Subgroups — C₂×#446×D₇₃ #33950337

Order 18688.

2222 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988718	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17988717	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17988716	C₂	1	2	yes	maximal, complemented
5	C₂×#17988715	C₂	1	2	yes	maximal, complemented
6	C₂×#17988714	C₂	1	1	yes	maximal, characteristic, complemented
7	#446×D₇₃	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₄⋊C₈×D₇₃	C₂	1	2	yes	maximal
9	C₂×C₄⋊C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#97×D₇₃	C₂	1	2	yes	maximal
11	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#446×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₈×D₇₃	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
16	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×Dic₇₃	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₁₄₆	C₂²	1	2	yes	—
20	C₂×#14556556	C₄	1	2	yes	—
21	C₂×#14556556	C₄	1	1	yes	characteristic
22	C₄×Q₈×D₇₃	C₄	1	8	yes	—
23	C₄×Q₈×D₇₃	C₂²	1	8	yes	—
24	C₂×C₄⋊C₄×D₇₃	C₄	1	2	yes	—
25	C₂×C₄⋊C₄×D₇₃	C₄	1	1	yes	characteristic
26	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×D₇₃	C₂²	1	2	yes	—
28	#17988718	C₂²	1	8	yes	complemented
29	#17988717	C₂²	1	8	yes	complemented
30	#17988716	C₂²	1	16	yes	complemented
31	#17988715	C₂²	1	16	yes	complemented
32	#17988714	C₂²	1	8	yes	complemented
33	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
34	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
35	C₂×#14556520	C₂²	1	2	yes	—
36	C₂×#14556520	C₂²	1	2	yes	—
37	C₂×#14556520	C₂²	1	2	yes	—
38	C₄⋊C₈×D₇₃	C₂²	1	8	yes	—
39	C₄⋊C₈×D₇₃	C₂²	1	16	yes	—
40	C₂×#14556502	C₂²	1	2	yes	—
41	C₂×#14556501	C₂²	1	2	yes	—
42	C₂×#14556501	C₂²	1	2	yes	—
43	#97×D₇₃	C₂²	1	16	yes	—
44	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₃	C₂²	1	8	yes	—
48	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
49	#446×C₇₃	C₂²	1	8	yes	complemented
50	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
52	C₂×#97×C₇₃	C₂²	1	2	yes	—
53	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
54	C₂²×Dic₁₄₆	C₂×C₄	1	2	yes	—
55	C₂²×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
56	C₂×Q₈×D₇₃	—	2	8	no	—
57	C₂×Q₈×D₇₃	C₂×C₄	1	8	yes	—
58	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
59	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
63	C₂²×#10596831	C₂³	1	1	yes	characteristic
64	C₂²×#10596831	C₂³	1	2	yes	—
65	C₂²×#10596831	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₇₃	—	2	4	no	—
67	C₂×C₈×D₇₃	—	2	8	no	—
68	C₂×C₈×D₇₃	Q₈	1	8	yes	complemented
69	C₂×C₈×D₇₃	C₂³	1	4	yes	—
70	C₂×C₈×D₇₃	C₂³	1	8	yes	—
71	C₂×C₈×D₇₃	C₂³	1	4	yes	—
72	Q₈×Dic₇₃	C₂×C₄	1	8	yes	—
73	C₄×Dic₁₄₆	C₂×C₄	1	4	yes	—
74	C₄×Dic₁₄₆	C₂×C₄	1	8	yes	—
75	C₄×Dic₁₄₆	C₂³	1	4	yes	—
