Subgroups — C₄×C₃⋊#95 #71533

Order 384.

752 conjugacy classes of subgroups.

The subgroup lattice has 148 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	C₂²×C₄×Dic₃	C₂	1	2	yes	maximal
3	C₂×C₃⋊#95	C₂	1	4	yes	maximal
4	C₄×#95	—	3	1	no	maximal, Sylow
5	C₂³×C₃×C₄	C₂²	1	2	yes	—
6	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂³×Dic₃	C₂²	1	4	yes	—
8	C₂×C₃×C₄²	—	2	4	no	—
9	C₂×C₃×C₄²	C₄	1	4	yes	complemented
10	C₂×C₄×Dic₃	—	2	4	no	—
11	C₂×C₄×Dic₃	—	2	4	no	—
12	C₂×C₄×Dic₃	C₄	1	8	yes	complemented
13	C₃⋊#95	C₄	1	16	yes	direct product factor
14	C₂²×C₄²	—	3	2	no	—
15	C₂²×C₄²	D₃	1	1	yes	characteristic
16	C₂×#95	—	3	4	no	—
17	C₂⁴×C₃	C₂³	1	1	yes	characteristic
18	C₂²×C₃×C₄	—	2	4	no	—
19	C₂²×C₃×C₄	—	2	4	no	—
20	C₂²×C₃×C₄	C₂×C₄	1	8	yes	—
21	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
22	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
23	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
24	C₂²×C₃×C₄	D₄	1	2	yes	—
25	C₂²×C₃×C₄	D₄	1	4	yes	—
26	C₂²×C₃×C₄	Q₈	1	2	yes	—
27	C₂²×Dic₃	—	2	4	no	—
28	C₂²×Dic₃	—	2	4	no	—
29	C₂²×Dic₃	—	2	8	no	—
30	C₂²×Dic₃	C₂×C₄	1	16	yes	—
31	C₂²×Dic₃	C₂×C₄	1	8	yes	—
32	C₃×C₄²	—	2	8	no	—
33	C₄×Dic₃	—	2	16	no	—
34	C₂³×C₄	—	3	4	no	—
35	C₂³×C₄	C₂×D₃	1	2	yes	—
36	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
37	C₂×C₄²	—	2	4	no	—
38	C₂×C₄²	—	3	8	no	—
39	C₂×C₄²	—	6	4	no	—
40	C₂×C₄²	—	6	4	no	—
41	C₂×C₄²	Dic₃	1	4	yes	complemented
42	#95	—	3	16	no	—
43	C₂³×C₃	C₂²×C₄	1	2	yes	—
44	C₂³×C₃	C₂²×C₄	1	4	yes	—
45	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
46	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
47	C₂³×C₃	C₂×D₄	1	2	yes	—
48	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
49	C₂³×C₃	#41	1	4	yes	—
50	C₂×C₃×C₄	—	2	4	no	—
51	C₂×C₃×C₄	—	2	4	no	—
52	C₂×C₃×C₄	—	2	16	no	—
53	C₂×C₃×C₄	C₄²	1	4	yes	—
54	C₂×C₃×C₄	C₄²	1	8	yes	complemented
55	C₂×C₃×C₄	C₂²⋊C₄	1	8	yes	—
56	C₂×C₃×C₄	C₂²⋊C₄	1	4	yes	—
57	C₂×C₃×C₄	C₄⋊C₄	1	8	yes	—
58	C₂×C₃×C₄	C₄⋊C₄	1	4	yes	—
59	C₂×Dic₃	—	2	8	no	—
60	C₂×Dic₃	—	2	8	no	—
61	C₂×Dic₃	—	2	16	no	—
62	C₂×Dic₃	—	2	16	no	—
63	C₂×Dic₃	C₄²	1	16	yes	complemented
64	C₂⁴	C₂²×D₃	1	1	yes	characteristic
65	C₂²×C₄	—	2	4	no	—
66	C₂²×C₄	—	2	4	no	—
67	C₂²×C₄	—	3	16	no	—
68	C₂²×C₄	—	3	8	no	—
69	C₂²×C₄	—	6	4	no	—
70	C₂²×C₄	—	6	8	no	—
71	C₂²×C₄	—	6	4	no	—
72	C₂²×C₄	Dic₆	1	2	yes	—
73	C₂²×C₄	C₄×D₃	1	8	yes	—
74	C₂²×C₄	C₄×D₃	1	4	yes	—
75	C₂²×C₄	D₁₂	1	2	yes	—
76	C₂²×C₄	C₂×Dic₃	1	4	yes	—
77	C₂²×C₄	C₂×Dic₃	1	2	yes	—
78	C₂²×C₄	#67	1	4	yes	—
79	C₄²	—	2	8	no	—
80	C₄²	—	6	16	no	—
81	C₂²×C₃	C₂×C₄²	1	4	yes	—
82	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
83	C₂²×C₃	C₂×C₄²	1	2	yes	—
84	C₂²×C₃	C₂×C₂²⋊C₄	1	2	yes	—
