Subgroups — #2178×D₇₃ #33239380

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#443×D₇₃	C₂	1	2	yes	maximal, complemented
3	#22611813	C₂	1	1	yes	maximal, characteristic, complemented
4	#22611812	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611811	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611810	C₂	1	2	yes	maximal, complemented
7	#22611809	C₂	1	2	yes	maximal, complemented
8	#368×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#359×D₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₃	C₂²	1	2	yes	—
13	#131×D₇₃	—	2	2	no	—
14	#17989020	C₄	1	1	yes	characteristic, complemented
15	#17989019	C₂²	1	1	yes	characteristic
16	#17989018	C₄	1	2	yes	complemented
17	#17989017	C₂²	1	2	yes	—
18	#17989016	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₇₃	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₇₃	C₄	1	2	yes	complemented
21	D₁₆×D₇₃	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
24	#17988705	C₂²	1	2	yes	complemented
25	#17988704	C₂²	1	2	yes	complemented
26	#17988703	C₂²	1	2	yes	complemented
27	#17988702	—	2	2	no	—
28	#17988701	—	2	2	no	—
29	#108×D₇₃	C₂²	1	2	yes	—
30	#104×D₇₃	—	2	2	no	—
31	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
32	#17988417	C₂²	1	1	yes	characteristic, complemented
33	#17988416	C₂²	1	2	yes	complemented
34	#17988395	C₂²	1	2	yes	complemented
35	#17988394	C₂²	1	2	yes	complemented
36	#17988393	C₂²	1	2	yes	complemented
37	C₄×#11924003	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
40	#508×C₇₃	C₂²	1	1	yes	characteristic
41	#443×C₇₃	C₂²	1	2	yes	complemented
42	#368×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#359×C₇₃	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#41×D₇₃	—	2	2	no	—
46	#14556614	C₂×C₄	1	2	yes	—
47	#14556613	C₂³	1	2	yes	—
48	#14556612	—	2	2	no	—
49	#14556611	—	2	2	no	—
50	#14556610	C₂×C₄	1	2	yes	—
51	Q₁₆×D₇₃	C₂×C₄	1	2	yes	—
52	SD₁₆×D₇₃	—	2	2	no	—
53	D₈×D₇₃	C₂×C₄	1	2	yes	—
54	#14556599	—	2	2	no	—
55	#14556599	—	4	2	no	—
56	#14556598	—	2	2	no	—
57	#14556597	—	2	2	no	—
58	#14556597	—	4	2	no	—
59	M₁₆×D₇₃	—	2	2	no	—
60	M₁₆×D₇₃	—	4	2	no	—
61	C₂×C₈×D₇₃	—	4	2	no	—
62	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
64	C₄²×D₇₃	D₄	1	1	yes	characteristic
65	Dic₅₈₄	C₂×C₄	1	1	yes	characteristic, complemented
66	#14556537	C₂×C₄	1	2	yes	complemented
67	#14556536	C₂×C₄	1	2	yes	complemented
68	#14556535	C₂×C₄	1	2	yes	complemented
69	#14556534	C₂×C₄	1	2	yes	complemented
70	D₁₁₆₈	C₂×C₄	1	1	yes	characteristic, complemented
71	#14556532	C₂×C₄	1	2	yes	complemented
72	C₂×#11924003	C₂³	1	1	yes	characteristic
73	C₂×#11924003	C₂³	1	1	yes	characteristic
74	C₁₆×D₇₃	—	2	1	no	—
75	C₁₆×D₇₃	—	2	1	no	—
76	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
80	#14556527	C₂³	1	2	yes	—
81	#14556526	—	2	2	no	—
