Subgroups — #2215×D₇₃ #33240398

Order 18688.

806 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#466×D₇₃	C₂	1	2	yes	maximal, complemented
4	#22612018	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612017	C₂	1	1	yes	maximal, characteristic, complemented
6	#22612016	C₂	1	2	yes	maximal, complemented
7	#22612015	C₂	1	2	yes	maximal, complemented
8	#22612014	C₂	1	1	yes	maximal, characteristic, complemented
9	#366×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2215	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₇₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	#121×D₇₃	—	2	2	no	—
15	C₂×D₁₁₆₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×#14556532	C₂²	1	2	yes	complemented
17	D₁₆×D₇₃	—	2	4	no	—
18	C₂²×#11924003	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₆×D₇₃	—	2	4	no	—
20	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic, complemented
24	#17988824	C₂²	1	2	yes	complemented
25	#17988823	C₂²	1	2	yes	complemented
26	#17988822	—	2	2	no	—
27	#17988821	—	2	2	no	—
28	#17988820	C₂²	1	2	yes	complemented
29	#107×D₇₃	C₂²	1	2	yes	—
30	#102×D₇₃	—	2	2	no	—
31	#17988413	C₂²	1	1	yes	characteristic, complemented
32	#17988412	C₂²	1	2	yes	complemented
33	#17988389	C₂²	1	2	yes	complemented
34	#17988388	C₂²	1	2	yes	complemented
35	#17988387	C₂²	1	2	yes	complemented
36	C₂×D₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#466×C₇₃	C₂²	1	2	yes	complemented
39	#366×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	#357×C₇₃	C₂²	1	2	yes	complemented
41	C₂×D₄×D₇₃	—	2	2	no	—
42	C₂×D₄×D₇₃	—	4	2	no	—
43	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
44	C₂×D₅₈₄	C₂³	1	2	yes	—
45	C₂×#11924013	—	2	2	no	—
46	D₈×D₇₃	—	2	4	no	—
47	D₈×D₇₃	—	2	4	no	—
48	C₂²×#10596831	D₄	1	1	yes	characteristic
49	C₂×C₈×D₇₃	—	2	2	no	—
50	C₂×C₈×D₇₃	—	2	2	no	—
51	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
52	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
55	#14556566	—	2	2	no	—
56	#14556565	—	2	2	no	—
57	#14556564	—	4	2	no	—
58	#14556563	—	4	2	no	—
59	#14556562	—	2	2	no	—
60	C₄⋊C₄×D₇₃	—	2	2	no	—
61	C₂²⋊C₄×D₇₃	—	4	2	no	—
62	D₁₁₆₈	—	2	2	no	—
63	#14556532	—	2	4	no	—
64	C₂×#11924003	—	2	2	no	—
65	C₂×#11924003	C₂³	1	1	yes	characteristic
66	C₂×#11924003	C₂³	1	1	yes	characteristic
67	C₁₆×D₇₃	—	2	2	no	—
68	C₁₆×D₇₃	—	2	2	no	—
69	C₁₆×D₇₃	—	2	2	no	—
70	C₁₆×D₇₃	D₄	1	4	yes	complemented
71	#14556525	C₂³	1	2	yes	—
72	#14556524	—	2	2	no	—
73	#14556513	—	2	2	no	—
74	#14556512	—	2	2	no	—
75	#14556511	—	2	2	no	—
76	C₂×D₈×C₇₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
78	#121×C₇₃	—	2	2	no	—
79	D₁₆×C₇₃	—	2	2	no	—
80	C₂×C₁₆×C₇₃	—	2	2	no	—
