Subgroups — #33055965

Order 18688.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620011	C₂	1	1	yes	maximal, characteristic
2	#22618906	C₂	1	1	yes	maximal, characteristic
3	#22608809	C₂	1	2	yes	maximal, complemented
4	#22608802	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	#22608714	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608378	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608342	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989121	C₂²	1	1	yes	characteristic
13	#17988917	C₄	1	1	yes	characteristic
14	#17988900	C₄	1	1	yes	characteristic
15	#17988894	C₄	1	2	yes	—
16	#17988809	C₄	1	2	yes	—
17	#17988743	C₄	1	1	yes	characteristic
18	#17988726	C₄	1	1	yes	characteristic
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	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₇₃	—	2	1	no	—
42	C₈×Q₈×C₇₃	—	2	1	no	—
43	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
44	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×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	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
78	#14556503	—	2	1	no	—
79	#14556503	—	2	1	no	—
80	#14556502	—	2	1	no	—
81	#14556502	—	2	1	no	—
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	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₇₃	—	2	1	no	—
88	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₇₃	—	2	1	no	—
91	C₄×Q₈×C₇₃	—	2	1	no	—
92	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×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	C₄×C₈×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	2	no	—
117	C₂×#10596831	—	2	1	no	—
118	C₂×#10596831	—	2	1	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	4	no	—
135	C₂×Q₈×C₇₃	—	2	1	no	—
136	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	4	1	no	—
145	C₂×C₈×C₇₃	—	4	2	no	—
146	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
154	C₄²×C₇₃	—	2	2	no	—
155	C₄²×C₇₃	—	2	2	no	—
156	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₃	#41	1	1	yes	characteristic
159	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₇₃	—	2	1	no	—
162	Q₈×C₇₃	—	2	4	no	—
163	Q₈×C₇₃	—	2	2	no	—
164	Q₈×C₇₃	#131	1	4	yes	—
165	C₂×C₄×C₇₃	—	2	4	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₇₃	—	4	2	no	—
180	C₂×Dic₇₃	—	2	1	no	—
181	C₂×Dic₇₃	—	2	1	no	—
182	C₂×Dic₇₃	—	2	1	no	—
183	D₂₉₂	—	2	2	no	—
184	C₄×D₇₃	—	4	1	no	—
185	C₄×D₇₃	—	4	1	no	—
186	Dic₁₄₆	—	2	2	no	—
187	C₈×C₇₃	—	2	1	no	—
188	C₈×C₇₃	—	2	1	no	—
189	C₈×C₇₃	—	2	1	no	—
190	C₈×C₇₃	—	4	2	no	—
191	C₈×C₇₃	#137	1	2	yes	—
192	#10596831	—	2	4	no	—
193	#10596831	—	2	2	no	—
194	#10596831	—	2	2	no	—
195	#10596831	—	4	1	no	—
196	#10596831	—	4	1	no	—
197	C₂²×C₇₃	—	2	1	no	—
198	C₂²×C₇₃	—	2	1	no	—
199	C₂²×C₇₃	#443	1	2	yes	—
200	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₇₃	—	4	1	no	—
202	C₂×D₇₃	—	4	1	no	—
203	C₂×D₇₃	—	4	1	no	—
204	C₄×C₇₃	—	2	4	no	—
205	C₄×C₇₃	—	2	1	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	4	2	no	—
210	C₄×C₇₃	C₂×#131	1	2	yes	—
211	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