82	#14556519	—	2	2	no	—
83	#14556518	—	2	2	no	—
84	#14556517	—	2	2	no	—
85	C₄×#10596831	D₄	1	1	yes	characteristic
86	C₈×Dic₇₃	D₄	1	1	yes	characteristic
87	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
88	#135×C₇₃	C₂³	1	2	yes	—
89	#131×C₇₃	—	2	2	no	—
90	Q₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₇₃	C₂×C₄	1	2	yes	complemented
92	D₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
95	#108×C₇₃	C₂³	1	2	yes	—
96	#104×C₇₃	—	2	2	no	—
97	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
98	#11924029	—	2	2	no	—
99	#11924028	—	2	2	no	—
100	#11924028	—	4	2	no	—
101	#11924027	—	2	2	no	—
102	#11924027	—	4	2	no	—
103	Q₈×D₇₃	—	2	2	no	—
104	D₄×D₇₃	—	2	2	no	—
105	D₄×D₇₃	—	4	2	no	—
106	C₂×C₄×D₇₃	—	2	1	no	—
107	C₂×C₄×D₇₃	—	4	2	no	—
108	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
109	Dic₂₉₂	C₂²×C₄	1	2	yes	—
110	#11924018	—	2	2	no	—
111	#11924017	—	2	2	no	—
112	#11924016	—	2	2	no	—
113	#11924015	—	2	2	no	—
114	D₅₈₄	C₂²×C₄	1	2	yes	—
115	#11924013	—	2	2	no	—
116	#11924012	—	2	2	no	—
117	#11924012	—	4	2	no	—
118	#11924011	—	4	2	no	—
119	#11924011	—	4	2	no	—
120	#11924011	—	4	2	no	—
121	C₂×#10596831	—	4	2	no	—
122	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
123	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
124	C₈×D₇₃	—	4	2	no	—
125	C₈×D₇₃	—	4	2	no	—
126	C₈×D₇₃	—	4	2	no	—
127	C₈×D₇₃	D₈	1	1	yes	characteristic
128	C₈×D₇₃	D₈	1	1	yes	characteristic
129	C₈×D₇₃	D₈	1	1	yes	characteristic
130	C₈×D₇₃	D₈	1	1	yes	characteristic
131	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₇₃	#41	1	1	yes	characteristic
134	C₈×D₇₃	#41	1	1	yes	characteristic
135	C₄×Dic₇₃	—	2	1	no	—
136	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
137	#11924003	—	2	1	no	—
138	#11924003	C₂²×C₄	1	1	yes	characteristic
139	#11924003	C₂²×C₄	1	1	yes	characteristic
140	#41×C₇₃	—	2	2	no	—
141	Q₁₆×C₇₃	C₂²×C₄	1	2	yes	—
142	SD₁₆×C₇₃	—	2	2	no	—
143	D₈×C₇₃	C₂²×C₄	1	2	yes	—
144	M₁₆×C₇₃	—	2	2	no	—
145	M₁₆×C₇₃	—	4	2	no	—
146	C₂×C₈×C₇₃	—	4	2	no	—
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₇₃	—	2	1	no	—
151	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₁₆×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×D₇₃	—	4	2	no	—
154	C₂²×D₇₃	#135	1	1	yes	characteristic
155	Q₈×C₇₃	—	2	2	no	—
156	D₄×C₇₃	—	2	2	no	—
157	D₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	4	2	no	—
160	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₇₃	—	4	2	no	—
162	C₂²⋊D₇₃	—	4	2	no	—
163	C₂²⋊D₇₃	—	4	2	no	—
164	C₂×Dic₇₃	—	2	1	no	—
165	C₂×Dic₇₃	—	4	2	no	—
166	C₂×Dic₇₃	#135	1	1	yes	characteristic
167	D₂₉₂	—	2	2	no	—
168	D₂₉₂	—	4	2	no	—
169	C₄×D₇₃	—	2	4	no	—
170	C₄×D₇₃	—	4	2	no	—
171	C₄×D₇₃	—	4	2	no	—
172	C₄×D₇₃	—	4	2	no	—
173	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
