Subgroups — #34012146

Order 18688.

586 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989643	C₂	1	1	yes	maximal, characteristic
3	#22624982	C₂	1	2	yes	maximal, complemented
4	#22624981	C₂	1	2	yes	maximal, complemented
5	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556666	—	2	1	no	—
7	C₂×#14556666	C₄	1	2	yes	complemented
8	#17989643	—	2	1	no	—
9	#17989643	—	2	1	no	—
10	#17989643	—	2	1	no	—
11	#17989643	—	2	1	no	—
12	#17989643	—	2	1	no	—
13	#17989643	—	2	1	no	—
14	#17989643	C₄	1	2	yes	complemented
15	#17989643	C₄	1	2	yes	complemented
16	C₂×#14556665	C₂²	1	2	yes	—
17	C₂×#14556665	C₂²	1	2	yes	—
18	C₂×#14556664	—	2	1	no	—
19	C₂×#14556664	C₄	1	2	yes	complemented
20	C₂×M₁₆×D₇₃	C₄	1	1	yes	characteristic
21	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
22	#117×D₇₃	C₄	1	1	yes	characteristic
23	#17988545	C₂²	1	1	yes	characteristic
24	#17988544	—	2	1	no	—
25	#17988543	C₂²	1	1	yes	characteristic
26	#17988542	C₄	1	1	yes	characteristic
27	#17988541	—	2	1	no	—
28	#97×D₇₃	—	2	1	no	—
29	C₄×C₈×D₇₃	—	2	1	no	—
30	#405×C₇₃	C₄	1	1	yes	characteristic
31	#14556666	—	2	2	no	—
32	#14556666	—	2	2	no	—
33	#14556666	—	2	2	no	—
34	#14556666	—	2	2	no	—
35	#14556665	—	2	2	no	—
36	#14556665	—	2	2	no	—
37	#14556665	—	2	2	no	—
38	#14556665	C₂×C₄	1	4	yes	complemented
39	#14556664	—	2	2	no	—
40	#14556664	—	2	2	no	—
41	#14556664	—	2	2	no	—
42	#14556664	—	2	2	no	—
43	C₂×#11924031	—	2	2	no	—
44	C₂×#11924031	C₂×C₄	1	4	yes	complemented
45	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
47	C₂×#11924011	—	2	1	no	—
48	M₁₆×D₇₃	—	2	1	no	—
49	M₁₆×D₇₃	—	2	1	no	—
50	M₁₆×D₇₃	C₈	1	2	yes	—
51	M₁₆×D₇₃	C₈	1	2	yes	—
52	C₂²×#10596831	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₇₃	—	2	1	no	—
54	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
65	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
66	#14556550	C₂×C₄	1	1	yes	characteristic
67	#14556549	—	2	1	no	—
68	#14556548	—	2	1	no	—
69	#14556547	C₈	1	2	yes	—
70	C₄⋊C₄×D₇₃	—	2	1	no	—
71	C₂²⋊C₄×D₇₃	C₈	1	2	yes	—
72	C₄²×D₇₃	—	2	1	no	—
73	#14556502	—	2	1	no	—
74	#14556501	—	2	1	no	—
75	#14556501	—	2	1	no	—
76	C₄×#10596831	—	2	1	no	—
77	C₈×Dic₇₃	—	2	1	no	—
78	C₈×Dic₇₃	—	2	1	no	—
79	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
81	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
82	#97×C₇₃	—	2	1	no	—
83	C₄×C₈×C₇₃	—	2	1	no	—
84	#11924031	—	2	4	no	—
85	#11924031	—	2	4	no	—
86	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
87	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₇₃	—	2	2	no	—
89	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₄⋊C₄	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	M₁₆	1	1	yes	characteristic
98	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
99	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
100	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
101	#11924012	—	2	1	no	—
102	#11924012	C₂×C₈	1	2	yes	—
103	#11924011	—	2	2	no	—
104	#11924011	—	2	2	no	—
105	C₂×#10596831	—	2	1	no	—
106	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
109	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
110	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
111	C₂×#10596831	C₂×Q₈	1	1	yes	characteristic
112	C₈×D₇₃	—	2	2	no	—
113	C₈×D₇₃	—	2	2	no	—