76	C₄×Dic₁₄₆	C₂³	1	8	yes	—
77	#14556556	C₂×C₄	1	16	yes	—
78	#14556556	C₂×C₄	1	8	yes	—
79	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂×#11924007	C₂×C₄	1	2	yes	—
82	C₂×#11924007	C₂×C₄	1	2	yes	—
83	C₂×#11924007	C₂×C₄	1	2	yes	—
84	C₄⋊C₄×D₇₃	C₂×C₄	1	16	yes	—
85	C₄⋊C₄×D₇₃	C₂×C₄	1	8	yes	—
86	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
87	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
89	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
92	C₄²×D₇₃	C₂×C₄	1	8	yes	—
93	C₄²×D₇₃	C₂×C₄	1	4	yes	—
94	C₄²×D₇₃	C₂³	1	4	yes	—
95	C₄²×D₇₃	C₂³	1	8	yes	—
96	C₄⋊#10596831	C₂³	1	8	yes	—
97	C₄⋊#10596831	C₂³	1	4	yes	—
98	#14556520	C₂³	1	8	yes	—
99	#14556520	C₂³	1	8	yes	—
100	#14556520	C₂³	1	8	yes	—
101	#14556502	C₂³	1	8	yes	—
102	#14556501	C₂³	1	8	yes	—
103	#14556501	C₂³	1	8	yes	—
104	C₄×#10596831	C₂³	1	4	yes	—
105	C₈×Dic₇₃	C₂³	1	4	yes	—
106	C₈×Dic₇₃	C₂³	1	4	yes	—
107	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₇₃	C₂×C₄	1	4	yes	—
112	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
117	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
118	C₄⋊C₈×C₇₃	C₂³	1	8	yes	—
119	#97×C₇₃	C₂³	1	8	yes	—
120	C₄×C₈×C₇₃	C₂³	1	4	yes	—
121	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×Dic₁₄₆	—	2	4	no	—
123	C₂×Dic₁₄₆	—	2	8	no	—
124	C₂×Dic₁₄₆	C₂²×C₄	1	4	yes	—
125	C₂×Dic₁₄₆	C₂²×C₄	1	8	yes	—
126	Q₈×D₇₃	—	2	32	no	—
127	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
130	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₇₃	—	2	8	no	—
133	C₂×C₄×D₇₃	—	2	4	no	—
134	C₂×C₄×D₇₃	—	2	8	no	—
135	C₂×C₄×D₇₃	M₁₆	1	8	yes	—
136	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
138	C₂×C₄×D₇₃	C₂²×C₄	1	8	yes	—
139	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
140	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
141	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
142	C₂×C₄×D₇₃	#41	1	4	yes	—
143	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
144	C₂×#10596831	—	2	2	no	—
145	C₂×#10596831	—	2	4	no	—
146	C₂×#10596831	C₂×Q₈	1	4	yes	complemented
147	C₂×#10596831	C₂⁴	1	2	yes	—
148	C₂×#10596831	C₂⁴	1	4	yes	—
149	C₂×#10596831	C₂⁴	1	2	yes	—
150	C₈×D₇₃	—	2	8	no	—
151	C₈×D₇₃	—	2	16	no	—
152	C₈×D₇₃	C₂×Q₈	1	16	yes	complemented
153	C₄⋊Dic₇₃	C₂²×C₄	1	8	yes	—
154	C₄⋊Dic₇₃	C₂²×C₄	1	4	yes	—
155	#11924007	C₂²×C₄	1	8	yes	—
156	#11924007	C₂²×C₄	1	8	yes	—
157	#11924007	C₂²×C₄	1	8	yes	—
158	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
159	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
160	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
161	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
162	C₄×Dic₇₃	C₂²×C₄	1	8	yes	—
163	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
164	C₄×Dic₇₃	C₂⁴	1	2	yes	—
165	C₄×Dic₇₃	C₂⁴	1	4	yes	—
166	C₂×Q₈×C₇₃	—	2	4	no	—
