Subgroups — #436×Dic₇₃ #33084366

Order 18688.

1254 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988665	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₇₃	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	#22609801	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609798	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609717	C₂	1	2	yes	maximal, complemented
8	#22609712	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₈×Dic₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#436×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11924012	C₂²	1	2	yes	—
13	C₂×D₄×Dic₇₃	C₄	1	2	yes	—
14	C₂²×C₄×Dic₇₃	C₂²	1	2	yes	—
15	#17988665	C₄	1	8	yes	complemented
16	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊#10596831	C₂²	1	2	yes	—
18	M₁₆×Dic₇₃	—	2	8	no	—
19	C₂×#14556501	C₂²	1	2	yes	—
20	C₂×#14556501	C₂²	1	2	yes	—
21	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
24	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₇₃	C₄	1	2	yes	—
28	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
29	C₂²⋊C₄×Dic₇₃	C₄	1	4	yes	—
30	C₄×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
31	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
32	#17988341	C₂²	1	2	yes	—
33	#17988341	C₂²	1	2	yes	—
34	#17988341	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
37	#436×C₇₃	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂³×Dic₇₃	C₂×C₄	1	4	yes	—
42	C₂×#11924012	—	2	4	no	—
43	C₂×#11924012	—	2	4	no	—
44	C₂×#11924012	C₂×C₄	1	8	yes	complemented
45	C₂²×#10596831	C₂³	1	2	yes	—
46	C₂²×#10596831	C₂³	1	1	yes	characteristic
47	C₂²×#10596831	C₂³	1	1	yes	characteristic
48	D₄×Dic₇₃	—	2	8	no	—
49	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊Dic₇₃	C₂×C₄	1	4	yes	—
51	C₂×C₄×Dic₇₃	—	2	4	no	—
52	C₂×C₄×Dic₇₃	—	2	4	no	—
53	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
55	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
58	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
59	C₄⋊#10596831	C₂×C₄	1	4	yes	complemented
60	C₂²⋊#10596831	C₂×C₄	1	8	yes	complemented
61	#14556501	—	2	4	no	—
62	#14556501	—	2	4	no	—
63	C₄×#10596831	C₂×C₄	1	4	yes	complemented
64	C₈×Dic₇₃	—	2	2	no	—
65	C₈×Dic₇₃	—	2	4	no	—
66	C₈×Dic₇₃	—	2	2	no	—
67	C₈×Dic₇₃	—	2	2	no	—
68	C₈×Dic₇₃	D₄	1	4	yes	complemented
69	#14556498	C₂×C₄	1	4	yes	—
70	#14556498	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
73	C₂×M₁₆×C₇₃	—	2	4	no	—
74	C₂×M₁₆×C₇₃	—	2	4	no	—
75	C₂×M₁₆×C₇₃	C₂×C₄	1	8	yes	complemented
76	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₃	C₂×C₄	1	4	yes	complemented
85	C₂²⋊C₈×C₇₃	C₂×C₄	1	8	yes	complemented
86	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
87	C₂²×Dic₇₃	—	2	8	no	—
88	C₂²×Dic₇₃	—	2	8	no	—
89	C₂²×Dic₇₃	—	2	8	no	—
90	C₂²×Dic₇₃	C₂²×C₄	1	4	yes	—
91	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
93	#11924012	—	2	16	no	—
94	C₂×#10596831	—	2	2	no	—
95	C₂×#10596831	—	2	1	no	—
96	C₂×#10596831	—	2	1	no	—
97	C₂×#10596831	—	2	2	no	—
98	C₂×#10596831	C₂²×C₄	1	2	yes	—
99	C₂×#10596831	C₂²×C₄	1	4	yes	—
100	C₂×#10596831	C₂²×C₄	1	2	yes	—
101	C₂×#10596831	C₂×D₄	1	2	yes	—
102	C₂×#10596831	#41	1	2	yes	—
