Subgroups — C₂×C₄×M₁₆×D₇₃ #33949368

Order 18688.

3950 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆×D₇₃	C₂	1	2	yes	maximal
2	C₂²×C₄²×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17988539	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×Dic₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#11924011	C₂	1	2	yes	maximal, complemented
7	C₄×M₁₆×D₇₃	C₂	1	16	yes	maximal, direct product factor
8	C₂×#97×D₇₃	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₇₃	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₄×D₇₃	C₄	1	2	yes	—
12	C₂³×C₄×D₇₃	C₂²	1	1	yes	characteristic
13	C₂²×#11924012	C₂²	1	2	yes	—
14	C₂²×#11924011	C₂²	1	4	yes	—
15	C₂×M₁₆×D₇₃	C₄	1	32	yes	direct product factor
16	C₂×M₁₆×D₇₃	C₂²	1	16	yes	—
17	C₂²×C₈×D₇₃	C₂²	1	4	yes	—
18	C₂²×C₄×Dic₇₃	C₄	1	2	yes	—
19	C₂²×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₇₃	C₄	1	8	yes	—
21	C₂×C₄²×D₇₃	C₄	1	2	yes	—
22	C₂×C₄²×D₇₃	C₄	1	2	yes	—
23	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄²×D₇₃	C₂²	1	8	yes	—
26	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
28	C₄×#11924012	C₂²	1	8	yes	complemented
29	#17988539	C₂²	1	16	yes	complemented
30	M₁₆×Dic₇₃	C₂²	1	16	yes	complemented
31	C₄×#11924011	C₂²	1	16	yes	complemented
32	C₂×#14556502	C₂²	1	2	yes	complemented
33	C₂×#14556501	C₂²	1	4	yes	complemented
34	#97×D₇₃	C₂²	1	16	yes	complemented
35	C₂×C₄×#10596831	C₂²	1	2	yes	complemented
36	C₂×C₈×Dic₇₃	C₂²	1	4	yes	complemented
37	C₄×C₈×D₇₃	C₂²	1	16	yes	complemented
38	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
39	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₇₃	C₂²	1	8	yes	complemented
41	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
42	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
43	C₂⁴×D₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×Dic₇₃	C₂×C₄	1	2	yes	—
45	C₂³×Dic₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₃	—	2	16	no	—
47	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
48	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
49	C₂²×C₄×D₇₃	C₂×C₄	1	16	yes	—
50	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
51	C₂²×C₄×D₇₃	C₂×C₄	1	4	yes	—
52	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄×D₇₃	C₂×C₄	1	16	yes	—
55	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
56	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
57	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
58	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
59	C₂×#11924012	C₂×C₄	1	16	yes	complemented
60	C₂×#11924012	C₂³	1	8	yes	—
61	C₂×#11924011	C₂×C₄	1	32	yes	complemented
62	C₂×#11924011	C₂³	1	16	yes	—