174	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
175	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
176	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
177	Dic₁₄₆	—	2	2	no	—
178	Dic₁₄₆	—	4	2	no	—
179	C₈×C₇₃	—	4	2	no	—
180	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
181	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
182	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
184	#10596831	—	4	2	no	—
185	#10596831	C₄×D₄	1	1	yes	characteristic
186	#10596831	C₄×D₄	1	1	yes	characteristic
187	#10596831	C₂×D₈	1	1	yes	characteristic
188	#10596831	C₂×D₈	1	1	yes	characteristic
189	C₂²×C₇₃	—	4	2	no	—
190	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
191	C₂×D₇₃	—	2	2	no	—
192	C₂×D₇₃	—	4	2	no	—
193	C₂×D₇₃	—	8	4	no	—
194	C₂×D₇₃	C₄×D₈	1	1	yes	characteristic
195	C₂×D₇₃	C₄×D₈	1	1	yes	characteristic
196	C₄×C₇₃	—	2	2	no	—
197	C₄×C₇₃	—	4	2	no	—
198	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
200	Dic₇₃	—	2	2	no	—
201	Dic₇₃	—	4	2	no	—
202	Dic₇₃	C₄×D₈	1	1	yes	characteristic
203	Dic₇₃	C₄×D₈	1	1	yes	characteristic
204	C₂×#2178	—	73	1	no	maximal, Sylow
205	C₂×C₇₃	—	2	1	no	—
206	C₂×C₇₃	—	8	2	no	—
207	C₂×C₇₃	C₂×C₄×D₈	1	1	yes	characteristic
208	D₇₃	—	2	1	no	—
209	D₇₃	—	8	2	no	—
210	D₇₃	#2178	1	2	yes	direct product factor
211	C₂×#508	—	73	1	no	—
212	C₂×#443	—	73	2	no	—
213	#2178	—	73	1	no	—
214	#2178	—	73	2	no	—
215	#2178	—	73	1	no	—
216	#2178	—	73	2	no	—
217	#2178	—	73	1	no	—
218	#2178	D₇₃	1	1	yes	characteristic, direct product factor
219	C₂×#368	—	73	1	no	—
220	C₂×#359	—	73	2	no	—
221	C₂×C₄×C₁₆	—	73	1	no	—
222	C₇₃	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	73	2	no	—
224	C₂×#131	—	146	2	no	—
225	#508	—	73	2	no	—
226	#508	—	73	1	no	—
227	#508	—	73	2	no	—
228	#508	—	73	1	no	—
229	#508	—	73	1	no	—
230	#508	C₂×D₇₃	1	1	yes	characteristic
231	C₂×Q₃₂	—	73	1	no	—
232	C₂×SD₃₂	—	73	2	no	—
233	C₂×D₁₆	—	73	1	no	—
234	C₂²×C₁₆	—	73	1	no	—
235	C₂²×C₁₆	—	73	1	no	—
236	#443	—	73	2	no	—
237	#443	—	73	2	no	—
238	#443	—	73	2	no	—
239	#443	—	146	2	no	—
240	#443	—	146	2	no	—
241	#443	C₂×D₇₃	1	2	yes	complemented
242	C₂×#108	—	73	2	no	—
243	C₂×#104	—	146	2	no	—
244	C₂×C₄×C₈	—	73	1	no	—
245	#368	—	73	1	no	—
246	#368	—	73	2	no	—
247	#368	C₂×D₇₃	1	1	yes	characteristic, complemented
248	#359	—	73	2	no	—
249	#359	—	73	2	no	—
250	#359	—	73	2	no	—
251	#359	C₂×D₇₃	1	2	yes	complemented
252	C₄×C₁₆	—	73	1	no	—
253	C₄×C₁₆	—	73	1	no	—
254	C₄×C₁₆	—	73	1	no	—
255	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
256	C₂×#41	—	146	2	no	—
257	#135	—	73	2	no	—
258	#135	—	73	2	no	—
259	#135	—	73	2	no	—
260	#135	—	146	2	no	—
261	#135	—	146	2	no	—
262	#135	C₂²×D₇₃	1	2	yes	—
263	C₂×Q₁₆	—	73	2	no	—
264	C₂×SD₁₆	—	146	2	no	—
265	C₂×D₈	—	73	2	no	—
266	#131	—	2	2	no	—
267	#131	—	292	2	no	—
268	#131	—	292	2	no	—