81	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
83	#107×C₇₃	C₂³	1	2	yes	—
84	#102×C₇₃	—	2	2	no	—
85	C₂³×D₇₃	—	4	2	no	—
86	C₂³×D₇₃	D₈	1	1	yes	characteristic
87	C₂×D₂₉₂	—	2	2	no	—
88	C₂×D₂₉₂	—	4	2	no	—
89	C₂×C₂²⋊D₇₃	—	4	2	no	—
90	C₂×C₂²⋊D₇₃	—	4	2	no	—
91	C₂×C₂²⋊D₇₃	—	4	2	no	—
92	D₄×D₇₃	—	4	4	no	—
93	D₄×D₇₃	—	4	4	no	—
94	D₄×D₇₃	—	8	8	no	—
95	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
96	C₂×C₄×D₇₃	—	2	2	no	—
97	C₂×C₄×D₇₃	—	2	2	no	—
98	C₂×C₄×D₇₃	—	4	2	no	—
99	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
100	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
103	D₅₈₄	—	2	2	no	—
104	D₅₈₄	—	2	2	no	—
105	#11924013	—	4	4	no	—
106	C₂×#10596831	—	2	2	no	—
107	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
108	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
109	C₈×D₇₃	—	2	2	no	—
110	C₈×D₇₃	—	2	1	no	—
111	C₈×D₇₃	—	2	1	no	—
112	C₈×D₇₃	—	2	2	no	—
113	C₈×D₇₃	C₂×D₄	1	2	yes	—
114	C₈×D₇₃	#41	1	2	yes	—
115	C₄⋊Dic₇₃	—	2	2	no	—
116	#11924007	—	4	2	no	—
117	C₂²⋊Dic₇₃	—	4	2	no	—
118	#11924005	—	4	2	no	—
119	#11924005	—	4	2	no	—
120	#11924003	—	2	1	no	—
121	#11924003	C₂×D₄	1	2	yes	complemented
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	4	2	no	—
124	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
125	D₈×C₇₃	—	2	2	no	—
126	D₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	1	no	—
128	C₂×C₈×C₇₃	—	2	1	no	—
129	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₂²⋊C₄×C₇₃	—	4	2	no	—
133	C₁₆×C₇₃	—	2	1	no	—
134	C₁₆×C₇₃	C₂×D₄	1	2	yes	complemented
135	C₂³×C₇₃	—	4	2	no	—
136	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
137	C₂²×D₇₃	—	2	2	no	—
138	C₂²×D₇₃	—	2	2	no	—
139	C₂²×D₇₃	—	4	2	no	—
140	C₂²×D₇₃	—	8	4	no	—
141	C₂²×D₇₃	—	8	4	no	—
142	C₂²×D₇₃	—	8	4	no	—
143	C₂²×D₇₃	D₁₆	1	4	yes	complemented
144	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
145	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
146	D₄×C₇₃	—	4	2	no	—
147	D₄×C₇₃	—	4	2	no	—
148	D₄×C₇₃	—	8	4	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	4	2	no	—
152	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
154	C₂²⋊D₇₃	—	8	4	no	—
155	C₂²⋊D₇₃	—	8	4	no	—
156	C₂²⋊D₇₃	—	8	4	no	—
157	C₂×Dic₇₃	—	2	2	no	—
158	C₂×Dic₇₃	—	4	2	no	—
159	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
160	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
161	D₂₉₂	—	4	2	no	—
162	D₂₉₂	—	4	2	no	—
163	D₂₉₂	—	8	4	no	—
164	C₄×D₇₃	—	2	2	no	—
165	C₄×D₇₃	—	2	1	no	—
166	C₄×D₇₃	—	2	1	no	—
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	—	8	4	no	—
169	C₄×D₇₃	#121	1	2	yes	—
170	C₄×D₇₃	#135	1	2	yes	—
171	C₈×C₇₃	—	2	1	no	—
