Subgroups — #33955841

Order 18688.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623321	C₂	1	2	yes	maximal, complemented
2	#22620590	C₂	1	2	yes	maximal, complemented
3	#22620581	C₂	1	2	yes	maximal, complemented
4	#22620570	C₂	1	4	yes	maximal, complemented
5	#22620559	C₂	1	4	yes	maximal, complemented
6	#22620548	C₂	1	4	yes	maximal, complemented
7	#22620445	C₂	1	1	yes	maximal, characteristic, complemented
8	#22620359	C₂	1	1	yes	maximal, characteristic, complemented
9	#22620277	C₂	1	2	yes	maximal, complemented
10	#22619540	C₂	1	2	yes	maximal, complemented
11	#22619512	C₂	1	2	yes	maximal, complemented
12	#22618733	C₂	1	2	yes	maximal, complemented
13	C₄×#14556613	C₂	1	2	yes	maximal, complemented
14	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#14556613	C₂²	1	2	yes	—
16	C₂×#14556613	C₂²	1	2	yes	—
17	#17989208	C₂²	1	8	yes	—
18	#17989199	C₂²	1	4	yes	—
19	#17989192	C₂²	1	4	yes	—
20	#17989184	—	2	4	no	—
21	#17989175	—	2	4	no	—
22	#17989144	C₂²	1	2	yes	—
23	#17989137	C₂²	1	2	yes	—
24	#17989115	—	2	8	no	—
25	#17989098	C₂²	1	4	yes	—
26	C₄×#11924028	C₂²	1	4	yes	—
27	#17988992	C₂²	1	2	yes	complemented
28	#17988989	C₂²	1	2	yes	complemented
29	#17988989	C₂²	1	2	yes	complemented
30	#17988985	C₂²	1	2	yes	complemented
31	#17988971	C₂²	1	2	yes	complemented
32	#17988971	C₂²	1	2	yes	complemented
33	#17988967	C₂²	1	1	yes	characteristic, complemented
34	#17988964	C₂²	1	1	yes	characteristic, complemented
35	#17988960	C₂²	1	2	yes	complemented
36	#17988956	C₂²	1	4	yes	complemented
37	#17988952	C₂²	1	4	yes	complemented
38	#17988947	C₂²	1	8	yes	complemented
39	#17988845	C₂²	1	4	yes	—
40	#17988840	C₂²	1	4	yes	—
41	#17988833	C₂²	1	8	yes	—
42	#17988828	C₂²	1	4	yes	—
43	#17988823	C₂²	1	4	yes	—
44	#17988816	C₂²	1	8	yes	—
45	#17988700	C₂²	1	4	yes	complemented
46	#17988695	C₂²	1	4	yes	complemented
47	#17988689	C₂²	1	8	yes	complemented
48	C₄×Dic₂₉₂	C₂²	1	4	yes	complemented
49	C₄×#11924017	C₂²	1	8	yes	complemented
50	C₄×D₅₈₄	C₂²	1	4	yes	complemented
51	#17988625	C₂²	1	2	yes	—
52	#17988625	C₂²	1	2	yes	—
53	#17988584	C₂²	1	4	yes	—
54	#17988584	C₂²	1	4	yes	—
55	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
56	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
57	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
58	#405×C₇₃	C₂²	1	2	yes	—
59	#405×C₇₃	C₂²	1	2	yes	—
60	#405×C₇₃	C₂²	1	2	yes	—
61	#405×C₇₃	C₂²	1	2	yes	—
62	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
63	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
66	C₂×#11924028	C₂³	1	4	yes	—
67	#14556613	—	2	8	no	—
68	#14556613	—	2	8	no	—
69	C₂×Dic₂₉₂	C₂³	1	2	yes	—
