Subgroups — #33056579

Order 18688.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620531	C₂	1	1	yes	maximal, characteristic
2	#22618906	C₂	1	1	yes	maximal, characteristic
3	#22608838	C₂	1	2	yes	maximal, complemented
4	#22608831	C₂	1	2	yes	maximal, complemented
5	C₈×#11924018	C₂	1	2	yes	maximal, complemented
6	C₈×#11924015	C₂	1	2	yes	maximal, complemented
7	#22608696	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608404	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608394	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989121	C₂²	1	1	yes	characteristic
13	#17988993	C₄	1	1	yes	characteristic
14	#17988979	C₄	1	1	yes	characteristic
15	#17988955	C₄	1	1	yes	characteristic
16	#17988949	C₄	1	1	yes	characteristic
17	#17988843	C₄	1	2	yes	—
18	#17988835	C₄	1	2	yes	—
19	#17988717	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
21	C₄×#11924018	C₂²	1	2	yes	—
22	C₄×#11924015	C₂²	1	2	yes	—
23	#17988666	C₂²	1	1	yes	characteristic
24	#17988658	—	2	1	no	—
25	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₇₃	—	2	1	no	—
27	#17988646	—	2	1	no	—
28	#17988644	C₂²	1	1	yes	characteristic
29	#17988640	C₂²	1	1	yes	characteristic
30	#17988541	—	2	1	no	—
31	C₄×#11924012	C₂²	1	1	yes	characteristic
32	#17988339	C₂²	1	2	yes	—
33	#17988337	C₂²	1	2	yes	—
34	Q₈⋊#10596831	C₂²	1	2	yes	—
35	Q₈⋊#10596831	C₂²	1	2	yes	—
36	#17988317	C₂²	1	2	yes	—
37	#17988314	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	C₈×#10596831	C₂²	1	2	yes	—
40	#533×C₇₃	C₂²	1	1	yes	characteristic
41	#446×C₇₃	—	2	1	no	—
42	#446×C₇₃	C₂²	1	2	yes	—
43	C₈×Q₈×C₇₃	—	2	1	no	—
44	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
45	#424×C₇₃	—	2	1	no	—
46	#423×C₇₃	C₂²	1	1	yes	characteristic
47	#405×C₇₃	—	2	1	no	—
48	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#11924018	C₂×C₄	1	2	yes	—
50	C₂×#11924015	C₂×C₄	1	2	yes	—
51	C₂×#11924012	C₂×C₄	1	2	yes	—
52	C₂×#11924011	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	1	no	—
54	#14556585	—	2	1	no	—
55	#14556583	C₂×C₄	1	1	yes	characteristic
56	#14556579	C₂×C₄	1	1	yes	characteristic
57	#14556574	—	2	1	no	—
58	#14556570	C₂×C₄	1	1	yes	characteristic
59	#14556565	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
61	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₇₃	—	2	1	no	—
63	#14556548	—	2	1	no	—
64	#14556524	C₂×C₄	1	2	yes	—
65	#14556522	C₂×C₄	1	2	yes	—
66	C₄⋊#10596831	—	2	1	no	—
67	C₄⋊#10596831	C₂³	1	1	yes	characteristic
68	C₄⋊#10596831	C₂³	1	1	yes	characteristic
69	#14556520	—	2	1	no	—
70	#14556520	—	2	1	no	—
71	#14556515	C₂×C₄	1	2	yes	—
72	#14556515	C₂×C₄	1	2	yes	—
73	#14556514	C₂×C₄	1	2	yes	—
74	#14556511	C₂×C₄	1	2	yes	—
75	C₂²⋊#10596831	—	2	1	no	—
76	C₂²⋊#10596831	—	2	1	no	—
77	#14556503	—	2	1	no	—
78	#14556503	—	2	1	no	—
79	#14556502	—	2	1	no	—
80	#14556502	C₂×C₄	1	1	yes	characteristic
81	#14556502	C₂×C₄	1	1	yes	characteristic
82	#14556501	—	2	1	no	—
