Subgroups — #33104066

Order 18688.

992 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988666	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988612	C₂	1	2	yes	maximal, complemented
4	#22612395	C₂	1	1	yes	maximal, characteristic
5	#22610649	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610649	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610115	C₂	1	2	yes	maximal, complemented
8	#22610110	C₂	1	2	yes	maximal, complemented
9	#22610083	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609912	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	2	yes	—
13	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	C₂×#14556548	C₂²	1	2	yes	—
16	#17988666	—	2	4	no	—
17	C₈×D₂₉₂	—	2	4	no	—
18	#17988612	—	2	8	no	—
19	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
20	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
23	C₂×#14556520	C₂²	1	2	yes	—
24	C₂×#14556520	C₂²	1	2	yes	—
25	C₂×#14556503	C₂²	1	2	yes	—
26	C₂×#14556503	C₂²	1	2	yes	—
27	#17988489	C₄	1	1	yes	characteristic
28	#17988489	C₄	1	1	yes	characteristic
29	#17988485	C₄	1	1	yes	characteristic
30	#17988485	C₄	1	1	yes	characteristic
31	#17988478	C₄	1	2	yes	—
32	#17988478	C₄	1	2	yes	—
33	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
34	C₄×#11924005	C₂²	1	2	yes	—
35	#17988341	C₂²	1	2	yes	—
36	#17988341	C₂²	1	2	yes	—
37	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₄³×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	#336×C₇₃	C₂²	1	1	yes	characteristic
44	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
46	C₂×#11924011	—	2	4	no	—
47	C₂×#11924011	—	2	4	no	—
48	C₂×#11924011	—	4	2	no	—
49	C₂²×#10596831	C₂³	1	2	yes	—
50	C₂²×#10596831	C₂³	1	2	yes	—
51	C₂×C₈×D₇₃	—	2	4	no	—
52	C₂×C₈×D₇₃	—	2	4	no	—
53	C₂×C₈×D₇₃	—	4	2	no	—
54	C₄×D₂₉₂	D₄	1	4	yes	—
55	C₄×D₂₉₂	Q₈	1	4	yes	—
56	#14556548	—	2	4	no	—
57	#14556548	—	2	4	no	—
58	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×#11924007	C₂×C₄	1	2	yes	—
62	C₂×#11924007	C₂×C₄	1	2	yes	—
63	C₂×#11924005	C₂×C₄	1	2	yes	—
64	C₂×#11924005	C₂×C₄	1	2	yes	—
65	C₂×#11924005	C₂×C₄	1	2	yes	—
66	C₂×#11924005	C₂×C₄	1	2	yes	—
67	C₂×#11924005	C₂×C₄	1	2	yes	—
68	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
69	C₄⋊#10596831	—	2	4	no	—
70	C₄⋊#10596831	—	2	2	no	—
71	C₄⋊#10596831	—	2	2	no	—
72	C₄⋊#10596831	—	4	2	no	—
73	#14556520	—	2	4	no	—
74	#14556520	—	2	4	no	—
75	#14556503	—	2	4	no	—
76	#14556503	—	2	4	no	—
77	#14556498	C₂×C₄	1	2	yes	—
78	#14556498	C₂×C₄	1	2	yes	—
79	#14556498	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₇₃	—	2	2	no	—
92	C₄⋊C₈×C₇₃	D₄	1	4	yes	complemented
93	C₄×C₈×C₇₃	—	2	2	no	—
94	C₄×C₈×C₇₃	—	2	2	no	—
95	C₂³×D₇₃	C₂²×C₄	1	2	yes	—
96	C₂×D₂₉₂	—	2	2	no	—
97	C₂×D₂₉₂	—	2	2	no	—
98	C₂×D₂₉₂	C₄⋊C₄	1	4	yes	—
99	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
101	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₇₃	—	2	2	no	—
103	C₂×C₄×D₇₃	—	2	2	no	—
104	C₂×C₄×D₇₃	—	2	2	no	—
105	C₂×C₄×D₇₃	—	2	2	no	—
106	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
107	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
108	#11924011	—	4	8	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	—	2	2	no	—
115	C₈×D₇₃	—	4	8	no	—
