Subgroups — #33004141

Order 18688.

522 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	C₂×C₈×C₂²⋊D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂²⋊#11924003	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17988366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17988366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17988362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂²⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
10	C₂²×#11924003	C₂²	1	1	yes	characteristic
11	C₂²×#11924003	C₂²	1	1	yes	characteristic
12	C₈×C₂²⋊D₇₃	—	2	2	no	—
13	C₈×C₂²⋊D₇₃	—	2	2	no	—
14	C₂×#14556520	C₄	1	1	yes	characteristic
15	C₂×C₂²⋊#10596831	C₄	1	1	yes	characteristic
16	C₂×#14556503	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	#17988405	—	2	2	no	—
19	C₂²⋊#11924003	—	2	2	no	—
20	#17988366	—	2	2	no	—
21	#17988366	—	2	2	no	—
22	#17988362	—	2	2	no	—
23	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²⋊C₁₆×C₇₃	—	2	2	no	—
27	C₂²×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
28	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
30	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×D₇₃	—	2	1	no	—
32	C₂×C₈×D₇₃	—	2	1	no	—
33	C₂×C₈×D₇₃	—	2	1	no	—
34	C₂×C₈×D₇₃	—	2	1	no	—
35	C₂×C₈×D₇₃	—	2	1	no	—
36	C₂×C₈×D₇₃	—	2	1	no	—
37	C₄×C₂²⋊D₇₃	—	2	2	no	—
38	C₄×C₂²⋊D₇₃	—	2	2	no	—
39	C₂×#11924007	C₈	1	1	yes	characteristic
40	C₂×C₂²⋊Dic₇₃	C₈	1	1	yes	characteristic
41	C₂×#11924005	C₈	1	1	yes	characteristic
42	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
43	C₂×#11924003	—	2	1	no	—
44	C₂×#11924003	—	2	1	no	—
45	C₂×#11924003	—	2	1	no	—
46	C₂×#11924003	—	2	1	no	—
47	C₂×#11924003	—	2	1	no	—
48	C₂×#11924003	D₄	1	2	yes	complemented
49	#14556520	—	2	2	no	—
50	C₂²⋊#10596831	—	2	2	no	—
51	#14556503	—	2	2	no	—
52	C₈×Dic₇₃	D₄	1	2	yes	—
53	C₈×Dic₇₃	D₄	1	2	yes	—
54	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₃	—	2	1	no	—
56	C₂²×C₈×C₇₃	—	2	1	no	—
57	C₂²×C₈×C₇₃	—	2	1	no	—
58	C₂²×C₈×C₇₃	—	2	1	no	—
59	C₂²×C₈×C₇₃	—	2	1	no	—
60	C₂²×C₈×C₇₃	—	2	1	no	—
61	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₆×C₇₃	—	2	1	no	—
64	C₂×C₁₆×C₇₃	—	2	1	no	—
65	C₂×C₁₆×C₇₃	—	2	1	no	—
66	C₂×C₁₆×C₇₃	—	2	1	no	—
67	C₂×C₁₆×C₇₃	—	2	1	no	—
68	C₂×C₁₆×C₇₃	D₄	1	2	yes	complemented
69	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
70	C₂×C₂²⋊D₇₃	—	2	2	no	—
71	C₂×C₂²⋊D₇₃	—	2	2	no	—
72	C₂×C₂²⋊D₇₃	—	2	2	no	—
73	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
