Subgroups — C₂×#5819 #87253

Order 384.

1460 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	#5819	C₂	1	16	yes	maximal, direct product factor
3	C₂×#948	C₂	1	8	yes	maximal, complemented
4	C₂²×#208	C₂	1	6	yes	maximal, complemented
5	C₂×#568	—	3	1	no	maximal, Sylow
6	C₂×C₃×#41	C₄	1	4	yes	—
7	C₂×C₃×#41	C₄	1	8	yes	—
8	C₂×C₃×#41	C₂²	1	4	yes	—
9	C₂×C₃×#41	C₂²	1	8	yes	—
10	C₂²×C₃×Q₈	C₄	1	1	yes	characteristic
11	C₂²×C₃×D₄	C₄	1	3	yes	—
12	C₂³×C₃×C₄	C₂²	1	3	yes	—
13	#948	C₂²	1	64	yes	complemented
14	C₂×#208	C₂²	1	4	yes	—
15	C₂×#208	C₂²	1	12	yes	complemented
16	C₂×#208	C₂²	1	48	yes	complemented
17	C₂²×C₃⋊C₈	C₂²	1	12	yes	complemented
18	C₂²×#41	D₃	1	1	yes	characteristic
19	#568	—	3	16	no	—
20	C₂×#131	—	3	8	no	—
21	C₂²×M₁₆	—	3	6	no	—
22	C₂⁴×C₃	C₂×C₄	1	3	yes	—
23	C₃×#41	C₂×C₄	1	16	yes	—
24	C₃×#41	C₂×C₄	1	32	yes	—
25	C₃×#41	C₂³	1	16	yes	—
26	C₂×C₃×Q₈	C₂×C₄	1	4	yes	—
27	C₂×C₃×Q₈	C₂×C₄	1	8	yes	—
28	C₂×C₃×D₄	C₂×C₄	1	12	yes	—
29	C₂×C₃×D₄	C₂×C₄	1	24	yes	—
30	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
31	C₂²×C₃×C₄	C₂×C₄	1	6	yes	—
32	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
33	C₂²×C₃×C₄	C₂³	1	6	yes	—
34	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₂²×C₃×C₄	C₂³	1	12	yes	—
36	#208	C₂³	1	16	yes	—
37	#208	C₂³	1	48	yes	complemented
38	C₂×C₃⋊C₈	C₂³	1	8	yes	—
39	C₂×C₃⋊C₈	C₂³	1	48	yes	complemented
40	C₂×#41	Dic₃	1	4	yes	—
41	C₂×#41	Dic₃	1	8	yes	—
42	C₂×#41	C₂×D₃	1	4	yes	—
43	C₂×#41	C₂×D₃	1	8	yes	—
44	C₂²×Q₈	Dic₃	1	1	yes	characteristic
45	C₂²×D₄	Dic₃	1	3	yes	—
46	C₂³×C₄	C₂×D₃	1	3	yes	—
47	#131	—	3	64	no	—
48	C₂×M₁₆	—	3	4	no	—
49	C₂×M₁₆	—	3	12	no	—
50	C₂×M₁₆	—	3	48	no	—
51	C₂²×C₈	—	3	12	no	—
52	C₂³×C₃	—	4	6	no	—
53	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
54	C₂³×C₃	C₂²×C₄	1	6	yes	—
55	C₂³×C₃	C₂²×C₄	1	12	yes	—
56	C₃×Q₈	C₂²×C₄	1	16	yes	—
57	C₃×D₄	C₂²×C₄	1	48	yes	—
58	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
59	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
61	C₂×C₃×C₄	C₂²×C₄	1	6	yes	—
62	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
63	C₂×C₃×C₄	C₂²×C₄	1	24	yes	—
64	C₂×C₃×C₄	C₂⁴	1	12	yes	—
65	C₂×C₃×C₄	C₂⁴	1	2	yes	—
66	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
67	C₃⋊C₈	C₂⁴	1	16	yes	—
68	C₂⁴	C₂×Dic₃	1	3	yes	—
69	#41	C₂×Dic₃	1	16	yes	—
70	#41	C₂×Dic₃	1	32	yes	—
71	#41	C₂²×D₃	1	16	yes	—
72	C₂×Q₈	C₂×Dic₃	1	4	yes	—
73	C₂×Q₈	C₂×Dic₃	1	8	yes	—
74	C₂×D₄	C₂×Dic₃	1	12	yes	—
75	C₂×D₄	C₂×Dic₃	1	24	yes	—
