Subgroups — #1842×D₇₃ #33086361

Order 18688.

1470 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₇₃	C₂	1	6	yes	maximal
2	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22610083	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610082	C₂	1	6	yes	maximal, complemented
5	C₇₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₇₃	C₂²	1	4	yes	—
7	C₂×C₄²×D₇₃	C₄	1	3	yes	—
8	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
9	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
10	C₂×C₄⋊#10596831	C₂²	1	6	yes	—
11	C₂×#14556520	C₂²	1	12	yes	—
12	C₄⋊C₈×D₇₃	—	2	24	no	—
13	C₄²×Dic₇₃	C₄	1	3	yes	—
14	C₄²×Dic₇₃	C₄	1	1	yes	characteristic
15	C₄²×Dic₇₃	C₂²	1	3	yes	—
16	C₂×C₄⋊C₈×C₇₃	C₂²	1	6	yes	—
17	C₄³×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₇₃	C₂×C₄	1	3	yes	—
19	C₂²×C₄×D₇₃	C₂×C₄	1	3	yes	—
20	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
21	C₂²×#10596831	C₂³	1	4	yes	—
22	C₂×C₈×D₇₃	—	2	24	no	—
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	C₂×C₄	1	3	yes	—
28	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
29	C₄²×D₇₃	—	2	12	no	—
30	C₄²×D₇₃	C₈	1	8	yes	complemented
31	C₄²×D₇₃	D₄	1	12	yes	—
32	C₄²×D₇₃	Q₈	1	12	yes	—
33	C₄⋊#10596831	—	2	12	no	—
34	#14556520	—	2	24	no	—
35	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
36	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
37	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
39	C₄⋊C₈×C₇₃	—	2	12	no	—
40	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
42	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
44	C₂×C₄×D₇₃	—	2	12	no	—
45	C₂×C₄×D₇₃	C₄⋊C₄	1	12	yes	—
46	C₂×C₄×D₇₃	C₄⋊C₄	1	12	yes	—
47	C₂×C₄×D₇₃	C₂×C₈	1	12	yes	—
48	C₂×C₄×D₇₃	M₁₆	1	12	yes	—
49	C₂×C₄×D₇₃	C₂×D₄	1	6	yes	—
50	C₂×C₄×D₇₃	C₂×Q₈	1	6	yes	—
51	C₂×#10596831	—	2	12	no	—
52	C₈×D₇₃	—	4	16	no	—
53	C₄×Dic₇₃	—	2	6	no	—
54	C₄×Dic₇₃	—	2	12	no	—
55	C₄×Dic₇₃	C₄⋊C₄	1	12	yes	—
56	C₄×Dic₇₃	C₄⋊C₄	1	12	yes	—
57	C₄×Dic₇₃	C₂×C₈	1	12	yes	complemented
58	C₄×Dic₇₃	C₂×D₄	1	6	yes	—
59	C₄×Dic₇₃	C₂×Q₈	1	6	yes	—
60	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
61	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
62	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
63	C₂×C₈×C₇₃	—	2	12	no	—
64	C₄²×C₇₃	—	2	6	no	—
65	C₄²×C₇₃	C₂×C₈	1	4	yes	complemented
66	C₄²×C₇₃	C₂×D₄	1	6	yes	—
67	C₄²×C₇₃	C₂×Q₈	1	6	yes	—
68	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
69	C₂²×D₇₃	C₂×C₄⋊C₄	1	6	yes	—
70	C₂²×D₇₃	C₂²×C₈	1	2	yes	—
71	C₂²×D₇₃	C₂×M₁₆	1	6	yes	—
72	C₂×C₄×C₇₃	—	2	6	no	—
