Subgroups — C₇₃×#59823 #32969227

Order 18688.

2388 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2732	C₂	1	4	yes	maximal, complemented
3	C₇₃×#2552	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2542	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2538	C₂	1	4	yes	maximal, complemented
6	C₇₃×#2538	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2454	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2417	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2366	C₂	1	2	yes	maximal
10	D₄×C₄⋊C₄×C₇₃	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic
14	#554×C₇₃	—	2	16	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#125×C₇₃	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	8	yes	—
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₇₃	C₂²	1	4	yes	—
30	#399×C₇₃	C₂²	1	8	yes	—
31	#398×C₇₃	C₂²	1	8	yes	—
32	#396×C₇₃	C₂²	1	8	yes	—
33	#396×C₇₃	C₂²	1	8	yes	—
34	#391×C₇₃	C₂²	1	2	yes	—
35	#391×C₇₃	C₂²	1	2	yes	—
36	#390×C₇₃	C₂²	1	2	yes	—
37	#390×C₇₃	C₂²	1	4	yes	—
38	#390×C₇₃	C₂²	1	2	yes	—
39	#390×C₇₃	C₂²	1	2	yes	—
40	#390×C₇₃	C₂²	1	4	yes	—
41	#389×C₇₃	C₂²	1	2	yes	—
42	#389×C₇₃	C₂²	1	4	yes	—
43	#389×C₇₃	C₂²	1	2	yes	—
44	#389×C₇₃	C₂²	1	2	yes	—
45	#389×C₇₃	C₂²	1	4	yes	—
46	#389×C₇₃	C₂²	1	2	yes	—
47	#386×C₇₃	C₂²	1	8	yes	—
48	#385×C₇₃	C₂²	1	8	yes	—
49	#384×C₇₃	C₂²	1	1	yes	characteristic
50	#384×C₇₃	C₂²	1	4	yes	—
51	#384×C₇₃	C₂²	1	1	yes	characteristic
52	#384×C₇₃	C₂²	1	1	yes	characteristic
53	#380×C₇₃	C₂²	1	8	yes	—
54	#380×C₇₃	C₂²	1	4	yes	—
55	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
59	C₄³×C₇₃	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
61	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
67	C₄⋊Q₈×C₇₃	—	2	4	no	—
68	C₄⋊Q₈×C₇₃	D₄	1	8	yes	complemented
69	#127×C₇₃	Q₈	1	8	yes	complemented
70	#125×C₇₃	—	2	16	no	—
71	C₂²⋊Q₈×C₇₃	—	2	32	no	—
72	C₂²⋊Q₈×C₇₃	—	2	16	no	—
73	C₂²⋊Q₈×C₇₃	—	4	8	no	—
74	C₄×Q₈×C₇₃	—	2	8	no	—
75	C₄×Q₈×C₇₃	—	4	4	no	—
76	C₄×D₄×C₇₃	—	2	16	no	—
77	C₄×D₄×C₇₃	—	2	8	no	—
78	C₄×D₄×C₇₃	—	2	8	no	—
79	C₄×D₄×C₇₃	—	4	8	no	—
80	C₄×D₄×C₇₃	—	4	4	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	16	no	—
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
106	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
109	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
115	#95×C₇₃	C₂³	1	4	yes	—
116	#95×C₇₃	C₂³	1	4	yes	—
117	#95×C₇₃	C₂³	1	4	yes	—
118	#95×C₇₃	C₂³	1	4	yes	—
119	#95×C₇₃	C₂³	1	8	yes	—
120	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
121	C₂×Q₈×C₇₃	—	2	4	no	—
122	C₂×Q₈×C₇₃	—	2	4	no	—
123	C₂×Q₈×C₇₃	—	2	4	no	—
124	C₂×Q₈×C₇₃	—	4	2	no	—
125	C₂×Q₈×C₇₃	—	4	2	no	—
126	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
127	C₂×D₄×C₇₃	—	2	4	no	—
128	C₂×D₄×C₇₃	—	2	4	no	—
129	C₂×D₄×C₇₃	—	2	4	no	—
130	C₂×D₄×C₇₃	—	2	4	no	—
131	C₂×D₄×C₇₃	—	4	2	no	—
132	C₂×D₄×C₇₃	—	4	2	no	—
133	C₂×D₄×C₇₃	C₂×Q₈	1	8	yes	—
134	C₂×D₄×C₇₃	C₂×Q₈	1	8	yes	—
135	C₂×D₄×C₇₃	C₂×Q₈	1	8	yes	—
136	C₂²×C₄×C₇₃	—	2	8	no	—
137	C₂²×C₄×C₇₃	—	2	8	no	—
138	C₂²×C₄×C₇₃	—	2	8	no	—
139	C₂²×C₄×C₇₃	—	2	16	no	—
140	C₂²×C₄×C₇₃	—	4	8	no	—
141	C₂²×C₄×C₇₃	—	4	8	no	—
142	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₇₃	—	2	4	no	—
155	C₄⋊C₄×C₇₃	—	2	16	no	—
156	C₄⋊C₄×C₇₃	—	2	4	no	—
157	C₄⋊C₄×C₇₃	—	2	8	no	—
158	C₄⋊C₄×C₇₃	—	2	16	no	—
159	C₄⋊C₄×C₇₃	—	2	4	no	—
160	C₄⋊C₄×C₇₃	—	2	4	no	—
161	C₄⋊C₄×C₇₃	—	2	4	no	—
162	C₄⋊C₄×C₇₃	—	2	4	no	—