74	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
75	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
76	C₂×C₄×D₇₃	—	2	1	no	—
77	C₂×C₄×D₇₃	—	2	1	no	—
78	C₂×C₄×D₇₃	—	2	1	no	—
79	C₂×C₄×D₇₃	—	2	1	no	—
80	C₂×C₄×D₇₃	—	2	1	no	—
81	C₂×C₄×D₇₃	—	2	1	no	—
82	C₂×#10596831	—	2	1	no	—
83	C₂×#10596831	—	2	1	no	—
84	C₂×#10596831	—	2	1	no	—
85	C₂×#10596831	—	2	1	no	—
86	C₂×#10596831	—	2	1	no	—
87	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
88	C₈×D₇₃	—	4	1	no	—
89	C₈×D₇₃	—	4	1	no	—
90	C₈×D₇₃	—	4	1	no	—
91	C₈×D₇₃	—	4	1	no	—
92	#11924007	—	2	2	no	—
93	C₂²⋊Dic₇₃	—	2	2	no	—
94	#11924005	—	2	2	no	—
95	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
96	C₄×Dic₇₃	M₁₆	1	2	yes	—
97	#11924003	—	2	2	no	—
98	#11924003	—	4	1	no	—
99	C₂⁴×C₇₃	C₂×C₈	1	1	yes	characteristic
100	C₂²×C₄×C₇₃	—	2	1	no	—
101	C₂²×C₄×C₇₃	—	2	1	no	—
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	—	2	1	no	—
104	C₂²×C₄×C₇₃	—	2	1	no	—
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₇₃	—	2	1	no	—
109	C₂×C₈×C₇₃	—	2	1	no	—
110	C₂×C₈×C₇₃	—	2	1	no	—
111	C₂×C₈×C₇₃	—	4	1	no	—
112	C₂×C₈×C₇₃	—	4	1	no	—
113	C₂×C₈×C₇₃	—	4	1	no	—
114	C₂×C₈×C₇₃	—	4	1	no	—
115	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
121	C₁₆×C₇₃	—	2	2	no	—
122	C₁₆×C₇₃	—	4	1	no	—
123	C₂³×C₇₃	—	2	1	no	—
124	C₂³×C₇₃	—	2	1	no	—
125	C₂³×C₇₃	—	2	1	no	—
126	C₂³×C₇₃	—	2	1	no	—
127	C₂³×C₇₃	—	2	1	no	—
128	C₂³×C₇₃	—	2	1	no	—
129	C₂³×C₇₃	M₃₂	1	2	yes	—
130	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
131	C₂²×D₇₃	—	2	1	no	—
132	C₂²×D₇₃	—	2	1	no	—
133	C₂²×D₇₃	—	2	1	no	—
134	C₂²×D₇₃	—	2	1	no	—
135	C₂²×D₇₃	—	2	1	no	—
136	C₂²×D₇₃	—	2	1	no	—
137	C₂²×D₇₃	M₃₂	1	2	yes	—
138	C₂×C₄×C₇₃	—	2	1	no	—
139	C₂×C₄×C₇₃	—	2	1	no	—
140	C₂×C₄×C₇₃	—	2	1	no	—
141	C₂×C₄×C₇₃	—	4	1	no	—
142	C₂×C₄×C₇₃	—	4	1	no	—
143	C₂×C₄×C₇₃	—	4	1	no	—
144	C₂×C₄×C₇₃	—	4	1	no	—
145	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
150	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
151	C₂²⋊D₇₃	—	2	8	no	—
152	C₂×Dic₇₃	—	2	1	no	—
153	C₂×Dic₇₃	—	2	1	no	—
154	C₂×Dic₇₃	—	2	1	no	—
155	C₂×Dic₇₃	—	2	1	no	—
156	C₂×Dic₇₃	—	2	1	no	—
157	C₂×Dic₇₃	—	2	1	no	—
158	C₂×Dic₇₃	—	2	1	no	—
159	C₂×Dic₇₃	C₂²⋊C₈	1	2	yes	—
160	C₂×Dic₇₃	C₂²⋊C₈	1	2	yes	—
161	C₄×D₇₃	—	4	1	no	—
162	C₄×D₇₃	—	4	1	no	—
163	C₄×D₇₃	—	4	1	no	—
164	C₄×D₇₃	—	4	1	no	—
165	C₈×C₇₃	—	4	1	no	—
166	C₈×C₇₃	#121	1	1	yes	characteristic
167	C₈×C₇₃	#121	1	1	yes	characteristic
