Subgroups — C₂×C₇₃×#3044 #32969823

Order 18688.

2666 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#536×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#519×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#3044	C₂	1	16	yes	maximal, direct product factor
6	C₂×#464×C₇₃	C₂	1	4	yes	maximal, complemented
7	C₂×#462×C₇₃	C₂	1	4	yes	maximal, complemented
8	C₂×#424×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#419×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#416×C₇₃	C₂	1	1	yes	maximal, characteristic
11	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₇₃	—	2	8	no	—
15	C₂×#137×C₇₃	C₂²	1	8	yes	—
16	C₂²×Q₁₆×C₇₃	—	2	8	no	—
17	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₇₃	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₇₃	C₂²	1	8	yes	complemented
20	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	#536×C₇₃	—	2	4	no	—
24	#536×C₇₃	C₂²	1	8	yes	—
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
26	C₂×#124×C₇₃	C₂²	1	2	yes	—
27	C₂×#123×C₇₃	—	2	2	no	—
28	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
29	#519×C₇₃	—	2	4	no	—
30	#519×C₇₃	C₂²	1	8	yes	complemented
31	C₂×C₄×Q₈×C₇₃	—	2	2	no	—
32	C₂×C₄×Q₈×C₇₃	C₂²	1	4	yes	—
33	C₂×#117×C₇₃	—	2	2	no	—
34	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
36	#464×C₇₃	C₂²	1	32	yes	complemented
37	#462×C₇₃	C₂²	1	32	yes	complemented
38	#424×C₇₃	C₂²	1	8	yes	complemented
39	C₂×C₄⋊C₈×C₇₃	C₂²	1	4	yes	—
40	#419×C₇₃	C₂²	1	8	yes	complemented
41	#416×C₇₃	C₂²	1	8	yes	—
42	C₂×#103×C₇₃	C₂²	1	2	yes	—
43	C₂×#103×C₇₃	C₂²	1	4	yes	—
44	C₂×#102×C₇₃	C₂²	1	2	yes	—
45	C₂×#41×C₇₃	—	2	2	no	—
46	C₂×#41×C₇₃	—	2	4	no	—
47	C₂×#41×C₇₃	—	2	4	no	—
48	C₂×#41×C₇₃	C₂³	1	4	yes	—
49	C₂²×Q₈×C₇₃	—	2	1	no	—
50	C₂²×Q₈×C₇₃	—	2	2	no	—
51	C₂²×Q₈×C₇₃	—	2	1	no	—
52	C₂²×Q₈×C₇₃	—	2	2	no	—
53	C₂²×Q₈×C₇₃	—	2	4	no	—
54	C₂²×Q₈×C₇₃	—	2	4	no	—
55	C₂²×Q₈×C₇₃	—	2	4	no	—
56	C₂²×Q₈×C₇₃	D₄	1	8	yes	—
57	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
60	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
61	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₇₃	—	2	1	no	—
63	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇₃	—	2	1	no	—
65	C₂³×C₄×C₇₃	—	2	1	no	—
66	C₂³×C₄×C₇₃	—	2	1	no	—
67	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
68	#137×C₇₃	—	2	32	no	—
69	C₂×Q₁₆×C₇₃	—	2	16	no	—
70	C₂×Q₁₆×C₇₃	—	2	32	no	—
71	C₂×Q₁₆×C₇₃	—	2	8	no	—
72	C₂×Q₁₆×C₇₃	C₂³	1	8	yes	—
73	C₂×Q₁₆×C₇₃	C₂³	1	16	yes	—
74	C₂×SD₁₆×C₇₃	—	2	8	no	—
75	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
76	C₂×M₁₆×C₇₃	—	2	4	no	—
77	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
78	C₂²×C₈×C₇₃	—	2	4	no	—
79	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
82	C₄⋊Q₈×C₇₃	—	2	4	no	—
83	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	—
84	#124×C₇₃	—	2	4	no	—
85	#124×C₇₃	C₂³	1	8	yes	—
86	#123×C₇₃	—	2	16	no	—
87	C₂²⋊Q₈×C₇₃	—	2	16	no	—
88	C₄×Q₈×C₇₃	—	2	16	no	—
89	C₄×Q₈×C₇₃	—	2	8	no	—
90	C₄×Q₈×C₇₃	C₂³	1	16	yes	—
91	#117×C₇₃	—	2	2	no	—
92	#117×C₇₃	—	2	16	no	—
93	#117×C₇₃	D₄	1	4	yes	—
94	#117×C₇₃	C₂³	1	4	yes	—
95	#117×C₇₃	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
97	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
98	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
103	C₂×C₄²×C₇₃	—	2	4	no	—
104	C₂×C₄²×C₇₃	—	2	1	no	—
105	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
106	C₄⋊C₈×C₇₃	C₂³	1	16	yes	—
107	#103×C₇₃	C₂³	1	8	yes	—
108	#103×C₇₃	C₂³	1	16	yes	—
109	#102×C₇₃	C₂³	1	8	yes	—
110	C₂⁴×C₇₃	—	2	1	no	—
111	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
112	#41×C₇₃	—	2	8	no	—
113	#41×C₇₃	—	2	8	no	—