163	C₄⋊C₄×C₇₃	—	2	4	no	—
164	C₄⋊C₄×C₇₃	—	2	4	no	—
165	C₄⋊C₄×C₇₃	—	4	2	no	—
166	C₄⋊C₄×C₇₃	—	4	2	no	—
167	C₄⋊C₄×C₇₃	—	4	2	no	—
168	C₄⋊C₄×C₇₃	—	4	4	no	—
169	C₄⋊C₄×C₇₃	—	4	8	no	—
170	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
171	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
172	C₂²⋊C₄×C₇₃	—	2	16	no	—
173	C₂²⋊C₄×C₇₃	—	2	8	no	—
174	C₂²⋊C₄×C₇₃	—	2	8	no	—
175	C₂²⋊C₄×C₇₃	—	4	4	no	—
176	C₂²⋊C₄×C₇₃	—	4	8	no	—
177	C₂²⋊C₄×C₇₃	—	4	8	no	—
178	C₄²×C₇₃	—	2	8	no	—
179	C₄²×C₇₃	—	2	2	no	—
180	C₄²×C₇₃	—	2	8	no	—
181	C₄²×C₇₃	—	2	2	no	—
182	C₄²×C₇₃	—	2	2	no	—
183	C₄²×C₇₃	—	4	1	no	—
184	C₄²×C₇₃	C₂×D₄	1	4	yes	—
185	C₄²×C₇₃	C₂×Q₈	1	4	yes	—
186	C₄²×C₇₃	#41	1	4	yes	—
187	C₂³×C₇₃	—	2	4	no	—
188	C₂³×C₇₃	—	2	4	no	—
189	C₂³×C₇₃	—	2	4	no	—
190	C₂³×C₇₃	—	2	4	no	—
191	C₂³×C₇₃	—	2	4	no	—
192	C₂³×C₇₃	—	2	4	no	—
193	C₂³×C₇₃	C₂²×Q₈	1	8	yes	—
194	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
195	Q₈×C₇₃	—	4	8	no	—
196	Q₈×C₇₃	—	4	8	no	—
197	D₄×C₇₃	—	2	16	no	—
198	D₄×C₇₃	—	2	16	no	—
199	D₄×C₇₃	—	4	8	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	2	4	no	—
210	C₂×C₄×C₇₃	—	2	4	no	—
211	C₂×C₄×C₇₃	—	2	4	no	—
212	C₂×C₄×C₇₃	—	2	4	no	—
213	C₂×C₄×C₇₃	—	2	1	no	—
214	C₂×C₄×C₇₃	—	2	4	no	—
215	C₂×C₄×C₇₃	—	2	1	no	—
216	C₂×C₄×C₇₃	—	2	4	no	—
217	C₂×C₄×C₇₃	—	2	4	no	—
218	C₂×C₄×C₇₃	—	2	4	no	—
219	C₂×C₄×C₇₃	—	2	4	no	—
220	C₂×C₄×C₇₃	—	2	1	no	—
221	C₂×C₄×C₇₃	—	2	4	no	—
222	C₂×C₄×C₇₃	—	2	4	no	—
223	C₂×C₄×C₇₃	—	4	16	no	—
224	C₂×C₄×C₇₃	—	8	16	no	—
225	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
227	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
230	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
231	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
232	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
233	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
234	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
236	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
238	C₂²×C₇₃	—	2	8	no	—
239	C₂²×C₇₃	—	2	8	no	—
240	C₂²×C₇₃	—	2	8	no	—
241	C₂²×C₇₃	—	4	4	no	—
242	C₂²×C₇₃	—	4	4	no	—
243	C₂²×C₇₃	—	4	4	no	—
244	C₂²×C₇₃	—	4	4	no	—
245	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
246	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
247	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
248	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
249	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	C₂²×C₇₃	#585	1	1	yes	characteristic
252	C₄×C₇₃	—	2	8	no	—
253	C₄×C₇₃	—	2	2	no	—
254	C₄×C₇₃	—	2	2	no	—
255	C₄×C₇₃	—	2	2	no	—
256	C₄×C₇₃	—	4	4	no	—
257	C₄×C₇₃	—	4	4	no	—
258	C₄×C₇₃	—	4	4	no	—
259	C₄×C₇₃	—	4	1	no	—
260	C₄×C₇₃	—	4	4	no	—
261	C₄×C₇₃	D₄×Q₈	1	4	yes	—
262	C₄×C₇₃	#550	1	4	yes	—
263	C₄×C₇₃	#554	1	4	yes	complemented
264	#59823	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂×C₇₃	—	4	8	no	—
266	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
267	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
268	C₂×C₇₃	C₂×#554	1	1	yes	characteristic
269	C₂×C₇₃	#3496	1	1	yes	characteristic
270	C₂×C₇₃	#3501	1	1	yes	characteristic
271	C₂×C₇₃	#3507	1	1	yes	characteristic
272	C₂×C₇₃	#3548	1	1	yes	characteristic
273	C₂×#554	C₂×C₇₃	1	2	yes	complemented
274	#2732	C₂×C₇₃	1	4	yes	complemented
275	#2552	C₂×C₇₃	1	2	yes	complemented
276	#2542	C₂×C₇₃	1	2	yes	complemented
277	#2538	C₂×C₇₃	1	2	yes	complemented
278	#2538	C₂×C₇₃	1	4	yes	complemented
