Subgroups — C₂×#4926 #82048

Order 384.

488 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×#830	C₂	1	2	yes	maximal
3	#4926	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₂×#803	C₂	1	2	yes	maximal, complemented
6	C₂×#432	—	3	1	no	maximal, Sylow
7	C₂³×C₃×C₄	C₄	1	1	yes	characteristic
8	C₂³×C₃×C₄	C₄	1	1	yes	characteristic
9	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄²	C₄	1	4	yes	—
12	C₂×C₃×C₄²	C₄	1	1	yes	characteristic
13	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²	C₂²	1	4	yes	—
16	C₂²×C₃⋊C₈	C₂²	1	4	yes	—
17	#830	C₂²	1	8	yes	—
18	C₄⋊(C₃⋊C₈)	C₂²	1	8	yes	complemented
19	#803	C₂²	1	8	yes	complemented
20	C₂²×C₄²	D₃	1	1	yes	characteristic
21	#432	—	3	8	no	—
22	C₂×C₄⋊C₈	—	3	2	no	—
23	C₂×C₂²⋊C₈	—	3	2	no	—
24	C₂×#97	—	3	2	no	—
25	C₂⁴×C₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄	—	2	4	no	—
27	C₂²×C₃×C₄	—	2	4	no	—
28	C₂²×C₃×C₄	—	2	4	no	—
29	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
32	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
36	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄	C₂³	1	2	yes	—
38	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
39	C₃×C₄²	C₂×C₄	1	4	yes	—
40	C₃×C₄²	C₂×C₄	1	4	yes	—
41	C₃×C₄²	C₂×C₄	1	2	yes	—
42	C₃×C₄²	C₂×C₄	1	2	yes	—
43	C₃×C₄²	C₂³	1	2	yes	—
44	C₃×C₄²	C₂³	1	2	yes	—
45	C₂×C₃⋊C₈	—	2	8	no	—
46	C₂×C₃⋊C₈	C₂³	1	8	yes	—
47	C₂³×C₄	Dic₃	1	1	yes	characteristic
48	C₂³×C₄	Dic₃	1	1	yes	characteristic
49	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
50	C₂²×C₈	—	3	4	no	—
51	C₂×C₄²	Dic₃	1	1	yes	characteristic
52	C₂×C₄²	Dic₃	1	4	yes	—
53	C₂×C₄²	Dic₃	1	1	yes	characteristic
54	C₂×C₄²	C₂×D₃	1	4	yes	—
55	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
57	C₄⋊C₈	—	3	8	no	—
58	C₂²⋊C₈	—	3	8	no	—
59	#97	—	3	8	no	—
60	C₂³×C₃	—	2	2	no	—
61	C₂³×C₃	—	2	2	no	—
62	C₂³×C₃	M₁₆	1	4	yes	—
63	C₂³×C₃	C₂²×C₄	1	2	yes	—
64	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄	—	2	2	no	—
66	C₂×C₃×C₄	—	2	8	no	—
67	C₂×C₃×C₄	—	2	2	no	—
68	C₂×C₃×C₄	—	2	2	no	—
69	C₂×C₃×C₄	—	2	2	no	—
70	C₂×C₃×C₄	—	2	4	no	—
71	C₂×C₃×C₄	—	2	8	no	—
72	C₂×C₃×C₄	—	2	4	no	—
73	C₂×C₃×C₄	M₁₆	1	4	yes	—
74	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
75	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
76	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
77	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
78	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
80	C₂×C₃×C₄	#41	1	4	yes	—
81	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
82	C₃⋊C₈	—	2	8	no	—
83	C₂⁴	C₂×Dic₃	1	1	yes	characteristic
84	C₂²×C₄	—	2	4	no	—
85	C₂²×C₄	—	2	4	no	—
86	C₂²×C₄	—	2	4	no	—
87	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
88	C₂²×C₄	C₂×Dic₃	1	2	yes	—
89	C₂²×C₄	C₂×Dic₃	1	4	yes	—
90	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
91	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