83	C₄×#10596831	C₂³	1	2	yes	—
84	C₄×#10596831	C₂³	1	2	yes	—
85	C₈×Dic₇₃	—	2	1	no	—
86	C₂×M₁₆×C₇₃	—	2	1	no	—
87	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	#125×C₇₃	—	2	1	no	—
92	C₂²⋊Q₈×C₇₃	—	2	1	no	—
93	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₇₃	—	2	1	no	—
95	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
96	#117×C₇₃	—	2	1	no	—
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	—	2	2	no	—
99	C₄⋊C₈×C₇₃	—	2	2	no	—
100	C₄⋊C₈×C₇₃	—	2	1	no	—
101	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
102	#97×C₇₃	—	2	2	no	—
103	C₄×C₈×C₇₃	—	2	2	no	—
104	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	1	no	—
112	#11924018	—	2	4	no	—
113	#11924015	—	2	4	no	—
114	#11924012	—	2	4	no	—
115	#11924011	—	4	2	no	—
116	C₂×#10596831	—	2	1	no	—
117	C₂×#10596831	—	2	1	no	—
118	C₂×#10596831	—	2	2	no	—
119	C₂×#10596831	C₂²×C₄	1	2	yes	—
120	C₂×#10596831	C₂²×C₄	1	2	yes	—
121	C₈×D₇₃	—	4	2	no	—
122	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
124	#11924007	—	2	1	no	—
125	#11924007	—	2	1	no	—
126	#11924007	—	2	1	no	—
127	#11924007	—	2	1	no	—
128	C₂²⋊Dic₇₃	—	2	1	no	—
129	#11924005	—	2	1	no	—
130	#11924005	—	2	1	no	—
131	#11924005	—	2	1	no	—
132	#11924005	—	2	1	no	—
133	C₄×Dic₇₃	—	2	1	no	—
134	C₂×Q₈×C₇₃	—	2	1	no	—
135	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
139	M₁₆×C₇₃	—	4	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	4	1	no	—
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₇₃	—	2	1	no	—
148	C₄⋊C₄×C₇₃	—	2	1	no	—
149	C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₇₃	—	2	2	no	—
154	C₄²×C₇₃	—	2	2	no	—
155	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₃	#41	1	1	yes	characteristic
158	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₇₃	—	2	1	no	—
161	Q₈×C₇₃	—	2	2	no	—
162	Q₈×C₇₃	—	2	2	no	—
163	Q₈×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₇₃	—	4	2	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	2	1	no	—
179	C₂×Dic₇₃	—	2	1	no	—
180	D₂₉₂	—	2	2	no	—
181	C₄×D₇₃	—	4	1	no	—
182	C₄×D₇₃	—	4	1	no	—
183	Dic₁₄₆	—	2	2	no	—
184	C₈×C₇₃	—	2	1	no	—
185	C₈×C₇₃	—	2	1	no	—
186	C₈×C₇₃	—	2	1	no	—
187	C₈×C₇₃	—	4	2	no	—
188	C₈×C₇₃	#137	1	2	yes	—
189	#10596831	—	2	2	no	—
190	#10596831	—	4	2	no	—
191	#10596831	—	4	1	no	—
192	#10596831	—	4	1	no	—
193	#10596831	#131	1	4	yes	—
194	C₂²×C₇₃	—	2	1	no	—
195	C₂²×C₇₃	—	2	1	no	—
196	C₂²×C₇₃	—	2	1	no	—
197	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₇₃	—	4	1	no	—
199	C₂×D₇₃	—	4	1	no	—
200	C₂×D₇₃	—	4	1	no	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	—	2	1	no	—
203	C₄×C₇₃	—	2	1	no	—
204	C₄×C₇₃	—	2	1	no	—
205	C₄×C₇₃	—	4	2	no	—
206	C₄×C₇₃	—	4	2	no	—
207	C₄×C₇₃	C₂×#131	1	2	yes	—
208	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
209	C₄×C₇₃	#575	1	1	yes	characteristic
210	Dic₇₃	—	4	1	no	—
211	Dic₇₃	—	4	1	no	—
212	Dic₇₃	—	4	1	no	—
213	#17965	—	73	1	no	maximal, Sylow
214	C₂×C₇₃	—	4	1	no	—
