Subgroups — #34030123

Order 18688.

682 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626294	C₂	1	2	yes	maximal, complemented
2	#22626292	C₂	1	2	yes	maximal, complemented
3	#22626291	C₂	1	2	yes	maximal, complemented
4	#22626289	C₂	1	2	yes	maximal, complemented
5	#22626264	C₂	1	2	yes	maximal, complemented
6	#22626159	C₂	1	2	yes	maximal
7	#22626138	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556666	C₂²	1	4	yes	—
10	#17989508	C₂²	1	4	yes	complemented
11	C₄⋊#11924031	C₂²	1	4	yes	complemented
12	#17989482	C₂²	1	4	yes	—
13	C₂²⋊#11924031	C₂²	1	4	yes	—
14	#17989475	C₂²	1	4	yes	complemented
15	#17989473	C₂²	1	4	yes	complemented
16	C₂²×C₈×D₇₃	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
19	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
21	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
22	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
25	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
31	#14556666	—	2	8	no	—
32	C₂×#11924031	C₂³	1	8	yes	—
33	C₂²×C₄×D₇₃	C₈	1	1	yes	characteristic
34	C₂²×C₄×D₇₃	C₈	1	1	yes	characteristic
35	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
37	C₂²×#10596831	C₂³	1	1	yes	characteristic
38	C₂×C₈×D₇₃	—	2	4	no	—
39	C₂×C₈×D₇₃	—	2	4	no	—
40	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×Dic₇₃	C₈	1	1	yes	characteristic
49	C₂×C₄×Dic₇₃	C₈	1	1	yes	characteristic
50	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₇₃	C₈	1	1	yes	characteristic
52	C₄²×D₇₃	C₈	1	1	yes	characteristic
53	C₄²×D₇₃	C₈	1	1	yes	characteristic
54	C₄²×D₇₃	C₈	1	1	yes	characteristic
55	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
60	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
61	C₄×#10596831	C₂³	1	1	yes	characteristic
62	C₄×#10596831	C₂³	1	1	yes	characteristic
63	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
64	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
65	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
70	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
78	#11924031	—	2	8	no	—
79	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
80	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
81	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
82	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
83	C₂×C₄×D₇₃	—	2	4	no	—
84	C₂×C₄×D₇₃	—	2	4	no	—
85	C₂×C₄×D₇₃	—	2	2	no	—
86	C₂×C₄×D₇₃	—	2	2	no	—
87	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×#10596831	—	2	2	no	—
100	C₂×#10596831	—	2	2	no	—
101	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
102	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
103	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
104	C₂×#10596831	C₂⁴	1	1	yes	characteristic
105	C₈×D₇₃	—	2	2	no	—
106	C₈×D₇₃	—	2	2	no	—
107	C₈×D₇₃	—	2	2	no	—
108	C₈×D₇₃	—	2	2	no	—
109	C₈×D₇₃	—	2	2	no	—
110	C₈×D₇₃	—	2	2	no	—
111	C₈×D₇₃	M₁₆	1	4	yes	—
112	C₈×D₇₃	#41	1	4	yes	—
113	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
114	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
115	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
118	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
119	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
120	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
121	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
122	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
135	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
136	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
139	C₂²×D₇₃	—	2	2	no	—
140	C₂²×D₇₃	—	2	2	no	—
141	C₂²×D₇₃	—	2	2	no	—
142	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
143	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₇₃	—	2	2	no	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×Dic₇₃	—	2	2	no	—