279	#2454	C₂×C₇₃	1	4	yes	complemented
280	#2417	C₂×C₇₃	1	4	yes	complemented
281	#2366	C₂×C₇₃	1	2	yes	—
282	D₄×C₄⋊C₄	C₂×C₇₃	1	2	yes	complemented
283	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
284	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
285	C₄×#127	C₂×C₇₃	1	1	yes	characteristic
286	C₇₃	#59823	1	1	yes	characteristic, direct product factor, Sylow
287	#554	—	2	16	no	—
288	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×#125	C₂²×C₇₃	1	4	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	8	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
295	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
300	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
301	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
302	C₂²×C₄⋊C₄	C₂²×C₇₃	1	4	yes	—
303	#399	C₂²×C₇₃	1	8	yes	—
304	#398	C₂²×C₇₃	1	8	yes	—
305	#396	C₂²×C₇₃	1	8	yes	—
306	#396	C₂²×C₇₃	1	8	yes	—
307	#391	C₂²×C₇₃	1	2	yes	—
308	#391	C₂²×C₇₃	1	2	yes	—
309	#390	C₂²×C₇₃	1	2	yes	—
310	#390	C₂²×C₇₃	1	2	yes	—
311	#390	C₂²×C₇₃	1	2	yes	—
312	#390	C₂²×C₇₃	1	4	yes	—
313	#390	C₂²×C₇₃	1	4	yes	—
314	#389	C₂²×C₇₃	1	2	yes	—
315	#389	C₂²×C₇₃	1	2	yes	—
316	#389	C₂²×C₇₃	1	2	yes	—
317	#389	C₂²×C₇₃	1	2	yes	—
318	#389	C₂²×C₇₃	1	4	yes	—
319	#389	C₂²×C₇₃	1	4	yes	—
320	#386	C₂²×C₇₃	1	8	yes	—
321	#385	C₂²×C₇₃	1	8	yes	—
322	#384	C₂²×C₇₃	1	1	yes	characteristic
323	#384	C₂²×C₇₃	1	1	yes	characteristic
324	#384	C₂²×C₇₃	1	1	yes	characteristic
325	#384	C₂²×C₇₃	1	4	yes	—
326	#380	C₂²×C₇₃	1	4	yes	—
327	#380	C₂²×C₇₃	1	8	yes	—
328	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
331	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
332	C₄³	C₂²×C₇₃	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
334	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
335	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
336	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
337	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
339	C₂³×C₄	C₂³×C₇₃	1	8	yes	—
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	D₄×C₇₃	1	8	yes	complemented
342	#127	Q₈×C₇₃	1	8	yes	complemented
343	#125	—	2	16	no	—
344	C₂²⋊Q₈	—	2	32	no	—
345	C₂²⋊Q₈	—	2	16	no	—
346	C₂²⋊Q₈	—	4	8	no	—
347	C₄×Q₈	—	2	8	no	—
348	C₄×Q₈	—	4	4	no	—
349	C₄×D₄	—	2	16	no	—
350	C₄×D₄	—	2	8	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	4	8	no	—
353	C₄×D₄	—	4	4	no	—
354	C₂×C₄⋊C₄	—	2	16	no	—
355	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
357	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
370	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
379	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
381	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
382	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
388	#95	C₂³×C₇₃	1	4	yes	—
389	#95	C₂³×C₇₃	1	4	yes	—
390	#95	C₂³×C₇₃	1	4	yes	—
391	#95	C₂³×C₇₃	1	4	yes	—
392	#95	C₂³×C₇₃	1	8	yes	—
393	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	C₂×Q₈×C₇₃	1	8	yes	—
407	C₂×D₄	C₂×Q₈×C₇₃	1	8	yes	—
408	C₂×D₄	C₂×Q₈×C₇₃	1	8	yes	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	16	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	16	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	—	4	8	no	—
443	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
444	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₂²⋊C₄	—	4	8	no	—