63	M₁₆×D₇₃	C₂×C₄	1	128	yes	direct product factor
64	C₂²×#10596831	C₂³	1	4	yes	—
65	C₂×C₈×D₇₃	C₂×C₄	1	32	yes	complemented
66	C₂×C₈×D₇₃	C₂³	1	16	yes	—
67	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
68	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₇₃	C₂×C₄	1	16	yes	—
71	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
77	C₄²×D₇₃	C₂×C₄	1	4	yes	—
78	C₄²×D₇₃	C₂×C₄	1	16	yes	—
79	C₄²×D₇₃	C₂×C₄	1	4	yes	—
80	C₄²×D₇₃	C₂×C₄	1	4	yes	—
81	C₄²×D₇₃	C₂×C₄	1	16	yes	—
82	C₄²×D₇₃	C₂×C₄	1	4	yes	—
83	C₄²×D₇₃	C₂³	1	4	yes	—
84	C₄²×D₇₃	C₂³	1	4	yes	—
85	C₄²×D₇₃	C₂³	1	4	yes	—
86	C₄²×D₇₃	C₂³	1	4	yes	—
87	#14556502	C₂³	1	8	yes	complemented
88	#14556501	C₂³	1	16	yes	complemented
89	C₄×#10596831	C₂³	1	8	yes	complemented
90	C₈×Dic₇₃	C₂³	1	16	yes	complemented
91	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
92	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₇₃	C₂×C₄	1	16	yes	complemented
94	C₂×M₁₆×C₇₃	C₂³	1	8	yes	—
95	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
96	C₂×C₄²×C₇₃	C₂×C₄	1	4	yes	—
97	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
101	#97×C₇₃	C₂³	1	8	yes	complemented
102	C₄×C₈×C₇₃	C₂³	1	8	yes	complemented
103	C₂³×D₇₃	—	2	8	no	—
104	C₂³×D₇₃	C₄²	1	8	yes	—
105	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂³×D₇₃	C₂²×C₄	1	4	yes	—
107	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₇₃	—	2	8	no	—
109	C₂²×Dic₇₃	C₄²	1	8	yes	—
110	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
111	C₂²×Dic₇₃	C₂²×C₄	1	8	yes	—
112	C₂²×Dic₇₃	C₂²×C₄	1	4	yes	—
113	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₇₃	—	2	8	no	—
117	C₂×C₄×D₇₃	—	2	8	no	—
118	C₂×C₄×D₇₃	—	2	8	no	—
119	C₂×C₄×D₇₃	—	2	64	no	—
120	C₂×C₄×D₇₃	C₄²	1	8	yes	—
121	C₂×C₄×D₇₃	C₄²	1	32	yes	—
122	C₂×C₄×D₇₃	C₄²	1	8	yes	—
123	C₂×C₄×D₇₃	M₁₆	1	16	yes	direct product factor
124	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
125	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
126	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
127	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
128	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
129	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
131	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
132	C₂×C₄×D₇₃	C₂²×C₄	1	32	yes	—
133	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
134	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
135	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
136	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
137	#11924012	C₂²×C₄	1	32	yes	complemented
138	#11924011	C₂²×C₄	1	64	yes	complemented
