Subgroups — C₂×#26013575 #36374190

Order 22336.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150217	C₂	1	2	yes	maximal
2	#26013575	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic
4	#19150217	—	2	2	no	—
5	#19150217	C₂²	1	4	yes	—
6	C₂×#14584095	—	2	2	no	—
7	C₂²×C₄×C₃₄₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₄₉	C₄	1	2	yes	—
9	C₂×C₈×C₃₄₉	C₄	1	2	yes	—
10	C₂×C₈×C₃₄₉	C₂²	1	2	yes	—
11	#14584095	—	2	4	no	—
12	C₂³×C₃₄₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₄₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₄₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₄₉	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₃₄₉	C₂³	1	1	yes	characteristic
19	C₈×C₃₄₉	C₂×C₄	1	4	yes	—
20	C₂²×C₃₄₉	—	2	2	no	—
21	C₂²×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₃₄₉	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
26	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₃₄₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃₄₉	—	2	1	no	—
29	C₂×C₃₄₉	—	2	1	no	—
30	C₂×C₃₄₉	#108	1	2	yes	complemented
31	C₂×C₃₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₃₄₉	C₂×#108	1	1	yes	characteristic, complemented, Sylow
33	C₂×#108	—	349	1	no	maximal, Sylow
34	C₂×M₁₆	—	349	2	no	—
35	C₂²×C₈	D₃₄₉	1	1	yes	characteristic
36	#108	—	349	4	no	—
37	C₂²×C₄	C₂×D₃₄₉	1	1	yes	characteristic
38	M₁₆	—	349	4	no	—
39	M₁₆	—	698	2	no	—
40	C₂×C₈	—	698	2	no	—
41	C₂×C₈	Dic₃₄₉	1	2	yes	—
42	C₂×C₈	Dic₃₄₉	1	2	yes	—
43	C₂×C₈	C₂×D₃₄₉	1	2	yes	—
44	C₂³	Dic₆₉₈	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₃₄₉	1	1	yes	characteristic
46	C₂×C₄	C₂×Dic₃₄₉	1	1	yes	characteristic
47	C₂×C₄	D₁₃₉₆	1	1	yes	characteristic
48	C₂×C₄	D₁₃₉₆	1	1	yes	characteristic
49	C₂×C₄	Dic₆₉₈	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₄₉	1	1	yes	characteristic
51	C₈	—	698	4	no	—
52	C₈	C₂×Dic₃₄₉	1	4	yes	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₃₄₉	1	1	yes	characteristic
55	C₂²	C₄⋊Dic₃₄₉	1	1	yes	characteristic
56	C₂²	C₂×Dic₆₉₈	1	1	yes	characteristic
57	C₄	C₄⋊Dic₃₄₉	1	1	yes	characteristic
58	C₄	C₄⋊Dic₃₄₉	1	1	yes	characteristic
59	C₄	C₂²×Dic₃₄₉	1	1	yes	characteristic
60	C₄	C₂×D₁₃₉₆	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	#26013575	1	2	yes	direct product factor
64	C₂	C₂×C₄⋊Dic₃₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₃₉₆
commutator	C₄×C₃₄₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₄₉
Fitting	C₂²×C₈×C₃₄₉	C₂
socle	C₂²×C₃₄₉	C₄⋊C₄
prime radical	C₂³×C₃₄₉	Q₈
cosocle	C₂×C₄×C₃₄₉	C₂³
hypercenter	C₂²×C₈	D₃₄₉
hypocenter	C₃₄₉	C₂×#108
LCS	G ▷ C₄×C₃₄₉ ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #26013575	C₂	direct (N × H)
30. C₂×C₃₄₉	#108	semidirect
32. C₃₄₉	C₂×#108	semidirect
63. C₂	#26013575	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×#19150217	2
#26013575	2
C₂²×C₈×C₃₄₉	2
C₂×#108	349

Subgroups — C2×#26013575 #36374190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26013575 #36374190