Subgroups — #33108486

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619380	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988702	C₂	1	2	yes	maximal, complemented
3	#22618496	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610760	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610706	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610638	C₂	1	2	yes	maximal, complemented
7	#22610261	C₂	1	2	yes	maximal, complemented
8	#22610206	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14556517	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556611	C₂²	1	2	yes	—
13	C₂×#14556597	C₂²	1	2	yes	—
14	C₄×#11924028	C₂²	1	1	yes	characteristic
15	#17988806	C₄	1	2	yes	complemented
16	#17988799	C₄	1	2	yes	complemented
17	#17988794	C₄	1	1	yes	characteristic, complemented
18	#17988789	C₄	1	1	yes	characteristic, complemented
19	#17988784	C₄	1	1	yes	characteristic, complemented
20	#17988779	C₄	1	1	yes	characteristic, complemented
21	#17988702	—	2	8	no	—
22	C₂×#14556526	C₂²	1	2	yes	—
23	#17988613	C₂²	1	2	yes	—
24	#17988612	—	2	2	no	—
25	#17988611	C₂²	1	1	yes	characteristic
26	#17988609	—	2	1	no	—
27	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
28	C₄⋊C₈×D₇₃	—	2	1	no	—
29	C₂×#14556518	C₂²	1	2	yes	—
30	C₂×#14556518	C₂²	1	2	yes	—
31	C₂×#14556517	C₂²	1	1	yes	characteristic
32	C₂×#14556517	C₂²	1	1	yes	characteristic
33	#17988583	C₂²	1	2	yes	—
34	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
35	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
36	#17988351	C₂²	1	2	yes	—
37	#17988348	C₂²	1	1	yes	characteristic
38	#17988348	C₂²	1	1	yes	characteristic
39	#17988341	C₂²	1	2	yes	—
40	C₂×#131×C₇₃	C₂²	1	2	yes	—
41	#532×C₇₃	C₂²	1	1	yes	characteristic
42	#436×C₇₃	—	2	1	no	—
43	#435×C₇₃	—	2	2	no	—
44	C₈×D₄×C₇₃	—	2	1	no	—
45	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
46	#408×C₇₃	C₂²	1	2	yes	—
47	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×#11924028	C₂³	1	1	yes	characteristic
49	#14556611	—	2	4	no	—
50	#14556611	—	2	4	no	—
51	C₂×#11924018	C₂×C₄	1	2	yes	—
52	C₂×#11924016	C₂×C₄	1	2	yes	—
53	C₂×#11924015	C₂×C₄	1	2	yes	—
54	C₂×#11924013	C₂×C₄	1	2	yes	—
55	#14556597	—	2	4	no	—
56	#14556597	—	4	2	no	—
57	C₂×#11924012	C₂³	1	2	yes	—
58	C₂×#11924011	—	2	2	no	—
59	C₂²×#10596831	C₂³	1	2	yes	—
60	C₂×C₈×D₇₃	—	2	2	no	—
61	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₇₃	—	2	1	no	—
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	#14556550	C₂³	1	1	yes	characteristic
68	#14556548	—	2	1	no	—
69	C₂×C₄×Dic₇₃	—	2	1	no	—
70	C₂×C₄×Dic₇₃	—	2	1	no	—
71	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
73	C₄²×D₇₃	—	2	1	no	—
74	#14556526	—	2	4	no	—
75	C₄⋊#10596831	—	2	1	no	—
76	C₄⋊#10596831	—	2	1	no	—