70	C₂×Dic₂₉₂	C₂³	1	2	yes	—
71	C₂×#11924017	C₂³	1	4	yes	—
72	C₂×#11924017	C₂³	1	4	yes	—
73	C₂×D₅₈₄	C₂³	1	2	yes	—
74	C₂×D₅₈₄	C₂³	1	2	yes	—
75	#14556591	C₂³	1	2	yes	—
76	#14556591	C₂³	1	4	yes	—
77	#14556588	C₂³	1	2	yes	—
78	#14556586	—	2	8	no	—
79	#14556584	—	2	8	no	—
80	#14556583	C₂³	1	4	yes	—
81	#14556581	—	2	8	no	—
82	#14556579	C₂³	1	4	yes	—
83	#14556577	—	2	8	no	—
84	#14556576	—	2	8	no	—
85	#14556574	—	2	4	no	—
86	#14556573	—	2	8	no	—
87	#14556570	—	2	4	no	—
88	#14556570	C₂³	1	8	yes	—
89	#14556569	—	2	8	no	—
90	#14556565	—	2	4	no	—
91	#14556565	C₂³	1	8	yes	—
92	#14556564	—	2	8	no	—
93	#14556560	—	2	4	no	—
94	C₄×Dic₁₄₆	—	2	4	no	—
95	C₄×Dic₁₄₆	C₂³	1	8	yes	—
96	C₄×D₂₉₂	—	2	4	no	—
97	C₄×D₂₉₂	C₂³	1	8	yes	—
98	C₄×C₂²⋊D₇₃	—	2	8	no	—
99	C₄×C₂²⋊D₇₃	—	2	8	no	—
100	#14556550	C₂³	1	4	yes	—
101	#14556548	—	2	4	no	—
102	C₄²×D₇₃	—	2	4	no	—
103	#14556525	C₂³	1	4	yes	—
104	#14556525	C₂³	1	4	yes	—
105	#14556523	C₂³	1	4	yes	—
106	#14556523	C₂³	1	4	yes	—
107	#14556516	C₂³	1	8	yes	—
108	#14556516	C₂³	1	8	yes	—
109	#14556513	C₂³	1	8	yes	—
110	#14556513	C₂³	1	8	yes	—
111	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₇₃	—	2	4	no	—
113	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
114	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
115	C₂²×C₈×C₇₃	—	2	4	no	—
116	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
120	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
122	#117×C₇₃	D₄	1	4	yes	—
123	#117×C₇₃	C₂³	1	2	yes	—
124	#117×C₇₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
127	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
129	#97×C₇₃	C₂³	1	2	yes	—
130	#97×C₇₃	C₂³	1	2	yes	—
131	#97×C₇₃	C₂³	1	2	yes	—
132	#97×C₇₃	C₂³	1	2	yes	—
133	C₄×C₈×C₇₃	C₂³	1	2	yes	—
134	C₄×C₈×C₇₃	C₂³	1	2	yes	—
135	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
139	#11924028	—	2	8	no	—
140	#11924028	—	2	8	no	—
141	C₂×Dic₁₄₆	—	2	4	no	—
142	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
143	C₂×D₂₉₂	—	2	4	no	—
144	C₂×D₂₉₂	C₂⁴	1	4	yes	—
145	C₂×C₂²⋊D₇₃	—	2	4	no	—
146	C₂×C₂²⋊D₇₃	—	2	8	no	—
147	C₂×C₄×D₇₃	—	2	4	no	—
148	C₂×C₄×D₇₃	—	2	8	no	—
149	Dic₂₉₂	—	2	4	no	—
150	Dic₂₉₂	—	2	4	no	—
151	#11924017	—	2	8	no	—
152	#11924017	—	2	8	no	—
153	D₅₈₄	—	2	4	no	—
154	D₅₈₄	—	2	4	no	—
155	C₄⋊Dic₇₃	—	2	4	no	—
156	C₄⋊Dic₇₃	—	2	4	no	—
157	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
158	#11924007	—	2	8	no	—
159	#11924007	—	2	8	no	—
160	#11924007	—	2	8	no	—
161	C₂²⋊Dic₇₃	—	2	4	no	—
162	C₂²⋊Dic₇₃	—	2	8	no	—
163	#11924005	—	2	8	no	—
164	#11924005	—	2	8	no	—
165	#11924005	—	2	8	no	—
166	C₄×Dic₇₃	—	2	4	no	—
167	C₄×Dic₇₃	—	2	8	no	—