451	C₄²	—	2	8	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	4	1	no	—
457	C₄²	C₂×D₄×C₇₃	1	4	yes	—
458	C₄²	C₂×Q₈×C₇₃	1	4	yes	—
459	C₄²	#41×C₇₃	1	4	yes	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	C₂²×Q₈×C₇₃	1	8	yes	—
467	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
468	Q₈	—	4	8	no	—
469	Q₈	—	4	8	no	—
470	D₄	—	2	16	no	—
471	D₄	—	2	16	no	—
472	D₄	—	4	8	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	4	16	no	—
497	C₂×C₄	—	8	16	no	—
498	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
500	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
502	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
503	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
504	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
505	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
506	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
507	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
508	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
509	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
510	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	8	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
519	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
520	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
521	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
522	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
523	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
524	C₂²	#585×C₇₃	1	1	yes	characteristic
525	C₄	—	2	8	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	4	no	—
534	C₄	D₄×Q₈×C₇₃	1	4	yes	—
535	C₄	#550×C₇₃	1	4	yes	—
536	C₄	#554×C₇₃	1	4	yes	complemented
537	C₂	—	4	8	no	—
538	C₂	C₂×D₄×Q₈×C₇₃	1	1	yes	characteristic
539	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
540	C₂	C₂×#554×C₇₃	1	1	yes	characteristic
541	C₂	C₇₃×#3496	1	1	yes	characteristic
542	C₂	C₇₃×#3501	1	1	yes	characteristic
543	C₂	C₇₃×#3507	1	1	yes	characteristic
544	C₂	C₇₃×#3548	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₇₃	C₂	semidirect
2. C₇₃×#2732	C₂	semidirect
3. C₇₃×#2552	C₂	semidirect
4. C₇₃×#2542	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2538	C₂	semidirect
7. C₇₃×#2454	C₂	semidirect
8. C₇₃×#2417	C₂	semidirect
10. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
11. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
12. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
68. C₄⋊Q₈×C₇₃	D₄	semidirect
69. #127×C₇₃	Q₈	semidirect
263. C₄×C₇₃	#554	semidirect
264. #59823	C₇₃	direct (N × H)
273. C₂×#554	C₂×C₇₃	semidirect
274. #2732	C₂×C₇₃	semidirect
275. #2552	C₂×C₇₃	semidirect
276. #2542	C₂×C₇₃	semidirect
277. #2538	C₂×C₇₃	semidirect
278. #2538	C₂×C₇₃	semidirect
279. #2454	C₂×C₇₃	semidirect
280. #2417	C₂×C₇₃	semidirect
282. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
283. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
284. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
286. C₇₃	#59823	direct (N × H)
341. C₄⋊Q₈	D₄×C₇₃	semidirect
342. #127	Q₈×C₇₃	semidirect
536. C₄	#554×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₇₃	2
C₇₃×#2732	2
C₇₃×#2552	2
C₇₃×#2542	2
C₇₃×#2538	2
C₇₃×#2454	2
C₇₃×#2417	2
C₇₃×#2366	2
D₄×C₄⋊C₄×C₇₃	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
#59823	73

Subgroups — C73×#59823 #32969227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59823 #32969227