Subgroups — #33056002

Order 18688.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619980	C₂	1	1	yes	maximal, characteristic
2	#22618906	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608769	C₂	1	2	yes	maximal, complemented
5	#22608762	C₂	1	2	yes	maximal, complemented
6	#22608756	C₂	1	2	yes	maximal, complemented
7	#22608745	C₂	1	2	yes	maximal, complemented
8	#22608716	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608375	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₇₃	—	2	1	no	—
13	#17989121	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	#17988923	C₄	1	1	yes	characteristic
16	#17988906	C₄	1	1	yes	characteristic
17	#17988888	C₄	1	2	yes	—
18	#17988803	C₄	1	2	yes	—
19	#17988740	C₄	1	1	yes	characteristic
20	#17988723	C₄	1	1	yes	characteristic
21	#17988717	C₂²	1	1	yes	characteristic, complemented
22	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
23	C₄×#11924017	C₂²	1	2	yes	—
24	C₄×D₅₈₄	C₂²	1	2	yes	—
25	#17988666	C₂²	1	1	yes	characteristic, complemented
26	#17988658	—	2	1	no	—
27	C₈×D₂₉₂	—	2	1	no	—
28	C₈×D₂₉₂	—	2	1	no	—
29	C₈×D₂₉₂	C₂²	1	2	yes	—
30	C₈×D₂₉₂	C₂²	1	2	yes	—
31	C₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
32	C₈×C₂²⋊D₇₃	—	2	1	no	—
33	#17988646	—	2	1	no	—
34	#17988644	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
36	C₂×#14556503	—	2	1	no	—
37	#17988541	—	2	1	no	—
38	#17988340	C₂²	1	2	yes	complemented
39	#17988338	C₂²	1	2	yes	complemented
40	#17988319	C₂²	1	2	yes	complemented
41	#17988316	C₂²	1	2	yes	—
42	#17988316	C₂²	1	2	yes	—
43	#17988316	C₂²	1	2	yes	complemented
44	#431×C₇₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#322×C₇₃	C₂²	1	2	yes	complemented
48	#322×C₇₃	C₂²	1	2	yes	complemented
49	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₇₃	—	2	1	no	—
51	C₂×#11924017	C₂×C₄	1	2	yes	—
52	C₂×D₅₈₄	C₂×C₄	1	2	yes	—
53	C₂×#11924011	—	2	1	no	—
54	C₂²×#10596831	—	2	1	no	—
55	C₂×C₈×D₇₃	—	2	1	no	—
56	C₂×C₈×D₇₃	—	2	2	no	—
57	C₂×C₈×D₇₃	—	2	2	no	—
58	C₂×C₈×D₇₃	—	4	4	no	—
59	#14556585	—	2	1	no	—
60	#14556583	C₂×C₄	1	1	yes	characteristic
61	#14556579	C₂×C₄	1	1	yes	characteristic
62	#14556574	—	2	1	no	—
63	#14556570	C₂×C₄	1	1	yes	characteristic
64	#14556565	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
66	C₄×D₂₉₂	—	2	1	no	—
67	C₄×D₂₉₂	—	2	1	no	—
68	C₄×D₂₉₂	C₂×C₄	1	2	yes	—
69	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
70	C₄×D₂₉₂	C₂³	1	2	yes	—
71	C₄×C₂²⋊D₇₃	—	2	1	no	—
72	#14556548	—	2	1	no	—
73	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×#11924005	—	2	1	no	—
75	#14556525	C₂×C₄	1	2	yes	—
76	#14556523	C₂×C₄	1	2	yes	—
77	C₄⋊#10596831	—	2	1	no	—
78	C₄⋊#10596831	C₂³	1	2	yes	—
79	C₄⋊#10596831	C₂³	1	1	yes	characteristic