168	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₃	—	2	2	no	—
170	C₂²×C₄×C₇₃	—	2	2	no	—
171	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₇₃	—	2	4	no	—
178	M₁₆×C₇₃	—	2	4	no	—
179	C₂×C₈×C₇₃	—	2	2	no	—
180	C₂×C₈×C₇₃	—	2	2	no	—
181	C₂×C₈×C₇₃	—	2	4	no	—
182	C₂×C₈×C₇₃	—	2	4	no	—
183	C₂×C₈×C₇₃	#41	1	4	yes	—
184	C₂×C₈×C₇₃	#41	1	4	yes	—
185	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
186	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
187	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
193	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
194	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
195	C₄²×C₇₃	C₂×D₄	1	2	yes	—
196	C₄²×C₇₃	C₂×D₄	1	2	yes	—
197	C₄²×C₇₃	C₂⁴	1	2	yes	—
198	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
199	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
200	C₂³×C₇₃	—	2	2	no	—
201	C₂³×C₇₃	—	4	2	no	—
202	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
204	C₂²×D₇₃	—	2	4	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	4	2	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
217	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
218	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
219	C₂²⋊D₇₃	—	4	8	no	—
220	C₂²⋊D₇₃	—	8	8	no	—
221	C₂×Dic₇₃	—	2	4	no	—
222	C₂×Dic₇₃	—	2	8	no	—
223	D₂₉₂	—	2	4	no	—
224	D₂₉₂	—	2	4	no	—
225	D₂₉₂	—	8	4	no	—
226	C₄×D₇₃	—	4	8	no	—
227	C₄×D₇₃	—	8	8	no	—
228	Dic₁₄₆	—	2	4	no	—
229	Dic₁₄₆	—	2	4	no	—
230	Dic₁₄₆	—	8	4	no	—
231	C₈×C₇₃	—	2	2	no	—
232	C₈×C₇₃	—	2	2	no	—
233	C₈×C₇₃	C₂×#41	1	2	yes	—
234	C₈×C₇₃	C₂×#41	1	2	yes	—
235	C₈×C₇₃	C₂×#41	1	2	yes	—
236	C₈×C₇₃	C₂×#41	1	2	yes	—
237	C₂²×C₇₃	—	2	2	no	—
238	C₂²×C₇₃	—	2	4	no	—
239	C₂²×C₇₃	—	2	2	no	—
240	C₂²×C₇₃	—	4	4	no	—
241	C₂²×C₇₃	#532	1	2	yes	—
242	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
243	C₂×D₇₃	—	4	8	no	—
244	C₂×D₇₃	—	4	4	no	—
245	C₄×C₇₃	—	2	2	no	—
246	C₄×C₇₃	—	2	4	no	—
247	C₄×C₇₃	—	2	2	no	—
248	C₄×C₇₃	—	2	2	no	—
249	C₄×C₇₃	#532	1	2	yes	—
250	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
251	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
252	Dic₇₃	—	4	8	no	—
253	Dic₇₃	—	4	4	no	—
254	#60682	—	73	1	no	maximal, Sylow
255	C₂×C₇₃	—	2	2	no	—
256	C₂×C₇₃	—	4	2	no	—
257	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
258	C₂×C₇₃	#3584	1	2	yes	—
259	D₇₃	—	8	4	no	—
260	#3455	—	73	2	no	—
261	#3177	—	73	2	no	—
262	#3176	—	73	2	no	—
263	#3175	—	73	4	no	—
264	#3174	—	73	4	no	—
265	#3173	—	73	4	no	—
266	#3160	—	73	1	no	—
267	#3147	—	73	1	no	—
268	#3135	—	73	2	no	—
269	#3054	—	73	2	no	—
270	#3050	—	73	2	no	—
271	#2943	—	73	2	no	—
272	C₄×#135	—	73	2	no	—
273	C₂×#405	D₇₃	1	1	yes	characteristic, complemented