77	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
78	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
79	C₄⋊#10596831	C₂×C₄	1	2	yes	—
80	#14556520	—	2	2	no	—
81	#14556520	—	2	2	no	—
82	#14556518	—	2	4	no	—
83	#14556518	—	4	2	no	—
84	#14556517	—	2	2	no	—
85	#14556517	D₄	1	4	yes	complemented
86	#14556515	C₂×C₄	1	2	yes	—
87	#14556515	C₂×C₄	1	2	yes	—
88	#14556512	C₂×C₄	1	2	yes	—
89	#14556512	C₂×C₄	1	2	yes	—
90	C₈×Dic₇₃	—	2	4	no	—
91	C₂×#41×C₇₃	C₂³	1	2	yes	—
92	#131×C₇₃	—	2	4	no	—
93	#131×C₇₃	—	4	2	no	—
94	C₂×M₁₆×C₇₃	—	2	2	no	—
95	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₇₃	—	2	2	no	—
98	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
101	#124×C₇₃	C₂×C₄	1	2	yes	—
102	#121×C₇₃	—	2	1	no	—
103	#121×C₇₃	—	2	1	no	—
104	C₄×D₄×C₇₃	—	2	1	no	—
105	C₄×D₄×C₇₃	—	2	1	no	—
106	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
108	C₄⋊C₈×C₇₃	D₄	1	2	yes	—
109	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
110	C₂²⋊C₈×C₇₃	—	2	2	no	—
111	C₂²⋊C₈×C₇₃	—	2	2	no	—
112	#97×C₇₃	—	2	1	no	—
113	C₄×C₈×C₇₃	—	2	1	no	—
114	#11924028	—	2	1	no	—
115	#11924028	—	2	1	no	—
116	#11924028	C₂×D₄	1	2	yes	—
117	#11924028	#41	1	2	yes	—
118	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₇₃	—	2	1	no	—
121	C₂²×Dic₇₃	—	2	1	no	—
122	C₂²×Dic₇₃	—	2	1	no	—
123	C₂×C₄×D₇₃	—	2	1	no	—
124	C₂×C₄×D₇₃	—	2	1	no	—
125	C₂×C₄×D₇₃	—	2	1	no	—
126	#11924018	—	2	4	no	—
127	#11924016	—	2	4	no	—
128	#11924015	—	2	4	no	—
129	#11924013	—	2	4	no	—
130	#11924012	—	2	2	no	—
131	#11924012	—	2	2	no	—
132	#11924011	—	4	4	no	—
133	C₂×#10596831	—	2	2	no	—
134	C₂×#10596831	—	2	2	no	—
135	C₂×#10596831	—	2	2	no	—
136	C₂×#10596831	C₂²×C₄	1	2	yes	—
137	C₂×#10596831	C₂²×C₄	1	2	yes	—
138	C₈×D₇₃	—	4	4	no	—
139	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	#11924007	—	2	1	no	—
142	#11924007	—	2	1	no	—
143	C₂²⋊Dic₇₃	—	2	1	no	—
144	#11924005	—	2	1	no	—
145	#11924005	—	2	1	no	—
146	C₄×Dic₇₃	—	2	4	no	—
147	C₄×Dic₇₃	—	2	1	no	—
148	C₄×Dic₇₃	—	2	1	no	—
149	C₄×Dic₇₃	—	2	1	no	—
150	C₄×Dic₇₃	—	2	1	no	—
151	C₄×Dic₇₃	—	2	1	no	—
152	C₄×Dic₇₃	—	2	1	no	—
153	C₄×Dic₇₃	—	4	2	no	—
154	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
155	#41×C₇₃	—	2	2	no	—
156	#41×C₇₃	—	2	2	no	—
157	#41×C₇₃	—	2	2	no	—
158	#41×C₇₃	—	2	2	no	—
159	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	1	no	—
162	C₂×D₄×C₇₃	—	2	1	no	—
163	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₇₃	—	2	2	no	—
165	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	M₁₆×C₇₃	—	2	1	no	—
169	M₁₆×C₇₃	—	2	1	no	—
170	M₁₆×C₇₃	—	2	1	no	—
171	M₁₆×C₇₃	—	4	4	no	—
172	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₇₃	—	2	1	no	—
174	C₂×C₈×C₇₃	—	2	2	no	—
175	C₂×C₈×C₇₃	—	2	2	no	—
176	C₂×C₈×C₇₃	—	2	1	no	—
