Subgroups — C₂×C₇₃×#1484 #32926863

Order 18688.

1354 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1484	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄⋊C₈×C₇₃	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₇₃	—	2	1	no	—
7	C₂²×M₁₆×C₇₃	—	2	1	no	—
8	#532×C₇₃	—	2	2	no	—
9	#532×C₇₃	—	2	2	no	—
10	#532×C₇₃	C₄	1	4	yes	—
11	#532×C₇₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
13	C₂×#127×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#124×C₇₃	—	2	1	no	—
15	C₂×#121×C₇₃	—	2	1	no	—
16	C₂×#121×C₇₃	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₇₃	—	2	1	no	—
18	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	#431×C₇₃	—	2	2	no	—
21	#431×C₇₃	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₇₃	—	2	1	no	—
24	C₄×M₁₆×C₇₃	—	2	2	no	—
25	C₄×M₁₆×C₇₃	C₂²	1	4	yes	complemented
26	C₂×#97×C₇₃	—	2	1	no	—
27	C₂×C₄×C₈×C₇₃	—	2	1	no	—
28	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
29	D₄⋊C₈×C₇₃	C₂²	1	16	yes	complemented
30	C₂×#41×C₇₃	—	2	4	no	—
31	C₂×#41×C₇₃	—	2	4	no	—
32	C₂×#41×C₇₃	—	4	8	no	—
33	C₂²×Q₈×C₇₃	—	2	1	no	—
34	C₂²×D₄×C₇₃	—	2	2	no	—
35	C₂²×D₄×C₇₃	—	2	1	no	—
36	C₂²×D₄×C₇₃	—	2	1	no	—
37	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₇₃	—	2	2	no	—
39	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
42	C₂×M₁₆×C₇₃	—	2	8	no	—
43	C₂×M₁₆×C₇₃	—	2	4	no	—
44	C₂²×C₈×C₇₃	—	2	2	no	—
45	C₂²×C₈×C₇₃	—	2	2	no	—
46	C₄⋊Q₈×C₇₃	—	2	2	no	—
47	C₄⋊Q₈×C₇₃	C₂×C₄	1	4	yes	—
48	#127×C₇₃	—	2	2	no	—
49	#127×C₇₃	C₂×C₄	1	4	yes	—
50	#124×C₇₃	—	2	4	no	—
51	#124×C₇₃	—	2	4	no	—
52	#121×C₇₃	—	2	4	no	—
53	#121×C₇₃	—	2	4	no	—
54	#121×C₇₃	—	2	4	no	—
55	#121×C₇₃	C₂×C₄	1	8	yes	—
56	C₄×D₄×C₇₃	—	2	4	no	—
57	C₄×D₄×C₇₃	—	2	4	no	—
58	C₄×D₄×C₇₃	—	2	2	no	—
59	C₄×D₄×C₇₃	—	2	2	no	—
60	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
61	C₄×D₄×C₇₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
66	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₃	D₄	1	2	yes	—
70	C₂×C₄²×C₇₃	D₄	1	2	yes	—
71	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₇₃	—	2	2	no	—
75	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₇₃	—	2	4	no	—
77	#97×C₇₃	—	2	4	no	—
78	C₄×C₈×C₇₃	—	2	4	no	—
79	C₄×C₈×C₇₃	—	2	2	no	—
80	C₄×C₈×C₇₃	C₂³	1	4	yes	—
81	C₂⁴×C₇₃	—	2	2	no	—
82	C₂⁴×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
83	#41×C₇₃	—	4	16	no	—
84	#41×C₇₃	—	4	16	no	—
85	C₂×Q₈×C₇₃	—	2	4	no	—
86	C₂×Q₈×C₇₃	—	4	4	no	—
87	C₂×D₄×C₇₃	—	2	8	no	—
88	C₂×D₄×C₇₃	—	2	2	no	—
89	C₂×D₄×C₇₃	—	2	4	no	—
90	C₂×D₄×C₇₃	—	2	4	no	—
91	C₂×D₄×C₇₃	—	2	8	no	—
92	C₂×D₄×C₇₃	—	4	4	no	—
93	C₂×D₄×C₇₃	—	4	8	no	—
94	C₂×D₄×C₇₃	—	4	4	no	—
95	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₇₃	—	2	4	no	—
97	C₂²×C₄×C₇₃	—	2	4	no	—
98	C₂²×C₄×C₇₃	—	2	4	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	4	no	—
101	C₂²×C₄×C₇₃	—	2	4	no	—
102	C₂²×C₄×C₇₃	—	4	8	no	—
103	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	M₁₆×C₇₃	—	2	16	no	—
116	C₂×C₈×C₇₃	—	2	8	no	—
117	C₂×C₈×C₇₃	—	2	4	no	—
118	C₂×C₈×C₇₃	—	2	4	no	—
119	C₂×C₈×C₇₃	—	4	4	no	—
120	C₄⋊C₄×C₇₃	—	2	4	no	—
121	C₄⋊C₄×C₇₃	—	2	2	no	—
122	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₇₃	—	2	8	no	—
124	C₂²⋊C₄×C₇₃	—	2	4	no	—
125	C₂²⋊C₄×C₇₃	—	2	4	no	—
126	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
131	C₄²×C₇₃	C₂×D₄	1	2	yes	—
132	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₇₃	C₂×D₄	1	2	yes	—