80	C₄⋊#10596831	C₂³	1	1	yes	characteristic
81	#14556520	—	2	1	no	—
82	#14556520	—	2	1	no	—
83	#14556516	C₂×C₄	1	2	yes	—
84	#14556513	C₂×C₄	1	2	yes	—
85	#14556513	C₂×C₄	1	2	yes	—
86	#14556513	C₂×C₄	1	2	yes	—
87	C₂²⋊#10596831	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	#14556503	—	2	1	no	—
90	#14556503	—	2	2	no	—
91	#14556503	—	2	2	no	—
92	#14556502	—	2	1	no	—
93	#14556501	—	2	1	no	—
94	C₈×Dic₇₃	—	2	1	no	—
95	C₂×M₁₆×C₇₃	—	2	1	no	—
96	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
102	#97×C₇₃	—	2	1	no	—
103	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	C₂³	1	2	yes	—
106	C₄×C₈×C₇₃	C₂³	1	2	yes	—
107	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂³×D₇₃	—	2	1	no	—
110	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₂₉₂	—	2	1	no	—
112	C₂×D₂₉₂	—	2	4	no	—
113	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
115	C₂×C₂²⋊D₇₃	—	2	1	no	—
116	C₂²×Dic₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	2	2	no	—
118	C₂×C₄×D₇₃	—	2	1	no	—
119	C₂×C₄×D₇₃	—	2	2	no	—
120	C₂×C₄×D₇₃	—	4	2	no	—
121	C₂×C₄×D₇₃	—	4	2	no	—
122	#11924017	—	2	4	no	—
123	D₅₈₄	—	2	4	no	—
124	#11924011	—	4	2	no	—
125	C₂×#10596831	—	2	1	no	—
126	C₂×#10596831	—	2	1	no	—
127	C₂×#10596831	—	2	2	no	—
128	C₂×#10596831	—	4	2	no	—
129	C₈×D₇₃	—	4	2	no	—
130	C₈×D₇₃	—	4	4	no	—
131	C₈×D₇₃	—	4	4	no	—
132	C₄⋊Dic₇₃	—	2	1	no	—
133	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
136	#11924007	—	2	1	no	—
137	#11924007	—	2	1	no	—
138	#11924007	—	2	1	no	—
139	#11924007	—	2	1	no	—
140	C₂²⋊Dic₇₃	—	2	1	no	—
141	#11924005	—	2	2	no	—
142	#11924005	—	2	1	no	—
143	#11924005	—	2	1	no	—
144	#11924005	—	2	1	no	—
145	#11924005	—	2	2	no	—
146	#11924005	—	2	1	no	—
147	C₄×Dic₇₃	—	2	1	no	—
148	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
151	M₁₆×C₇₃	—	4	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	4	1	no	—
155	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇₃	#41	1	1	yes	characteristic
164	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
165	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₇₃	—	2	4	no	—
167	C₂²×D₇₃	—	2	2	no	—
168	C₂²×D₇₃	—	2	1	no	—
169	C₂²×D₇₃	—	4	2	no	—
170	C₂²×D₇₃	—	4	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	4	2	no	—
182	C₂×Dic₇₃	—	2	1	no	—
183	C₂×Dic₇₃	—	2	1	no	—
184	C₂×Dic₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	2	1	no	—
186	C₂×Dic₇₃	—	4	2	no	—
187	D₂₉₂	—	2	4	no	—
188	D₂₉₂	—	2	2	no	—
189	D₂₉₂	—	2	2	no	—
190	D₂₉₂	#131	1	4	yes	—
191	C₄×D₇₃	—	4	4	no	—
192	C₄×D₇₃	—	4	2	no	—
193	C₄×D₇₃	—	4	1	no	—
194	C₄×D₇₃	—	4	1	no	—
195	C₄×D₇₃	—	4	2	no	—
196	Dic₁₄₆	—	2	2	no	—
197	C₈×C₇₃	—	2	2	no	—
198	C₈×C₇₃	—	2	2	no	—
199	C₈×C₇₃	—	2	1	no	—
200	C₈×C₇₃	—	2	1	no	—
201	C₈×C₇₃	—	2	1	no	—
202	C₈×C₇₃	—	4	2	no	—