155	C₂×Dic₇₃	—	2	2	no	—
156	C₂×Dic₇₃	M₃₂	1	4	yes	complemented
157	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
160	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
161	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
163	C₄×D₇₃	—	2	2	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	—	2	2	no	—
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	2	no	—
171	C₄×D₇₃	—	2	2	no	—
172	C₄×D₇₃	—	2	2	no	—
173	C₄×D₇₃	—	2	2	no	—
174	C₄×D₇₃	M₃₂	1	4	yes	complemented
175	C₄×D₇₃	#117	1	2	yes	—
176	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
177	C₈×C₇₃	—	2	1	no	—
178	C₈×C₇₃	—	2	1	no	—
179	C₈×C₇₃	#117	1	2	yes	—
180	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
181	#10596831	—	2	1	no	—
182	#10596831	—	2	1	no	—
183	#10596831	C₂×M₁₆	1	2	yes	—
184	#10596831	C₂×#41	1	2	yes	—
185	C₂²×C₇₃	—	2	1	no	—
186	C₂²×C₇₃	—	2	1	no	—
187	C₂²×C₇₃	C₂×M₃₂	1	2	yes	—
188	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
189	C₂×D₇₃	—	2	8	no	—
190	C₂×D₇₃	—	2	1	no	—
191	C₂×D₇₃	—	2	1	no	—
192	C₂×D₇₃	—	2	1	no	—
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	#431	1	2	yes	—
195	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	C₂×M₃₂	1	2	yes	—
201	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
202	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	—	2	1	no	—
205	Dic₇₃	#431	1	2	yes	—
206	Dic₇₃	C₂×M₃₂	1	2	yes	—
207	Dic₇₃	C₂×M₃₂	1	2	yes	—
208	Dic₇₃	C₂×M₃₂	1	2	yes	—
209	#33418	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	2	2	no	—
211	C₂×C₇₃	C₂×#431	1	1	yes	characteristic
212	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
213	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
214	D₇₃	—	2	2	no	—
215	D₇₃	—	2	2	no	—
216	C₂²×C₄×C₈	—	73	1	no	—
217	#2163	—	73	2	no	—
218	#2163	—	73	2	no	—
219	#2162	—	73	2	no	—
220	#2162	—	73	2	no	—
221	#2150	—	73	2	no	—
222	#2112	—	73	2	no	—
223	C₄×M₃₂	—	73	2	no	—
224	C₇₃	#33418	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₈	—	73	1	no	—
226	C₂³×C₈	—	73	1	no	—
227	C₂²×C₄²	—	73	1	no	—
228	C₂×M₃₂	—	73	4	no	—
229	C₂×C₄×C₈	—	73	1	no	—
230	C₂×C₄×C₈	—	73	1	no	—
231	C₂×C₄×C₈	—	73	1	no	—
232	C₂×C₄×C₈	—	73	1	no	—
233	C₂×C₄×C₈	—	73	1	no	—
234	C₂×C₄×C₈	—	73	1	no	—
235	C₂×C₄×C₈	—	73	1	no	—
236	C₂×C₄×C₈	—	73	1	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	#64408	1	1	yes	characteristic
241	C₄⋊C₁₆	—	73	4	no	—
242	C₄⋊C₁₆	—	73	4	no	—
243	C₂²⋊C₁₆	—	73	4	no	—
244	C₂²⋊C₁₆	—	73	4	no	—
245	#346	—	73	4	no	—
246	C₄×C₁₆	—	73	4	no	—
247	C₂³×C₄	—	73	1	no	—
248	C₂³×C₄	—	73	1	no	—
249	C₂³×C₄	—	73	1	no	—
250	C₂²×C₈	—	73	1	no	—
251	C₂²×C₈	—	73	1	no	—
252	C₂²×C₈	—	73	1	no	—
253	C₂²×C₈	—	73	1	no	—
254	C₂²×C₈	—	73	1	no	—
255	C₂²×C₈	—	73	1	no	—
256	C₂²×C₈	—	73	1	no	—
257	C₂²×C₈	—	73	1	no	—
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	146	4	no	—
261	C₂²×C₈	—	146	4	no	—
262	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
263	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
264	C₂×C₄²	—	73	1	no	—
265	C₂×C₄²	—	73	1	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	73	1	no	—
268	C₂×C₄²	—	73	1	no	—
269	C₂×C₄²	—	73	1	no	—
270	C₂×C₄²	—	73	1	no	—
271	C₂×C₄²	—	73	1	no	—
272	C₂×C₄²	—	73	1	no	—
273	C₂×C₄²	—	73	1	no	—
274	C₂×C₄²	—	73	1	no	—
275	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
276	M₃₂	—	146	8	no	—
277	C₂×C₁₆	—	73	8	no	—
278	C₄×C₈	—	73	1	no	—
279	C₄×C₈	—	73	1	no	—
280	C₄×C₈	—	73	1	no	—
281	C₄×C₈	—	73	1	no	—
282	C₄×C₈	—	73	1	no	—
283	C₄×C₈	—	73	1	no	—
284	C₄×C₈	—	73	1	no	—
285	C₄×C₈	—	73	1	no	—
286	C₄×C₈	—	73	1	no	—
287	C₄×C₈	—	73	1	no	—
288	C₄×C₈	—	73	1	no	—
289	C₄×C₈	—	73	1	no	—
290	C₄×C₈	C₂×#64408	1	1	yes	characteristic
291	C₄×C₈	C₂×#64408	1	1	yes	characteristic
292	C₄×C₈	C₂×#64408	1	1	yes	characteristic