116	C₄⋊Dic₇₃	—	2	2	no	—
117	C₄⋊Dic₇₃	—	2	2	no	—
118	C₄⋊Dic₇₃	C₄⋊C₄	1	4	yes	—
119	#11924007	—	2	4	no	—
120	#11924007	—	2	4	no	—
121	#11924005	—	2	4	no	—
122	#11924005	—	2	4	no	—
123	#11924005	—	2	4	no	—
124	#11924005	—	4	2	no	—
125	#11924005	C₄⋊C₄	1	8	yes	—
126	C₄×Dic₇₃	—	2	2	no	—
127	C₄×Dic₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	—	2	1	no	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	2	1	no	—
140	C₂×C₈×C₇₃	—	2	1	no	—
141	C₂×C₈×C₇₃	—	2	1	no	—
142	C₂×C₈×C₇₃	—	2	1	no	—
143	C₂×C₈×C₇₃	—	2	1	no	—
144	C₂×C₈×C₇₃	—	2	1	no	—
145	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
147	C₄²×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	1	no	—
151	C₄²×C₇₃	—	2	1	no	—
152	C₄²×C₇₃	—	4	1	no	—
153	C₄²×C₇₃	C₂×D₄	1	2	yes	—
154	C₄²×C₇₃	C₂×D₄	1	2	yes	—
155	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
156	C₄²×C₇₃	#41	1	2	yes	—
157	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
158	C₂²×D₇₃	—	2	2	no	—
159	C₂²×D₇₃	—	2	2	no	—
160	C₂²×D₇₃	—	2	2	no	—
161	C₂²×D₇₃	—	2	2	no	—
162	C₂²×D₇₃	—	2	2	no	—
163	C₂²×D₇₃	—	2	2	no	—
164	C₂²×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₇₃	#131	1	2	yes	—
181	C₂×C₄×C₇₃	#131	1	2	yes	—
182	C₂×C₄×C₇₃	#131	1	2	yes	—
183	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×Dic₇₃	—	2	2	no	—
190	C₂×Dic₇₃	—	2	2	no	—
191	C₂×Dic₇₃	—	2	2	no	—
192	C₂×Dic₇₃	—	2	2	no	—
193	C₂×Dic₇₃	—	2	2	no	—
194	C₂×Dic₇₃	—	2	2	no	—
195	C₂×Dic₇₃	—	2	2	no	—
196	C₂×Dic₇₃	—	2	2	no	—
197	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
198	D₂₉₂	—	2	8	no	—
199	C₄×D₇₃	—	2	4	no	—
200	C₄×D₇₃	—	2	4	no	—
201	C₄×D₇₃	—	2	4	no	—
202	C₄×D₇₃	—	2	4	no	—
203	C₈×C₇₃	—	2	2	no	—
204	C₈×C₇₃	—	2	2	no	—
205	C₈×C₇₃	—	4	1	no	—
206	C₈×C₇₃	—	4	1	no	—
207	#10596831	—	4	2	no	—
208	#10596831	—	4	2	no	—
209	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
210	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₇₃	#520	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
213	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
214	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
215	C₂²×C₇₃	#568	1	1	yes	characteristic
216	C₂×D₇₃	—	2	4	no	—
217	C₂×D₇₃	—	2	4	no	—
218	C₂×D₇₃	—	2	4	no	—
219	C₂×D₇₃	—	4	2	no	—
220	C₂×D₇₃	—	4	2	no	—
221	C₂×D₇₃	—	4	2	no	—
222	C₂×D₇₃	—	4	2	no	—
223	C₄×C₇₃	—	2	2	no	—
224	C₄×C₇₃	—	2	2	no	—
225	C₄×C₇₃	—	2	2	no	—
226	C₄×C₇₃	—	2	2	no	—
227	C₄×C₇₃	—	4	1	no	—
228	C₄×C₇₃	#424	1	4	yes	complemented
229	C₄×C₇₃	D₄²	1	1	yes	characteristic
230	C₄×C₇₃	#547	1	1	yes	characteristic
231	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
232	C₄×C₇₃	#554	1	1	yes	characteristic
233	Dic₇₃	—	2	4	no	—
234	Dic₇₃	—	4	2	no	—
235	Dic₇₃	—	4	2	no	—
236	#22651	—	73	1	no	maximal, Sylow
237	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₇₃	C₂×#424	1	1	yes	characteristic
239	C₂×C₇₃	#2906	1	1	yes	characteristic
240	C₂×C₇₃	#2931	1	1	yes	characteristic
241	C₂×C₇₃	#2935	1	1	yes	characteristic
242	C₂×C₇₃	#2993	1	1	yes	characteristic
243	C₂×C₇₃	#2994	1	1	yes	characteristic
244	D₇₃	—	4	4	no	—
245	C₂×#436	—	73	1	no	—
246	C₂×C₈×D₄	—	73	1	no	—
247	C₂×#424	—	73	2	no	—
248	#2293	—	73	1	no	—
249	#1939	—	73	1	no	—
250	#1939	—	73	1	no	—
251	#1851	—	73	2	no	—
252	#1850	—	73	2	no	—