114	#41×C₇₃	—	4	8	no	—
115	C₂×Q₈×C₇₃	—	2	8	no	—
116	C₂×Q₈×C₇₃	—	2	16	no	—
117	C₂×Q₈×C₇₃	—	2	4	no	—
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	2	4	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	1	no	—
122	C₂×Q₈×C₇₃	—	2	4	no	—
123	C₂×Q₈×C₇₃	—	2	8	no	—
124	C₂×Q₈×C₇₃	—	2	4	no	—
125	C₂×Q₈×C₇₃	—	2	8	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	4	no	—
128	C₂×Q₈×C₇₃	—	2	8	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	—	4	4	no	—
131	C₂×Q₈×C₇₃	—	4	8	no	—
132	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
133	C₂×Q₈×C₇₃	C₂×D₄	1	16	yes	—
134	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
135	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
137	C₂×D₄×C₇₃	—	2	4	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	2	1	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	4	4	no	—
142	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₇₃	—	2	8	no	—
144	C₂²×C₄×C₇₃	—	2	4	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	4	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	2	no	—
149	C₂²×C₄×C₇₃	—	2	1	no	—
150	C₂²×C₄×C₇₃	—	2	4	no	—
151	C₂²×C₄×C₇₃	—	4	4	no	—
152	C₂²×C₄×C₇₃	—	4	4	no	—
153	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₇₃	#41	1	4	yes	—
158	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₇₃	—	2	32	no	—
161	Q₁₆×C₇₃	—	2	16	no	—
162	SD₁₆×C₇₃	—	2	16	no	—
163	M₁₆×C₇₃	—	2	8	no	—
164	C₂×C₈×C₇₃	—	2	4	no	—
165	C₂×C₈×C₇₃	—	2	8	no	—
166	C₂×C₈×C₇₃	—	2	4	no	—
167	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
168	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
169	C₄⋊C₄×C₇₃	—	2	16	no	—
170	C₄⋊C₄×C₇₃	—	2	16	no	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
173	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
174	C₂²⋊C₄×C₇₃	—	2	4	no	—
175	C₂²⋊C₄×C₇₃	—	2	16	no	—
176	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
177	C₄²×C₇₃	—	2	16	no	—
178	C₄²×C₇₃	—	2	4	no	—
179	C₄²×C₇₃	C₂×D₄	1	4	yes	—
180	C₄²×C₇₃	C₂⁴	1	4	yes	—
181	C₂³×C₇₃	—	2	4	no	—
182	C₂³×C₇₃	—	2	2	no	—
183	C₂³×C₇₃	—	4	2	no	—
184	C₂³×C₇₃	—	4	4	no	—
185	C₂³×C₇₃	#121	1	4	yes	—
186	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
187	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₇₃	—	2	16	no	—
189	Q₈×C₇₃	—	2	8	no	—
190	Q₈×C₇₃	—	2	4	no	—
191	Q₈×C₇₃	—	2	4	no	—
192	Q₈×C₇₃	—	2	2	no	—
193	Q₈×C₇₃	—	2	4	no	—
194	Q₈×C₇₃	—	2	2	no	—
195	Q₈×C₇₃	—	4	8	no	—
196	Q₈×C₇₃	—	4	4	no	—
197	Q₈×C₇₃	—	4	2	no	—
198	Q₈×C₇₃	C₂²×D₄	1	8	yes	—
199	D₄×C₇₃	—	2	2	no	—
200	D₄×C₇₃	—	2	2	no	—
201	D₄×C₇₃	—	4	8	no	—
202	D₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	2	16	no	—
204	C₂×C₄×C₇₃	—	2	8	no	—
205	C₂×C₄×C₇₃	—	2	8	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	8	no	—
212	C₂×C₄×C₇₃	—	4	4	no	—
213	C₂×C₄×C₇₃	—	4	4	no	—
214	C₂×C₄×C₇₃	—	4	8	no	—
215	C₂×C₄×C₇₃	#121	1	4	yes	—
216	C₂×C₄×C₇₃	#121	1	8	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
218	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
224	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₇₃	—	2	4	no	—
226	C₈×C₇₃	—	2	4	no	—
227	C₂²×C₇₃	—	2	8	no	—
228	C₂²×C₇₃	—	2	4	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	8	4	no	—
232	C₂²×C₇₃	C₂×#121	1	4	yes	—
233	C₂²×C₇₃	C₂×#121	1	2	yes	—
234	C₂²×C₇₃	#578	1	4	yes	—
235	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
236	C₄×C₇₃	—	2	8	no	—
237	C₄×C₇₃	—	2	8	no	—
238	C₄×C₇₃	—	4	2	no	—
239	C₄×C₇₃	—	4	4	no	—
240	C₄×C₇₃	—	4	4	no	—
241	C₄×C₇₃	C₂×#121	1	4	yes	—
242	C₄×C₇₃	C₂×#121	1	2	yes	—
243	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
244	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