168	C₈×C₇₃	#124	1	1	yes	characteristic
169	C₈×C₇₃	#127	1	1	yes	characteristic
170	#10596831	—	2	2	no	—
171	#10596831	—	4	1	no	—
172	C₂²×C₇₃	—	2	2	no	—
173	C₂²×C₇₃	—	2	2	no	—
174	C₂²×C₇₃	—	2	2	no	—
175	C₂²×C₇₃	—	4	1	no	—
176	C₂²×C₇₃	—	4	1	no	—
177	C₂²×C₇₃	—	4	1	no	—
178	C₂²×C₇₃	—	4	1	no	—
179	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
180	C₂²×C₇₃	C₈×D₄	1	1	yes	characteristic
181	C₂²×C₇₃	C₈×D₄	1	1	yes	characteristic
182	C₂²×C₇₃	C₂×M₃₂	1	1	yes	characteristic
183	C₂²×C₇₃	C₂×M₃₂	1	1	yes	characteristic
184	C₂²×C₇₃	#504	1	1	yes	characteristic
185	C₂²×C₇₃	#504	1	1	yes	characteristic
186	C₂×D₇₃	—	2	2	no	—
187	C₂×D₇₃	—	2	2	no	—
188	C₂×D₇₃	—	2	2	no	—
189	C₂×D₇₃	—	4	1	no	—
190	C₂×D₇₃	—	4	1	no	—
191	C₂×D₇₃	—	4	1	no	—
192	C₂×D₇₃	—	4	1	no	—
193	C₄×C₇₃	—	4	1	no	—
194	C₄×C₇₃	#390	1	1	yes	characteristic
195	C₄×C₇₃	#408	1	1	yes	characteristic
196	C₄×C₇₃	#436	1	1	yes	characteristic
197	C₄×C₇₃	#436	1	1	yes	characteristic
198	Dic₇₃	—	2	2	no	—
199	Dic₇₃	—	2	2	no	—
200	Dic₇₃	—	4	1	no	—
201	#13190	—	73	1	no	maximal, Sylow
202	C₂×C₇₃	—	4	2	no	—
203	C₂×C₇₃	#1954	1	1	yes	characteristic
204	C₂×C₇₃	#2112	1	1	yes	characteristic
205	C₂×C₇₃	#2113	1	1	yes	characteristic
206	C₂×C₇₃	#2168	1	1	yes	characteristic
207	C₂×C₇₃	#2168	1	1	yes	characteristic
208	C₂×C₇₃	#2168	1	1	yes	characteristic
209	C₂×C₇₃	#2168	1	1	yes	characteristic
210	D₇₃	—	4	2	no	—
211	C₂×C₈×D₄	—	73	1	no	—
212	C₂×C₄⋊C₁₆	—	73	1	no	—
213	C₂×C₂²⋊C₁₆	—	73	1	no	—
214	C₂×C₂²⋊C₁₆	—	73	1	no	—
215	C₂×C₂²⋊C₁₆	—	73	1	no	—
216	C₂×C₂²⋊C₁₆	D₇₃	1	1	yes	characteristic, complemented
217	C₂×#346	—	73	1	no	—
218	C₇₃	#13190	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₈	—	73	1	no	—
220	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
221	C₂×C₄×D₄	—	73	1	no	—
222	C₂²×C₁₆	—	73	1	no	—
223	C₂²×C₁₆	—	73	1	no	—
224	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
225	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
226	C₈×D₄	—	146	2	no	—
227	C₈×D₄	—	146	2	no	—
228	C₂×C₄⋊C₈	—	73	1	no	—
229	C₂×C₂²⋊C₈	—	73	1	no	—
230	C₂×C₂²⋊C₈	—	73	1	no	—
231	C₂×C₄×C₈	—	73	1	no	—
232	C₄⋊C₁₆	—	146	2	no	—
233	C₂²⋊C₁₆	—	2	2	no	—
234	C₂²⋊C₁₆	—	146	2	no	—
235	C₂²⋊C₁₆	—	146	2	no	—
236	C₂²⋊C₁₆	—	146	2	no	—
237	#346	—	146	2	no	—
238	C₂²×D₄	—	73	1	no	—
239	C₂³×C₄	—	73	1	no	—
240	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	73	1	no	—
248	C₂²×C₈	—	73	1	no	—
249	C₂²×C₈	—	146	1	no	—
250	C₂²×C₈	—	146	1	no	—
251	C₂²×C₈	—	146	1	no	—