172	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
174	#10596831	—	2	1	no	—
175	#10596831	#121	1	2	yes	—
176	C₂²×C₇₃	—	2	1	no	—
177	C₂²×C₇₃	—	2	1	no	—
178	C₂²×C₇₃	—	8	2	no	—
179	C₂²×C₇₃	—	8	2	no	—
180	C₂²×C₇₃	—	8	2	no	—
181	C₂²×C₇₃	C₂×D₁₆	1	2	yes	complemented
182	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₇₃	—	2	1	no	—
184	C₂×D₇₃	—	2	1	no	—
185	C₂×D₇₃	—	2	8	no	—
186	C₂×D₇₃	—	8	2	no	—
187	C₂×D₇₃	—	8	2	no	—
188	C₂×D₇₃	—	8	2	no	—
189	C₂×D₇₃	—	16	8	no	—
190	C₂×D₇₃	#466	1	2	yes	—
191	C₂×D₇₃	C₂×D₁₆	1	2	yes	—
192	C₂×D₇₃	C₂×D₁₆	1	2	yes	complemented
193	C₂×D₇₃	#508	1	2	yes	—
194	C₄×C₇₃	—	2	1	no	—
195	C₄×C₇₃	—	8	2	no	—
196	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
197	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
198	Dic₇₃	—	2	1	no	—
199	Dic₇₃	—	8	2	no	—
200	Dic₇₃	#466	1	2	yes	—
201	C₂×#2215	—	73	1	no	maximal, Sylow
202	C₂×C₇₃	—	2	2	no	—
203	C₂×C₇₃	—	16	2	no	—
204	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
205	C₂×C₇₃	C₂²×D₁₆	1	1	yes	characteristic
206	C₂×C₇₃	C₂×#508	1	1	yes	characteristic
207	D₇₃	—	2	2	no	—
208	D₇₃	—	16	2	no	—
209	D₇₃	#2215	1	4	yes	direct product factor
210	C₂²×D₁₆	—	73	1	no	—
211	C₂³×C₁₆	—	73	1	no	—
212	C₂×#466	—	73	2	no	—
213	#2215	—	73	1	no	—
214	#2215	—	73	1	no	—
215	#2215	—	73	2	no	—
216	#2215	—	73	1	no	—
217	#2215	—	73	2	no	—
218	#2215	D₇₃	1	1	yes	characteristic, direct product factor
219	C₂×#366	—	73	1	no	—
220	C₂×#357	—	73	2	no	—
221	C₇₃	C₂×#2215	1	1	yes	characteristic, complemented, Sylow
222	C₂²×D₈	—	73	2	no	—
223	C₂³×C₈	—	73	1	no	—
224	C₂×#121	—	146	2	no	—
225	C₂×D₁₆	—	73	2	no	—
226	C₂×D₁₆	—	73	1	no	—
227	C₂×D₁₆	—	146	4	no	—
228	C₂×D₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
229	C₂²×C₁₆	—	73	1	no	—
230	C₂²×C₁₆	—	73	1	no	—
231	C₂²×C₁₆	—	73	1	no	—
232	C₂²×C₁₆	—	73	1	no	—
233	C₂²×C₁₆	—	73	1	no	—
234	C₂²×C₁₆	—	146	4	no	—
235	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
236	#466	—	73	2	no	—
237	#466	—	73	2	no	—
238	#466	—	73	2	no	—
239	#466	—	146	2	no	—
240	#466	—	146	2	no	—
241	#466	C₂×D₇₃	1	2	yes	complemented
242	C₂×#107	—	73	2	no	—
243	C₂×#102	—	146	2	no	—
244	#366	—	73	1	no	—
245	#366	—	73	2	no	—
246	#366	C₂×D₇₃	1	1	yes	characteristic, complemented
247	#357	—	73	2	no	—
248	#357	—	73	2	no	—
249	#357	—	73	2	no	—
250	#357	C₂×D₇₃	1	2	yes	complemented
251	C₂²×D₄	—	292	2	no	—
252	C₂²×D₄	—	146	2	no	—
253	C₂³×C₄	—	73	1	no	—
254	C₂×D₈	—	73	2	no	—
255	C₂×D₈	—	146	4	no	—
256	C₂×D₈	—	146	4	no	—
257	C₂×D₈	—	146	2	no	—
258	C₂×D₈	C₂²×D₇₃	1	2	yes	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	1	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	146	2	no	—
265	C₂²×C₈	—	146	2	no	—