203	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
204	#10596831	—	4	2	no	—
205	#10596831	—	4	1	no	—
206	#10596831	—	4	1	no	—
207	C₂²×C₇₃	—	2	1	no	—
208	C₂²×C₇₃	—	2	1	no	—
209	C₂²×C₇₃	#444	1	2	yes	—
210	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₇₃	—	2	4	no	—
212	C₂×D₇₃	—	4	8	no	—
213	C₂×D₇₃	—	4	2	no	—
214	C₂×D₇₃	—	4	2	no	—
215	C₂×D₇₃	—	4	1	no	—
216	C₂×D₇₃	—	4	1	no	—
217	C₂×D₇₃	—	4	1	no	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	—	2	1	no	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	—	2	1	no	—
222	C₄×C₇₃	C₂×#131	1	2	yes	—
223	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₄×C₇₃	#575	1	1	yes	characteristic
225	Dic₇₃	—	4	1	no	—
226	Dic₇₃	—	4	2	no	—
227	Dic₇₃	—	4	1	no	—
228	Dic₇₃	—	4	1	no	—
229	#17914	—	73	1	no	maximal, Sylow
230	C₂×C₇₃	—	2	2	no	—
231	C₂×C₇₃	#2929	1	1	yes	characteristic
232	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
234	D₇₃	—	4	4	no	—
235	D₇₃	—	8	1	no	—
236	#3105	—	73	1	no	—
237	#2966	—	73	1	no	—
238	C₂×C₈×D₄	—	73	1	no	—
239	#1582	—	73	2	no	—
240	#1581	—	73	2	no	—
241	#1580	—	73	2	no	—
242	SD₁₆⋊C₈	—	73	2	no	—
243	#1573	—	73	1	no	—
244	#1490	—	73	1	no	—
245	#1483	—	73	1	no	—
246	#1451	D₇₃	1	1	yes	characteristic, complemented
247	C₇₃	#17914	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₈	—	146	1	no	—
249	#529	—	73	1	no	—
250	C₂×C₄×D₄	—	73	1	no	—
251	#484	—	73	1	no	—
252	#481	—	73	1	no	—
253	#478	—	73	2	no	—
254	#463	—	73	2	no	—
255	#450	—	73	1	no	—
256	#447	—	73	1	no	—
257	#446	—	73	1	no	—
258	C₈×Q₈	—	73	1	no	—
259	C₄×SD₁₆	—	73	2	no	—
260	C₄×D₈	—	73	2	no	—
261	#436	—	73	1	no	—
262	#435	—	146	1	no	—
263	C₈×D₄	—	73	2	no	—
264	C₈×D₄	—	73	1	no	—
265	C₈×D₄	—	73	2	no	—
266	C₈×D₄	—	146	1	no	—
267	C₈×D₄	—	146	1	no	—
268	C₈×D₄	—	146	1	no	—
269	#433	—	146	1	no	—
270	#432	—	73	1	no	—
271	#431	C₂×D₇₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	73	1	no	—
273	C₂×C₂²⋊C₈	—	146	1	no	—
274	#405	—	146	1	no	—
275	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
277	#335	—	73	2	no	—
278	#334	—	73	2	no	—
279	Q₈⋊C₈	—	73	2	no	—
280	D₄⋊C₈	—	73	2	no	—
281	D₄⋊C₈	—	73	2	no	—
282	D₄⋊C₈	—	73	2	no	—
283	#322	C₂×D₇₃	1	2	yes	complemented
284	#322	C₂×D₇₃	1	2	yes	complemented
285	C₂²×D₄	—	73	1	no	—
286	C₂³×C₄	—	146	1	no	—
287	C₂×SD₁₆	—	73	2	no	—
288	C₂×D₈	—	73	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	146	1	no	—
291	C₂²×C₈	—	292	4	no	—
292	C₂²×C₈	—	146	1	no	—
293	C₂²×C₈	—	146	2	no	—
294	C₂²×C₈	—	146	2	no	—
295	C₂²×C₈	—	146	1	no	—
296	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
297	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
298	#126	—	146	1	no	—
299	#125	—	73	1	no	—
300	#124	—	73	1	no	—
301	#123	—	146	1	no	—
302	C₂²⋊Q₈	—	73	1	no	—