274	C₇₃	#60682	1	1	yes	characteristic, complemented, Sylow
275	C₂×#135	—	73	2	no	—
276	C₂×#135	—	73	2	no	—
277	C₂²×M₁₆	C₂×D₇₃	1	1	yes	characteristic
278	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
279	#542	—	73	8	no	—
280	#541	—	73	4	no	—
281	#540	—	73	4	no	—
282	#539	—	146	4	no	—
283	#538	—	146	4	no	—
284	#533	—	73	2	no	—
285	#532	—	73	2	no	—
286	#529	—	146	8	no	—
287	#525	—	73	4	no	—
288	C₄×#41	—	73	4	no	—
289	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
290	#500	—	73	2	no	—
291	#499	—	73	2	no	—
292	#499	—	73	2	no	—
293	#498	—	73	2	no	—
294	#495	—	73	2	no	—
295	#495	—	73	2	no	—
296	#494	—	73	1	no	—
297	#493	—	73	1	no	—
298	#492	—	73	2	no	—
299	#491	—	73	4	no	—
300	#490	—	73	4	no	—
301	#489	—	73	8	no	—
302	#470	—	73	4	no	—
303	#469	—	73	4	no	—
304	#468	—	73	8	no	—
305	#467	—	73	4	no	—
306	#466	—	73	4	no	—
307	#465	—	73	8	no	—
308	#442	—	73	4	no	—
309	#441	—	73	4	no	—
310	#440	—	73	8	no	—
311	C₄×Q₁₆	—	73	4	no	—
312	C₄×SD₁₆	—	73	8	no	—
313	C₄×D₈	—	73	4	no	—
314	#427	—	73	2	no	—
315	#427	—	73	2	no	—
316	#416	—	73	4	no	—
317	#416	—	73	4	no	—
318	#405	C₂×D₇₃	1	2	yes	—
319	#405	C₂×D₇₃	1	2	yes	—
320	#405	C₂×D₇₃	1	2	yes	—
321	#405	C₂×D₇₃	1	2	yes	—
322	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
323	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
326	C₂×#41	—	73	4	no	—
327	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
328	#135	—	146	8	no	—
329	#135	—	146	8	no	—
330	C₂×Q₁₆	—	73	2	no	—
331	C₂×Q₁₆	—	73	2	no	—
332	C₂×SD₁₆	—	73	4	no	—
333	C₂×SD₁₆	—	73	4	no	—
334	C₂×D₈	—	73	2	no	—
335	C₂×D₈	—	73	2	no	—
336	C₂×M₁₆	—	2	4	no	—
337	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
338	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
339	C₂²×C₈	—	2	4	no	—
340	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
342	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
343	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
346	C₄⋊Q₈	—	73	4	no	—
347	C₄⋊Q₈	—	73	2	no	—
348	#127	—	73	2	no	—
349	#126	—	146	8	no	—
350	#126	—	146	8	no	—
351	#125	—	73	4	no	—
352	#125	—	146	8	no	—
353	#124	—	73	4	no	—
354	#124	—	146	8	no	—
355	#123	—	146	4	no	—
356	#123	—	146	8	no	—
357	#123	—	146	8	no	—
358	C₂²⋊Q₈	—	73	8	no	—
359	C₂²⋊Q₈	—	146	4	no	—
360	C₂²⋊Q₈	—	146	8	no	—
361	#121	—	73	8	no	—
362	#121	—	146	4	no	—
363	#121	—	146	8	no	—
364	#120	—	146	4	no	—
365	C₄×Q₈	—	73	8	no	—
366	C₄×Q₈	—	146	4	no	—
367	C₄×D₄	—	73	8	no	—
368	C₄×D₄	—	146	8	no	—
369	C₄×D₄	—	146	8	no	—
370	C₄×D₄	—	146	4	no	—
371	#117	—	73	4	no	—
372	#117	—	146	4	no	—
373	#117	D₂₉₂	1	4	yes	—
374	#117	C₂²×D₇₃	1	2	yes	—