134	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
136	C₂³×C₇₃	—	2	2	no	—
137	C₂³×C₇₃	—	2	2	no	—
138	C₂³×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	—	2	4	no	—
140	C₂³×C₇₃	—	4	4	no	—
141	C₂³×C₇₃	—	4	4	no	—
142	C₂³×C₇₃	—	4	4	no	—
143	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	Q₈×C₇₃	—	4	8	no	—
146	D₄×C₇₃	—	2	8	no	—
147	D₄×C₇₃	—	4	8	no	—
148	D₄×C₇₃	—	4	16	no	—
149	D₄×C₇₃	—	4	4	no	—
150	D₄×C₇₃	—	4	8	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	2	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	—	2	4	no	—
155	C₂×C₄×C₇₃	—	2	4	no	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	2	4	no	—
158	C₂×C₄×C₇₃	—	2	4	no	—
159	C₂×C₄×C₇₃	—	2	4	no	—
160	C₂×C₄×C₇₃	—	2	4	no	—
161	C₂×C₄×C₇₃	—	4	4	no	—
162	C₂×C₄×C₇₃	—	4	8	no	—
163	C₂×C₄×C₇₃	—	4	8	no	—
164	C₂×C₄×C₇₃	#104	1	4	yes	—
165	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₇₃	#131	1	4	yes	—
172	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
173	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₇₃	—	2	8	no	—
177	C₈×C₇₃	—	4	4	no	—
178	C₂²×C₇₃	—	2	2	no	—
179	C₂²×C₇₃	—	2	2	no	—
180	C₂²×C₇₃	—	2	2	no	—
181	C₂²×C₇₃	—	4	4	no	—
182	C₂²×C₇₃	—	4	4	no	—
183	C₂²×C₇₃	—	4	4	no	—
184	C₂²×C₇₃	—	4	4	no	—
185	C₂²×C₇₃	—	8	8	no	—
186	C₂²×C₇₃	#408	1	2	yes	—
187	C₂²×C₇₃	#418	1	2	yes	—
188	C₂²×C₇₃	C₂×#104	1	2	yes	—
189	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	2	1	no	—
193	C₄×C₇₃	—	2	1	no	—
194	C₄×C₇₃	—	4	4	no	—
195	C₄×C₇₃	#408	1	2	yes	—
196	C₄×C₇₃	#418	1	2	yes	—
197	C₄×C₇₃	C₂×#104	1	4	yes	—
198	C₄×C₇₃	C₂×#131	1	2	yes	—
199	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	C₂×#1484	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂×C₇₃	—	4	2	no	—
202	C₂×C₇₃	—	8	4	no	—
203	C₂×C₇₃	#1484	1	4	yes	direct product factor
204	C₂×C₇₃	C₂×#408	1	1	yes	characteristic
205	C₂×C₇₃	C₂×#418	1	1	yes	characteristic
206	C₂×C₇₃	C₂²×#104	1	1	yes	characteristic
207	C₂×#532	C₂×C₇₃	1	1	yes	characteristic
208	C₂×#431	C₂×C₇₃	1	1	yes	characteristic, complemented
209	C₂×C₄×M₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
210	#1484	C₂×C₇₃	1	8	yes	direct product factor
211	C₂×D₄⋊C₈	C₂×C₇₃	1	4	yes	complemented
212	C₇₃	C₂×#1484	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²×#41	—	2	1	no	—
214	C₂²×M₁₆	—	2	1	no	—
215	#532	—	2	2	no	—
216	#532	—	2	2	no	—
217	#532	C₄×C₇₃	1	4	yes	—
218	#532	C₂²×C₇₃	1	4	yes	—
219	C₂×C₄⋊Q₈	C₄×C₇₃	1	1	yes	characteristic
220	C₂×#127	C₄×C₇₃	1	1	yes	characteristic
221	C₂×#124	—	2	1	no	—
222	C₂×#121	—	2	1	no	—
223	C₂×#121	C₄×C₇₃	1	2	yes	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
226	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
227	#431	—	2	2	no	—
228	#431	C₂²×C₇₃	1	4	yes	complemented
229	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
230	C₂×C₂²⋊C₈	—	2	1	no	—
231	C₄×M₁₆	—	2	2	no	—
232	C₄×M₁₆	C₂²×C₇₃	1	4	yes	complemented
233	C₂×#97	—	2	1	no	—
234	C₂×C₄×C₈	—	2	1	no	—
235	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
236	D₄⋊C₈	C₂²×C₇₃	1	16	yes	complemented
237	C₂×#41	—	2	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	4	8	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
249	C₂×M₁₆	—	2	8	no	—
250	C₂×M₁₆	—	2	4	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	C₂×C₄×C₇₃	1	4	yes	—
255	#127	—	2	2	no	—
256	#127	C₂×C₄×C₇₃	1	4	yes	—
257	#124	—	2	4	no	—
258	#124	—	2	4	no	—