85	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₃	C₂×C₄⋊C₄	1	2	yes	—
87	C₂²×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₃	#117	1	4	yes	—
89	C₂²×C₃	#117	1	2	yes	—
90	C₂²×C₃	C₄×D₄	1	4	yes	—
91	C₂²×C₃	C₄×D₄	1	8	yes	—
92	C₂²×C₃	C₄×Q₈	1	4	yes	—
93	C₃×C₄	—	2	8	no	—
94	C₃×C₄	#95	1	8	yes	complemented
95	Dic₃	—	2	16	no	—
96	C₂³	C₂×Dic₆	1	1	yes	characteristic
97	C₂³	C₂×C₄×D₃	1	4	yes	—
98	C₂³	C₂×C₄×D₃	1	2	yes	—
99	C₂³	C₂×D₁₂	1	1	yes	characteristic
100	C₂³	#235	1	4	yes	—
101	C₂³	C₂²×Dic₃	1	1	yes	characteristic
102	C₂³	C₂×#67	1	2	yes	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	16	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	3	16	no	—
107	C₂×C₄	—	6	8	no	—
108	C₂×C₄	—	6	16	no	—
109	C₂×C₄	—	6	8	no	—
110	C₂×C₄	—	6	16	no	—
111	C₂×C₄	C₄×Dic₃	1	4	yes	—
112	C₂×C₄	C₄×Dic₃	1	8	yes	complemented
113	C₂×C₄	Dic₃⋊C₄	1	8	yes	—
114	C₂×C₄	C₄⋊Dic₃	1	4	yes	—
115	C₂×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
116	C₂×C₄	#217	1	4	yes	—
117	C₂×C₃	C₄³	1	1	yes	characteristic
118	C₂×C₃	C₂×#95	1	1	yes	characteristic
119	C₂×C₃	#376	1	1	yes	characteristic
120	C₂×C₃	C₄×C₂²⋊C₄	1	4	yes	—
121	C₂×C₃	C₄×C₂²⋊C₄	1	2	yes	—
122	C₂×C₃	C₄×C₄⋊C₄	1	4	yes	—
123	C₂×C₃	C₄×C₄⋊C₄	1	2	yes	—
124	C₂²	C₄×Dic₆	1	4	yes	—
125	C₂²	C₄²×D₃	1	4	yes	—
126	C₂²	#872	1	4	yes	—
127	C₂²	C₄×D₁₂	1	4	yes	—
128	C₂²	C₂×C₄×Dic₃	1	1	yes	characteristic
129	C₂²	C₂×C₄×Dic₃	1	2	yes	—
130	C₂²	C₂×Dic₃⋊C₄	1	2	yes	—
131	C₂²	C₂×C₄⋊Dic₃	1	1	yes	characteristic
132	C₂²	#926	1	2	yes	—
133	C₂²	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
134	C₂²	C₄×#67	1	8	yes	—
135	C₂²	C₂×#217	1	1	yes	characteristic
136	C₄	—	2	8	no	—
137	C₄	—	6	16	no	—
138	C₄	C₃⋊#95	1	8	yes	direct product factor
139	C₃	C₄×#95	1	1	yes	characteristic, complemented, Sylow
140	C₂	C₄²×Dic₃	1	1	yes	characteristic
141	C₂	C₄×Dic₃⋊C₄	1	4	yes	—
142	C₂	#4932	1	1	yes	characteristic
143	C₂	C₄×C₄⋊Dic₃	1	2	yes	—
144	C₂	C₄×(C₂×D₃)⋊C₄	1	4	yes	—
145	C₂	C₂×C₃⋊#95	1	1	yes	characteristic
146	C₂	C₄×#217	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₃
commutator	C₂×C₃	C₄³
Frattini	C₂⁴	C₂²×D₃
Fitting	C₂²×C₃×C₄²	C₂
socle, prime radical, cosocle	C₂⁴×C₃	C₂³
hypercenter	C₂²×C₄²	D₃
hypocenter	C₃	C₄×#95
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
9. C₂×C₃×C₄²	C₄	semidirect
12. C₂×C₄×Dic₃	C₄	semidirect
13. C₃⋊#95	C₄	direct (N × H)
41. C₂×C₄²	Dic₃	semidirect
54. C₂×C₃×C₄	C₄²	semidirect
63. C₂×Dic₃	C₄²	semidirect
94. C₃×C₄	#95	semidirect
112. C₂×C₄	C₄×Dic₃	semidirect
138. C₄	C₃⋊#95	direct (N × H)
139. C₃	C₄×#95	semidirect

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
C₂²×C₄×Dic₃	2
C₂×C₃⋊#95	2
C₄×#95	3

Subgroups — C4×C3⋊#95 #71533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊#95 #71533