92	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
93	C₂²×C₄	C₂×Dic₃	1	4	yes	—
94	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₃	1	2	yes	—
96	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
97	C₂×C₈	—	3	8	no	—
98	C₂×C₈	—	6	8	no	—
99	C₄²	C₂×Dic₃	1	4	yes	—
100	C₄²	C₂×Dic₃	1	4	yes	—
101	C₄²	C₂×Dic₃	1	2	yes	—
102	C₄²	C₂×Dic₃	1	2	yes	—
103	C₄²	C₂²×D₃	1	2	yes	—
104	C₄²	C₂²×D₃	1	2	yes	—
105	C₂²×C₃	—	2	2	no	—
106	C₂²×C₃	—	2	2	no	—
107	C₂²×C₃	—	2	8	no	—
108	C₂²×C₃	#117	1	2	yes	—
109	C₂²×C₃	C₂×M₁₆	1	4	yes	—
110	C₂²×C₃	C₂×M₁₆	1	2	yes	—
111	C₂²×C₃	C₂×M₁₆	1	2	yes	—
112	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
113	C₃×C₄	—	2	2	no	—
114	C₃×C₄	—	2	2	no	—
115	C₃×C₄	—	2	2	no	—
116	C₃×C₄	—	2	2	no	—
117	C₃×C₄	#117	1	2	yes	—
118	C₃×C₄	C₂×M₁₆	1	4	yes	—
119	C₃×C₄	C₂×#41	1	2	yes	—
120	C₂³	—	2	2	no	—
121	C₂³	—	2	2	no	—
122	C₂³	#208	1	4	yes	—
123	C₂³	C₂²×Dic₃	1	2	yes	—
124	C₂³	C₂²×Dic₃	1	1	yes	characteristic
125	C₂×C₄	—	2	8	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	8	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	#208	1	4	yes	—
134	C₂×C₄	#235	1	4	yes	—
135	C₂×C₄	C₂²×Dic₃	1	2	yes	—
136	C₂×C₄	C₂²×Dic₃	1	2	yes	—
137	C₂×C₄	C₂²×Dic₃	1	2	yes	—
138	C₂×C₄	C₂²×Dic₃	1	2	yes	—
139	C₂×C₄	C₂²×Dic₃	1	2	yes	—
140	C₂×C₄	C₂²×Dic₃	1	1	yes	characteristic
141	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
142	C₈	—	6	8	no	—
143	C₂×C₃	—	2	4	no	—
144	C₂×C₃	#432	1	4	yes	complemented
145	C₂×C₃	C₂×#117	1	1	yes	characteristic
146	C₂×C₃	C₂²×M₁₆	1	1	yes	characteristic
147	C₂×C₃	C₂²×M₁₆	1	1	yes	characteristic
148	C₂²	—	2	8	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	2	2	no	—
151	C₂²	C₂×#208	1	4	yes	—
152	C₂²	C₂×#208	1	2	yes	—
153	C₂²	C₂×#208	1	2	yes	—
154	C₂²	#926	1	2	yes	—
155	C₂²	C₂³×Dic₃	1	1	yes	characteristic
156	C₄	—	2	2	no	—
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	2	2	no	—
160	C₄	C₂×#208	1	4	yes	—
161	C₄	#926	1	2	yes	—
162	C₄	C₂×#235	1	2	yes	—
163	C₃	C₂×#432	1	1	yes	characteristic, complemented, Sylow
164	C₂	—	2	4	no	—
165	C₂	#4926	1	4	yes	direct product factor
166	C₂	C₂²×#208	1	1	yes	characteristic
167	C₂	C₂²×#208	1	1	yes	characteristic
168	C₂	C₂×#926	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₂²×C₃×C₄²	C₂
socle	C₂³×C₃	C₂²×C₄
prime radical	C₂⁴×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	C₂²×C₄²	D₃
hypocenter	C₃	C₂×#432
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. #4926	C₂	direct (N × H)
4. C₂×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₂×#803	C₂	semidirect
18. C₄⋊(C₃⋊C₈)	C₂²	semidirect
19. #803	C₂²	semidirect
144. C₂×C₃	#432	semidirect
163. C₃	C₂×#432	semidirect
165. C₂	#4926	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×C₄²	2
C₂×#830	2
#4926	2
C₂×C₄⋊(C₃⋊C₈)	2
C₂×#803	2
C₂×#432	3

Subgroups — C2×#4926 #82048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4926 #82048