Subgroups — #405×Dic₇₃ #33083321

Order 18688.

1526 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988545	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988543	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988542	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	#117×Dic₇₃	C₂	1	1	yes	maximal, characteristic
7	#22609619	C₂	1	2	yes	maximal, complemented
8	#22609617	C₂	1	2	yes	maximal, complemented
9	#97×Dic₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₇₃	C₂	1	2	yes	maximal, complemented
11	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11924012	C₂²	1	1	yes	characteristic
13	C₂³×#10596831	C₂²	1	1	yes	characteristic
14	C₂×#14556550	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
16	#17988545	C₄	1	8	yes	complemented
17	#17988543	C₄	1	8	yes	complemented
18	#17988542	C₄	1	8	yes	complemented
19	M₁₆×Dic₇₃	C₄	1	8	yes	complemented
20	C₂×#14556502	C₂²	1	2	yes	—
21	C₂×#14556501	C₂²	1	2	yes	—
22	C₂×#14556501	C₂²	1	2	yes	—
23	C₂×#14556501	C₂²	1	2	yes	—
24	C₂×C₄×#10596831	C₂²	1	2	yes	—
25	C₂×C₈×Dic₇₃	C₄	1	8	yes	complemented
26	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
28	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
32	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
33	C₄⋊C₄×Dic₇₃	C₄	1	4	yes	—
34	C₂²⋊C₄×Dic₇₃	C₄	1	4	yes	—
35	#17988433	C₂²	1	2	yes	—
36	C₄²×Dic₇₃	C₂²	1	2	yes	—
37	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
40	#405×C₇₃	C₄	1	8	yes	complemented
41	C₂×#97×C₇₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
43	C₂³×Dic₇₃	C₂×C₄	1	2	yes	—
44	C₂×#11924012	C₂×C₄	1	4	yes	—
45	C₂×#11924012	C₂×C₄	1	4	yes	—
46	C₂×#11924012	C₂×C₄	1	4	yes	—
47	C₂²×#10596831	C₂×C₄	1	4	yes	—
48	C₂²×#10596831	C₂×C₄	1	4	yes	—
49	C₂²×#10596831	C₂×C₄	1	4	yes	—
50	C₂²×#10596831	C₂³	1	1	yes	characteristic
51	C₂²×#10596831	C₂³	1	2	yes	—
52	C₂²×#10596831	C₂³	1	1	yes	characteristic
53	#14556550	C₂×C₄	1	4	yes	—
54	#14556550	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₇₃	C₂×C₄	1	8	yes	—
58	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
63	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
64	#14556502	C₂×C₄	1	8	yes	complemented
65	#14556501	C₂×C₄	1	8	yes	—
66	#14556501	C₂×C₄	1	8	yes	complemented
67	#14556501	C₂×C₄	1	8	yes	complemented
68	C₄×#10596831	C₂×C₄	1	8	yes	complemented
69	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
70	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
71	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
72	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
73	C₈×Dic₇₃	C₂×C₄	1	8	yes	—
74	C₈×Dic₇₃	C₂×C₄	1	8	yes	complemented
75	C₈×Dic₇₃	C₂×C₄	1	8	yes	complemented
76	#14556498	C₂×C₄	1	8	yes	—
77	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
79	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
80	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
81	C₂²×C₈×C₇₃	C₂×C₄	1	4	yes	—
82	C₂²×C₈×C₇₃	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₇₃	C₂×C₄	1	4	yes	—
84	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
85	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
87	#117×C₇₃	C₂×C₄	1	4	yes	—
88	#117×C₇₃	C₂×C₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
92	#97×C₇₃	C₂×C₄	1	8	yes	complemented
93	C₄×C₈×C₇₃	C₂×C₄	1	8	yes	complemented
94	C₂²×Dic₇₃	—	2	8	no	—
95	C₂²×Dic₇₃	C₄²	1	8	yes	—
96	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₇₃	C₂²×C₄	1	4	yes	—