212	C₄×C₇₃	#575	1	1	yes	characteristic
213	Dic₇₃	—	4	1	no	—
214	Dic₇₃	—	4	1	no	—
215	Dic₇₃	—	4	1	no	—
216	#17911	—	73	1	no	maximal, Sylow
217	C₂×C₇₃	—	2	2	no	—
218	C₂×C₇₃	#2929	1	1	yes	characteristic
219	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
220	C₂×C₇₃	C₂×#443	1	1	yes	characteristic
221	D₇₃	—	8	1	no	—
222	#3108	—	73	1	no	—
223	#2966	—	73	1	no	—
224	C₂×C₈×Q₈	D₇₃	1	1	yes	characteristic, complemented
225	#1588	—	73	2	no	—
226	#1587	—	73	2	no	—
227	C₈×Q₁₆	—	73	2	no	—
228	C₈×SD₁₆	—	73	2	no	—
229	#1573	—	73	1	no	—
230	#1491	—	73	1	no	—
231	#1483	—	73	1	no	—
232	C₈×M₁₆	—	73	1	no	—
233	C₇₃	#17911	1	1	yes	characteristic, complemented, Sylow
234	#529	—	73	1	no	—
235	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
236	#483	—	73	1	no	—
237	#480	—	73	1	no	—
238	#479	—	73	2	no	—
239	#464	—	73	2	no	—
240	#451	—	73	1	no	—
241	#448	—	73	1	no	—
242	#446	—	73	1	no	—
243	C₈×Q₈	—	2	1	no	—
244	C₈×Q₈	—	2	1	no	—
245	C₈×Q₈	—	73	1	no	—
246	C₈×Q₈	C₂×D₇₃	1	2	yes	—
247	C₈×Q₈	C₂×D₇₃	1	2	yes	—
248	C₄×Q₁₆	—	73	2	no	—
249	C₄×SD₁₆	—	73	2	no	—
250	#436	—	73	1	no	—
251	#435	—	146	1	no	—
252	C₈×D₄	—	73	1	no	—
253	C₈×D₄	—	146	1	no	—
254	#433	—	146	1	no	—
255	#432	—	73	1	no	—
256	#431	—	73	1	no	—
257	C₂×C₄⋊C₈	—	2	1	no	—
258	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
259	#405	—	146	1	no	—
260	C₄×M₁₆	—	73	1	no	—
261	C₂×C₄×C₈	—	2	1	no	—
262	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
263	#335	—	73	2	no	—
264	#334	—	73	2	no	—
265	Q₈⋊C₈	—	73	2	no	—
266	Q₈⋊C₈	—	73	2	no	—
267	Q₈⋊C₈	—	73	2	no	—
268	D₄⋊C₈	—	73	2	no	—
269	#322	—	73	2	no	—
270	C₈²	—	73	2	no	—
271	C₂²×Q₈	C₄×D₇₃	1	1	yes	characteristic
272	C₂×Q₁₆	—	73	2	no	—
273	C₂×SD₁₆	—	73	2	no	—
274	C₂×M₁₆	—	146	1	no	—
275	C₂×M₁₆	—	146	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	146	1	no	—
278	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
280	#126	—	146	1	no	—
281	#125	—	73	1	no	—
282	#124	—	73	1	no	—
283	#123	—	146	1	no	—
284	C₂²⋊Q₈	—	73	1	no	—
285	#121	—	73	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	73	1	no	—
289	C₄×Q₈	C₄×D₇₃	1	2	yes	—
290	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
291	C₄×D₄	—	73	1	no	—
292	C₄×D₄	—	146	1	no	—
293	#117	—	146	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
298	#107	—	73	2	no	—
299	#106	—	73	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	73	2	no	—
304	C₄⋊C₈	—	73	1	no	—
305	C₄⋊C₈	—	73	1	no	—
306	C₄⋊C₈	—	146	1	no	—
307	C₄⋊C₈	—	146	1	no	—
308	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
309	#103	—	73	2	no	—
310	#103	—	73	2	no	—
311	#103	—	73	2	no	—
312	#102	—	73	2	no	—
313	C₂²⋊C₈	—	73	1	no	—
314	C₂²⋊C₈	—	73	1	no	—
315	C₂²⋊C₈	—	146	1	no	—
316	C₂²⋊C₈	—	146	1	no	—
317	C₂²⋊C₈	—	146	1	no	—
318	#97	—	146	1	no	—
319	#97	—	146	1	no	—
320	#97	—	146	1	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	73	2	no	—
324	C₄×C₈	—	73	2	no	—
325	C₄×C₈	—	146	1	no	—
326	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	73	1	no	—
333	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