139	C₂×#10596831	C₂²×C₄	1	16	yes	complemented
140	C₂×#10596831	C₂⁴	1	8	yes	—
141	C₈×D₇₃	C₂²×C₄	1	64	yes	complemented
142	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
143	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
144	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
145	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
146	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
147	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
148	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
149	C₄×Dic₇₃	C₂⁴	1	2	yes	—
150	C₄×Dic₇₃	C₂⁴	1	2	yes	—
151	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	—	2	8	no	—
153	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₇₃	C₂²×C₄	1	8	yes	—
155	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
161	M₁₆×C₇₃	C₂²×C₄	1	32	yes	complemented
162	C₂×C₈×C₇₃	C₂²×C₄	1	16	yes	complemented
163	C₂×C₈×C₇₃	C₂⁴	1	8	yes	—
164	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
165	C₄²×C₇₃	C₂²×C₄	1	8	yes	—
166	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
167	C₄²×C₇₃	C₂⁴	1	2	yes	—
168	C₄²×C₇₃	C₂⁴	1	2	yes	—
169	C₂³×C₇₃	—	2	4	no	—
170	C₂³×C₇₃	C₂×C₄²	1	4	yes	—
171	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
172	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
173	C₂²×D₇₃	—	2	4	no	—
174	C₂²×D₇₃	—	2	16	no	—
175	C₂²×D₇₃	—	2	32	no	—
176	C₂²×D₇₃	C₂×C₄²	1	4	yes	—
177	C₂²×D₇₃	C₂×C₄²	1	16	yes	—
178	C₂²×D₇₃	C₂×C₄²	1	4	yes	—
179	C₂²×D₇₃	C₂×M₁₆	1	8	yes	—
180	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
181	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₇₃	—	2	4	no	—
183	C₂×C₄×C₇₃	—	2	16	no	—
184	C₂×C₄×C₇₃	C₂×C₄²	1	8	yes	—
185	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
186	C₂×C₄×C₇₃	C₂×M₁₆	1	8	yes	complemented
187	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
190	C₂×C₄×C₇₃	C₂³×C₄	1	8	yes	—
191	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
194	C₂×Dic₇₃	—	2	4	no	—
195	C₂×Dic₇₃	—	2	16	no	—
196	C₂×Dic₇₃	C₂×C₄²	1	16	yes	—
197	C₂×Dic₇₃	C₂×C₄²	1	4	yes	—
198	C₂×Dic₇₃	C₂×C₄²	1	4	yes	—
199	C₂×Dic₇₃	C₂×M₁₆	1	8	yes	complemented
200	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
201	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
202	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
203	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
204	C₄×D₇₃	—	2	16	no	—
205	C₄×D₇₃	—	2	16	no	—
206	C₄×D₇₃	—	2	16	no	—
207	C₄×D₇₃	C₂×C₄²	1	16	yes	—
208	C₄×D₇₃	C₂×C₄²	1	8	yes	—
209	C₄×D₇₃	C₂×C₄²	1	8	yes	—
210	C₄×D₇₃	C₂×C₄²	1	16	yes	—
211	C₄×D₇₃	C₂×M₁₆	1	32	yes	direct product factor
212	C₄×D₇₃	C₂³×C₄	1	8	yes	—
213	C₄×D₇₃	C₂³×C₄	1	8	yes	—
