Subgroups — C₂×#10593259 #11800471

Order 1152.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3708	C₂	1	1	yes	maximal, characteristic
2	#10593259	C₂	1	4	yes	maximal, direct product factor
3	C₂×#63725	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
5	C₂×#3708	C₄	1	2	yes	—
6	C₂×#3708	C₄	1	1	yes	characteristic
7	C₂×#3708	C₂²	1	1	yes	characteristic
8	C₂×#3708	C₂²	1	2	yes	—
9	#63725	C₂²	1	4	yes	complemented
10	C₂²×C₃²×C₄	C₈	1	1	yes	characteristic
11	C₂×C₃⋊(C₃⋊C₈)	C₈	1	2	yes	—
12	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
13	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
15	#3708	C₂×C₄	1	1	yes	characteristic
16	#3708	C₂×C₄	1	2	yes	—
17	#3708	C₂³	1	1	yes	characteristic
18	C₂×M₆₄	—	9	1	no	maximal, Sylow
19	C₂²×C₃⋊C₈	—	12	1	no	—
20	C₂³×C₃²	C₁₆	1	1	yes	characteristic
21	C₂×C₃²×C₄	C₁₆	1	2	yes	—
22	C₂×C₃²×C₄	C₁₆	1	1	yes	characteristic
23	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
24	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
25	C₃⋊(C₃⋊C₈)	C₂×C₈	1	1	yes	characteristic
26	C₃⋊(C₃⋊C₈)	C₂×C₈	1	2	yes	—
27	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₁₆	—	9	1	no	—
29	M₆₄	—	9	4	no	—
30	C₂×C₃₂	—	9	2	no	—
31	C₂²×C₃×C₄	—	4	1	no	—
32	C₂×C₃⋊C₈	—	12	2	no	—
33	C₂×C₃⋊C₈	—	12	1	no	—
34	C₂×C₃⋊C₈	—	12	2	no	—
35	C₂×C₃⋊C₈	—	12	1	no	—
36	C₂²×C₃²	—	2	2	no	—
37	C₂²×C₃²	C₂×C₁₆	1	2	yes	—
38	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
39	C₃²×C₄	C₂×C₁₆	1	2	yes	—
40	C₃²×C₄	C₂×C₁₆	1	1	yes	characteristic
41	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₈	—	9	1	no	—
43	C₂×C₁₆	—	9	2	no	—
44	C₂×C₁₆	—	9	1	no	—
45	C₂×C₁₆	—	9	1	no	—
46	C₂×C₁₆	—	9	2	no	—
47	C₃₂	—	9	4	no	—
48	C₂³×C₃	—	4	1	no	—
49	C₂×C₃×C₄	—	4	2	no	—
50	C₂×C₃×C₄	—	4	1	no	—
51	C₂×C₃×C₄	—	4	1	no	—
52	C₂×C₃×C₄	—	4	2	no	—
53	C₃⋊C₈	—	12	2	no	—
54	C₃⋊C₈	—	12	1	no	—
55	C₃⋊C₈	—	12	1	no	—
56	C₂×C₃²	—	2	2	no	—
57	C₂×C₃²	M₆₄	1	2	yes	complemented
58	C₂×C₃²	C₂²×C₁₆	1	1	yes	characteristic
59	C₂²×C₄	AGL(1,𝔽₉)	1	1	yes	characteristic
60	C₂×C₈	—	9	2	no	—
61	C₂×C₈	—	9	2	no	—
62	C₂×C₈	—	9	1	no	—
63	C₂×C₈	—	9	1	no	—
64	C₁₆	—	9	1	no	—
65	C₁₆	—	9	1	no	—
66	C₁₆	—	9	2	no	—
67	C₂²×C₃	—	4	4	no	—
68	C₂²×C₃	—	4	2	no	—
69	C₂²×C₃	—	4	1	no	—
70	C₃×C₄	—	4	1	no	—
71	C₃×C₄	—	4	2	no	—
72	C₃×C₄	—	4	1	no	—
73	C₃²	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
74	C₂³	#3771	1	1	yes	characteristic
75	C₂×C₄	#3771	1	1	yes	characteristic
76	C₂×C₄	#3771	1	2	yes	—
77	C₂×C₄	C₂×AGL(1,𝔽₉)	1	2	yes	—
78	C₂×C₄	C₂×AGL(1,𝔽₉)	1	1	yes	characteristic
79	C₈	—	9	1	no	—
80	C₈	—	9	2	no	—
81	C₈	—	9	1	no	—
82	C₂×C₃	—	4	4	no	—
83	C₂×C₃	—	4	1	no	—
84	C₂×C₃	—	4	2	no	—
85	C₂²	—	2	2	no	—
86	C₂²	C₂×#3771	1	2	yes	—
87	C₂²	C₂×#3771	1	1	yes	characteristic
88	C₄	C₂×#3771	1	2	yes	—
89	C₄	C₂×#3771	1	1	yes	characteristic
90	C₄	C₂²×AGL(1,𝔽₉)	1	1	yes	characteristic
91	C₃	—	4	1	no	—
92	C₂	—	2	2	no	—
93	C₂	#10593259	1	2	yes	direct product factor
94	C₂	C₂²×#3771	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×AGL(1,𝔽₉)
commutator	C₂×C₃²	C₂²×C₁₆
Frattini	C₄	C₂²×AGL(1,𝔽₉)
Fitting	C₂²×C₃²×C₄	C₈
socle	C₂²×C₃²	C₂×C₁₆
prime radical	C₂³×C₃²	C₁₆
cosocle	#3708	C₂³
hypercenter	C₂²×C₄	AGL(1,𝔽₉)
hypocenter	C₃²	C₂×M₆₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #10593259	C₂	direct (N × H)
3. C₂×#63725	C₂	semidirect
9. #63725	C₂²	semidirect
57. C₂×C₃²	M₆₄	semidirect
73. C₃²	C₂×M₆₄	semidirect
93. C₂	#10593259	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3708	2
#10593259	2
C₂×#63725	2
C₂×M₆₄	9

Subgroups — C2×#10593259 #11800471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10593259 #11800471