293	C₄×C₈	C₂×#64408	1	1	yes	characteristic
294	C₂⁴	—	73	1	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	146	2	no	—
311	C₂²×C₄	—	146	2	no	—
312	C₂²×C₄	—	146	4	no	—
313	C₂²×C₄	—	146	4	no	—
314	C₂²×C₄	#11924036	1	1	yes	characteristic
315	C₂²×C₄	#11924036	1	1	yes	characteristic
316	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	73	1	no	—
320	C₂×C₈	—	73	1	no	—
321	C₂×C₈	—	73	4	no	—
322	C₂×C₈	—	73	4	no	—
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	—	146	2	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	—	146	2	no	—
331	C₂×C₈	—	146	2	no	—
332	C₂×C₈	—	146	2	no	—
333	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
334	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
335	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
336	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
337	C₄²	—	73	1	no	—
338	C₄²	—	73	1	no	—
339	C₄²	—	73	1	no	—
340	C₄²	—	73	1	no	—
341	C₄²	—	73	1	no	—
342	C₄²	—	73	1	no	—
343	C₄²	—	73	1	no	—
344	C₄²	—	73	1	no	—
345	C₄²	—	73	1	no	—
346	C₄²	—	73	1	no	—
347	C₄²	—	73	1	no	—
348	C₄²	—	73	1	no	—
349	C₄²	#11924036	1	1	yes	characteristic
350	C₄²	#11924036	1	1	yes	characteristic
351	C₄²	C₂²×#64408	1	1	yes	characteristic
352	C₄²	C₂²×#64408	1	1	yes	characteristic
353	C₁₆	—	146	8	no	—
354	C₂³	—	73	1	no	—
355	C₂³	—	73	1	no	—
356	C₂³	—	146	2	no	—
357	C₂³	—	146	2	no	—
358	C₂³	—	146	2	no	—
359	C₂³	C₂×#11924036	1	1	yes	characteristic
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	73	4	no	—
365	C₂×C₄	—	73	1	no	—
366	C₂×C₄	—	73	1	no	—
367	C₂×C₄	—	73	1	no	—
368	C₂×C₄	—	73	1	no	—
369	C₂×C₄	—	73	4	no	—
370	C₂×C₄	—	73	2	no	—
371	C₂×C₄	—	73	2	no	—
372	C₂×C₄	—	73	1	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	2	no	—
378	C₂×C₄	—	146	2	no	—
379	C₂×C₄	—	146	2	no	—
380	C₂×C₄	—	146	2	no	—
381	C₂×C₄	—	146	2	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	2	no	—
385	C₂×C₄	—	146	1	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
388	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
389	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
390	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
391	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
392	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	73	2	no	—
396	C₈	—	73	2	no	—
397	C₈	—	146	1	no	—
398	C₈	—	146	1	no	—
399	C₈	#14556670	1	2	yes	—
400	C₈	D₇₃⋊M₁₆	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	73	2	no	—
404	C₂²	—	73	2	no	—
405	C₂²	—	146	8	no	—
406	C₂²	—	146	1	no	—
407	C₂²	—	146	1	no	—
408	C₂²	—	146	1	no	—
409	C₂²	—	146	1	no	—
410	C₂²	#17989643	1	2	yes	—
411	C₂²	C₂²×#11924036	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	73	2	no	—
417	C₄	—	73	2	no	—
418	C₄	—	73	2	no	—
419	C₄	—	73	2	no	—
420	C₄	—	146	1	no	—
421	C₄	—	146	1	no	—
422	C₄	#17989643	1	2	yes	—
423	C₄	C₂×#14556670	1	1	yes	characteristic
424	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	146	2	no	—
427	C₂	—	146	2	no	—
428	C₂	#22626595	1	1	yes	characteristic
429	C₂	C₂×#17989643	1	1	yes	characteristic
430	C₂	C₂×#17989643	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#33418
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #22626294	C₂	semidirect
2. #22626292	C₂	semidirect
3. #22626291	C₂	semidirect
4. #22626289	C₂	semidirect
5. #22626264	C₂	semidirect
7. #22626138	C₂	semidirect
10. #17989508	C₂²	semidirect
11. C₄⋊#11924031	C₂²	semidirect
14. #17989475	C₂²	semidirect
15. #17989473	C₂²	semidirect
156. C₂×Dic₇₃	M₃₂	semidirect
174. C₄×D₇₃	M₃₂	semidirect
224. C₇₃	#33418	semidirect

Maximal subgroups

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

subgroup	index
#22626294	2
#22626292	2
#22626291	2
#22626289	2
#22626264	2
#22626159	2
#22626138	2
C₂×C₄×C₈×D₇₃	2
#33418	73