114	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₈×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
123	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
124	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
125	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊Dic₇₃	—	2	1	no	—
131	#11924007	—	2	2	no	—
132	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
133	#11924005	—	2	2	no	—
134	C₄×Dic₇₃	—	2	1	no	—
135	C₄×Dic₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	M₁₆×C₇₃	—	2	1	no	—
138	M₁₆×C₇₃	C₂×C₈	1	2	yes	—
139	C₂×C₈×C₇₃	—	2	1	no	—
140	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
142	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₂²⋊C₄×C₇₃	C₂×C₈	1	2	yes	—
148	C₄²×C₇₃	—	2	1	no	—
149	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂²×D₇₃	—	4	2	no	—
151	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
152	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
153	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
154	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
155	C₂²×D₇₃	C₄⋊C₈	1	1	yes	characteristic
156	C₂²×D₇₃	C₄⋊C₈	1	1	yes	characteristic
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
168	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
169	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
170	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
171	C₄×D₇₃	—	4	4	no	—
172	C₄×D₇₃	#95	1	1	yes	characteristic
173	C₄×D₇₃	#95	1	1	yes	characteristic
174	C₄×D₇₃	#95	1	1	yes	characteristic
175	C₄×D₇₃	#95	1	1	yes	characteristic
176	C₄×D₇₃	#97	1	1	yes	characteristic
177	C₄×D₇₃	#97	1	1	yes	characteristic
178	C₄×D₇₃	#97	1	1	yes	characteristic
179	C₄×D₇₃	#97	1	1	yes	characteristic
180	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
181	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
182	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
183	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
184	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
185	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
186	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
187	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
188	C₈×C₇₃	—	2	2	no	—
189	C₈×C₇₃	#95	1	1	yes	characteristic
190	C₈×C₇₃	#95	1	1	yes	characteristic
191	C₈×C₇₃	#95	1	1	yes	characteristic
192	C₈×C₇₃	#95	1	1	yes	characteristic
193	#10596831	—	2	2	no	—
194	#10596831	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	#10596831	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
197	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₇₃	—	4	1	no	—
199	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
200	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
201	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
202	C₂×D₇₃	—	2	2	no	—
203	C₂×D₇₃	—	2	2	no	—
204	C₂×D₇₃	—	2	2	no	—
205	C₂×D₇₃	—	4	1	no	—
206	C₂×D₇₃	—	4	1	no	—
207	C₂×D₇₃	—	4	1	no	—
208	C₂×D₇₃	#336	1	1	yes	characteristic
209	C₂×D₇₃	#336	1	1	yes	characteristic
210	C₂×D₇₃	#336	1	1	yes	characteristic
211	C₂×D₇₃	#336	1	1	yes	characteristic
212	C₄×C₇₃	—	4	2	no	—
213	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
214	C₄×C₇₃	C₂×#97	1	1	yes	characteristic
215	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