334	C₂×D₄	—	73	1	no	—
335	C₂×D₄	—	146	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	146	1	no	—
339	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
341	C₂²×C₄	#11924028	1	1	yes	characteristic
342	Q₁₆	—	146	4	no	—
343	SD₁₆	—	146	4	no	—
344	M₁₆	—	292	2	no	—
345	M₁₆	—	146	4	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	292	2	no	—
351	C₂×C₈	—	73	2	no	—
352	C₂×C₈	—	73	2	no	—
353	C₂×C₈	—	146	1	no	—
354	C₂×C₈	—	146	1	no	—
355	C₂×C₈	—	146	2	no	—
356	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
358	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	73	1	no	—
364	C₄⋊C₄	—	73	1	no	—
365	C₄⋊C₄	—	146	1	no	—
366	C₄⋊C₄	—	146	1	no	—
367	C₄⋊C₄	—	146	1	no	—
368	C₄⋊C₄	—	146	1	no	—
369	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
370	C₂²⋊C₄	—	146	1	no	—
371	C₂²⋊C₄	—	146	1	no	—
372	C₂²⋊C₄	—	146	1	no	—
373	C₂²⋊C₄	—	146	1	no	—
374	C₂²⋊C₄	—	146	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	146	1	no	—
378	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
379	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
380	C₄²	#11924028	1	1	yes	characteristic
381	C₄²	C₂³×D₇₃	1	1	yes	characteristic
382	C₂³	—	146	1	no	—
383	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	146	2	no	—
387	Q₈	#14556597	1	4	yes	—
388	D₄	—	292	2	no	—
389	D₄	—	146	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	292	1	no	—
399	C₂×C₄	—	292	1	no	—
400	C₂×C₄	—	146	1	no	—
401	C₂×C₄	—	146	1	no	—
402	C₂×C₄	—	146	1	no	—
403	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
404	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	292	1	no	—
414	C₈	—	292	1	no	—
415	C₈	—	146	4	no	—
416	C₈	—	146	2	no	—
417	C₈	—	146	2	no	—
418	C₈	#14556622	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	292	1	no	—
422	C₂²	—	292	1	no	—
423	C₂²	—	292	1	no	—
424	C₂²	#17988702	1	2	yes	—
425	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	292	1	no	—
433	C₄	—	292	1	no	—
434	C₄	—	292	1	no	—
435	C₄	C₂×#14556597	1	2	yes	—
436	C₄	C₂×#14556622	1	1	yes	characteristic
437	C₄	#17989385	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	584	1	no	—
440	C₂	#22618625	1	1	yes	characteristic
441	C₂	C₄×#14556622	1	1	yes	characteristic
442	C₂	C₂×#17988702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×C₈×Q₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#14556565	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₂×C₈×Q₈	D₇₃
hypocenter	C₇₃	#17911
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. #22608809	C₂	semidirect
4. #22608802	C₂	semidirect
5. C₈×#11924018	C₂	semidirect
6. C₈×#11924015	C₂	semidirect
7. #22608714	C₂	semidirect
8. #22608378	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₂×C₈×Q₈×C₇₃	C₂	semidirect
224. C₂×C₈×Q₈	D₇₃	semidirect
233. C₇₃	#17911	semidirect

Maximal subgroups

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

subgroup	index
#22620011	2
#22618906	2
#22608809	2
#22608802	2
C₈×#11924018	2
C₈×#11924015	2
#22608714	2
#22608378	2
#22608342	2
C₈×#11924012	2
C₂×C₈×Q₈×C₇₃	2
#17911	73