266	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
267	#121	—	2	2	no	—
268	#121	—	292	2	no	—
269	#121	—	292	2	no	—
270	#121	—	146	2	no	—
271	#121	—	146	2	no	—
272	#121	—	146	2	no	—
273	C₂×C₄⋊C₄	—	146	2	no	—
274	C₂×C₂²⋊C₄	—	292	2	no	—
275	D₁₆	—	2	2	no	—
276	D₁₆	—	146	4	no	—
277	D₁₆	—	146	2	no	—
278	C₂×C₁₆	—	2	2	no	—
279	C₂×C₁₆	—	73	1	no	—
280	C₂×C₁₆	—	73	4	no	—
281	C₂×C₁₆	—	73	1	no	—
282	C₂×C₁₆	—	146	2	no	—
283	C₂×C₁₆	—	146	2	no	—
284	C₂×C₁₆	—	146	2	no	—
285	C₂×C₁₆	—	146	2	no	—
286	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
287	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
288	#107	—	73	2	no	—
289	#107	—	146	2	no	—
290	#107	C₂²×D₇₃	1	2	yes	—
291	#102	—	2	2	no	—
292	#102	—	146	2	no	—
293	#102	—	146	2	no	—
294	#102	—	146	2	no	—
295	C₂⁴	—	292	2	no	—
296	C₂⁴	—	73	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	292	2	no	—
300	C₂×D₄	—	292	2	no	—
301	C₂×D₄	—	292	2	no	—
302	C₂×D₄	—	292	4	no	—
303	C₂×D₄	—	292	4	no	—
304	C₂×D₄	—	292	2	no	—
305	C₂×D₄	—	584	8	no	—
306	C₂×D₄	—	146	2	no	—
307	C₂²×C₄	—	292	2	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	146	2	no	—
314	C₂²×C₄	—	146	2	no	—
315	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	292	4	no	—
319	D₈	—	146	2	no	—
320	D₈	—	146	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	73	2	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	—	146	2	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	—	146	1	no	—
331	C₂×C₈	—	146	1	no	—
332	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
333	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	292	2	no	—
336	C₄⋊C₄	—	146	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	292	2	no	—
339	C₂²⋊C₄	—	292	2	no	—
340	C₂²⋊C₄	—	292	2	no	—
341	C₁₆	—	2	1	no	—
342	C₁₆	—	73	2	no	—
343	C₁₆	—	146	1	no	—
344	C₁₆	D₄×D₇₃	1	2	yes	complemented
345	C₂³	—	4	2	no	—
346	C₂³	—	292	2	no	—
347	C₂³	—	584	4	no	—
348	C₂³	—	584	4	no	—
349	C₂³	—	584	4	no	—
350	C₂³	—	73	1	no	—
351	C₂³	—	73	4	no	—
352	C₂³	—	73	1	no	—
353	C₂³	—	146	2	no	—
354	C₂³	—	146	2	no	—
355	C₂³	D₈×D₇₃	1	1	yes	characteristic
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	4	no	—
359	D₄	—	292	2	no	—
360	D₄	—	292	2	no	—
361	D₄	—	584	4	no	—
362	D₄	—	584	4	no	—
363	D₄	—	584	4	no	—
364	D₄	—	584	4	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	292	2	no	—
369	C₂×C₄	—	584	4	no	—
370	C₂×C₄	—	73	1	no	—
371	C₂×C₄	—	73	2	no	—
372	C₂×C₄	—	73	2	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	146	2	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	2	no	—
377	C₂×C₄	—	146	1	no	—
378	C₂×C₄	—	146	1	no	—
379	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	73	2	no	—