76	C₂²×C₄	C₂×Dic₃	1	3	yes	—
77	C₂²×C₄	C₂×Dic₃	1	6	yes	—
78	C₂²×C₄	C₂×Dic₃	1	12	yes	—
79	C₂²×C₄	C₂²×D₃	1	12	yes	—
80	C₂²×C₄	C₂²×D₃	1	6	yes	—
81	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
82	M₁₆	—	3	16	no	—
83	M₁₆	—	3	48	no	—
84	C₂×C₈	—	3	48	no	—
85	C₂×C₈	—	3	8	no	—
86	C₂²×C₃	—	2	2	no	—
87	C₂²×C₃	—	2	12	no	—
88	C₂²×C₃	—	4	12	no	—
89	C₂²×C₃	C₂³×C₄	1	2	yes	—
90	C₂²×C₃	C₂³×C₄	1	12	yes	—
91	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
92	C₃×C₄	C₂³×C₄	1	2	yes	—
93	C₃×C₄	C₂³×C₄	1	1	yes	characteristic
94	C₃×C₄	C₂³×C₄	1	12	yes	—
95	C₃×C₄	C₂⁵	1	1	yes	characteristic
96	C₂³	—	4	6	no	—
97	C₂³	C₂²×Dic₃	1	1	yes	characteristic
98	C₂³	C₂²×Dic₃	1	6	yes	—
99	C₂³	C₂²×Dic₃	1	12	yes	—
100	Q₈	C₂²×Dic₃	1	16	yes	—
101	D₄	C₂²×Dic₃	1	48	yes	—
102	C₂×C₄	C₂²×Dic₃	1	1	yes	characteristic
103	C₂×C₄	C₂²×Dic₃	1	2	yes	—
104	C₂×C₄	C₂²×Dic₃	1	12	yes	—
105	C₂×C₄	C₂²×Dic₃	1	6	yes	—
106	C₂×C₄	C₂²×Dic₃	1	24	yes	—
107	C₂×C₄	C₂²×Dic₃	1	12	yes	—
108	C₂×C₄	C₂³×D₃	1	12	yes	—
109	C₂×C₄	C₂³×D₃	1	2	yes	—
110	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
111	C₈	—	3	16	no	—
112	C₂×C₃	—	2	2	no	—
113	C₂×C₃	—	2	12	no	—
114	C₂×C₃	#568	1	2	yes	complemented
115	C₂×C₃	C₂⁴×C₄	1	1	yes	characteristic
116	C₂²	—	2	2	no	—
117	C₂²	—	2	12	no	—
118	C₂²	—	4	12	no	—
119	C₂²	C₂³×Dic₃	1	2	yes	—
120	C₂²	C₂³×Dic₃	1	12	yes	—
121	C₂²	C₂³×Dic₃	1	1	yes	characteristic
122	C₄	C₂³×Dic₃	1	2	yes	—
123	C₄	C₂³×Dic₃	1	1	yes	characteristic
124	C₄	C₂³×Dic₃	1	12	yes	—
125	C₄	C₂⁴×D₃	1	1	yes	characteristic
126	C₃	C₂×#568	1	1	yes	characteristic, complemented, Sylow
127	C₂	—	2	2	no	—
128	C₂	—	2	12	no	—
129	C₂	#5819	1	2	yes	direct product factor
130	C₂	C₂⁴×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator	C₂×C₃	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₃
Fitting, prime radical	C₂²×C₃×#41	C₂
socle	C₂²×C₃	C₂³×C₄
cosocle	C₃×C₄	C₂⁵
hypercenter	C₂²×#41	D₃
hypocenter	C₃	C₂×#568
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
2. #5819	C₂	direct (N × H)
3. C₂×#948	C₂	semidirect
4. C₂²×#208	C₂	semidirect
13. #948	C₂²	semidirect
15. C₂×#208	C₂²	semidirect
16. C₂×#208	C₂²	semidirect
17. C₂²×C₃⋊C₈	C₂²	semidirect
37. #208	C₂³	semidirect
39. C₂×C₃⋊C₈	C₂³	semidirect
114. C₂×C₃	#568	semidirect
126. C₃	C₂×#568	semidirect
129. C₂	#5819	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#41	2
#5819	2
C₂×#948	2
C₂²×#208	2
C₂×#568	3

Subgroups — C2×#5819 #87253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#5819 #87253