167	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₇₃	—	2	2	no	—
174	C₂×C₈×C₇₃	—	2	4	no	—
175	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	complemented
176	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
177	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
178	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
179	C₄⋊C₄×C₇₃	C₂²×C₄	1	8	yes	—
180	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
181	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
182	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
183	C₄²×C₇₃	C₂⁴	1	2	yes	—
184	C₄²×C₇₃	C₂⁴	1	4	yes	—
185	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
186	C₂²×D₇₃	C₄×Q₈	1	4	yes	—
187	C₂²×D₇₃	C₂×M₁₆	1	4	yes	—
188	C₂²×D₇₃	#131	1	4	yes	—
189	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
190	Q₈×C₇₃	—	2	8	no	—
191	C₂×C₄×C₇₃	—	2	4	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	4	no	—
194	C₂×C₄×C₇₃	C₂×M₁₆	1	4	yes	—
195	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
197	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
198	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
201	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
203	C₂×Dic₇₃	—	2	4	no	—
204	C₂×Dic₇₃	—	2	2	no	—
205	C₂×Dic₇₃	—	2	4	no	—
206	C₂×Dic₇₃	C₄×Q₈	1	4	yes	—
207	C₂×Dic₇₃	C₂×M₁₆	1	4	yes	—
208	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
209	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
210	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
211	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
212	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
213	C₄×D₇₃	—	2	16	no	—
214	C₄×D₇₃	—	2	8	no	—
215	C₄×D₇₃	—	2	16	no	—
216	C₄×D₇₃	C₄×Q₈	1	8	yes	—
217	C₄×D₇₃	C₂×M₁₆	1	16	yes	—
218	C₄×D₇₃	C₂²×Q₈	1	4	yes	—
219	C₄×D₇₃	C₂×#41	1	4	yes	—
220	Dic₁₄₆	—	2	8	no	—
221	Dic₁₄₆	—	2	16	no	—
222	C₈×C₇₃	—	2	2	no	—
223	C₈×C₇₃	—	2	4	no	—
224	C₈×C₇₃	C₂²×Q₈	1	4	yes	complemented
225	#10596831	—	2	2	no	—
226	#10596831	—	2	4	no	—
227	#10596831	C₂²×Q₈	1	4	yes	complemented
228	C₂²×C₇₃	C₂×C₄×Q₈	1	2	yes	—
229	C₂²×C₇₃	C₂²×M₁₆	1	2	yes	—
230	C₂²×C₇₃	C₂×#131	1	2	yes	—
231	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
232	C₂×D₇₃	#446	1	16	yes	direct product factor
233	C₂×D₇₃	C₂×C₄×Q₈	1	4	yes	—
234	C₂×D₇₃	C₂²×M₁₆	1	4	yes	—
235	C₂×D₇₃	C₂×#131	1	4	yes	—
236	C₄×C₇₃	—	2	4	no	—
237	C₄×C₇₃	—	2	2	no	—
238	C₄×C₇₃	—	2	4	no	—
239	C₄×C₇₃	C₂×C₄×Q₈	1	2	yes	—
240	C₄×C₇₃	C₂²×M₁₆	1	4	yes	—
241	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
242	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
243	Dic₇₃	—	2	4	no	—
244	Dic₇₃	—	2	2	no	—
245	Dic₇₃	—	2	4	no	—
246	Dic₇₃	C₂×C₄×Q₈	1	4	yes	—
247	Dic₇₃	C₂²×M₁₆	1	4	yes	—
248	C₂²×#446	—	73	1	no	maximal, Sylow
249	C₂×C₇₃	C₂×#446	1	4	yes	complemented
