂²×C₉₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₉₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₉₇	C₂²×C₈	1	6	yes	—
41	C₄×C₉₇	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₉₇	—	2	6	no	—
43	C₂×C₉₇	#504	1	2	yes	complemented
44	C₂×C₉₇	C₂³×C₈	1	1	yes	characteristic
45	C₂×#504	—	97	1	no	maximal, Sylow
46	C₉₇	C₂×#504	1	1	yes	characteristic, complemented, Sylow
47	C₂×#131	—	97	1	no	—
48	#504	—	97	8	no	—
49	C₂×M₃₂	—	97	3	no	—
50	C₂²×C₁₆	—	97	3	no	—
51	C₂×#41	#87604	1	1	yes	characteristic
52	#131	—	97	4	no	—
53	#131	—	97	4	no	—
54	C₂×M₁₆	—	97	3	no	—
55	C₂²×C₈	—	97	3	no	—
56	M₃₂	—	97	12	no	—
57	C₂×C₁₆	—	97	1	no	—
58	C₂×C₁₆	—	97	3	no	—
59	C₂×C₁₆	—	97	12	no	—
60	#41	#11715897	1	4	yes	—
61	#41	C₂×#87604	1	4	yes	—
62	C₂×Q₈	#11715897	1	1	yes	characteristic
63	C₂×D₄	#11715897	1	3	yes	—
64	C₂²×C₄	C₂×#87604	1	3	yes	—
65	M₁₆	—	97	12	no	—
66	C₂×C₈	—	97	6	no	—
67	C₂×C₈	—	97	6	no	—
68	C₂×C₈	—	97	3	no	—
69	C₂×C₈	—	97	1	no	—
70	C₁₆	—	97	2	no	—
71	C₁₆	—	97	6	no	—
72	C₂³	C₂×#11715897	1	3	yes	—
73	Q₈	C₂×#11715897	1	4	yes	—
74	D₄	C₂×#11715897	1	12	yes	—
75	C₂×C₄	C₂×#11715897	1	3	yes	—
76	C₂×C₄	C₂×#11715897	1	6	yes	—
77	C₂×C₄	C₂²×#87604	1	6	yes	—
78	C₂×C₄	C₂²×#87604	1	1	yes	characteristic
79	C₈	—	97	1	no	—
80	C₈	—	97	1	no	—
81	C₈	—	97	6	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#11715897	1	6	yes	—
84	C₂²	C₂²×#11715897	1	1	yes	characteristic
85	C₄	C₂²×#11715897	1	1	yes	characteristic
86	C₄	C₂²×#11715897	1	6	yes	—
87	C₄	C₂³×#87604	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#20261793	1	2	yes	direct product factor
90	C₂	C₂³×#11715897	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#87604
commutator	C₂×C₉₇	C₂³×C₈
Frattini	C₄	C₂³×#87604
Fitting, prime radical	C₂×#41×C₉₇	C₄
socle	C₂²×C₉₇	C₂²×C₈
cosocle	#11715895	C₂⁴
hypercenter	C₂×#41	#87604
hypocenter	C₉₇	C₂×#504
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #20261793	C₂	direct (N × H)
2. C₂×#15690884	C₂	semidirect
3. C₂²×#13095514	C₂	semidirect
5. #15690884	C₂²	semidirect
8. C₂×#13095514	C₂²	semidirect
43. C₂×C₉₇	#504	semidirect
46. C₉₇	C₂×#504	semidirect
89. C₂	#20261793	direct (N × H)

Maximal subgroups

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

subgroup	index
#20261793	2
C₂×#15690884	2
C₂²×#13095514	2
C₂×#15690817	2
C₂×#504	97

Subgroups — C2×#20261793 #27158700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20261793 #27158700