Subgroups — C₄×#20269772 #41003310

Order 26944.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269772	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₁₆₈₄	C₂	1	3	yes	maximal, complemented
4	#27212328	C₂	1	3	yes	maximal, complemented
5	#27212324	C₂	1	3	yes	maximal, complemented
6	C₄²×D₄₂₁	C₂	1	3	yes	maximal, complemented
7	C₄×Q₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#20269772	C₄	1	8	yes	direct product factor
9	C₂×D₁₆₈₄	C₂²	1	3	yes	—
10	C₂×C₄×D₄₂₁	C₂²	1	3	yes	—
11	C₂×C₄×D₄₂₁	C₂²	1	3	yes	—
12	C₂×C₄×D₄₂₁	C₂²	1	3	yes	—
13	C₄⋊Dic₄₂₁	C₂²	1	3	yes	—
14	#20269748	C₂²	1	6	yes	—
15	C₄×Dic₄₂₁	C₂²	1	1	yes	characteristic
16	C₄×Dic₄₂₁	C₂²	1	3	yes	—
17	C₄×Dic₄₂₁	C₂²	1	3	yes	—
18	C₂×Q₈×C₄₂₁	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₄₂₁	C₂²	1	3	yes	—
20	C₄²×C₄₂₁	C₂²	1	3	yes	—
21	C₂²×D₄₂₁	C₂³	1	3	yes	—
22	D₁₆₈₄	C₂×C₄	1	12	yes	complemented
23	C₂×Dic₄₂₁	C₂³	1	3	yes	—
24	C₂×Dic₄₂₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₂₁	C₂³	1	1	yes	characteristic
26	C₄×D₄₂₁	—	2	6	no	—
27	C₄×D₄₂₁	—	2	6	no	—
28	C₄×D₄₂₁	C₂×C₄	1	12	yes	complemented
29	Q₈×C₄₂₁	C₂×C₄	1	4	yes	complemented
30	C₂×C₄×C₄₂₁	C₂³	1	3	yes	—
31	C₂×C₄×C₄₂₁	C₂³	1	3	yes	—
32	C₂×C₄×C₄₂₁	C₂³	1	1	yes	characteristic
33	C₂²×C₄₂₁	C₂⁴	1	1	yes	characteristic
34	C₂×D₄₂₁	—	2	3	no	—
35	C₂×D₄₂₁	—	2	3	no	—
36	C₂×D₄₂₁	C₂²×C₄	1	6	yes	—
37	C₄×C₄₂₁	—	2	3	no	—
38	C₄×C₄₂₁	C₂²×C₄	1	6	yes	—
39	C₄×C₄₂₁	#41	1	2	yes	complemented
40	Dic₄₂₁	—	2	3	no	—
41	Dic₄₂₁	C₂²×C₄	1	2	yes	—
42	Dic₄₂₁	#41	1	2	yes	complemented
43	C₂×C₄₂₁	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₄₂₁	C₂×#41	1	1	yes	characteristic
45	C₂×C₄₂₁	C₂×#41	1	1	yes	characteristic
46	D₄₂₁	—	2	6	no	—
47	C₄₂₁	C₄×#41	1	1	yes	characteristic, complemented, Sylow
48	C₄×#41	—	421	1	no	maximal, Sylow
49	C₂×#41	—	421	1	no	—
50	C₄×Q₈	—	421	1	no	—
51	C₄×Q₈	D₄₂₁	1	1	yes	characteristic, complemented
52	C₄×D₄	—	421	3	no	—
53	C₄×D₄	—	421	3	no	—
54	#117	—	421	3	no	—
55	C₂×C₄²	—	421	3	no	—
56	#41	—	421	8	no	—
57	C₂×Q₈	C₂×D₄₂₁	1	1	yes	characteristic
58	C₂×D₄	—	421	3	no	—
59	C₂²×C₄	—	421	3	no	—
60	C₂²×C₄	—	421	3	no	—
61	C₂²×C₄	—	421	3	no	—
62	C₄⋊C₄	—	421	3	no	—
63	C₄⋊C₄	C₂×D₄₂₁	1	3	yes	—
64	C₂²⋊C₄	—	421	6	no	—
65	C₄²	—	421	3	no	—
66	C₄²	—	421	3	no	—
67	C₄²	—	421	1	no	—
68	C₄²	C₂×D₄₂₁	1	3	yes	—
69	C₂³	—	421	3	no	—
70	Q₈	C₄×D₄₂₁	1	4	yes	complemented
71	D₄	—	421	12	no	—
72	C₂×C₄	—	842	6	no	—
73	C₂×C₄	—	842	6	no	—
74	C₂×C₄	—	421	3	no	—
75	C₂×C₄	—	421	1	no	—
76	C₂×C₄	—	421	1	no	—
77	C₂×C₄	—	421	12	no	—
78	C₂×C₄	C₂²×D₄₂₁	1	3	yes	—
79	C₂×C₄	C₂²×D₄₂₁	1	3	yes	—
80	C₂×C₄	C₂²×D₄₂₁	1	1	yes	characteristic
81	C₂²	—	842	3	no	—
82	C₂²	—	842	3	no	—
83	C₂²	—	421	6	no	—
84	C₂²	C₂³×D₄₂₁	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	842	3	no	—
87	C₄	—	421	2	no	—
88	C₄	—	421	2	no	—
89	C₄	C₂×C₄×D₄₂₁	1	6	yes	—
90	C₄	#20269772	1	2	yes	direct product factor
91	C₂	—	842	6	no	—
92	C₂	C₂²×C₄×D₄₂₁	1	1	yes	characteristic
93	C₂	#41×D₄₂₁	1	1	yes	characteristic
94	C₂	C₂×#20269772	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₂₁
commutator	C₂×C₄₂₁	C₂³×C₄
Frattini	C₂²	C₂³×D₄₂₁
Fitting	C₄×Q₈×C₄₂₁	C₂
socle, cosocle	C₂²×C₄₂₁	C₂⁴
prime radical	C₂×#20269772	C₂
hypercenter	C₄×Q₈	D₄₂₁
hypocenter	C₄₂₁	C₄×#41
LCS	G ▷ C₂×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₄₂₁	C₂	semidirect
3. C₄×D₁₆₈₄	C₂	semidirect
4. #27212328	C₂	semidirect
5. #27212324	C₂	semidirect
6. C₄²×D₄₂₁	C₂	semidirect
7. C₄×Q₈×C₄₂₁	C₂	semidirect
8. #20269772	C₄	direct (N × H)
22. D₁₆₈₄	C₂×C₄	semidirect
28. C₄×D₄₂₁	C₂×C₄	semidirect
29. Q₈×C₄₂₁	C₂×C₄	semidirect
39. C₄×C₄₂₁	#41	semidirect
42. Dic₄₂₁	#41	semidirect
47. C₄₂₁	C₄×#41	semidirect
51. C₄×Q₈	D₄₂₁	semidirect
70. Q₈	C₄×D₄₂₁	semidirect
90. C₄	#20269772	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×#20269772	2
Q₈×Dic₄₂₁	2
C₄×D₁₆₈₄	2
#27212328	2
#27212324	2
C₄²×D₄₂₁	2
C₄×Q₈×C₄₂₁	2
C₄×#41	421

Subgroups — C4×#20269772 #41003310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#20269772 #41003310