177	C₂×C₈×C₇₃	—	4	4	no	—
178	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₇₃	—	2	1	no	—
181	C₄⋊C₄×C₇₃	—	2	1	no	—
182	C₂²⋊C₄×C₇₃	—	2	2	no	—
183	C₂²⋊C₄×C₇₃	—	2	2	no	—
184	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
190	C₂²×D₇₃	—	2	1	no	—
191	Q₈×C₇₃	—	2	2	no	—
192	Q₈×C₇₃	—	2	2	no	—
193	D₄×C₇₃	—	2	2	no	—
194	D₄×C₇₃	—	2	2	no	—
195	D₄×C₇₃	—	4	2	no	—
196	D₄×C₇₃	—	4	2	no	—
197	D₄×C₇₃	—	4	2	no	—
198	D₄×C₇₃	—	8	1	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂²⋊D₇₃	—	2	2	no	—
215	C₂²⋊D₇₃	—	2	2	no	—
216	C₂×Dic₇₃	—	2	2	no	—
217	C₂×Dic₇₃	—	2	2	no	—
218	C₂×Dic₇₃	—	2	1	no	—
219	C₂×Dic₇₃	—	2	2	no	—
220	C₂×Dic₇₃	—	2	2	no	—
221	C₂×Dic₇₃	—	2	1	no	—
222	C₂×Dic₇₃	—	2	1	no	—
223	C₂×Dic₇₃	—	4	1	no	—
224	C₂×Dic₇₃	—	4	1	no	—
225	D₂₉₂	—	2	1	no	—
226	D₂₉₂	C₄×D₄	1	2	yes	—
227	C₄×D₇₃	—	2	2	no	—
228	C₄×D₇₃	—	2	2	no	—
229	C₄×D₇₃	—	4	2	no	—
230	C₄×D₇₃	—	8	1	no	—
231	Dic₁₄₆	—	2	1	no	—
232	Dic₁₄₆	C₄×D₄	1	2	yes	—
233	C₈×C₇₃	—	2	2	no	—
234	C₈×C₇₃	—	2	2	no	—
235	C₈×C₇₃	—	2	2	no	—
236	C₈×C₇₃	—	4	1	no	—
237	#10596831	—	2	2	no	—
238	#10596831	—	2	2	no	—
239	#10596831	—	4	2	no	—
240	C₂²×C₇₃	—	2	1	no	—
241	C₂²×C₇₃	—	2	1	no	—
242	C₂²×C₇₃	—	4	2	no	—
243	C₂²×C₇₃	—	4	2	no	—
244	C₂²×C₇₃	—	4	2	no	—
245	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₇₃	#547	1	1	yes	characteristic
247	C₂²×C₇₃	#553	1	1	yes	characteristic
248	C₂×D₇₃	—	2	2	no	—
249	C₂×D₇₃	—	4	1	no	—
250	C₂×D₇₃	—	4	1	no	—
251	C₄×C₇₃	—	2	1	no	—
252	C₄×C₇₃	—	2	1	no	—
253	C₄×C₇₃	—	2	1	no	—
254	C₄×C₇₃	—	4	2	no	—
255	C₄×C₇₃	#443	1	2	yes	complemented
256	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₇₃	#520	1	1	yes	characteristic
258	C₄×C₇₃	D₄²	1	1	yes	characteristic
259	C₄×C₇₃	#548	1	1	yes	characteristic
260	Dic₇₃	—	2	4	no	—
261	Dic₇₃	—	2	2	no	—
262	Dic₇₃	—	4	2	no	—
263	Dic₇₃	—	4	1	no	—
264	Dic₇₃	—	4	1	no	—
265	#23015	—	73	1	no	maximal, Sylow
266	C₂×C₇₃	—	2	1	no	—
267	C₂×C₇₃	—	2	1	no	—
268	C₂×C₇₃	—	8	2	no	—
269	C₂×C₇₃	#2361	1	1	yes	characteristic
270	C₂×C₇₃	C₂×#443	1	1	yes	characteristic
271	C₂×C₇₃	#2956	1	1	yes	characteristic
272	D₇₃	—	4	2	no	—
273	#3035	—	73	1	no	—
274	C₂×#443	—	73	2	no	—
275	#2935	D₇₃	1	1	yes	characteristic, complemented
276	#2906	—	73	1	no	—
277	#1962	—	73	1	no	—
278	#1950	—	73	1	no	—
279	#1937	—	73	2	no	—
280	#1876	—	73	2	no	—
281	#1866	—	73	2	no	—
282	C₄×C₄⋊C₈	—	73	1	no	—
283	C₄×#104	—	73	1	no	—
284	C₇₃	#23015	1	1	yes	characteristic, complemented, Sylow
285	C₂×#135	—	73	2	no	—
286	C₂×#131	—	73	2	no	—
287	C₂×#131	C₂×D₇₃	1	2	yes	—
288	#532	C₂×D₇₃	1	1	yes	characteristic
289	C₄×#41	—	73	1	no	—
290	#464	—	73	2	no	—
291	#463	—	73	2	no	—
292	#462	—	73	1	no	—
293	#461	—	73	1	no	—
294	#460	—	73	1	no	—
295	#459	—	73	1	no	—
296	#443	—	146	8	no	—
297	#436	—	2	1	no	—
298	#435	—	2	2	no	—