98	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
99	#11924012	C₄²	1	16	yes	complemented
100	C₂×#10596831	C₄²	1	16	yes	complemented
101	C₂×#10596831	C₂²×C₄	1	2	yes	—
102	C₂×#10596831	C₂²×C₄	1	2	yes	—
103	C₂×#10596831	C₂²×C₄	1	4	yes	—
104	C₂×#10596831	C₂²×C₄	1	2	yes	—
105	C₂×#10596831	C₂²×C₄	1	4	yes	—
106	C₂×#10596831	C₂²×C₄	1	2	yes	—
107	C₂×#10596831	C₂²×C₄	1	4	yes	—
108	C₂×#10596831	C₂²×C₄	1	2	yes	—
109	C₂×#10596831	C₂²×C₄	1	2	yes	—
110	C₄⋊Dic₇₃	C₄²	1	8	yes	—
111	C₂²⋊Dic₇₃	C₄²	1	8	yes	—
112	C₄×Dic₇₃	—	2	16	no	—
113	C₄×Dic₇₃	C₄²	1	8	yes	—
114	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
115	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
116	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
117	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
118	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
119	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
120	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₇₃	C₄²	1	16	yes	complemented
131	C₂×C₈×C₇₃	C₄²	1	16	yes	complemented
132	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
140	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₄²	1	8	yes	—
142	C₂²⋊C₄×C₇₃	C₄²	1	8	yes	—
143	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
144	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
145	C₂³×C₇₃	—	2	4	no	—
146	C₂³×C₇₃	C₂×C₄²	1	2	yes	—
147	C₂³×C₇₃	C₂×C₄²	1	2	yes	—
148	C₂³×C₇₃	C₂×C₄²	1	2	yes	—
149	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₃	—	2	8	no	—
151	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
154	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
155	C₂×C₄×C₇₃	C₂×C₄²	1	8	yes	—
156	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
158	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×Dic₇₃	—	2	8	no	—
166	C₂×Dic₇₃	—	2	4	no	—
167	C₂×Dic₇₃	—	2	16	no	—
168	C₂×Dic₇₃	C₂×C₄²	1	4	yes	—
169	C₂×Dic₇₃	C₂×C₄²	1	8	yes	—
170	C₂×Dic₇₃	C₂×C₄²	1	4	yes	—
171	C₂×Dic₇₃	#131	1	8	yes	—
172	C₈×C₇₃	C₂×C₄²	1	4	yes	—
173	C₈×C₇₃	C₂×C₄²	1	4	yes	—
174	C₈×C₇₃	C₂×C₄²	1	8	yes	—
175	#10596831	C₂×C₄²	1	4	yes	—
176	#10596831	C₂×C₄²	1	4	yes	—
177	#10596831	C₂×C₄²	1	8	yes	—
178	C₂²×C₇₃	—	2	4	no	—
179	C₂²×C₇₃	—	2	4	no	—
180	C₂²×C₇₃	—	2	4	no	—
181	C₂²×C₇₃	C₄³	1	4	yes	—
182	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
184	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
185	C₂²×C₇₃	C₂×#131	1	4	yes	—
186	C₄×C₇₃	—	2	8	no	—
187	C₄×C₇₃	C₄³	1	4	yes	—
188	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
189	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
192	Dic₇₃	—	2	4	no	—
193	Dic₇₃	—	2	8	no	—
194	Dic₇₃	#405	1	8	yes	direct product factor
195	C₄×#405	—	73	1	no	maximal, Sylow
196	C₂×C₇₃	—	2	4	no	—
197	C₂×C₇₃	C₂×C₄³	1	1	yes	characteristic
198	C₂×C₇₃	C₂×#405	1	2	yes	—
199	C₂×C₇₃	C₄×#131	1	2	yes	—
200	C₂×C₇₃	C₄×#131	1	2	yes	—
201	C₂×#405	—	73	1	no	—
202	C₂×#405	—	73	1	no	—
203	C₂×#405	—	73	1	no	—
204	C₂×#405	D₇₃	1	1	yes	characteristic
205	C₂×C₄×M₁₆	—	73	1	no	—
206	C₂²×C₄×C₈	—	73	1	no	—
207	C₄×#117	—	73	1	no	—
208	#1726	—	73	2	no	—
209	#1726	—	73	2	no	—
210	C₄×#97	—	73	2	no	—
211	C₄²×C₈	—	73	2	no	—
212	C₇₃	C₄×#405	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	73	1	no	—
214	C₂²×M₁₆	C₂×D₇₃	1	1	yes	characteristic
215	C₂³×C₈	—	73	1	no	—
216	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
217	C₂×#117	—	73	1	no	—