269	#131	—	146	2	no	—
270	#131	—	146	2	no	—
271	#131	—	146	2	no	—
272	C₂×M₁₆	—	292	2	no	—
273	C₂×M₁₆	—	146	2	no	—
274	C₂²×C₈	—	292	2	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	Q₃₂	—	73	2	no	—
279	Q₃₂	—	73	1	no	—
280	Q₃₂	C₄×D₇₃	1	1	yes	characteristic, complemented
281	SD₃₂	—	73	2	no	—
282	SD₃₂	—	73	2	no	—
283	SD₃₂	—	73	2	no	—
284	SD₃₂	C₄×D₇₃	1	2	yes	complemented
285	D₁₆	—	73	2	no	—
286	D₁₆	—	73	1	no	—
287	D₁₆	C₄×D₇₃	1	1	yes	characteristic, complemented
288	C₂×C₁₆	—	73	1	no	—
289	C₂×C₁₆	—	73	1	no	—
290	C₂×C₁₆	—	73	1	no	—
291	C₂×C₁₆	—	73	1	no	—
292	C₂×C₁₆	—	73	1	no	—
293	C₂×C₁₆	—	73	1	no	—
294	C₂×C₁₆	—	146	1	no	—
295	C₂×C₁₆	—	146	1	no	—
296	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
298	#108	—	73	2	no	—
299	#108	—	146	2	no	—
300	#108	C₂²×D₇₃	1	2	yes	—
301	#104	—	2	2	no	—
302	#104	—	146	2	no	—
303	#104	—	146	2	no	—
304	#104	—	146	2	no	—
305	C₄×C₈	—	73	1	no	—
306	C₄×C₈	—	73	1	no	—
307	C₄×C₈	—	73	1	no	—
308	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
309	#41	—	2	2	no	—
310	#41	—	292	2	no	—
311	#41	—	292	2	no	—
312	#41	—	146	2	no	—
313	#41	—	146	2	no	—
314	#41	—	146	2	no	—
315	C₂×Q₈	—	146	2	no	—
316	C₂×D₄	—	292	2	no	—
317	C₂×D₄	—	146	2	no	—
318	C₂²×C₄	—	292	2	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	146	1	no	—
321	Q₁₆	—	73	2	no	—
322	Q₁₆	—	146	2	no	—
323	Q₁₆	C₂×C₄×D₇₃	1	2	yes	—
324	SD₁₆	—	2	2	no	—
325	SD₁₆	—	146	2	no	—
326	SD₁₆	—	146	2	no	—
327	SD₁₆	—	146	2	no	—
328	D₈	—	73	2	no	—
329	D₈	—	146	2	no	—
330	D₈	C₂×C₄×D₇₃	1	2	yes	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	—	292	2	no	—
334	M₁₆	—	292	2	no	—
335	M₁₆	—	292	2	no	—
336	M₁₆	—	292	2	no	—
337	M₁₆	—	146	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	292	2	no	—
340	C₂×C₈	—	292	2	no	—
341	C₂×C₈	—	292	2	no	—
342	C₂×C₈	—	292	2	no	—
343	C₂×C₈	—	73	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	1	no	—
349	C₂×C₈	—	73	1	no	—
350	C₂×C₈	—	73	1	no	—
351	C₂×C₈	—	73	1	no	—
352	C₂×C₈	—	73	1	no	—
353	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
355	C₄²	—	73	1	no	—
356	C₄²	—	146	1	no	—
357	C₄²	D₄×D₇₃	1	1	yes	characteristic
358	C₁₆	—	2	1	no	—
359	C₁₆	—	73	1	no	—
360	C₁₆	—	73	1	no	—
361	C₁₆	—	146	1	no	—
362	C₁₆	C₂×C₄×D₇₃	1	1	yes	characteristic
363	C₁₆	C₂×C₄×D₇₃	1	1	yes	characteristic
364	C₂³	—	292	2	no	—
365	C₂³	—	73	1	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	292	2	no	—
368	Q₈	—	146	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	292	2	no	—
372	D₄	—	292	2	no	—
373	D₄	—	292	2	no	—
374	D₄	—	292	2	no	—
375	D₄	—	146	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	292	2	no	—
379	C₂×C₄	—	292	2	no	—
380	C₂×C₄	—	292	2	no	—
381	C₂×C₄	—	292	2	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	146	4	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	292	2	no	—