375	#117	C₂²×D₇₃	1	2	yes	—
376	C₂×C₄⋊C₄	D₂₉₂	1	2	yes	—
377	C₂×C₂²⋊C₄	D₂₉₂	1	2	yes	—
378	C₂×C₄²	—	146	4	no	—
379	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
381	#107	—	73	4	no	—
382	#107	—	73	4	no	—
383	#106	—	73	4	no	—
384	#106	—	73	4	no	—
385	#103	—	73	8	no	—
386	#103	—	73	8	no	—
387	#102	—	73	8	no	—
388	#102	—	73	8	no	—
389	#97	C₂²×D₇₃	1	2	yes	—
390	#97	C₂²×D₇₃	1	2	yes	—
391	#97	C₂²×D₇₃	1	2	yes	—
392	#97	C₂²×D₇₃	1	2	yes	—
393	C₄×C₈	C₂²×D₇₃	1	2	yes	—
394	C₄×C₈	C₂²×D₇₃	1	2	yes	—
395	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
399	C₂⁴	C₂×D₂₉₂	1	1	yes	characteristic
400	#41	—	146	8	no	—
401	#41	—	146	8	no	—
402	C₂×Q₈	—	73	4	no	—
403	C₂×Q₈	—	146	4	no	—
404	C₂×D₄	—	73	4	no	—
405	C₂×D₄	—	146	4	no	—
406	C₂×D₄	—	146	8	no	—
407	C₂×D₄	—	146	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	146	4	no	—
411	C₂²×C₄	—	146	8	no	—
412	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
414	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
415	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
416	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
417	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
418	Q₁₆	—	146	4	no	—
419	Q₁₆	—	146	4	no	—
420	SD₁₆	—	146	8	no	—
421	SD₁₆	—	146	8	no	—
422	D₈	—	146	4	no	—
423	D₈	—	146	4	no	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	4	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	#11924028	1	4	yes	—
431	C₂×C₈	#11924028	1	4	yes	—
432	C₂×C₈	C₂³×D₇₃	1	2	yes	—
433	C₂×C₈	C₂³×D₇₃	1	2	yes	—
434	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
435	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
436	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
437	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
438	C₄⋊C₄	—	73	8	no	—
439	C₄⋊C₄	—	146	8	no	—
440	C₄⋊C₄	—	146	8	no	—
441	C₄⋊C₄	—	146	8	no	—
442	C₄⋊C₄	—	146	4	no	—
443	C₄⋊C₄	—	146	4	no	—
444	C₄⋊C₄	C₂×D₂₉₂	1	4	yes	—
445	C₄⋊C₄	C₂×D₂₉₂	1	4	yes	—
446	C₂²⋊C₄	—	146	4	no	—
447	C₂²⋊C₄	—	146	8	no	—
448	C₂²⋊C₄	—	146	8	no	—
449	C₂²⋊C₄	—	146	8	no	—
450	C₂²⋊C₄	—	146	8	no	—
451	C₂²⋊C₄	C₂×D₂₉₂	1	4	yes	—
452	C₂²⋊C₄	C₂×D₂₉₂	1	4	yes	—
453	C₄²	—	146	8	no	—
454	C₄²	—	146	4	no	—
455	C₄²	C₂×D₂₉₂	1	2	yes	—
456	C₄²	C₂×D₂₉₂	1	2	yes	—
457	C₄²	C₂³×D₇₃	1	2	yes	—
458	C₄²	C₂³×D₇₃	1	1	yes	characteristic
459	C₄²	C₂³×D₇₃	1	1	yes	characteristic
460	C₂³	—	2	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	146	4	no	—
463	C₂³	C₂²×D₂₉₂	1	2	yes	—
464	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
465	Q₈	—	584	4	no	—
466	Q₈	—	146	4	no	—
467	Q₈	—	146	4	no	—
468	D₄	—	292	8	no	—
469	D₄	—	584	4	no	—
470	D₄	—	584	8	no	—
471	D₄	—	146	4	no	—