218	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
219	C₂²×C₄²	—	73	1	no	—
220	#405	—	73	8	no	—
221	#405	—	73	8	no	—
222	#405	—	73	8	no	—
223	#405	Dic₇₃	1	8	yes	direct product factor
224	C₄×M₁₆	—	73	8	no	—
225	C₂×#97	—	73	2	no	—
226	C₂×#97	—	73	2	no	—
227	C₂×#97	—	73	2	no	—
228	C₂×#97	—	73	2	no	—
229	C₂×#97	C₂×D₇₃	1	2	yes	—
230	C₂×C₄×C₈	—	73	8	no	—
231	C₂×C₄×C₈	—	73	1	no	—
232	C₂×C₄×C₈	—	73	1	no	—
233	C₂×C₄×C₈	—	73	2	no	—
234	C₂×C₄×C₈	—	73	2	no	—
235	C₂×C₄×C₈	—	73	1	no	—
236	C₂×C₄×C₈	—	73	1	no	—
237	C₂×C₄×C₈	—	73	2	no	—
238	C₂×C₄×C₈	—	73	2	no	—
239	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
240	C₄×C₄⋊C₄	—	73	4	no	—
241	C₄×C₂²⋊C₄	—	73	4	no	—
242	#376	—	73	2	no	—
243	C₄³	—	73	2	no	—
244	C₂³×C₄	—	73	2	no	—
245	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
246	C₂×M₁₆	—	73	4	no	—
247	C₂×M₁₆	—	73	4	no	—
248	C₂×M₁₆	—	73	4	no	—
249	C₂×M₁₆	C₄×D₇₃	1	4	yes	—
250	C₂×M₁₆	C₄×D₇₃	1	4	yes	—
251	C₂×M₁₆	C₂×Dic₇₃	1	4	yes	—
252	C₂²×C₈	—	73	4	no	—
253	C₂²×C₈	—	73	4	no	—
254	C₂²×C₈	—	73	4	no	—
255	C₂²×C₈	—	73	1	no	—
256	C₂²×C₈	—	73	1	no	—
257	C₂²×C₈	—	73	2	no	—
258	C₂²×C₈	C₄×D₇₃	1	4	yes	—
259	C₂²×C₈	C₄×D₇₃	1	4	yes	—
260	C₂²×C₈	C₂×Dic₇₃	1	4	yes	—
261	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
263	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
264	#117	—	73	4	no	—
265	#117	—	73	4	no	—
266	#117	C₄×D₇₃	1	4	yes	—
267	#117	C₂×Dic₇₃	1	4	yes	—
268	C₂×C₄⋊C₄	—	73	2	no	—
269	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
270	C₂×C₂²⋊C₄	—	73	2	no	—
271	C₂×C₂²⋊C₄	C₄×D₇₃	1	2	yes	—
272	C₂×C₄²	—	73	2	no	—
273	C₂×C₄²	—	73	4	no	—
274	C₂×C₄²	—	73	4	no	—
275	C₂×C₄²	—	73	2	no	—
276	C₂×C₄²	—	73	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	8	no	—
279	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
280	#97	—	73	8	no	—
281	#97	—	73	8	no	—
282	#97	—	73	8	no	—
283	#97	—	73	8	no	—
284	#97	C₂×Dic₇₃	1	8	yes	complemented
285	C₄×C₈	—	73	4	no	—
286	C₄×C₈	—	73	4	no	—
287	C₄×C₈	—	73	4	no	—
288	C₄×C₈	—	73	4	no	—
289	C₄×C₈	—	73	8	no	—
290	C₄×C₈	—	73	8	no	—
291	C₄×C₈	—	73	8	no	—
292	C₄×C₈	—	73	8	no	—
293	C₄×C₈	C₂×Dic₇₃	1	8	yes	complemented
294	#95	—	73	8	no	—
295	C₂⁴	C₂×C₄×D₇₃	1	1	yes	characteristic
296	C₂²×C₄	—	73	2	no	—
297	C₂²×C₄	—	73	8	no	—
298	C₂²×C₄	—	73	2	no	—
299	C₂²×C₄	—	73	4	no	—
300	C₂²×C₄	—	146	8	no	—
301	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
302	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
304	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
309	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
310	M₁₆	—	73	16	no	—
311	M₁₆	C₄×Dic₇₃	1	16	yes	complemented
312	C₂×C₈	—	73	16	no	—
313	C₂×C₈	—	73	2	no	—
314	C₂×C₈	—	73	2	no	—
315	C₂×C₈	—	73	2	no	—
316	C₂×C₈	—	73	2	no	—
317	C₂×C₈	—	73	4	no	—
318	C₂×C₈	—	73	4	no	—
319	C₂×C₈	—	73	4	no	—
320	C₂×C₈	—	73	2	no	—
321	C₂×C₈	—	73	2	no	—
322	C₂×C₈	C₄×Dic₇₃	1	16	yes	complemented
323	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
324	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
325	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
326	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
327	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
328	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
329	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
330	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
331	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