252	C₂²×C₈	—	146	1	no	—
253	C₂²×C₈	—	146	1	no	—
254	C₂²×C₈	—	146	1	no	—
255	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
257	C₄×D₄	—	146	2	no	—
258	C₄×D₄	—	146	2	no	—
259	C₂×C₄⋊C₄	—	73	1	no	—
260	C₂×C₂²⋊C₄	—	73	1	no	—
261	C₂×C₂²⋊C₄	—	73	1	no	—
262	C₂×C₄²	—	73	1	no	—
263	C₂×C₁₆	—	2	1	no	—
264	C₂×C₁₆	—	2	1	no	—
265	C₂×C₁₆	—	2	1	no	—
266	C₂×C₁₆	—	2	1	no	—
267	C₂×C₁₆	—	2	1	no	—
268	C₂×C₁₆	—	73	2	no	—
269	C₂×C₁₆	—	146	1	no	—
270	C₂×C₁₆	—	146	1	no	—
271	C₂×C₁₆	—	146	1	no	—
272	C₂×C₁₆	—	146	1	no	—
273	C₂×C₁₆	—	146	1	no	—
274	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	complemented
275	C₄⋊C₈	—	146	2	no	—
276	C₂²⋊C₈	—	146	2	no	—
277	C₂²⋊C₈	—	146	2	no	—
278	C₄×C₈	—	73	2	no	—
279	C₄×C₈	—	73	2	no	—
280	C₂⁴	—	73	1	no	—
281	C₂⁴	C₈×D₇₃	1	1	yes	characteristic
282	C₂×D₄	—	146	2	no	—
283	C₂×D₄	—	146	2	no	—
284	C₂×D₄	—	146	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	73	1	no	—
292	C₂²×C₄	—	73	1	no	—
293	C₂²×C₄	—	73	1	no	—
294	C₂²×C₄	—	146	1	no	—
295	C₂²×C₄	—	146	1	no	—
296	C₂²×C₄	—	146	1	no	—
297	C₂²×C₄	—	146	1	no	—
298	C₂²×C₄	—	146	1	no	—
299	C₂²×C₄	—	146	1	no	—
300	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	292	1	no	—
310	C₂×C₈	—	292	1	no	—
311	C₂×C₈	—	292	1	no	—
312	C₂×C₈	—	292	1	no	—
313	C₂×C₈	—	73	2	no	—
314	C₂×C₈	—	146	1	no	—
315	C₂×C₈	—	146	1	no	—
316	C₂×C₈	—	146	1	no	—
317	C₂×C₈	—	146	1	no	—
318	C₂×C₈	—	146	1	no	—
319	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
320	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
321	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
322	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
323	C₂×C₈	#11924027	1	1	yes	characteristic
324	C₂×C₈	#11924028	1	1	yes	characteristic
325	C₄⋊C₄	—	146	2	no	—
326	C₂²⋊C₄	—	146	2	no	—
327	C₂²⋊C₄	—	146	2	no	—
328	C₄²	—	73	2	no	—
329	C₄²	—	73	2	no	—
330	C₁₆	—	2	2	no	—
331	C₁₆	—	4	1	no	—
332	C₁₆	—	292	1	no	—
333	C₁₆	—	146	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	73	2	no	—
341	C₂³	—	146	1	no	—
342	C₂³	—	146	1	no	—
343	C₂³	—	146	1	no	—
344	C₂³	—	146	1	no	—
345	C₂³	—	146	1	no	—
346	C₂³	—	146	1	no	—
347	C₂³	#14556530	1	2	yes	—
348	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
349	D₄	—	146	8	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	292	1	no	—
358	C₂×C₄	—	292	1	no	—
359	C₂×C₄	—	292	1	no	—
360	C₂×C₄	—	292	1	no	—
361	C₂×C₄	—	73	2	no	—
362	C₂×C₄	—	73	2	no	—
363	C₂×C₄	—	146	1	no	—
364	C₂×C₄	—	146	1	no	—
365	C₂×C₄	—	146	1	no	—