103	C₄⋊Dic₇₃	—	2	4	no	—
104	C₂²⋊Dic₇₃	—	2	8	no	—
105	C₄×Dic₇₃	—	2	2	no	—
106	C₄×Dic₇₃	—	2	1	no	—
107	C₄×Dic₇₃	—	2	1	no	—
108	C₄×Dic₇₃	—	2	2	no	—
109	C₄×Dic₇₃	—	2	8	no	—
110	C₄×Dic₇₃	—	2	4	no	—
111	C₄×Dic₇₃	M₁₆	1	8	yes	complemented
112	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
113	C₄×Dic₇₃	#41	1	2	yes	—
114	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	C₄²	1	4	yes	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₇₃	—	2	16	no	—
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	1	no	—
131	C₂×C₈×C₇₃	—	2	1	no	—
132	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₇₃	#41	1	2	yes	—
137	C₄⋊C₄×C₇₃	C₄²	1	4	yes	—
138	C₂²⋊C₄×C₇₃	C₄²	1	8	yes	—
139	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
141	C₂³×C₇₃	—	2	2	no	—
142	C₂³×C₇₃	—	2	2	no	—
143	C₂³×C₇₃	—	2	4	no	—
144	C₂³×C₇₃	—	2	4	no	—
145	C₂³×C₇₃	C₂×C₄²	1	4	yes	—
146	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
147	D₄×C₇₃	—	2	8	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	4	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	2	4	no	—
155	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×M₁₆	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	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₇₃	—	2	2	no	—
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	4	no	—
168	C₂×Dic₇₃	—	2	4	no	—
169	C₂×Dic₇₃	—	2	4	no	—
170	C₂×Dic₇₃	—	4	16	no	—
171	C₂×Dic₇₃	C₄×D₄	1	4	yes	—
172	C₂×Dic₇₃	C₂×M₁₆	1	4	yes	—
173	C₂×Dic₇₃	C₂×M₁₆	1	4	yes	—
174	C₂×Dic₇₃	#131	1	4	yes	—
175	C₈×C₇₃	—	2	4	no	—
176	C₈×C₇₃	—	2	2	no	—
177	C₈×C₇₃	C₄×D₄	1	4	yes	complemented
178	#10596831	—	2	4	no	—
179	#10596831	—	2	2	no	—
180	#10596831	C₄×D₄	1	4	yes	complemented
181	C₂²×C₇₃	—	2	4	no	—
182	C₂²×C₇₃	—	2	4	no	—
183	C₂²×C₇₃	—	2	4	no	—
184	C₂²×C₇₃	—	4	4	no	—
185	C₂²×C₇₃	—	4	4	no	—
186	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
187	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
189	C₂²×C₇₃	C₂²×M₁₆	1	2	yes	—
190	C₂²×C₇₃	C₂×#131	1	2	yes	—
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	2	4	no	—
193	C₄×C₇₃	C₄×M₁₆	1	4	yes	complemented
194	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
197	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
198	Dic₇₃	—	2	4	no	—
199	Dic₇₃	—	4	4	no	—
200	Dic₇₃	#436	1	8	yes	direct product factor
201	C₄×#436	—	73	1	no	maximal, Sylow
202	C₂×C₇₃	—	4	4	no	—
203	C₂×C₇₃	C₄²×D₄	1	1	yes	characteristic
204	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
205	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
206	C₂×C₇₃	C₂×#436	1	2	yes	—
207	C₂×C₇₃	#2965	1	2	yes	—
208	C₂×#436	—	73	1	no	—
209	C₂×#436	D₇₃	1	1	yes	characteristic
210	C₂×C₄×M₁₆	—	73	2	no	—
211	C₄²×D₄	—	73	1	no	—
212	#1770	—	73	1	no	—
213	#1770	—	73	1	no	—
214	C₄×C₄⋊C₈	—	73	1	no	—
215	#1753	—	73	2	no	—
216	#1753	—	73	2	no	—
217	C₄×C₂²⋊C₈	—	73	2	no	—
218	C₄²×C₈	—	73	1	no	—
219	C₇₃	C₄×#436	1	1	yes	characteristic, complemented, Sylow
220	C₂²×M₁₆	—	73	2	no	—
221	C₂²×M₁₆	C₂×D₇₃	1	2	yes	—
222	C₂×C₄×D₄	—	73	2	no	—
223	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
224	C₂²×C₄²	—	73	2	no	—
225	#436	—	73	8	no	—
226	#436	Dic₇₃	1	8	yes	direct product factor