332	C₄⋊C₄	—	73	8	no	—
333	C₄⋊C₄	C₄×Dic₇₃	1	8	yes	—
334	C₂²⋊C₄	—	73	8	no	—
335	C₂²⋊C₄	C₄×Dic₇₃	1	8	yes	—
336	C₄²	—	73	8	no	—
337	C₄²	—	73	2	no	—
338	C₄²	—	73	2	no	—
339	C₄²	—	73	2	no	—
340	C₄²	—	73	4	no	—
341	C₄²	—	73	4	no	—
342	C₄²	—	73	2	no	—
343	C₄²	—	146	16	no	—
344	C₄²	C₂×C₄×D₇₃	1	4	yes	—
345	C₄²	C₂²×Dic₇₃	1	4	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	C₄²×D₇₃	1	2	yes	—
348	C₂³	C₄²×D₇₃	1	2	yes	—
349	C₂³	C₂×C₄×Dic₇₃	1	2	yes	—
350	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	73	4	no	—
353	C₂×C₄	—	73	8	no	—
354	C₂×C₄	—	73	4	no	—
355	C₂×C₄	—	73	8	no	—
356	C₂×C₄	—	146	16	no	—
357	C₂×C₄	—	146	8	no	—
358	C₂×C₄	—	146	4	no	—
359	C₂×C₄	C₄²×D₇₃	1	2	yes	—
360	C₂×C₄	C₄²×D₇₃	1	2	yes	—
361	C₂×C₄	C₄²×D₇₃	1	4	yes	—
362	C₂×C₄	C₄²×D₇₃	1	4	yes	—
363	C₂×C₄	C₂×C₄×Dic₇₃	1	8	yes	—
364	C₂×C₄	C₂×C₄×Dic₇₃	1	2	yes	—
365	C₂×C₄	C₂×C₄×Dic₇₃	1	4	yes	—
366	C₂×C₄	C₂×C₄×Dic₇₃	1	4	yes	—
367	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
373	C₈	—	73	4	no	—
374	C₈	—	73	4	no	—
375	C₈	—	73	8	no	—
376	C₈	C₂×C₄×Dic₇₃	1	4	yes	—
377	C₈	C₂×C₄×Dic₇₃	1	4	yes	—
378	C₈	C₂×C₄×Dic₇₃	1	8	yes	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	C₄²×Dic₇₃	1	4	yes	—
383	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
384	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
385	C₂²	C₂²×C₄×Dic₇₃	1	1	yes	characteristic
386	C₂²	#131×D₇₃	1	4	yes	—
387	C₄	—	2	8	no	—
388	C₄	—	73	8	no	—
389	C₄	—	146	4	no	—
390	C₄	—	146	8	no	—
391	C₄	C₄²×Dic₇₃	1	4	yes	—
392	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
393	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
394	C₄	C₂²×C₄×Dic₇₃	1	1	yes	characteristic
395	C₄	C₂²×C₄×Dic₇₃	1	1	yes	characteristic
396	C₂	—	2	4	no	—
397	C₂	C₂×C₄²×Dic₇₃	1	1	yes	characteristic
398	C₂	#405×D₇₃	1	2	yes	—
399	C₂	#131×Dic₇₃	1	2	yes	—
400	C₂	#22618353	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₇₃
commutator	C₂×C₇₃	C₂×C₄³
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₂×#405×C₇₃	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂⁴×C₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#405	D₇₃
hypocenter	C₇₃	C₄×#405
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
7. #22609619	C₂	semidirect
8. #22609617	C₂	semidirect
9. #97×Dic₇₃	C₂	semidirect
10. C₄×C₈×Dic₇₃	C₂	semidirect
16. #17988545	C₄	semidirect
17. #17988543	C₄	semidirect
18. #17988542	C₄	semidirect
19. M₁₆×Dic₇₃	C₄	semidirect
25. C₂×C₈×Dic₇₃	C₄	semidirect
40. #405×C₇₃	C₄	semidirect
64. #14556502	C₂×C₄	semidirect
66. #14556501	C₂×C₄	semidirect
67. #14556501	C₂×C₄	semidirect
68. C₄×#10596831	C₂×C₄	semidirect
74. C₈×Dic₇₃	C₂×C₄	semidirect
75. C₈×Dic₇₃	C₂×C₄	semidirect
92. #97×C₇₃	C₂×C₄	semidirect
93. C₄×C₈×C₇₃	C₂×C₄	semidirect
99. #11924012	C₄²	semidirect
100. C₂×#10596831	C₄²	semidirect
130. M₁₆×C₇₃	C₄²	semidirect
131. C₂×C₈×C₇₃	C₄²	semidirect
194. Dic₇₃	#405	direct (N × H)
212. C₇₃	C₄×#405	semidirect
223. #405	Dic₇₃	direct (N × H)
284. #97	C₂×Dic₇₃	semidirect
293. C₄×C₈	C₂×Dic₇₃	semidirect
311. M₁₆	C₄×Dic₇₃	semidirect
322. C₂×C₈	C₄×Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988545	2
C₂×#17988543	2
C₂×#17988542	2
C₂×M₁₆×Dic₇₃	2
C₂²×C₈×Dic₇₃	2
#117×Dic₇₃	2
#22609619	2
#22609617	2
#97×Dic₇₃	2
C₄×C₈×Dic₇₃	2
C₂×#405×C₇₃	2
C₄×#405	73

Subgroups — #405×Dic73 #33083321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #405×Dic₇₃ #33083321