214	C₈×C₇₃	C₂³×C₄	1	16	yes	complemented
215	#10596831	C₂³×C₄	1	16	yes	complemented
216	C₂²×C₇₃	—	2	8	no	—
217	C₂²×C₇₃	—	2	4	no	—
218	C₂²×C₇₃	C₂²×C₄²	1	4	yes	—
219	C₂²×C₇₃	C₂²×C₄²	1	2	yes	—
220	C₂²×C₇₃	C₂²×M₁₆	1	4	yes	—
221	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
222	C₂×D₇₃	—	2	8	no	—
223	C₂×D₇₃	—	2	4	no	—
224	C₂×D₇₃	—	2	32	no	—
225	C₂×D₇₃	C₄×M₁₆	1	16	yes	direct product factor
226	C₂×D₇₃	C₂²×C₄²	1	4	yes	—
227	C₂×D₇₃	C₂²×C₄²	1	4	yes	—
228	C₂×D₇₃	C₂²×M₁₆	1	8	yes	—
229	C₄×C₇₃	—	2	4	no	—
230	C₄×C₇₃	C₂²×C₄²	1	2	yes	—
231	C₄×C₇₃	C₂²×C₄²	1	4	yes	—
232	C₄×C₇₃	C₂²×M₁₆	1	8	yes	complemented
233	C₄×C₇₃	C₂⁴×C₄	1	2	yes	—
234	Dic₇₃	—	2	4	no	—
235	Dic₇₃	C₂²×C₄²	1	4	yes	—
236	Dic₇₃	C₂²×C₄²	1	4	yes	—
237	Dic₇₃	C₂²×M₁₆	1	8	yes	complemented
238	C₂²×C₄×M₁₆	—	73	1	no	maximal, Sylow
239	C₂×C₇₃	—	2	4	no	—
240	C₂×C₇₃	C₂×C₄×M₁₆	1	4	yes	complemented
241	C₂×C₇₃	C₂³×C₄²	1	1	yes	characteristic
242	C₂×C₇₃	C₂³×M₁₆	1	2	yes	—
243	D₇₃	—	2	4	no	—
244	D₇₃	C₂×C₄×M₁₆	1	8	yes	direct product factor
245	C₂³×M₁₆	—	73	2	no	—
246	C₂³×C₄²	—	73	1	no	—
247	C₂×C₄×M₁₆	—	73	1	no	—
248	C₂×C₄×M₁₆	—	73	16	no	—
249	C₂×C₄×M₁₆	—	73	2	no	—
250	C₂×C₄×M₁₆	—	73	2	no	—
251	C₂×C₄×M₁₆	—	73	2	no	—
252	C₂×C₄×M₁₆	D₇₃	1	1	yes	characteristic, direct product factor
253	C₂²×#97	—	73	2	no	—
254	C₂²×C₄×C₈	—	73	2	no	—
255	C₇₃	C₂²×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
256	C₂⁴×C₄	—	73	1	no	—
257	C₂⁴×C₄	—	73	2	no	—
258	C₂²×M₁₆	—	73	2	no	—
259	C₂²×M₁₆	—	73	32	no	—
260	C₂²×M₁₆	—	73	16	no	—
261	C₂²×M₁₆	—	73	4	no	—
262	C₂²×M₁₆	C₂×D₇₃	1	2	yes	—
263	C₂³×C₈	—	73	4	no	—
264	C₂²×C₄²	—	73	2	no	—
265	C₂²×C₄²	—	73	1	no	—
266	C₂²×C₄²	—	73	2	no	—
267	C₂²×C₄²	—	73	2	no	—
268	C₂²×C₄²	—	73	8	no	—
269	C₂²×C₄²	—	73	1	no	—
270	C₂²×C₄²	—	73	1	no	—
271	C₂²×C₄²	—	73	8	no	—
272	C₂²×C₄²	—	73	1	no	—
273	C₂²×C₄²	—	73	1	no	—
274	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
275	C₄×M₁₆	—	73	16	no	—
276	C₄×M₁₆	—	73	8	no	—
277	C₄×M₁₆	—	73	16	no	—
278	C₄×M₁₆	—	73	16	no	—
279	C₄×M₁₆	C₂×D₇₃	1	8	yes	direct product factor
280	C₂×#97	—	73	4	no	—
281	C₂×#97	—	73	2	no	—
282	C₂×#97	—	73	16	no	—
283	C₂×#97	C₂×D₇₃	1	2	yes	complemented
284	C₂×C₄×C₈	—	73	4	no	—
285	C₂×C₄×C₈	—	73	2	no	—
286	C₂×C₄×C₈	—	73	16	no	—
287	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	complemented
288	C₂⁵	—	73	1	no	—
289	C₂³×C₄	—	73	1	no	—
290	C₂³×C₄	—	73	16	no	—
291	C₂³×C₄	—	73	1	no	—
292	C₂³×C₄	—	73	4	no	—
293	C₂³×C₄	—	73	1	no	—
294	C₂³×C₄	—	73	2	no	—
295	C₂³×C₄	—	73	1	no	—
296	C₂³×C₄	—	73	4	no	—
297	C₂³×C₄	—	73	1	no	—
298	C₂³×C₄	—	73	2	no	—
299	C₂³×C₄	—	73	2	no	—
300	C₂³×C₄	—	73	16	no	—
301	C₂³×C₄	—	73	2	no	—