215	C₂×C₇₃	#2931	1	1	yes	characteristic
216	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
217	C₂×C₇₃	#2955	1	1	yes	characteristic
218	D₇₃	—	8	1	no	—
219	#3172	—	73	1	no	—
220	#2966	—	73	1	no	—
221	#2960	D₇₃	1	1	yes	characteristic, complemented
222	#1593	—	73	2	no	—
223	#1592	—	73	2	no	—
224	C₈×Q₁₆	—	73	2	no	—
225	C₈×SD₁₆	—	73	2	no	—
226	#1569	—	73	1	no	—
227	#1497	—	73	1	no	—
228	#1495	—	73	1	no	—
229	C₈×M₁₆	—	73	1	no	—
230	C₇₃	#17965	1	1	yes	characteristic, complemented, Sylow
231	#533	C₂×D₇₃	1	1	yes	characteristic
232	#529	—	73	1	no	—
233	#501	—	73	1	no	—
234	#497	—	73	1	no	—
235	#491	—	73	1	no	—
236	#489	—	73	1	no	—
237	#470	—	73	2	no	—
238	#468	—	73	2	no	—
239	#446	—	2	1	no	—
240	#446	—	73	1	no	—
241	#446	C₂×D₇₃	1	2	yes	—
242	C₈×Q₈	—	2	1	no	—
243	C₈×Q₈	—	73	1	no	—
244	C₈×Q₈	C₂×D₇₃	1	2	yes	—
245	C₄×Q₁₆	—	73	2	no	—
246	C₄×SD₁₆	—	73	2	no	—
247	#436	—	73	1	no	—
248	#435	—	146	1	no	—
249	C₈×D₄	—	73	1	no	—
250	C₈×D₄	—	146	1	no	—
251	#433	—	146	1	no	—
252	#432	—	73	1	no	—
253	#431	—	73	1	no	—
254	#424	—	2	1	no	—
255	#423	C₂×D₇₃	1	1	yes	characteristic
256	#405	—	2	1	no	—
257	#405	—	146	1	no	—
258	C₄×M₁₆	—	73	1	no	—
259	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
260	#335	—	73	2	no	—
261	#334	—	73	2	no	—
262	Q₈⋊C₈	—	73	2	no	—
263	Q₈⋊C₈	—	73	2	no	—
264	Q₈⋊C₈	—	73	2	no	—
265	D₄⋊C₈	—	73	2	no	—
266	#322	—	73	2	no	—
267	C₈²	—	73	2	no	—
268	C₂×Q₁₆	—	73	2	no	—
269	C₂×SD₁₆	—	73	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	73	2	no	—
272	C₂×M₁₆	—	146	1	no	—
273	C₂²×C₈	—	146	1	no	—
274	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
276	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
278	#126	—	146	1	no	—
279	#125	—	2	1	no	—
280	#125	—	73	1	no	—
281	#124	—	73	1	no	—
282	#123	—	146	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	73	1	no	—
285	C₂²⋊Q₈	C₄×D₇₃	1	2	yes	—
286	#121	—	73	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	73	1	no	—
289	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
290	C₄×D₄	—	73	1	no	—
291	C₄×D₄	—	146	1	no	—
292	#117	—	2	1	no	—
293	#117	—	146	1	no	—
294	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
295	#107	—	73	2	no	—
296	#106	—	73	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	73	1	no	—
301	C₄⋊C₈	—	73	1	no	—
302	C₄⋊C₈	—	146	1	no	—
303	C₄⋊C₈	—	146	1	no	—
304	C₄⋊C₈	—	146	1	no	—
305	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
306	#103	—	73	2	no	—
307	#103	—	73	2	no	—
308	#103	—	73	2	no	—
309	#102	—	73	2	no	—
310	C₂²⋊C₈	—	146	1	no	—
311	C₂²⋊C₈	—	146	1	no	—
312	C₂²⋊C₈	—	146	1	no	—
313	C₂²⋊C₈	—	146	1	no	—
314	#97	—	2	2	no	—
315	#97	—	73	1	no	—
316	#97	—	73	1	no	—
317	#97	—	146	1	no	—
318	#97	—	146	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	73	2	no	—
321	C₄×C₈	—	73	2	no	—
322	C₄×C₈	—	146	1	no	—
323	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
324	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	73	1	no	—
