Subgroups — C₂×#994 #5943

Order 192.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#994	C₂	1	4	yes	maximal, direct product factor
2	C₂×#41⋊C₃	C₂	1	3	yes	maximal, complemented
3	C₂×H(5,𝔽₂)	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×C₃×Q₈	—	4	1	no	maximal
5	#41⋊C₃	C₂²	1	6	yes	complemented
6	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
7	H(5,𝔽₂)	—	3	4	no	—
8	H(5,𝔽₂)	C₂×C₃	1	4	yes	complemented
9	C₂×#41	—	3	1	no	—
10	C₂×#41	C₂×C₃	1	3	yes	—
11	C₂²×D₄	—	3	3	no	—
12	C₃×Q₈	—	4	4	no	—
13	C₂×C₃×C₄	—	4	3	no	—
14	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic, complemented
15	C₂⁴	—	3	2	no	—
16	#41	—	3	4	no	—
17	#41	—	3	4	no	—
18	#41	—	3	6	no	—
19	#41	C₂²×C₃	1	6	yes	—
20	C₂×Q₈	A₄	1	1	yes	characteristic
21	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×D₄	—	3	3	no	—
23	C₂×D₄	—	3	12	no	—
24	C₂×D₄	—	3	12	no	—
25	C₂×D₄	—	3	3	no	—
26	C₂²×C₄	—	3	3	no	—
27	C₂²×C₃	—	4	1	no	—
28	C₃×C₄	—	4	6	no	—
29	C₂³	—	3	8	no	—
30	C₂³	—	3	3	no	—
31	C₂³	—	12	4	no	—
32	Q₈	—	3	1	no	—
33	Q₈	C₂×A₄	1	4	yes	—
34	Q₈	C₂³×C₃	1	1	yes	characteristic
35	D₄	—	3	6	no	—
36	D₄	—	3	6	no	—
37	D₄	—	3	12	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	6	no	—
40	C₂×C₄	—	3	6	no	—
41	C₂×C₄	C₂×A₄	1	3	yes	—
42	C₂×C₃	—	4	2	no	—
43	C₂×C₃	—	4	1	no	—
44	C₂²	—	3	6	no	—
45	C₂²	—	6	6	no	—
46	C₂²	—	12	8	no	—
47	C₂²	C₂²×A₄	1	1	yes	characteristic
48	C₄	—	3	1	no	—
49	C₄	—	3	1	no	—
50	C₄	C₂²×A₄	1	6	yes	—
51	C₃	—	4	1	no	Sylow
52	C₂	—	6	6	no	—
53	C₂	#994	1	2	yes	direct product factor
54	C₂	C₂³×A₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×A₄
commutator, cosocle, hypocenter	Q₈	C₂³×C₃
Frattini	C₂	C₂³×A₄
Fitting	C₂×H(5,𝔽₂)	C₃
hypercenter	C₂×Q₈	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

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