392	C₈	—	73	1	no	—
393	C₈	—	73	1	no	—
394	C₈	—	73	1	no	—
395	C₈	—	73	1	no	—
396	C₈	D₈×D₇₃	1	1	yes	characteristic
397	C₈	D₈×D₇₃	1	1	yes	characteristic
398	C₈	C₂²×C₄×D₇₃	1	1	yes	characteristic
399	C₈	#41×D₇₃	1	1	yes	characteristic
400	C₂²	—	4	2	no	—
401	C₂²	—	292	2	no	—
402	C₂²	—	584	4	no	—
403	C₂²	—	73	1	no	—
404	C₂²	—	73	1	no	—
405	C₂²	—	146	2	no	—
406	C₂²	#135×D₇₃	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	292	2	no	—
410	C₄	—	73	1	no	—
411	C₄	—	73	1	no	—
412	C₄	—	146	2	no	—
413	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
414	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	—	584	2	no	—
418	C₂	—	73	2	no	—
419	C₂	—	146	1	no	—
420	C₂	C₄×D₈×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₇₃
commutator	C₈×C₇₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2178	C₂
socle	C₂×C₇₃	C₂×C₄×D₈
prime radical	#508×D₇₃	C₂
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	#2178	D₇₃
hypocenter	C₇₃	C₂×#2178
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #443×D₇₃	C₂	semidirect
3. #22611813	C₂	semidirect
4. #22611812	C₂	semidirect
5. #22611811	C₂	semidirect
6. #22611810	C₂	semidirect
7. #22611809	C₂	semidirect
8. #368×D₇₃	C₂	semidirect
9. #359×D₇₃	C₂	semidirect
10. C₄×C₁₆×D₇₃	C₂	semidirect
11. C₇₃×#2178	C₂	semidirect
14. #17989020	C₄	semidirect
16. #17989018	C₄	semidirect
18. #17989016	C₄	semidirect
19. Q₃₂×D₇₃	C₄	semidirect
20. SD₃₂×D₇₃	C₄	semidirect
21. D₁₆×D₇₃	C₄	semidirect
24. #17988705	C₂²	semidirect
25. #17988704	C₂²	semidirect
26. #17988703	C₂²	semidirect
32. #17988417	C₂²	semidirect
33. #17988416	C₂²	semidirect
34. #17988395	C₂²	semidirect
35. #17988394	C₂²	semidirect
36. #17988393	C₂²	semidirect
37. C₄×#11924003	C₂²	semidirect
38. C₁₆×Dic₇₃	C₂²	semidirect
39. C₁₆×Dic₇₃	C₂²	semidirect
41. #443×C₇₃	C₂²	semidirect
42. #368×C₇₃	C₂²	semidirect
43. #359×C₇₃	C₂²	semidirect
44. C₄×C₁₆×C₇₃	C₂²	semidirect
65. Dic₅₈₄	C₂×C₄	semidirect
66. #14556537	C₂×C₄	semidirect
67. #14556536	C₂×C₄	semidirect
68. #14556535	C₂×C₄	semidirect
69. #14556534	C₂×C₄	semidirect
70. D₁₁₆₈	C₂×C₄	semidirect
71. #14556532	C₂×C₄	semidirect
90. Q₃₂×C₇₃	C₂×C₄	semidirect
91. SD₃₂×C₇₃	C₂×C₄	semidirect
92. D₁₆×C₇₃	C₂×C₄	semidirect
210. D₇₃	#2178	direct (N × H)
218. #2178	D₇₃	direct (N × H)
222. C₇₃	C₂×#2178	semidirect
241. #443	C₂×D₇₃	semidirect
247. #368	C₂×D₇₃	semidirect
251. #359	C₂×D₇₃	semidirect
255. C₄×C₁₆	C₂×D₇₃	semidirect
280. Q₃₂	C₄×D₇₃	semidirect
284. SD₃₂	C₄×D₇₃	semidirect
287. D₁₆	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#508×D₇₃	2
#443×D₇₃	2
#22611813	2
#22611812	2
#22611811	2
#22611810	2
#22611809	2
#368×D₇₃	2
#359×D₇₃	2
C₄×C₁₆×D₇₃	2
C₇₃×#2178	2
C₂×#2178	73

Subgroups — #2178×D73 #33239380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2178×D₇₃ #33239380