216	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
217	Dic₇₃	—	4	2	no	—
218	Dic₇₃	#336	1	1	yes	characteristic
219	Dic₇₃	#336	1	1	yes	characteristic
220	Dic₇₃	#336	1	1	yes	characteristic
221	Dic₇₃	#336	1	1	yes	characteristic
222	C₂×#1378	—	73	1	no	maximal, Sylow
223	C₂×C₇₃	—	2	1	no	—
224	C₂×C₇₃	—	2	1	no	—
225	C₂×C₇₃	—	2	1	no	—
226	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
227	D₇₃	—	2	1	no	—
228	D₇₃	—	2	1	no	—
229	D₇₃	—	2	1	no	—
230	D₇₃	#1378	1	2	yes	complemented
231	C₂²×M₃₂	—	73	1	no	—
232	C₂²×M₃₂	—	73	1	no	—
233	C₂×#405	—	73	1	no	—
234	#1378	—	73	2	no	—
235	#1378	—	73	2	no	—
236	C₇₃	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
237	C₂²×M₁₆	—	73	1	no	—
238	C₂³×C₈	—	73	1	no	—
239	C₂×#117	—	73	1	no	—
240	C₂×M₃₂	—	73	2	no	—
241	C₂×M₃₂	—	73	2	no	—
242	C₂×M₃₂	—	73	2	no	—
243	C₂×M₃₂	—	73	2	no	—
244	C₂×M₃₂	—	73	2	no	—
245	C₂×M₃₂	—	146	1	no	—
246	C₂×M₃₂	—	146	1	no	—
247	C₂×M₃₂	—	146	1	no	—
248	C₂×M₃₂	—	146	1	no	—
249	C₂×M₃₂	—	146	1	no	—
250	C₂×M₃₂	—	146	1	no	—
251	C₂×M₃₂	—	146	1	no	—
252	C₂²×C₁₆	—	73	2	no	—
253	C₂²×C₁₆	—	146	1	no	—
254	#405	—	73	1	no	—
255	#405	—	73	1	no	—
256	#405	—	73	1	no	—
257	#405	—	146	1	no	—
258	#405	—	146	1	no	—
259	#405	#64408	1	1	yes	characteristic
260	C₂×#97	—	146	1	no	—
261	C₂×C₄×C₈	—	146	1	no	—
262	C₂³×C₄	—	73	1	no	—
263	C₂×M₁₆	—	73	1	no	—
264	C₂×M₁₆	—	73	2	no	—
265	C₂×M₁₆	—	73	2	no	—
266	C₂×M₁₆	—	146	1	no	—
267	C₂×M₁₆	—	146	1	no	—
268	C₂×M₁₆	—	146	1	no	—
269	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
270	C₂²×C₈	—	73	1	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	1	no	—
273	C₂²×C₈	—	73	1	no	—
274	C₂²×C₈	—	73	1	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂²×C₈	—	73	1	no	—
278	C₂²×C₈	—	73	1	no	—
279	C₂²×C₈	—	73	1	no	—
280	C₂²×C₈	—	73	1	no	—
281	C₂²×C₈	—	73	1	no	—
282	C₂²×C₈	—	73	1	no	—
283	C₂²×C₈	—	146	1	no	—
284	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
285	#117	—	73	1	no	—
286	#117	—	73	2	no	—
287	#117	—	146	1	no	—
288	#117	—	146	1	no	—
289	#117	C₂×#64408	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	146	1	no	—
291	C₂×C₂²⋊C₄	—	73	2	no	—
292	C₂×C₄²	—	146	1	no	—
293	M₃₂	—	73	4	no	—
294	M₃₂	—	146	2	no	—
295	M₃₂	—	146	2	no	—
296	M₃₂	—	146	2	no	—
297	M₃₂	—	146	2	no	—
298	M₃₂	—	146	2	no	—
299	M₃₂	—	146	2	no	—
300	M₃₂	—	146	2	no	—
301	C₂×C₁₆	—	73	4	no	—
302	C₂×C₁₆	—	146	2	no	—
303	C₂×C₁₆	—	146	2	no	—
304	C₂×C₁₆	—	146	2	no	—
305	C₂×C₁₆	—	146	2	no	—
306	C₂×C₁₆	—	146	2	no	—
307	#97	—	2	1	no	—
308	#97	—	146	1	no	—
309	#97	—	146	1	no	—
310	#97	—	146	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	146	1	no	—
313	C₄×C₈	—	146	1	no	—
314	C₄×C₈	—	146	1	no	—
315	C₂⁴	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	—	73	1	no	—
323	C₂²×C₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	—	73	1	no	—
327	C₂²×C₄	—	73	1	no	—
328	C₂²×C₄	—	73	1	no	—
329	C₂²×C₄	—	146	2	no	—
330	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
331	M₁₆	—	2	1	no	—
332	M₁₆	—	73	2	no	—
333	M₁₆	—	146	2	no	—
334	M₁₆	—	146	2	no	—
335	M₁₆	—	146	1	no	—
336	M₁₆	#11924036	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	73	1	no	—
339	C₂×C₈	—	73	1	no	—
340	C₂×C₈	—	73	1	no	—
341	C₂×C₈	—	73	1	no	—
342	C₂×C₈	—	73	1	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	—	73	1	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	73	1	no	—