302	C₂³×C₄	—	73	2	no	—
303	C₂³×C₄	—	146	16	no	—
304	C₂³×C₄	C₄×D₇₃	1	2	yes	—
305	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
306	C₂×M₁₆	—	73	16	no	—
307	C₂×M₁₆	—	73	8	no	—
308	C₂×M₁₆	—	73	128	no	—
309	C₂×M₁₆	—	73	32	no	—
310	C₂×M₁₆	—	73	16	no	—
311	C₂×M₁₆	C₄×D₇₃	1	16	yes	direct product factor
312	C₂×M₁₆	C₂²×D₇₃	1	8	yes	—
313	C₂²×C₈	—	73	4	no	—
314	C₂²×C₈	—	73	32	no	—
315	C₂²×C₈	—	73	16	no	—
316	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
317	C₂×C₄²	—	73	2	no	—
318	C₂×C₄²	—	73	2	no	—
319	C₂×C₄²	—	73	2	no	—
320	C₂×C₄²	—	73	16	no	—
321	C₂×C₄²	—	73	2	no	—
322	C₂×C₄²	—	73	2	no	—
323	C₂×C₄²	—	73	4	no	—
324	C₂×C₄²	—	73	1	no	—
325	C₂×C₄²	—	73	1	no	—
326	C₂×C₄²	—	73	4	no	—
327	C₂×C₄²	—	73	16	no	—
328	C₂×C₄²	—	73	4	no	—
329	C₂×C₄²	—	73	4	no	—
330	C₂×C₄²	—	73	16	no	—
331	C₂×C₄²	—	73	4	no	—
332	C₂×C₄²	—	73	4	no	—
333	C₂×C₄²	—	73	4	no	—
334	C₂×C₄²	—	73	4	no	—
335	C₂×C₄²	—	73	4	no	—
336	C₂×C₄²	—	73	4	no	—
337	C₂×C₄²	C₄×D₇₃	1	2	yes	—
338	C₂×C₄²	C₄×D₇₃	1	4	yes	—
339	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
341	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
342	#97	—	73	16	no	—
343	#97	—	73	8	no	—
344	#97	C₂²×D₇₃	1	8	yes	complemented
345	C₄×C₈	—	73	16	no	—
346	C₄×C₈	—	73	8	no	—
347	C₄×C₈	C₂²×D₇₃	1	8	yes	complemented
348	C₂⁴	—	73	1	no	—
349	C₂⁴	—	73	8	no	—
350	C₂⁴	—	73	4	no	—
351	C₂⁴	—	73	1	no	—
352	C₂⁴	—	146	8	no	—
353	C₂⁴	C₂×C₄×D₇₃	1	1	yes	characteristic
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	73	8	no	—
356	C₂²×C₄	—	73	4	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	2	no	—
360	C₂²×C₄	—	73	8	no	—
361	C₂²×C₄	—	73	32	no	—
362	C₂²×C₄	—	73	8	no	—
363	C₂²×C₄	—	73	16	no	—
364	C₂²×C₄	—	73	2	no	—
365	C₂²×C₄	—	73	4	no	—
366	C₂²×C₄	—	73	4	no	—
367	C₂²×C₄	—	73	2	no	—
368	C₂²×C₄	—	73	8	no	—
369	C₂²×C₄	—	73	8	no	—
370	C₂²×C₄	—	73	32	no	—
371	C₂²×C₄	—	73	8	no	—
372	C₂²×C₄	—	73	2	no	—
373	C₂²×C₄	—	73	2	no	—
374	C₂²×C₄	—	73	8	no	—
375	C₂²×C₄	—	73	2	no	—
376	C₂²×C₄	—	73	8	no	—
377	C₂²×C₄	—	73	8	no	—
378	C₂²×C₄	—	73	8	no	—
379	C₂²×C₄	—	146	8	no	—
380	C₂²×C₄	—	146	64	no	—
381	C₂²×C₄	—	146	8	no	—
382	C₂²×C₄	—	146	8	no	—
383	C₂²×C₄	—	146	8	no	—
384	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
385	C₂²×C₄	C₂×C₄×D₇₃	1	8	yes	—
386	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
387	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₇₃	1	8	yes	—
389	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
390	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
391	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
392	M₁₆	—	73	32	no	—
393	M₁₆	—	73	64	no	—