472	D₄	—	146	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	292	8	no	—
480	C₂×C₄	—	584	8	no	—
481	C₂×C₄	—	146	8	no	—
482	C₂×C₄	—	146	4	no	—
483	C₂×C₄	C₂²×D₂₉₂	1	4	yes	—
484	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
485	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
486	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
487	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
488	C₂×C₄	C₂×#11924028	1	2	yes	—
489	C₂×C₄	C₂×#11924028	1	2	yes	—
490	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂×#11924028	1	2	yes	—
494	C₈	C₂×#11924028	1	2	yes	—
495	C₈	C₂×#11924028	1	2	yes	—
496	C₈	C₂×#11924028	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	292	8	no	—
502	C₂²	—	292	4	no	—
503	C₂²	#17989137	1	2	yes	—
504	C₂²	C₂³×D₂₉₂	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	292	8	no	—
510	C₄	—	292	4	no	—
511	C₄	#17989137	1	2	yes	—
512	C₄	C₂²×#11924028	1	1	yes	characteristic
513	C₄	C₂²×#11924028	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	2	no	—
516	C₂	—	584	4	no	—
517	C₂	C₂×#17989137	1	1	yes	characteristic
518	C₂	#22624705	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉₂
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×#405×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₂×#405	D₇₃
hypocenter	C₇₃	#60682
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #22623321	C₂	semidirect
2. #22620590	C₂	semidirect
3. #22620581	C₂	semidirect
4. #22620570	C₂	semidirect
5. #22620559	C₂	semidirect
6. #22620548	C₂	semidirect
7. #22620445	C₂	semidirect
8. #22620359	C₂	semidirect
9. #22620277	C₂	semidirect
10. #22619540	C₂	semidirect
11. #22619512	C₂	semidirect
12. #22618733	C₂	semidirect
13. C₄×#14556613	C₂	semidirect
14. C₂×#405×C₇₃	C₂	semidirect
27. #17988992	C₂²	semidirect
28. #17988989	C₂²	semidirect
29. #17988989	C₂²	semidirect
30. #17988985	C₂²	semidirect
31. #17988971	C₂²	semidirect
32. #17988971	C₂²	semidirect
33. #17988967	C₂²	semidirect
34. #17988964	C₂²	semidirect
35. #17988960	C₂²	semidirect
36. #17988956	C₂²	semidirect
37. #17988952	C₂²	semidirect
38. #17988947	C₂²	semidirect
45. #17988700	C₂²	semidirect
46. #17988695	C₂²	semidirect
47. #17988689	C₂²	semidirect
48. C₄×Dic₂₉₂	C₂²	semidirect
49. C₄×#11924017	C₂²	semidirect
50. C₄×D₅₈₄	C₂²	semidirect
273. C₂×#405	D₇₃	semidirect
274. C₇₃	#60682	semidirect

Maximal subgroups

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

subgroup	index
#22623321	2
#22620590	2
#22620581	2
#22620570	2
#22620559	2
#22620548	2
#22620445	2
#22620359	2
#22620277	2
#22619540	2
#22619512	2
#22618733	2
C₄×#14556613	2
C₂×#405×C₇₃	2
#60682	73