250	C₂×C₇₃	C₂²×C₄×Q₈	1	1	yes	characteristic
251	C₂×C₇₃	C₂³×M₁₆	1	1	yes	characteristic
252	C₂×C₇₃	C₂²×#131	1	1	yes	characteristic
253	D₇₃	C₂×#446	1	8	yes	direct product factor
254	C₂²×C₄×Q₈	—	73	1	no	—
255	C₂×#446	—	73	16	no	—
256	C₂×#446	—	73	1	no	—
257	C₂×#446	—	73	2	no	—
258	C₂×#446	—	73	2	no	—
259	C₂×#446	—	73	1	no	—
260	C₂×#446	—	73	1	no	—
261	C₂×#446	D₇₃	1	1	yes	characteristic, direct product factor
262	C₂²×C₄⋊C₈	—	73	2	no	—
263	C₂²×C₄⋊C₈	—	73	1	no	—
264	C₂²×#97	—	73	2	no	—
265	C₂²×C₄×C₈	—	73	1	no	—
266	C₇₃	C₂²×#446	1	1	yes	characteristic, complemented, Sylow
267	C₂³×Q₈	—	73	1	no	—
268	C₂³×C₈	—	73	1	no	—
269	C₂³×C₈	—	73	1	no	—
270	C₂³×C₈	—	73	2	no	—
271	C₂×C₄×Q₈	—	73	1	no	—
272	C₂×C₄×Q₈	—	73	8	no	—
273	C₂×C₄×Q₈	—	73	8	no	—
274	C₂×C₄×Q₈	—	73	2	no	—
275	C₂×C₄×Q₈	—	73	1	no	—
276	C₂×C₄×Q₈	—	73	2	no	—
277	C₂×C₄×Q₈	—	73	1	no	—
278	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	73	1	no	—
280	C₂²×C₄⋊C₄	—	73	2	no	—
281	C₂²×C₄²	—	73	1	no	—
282	C₂²×C₄²	—	73	2	no	—
283	#446	—	73	8	no	—
284	#446	—	73	8	no	—
285	#446	—	73	16	no	—
286	#446	—	73	16	no	—
287	#446	—	73	8	no	—
288	#446	C₂×D₇₃	1	8	yes	direct product factor
289	C₂×C₄⋊C₈	—	73	2	no	—
290	C₂×C₄⋊C₈	—	73	2	no	—
291	C₂×C₄⋊C₈	—	73	2	no	—
292	C₂×C₄⋊C₈	—	73	1	no	—
293	C₂×C₄⋊C₈	—	73	2	no	—
294	C₂×C₄⋊C₈	—	73	8	no	—
295	C₂×C₄⋊C₈	—	73	16	no	—
296	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂×D₇₃	1	2	yes	—
298	C₂×#97	—	73	2	no	—
299	C₂×#97	—	73	2	no	—
300	C₂×#97	—	73	2	no	—
301	C₂×#97	—	73	16	no	—
302	C₂×#97	C₂×D₇₃	1	2	yes	—
303	C₂×C₄×C₈	—	73	1	no	—
304	C₂×C₄×C₈	—	73	1	no	—
305	C₂×C₄×C₈	—	73	1	no	—
306	C₂×C₄×C₈	—	73	8	no	—
307	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
308	C₂²×Q₈	—	73	8	no	—
309	C₂²×Q₈	—	73	2	no	—
310	C₂²×Q₈	—	73	1	no	—
311	C₂²×Q₈	—	146	8	no	—
312	C₂²×Q₈	C₄×D₇₃	1	1	yes	characteristic
313	C₂³×C₄	—	73	1	no	—
314	C₂³×C₄	—	73	1	no	—
315	C₂³×C₄	—	73	1	no	—
316	C₂³×C₄	—	73	2	no	—
317	C₂³×C₄	—	73	2	no	—
318	C₂²×C₈	—	73	1	no	—
319	C₂²×C₈	—	73	8	no	—
320	C₂²×C₈	—	73	4	no	—
321	C₂²×C₈	—	73	1	no	—
322	C₂²×C₈	—	73	2	no	—
323	C₂²×C₈	—	73	4	no	—
324	C₂²×C₈	—	73	8	no	—
325	C₂²×C₈	—	146	4	no	—
326	C₂²×C₈	—	146	8	no	—
327	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
329	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₄×Q₈	—	73	8	no	—
331	C₄×Q₈	—	73	16	no	—
332	C₄×Q₈	—	73	8	no	—
333	C₄×Q₈	—	73	8	no	—
334	C₄×Q₈	—	73	4	no	—
335	C₄×Q₈	—	73	8	no	—
336	C₄×Q₈	—	73	4	no	—
337	C₄×Q₈	C₄×D₇₃	1	4	yes	—
338	C₄×Q₈	C₂²×D₇₃	1	4	yes	—
339	C₂×C₄⋊C₄	—	73	2	no	—
340	C₂×C₄⋊C₄	—	73	2	no	—
341	C₂×C₄⋊C₄	—	73	2	no	—
342	C₂×C₄⋊C₄	—	73	2	no	—
343	C₂×C₄⋊C₄	—	73	1	no	—
344	C₂×C₄⋊C₄	—	73	8	no	—
345	C₂×C₄⋊C₄	—	73	16	no	—
346	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
348	C₂×C₄²	—	73	1	no	—
