Subgroups — C₄²×#11924038 #34019793

Order 18688.

1734 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11924038	C₂	1	6	yes	maximal
2	C₄×#14556646	C₂	1	6	yes	maximal, complemented
3	C₄²×#10596833	C₂	1	2	yes	maximal, complemented
4	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924038	C₂²	1	4	yes	—
6	C₄×#11924038	C₄	1	48	yes	direct product factor
7	C₂×#14556646	C₂²	1	12	yes	—
8	C₂×C₄×#10596833	C₂²	1	12	yes	—
9	C₂×C₄²×D₇₃	C₄	1	3	yes	—
10	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
11	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
12	C₄²×Dic₇₃	C₄	1	3	yes	—
13	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₄²×Dic₇₃	C₂²	1	3	yes	—
15	C₄³×C₇₃	C₄	1	1	yes	characteristic
16	C₂×#11924038	C₂×C₄	1	48	yes	—
17	C₂²×#10596833	C₂³	1	8	yes	—
18	#14556646	C₂×C₄	1	48	yes	complemented
19	C₄×#10596833	C₂×C₄	1	48	yes	complemented
20	C₂²×C₄×D₇₃	C₂×C₄	1	3	yes	—
21	C₂²×C₄×D₇₃	C₂×C₄	1	3	yes	—
22	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
23	C₂×C₄×Dic₇₃	C₂×C₄	1	6	yes	—
24	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
25	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
26	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
27	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
28	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
29	C₄²×D₇₃	—	2	12	no	—
30	C₄²×D₇₃	—	2	4	no	—
31	C₄²×D₇₃	C₂×C₄	1	24	yes	—
32	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
33	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
34	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
35	#11924038	C₄²	1	64	yes	direct product factor
36	C₂×#10596833	C₂²×C₄	1	48	yes	—
37	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
39	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
40	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×D₇₃	—	2	6	no	—
42	C₂×C₄×D₇₃	—	2	6	no	—
43	C₂×C₄×D₇₃	—	2	12	no	—
44	C₂×C₄×D₇₃	C₄²	1	12	yes	—
45	C₂×C₄×D₇₃	C₄²	1	12	yes	—
46	C₂×C₄×D₇₃	C₂²×C₄	1	12	yes	—
47	C₄×Dic₇₃	—	2	6	no	—
48	C₄×Dic₇₃	—	2	12	no	—
49	C₄×Dic₇₃	C₄²	1	12	yes	—
50	C₄×Dic₇₃	M₁₆	1	12	yes	complemented
51	C₄×Dic₇₃	C₂²×C₄	1	12	yes	—
52	C₄×Dic₇₃	C₂²×C₄	1	12	yes	—
53	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
54	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
56	C₄²×C₇₃	—	2	6	no	—
57	C₄²×C₇₃	C₄²	1	12	yes	—