253	#1842	—	73	1	no	—
254	#1798	—	73	2	no	—
255	C₄×C₄⋊C₈	D₇₃	1	1	yes	characteristic, complemented
256	C₇₃	#22651	1	1	yes	characteristic, complemented, Sylow
257	C₂²×M₁₆	—	73	2	no	—
258	C₂³×C₈	—	73	2	no	—
259	C₂×C₄×D₄	—	73	1	no	—
260	C₂×#117	—	73	2	no	—
261	#436	—	146	4	no	—
262	C₈×D₄	—	146	4	no	—
263	#424	—	146	8	no	—
264	C₂×C₄⋊C₈	—	73	2	no	—
265	C₂×C₄⋊C₈	—	73	2	no	—
266	C₂×C₄⋊C₈	—	73	2	no	—
267	C₂×C₄⋊C₈	—	73	2	no	—
268	C₂×C₄⋊C₈	—	73	1	no	—
269	C₂×C₄⋊C₈	—	73	1	no	—
270	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	—	73	2	no	—
273	C₂×C₂²⋊C₈	—	73	2	no	—
274	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
276	#390	—	73	1	no	—
277	#390	—	73	1	no	—
278	#389	—	73	1	no	—
279	#389	—	73	1	no	—
280	#388	—	73	2	no	—
281	#388	—	73	2	no	—
282	C₄×C₄⋊C₄	—	73	1	no	—
283	C₄×C₂²⋊C₄	—	73	2	no	—
284	C₄³	C₂×D₇₃	1	1	yes	characteristic
285	#336	—	73	2	no	—
286	#336	—	73	2	no	—
287	#336	C₂×D₇₃	1	1	yes	characteristic
288	#336	C₂×D₇₃	1	1	yes	characteristic
289	C₂²×D₄	—	73	1	no	—
290	C₂³×C₄	—	73	2	no	—
291	C₂×M₁₆	—	292	2	no	—
292	C₂×M₁₆	—	146	4	no	—
293	C₂×M₁₆	—	146	4	no	—
294	C₂²×C₈	—	292	2	no	—
295	C₂²×C₈	—	73	2	no	—
296	C₂²×C₈	—	73	2	no	—
297	C₂²×C₈	—	146	4	no	—
298	C₂²×C₈	—	146	4	no	—
299	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
302	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
303	C₄×D₄	—	73	4	no	—
304	C₄×D₄	—	73	4	no	—
305	#117	—	146	4	no	—
306	#117	—	146	4	no	—
307	C₂×C₄⋊C₄	—	73	1	no	—
308	C₂×C₄⋊C₄	—	73	2	no	—
309	C₂×C₄⋊C₄	—	73	2	no	—
310	C₂×C₄⋊C₄	—	73	1	no	—
311	C₂×C₄⋊C₄	—	73	1	no	—
312	C₂×C₂²⋊C₄	—	73	2	no	—
313	C₂×C₂²⋊C₄	—	73	2	no	—
314	C₂×C₂²⋊C₄	—	73	2	no	—
315	C₂×C₂²⋊C₄	—	73	2	no	—
316	C₂×C₂²⋊C₄	—	73	2	no	—
317	C₂×C₄²	—	73	2	no	—
318	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
319	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
320	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
321	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	292	2	no	—
327	C₄⋊C₈	—	146	4	no	—
328	C₄⋊C₈	—	146	4	no	—
329	C₄⋊C₈	—	146	2	no	—
330	C₄⋊C₈	—	146	2	no	—
331	C₄⋊C₈	—	146	4	no	—
332	C₄⋊C₈	D₂₉₂	1	4	yes	complemented
333	C₂²⋊C₈	—	146	4	no	—
334	C₂²⋊C₈	—	146	4	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	—	2	2	no	—
337	#95	—	73	2	no	—
338	#95	—	73	2	no	—
339	#95	—	73	2	no	—
340	C₂⁴	—	73	2	no	—
341	C₂×D₄	—	73	4	no	—
342	C₂×D₄	—	146	2	no	—
343	C₂×D₄	—	146	2	no	—
344	C₂²×C₄	—	73	2	no	—
345	C₂²×C₄	—	73	4	no	—
346	C₂²×C₄	—	73	4	no	—
347	C₂²×C₄	—	73	2	no	—
348	C₂²×C₄	—	73	2	no	—
349	C₂²×C₄	—	146	2	no	—
350	C₂²×C₄	—	146	2	no	—
351	C₂²×C₄	—	146	2	no	—
352	C₂²×C₄	—	146	2	no	—
353	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
360	M₁₆	—	292	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	292	8	no	—
372	C₂×C₈	—	146	2	no	—
373	C₂×C₈	—	146	2	no	—
374	C₂×C₈	—	146	2	no	—
375	C₂×C₈	—	146	2	no	—
376	C₂×C₈	—	146	2	no	—
377	C₂×C₈	—	146	2	no	—
378	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
379	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
380	C₄⋊C₄	—	73	4	no	—
381	C₄⋊C₄	—	146	4	no	—
382	C₄⋊C₄	—	146	4	no	—
383	C₄⋊C₄	—	146	2	no	—
384	C₄⋊C₄	—	146	2	no	—
385	C₂²⋊C₄	—	292	2	no	—
386	C₂²⋊C₄	—	73	8	no	—
387	C₂²⋊C₄	—	146	4	no	—
388	C₂²⋊C₄	—	146	4	no	—
