Subgroups — C₄×#13133819 #20293097

Order 6848.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133819	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄₂₈	C₂	1	3	yes	maximal, complemented
4	#16812071	C₂	1	3	yes	maximal, complemented
5	#16812067	C₂	1	3	yes	maximal, complemented
6	C₄²×D₁₀₇	C₂	1	3	yes	maximal, complemented
7	C₄×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#13133819	C₄	1	8	yes	direct product factor
9	C₂×D₄₂₈	C₂²	1	3	yes	—
10	C₂×C₄×D₁₀₇	C₂²	1	3	yes	—
11	C₂×C₄×D₁₀₇	C₂²	1	3	yes	—
12	C₂×C₄×D₁₀₇	C₂²	1	3	yes	—
13	C₄⋊Dic₁₀₇	C₂²	1	3	yes	—
14	(C₂×D₁₀₇)⋊C₄	C₂²	1	6	yes	—
15	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
16	C₄×Dic₁₀₇	C₂²	1	3	yes	—
17	C₄×Dic₁₀₇	C₂²	1	3	yes	—
18	C₂×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₁₀₇	C₂²	1	3	yes	—
20	C₄²×C₁₀₇	C₂²	1	3	yes	—
21	C₂²×D₁₀₇	C₂³	1	3	yes	—
22	Q₈×C₁₀₇	C₂×C₄	1	4	yes	complemented
23	C₂×C₄×C₁₀₇	C₂³	1	3	yes	—
24	C₂×C₄×C₁₀₇	C₂³	1	3	yes	—
25	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₁₀₇	C₂³	1	3	yes	—
27	C₂×Dic₁₀₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₁₀₇	C₂³	1	1	yes	characteristic
29	D₄₂₈	C₂×C₄	1	12	yes	complemented
30	C₄×D₁₀₇	—	2	6	no	—
31	C₄×D₁₀₇	—	2	6	no	—
32	C₄×D₁₀₇	C₂×C₄	1	12	yes	complemented
33	C₂²×C₁₀₇	C₂⁴	1	1	yes	characteristic
34	C₂×D₁₀₇	—	2	3	no	—
35	C₂×D₁₀₇	—	2	3	no	—
36	C₂×D₁₀₇	C₂²×C₄	1	6	yes	—
37	C₄×C₁₀₇	—	2	3	no	—
38	C₄×C₁₀₇	C₂²×C₄	1	6	yes	—
39	C₄×C₁₀₇	#41	1	2	yes	complemented
40	Dic₁₀₇	—	2	3	no	—
41	Dic₁₀₇	C₂²×C₄	1	2	yes	—
42	Dic₁₀₇	#41	1	2	yes	complemented
43	C₂×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₁₀₇	C₂×#41	1	1	yes	characteristic
45	C₂×C₁₀₇	C₂×#41	1	1	yes	characteristic
46	D₁₀₇	—	2	6	no	—
47	C₁₀₇	C₄×#41	1	1	yes	characteristic, complemented, Sylow
48	C₄×#41	—	107	1	no	maximal, Sylow
49	C₂×#41	—	107	1	no	—
50	C₄×Q₈	—	107	1	no	—
51	C₄×Q₈	D₁₀₇	1	1	yes	characteristic, complemented
52	C₄×D₄	—	107	3	no	—
53	C₄×D₄	—	107	3	no	—
54	#117	—	107	3	no	—
55	C₂×C₄²	—	107	3	no	—
56	#41	—	107	8	no	—
57	C₂×Q₈	C₂×D₁₀₇	1	1	yes	characteristic
58	C₂×D₄	—	107	3	no	—
59	C₂²×C₄	—	107	3	no	—
60	C₂²×C₄	—	107	3	no	—
61	C₂²×C₄	—	107	3	no	—
62	C₄⋊C₄	—	107	3	no	—
63	C₄⋊C₄	C₂×D₁₀₇	1	3	yes	—
64	C₂²⋊C₄	—	107	6	no	—
65	C₄²	—	107	3	no	—
66	C₄²	—	107	3	no	—
67	C₄²	—	107	1	no	—
68	C₄²	C₂×D₁₀₇	1	3	yes	—
69	C₂³	—	107	3	no	—
70	Q₈	C₄×D₁₀₇	1	4	yes	complemented
71	D₄	—	107	12	no	—
72	C₂×C₄	—	107	1	no	—
73	C₂×C₄	—	107	1	no	—
74	C₂×C₄	—	107	12	no	—
75	C₂×C₄	—	107	3	no	—
76	C₂×C₄	—	214	6	no	—
77	C₂×C₄	—	214	6	no	—
78	C₂×C₄	C₂²×D₁₀₇	1	3	yes	—
79	C₂×C₄	C₂²×D₁₀₇	1	3	yes	—
80	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
81	C₂²	—	107	6	no	—
82	C₂²	—	214	3	no	—
83	C₂²	—	214	3	no	—
84	C₂²	C₂³×D₁₀₇	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	107	2	no	—
87	C₄	—	107	2	no	—
88	C₄	—	214	3	no	—
89	C₄	C₂×C₄×D₁₀₇	1	6	yes	—
90	C₄	#13133819	1	2	yes	direct product factor
91	C₂	—	214	6	no	—
92	C₂	C₂²×C₄×D₁₀₇	1	1	yes	characteristic
93	C₂	#41×D₁₀₇	1	1	yes	characteristic
94	C₂	C₂×#13133819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₀₇
commutator	C₂×C₁₀₇	C₂³×C₄
Frattini	C₂²	C₂³×D₁₀₇
Fitting	C₄×Q₈×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂⁴
hypercenter	C₄×Q₈	D₁₀₇
hypocenter	C₁₀₇	C₄×#41
LCS	G ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₁₀₇	C₂	semidirect
3. C₄×D₄₂₈	C₂	semidirect
4. #16812071	C₂	semidirect
5. #16812067	C₂	semidirect
6. C₄²×D₁₀₇	C₂	semidirect
7. C₄×Q₈×C₁₀₇	C₂	semidirect
8. #13133819	C₄	direct (N × H)
22. Q₈×C₁₀₇	C₂×C₄	semidirect
29. D₄₂₈	C₂×C₄	semidirect
32. C₄×D₁₀₇	C₂×C₄	semidirect
39. C₄×C₁₀₇	#41	semidirect
42. Dic₁₀₇	#41	semidirect
47. C₁₀₇	C₄×#41	semidirect
51. C₄×Q₈	D₁₀₇	semidirect
70. Q₈	C₄×D₁₀₇	semidirect
90. C₄	#13133819	direct (N × H)

Subgroups — C4×#13133819 #20293097

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13133819 #20293097