227	C₂×C₄⋊C₈	—	73	1	no	—
228	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	—	73	2	no	—
230	C₂×C₂²⋊C₈	C₂×D₇₃	1	2	yes	—
231	C₄×M₁₆	—	146	8	no	—
232	C₂×#97	—	73	2	no	—
233	C₂×#97	—	73	2	no	—
234	C₂×C₄×C₈	—	73	1	no	—
235	C₂×C₄×C₈	—	73	1	no	—
236	C₂×C₄×C₈	—	73	2	no	—
237	C₂×C₄×C₈	—	73	1	no	—
238	C₂×C₄×C₈	—	73	1	no	—
239	C₂×C₄×C₈	—	73	1	no	—
240	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	—	73	2	no	—
242	C₄×C₄⋊C₄	—	73	1	no	—
243	C₄×C₂²⋊C₄	—	73	2	no	—
244	C₄×C₂²⋊C₄	—	73	4	no	—
245	C₄³	—	73	1	no	—
246	#336	—	73	2	no	—
247	#336	—	73	2	no	—
248	#336	—	73	2	no	—
249	C₂²×D₄	C₄×D₇₃	1	1	yes	characteristic
250	C₂³×C₄	—	73	4	no	—
251	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	73	8	no	—
255	C₂×M₁₆	—	146	4	no	—
256	C₂×M₁₆	—	146	4	no	—
257	C₂×M₁₆	C₂×Dic₇₃	1	8	yes	complemented
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	2	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
262	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
264	C₄×D₄	—	146	8	no	—
265	C₄×D₄	C₄×D₇₃	1	4	yes	—
266	C₄×D₄	C₂×Dic₇₃	1	4	yes	—
267	C₂×C₄⋊C₄	—	73	2	no	—
268	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	73	4	no	—
270	C₂×C₂²⋊C₄	C₄×D₇₃	1	2	yes	—
271	C₂×C₄²	—	73	2	no	—
272	C₂×C₄²	—	73	1	no	—
273	C₂×C₄²	—	73	2	no	—
274	C₂×C₄²	—	73	4	no	—
275	C₂×C₄²	—	73	1	no	—
276	C₂×C₄²	—	73	2	no	—
277	C₂×C₄²	—	146	4	no	—
278	C₂×C₄²	—	146	4	no	—
279	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
280	C₄⋊C₈	—	73	4	no	—
281	C₄⋊C₈	C₂×Dic₇₃	1	4	yes	complemented
282	C₂²⋊C₈	—	73	8	no	—
283	C₂²⋊C₈	C₂×Dic₇₃	1	8	yes	complemented
284	#97	—	146	4	no	—
285	#97	—	146	4	no	—
286	C₄×C₈	—	73	4	no	—
287	C₄×C₈	—	73	4	no	—
288	C₄×C₈	—	146	2	no	—
289	C₄×C₈	—	146	4	no	—
290	C₄×C₈	—	146	2	no	—
291	C₄×C₈	—	146	2	no	—
292	C₄×C₈	C₂×Dic₇₃	1	4	yes	complemented
293	#95	—	73	4	no	—
294	#95	—	73	2	no	—
295	C₂⁴	C₂×C₄×D₇₃	1	2	yes	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	C₄×Dic₇₃	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	73	2	no	—
303	C₂²×C₄	—	73	2	no	—
304	C₂²×C₄	—	73	4	no	—
305	C₂²×C₄	—	146	8	no	—
306	C₂²×C₄	—	146	8	no	—
307	C₂²×C₄	—	146	8	no	—
308	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
311	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
313	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
314	M₁₆	—	2	16	no	—
315	M₁₆	—	146	16	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	73	2	no	—
321	C₂×C₈	—	73	2	no	—
322	C₂×C₈	—	73	2	no	—
323	C₂×C₈	—	73	2	no	—
324	C₂×C₈	—	73	4	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	—	146	1	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	—	146	1	no	—
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	C₂×C₈	D₄×D₇₃	1	2	yes	—
333	C₂×C₈	#11924027	1	2	yes	—
334	C₄⋊C₄	—	146	4	no	—
335	C₄⋊C₄	C₄×Dic₇₃	1	4	yes	—
336	C₂²⋊C₄	—	146	8	no	—
337	C₂²⋊C₄	C₄×Dic₇₃	1	8	yes	—
338	C₄²	—	73	8	no	—
339	C₄²	—	73	2	no	—
340	C₄²	—	73	2	no	—
341	C₄²	—	146	4	no	—
342	C₄²	—	146	8	no	—
343	C₄²	—	146	2	no	—
344	C₄²	—	146	1	no	—
345	C₄²	—	146	2	no	—
346	C₄²	—	146	1	no	—
347	C₄²	C₂×C₄×D₇₃	1	2	yes	—
348	C₄²	C₂²×Dic₇₃	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	C₂×C₄×Dic₇₃	1	4	yes	—