389	C₂²⋊C₄	—	146	4	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	146	2	no	—
397	C₄²	—	146	2	no	—
398	C₄²	D₄×D₇₃	1	2	yes	—
399	C₄²	C₂×D₂₉₂	1	2	yes	—
400	C₄²	Q₈×D₇₃	1	2	yes	—
401	C₄²	#11924028	1	2	yes	—
402	C₂³	—	73	4	no	—
403	C₂³	—	146	2	no	—
404	C₂³	—	146	2	no	—
405	C₂³	—	146	2	no	—
406	C₂³	—	146	2	no	—
407	C₂³	—	146	2	no	—
408	C₂³	—	146	2	no	—
409	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
410	D₄	—	146	8	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	73	4	no	—
423	C₂×C₄	—	146	2	no	—
424	C₂×C₄	—	146	2	no	—
425	C₂×C₄	—	146	2	no	—
426	C₂×C₄	—	146	2	no	—
427	C₂×C₄	—	146	2	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	—	146	2	no	—
430	C₂×C₄	—	146	2	no	—
431	C₂×C₄	—	146	4	no	—
432	C₂×C₄	—	146	4	no	—
433	C₂×C₄	—	146	4	no	—
434	C₂×C₄	—	146	4	no	—
435	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
436	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
437	C₂×C₄	C₄×D₂₉₂	1	2	yes	—
438	C₂×C₄	C₄×D₂₉₂	1	2	yes	—
439	C₂×C₄	#14556597	1	2	yes	—
440	C₂×C₄	#14556597	1	2	yes	—
441	C₂×C₄	#14556599	1	2	yes	—
442	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
444	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
446	C₂×C₄	#14556637	1	1	yes	characteristic
447	C₂×C₄	#14556638	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	1	no	—
452	C₈	—	292	2	no	—
453	C₈	—	292	2	no	—
454	C₂²	—	292	2	no	—
455	C₂²	—	292	2	no	—
456	C₂²	—	292	2	no	—
457	C₂²	—	292	2	no	—
458	C₂²	—	146	4	no	—
459	C₂²	—	146	4	no	—
460	C₂²	—	146	4	no	—
461	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
462	C₂²	C₂×C₄×D₂₉₂	1	1	yes	characteristic
463	C₂²	#17989067	1	1	yes	characteristic
464	C₂²	C₂×#14556597	1	1	yes	characteristic
465	C₂²	C₂×#14556597	1	1	yes	characteristic
466	C₂²	C₂×#14556599	1	1	yes	characteristic
467	C₂²	#17989353	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	292	2	no	—
474	C₄	—	292	2	no	—
475	C₄	—	146	4	no	—
476	C₄	#17988612	1	4	yes	complemented
477	C₄	D₄×D₂₉₂	1	1	yes	characteristic
478	C₄	#17989242	1	1	yes	characteristic
479	C₄	Q₈×D₂₉₂	1	1	yes	characteristic
480	C₄	#17989297	1	1	yes	characteristic
481	C₂	—	292	4	no	—
482	C₂	C₄⋊C₄×D₂₉₂	1	1	yes	characteristic
483	C₂	C₂×#17988612	1	1	yes	characteristic
484	C₂	#22618496	1	1	yes	characteristic
485	C₂	#22618644	1	1	yes	characteristic
486	C₂	#22618677	1	1	yes	characteristic
487	C₂	#22619082	1	1	yes	characteristic
488	C₂	#22619093	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₄×C₄⋊C₈×C₇₃	C₂
prime radical	C₂²×D₂₉₂	C₂×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₇₃
hypocenter	C₇₃	#22651
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#17988612	C₂	semidirect
5. #22610649	C₂	semidirect
6. #22610649	C₂	semidirect
7. #22610115	C₂	semidirect
8. #22610110	C₂	semidirect
9. #22610083	C₂	semidirect
10. #22609912	C₂	semidirect
11. C₄×C₄⋊C₈×C₇₃	C₂	semidirect
92. C₄⋊C₈×C₇₃	D₄	semidirect
228. C₄×C₇₃	#424	semidirect
255. C₄×C₄⋊C₈	D₇₃	semidirect
256. C₇₃	#22651	semidirect
332. C₄⋊C₈	D₂₉₂	semidirect
476. C₄	#17988612	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988666	2
C₂×C₈×D₂₉₂	2
C₂×#17988612	2
#22612395	2
#22610649	2
#22610115	2
#22610110	2
#22610083	2
#22609912	2
C₄×C₄⋊C₈×C₇₃	2
#22651	73