245	C₂×#3044	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂×C₇₃	—	2	4	no	—
247	C₂×C₇₃	—	8	2	no	—
248	C₂×C₇₃	#3044	1	4	yes	direct product factor
249	C₂×C₇₃	C₂²×#121	1	1	yes	characteristic
250	C₂×C₇₃	C₂×#578	1	2	yes	—
251	C₂²×#137	C₂×C₇₃	1	1	yes	characteristic
252	C₂³×Q₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
253	C₂×#536	C₂×C₇₃	1	1	yes	characteristic
254	C₂×#519	C₂×C₇₃	1	1	yes	characteristic, complemented
255	#3044	C₂×C₇₃	1	16	yes	direct product factor
256	C₂×#464	C₂×C₇₃	1	4	yes	complemented
257	C₂×#462	C₂×C₇₃	1	4	yes	complemented
258	C₂×#424	C₂×C₇₃	1	1	yes	characteristic, complemented
259	C₂×#419	C₂×C₇₃	1	1	yes	characteristic, complemented
260	C₂×#416	C₂×C₇₃	1	1	yes	characteristic
261	C₇₃	C₂×#3044	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
263	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
264	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
265	C₂×#137	—	2	8	no	—
266	C₂×#137	C₂²×C₇₃	1	8	yes	—
267	C₂²×Q₁₆	—	2	8	no	—
268	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
269	C₂²×Q₁₆	C₂²×C₇₃	1	4	yes	—
270	C₂²×Q₁₆	C₂²×C₇₃	1	8	yes	complemented
271	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
272	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
274	#536	—	2	4	no	—
275	#536	C₂²×C₇₃	1	8	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
277	C₂×#124	C₂²×C₇₃	1	2	yes	—
278	C₂×#123	—	2	2	no	—
279	C₂×C₂²⋊Q₈	—	2	2	no	—
280	#519	—	2	4	no	—
281	#519	C₂²×C₇₃	1	8	yes	complemented
282	C₂×C₄×Q₈	—	2	2	no	—
283	C₂×C₄×Q₈	C₂²×C₇₃	1	4	yes	—
284	C₂×#117	—	2	2	no	—
285	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
287	#464	C₂²×C₇₃	1	32	yes	complemented
288	#462	C₂²×C₇₃	1	32	yes	complemented
289	#424	C₂²×C₇₃	1	8	yes	complemented
290	C₂×C₄⋊C₈	C₂²×C₇₃	1	4	yes	—
291	#419	C₂²×C₇₃	1	8	yes	complemented
292	#416	C₂²×C₇₃	1	8	yes	—
293	C₂×#103	C₂²×C₇₃	1	2	yes	—
294	C₂×#103	C₂²×C₇₃	1	4	yes	—
295	C₂×#102	C₂²×C₇₃	1	2	yes	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	4	no	—
299	C₂×#41	C₂³×C₇₃	1	4	yes	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	—	2	2	no	—
304	C₂²×Q₈	—	2	4	no	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	—	2	4	no	—
307	C₂²×Q₈	D₄×C₇₃	1	8	yes	—
308	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
309	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
311	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
312	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
319	#137	—	2	32	no	—
320	C₂×Q₁₆	—	2	16	no	—
321	C₂×Q₁₆	—	2	32	no	—
322	C₂×Q₁₆	—	2	8	no	—
323	C₂×Q₁₆	C₂³×C₇₃	1	16	yes	—
324	C₂×Q₁₆	C₂³×C₇₃	1	8	yes	—
325	C₂×SD₁₆	—	2	8	no	—
326	C₂×SD₁₆	C₂³×C₇₃	1	8	yes	—
327	C₂×M₁₆	—	2	4	no	—
328	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
331	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
332	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
333	C₄⋊Q₈	—	2	4	no	—
334	C₄⋊Q₈	C₂³×C₇₃	1	8	yes	—
335	#124	—	2	4	no	—
336	#124	C₂³×C₇₃	1	8	yes	—
337	#123	—	2	16	no	—
338	C₂²⋊Q₈	—	2	16	no	—
339	C₄×Q₈	—	2	16	no	—
340	C₄×Q₈	—	2	8	no	—
341	C₄×Q₈	C₂³×C₇₃	1	16	yes	—
342	#117	—	2	2	no	—
343	#117	—	2	16	no	—
344	#117	D₄×C₇₃	1	4	yes	—
345	#117	C₂³×C₇₃	1	4	yes	—
346	#117	C₂³×C₇₃	1	4	yes	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	4	no	—
353	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
357	C₄⋊C₈	C₂³×C₇₃	1	16	yes	—
358	#103	C₂³×C₇₃	1	8	yes	—
359	#103	C₂³×C₇₃	1	16	yes	—
360	#102	C₂³×C₇₃	1	8	yes	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	4	8	no	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	2	16	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	8	no	—