259	#121	—	2	4	no	—
260	#121	—	2	4	no	—
261	#121	—	2	4	no	—
262	#121	C₂×C₄×C₇₃	1	8	yes	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	C₂×C₄×C₇₃	1	4	yes	—
268	C₄×D₄	C₂³×C₇₃	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
275	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₇₃	1	2	yes	—
278	C₂×C₄²	D₄×C₇₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
283	C₂²⋊C₈	—	2	4	no	—
284	#97	—	2	4	no	—
285	C₄×C₈	—	2	4	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	C₂³×C₇₃	1	4	yes	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
290	#41	—	4	16	no	—
291	#41	—	4	16	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	4	8	no	—
310	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
313	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
322	M₁₆	—	2	16	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	4	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	C₂²×C₄×C₇₃	1	4	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
334	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
335	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
336	C₄²	C₂²×C₄×C₇₃	1	1	yes	characteristic
337	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
338	C₄²	C₂×D₄×C₇₃	1	2	yes	—
339	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₇₃	1	2	yes	—
341	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
342	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
351	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
352	Q₈	—	4	8	no	—
353	D₄	—	2	8	no	—
354	D₄	—	4	8	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	#104×C₇₃	1	4	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
378	C₂×C₄	#131×C₇₃	1	4	yes	—
379	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
380	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
383	C₈	—	2	8	no	—
384	C₈	—	4	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	8	8	no	—
393	C₂²	#408×C₇₃	1	2	yes	—
394	C₂²	#418×C₇₃	1	2	yes	—
395	C₂²	C₂×#104×C₇₃	1	2	yes	—
396	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	4	no	—
402	C₄	#408×C₇₃	1	2	yes	—
403	C₄	#418×C₇₃	1	2	yes	—
404	C₄	C₂×#104×C₇₃	1	4	yes	—
405	C₄	C₂×#131×C₇₃	1	2	yes	—
406	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	—	8	4	no	—
409	C₂	C₇₃×#1484	1	4	yes	direct product factor
410	C₂	C₂×#408×C₇₃	1	1	yes	characteristic
411	C₂	C₂×#418×C₇₃	1	1	yes	characteristic
412	C₂	C₂²×#104×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₄²	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₇₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₇₃	C₂	semidirect
3. C₂×C₄×M₁₆×C₇₃	C₂	semidirect
4. C₇₃×#1484	C₂	direct (N × H)
5. C₂×D₄⋊C₈×C₇₃	C₂	semidirect
21. #431×C₇₃	C₂²	semidirect
25. C₄×M₁₆×C₇₃	C₂²	semidirect
29. D₄⋊C₈×C₇₃	C₂²	semidirect
200. C₂×#1484	C₇₃	direct (N × H)
203. C₂×C₇₃	#1484	direct (N × H)
208. C₂×#431	C₂×C₇₃	semidirect
209. C₂×C₄×M₁₆	C₂×C₇₃	semidirect
210. #1484	C₂×C₇₃	direct (N × H)
211. C₂×D₄⋊C₈	C₂×C₇₃	semidirect
212. C₇₃	C₂×#1484	direct (N × H)
228. #431	C₂²×C₇₃	semidirect
232. C₄×M₁₆	C₂²×C₇₃	semidirect
236. D₄⋊C₈	C₂²×C₇₃	semidirect
409. C₂	C₇₃×#1484	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×#532×C₇₃	2
C₂×#431×C₇₃	2
C₂×C₄×M₁₆×C₇₃	2
C₇₃×#1484	2
C₂×D₄⋊C₈×C₇₃	2
C₂×#1484	73

Subgroups — C2×C73×#1484 #32926863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#1484 #32926863