Subgroups — C₄×#20269913 #41013300

Order 27008.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269913	C₂	1	2	yes	maximal
2	C₄×#16809946	C₂	1	2	yes	maximal
3	#27212911	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#16809946	C₂²	1	4	yes	—
6	#20269913	C₄	1	8	yes	direct product factor
7	#20269888	—	2	2	no	—
8	C₄×C₂₁₁⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₁₁	C₄	1	4	yes	—
13	#16809946	—	2	4	no	—
14	#16809946	C₂×C₄	1	8	yes	—
15	C₂×C₂₁₁⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₂₁₁	Q₈	1	2	yes	—
17	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₂₁₁	—	2	2	no	—
19	C₂×C₈×C₂₁₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₂₁₁	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₂₁₁	C₂×C₄	1	2	yes	—
22	C₄²×C₂₁₁	C₂×C₄	1	2	yes	—
23	C₄²×C₂₁₁	D₄	1	1	yes	characteristic
24	C₄²×C₂₁₁	D₄	1	1	yes	characteristic
25	C₂₁₁⋊C₈	—	2	8	no	—
26	C₂³×C₂₁₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₂₁₁	—	2	4	no	—
28	C₂×C₄×C₂₁₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₁₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₂₁₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₁₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₁₁	#41	1	2	yes	—
34	C₈×C₂₁₁	—	2	2	no	—
35	C₈×C₂₁₁	C₄²	1	4	yes	—
36	C₂²×C₂₁₁	—	2	2	no	—
37	C₂²×C₂₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₁₁	C₄×Q₈	1	2	yes	—
39	C₄×C₂₁₁	—	2	2	no	—
40	C₄×C₂₁₁	#108	1	4	yes	complemented
41	C₄×C₂₁₁	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₂₁₁	#117	1	1	yes	characteristic
43	C₄×C₂₁₁	C₄×D₄	1	2	yes	—
44	C₂×C₂₁₁	—	2	2	no	—
45	C₂×C₂₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₂₁₁	C₂×#108	1	2	yes	—
47	C₂₁₁	C₄×#108	1	1	yes	characteristic, complemented, Sylow
48	C₄×#108	—	211	1	no	maximal, Sylow
49	C₂×#108	—	211	2	no	—
50	C₄×M₁₆	—	211	2	no	—
51	C₂×C₄×C₈	D₂₁₁	1	1	yes	characteristic
52	#341	—	211	2	no	—
53	C₂×M₁₆	—	211	4	no	—
54	C₂²×C₈	C₂×D₂₁₁	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₂₁₁	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₂₁₁	1	1	yes	characteristic
57	#108	—	211	8	no	—
58	#97	—	422	2	no	—
59	C₄×C₈	—	422	2	no	—
60	C₄×C₈	Dic₂₁₁	1	4	yes	—
61	C₂²×C₄	Dic₄₂₂	1	2	yes	—
62	C₂²×C₄	C₂²×D₂₁₁	1	1	yes	characteristic
63	M₁₆	—	422	4	no	—
64	M₁₆	—	211	8	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	422	4	no	—
67	C₂×C₈	C₄×D₂₁₁	1	4	yes	—
68	C₂×C₈	C₂×Dic₂₁₁	1	2	yes	—
69	C₂×C₈	C₂×Dic₂₁₁	1	2	yes	—
70	C₄²	C₂×Dic₂₁₁	1	2	yes	—
71	C₄²	D₈₄₄	1	1	yes	characteristic
72	C₄²	D₈₄₄	1	1	yes	characteristic
73	C₂³	C₂×Dic₄₂₂	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₂₁₁	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₂₁₁	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₂₁₁	1	2	yes	—
78	C₂×C₄	C₂²×Dic₂₁₁	1	1	yes	characteristic
79	C₂×C₄	C₂×D₈₄₄	1	1	yes	characteristic
80	C₂×C₄	#16809962	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	422	8	no	—
83	C₈	C₄×Dic₂₁₁	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₂₁₁	1	1	yes	characteristic
86	C₂²	C₄×Dic₄₂₂	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#20269913	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₂₁₁	1	1	yes	characteristic
90	C₄	#20269936	1	1	yes	characteristic
91	C₄	C₄×D₈₄₄	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₂₁₁	1	1	yes	characteristic
94	C₂	C₂×#20269913	1	2	yes	—

	subgroup	G/H
center	C₄²	D₈₄₄
commutator	C₄×C₂₁₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₁₁
Fitting	C₂×C₄×C₈×C₂₁₁	C₂
socle	C₂²×C₂₁₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₁₁	C₂³
hypercenter	C₂×C₄×C₈	D₂₁₁
hypocenter	C₂₁₁	C₄×#108
LCS	G ▷ C₄×C₂₁₁ ▷ C₂×C₂₁₁ ▷ C₂₁₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #20269913	C₄	direct (N × H)
40. C₄×C₂₁₁	#108	semidirect
47. C₂₁₁	C₄×#108	semidirect
88. C₄	#20269913	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×#20269913	2
C₄×#16809946	2
#27212911	2
C₂×C₄×C₈×C₂₁₁	2
C₄×#108	211

Subgroups — C4×#20269913 #41013300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#20269913 #41013300