383	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
384	C₂×Q₈	C₂×D₄×C₇₃	1	16	yes	—
385	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
386	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
387	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
408	C₂²×C₄	#41×C₇₃	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
411	Q₁₆	—	2	32	no	—
412	Q₁₆	—	2	16	no	—
413	SD₁₆	—	2	16	no	—
414	M₁₆	—	2	8	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
419	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
420	C₄⋊C₄	—	2	16	no	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
424	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
428	C₄²	—	2	16	no	—
429	C₄²	—	2	4	no	—
430	C₄²	C₂×D₄×C₇₃	1	4	yes	—
431	C₄²	C₂⁴×C₇₃	1	4	yes	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	4	no	—
436	C₂³	#121×C₇₃	1	4	yes	—
437	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
438	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
439	Q₈	—	2	16	no	—
440	Q₈	—	2	8	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	2	4	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	2	4	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	8	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	C₂²×D₄×C₇₃	1	8	yes	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	8	no	—
453	D₄	—	4	2	no	—
454	C₂×C₄	—	2	16	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	#121×C₇₃	1	4	yes	—
467	C₂×C₄	#121×C₇₃	1	8	yes	—
468	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
469	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
473	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
474	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
475	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	2	4	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	4	no	—
483	C₂²	C₂×#121×C₇₃	1	4	yes	—
484	C₂²	C₂×#121×C₇₃	1	2	yes	—
485	C₂²	#578×C₇₃	1	4	yes	—
486	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
487	C₄	—	2	8	no	—
488	C₄	—	2	8	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	C₂×#121×C₇₃	1	4	yes	—
493	C₄	C₂×#121×C₇₃	1	2	yes	—
494	C₄	C₂³×D₄×C₇₃	1	1	yes	characteristic
495	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
496	C₂	—	2	4	no	—
497	C₂	—	8	2	no	—
498	C₂	C₇₃×#3044	1	4	yes	direct product factor
499	C₂	C₂²×#121×C₇₃	1	1	yes	characteristic
500	C₂	C₂×#578×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×Q₁₆×C₇₃	C₂	semidirect
4. C₂×#519×C₇₃	C₂	semidirect
5. C₇₃×#3044	C₂	direct (N × H)
6. C₂×#464×C₇₃	C₂	semidirect
7. C₂×#462×C₇₃	C₂	semidirect
8. C₂×#424×C₇₃	C₂	semidirect
9. C₂×#419×C₇₃	C₂	semidirect
19. C₂²×Q₁₆×C₇₃	C₂²	semidirect
30. #519×C₇₃	C₂²	semidirect
36. #464×C₇₃	C₂²	semidirect
37. #462×C₇₃	C₂²	semidirect
38. #424×C₇₃	C₂²	semidirect
40. #419×C₇₃	C₂²	semidirect
245. C₂×#3044	C₇₃	direct (N × H)
248. C₂×C₇₃	#3044	direct (N × H)
252. C₂³×Q₁₆	C₂×C₇₃	semidirect
254. C₂×#519	C₂×C₇₃	semidirect
255. #3044	C₂×C₇₃	direct (N × H)
256. C₂×#464	C₂×C₇₃	semidirect
257. C₂×#462	C₂×C₇₃	semidirect
258. C₂×#424	C₂×C₇₃	semidirect
259. C₂×#419	C₂×C₇₃	semidirect
261. C₇₃	C₂×#3044	direct (N × H)
270. C₂²×Q₁₆	C₂²×C₇₃	semidirect
281. #519	C₂²×C₇₃	semidirect
287. #464	C₂²×C₇₃	semidirect
288. #462	C₂²×C₇₃	semidirect
289. #424	C₂²×C₇₃	semidirect
291. #419	C₂²×C₇₃	semidirect
498. C₂	C₇₃×#3044	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×#137×C₇₃	2
C₂³×Q₁₆×C₇₃	2
C₂×#536×C₇₃	2
C₂×#519×C₇₃	2
C₇₃×#3044	2
C₂×#464×C₇₃	2
C₂×#462×C₇₃	2
C₂×#424×C₇₃	2
C₂×#419×C₇₃	2
C₂×#416×C₇₃	2
C₂×#3044	73

Subgroups — C2×C73×#3044 #32969823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3044 #32969823