349	C₂×C₄²	—	73	2	no	—
350	C₂×C₄²	—	73	1	no	—
351	C₂×C₄²	—	73	2	no	—
352	C₂×C₄²	—	73	1	no	—
353	C₂×C₄²	—	73	2	no	—
354	C₂×C₄²	—	73	4	no	—
355	C₂×C₄²	—	73	8	no	—
356	C₂×C₄²	—	73	4	no	—
357	C₂×C₄²	—	73	8	no	—
358	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
359	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
360	C₄⋊C₈	—	73	8	no	—
361	C₄⋊C₈	—	73	8	no	—
362	C₄⋊C₈	—	73	8	no	—
363	C₄⋊C₈	—	73	4	no	—
364	C₄⋊C₈	—	73	8	no	—
365	C₄⋊C₈	C₂²×D₇₃	1	4	yes	—
366	C₄⋊C₈	C₂²×D₇₃	1	8	yes	—
367	#97	—	73	8	no	—
368	#97	—	73	8	no	—
369	#97	—	73	8	no	—
370	#97	C₂²×D₇₃	1	8	yes	—
371	C₄×C₈	—	73	4	no	—
372	C₄×C₈	—	73	4	no	—
373	C₄×C₈	—	73	4	no	—
374	C₄×C₈	C₂²×D₇₃	1	4	yes	—
375	C₂⁴	—	73	1	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	73	8	no	—
378	C₂×Q₈	—	73	4	no	—
379	C₂×Q₈	—	146	8	no	—
380	C₂×Q₈	—	146	32	no	—
381	C₂×Q₈	—	146	4	no	—
382	C₂×Q₈	C₂×C₄×D₇₃	1	4	yes	—
383	C₂²×C₄	—	73	1	no	—
384	C₂²×C₄	—	73	1	no	—
385	C₂²×C₄	—	73	8	no	—
386	C₂²×C₄	—	73	2	no	—
387	C₂²×C₄	—	73	4	no	—
388	C₂²×C₄	—	73	4	no	—
389	C₂²×C₄	—	73	4	no	—
390	C₂²×C₄	—	73	2	no	—
391	C₂²×C₄	—	73	1	no	—
392	C₂²×C₄	—	73	2	no	—
393	C₂²×C₄	—	73	2	no	—
394	C₂²×C₄	—	73	4	no	—
395	C₂²×C₄	—	73	8	no	—
396	C₂²×C₄	—	73	8	no	—
397	C₂²×C₄	—	146	4	no	—
398	C₂²×C₄	—	146	8	no	—
399	C₂²×C₄	—	146	8	no	—
400	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
402	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
403	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	73	4	no	—
408	C₂×C₈	—	73	2	no	—
409	C₂×C₈	—	73	16	no	—
410	C₂×C₈	—	73	2	no	—
411	C₂×C₈	—	73	4	no	—
412	C₂×C₈	—	146	8	no	—
413	C₂×C₈	—	146	16	no	—
414	C₂×C₈	—	146	2	no	—
415	C₂×C₈	—	146	4	no	—
416	C₂×C₈	Q₈×D₇₃	1	4	yes	complemented
417	C₂×C₈	C₂³×D₇₃	1	2	yes	—
418	C₂×C₈	C₂³×D₇₃	1	4	yes	—
419	C₂×C₈	C₂³×D₇₃	1	2	yes	—
420	C₄⋊C₄	—	73	8	no	—
421	C₄⋊C₄	—	73	8	no	—
422	C₄⋊C₄	—	73	8	no	—
423	C₄⋊C₄	—	73	8	no	—
424	C₄⋊C₄	—	73	4	no	—
425	C₄⋊C₄	C₂×C₄×D₇₃	1	8	yes	—
426	C₄⋊C₄	C₂×C₄×D₇₃	1	4	yes	—
427	C₄²	—	73	4	no	—
428	C₄²	—	73	8	no	—
429	C₄²	—	73	4	no	—
430	C₄²	—	73	8	no	—
431	C₄²	—	73	2	no	—
432	C₄²	—	73	4	no	—
433	C₄²	—	73	2	no	—
434	C₄²	—	73	4	no	—
435	C₄²	C₂×C₄×D₇₃	1	4	yes	—
436	C₄²	C₂×C₄×D₇₃	1	2	yes	—
437	C₄²	C₂³×D₇₃	1	2	yes	—
438	C₄²	C₂³×D₇₃	1	4	yes	—
439	C₂³	—	73	2	no	—
440	C₂³	—	73	4	no	—
441	C₂³	—	73	4	no	—
442	C₂³	—	73	4	no	—
443	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
444	Q₈	—	2	8	no	—
445	Q₈	—	146	16	no	—
446	Q₈	—	146	8	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	73	2	no	—
451	C₂×C₄	—	73	2	no	—
452	C₂×C₄	—	73	4	no	—
453	C₂×C₄	—	73	4	no	—
454	C₂×C₄	—	73	4	no	—
455	C₂×C₄	—	73	4	no	—
456	C₂×C₄	—	73	8	no	—
457	C₂×C₄	—	73	16	no	—
458	C₂×C₄	—	73	2	no	—
459	C₂×C₄	—	73	4	no	—
460	C₂×C₄	—	73	4	no	—
461	C₂×C₄	—	146	16	no	—
