Subgroups — (C₂×#13063703)⋊C₈ #36375009

Order 22336.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₄₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#13063703	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₃₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13063703	C₄	1	2	yes	—
5	D₃₄₉⋊C₈	—	2	1	no	—
6	D₃₄₉⋊C₈	—	2	1	no	—
7	C₂×#14584102	C₄	1	2	yes	complemented
8	C₄×#13063703	—	2	1	no	—
9	C₄×#13063703	—	2	1	no	—
10	C₂×C₄×D₃₄₉	C₂²	1	1	yes	characteristic
11	C₂×#14584095	C₄	1	1	yes	characteristic, complemented
12	C₈×D₃₄₉	—	2	1	no	—
13	C₈×D₃₄₉	—	2	1	no	—
14	C₂×C₈×C₃₄₉	C₄	1	1	yes	characteristic, complemented
15	C₂×#13063703	—	2	2	no	—
16	C₂×#13063703	—	2	2	no	—
17	C₂×#13063703	C₈	1	4	yes	complemented
18	#14584102	—	2	2	no	—
19	C₂²×D₃₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₄₉	C₂×C₄	1	1	yes	characteristic
21	C₄×D₃₄₉	D₄	1	1	yes	characteristic
22	C₄×D₃₄₉	D₄	1	1	yes	characteristic
23	C₄×D₃₄₉	D₄	1	1	yes	characteristic
24	C₄×D₃₄₉	Q₈	1	1	yes	characteristic
25	#14584095	—	2	1	no	—
26	C₂×C₄×C₃₄₉	C₂×C₄	1	1	yes	characteristic
27	C₈×C₃₄₉	—	2	1	no	—
28	C₂²×C₃₄₉	C₄²	1	1	yes	characteristic
29	C₂×D₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₃₄₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₃₄₉	C₂×C₈	1	2	yes	—
32	C₂×D₃₄₉	M₁₆	1	2	yes	—
33	#13063703	—	2	4	no	—
34	C₄×C₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₃₄₉	C₄⋊C₄	1	1	yes	characteristic
36	Dic₃₄₉	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₃₄₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₃₄₉	#95	1	1	yes	characteristic
39	C₂×C₃₄₉	C₄×C₈	1	1	yes	characteristic
40	C₂×C₃₄₉	#97	1	1	yes	characteristic
41	D₃₄₉	C₂²⋊C₈	1	2	yes	—
42	D₃₄₉	C₄⋊C₈	1	2	yes	—
43	C₃₄₉	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	349	1	no	maximal, Sylow
45	C₂²×C₈	—	349	1	no	—
46	C₂²×C₈	—	349	1	no	—
47	C₂×C₄²	—	349	1	no	—
48	C₂²×C₄	—	349	1	no	—
49	C₂²×C₄	—	349	2	no	—
50	C₂×C₈	—	349	2	no	—
51	C₂×C₈	—	349	1	no	—
52	C₂×C₈	—	698	1	no	—
53	C₂×C₈	—	698	1	no	—
54	C₂×C₈	—	698	1	no	—
55	C₂×C₈	—	698	1	no	—
56	C₂×C₈	#13063703	1	1	yes	characteristic, complemented
57	C₄²	—	698	1	no	—
58	C₄²	—	698	1	no	—
59	C₂³	—	349	1	no	—
60	C₂×C₄	—	349	1	no	—
61	C₂×C₄	—	349	1	no	—
62	C₂×C₄	—	349	1	no	—
63	C₂×C₄	—	349	1	no	—
64	C₂×C₄	—	349	1	no	—
65	C₂×C₄	—	349	4	no	—
66	C₂×C₄	—	698	2	no	—
67	C₂×C₄	—	698	2	no	—
68	C₂×C₄	C₂×#13063703	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	698	2	no	—
71	C₈	—	698	1	no	—
72	C₂²	—	349	1	no	—
73	C₂²	—	349	1	no	—
74	C₂²	—	349	2	no	—
75	C₂²	—	349	2	no	—
76	C₂²	C₄×#13063703	1	1	yes	characteristic
77	C₄	—	349	1	no	—
78	C₄	—	349	1	no	—
79	C₄	—	698	4	no	—
80	C₄	C₂²⋊#13063703	1	1	yes	characteristic
81	C₄	C₄⋊#13063703	1	1	yes	characteristic
82	C₂	—	349	2	no	—
83	C₂	—	349	2	no	—
84	C₂	(C₂×#13063703)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#13063703	1	1	yes	characteristic
86	C₂	#26013693	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#13063703
commutator	C₂×C₃₄₉	C₄×C₈
Fitting	C₂×C₈×C₃₄₉	C₄
socle	C₂²×C₃₄₉	C₄²
prime radical	C₂²×D₃₄₉	C₂×C₄
cosocle	C₂×C₄×D₃₄₉	C₂²
hypercenter	C₂×C₈	#13063703
hypocenter	C₃₄₉	#336
LCS	G ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#14584102	C₄	semidirect
11. C₂×#14584095	C₄	semidirect
14. C₂×C₈×C₃₄₉	C₄	semidirect
17. C₂×#13063703	C₈	semidirect
43. C₃₄₉	#336	semidirect
56. C₂×C₈	#13063703	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₄₉⋊C₈	2
C₂×C₄×#13063703	2
C₂×C₈×D₃₄₉	2
#336	349

Subgroups — (C2×#13063703)⋊C8 #36375009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#13063703)⋊C₈ #36375009