73	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	6	yes	—
74	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	6	yes	—
75	C₂×C₄×C₇₃	C₂²×C₈	1	6	yes	—
76	C₂×C₄×C₇₃	C₂×M₁₆	1	6	yes	—
77	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
78	C₂×C₄×C₇₃	C₂²×Q₈	1	3	yes	—
79	C₂×Dic₇₃	—	2	6	no	—
80	C₂×Dic₇₃	C₂×C₄⋊C₄	1	6	yes	—
81	C₂×Dic₇₃	C₂×C₄⋊C₄	1	6	yes	—
82	C₂×Dic₇₃	C₂×C₄⋊C₄	1	6	yes	—
83	C₂×Dic₇₃	C₂²×C₈	1	6	yes	—
84	C₂×Dic₇₃	C₂×M₁₆	1	6	yes	—
85	C₄×D₇₃	—	2	24	no	—
86	C₄×D₇₃	C₄⋊C₈	1	48	yes	complemented
87	C₄×D₇₃	#127	1	4	yes	—
88	C₄×D₇₃	C₄⋊Q₈	1	12	yes	—
89	C₈×C₇₃	—	4	4	no	—
90	#10596831	—	4	4	no	—
91	C₂²×C₇₃	C₂²×C₄⋊C₄	1	3	yes	—
92	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
93	C₂²×C₇₃	C₂²×M₁₆	1	3	yes	—
94	C₂×D₇₃	#384	1	4	yes	—
95	C₂×D₇₃	C₂×C₄⋊C₈	1	12	yes	—
96	C₂×D₇₃	#423	1	12	yes	—
97	C₄×C₇₃	—	2	6	no	—
98	C₄×C₇₃	C₂×C₄⋊C₈	1	12	yes	complemented
99	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
100	C₄×C₇₃	C₂×C₄⋊Q₈	1	3	yes	—
101	Dic₇₃	—	2	6	no	—
102	Dic₇₃	#384	1	4	yes	—
103	Dic₇₃	C₂×C₄⋊C₈	1	12	yes	complemented
104	C₂×#1842	—	73	1	no	maximal, Sylow
105	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
106	C₂×C₇₃	C₂²×C₄⋊C₈	1	3	yes	—
107	C₂×C₇₃	C₂×#423	1	3	yes	—
108	D₇₃	#1842	1	8	yes	direct product factor
109	C₂²×C₄⋊C₈	—	73	6	no	—
110	C₂×C₄³	—	73	1	no	—
111	#1842	—	73	6	no	—
112	#1842	—	73	1	no	—
113	#1842	D₇₃	1	1	yes	characteristic, direct product factor
114	C₇₃	C₂×#1842	1	1	yes	characteristic, complemented, Sylow
115	C₂³×C₈	—	73	4	no	—
116	C₂²×C₄²	—	73	1	no	—
117	C₂²×C₄²	—	73	3	no	—
118	C₂²×C₄²	—	73	3	no	—
119	C₂×C₄⋊C₈	—	73	12	no	—
120	C₂×C₄⋊C₈	—	73	6	no	—
121	C₂×C₄⋊C₈	—	146	24	no	—
122	C₂×C₄⋊C₈	C₂×D₇₃	1	6	yes	—
123	C₄³	—	73	3	no	—
124	C₄³	—	73	1	no	—
125	C₄³	—	73	3	no	—
126	C₄³	C₂×D₇₃	1	1	yes	characteristic
127	C₂³×C₄	—	73	3	no	—
128	C₂³×C₄	—	73	1	no	—
129	C₂³×C₄	—	73	3	no	—
130	C₂²×C₈	—	73	4	no	—
131	C₂²×C₈	—	146	24	no	—
132	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
133	C₂×C₄²	—	73	3	no	—
134	C₂×C₄²	—	73	3	no	—
135	C₂×C₄²	—	73	3	no	—
136	C₂×C₄²	—	73	3	no	—
137	C₂×C₄²	—	73	8	no	—
138	C₂×C₄²	—	73	12	no	—
139	C₂×C₄²	—	73	12	no	—
140	C₂×C₄²	—	73	6	no	—
141	C₂×C₄²	—	73	3	no	—
142	C₂×C₄²	—	146	12	no	—
143	C₂×C₄²	C₄×D₇₃	1	3	yes	—
144	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
145	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
146	C₄⋊C₈	—	2	12	no	—
147	C₄⋊C₈	—	146	24	no	—
148	C₄⋊C₈	—	146	12	no	—
149	C₂⁴	—	73	1	no	—
150	C₂²×C₄	—	73	1	no	—
151	C₂²×C₄	—	73	3	no	—
152	C₂²×C₄	—	73	12	no	—
153	C₂²×C₄	—	73	12	no	—