356	C₂×C₈	—	73	1	no	—
357	C₂×C₈	—	73	1	no	—
358	C₂×C₈	—	73	1	no	—
359	C₂×C₈	—	73	1	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	—	146	2	no	—
362	C₂×C₈	—	146	1	no	—
363	C₂×C₈	C₄×#64408	1	1	yes	characteristic
364	C₂×C₈	C₄×#64408	1	1	yes	characteristic
365	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
366	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
367	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
368	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	146	2	no	—
371	C₄⋊C₄	—	146	1	no	—
372	C₂²⋊C₄	—	73	2	no	—
373	C₂²⋊C₄	—	146	2	no	—
374	C₂²⋊C₄	#11924036	1	2	yes	—
375	C₄²	—	2	1	no	—
376	C₄²	—	146	2	no	—
377	C₄²	—	146	1	no	—
378	C₁₆	—	146	4	no	—
379	C₁₆	—	146	4	no	—
380	C₂³	—	292	2	no	—
381	C₂³	—	73	1	no	—
382	C₂³	—	73	1	no	—
383	C₂³	—	73	1	no	—
384	C₂³	—	73	1	no	—
385	C₂³	—	73	1	no	—
386	C₂³	—	73	1	no	—
387	C₂³	C₂×#11924036	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	292	4	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	73	1	no	—
407	C₂×C₄	—	73	1	no	—
408	C₂×C₄	—	73	1	no	—
409	C₂×C₄	—	73	1	no	—
410	C₂×C₄	—	73	1	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
414	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
416	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
417	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
418	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	73	1	no	—
421	C₈	—	73	1	no	—
422	C₈	—	73	1	no	—
423	C₈	—	73	1	no	—
424	C₈	—	146	2	no	—
425	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
426	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
427	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
428	C₈	(C₂×#64408)⋊C₄	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	292	1	no	—
431	C₂²	—	292	1	no	—
432	C₂²	—	292	1	no	—
433	C₂²	—	73	1	no	—
434	C₂²	—	73	1	no	—
435	C₂²	—	73	1	no	—
436	C₂²	—	73	1	no	—
437	C₂²	—	146	2	no	—
438	C₂²	—	146	2	no	—
439	C₂²	—	146	2	no	—
440	C₂²	C₄×#11924036	1	1	yes	characteristic
441	C₂²	#17989555	1	1	yes	characteristic
442	C₂²	#17989588	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	292	2	no	—
445	C₄	—	73	1	no	—
446	C₄	—	73	1	no	—
447	C₄	—	73	1	no	—
448	C₄	—	73	1	no	—
449	C₄	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
450	C₄	#17989546	1	1	yes	characteristic
451	C₄	#17989555	1	1	yes	characteristic
452	C₄	#17989588	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	73	2	no	—
457	C₂	—	146	1	no	—
458	C₂	—	146	1	no	—
459	C₂	—	146	1	no	—
460	C₂	#22625592	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×#64408)⋊C₄
commutator	C₂²×C₇₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#64408
Fitting	#405×C₇₃	C₄
socle	C₂×C₇₃	C₂×#336
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₂²×#10596831	C₂³
hypercenter	#405	#64408
hypocenter	C₇₃	C₂×#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #22624982	C₂	semidirect
4. #22624981	C₂	semidirect
7. C₂×#14556666	C₄	semidirect
14. #17989643	C₄	semidirect
15. #17989643	C₄	semidirect
19. C₂×#14556664	C₄	semidirect
38. #14556665	C₂×C₄	semidirect
44. C₂×#11924031	C₂×C₄	semidirect
230. D₇₃	#1378	semidirect
236. C₇₃	C₂×#1378	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989643	2
#22624982	2
#22624981	2
#405×D₇₃	2
C₂×#1378	73