Subgroups — C₂×#444 #2954

Order 128.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×#131	C₂	1	2	yes	maximal, complemented
3	#444	C₂	1	8	yes	maximal, direct product factor
4	C₂×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#104	C₂	1	2	yes	maximal, complemented
6	C₂×#97	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#41	C₂²	1	2	yes	—
8	#135	C₄	1	4	yes	complemented
9	#135	C₂²	1	4	yes	—
10	C₂×Q₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×SD₁₆	C₄	1	2	yes	complemented
12	C₂×D₈	C₄	1	1	yes	characteristic, complemented
13	#131	—	2	4	no	—
14	#131	C₂²	1	8	yes	complemented
15	C₂×M₁₆	—	2	2	no	—
16	C₂×M₁₆	C₂²	1	2	yes	—
17	C₂²×C₈	—	2	2	no	—
18	C₂²×C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄²	C₂²	1	1	yes	characteristic
21	#108	C₂²	1	4	yes	complemented
22	#104	C₂²	1	8	yes	complemented
23	#97	C₂²	1	4	yes	complemented
24	#41	—	2	2	no	—
25	#41	—	2	2	no	—
26	#41	C₂×C₄	1	4	yes	—
27	#41	C₂³	1	4	yes	—
28	C₂×Q₈	C₂×C₄	1	2	yes	—
29	C₂×D₄	—	2	2	no	—
30	C₂×D₄	C₂×C₄	1	2	yes	—
31	C₂²×C₄	—	2	2	no	—
32	C₂²×C₄	—	2	1	no	—
33	C₂²×C₄	C₂³	1	1	yes	characteristic
34	Q₁₆	C₂×C₄	1	4	yes	complemented
35	SD₁₆	C₂×C₄	1	8	yes	complemented
36	D₈	C₂×C₄	1	4	yes	complemented
37	M₁₆	—	2	2	no	—
38	M₁₆	—	2	8	no	—
39	M₁₆	C₂³	1	4	yes	—
40	C₂×C₈	—	2	2	no	—
41	C₂×C₈	—	2	8	no	—
42	C₂×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈	C₂×C₄	1	2	yes	—
45	C₂×C₈	D₄	1	2	yes	—
46	C₂×C₈	D₄	1	2	yes	—
47	C₂×C₈	C₂³	1	2	yes	—
48	C₂×C₈	C₂³	1	2	yes	—
49	C₄²	—	2	1	no	—
50	C₄²	C₂³	1	2	yes	—
51	C₂³	—	2	2	no	—
52	C₂³	#41	1	1	yes	characteristic
53	Q₈	—	2	2	no	—
54	Q₈	C₂²×C₄	1	4	yes	—
55	D₄	—	2	4	no	—
56	D₄	—	2	4	no	—
57	D₄	—	2	2	no	—
58	D₄	C₂²×C₄	1	4	yes	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄	#41	1	1	yes	characteristic
69	C₂×C₄	C₂⁴	1	1	yes	characteristic
70	C₈	—	2	4	no	—
71	C₈	C₂²×C₄	1	2	yes	—
72	C₈	C₂²×C₄	1	2	yes	—
73	C₈	C₂×D₄	1	4	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	—	2	4	no	—
76	C₂²	—	4	4	no	—
77	C₂²	C₄×D₄	1	1	yes	characteristic
78	C₂²	C₄×D₄	1	1	yes	characteristic
79	C₂²	C₂×#41	1	1	yes	characteristic
80	C₄	—	2	4	no	—
81	C₄	—	4	2	no	—
82	C₄	C₄×D₄	1	1	yes	characteristic
83	C₄	C₄×D₄	1	1	yes	characteristic
84	C₄	C₂³×C₄	1	1	yes	characteristic
85	C₄	C₂²×D₄	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	4	4	no	—
89	C₂	#444	1	2	yes	direct product factor
90	C₂	C₂×C₄×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂²	C₄×D₄
prime radical	C₂×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#131	C₂	semidirect
3. #444	C₂	direct (N × H)
4. C₂×#108	C₂	semidirect
5. C₂×#104	C₂	semidirect
6. C₂×#97	C₂	semidirect
8. #135	C₄	semidirect
10. C₂×Q₁₆	C₄	semidirect
11. C₂×SD₁₆	C₄	semidirect
12. C₂×D₈	C₄	semidirect
14. #131	C₂²	semidirect
21. #108	C₂²	semidirect
22. #104	C₂²	semidirect
23. #97	C₂²	semidirect
34. Q₁₆	C₂×C₄	semidirect
35. SD₁₆	C₂×C₄	semidirect
36. D₈	C₂×C₄	semidirect
89. C₂	#444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#135	2
C₂×#131	2
#444	2
C₂×#108	2
C₂×#104	2
C₂×#97	2

Subgroups — C2×#444 #2954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#444 #2954