154	C₂²×C₄	—	73	12	no	—
155	C₂²×C₄	—	73	6	no	—
156	C₂²×C₄	—	73	6	no	—
157	C₂²×C₄	—	73	3	no	—
158	C₂²×C₄	—	73	12	no	—
159	C₂²×C₄	—	146	12	no	—
160	C₂²×C₄	C₂×C₄×D₇₃	1	3	yes	—
161	C₂²×C₄	C₂×C₄×D₇₃	1	3	yes	—
162	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
163	C₂×C₈	—	2	12	no	—
164	C₂×C₈	—	292	16	no	—
165	C₂×C₈	—	146	12	no	—
166	C₄²	—	2	6	no	—
167	C₄²	—	73	12	no	—
168	C₄²	—	73	12	no	—
169	C₄²	—	73	12	no	—
170	C₄²	—	73	6	no	—
171	C₄²	—	73	6	no	—
172	C₄²	—	146	12	no	—
173	C₄²	—	146	6	no	—
174	C₄²	C₈×D₇₃	1	4	yes	complemented
175	C₄²	D₄×D₇₃	1	6	yes	—
176	C₄²	Q₈×D₇₃	1	6	yes	—
177	C₂³	—	73	6	no	—
178	C₂³	—	73	2	no	—
179	C₂³	—	73	6	no	—
180	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
181	C₂×C₄	—	2	6	no	—
182	C₂×C₄	—	73	6	no	—
183	C₂×C₄	—	73	6	no	—
184	C₂×C₄	—	73	6	no	—
185	C₂×C₄	—	73	6	no	—
186	C₂×C₄	—	73	4	no	—
187	C₂×C₄	—	73	12	no	—
188	C₂×C₄	—	73	48	no	—
189	C₂×C₄	—	73	6	no	—
190	C₂×C₄	—	146	24	no	—
191	C₂×C₄	—	146	6	no	—
192	C₂×C₄	C₄⋊C₄×D₇₃	1	6	yes	—
193	C₂×C₄	C₄⋊C₄×D₇₃	1	6	yes	—
194	C₂×C₄	C₂×C₈×D₇₃	1	6	yes	—
195	C₂×C₄	M₁₆×D₇₃	1	6	yes	—
196	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
197	C₂×C₄	C₂×Q₈×D₇₃	1	3	yes	—
198	C₈	—	4	4	no	—
199	C₈	—	292	4	no	—
200	C₂²	—	73	4	no	—
201	C₂²	—	73	12	no	—
202	C₂²	—	73	12	no	—
203	C₂²	C₂×C₄⋊C₄×D₇₃	1	3	yes	—
204	C₂²	C₂²×C₈×D₇₃	1	1	yes	characteristic
205	C₂²	C₂×M₁₆×D₇₃	1	3	yes	—
206	C₄	—	2	6	no	—
207	C₄	—	73	4	no	—
208	C₄	—	73	12	no	—
209	C₄	—	146	6	no	—
210	C₄	C₄⋊C₈×D₇₃	1	12	yes	complemented
211	C₄	#127×D₇₃	1	1	yes	characteristic
212	C₄	C₄⋊Q₈×D₇₃	1	3	yes	—
213	C₂	—	73	8	no	—
214	C₂	#384×D₇₃	1	1	yes	characteristic
215	C₂	C₂×C₄⋊C₈×D₇₃	1	3	yes	—
216	C₂	#423×D₇₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂³×C₈
Fitting	C₇₃×#1842	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1842	D₇₃
hypocenter	C₇₃	C₂×#1842
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
3. #22610083	C₂	semidirect
4. #22610082	C₂	semidirect
5. C₇₃×#1842	C₂	semidirect
30. C₄²×D₇₃	C₈	semidirect
57. C₄×Dic₇₃	C₂×C₈	semidirect
65. C₄²×C₇₃	C₂×C₈	semidirect
86. C₄×D₇₃	C₄⋊C₈	semidirect
98. C₄×C₇₃	C₂×C₄⋊C₈	semidirect
103. Dic₇₃	C₂×C₄⋊C₈	semidirect
108. D₇₃	#1842	direct (N × H)
113. #1842	D₇₃	direct (N × H)
114. C₇₃	C₂×#1842	semidirect
174. C₄²	C₈×D₇₃	semidirect
210. C₄	C₄⋊C₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₇₃	2
C₄³×D₇₃	2
#22610083	2
#22610082	2
C₇₃×#1842	2
C₂×#1842	73

Subgroups — #1842×D73 #33086361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1842×D₇₃ #33086361