383	C₈	—	146	1	no	—
384	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
385	C₈	#41×D₇₃	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	584	2	no	—
392	C₂²	—	584	2	no	—
393	C₂²	—	584	2	no	—
394	C₂²	—	73	2	no	—
395	C₂²	—	73	2	no	—
396	C₂²	—	73	2	no	—
397	C₂²	—	73	2	no	—
398	C₂²	—	1168	8	no	—
399	C₂²	—	146	8	no	—
400	C₂²	—	146	1	no	—
401	C₂²	—	146	1	no	—
402	C₂²	D₁₆×D₇₃	1	2	yes	complemented
403	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	584	2	no	—
407	C₄	—	73	2	no	—
408	C₄	—	146	1	no	—
409	C₄	#121×D₇₃	1	1	yes	characteristic
410	C₄	#135×D₇₃	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	16	2	no	—
413	C₂	—	73	4	no	—
414	C₂	—	1168	2	no	—
415	C₂	—	146	2	no	—
416	C₂	#466×D₇₃	1	1	yes	characteristic
417	C₂	C₂×D₁₆×D₇₃	1	1	yes	characteristic
418	C₂	#508×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2215	C₂
socle	C₂²×C₇₃	C₂²×D₈
hypercenter	#2215	D₇₃
hypocenter	C₇₃	C₂×#2215
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2215

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×D₇₃	C₂	semidirect
2. C₂²×C₁₆×D₇₃	C₂	semidirect
3. #466×D₇₃	C₂	semidirect
4. #22612018	C₂	semidirect
5. #22612017	C₂	semidirect
6. #22612016	C₂	semidirect
7. #22612015	C₂	semidirect
8. #22612014	C₂	semidirect
9. #366×D₇₃	C₂	semidirect
10. #357×D₇₃	C₂	semidirect
11. C₇₃×#2215	C₂	semidirect
15. C₂×D₁₁₆₈	C₂²	semidirect
16. C₂×#14556532	C₂²	semidirect
18. C₂²×#11924003	C₂²	semidirect
22. C₂×C₁₆×D₇₃	C₂²	semidirect
23. C₂×C₁₆×D₇₃	C₂²	semidirect
24. #17988824	C₂²	semidirect
25. #17988823	C₂²	semidirect
28. #17988820	C₂²	semidirect
31. #17988413	C₂²	semidirect
32. #17988412	C₂²	semidirect
33. #17988389	C₂²	semidirect
34. #17988388	C₂²	semidirect
35. #17988387	C₂²	semidirect
36. C₂×D₁₆×C₇₃	C₂²	semidirect
37. C₂²×C₁₆×C₇₃	C₂²	semidirect
38. #466×C₇₃	C₂²	semidirect
39. #366×C₇₃	C₂²	semidirect
40. #357×C₇₃	C₂²	semidirect
70. C₁₆×D₇₃	D₄	semidirect
121. #11924003	C₂×D₄	semidirect
134. C₁₆×C₇₃	C₂×D₄	semidirect
143. C₂²×D₇₃	D₁₆	semidirect
181. C₂²×C₇₃	C₂×D₁₆	semidirect
192. C₂×D₇₃	C₂×D₁₆	semidirect
209. D₇₃	#2215	direct (N × H)
218. #2215	D₇₃	direct (N × H)
221. C₇₃	C₂×#2215	semidirect
228. C₂×D₁₆	C₂×D₇₃	semidirect
235. C₂²×C₁₆	C₂×D₇₃	semidirect
241. #466	C₂×D₇₃	semidirect
246. #366	C₂×D₇₃	semidirect
250. #357	C₂×D₇₃	semidirect
344. C₁₆	D₄×D₇₃	semidirect
402. C₂²	D₁₆×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₇₃	2
C₂²×C₁₆×D₇₃	2
#466×D₇₃	2
#22612018	2
#22612017	2
#22612016	2
#22612015	2
#22612014	2
#366×D₇₃	2
#357×D₇₃	2
C₇₃×#2215	2
C₂×#2215	73

Subgroups — #2215×D73 #33240398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2215×D₇₃ #33240398