394	M₁₆	C₂×C₄×D₇₃	1	32	yes	direct product factor
395	C₂×C₈	—	73	16	no	—
396	C₂×C₈	—	73	8	no	—
397	C₂×C₈	—	73	64	no	—
398	C₂×C₈	C₂×C₄×D₇₃	1	16	yes	complemented
399	C₂×C₈	C₂³×D₇₃	1	8	yes	—
400	C₄²	—	73	8	no	—
401	C₄²	—	73	2	no	—
402	C₄²	—	73	8	no	—
403	C₄²	—	73	8	no	—
404	C₄²	—	73	8	no	—
405	C₄²	—	73	8	no	—
406	C₄²	—	73	2	no	—
407	C₄²	—	73	2	no	—
408	C₄²	—	73	2	no	—
409	C₄²	C₂×C₄×D₇₃	1	2	yes	—
410	C₄²	C₂×C₄×D₇₃	1	8	yes	—
411	C₄²	C₂×C₄×D₇₃	1	2	yes	—
412	C₄²	C₂³×D₇₃	1	2	yes	—
413	C₄²	C₂³×D₇₃	1	2	yes	—
414	C₂³	—	2	4	no	—
415	C₂³	—	73	2	no	—
416	C₂³	—	73	4	no	—
417	C₂³	—	73	8	no	—
418	C₂³	—	73	2	no	—
419	C₂³	—	73	16	no	—
420	C₂³	—	73	4	no	—
421	C₂³	—	146	16	no	—
422	C₂³	—	146	32	no	—
423	C₂³	—	146	4	no	—
424	C₂³	C₄²×D₇₃	1	4	yes	—
425	C₂³	C₂²×C₄×D₇₃	1	2	yes	—
426	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	16	no	—
429	C₂×C₄	—	73	2	no	—
430	C₂×C₄	—	73	2	no	—
431	C₂×C₄	—	73	4	no	—
432	C₂×C₄	—	73	16	no	—
433	C₂×C₄	—	73	4	no	—
434	C₂×C₄	—	73	4	no	—
435	C₂×C₄	—	73	8	no	—
436	C₂×C₄	—	73	8	no	—
437	C₂×C₄	—	73	8	no	—
438	C₂×C₄	—	73	8	no	—
439	C₂×C₄	—	73	16	no	—
440	C₂×C₄	—	73	16	no	—
441	C₂×C₄	—	73	8	no	—
442	C₂×C₄	—	73	32	no	—
443	C₂×C₄	—	73	4	no	—
444	C₂×C₄	—	146	16	no	—
445	C₂×C₄	—	146	16	no	—
446	C₂×C₄	—	146	16	no	—
447	C₂×C₄	—	146	4	no	—
448	C₂×C₄	—	146	16	no	—
449	C₂×C₄	C₄²×D₇₃	1	8	yes	—
450	C₂×C₄	C₄²×D₇₃	1	4	yes	—
451	C₂×C₄	M₁₆×D₇₃	1	8	yes	direct product factor
452	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
453	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
454	C₂×C₄	C₂²×C₄×D₇₃	1	8	yes	—
455	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
456	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
458	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
459	C₈	—	73	16	no	—
460	C₈	C₂²×C₄×D₇₃	1	16	yes	complemented
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	73	4	no	—
464	C₂²	—	73	8	no	—
465	C₂²	—	73	16	no	—
466	C₂²	—	73	4	no	—
467	C₂²	—	146	32	no	—
468	C₂²	—	146	4	no	—
469	C₂²	—	146	8	no	—
470	C₂²	C₂×C₄²×D₇₃	1	4	yes	—
471	C₂²	C₂×C₄²×D₇₃	1	2	yes	—
472	C₂²	C₂×M₁₆×D₇₃	1	4	yes	—
473	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	73	4	no	—
476	C₄	—	73	4	no	—
477	C₄	—	73	8	no	—
478	C₄	—	146	4	no	—
479	C₄	C₂×C₄²×D₇₃	1	2	yes	—
480	C₄	C₂×C₄²×D₇₃	1	4	yes	—
481	C₄	C₂×M₁₆×D₇₃	1	8	yes	direct product factor
482	C₄	C₂³×C₄×D₇₃	1	2	yes	—
483	C₂	—	2	4	no	—
484	C₂	—	73	8	no	—
485	C₂	—	146	4	no	—
486	C₂	C₄×M₁₆×D₇₃	1	4	yes	direct product factor
487	C₂	C₂²×C₄²×D₇₃	1	1	yes	characteristic
488	C₂	C₂²×M₁₆×D₇₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₇₃