303	#121	—	73	1	no	—
304	C₄×Q₈	—	73	1	no	—
305	C₄×D₄	—	73	2	no	—
306	C₄×D₄	—	73	2	no	—
307	C₄×D₄	—	73	1	no	—
308	C₄×D₄	—	146	1	no	—
309	C₄×D₄	—	146	1	no	—
310	C₄×D₄	—	146	1	no	—
311	#117	—	146	1	no	—
312	C₂×C₄⋊C₄	—	73	1	no	—
313	C₂×C₂²⋊C₄	—	146	1	no	—
314	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
315	#107	—	73	2	no	—
316	#106	—	73	2	no	—
317	C₄⋊C₈	—	73	1	no	—
318	C₄⋊C₈	—	73	1	no	—
319	C₄⋊C₈	—	73	2	no	—
320	C₄⋊C₈	—	146	1	no	—
321	C₄⋊C₈	—	146	1	no	—
322	C₄⋊C₈	—	146	1	no	—
323	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
324	#103	—	73	2	no	—
325	#102	—	73	2	no	—
326	#102	—	73	2	no	—
327	#102	—	73	2	no	—
328	C₂²⋊C₈	—	146	1	no	—
329	C₂²⋊C₈	—	146	2	no	—
330	C₂²⋊C₈	—	146	2	no	—
331	C₂²⋊C₈	—	146	1	no	—
332	C₂²⋊C₈	—	146	1	no	—
333	C₂²⋊C₈	C₄×D₇₃	1	1	yes	characteristic
334	C₂²⋊C₈	C₄×D₇₃	1	1	yes	characteristic
335	#97	—	2	1	no	—
336	#97	—	146	1	no	—
337	#97	—	146	1	no	—
338	C₄×C₈	—	146	1	no	—
339	C₄×C₈	D₂₉₂	1	1	yes	characteristic
340	C₄×C₈	D₂₉₂	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₇₃	1	2	yes	—
342	C₄×C₈	C₂²×D₇₃	1	2	yes	—
343	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
345	C₂⁴	—	146	1	no	—
346	C₂×Q₈	—	73	1	no	—
347	C₂×D₄	—	73	2	no	—
348	C₂×D₄	—	73	1	no	—
349	C₂×D₄	—	146	4	no	—
350	C₂×D₄	—	146	1	no	—
351	C₂×D₄	—	146	1	no	—
352	C₂²×C₄	—	292	2	no	—
353	C₂²×C₄	—	292	2	no	—
354	C₂²×C₄	—	146	1	no	—
355	C₂²×C₄	—	146	2	no	—
356	C₂²×C₄	—	146	1	no	—
357	C₂²×C₄	—	146	2	no	—
358	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
360	C₂²×C₄	#11924028	1	1	yes	characteristic
361	SD₁₆	—	146	4	no	—
362	D₈	—	146	4	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	—	292	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	292	4	no	—
369	C₂×C₈	—	292	2	no	—
370	C₂×C₈	—	292	2	no	—
371	C₂×C₈	—	292	4	no	—
372	C₂×C₈	—	146	1	no	—
373	C₂×C₈	—	146	1	no	—
374	C₂×C₈	—	146	2	no	—
375	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
377	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
378	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
379	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
380	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
381	C₄⋊C₄	—	73	1	no	—
382	C₄⋊C₄	—	73	1	no	—
383	C₄⋊C₄	—	73	2	no	—
384	C₄⋊C₄	—	146	1	no	—
385	C₄⋊C₄	—	146	1	no	—
386	C₄⋊C₄	—	146	1	no	—
387	C₄⋊C₄	—	146	1	no	—
388	C₄⋊C₄	—	146	1	no	—
389	C₂²⋊C₄	—	146	1	no	—
390	C₂²⋊C₄	—	146	2	no	—
391	C₂²⋊C₄	—	146	1	no	—
392	C₂²⋊C₄	—	146	1	no	—
393	C₂²⋊C₄	—	146	1	no	—
394	C₂²⋊C₄	—	146	2	no	—
395	C₂²⋊C₄	—	146	1	no	—
396	C₄²	—	146	1	no	—
397	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
398	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
399	C₄²	#11924028	1	1	yes	characteristic