58	C₄²×C₇₃	M₁₆	1	4	yes	complemented
59	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
60	C₂²×D₇₃	—	2	3	no	—
61	C₂²×D₇₃	—	2	1	no	—
62	C₂²×D₇₃	C₂×C₄²	1	6	yes	—
63	C₂×C₄×C₇₃	—	2	6	no	—
64	C₂×C₄×C₇₃	C₂×C₄²	1	6	yes	—
65	C₂×C₄×C₇₃	C₂×C₄²	1	6	yes	—
66	C₂×C₄×C₇₃	C₂×C₄²	1	6	yes	—
67	C₂×C₄×C₇₃	C₂×M₁₆	1	6	yes	—
68	C₂×C₄×C₇₃	C₂×M₁₆	1	6	yes	—
69	C₂×Dic₇₃	—	2	3	no	—
70	C₂×Dic₇₃	—	2	3	no	—
71	C₂×Dic₇₃	C₂×C₄²	1	6	yes	—
72	C₂×Dic₇₃	C₂×C₄²	1	6	yes	—
73	C₂×Dic₇₃	C₂×M₁₆	1	12	yes	—
74	C₂×Dic₇₃	C₂³×C₄	1	6	yes	—
75	C₄×D₇₃	—	2	24	no	—
76	C₄×D₇₃	—	2	24	no	—
77	C₄×D₇₃	C₂×C₄²	1	16	yes	—
78	#10596833	C₂×C₄²	1	32	yes	complemented
79	C₂²×C₇₃	C₂²×C₄²	1	3	yes	—
80	C₂²×C₇₃	C₂²×M₁₆	1	3	yes	—
81	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
82	C₂×D₇₃	—	2	6	no	—
83	C₂×D₇₃	—	2	6	no	—
84	C₂×D₇₃	C₄³	1	4	yes	—
85	C₄×C₇₃	—	2	6	no	—
86	C₄×C₇₃	C₄³	1	4	yes	—
87	C₄×C₇₃	C₄×M₁₆	1	12	yes	complemented
88	Dic₇₃	—	2	6	no	—
89	Dic₇₃	C₄×M₁₆	1	12	yes	complemented
90	Dic₇₃	C₂²×C₄²	1	4	yes	—
91	C₄²×M₁₆	—	73	1	no	maximal, Sylow
92	C₂×C₇₃	C₂×C₄³	1	1	yes	characteristic
93	C₂×C₇₃	C₂×C₄×M₁₆	1	3	yes	—
94	C₂×C₇₃	C₂×C₄×M₁₆	1	3	yes	—
95	D₇₃	—	2	4	no	—
96	C₂×C₄×M₁₆	—	73	6	no	—
97	C₂×C₄³	—	73	1	no	—
98	C₄×#97	—	73	6	no	—
99	C₄²×C₈	—	73	2	no	—
100	C₇₃	C₄²×M₁₆	1	1	yes	characteristic, complemented, Sylow
101	C₂²×M₁₆	—	73	4	no	—
102	C₂²×C₄²	—	73	3	no	—
103	C₂²×C₄²	—	73	3	no	—
104	C₂²×C₄²	—	73	1	no	—
105	C₄×M₁₆	—	73	48	no	—
106	C₂×#97	—	73	12	no	—
107	C₂×C₄×C₈	—	73	12	no	—
108	C₄³	—	73	3	no	—
109	C₄³	—	73	3	no	—
110	C₄³	—	73	1	no	—
111	C₄³	#64408	1	1	yes	characteristic
112	C₂³×C₄	—	73	1	no	—
113	C₂³×C₄	—	73	3	no	—
114	C₂³×C₄	—	73	3	no	—
115	C₂×M₁₆	—	73	48	no	—
116	C₂²×C₈	—	73	8	no	—
117	C₂×C₄²	—	73	3	no	—
118	C₂×C₄²	—	73	3	no	—
119	C₂×C₄²	—	73	3	no	—
120	C₂×C₄²	—	73	3	no	—
121	C₂×C₄²	—	73	24	no	—
122	C₂×C₄²	—	73	6	no	—
123	C₂×C₄²	—	73	3	no	—
124	C₂×C₄²	—	146	12	no	—
125	C₂×C₄²	—	146	4	no	—
126	C₂×C₄²	C₂×#64408	1	3	yes	—
127	C₂×C₄²	C₂×#64408	1	3	yes	—
128	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
129	#97	—	73	48	no	—
130	C₄×C₈	—	73	48	no	—
131	C₂⁴	—	73	1	no	—
132	C₂²×C₄	—	73	3	no	—
133	C₂²×C₄	—	73	1	no	—
134	C₂²×C₄	—	73	12	no	—
135	C₂²×C₄	—	73	3	no	—
136	C₂²×C₄	—	73	12	no	—
137	C₂²×C₄	—	73	12	no	—
138	C₂²×C₄	—	146	12	no	—
139	C₂²×C₄	—	146	6	no	—
140	C₂²×C₄	—	146	6	no	—