366	C₂×C₄	—	146	1	no	—
367	C₂×C₄	—	146	1	no	—
368	C₂×C₄	—	146	1	no	—
369	C₂×C₄	—	146	1	no	—
370	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
371	C₂×C₄	#14556551	1	1	yes	characteristic
372	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
373	C₂×C₄	M₁₆×D₇₃	1	1	yes	characteristic
374	C₂×C₄	#14556597	1	1	yes	characteristic
375	C₂×C₄	#14556599	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	292	1	no	—
378	C₈	—	146	2	no	—
379	C₈	#14556563	1	1	yes	characteristic
380	C₈	#14556564	1	1	yes	characteristic
381	C₈	#14556577	1	1	yes	characteristic
382	C₈	#14556587	1	1	yes	characteristic
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	292	1	no	—
391	C₂²	—	292	1	no	—
392	C₂²	—	292	1	no	—
393	C₂²	—	292	1	no	—
394	C₂²	—	146	2	no	—
395	C₂²	—	146	2	no	—
396	C₂²	—	146	2	no	—
397	C₂²	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
398	C₂²	#17988650	1	1	yes	characteristic
399	C₂²	C₈×C₂²⋊D₇₃	1	1	yes	characteristic
400	C₂²	M₃₂×D₇₃	1	1	yes	characteristic
401	C₂²	C₂×#14556530	1	1	yes	characteristic
402	C₂²	#17989003	1	1	yes	characteristic
403	C₂²	#17989005	1	1	yes	characteristic
404	C₄	—	4	1	no	—
405	C₄	—	292	1	no	—
406	C₄	—	146	2	no	—
407	C₄	—	146	2	no	—
408	C₄	#17988487	1	1	yes	characteristic
409	C₄	#17988552	1	1	yes	characteristic
410	C₄	#17988662	1	1	yes	characteristic
411	C₄	#17988663	1	1	yes	characteristic
412	C₂	—	4	2	no	—
413	C₂	—	292	2	no	—
414	C₂	#22610723	1	1	yes	characteristic
415	C₂	#22611540	1	1	yes	characteristic
416	C₂	#22611543	1	1	yes	characteristic
417	C₂	#22611753	1	1	yes	characteristic
418	C₂	#22611754	1	1	yes	characteristic
419	C₂	#22611756	1	1	yes	characteristic
420	C₂	#22611759	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₇₃
commutator, socle	C₂³×C₇₃	C₂²×C₈
Fitting	C₂×C₂²⋊C₁₆×C₇₃	C₂
prime radical	C₂²×C₂²⋊D₇₃	C₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₇₃
hypocenter	C₇₃	#13190
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#17988405	C₂	semidirect
3. C₂×C₂²⋊#11924003	C₂	semidirect
4. C₂×#17988366	C₂	semidirect
5. C₂×#17988366	C₂	semidirect
6. C₂×#17988362	C₂	semidirect
7. C₂×C₂²⋊C₁₆×C₇₃	C₂	semidirect
48. C₂×#11924003	D₄	semidirect
68. C₂×C₁₆×C₇₃	D₄	semidirect
216. C₂×C₂²⋊C₁₆	D₇₃	semidirect
218. C₇₃	#13190	semidirect
274. C₂×C₁₆	C₂²⋊D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂²⋊D₇₃	2
C₂×#17988405	2
C₂×C₂²⋊#11924003	2
C₂×#17988366	2
C₂×#17988362	2
C₂×C₂²⋊C₁₆×C₇₃	2
#13190	73