400	C₄²	C₂³×D₇₃	1	1	yes	characteristic
401	C₂³	—	292	2	no	—
402	C₂³	—	292	2	no	—
403	C₂³	—	146	4	no	—
404	C₂³	—	146	1	no	—
405	C₂³	—	146	2	no	—
406	C₂³	C₄×D₂₉₂	1	1	yes	characteristic
407	Q₈	—	146	2	no	—
408	D₄	—	292	2	no	—
409	D₄	—	73	4	no	—
410	D₄	—	146	4	no	—
411	D₄	—	146	2	no	—
412	D₄	—	146	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	292	4	no	—
418	C₂×C₄	—	292	2	no	—
419	C₂×C₄	—	292	2	no	—
420	C₂×C₄	—	292	1	no	—
421	C₂×C₄	—	292	1	no	—
422	C₂×C₄	—	292	2	no	—
423	C₂×C₄	—	146	1	no	—
424	C₂×C₄	—	146	1	no	—
425	C₂×C₄	—	146	1	no	—
426	C₂×C₄	—	146	2	no	—
427	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
428	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
429	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
432	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	2	2	no	—
437	C₈	—	2	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	292	2	no	—
440	C₈	—	292	1	no	—
441	C₈	—	292	1	no	—
442	C₈	#14556619	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	292	8	no	—
446	C₂²	—	292	2	no	—
447	C₂²	—	292	2	no	—
448	C₂²	—	292	1	no	—
449	C₂²	—	292	1	no	—
450	C₂²	—	292	1	no	—
451	C₂²	—	146	4	no	—
452	C₂²	#17988710	1	2	yes	—
453	C₂²	C₂×C₄×D₂₉₂	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	292	1	no	—
459	C₄	—	292	2	no	—
460	C₄	—	292	1	no	—
461	C₄	—	292	1	no	—
462	C₄	#131×D₇₃	1	2	yes	—
463	C₄	C₂×#14556619	1	1	yes	characteristic
464	C₄	#17989387	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	292	4	no	—
467	C₂	—	584	1	no	—
468	C₂	#22618627	1	1	yes	characteristic
469	C₂	C₄×#14556619	1	1	yes	characteristic
470	C₂	C₂×#17988710	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1451	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#17988723	C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1451	D₇₃
hypocenter	C₇₃	#17914
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #22618906	C₂	semidirect
3. C₂×C₈×D₂₉₂	C₂	semidirect
4. #22608769	C₂	semidirect
5. #22608762	C₂	semidirect
6. #22608756	C₂	semidirect
7. #22608745	C₂	semidirect
8. #22608716	C₂	semidirect
9. #22608375	C₂	semidirect
10. #22608345	C₂	semidirect
11. C₇₃×#1451	C₂	semidirect
21. #17988717	C₂²	semidirect
22. C₈×Dic₁₄₆	C₂²	semidirect
25. #17988666	C₂²	semidirect
31. C₈×D₂₉₂	C₂²	semidirect
38. #17988340	C₂²	semidirect
39. #17988338	C₂²	semidirect
40. #17988319	C₂²	semidirect
43. #17988316	C₂²	semidirect
47. #322×C₇₃	C₂²	semidirect
48. #322×C₇₃	C₂²	semidirect
246. #1451	D₇₃	semidirect
247. C₇₃	#17914	semidirect
283. #322	C₂×D₇₃	semidirect
284. #322	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22619980	2
#22618906	2
C₂×C₈×D₂₉₂	2
#22608769	2
#22608762	2
#22608756	2
#22608745	2
#22608716	2
#22608375	2
#22608345	2
C₇₃×#1451	2
#17914	73