141	C₂²×C₄	C₂²×#64408	1	3	yes	—
142	C₂²×C₄	C₂²×#64408	1	3	yes	—
143	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
144	M₁₆	—	73	64	no	—
145	C₂×C₈	—	73	48	no	—
146	C₄²	—	2	6	no	—
147	C₄²	—	73	12	no	—
148	C₄²	—	73	12	no	—
149	C₄²	—	73	12	no	—
150	C₄²	—	73	12	no	—
151	C₄²	—	146	12	no	—
152	C₄²	—	146	6	no	—
153	C₄²	C₄×#64408	1	12	yes	—
154	C₄²	#11924038	1	4	yes	direct product factor
155	C₂³	—	73	6	no	—
156	C₂³	—	146	3	no	—
157	C₂³	—	146	1	no	—
158	C₂³	C₂³×#64408	1	1	yes	characteristic
159	C₂×C₄	—	2	6	no	—
160	C₂×C₄	—	73	6	no	—
161	C₂×C₄	—	73	6	no	—
162	C₂×C₄	—	73	12	no	—
163	C₂×C₄	—	73	16	no	—
164	C₂×C₄	—	73	6	no	—
165	C₂×C₄	—	146	24	no	—
166	C₂×C₄	—	146	3	no	—
167	C₂×C₄	—	146	3	no	—
168	C₂×C₄	—	146	24	no	—
169	C₂×C₄	C₂×C₄×#64408	1	6	yes	—
170	C₂×C₄	C₂×C₄×#64408	1	6	yes	—
171	C₂×C₄	C₂×C₄×#64408	1	6	yes	—
172	C₂×C₄	D₇₃⋊M₁₆	1	6	yes	—
173	C₂×C₄	C₂×#11924038	1	6	yes	—
174	C₈	—	73	32	no	—
175	C₂²	—	73	4	no	—
176	C₂²	—	146	6	no	—
177	C₂²	—	146	6	no	—
178	C₂²	C₂²×C₄×#64408	1	3	yes	—
179	C₂²	C₂×D₇₃⋊M₁₆	1	3	yes	—
180	C₂²	C₂²×#11924038	1	1	yes	characteristic
181	C₄	—	2	6	no	—
182	C₄	—	73	4	no	—
183	C₄	—	73	12	no	—
184	C₄	—	146	6	no	—
185	C₄	C₄²×#64408	1	4	yes	—
186	C₄	C₄×#11924038	1	12	yes	direct product factor
187	C₂	—	146	4	no	—
188	C₂	C₂×C₄²×#64408	1	1	yes	characteristic
189	C₂	C₄×D₇₃⋊M₁₆	1	3	yes	—
190	C₂	C₂×C₄×#11924038	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×#64408
commutator	C₂×C₇₃	C₂×C₄³
Frattini	C₂³	C₂³×#64408
Fitting	C₄³×C₇₃	C₄
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×Dic₇₃	C₂⁴
hypercenter	C₄³	#64408
hypocenter	C₇₃	C₄²×M₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄×#14556646	C₂	semidirect
3. C₄²×#10596833	C₂	semidirect
6. C₄×#11924038	C₄	direct (N × H)
18. #14556646	C₂×C₄	semidirect
19. C₄×#10596833	C₂×C₄	semidirect
35. #11924038	C₄²	direct (N × H)
50. C₄×Dic₇₃	M₁₆	semidirect
58. C₄²×C₇₃	M₁₆	semidirect
78. #10596833	C₂×C₄²	semidirect
87. C₄×C₇₃	C₄×M₁₆	semidirect
89. Dic₇₃	C₄×M₁₆	semidirect
100. C₇₃	C₄²×M₁₆	semidirect
154. C₄²	#11924038	direct (N × H)
186. C₄	C₄×#11924038	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×C₄×#11924038	2
C₄×#14556646	2
C₄²×#10596833	2
C₄³×D₇₃	2
C₄²×M₁₆	73

Subgroups — C42×#11924038 #34019793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#11924038 #34019793