462	C₂×C₄	—	146	8	no	—
463	C₂×C₄	—	146	16	no	—
464	C₂×C₄	—	146	4	no	—
465	C₂×C₄	—	146	2	no	—
466	C₂×C₄	—	146	4	no	—
467	C₂×C₄	M₁₆×D₇₃	1	4	yes	—
468	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
469	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
470	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
471	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
473	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
474	C₂×C₄	#41×D₇₃	1	2	yes	—
475	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₈	—	73	4	no	—
479	C₈	—	146	2	no	—
480	C₈	—	146	4	no	—
481	C₈	C₂×Q₈×D₇₃	1	4	yes	complemented
482	C₂²	—	73	4	no	—
483	C₂²	—	73	4	no	—
484	C₂²	—	73	4	no	—
485	C₂²	—	73	16	no	—
486	C₂²	C₄×Q₈×D₇₃	1	2	yes	—
487	C₂²	C₂×M₁₆×D₇₃	1	2	yes	—
488	C₂²	#131×D₇₃	1	2	yes	—
489	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
490	C₄	—	2	4	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	4	no	—
493	C₄	—	73	4	no	—
494	C₄	—	73	4	no	—
495	C₄	—	146	4	no	—
496	C₄	—	146	2	no	—
497	C₄	—	146	4	no	—
498	C₄	C₄×Q₈×D₇₃	1	2	yes	—
499	C₄	C₂×M₁₆×D₇₃	1	4	yes	—
500	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
501	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
502	C₂	—	73	8	no	—
503	C₂	#446×D₇₃	1	4	yes	direct product factor
504	C₂	C₂×C₄×Q₈×D₇₃	1	1	yes	characteristic
505	C₂	C₂²×M₁₆×D₇₃	1	1	yes	characteristic
506	C₂	C₂×#131×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×#446×C₇₃	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂×#446	D₇₃
hypocenter	C₇₃	C₂²×#446
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
2. C₂×#17988718	C₂	semidirect
3. C₂×#17988717	C₂	semidirect
4. C₂×#17988716	C₂	semidirect
5. C₂×#17988715	C₂	semidirect
6. C₂×#17988714	C₂	semidirect
7. #446×D₇₃	C₂	direct (N × H)
12. C₂×#446×C₇₃	C₂	semidirect
28. #17988718	C₂²	semidirect
29. #17988717	C₂²	semidirect
30. #17988716	C₂²	semidirect
31. #17988715	C₂²	semidirect
32. #17988714	C₂²	semidirect
49. #446×C₇₃	C₂²	semidirect
68. C₂×C₈×D₇₃	Q₈	semidirect
146. C₂×#10596831	C₂×Q₈	semidirect
152. C₈×D₇₃	C₂×Q₈	semidirect
175. C₂×C₈×C₇₃	C₂×Q₈	semidirect
224. C₈×C₇₃	C₂²×Q₈	semidirect
227. #10596831	C₂²×Q₈	semidirect
232. C₂×D₇₃	#446	direct (N × H)
249. C₂×C₇₃	C₂×#446	semidirect
253. D₇₃	C₂×#446	direct (N × H)
261. C₂×#446	D₇₃	direct (N × H)
266. C₇₃	C₂²×#446	semidirect
288. #446	C₂×D₇₃	direct (N × H)
416. C₂×C₈	Q₈×D₇₃	semidirect
481. C₈	C₂×Q₈×D₇₃	semidirect
503. C₂	#446×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
C₂×C₄×Q₈×D₇₃	2
C₂×#17988718	2
C₂×#17988717	2
C₂×#17988716	2
C₂×#17988715	2
C₂×#17988714	2
#446×D₇₃	2
C₂×C₄⋊C₈×D₇₃	2
C₂×#97×D₇₃	2
C₂×C₄×C₈×D₇₃	2
C₂×#446×C₇₃	2
C₂²×#446	73

Subgroups — C2×#446×D73 #33950337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#446×D₇₃ #33950337