commutator	C₂×C₇₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×C₄×M₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂⁴×D₇₃	C₂×C₄
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₇₃
hypocenter	C₇₃	C₂²×C₄×M₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#11924012	C₂	semidirect
4. C₂×#17988539	C₂	semidirect
5. C₂×M₁₆×Dic₇₃	C₂	semidirect
6. C₂×C₄×#11924011	C₂	semidirect
7. C₄×M₁₆×D₇₃	C₂	direct (N × H)
8. C₂×#97×D₇₃	C₂	semidirect
9. C₂×C₄×C₈×D₇₃	C₂	semidirect
10. C₂×C₄×M₁₆×C₇₃	C₂	semidirect
15. C₂×M₁₆×D₇₃	C₄	direct (N × H)
28. C₄×#11924012	C₂²	semidirect
29. #17988539	C₂²	semidirect
30. M₁₆×Dic₇₃	C₂²	semidirect
31. C₄×#11924011	C₂²	semidirect
32. C₂×#14556502	C₂²	semidirect
33. C₂×#14556501	C₂²	semidirect
34. #97×D₇₃	C₂²	semidirect
35. C₂×C₄×#10596831	C₂²	semidirect
36. C₂×C₈×Dic₇₃	C₂²	semidirect
37. C₄×C₈×D₇₃	C₂²	semidirect
40. C₄×M₁₆×C₇₃	C₂²	semidirect
41. C₂×#97×C₇₃	C₂²	semidirect
42. C₂×C₄×C₈×C₇₃	C₂²	semidirect
59. C₂×#11924012	C₂×C₄	semidirect
61. C₂×#11924011	C₂×C₄	semidirect
63. M₁₆×D₇₃	C₂×C₄	direct (N × H)
65. C₂×C₈×D₇₃	C₂×C₄	semidirect
87. #14556502	C₂³	semidirect
88. #14556501	C₂³	semidirect
89. C₄×#10596831	C₂³	semidirect
90. C₈×Dic₇₃	C₂³	semidirect
93. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
101. #97×C₇₃	C₂³	semidirect
102. C₄×C₈×C₇₃	C₂³	semidirect
123. C₂×C₄×D₇₃	M₁₆	direct (N × H)
137. #11924012	C₂²×C₄	semidirect
138. #11924011	C₂²×C₄	semidirect
139. C₂×#10596831	C₂²×C₄	semidirect
141. C₈×D₇₃	C₂²×C₄	semidirect
161. M₁₆×C₇₃	C₂²×C₄	semidirect
162. C₂×C₈×C₇₃	C₂²×C₄	semidirect
186. C₂×C₄×C₇₃	C₂×M₁₆	semidirect
199. C₂×Dic₇₃	C₂×M₁₆	semidirect
211. C₄×D₇₃	C₂×M₁₆	direct (N × H)
214. C₈×C₇₃	C₂³×C₄	semidirect
215. #10596831	C₂³×C₄	semidirect
225. C₂×D₇₃	C₄×M₁₆	direct (N × H)
232. C₄×C₇₃	C₂²×M₁₆	semidirect
237. Dic₇₃	C₂²×M₁₆	semidirect
240. C₂×C₇₃	C₂×C₄×M₁₆	semidirect
244. D₇₃	C₂×C₄×M₁₆	direct (N × H)
252. C₂×C₄×M₁₆	D₇₃	direct (N × H)
255. C₇₃	C₂²×C₄×M₁₆	semidirect
279. C₄×M₁₆	C₂×D₇₃	direct (N × H)
283. C₂×#97	C₂×D₇₃	semidirect
287. C₂×C₄×C₈	C₂×D₇₃	semidirect
311. C₂×M₁₆	C₄×D₇₃	direct (N × H)
344. #97	C₂²×D₇₃	semidirect
347. C₄×C₈	C₂²×D₇₃	semidirect
394. M₁₆	C₂×C₄×D₇₃	direct (N × H)
398. C₂×C₈	C₂×C₄×D₇₃	semidirect
451. C₂×C₄	M₁₆×D₇₃	direct (N × H)
460. C₈	C₂²×C₄×D₇₃	semidirect
481. C₄	C₂×M₁₆×D₇₃	direct (N × H)
486. C₂	C₄×M₁₆×D₇₃	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×M₁₆×D₇₃	2
C₂²×C₄²×D₇₃	2
C₂×C₄×#11924012	2
C₂×#17988539	2
C₂×M₁₆×Dic₇₃	2
C₂×C₄×#11924011	2
C₄×M₁₆×D₇₃	2
C₂×#97×D₇₃	2
C₂×C₄×C₈×D₇₃	2
C₂×C₄×M₁₆×C₇₃	2
C₂²×C₄×M₁₆	73

Subgroups — C2×C4×M16×D73 #33949368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×M₁₆×D₇₃ #33949368