329	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
330	C₂×D₄	—	73	1	no	—
331	C₂×D₄	—	146	1	no	—
332	C₂²×C₄	—	146	1	no	—
333	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
335	C₂²×C₄	#11924028	1	1	yes	characteristic
336	Q₁₆	—	146	4	no	—
337	SD₁₆	—	146	4	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	292	2	no	—
340	M₁₆	—	146	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	292	2	no	—
345	C₂×C₈	—	73	2	no	—
346	C₂×C₈	—	73	2	no	—
347	C₂×C₈	—	146	1	no	—
348	C₂×C₈	—	146	1	no	—
349	C₂×C₈	—	146	2	no	—
350	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	73	1	no	—
360	C₄⋊C₄	—	73	1	no	—
361	C₄⋊C₄	—	146	1	no	—
362	C₄⋊C₄	—	146	1	no	—
363	C₄⋊C₄	—	146	1	no	—
364	C₄⋊C₄	—	146	1	no	—
365	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	146	1	no	—
368	C₂²⋊C₄	—	146	1	no	—
369	C₂²⋊C₄	—	146	1	no	—
370	C₂²⋊C₄	—	146	1	no	—
371	C₂²⋊C₄	—	146	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	146	1	no	—
374	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
376	C₄²	#11924028	1	1	yes	characteristic
377	C₄²	C₂³×D₇₃	1	1	yes	characteristic
378	C₂³	—	146	1	no	—
379	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	146	2	no	—
384	D₄	—	292	2	no	—
385	D₄	—	146	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	292	1	no	—
393	C₂×C₄	—	292	1	no	—
394	C₂×C₄	—	146	1	no	—
395	C₂×C₄	—	146	1	no	—
396	C₂×C₄	—	146	1	no	—
397	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
399	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	292	2	no	—
408	C₈	—	292	1	no	—
409	C₈	—	292	1	no	—
410	C₈	—	73	4	no	—
411	C₈	—	146	2	no	—
412	C₈	#14556622	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	292	1	no	—
417	C₂²	—	292	1	no	—
418	C₂²	—	292	1	no	—
419	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	292	1	no	—
427	C₄	—	292	1	no	—
428	C₄	—	292	1	no	—
429	C₄	#131×D₇₃	1	2	yes	—
430	C₄	C₂×#14556622	1	1	yes	characteristic
431	C₄	#17989385	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	584	1	no	—
434	C₂	#22618641	1	1	yes	characteristic
435	C₂	C₄×#14556622	1	1	yes	characteristic
436	C₂	#22618832	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#2960	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#14556565	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#2960	D₇₃
hypocenter	C₇₃	#17965
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #22608838	C₂	semidirect
4. #22608831	C₂	semidirect
5. C₈×#11924018	C₂	semidirect
6. C₈×#11924015	C₂	semidirect
7. #22608696	C₂	semidirect
8. #22608404	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₇₃×#2960	C₂	semidirect
221. #2960	D₇₃	semidirect
230. C₇₃	#17965	semidirect

Maximal subgroups

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

subgroup	index
#22620531	2
#22618906	2
#22608838	2
#22608831	2
C₈×#11924018	2
C₈×#11924015	2
#22608696	2
#22608404	2
#22608394	2
C₈×#11924012	2
C₇₃×#2960	2
#17965	73