354	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
355	D₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	292	16	no	—
364	C₂×C₄	—	73	4	no	—
365	C₂×C₄	—	73	4	no	—
366	C₂×C₄	—	73	4	no	—
367	C₂×C₄	—	73	4	no	—
368	C₂×C₄	—	146	4	no	—
369	C₂×C₄	—	146	4	no	—
370	C₂×C₄	—	146	4	no	—
371	C₂×C₄	—	146	2	no	—
372	C₂×C₄	—	146	2	no	—
373	C₂×C₄	C₂×C₄×Dic₇₃	1	2	yes	—
374	C₂×C₄	C₂×C₄×Dic₇₃	1	4	yes	—
375	C₂×C₄	C₂×C₄×Dic₇₃	1	2	yes	—
376	C₂×C₄	M₁₆×D₇₃	1	4	yes	—
377	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
381	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
382	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	2	no	—
385	C₈	—	73	4	no	—
386	C₈	—	146	4	no	—
387	C₈	—	146	2	no	—
388	C₈	D₄×Dic₇₃	1	4	yes	complemented
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₂²×C₄×Dic₇₃	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
396	C₂²	C₄×#11924027	1	1	yes	characteristic
397	C₂²	C₂×M₁₆×D₇₃	1	2	yes	—
398	C₂²	#131×D₇₃	1	2	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	2	no	—
401	C₄	—	292	4	no	—
402	C₄	—	73	8	no	—
403	C₄	—	146	4	no	—
404	C₄	M₁₆×Dic₇₃	1	4	yes	complemented
405	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
406	C₄	C₂×D₄×Dic₇₃	1	1	yes	characteristic
407	C₄	C₄×#11924027	1	1	yes	characteristic
408	C₄	#41×Dic₇₃	1	1	yes	characteristic
409	C₂	—	4	4	no	—
410	C₂	C₄×D₄×Dic₇₃	1	1	yes	characteristic
411	C₂	C₂×M₁₆×Dic₇₃	1	1	yes	characteristic
412	C₂	#131×Dic₇₃	1	1	yes	characteristic
413	C₂	#436×D₇₃	1	2	yes	—
414	C₂	#22618894	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂²×C₄²
Fitting	C₂×#436×C₇₃	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂²×D₄×C₇₃	C₂×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#436	D₇₃
hypocenter	C₇₃	C₄×#436
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×Dic₇₃	C₂	semidirect
4. #22609801	C₂	semidirect
5. #22609798	C₂	semidirect
6. C₄⋊C₈×Dic₇₃	C₂	semidirect
7. #22609717	C₂	semidirect
8. #22609712	C₂	semidirect
9. C₂²⋊C₈×Dic₇₃	C₂	semidirect
10. C₄×C₈×Dic₇₃	C₂	semidirect
15. #17988665	C₄	semidirect
37. #436×C₇₃	C₄	semidirect
44. C₂×#11924012	C₂×C₄	semidirect
59. C₄⋊#10596831	C₂×C₄	semidirect
60. C₂²⋊#10596831	C₂×C₄	semidirect
63. C₄×#10596831	C₂×C₄	semidirect
68. C₈×Dic₇₃	D₄	semidirect
75. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
84. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
85. C₂²⋊C₈×C₇₃	C₂×C₄	semidirect
86. C₄×C₈×C₇₃	C₂×C₄	semidirect
111. C₄×Dic₇₃	M₁₆	semidirect
177. C₈×C₇₃	C₄×D₄	semidirect
180. #10596831	C₄×D₄	semidirect
193. C₄×C₇₃	C₄×M₁₆	semidirect
200. Dic₇₃	#436	direct (N × H)
219. C₇₃	C₄×#436	semidirect
226. #436	Dic₇₃	direct (N × H)
257. C₂×M₁₆	C₂×Dic₇₃	semidirect
281. C₄⋊C₈	C₂×Dic₇₃	semidirect
283. C₂²⋊C₈	C₂×Dic₇₃	semidirect
292. C₄×C₈	C₂×Dic₇₃	semidirect
388. C₈	D₄×Dic₇₃	semidirect
404. C₄	M₁₆×Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988665	2
C₂×M₁₆×Dic₇₃	2
C₄×D₄×Dic₇₃	2
#22609801	2
#22609798	2
C₄⋊C₈×Dic₇₃	2
#22609717	2
#22609712	2
C₂²⋊C₈×Dic₇₃	2
C₄×C₈×Dic₇₃	2
C₂×#436×C₇₃	2
C₄×#436	73

Subgroups — #436×Dic73 #33084366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #436×Dic₇₃ #33084366