299	C₈×D₄	—	2	1	no	—
300	C₂×#108	—	73	2	no	—
301	#424	—	73	2	no	—
302	#424	—	146	2	no	—
303	#423	—	73	1	no	—
304	#423	—	146	1	no	—
305	C₂×C₄⋊C₈	—	73	1	no	—
306	C₂×C₄⋊C₈	—	146	1	no	—
307	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
308	C₂×#104	—	73	2	no	—
309	C₂×#104	—	73	1	no	—
310	C₂×#104	—	73	2	no	—
311	C₂×#104	—	73	1	no	—
312	#416	—	73	2	no	—
313	#408	C₂×D₇₃	1	2	yes	—
314	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
315	C₂×C₄×C₈	—	73	2	no	—
316	C₄³	—	73	1	no	—
317	#341	—	73	2	no	—
318	#339	—	73	1	no	—
319	#339	—	73	1	no	—
320	#336	—	73	2	no	—
321	C₂×#41	—	73	1	no	—
322	C₂×#41	C₂²×D₇₃	1	2	yes	—
323	#135	—	146	4	no	—
324	#135	—	146	4	no	—
325	C₂×Q₁₆	—	73	2	no	—
326	C₂×SD₁₆	—	73	2	no	—
327	C₂×SD₁₆	—	73	2	no	—
328	C₂×D₈	—	73	2	no	—
329	#131	—	2	4	no	—
330	#131	—	4	2	no	—
331	#131	—	292	2	no	—
332	#131	—	146	4	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	73	2	no	—
335	C₂×M₁₆	—	146	2	no	—
336	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
337	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	73	2	no	—
340	C₂²×C₈	—	146	2	no	—
341	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
342	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
343	#127	C₄×D₇₃	1	1	yes	characteristic
344	#124	C₄×D₇₃	1	2	yes	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	C₄×Q₈	—	73	1	no	—
348	C₄×Q₈	—	73	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	73	1	no	—
352	C₄×D₄	—	73	1	no	—
353	C₄×D₄	—	146	1	no	—
354	C₄×D₄	—	146	1	no	—
355	#117	—	73	1	no	—
356	#117	—	146	1	no	—
357	C₂×C₄²	—	73	1	no	—
358	C₂×C₄²	—	73	1	no	—
359	C₂×C₄²	—	146	1	no	—
360	C₂×C₄²	—	146	1	no	—
361	C₂×C₄²	—	146	1	no	—
362	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
363	#108	—	146	4	no	—
364	C₄⋊C₈	—	73	1	no	—
365	C₄⋊C₈	—	73	1	no	—
366	C₄⋊C₈	—	73	2	no	—
367	C₄⋊C₈	—	146	2	no	—
368	C₄⋊C₈	—	146	2	no	—
369	C₄⋊C₈	—	146	1	no	—
370	C₄⋊C₈	—	146	1	no	—
371	C₄⋊C₈	C₂²⋊D₇₃	1	1	yes	characteristic
372	C₄⋊C₈	C₂²⋊D₇₃	1	1	yes	characteristic
373	C₄⋊C₈	C₂²⋊D₇₃	1	2	yes	—
374	#104	—	292	2	no	—
375	#104	—	73	4	no	—
376	#104	—	146	4	no	—
377	#104	—	146	2	no	—
378	#103	—	73	2	no	—
379	#103	—	73	2	no	—
380	#102	—	73	2	no	—
381	#102	—	73	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	#97	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	C₄×C₈	—	146	4	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	73	2	no	—
392	#41	—	73	2	no	—
393	#41	—	146	1	no	—
394	#41	—	146	1	no	—
395	C₂×Q₈	—	73	1	no	—
396	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	73	1	no	—
401	C₂×D₄	—	146	1	no	—
402	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	146	1	no	—
405	C₂²×C₄	—	146	1	no	—
406	C₂²×C₄	—	146	1	no	—
407	C₂²×C₄	—	146	1	no	—
408	C₂²×C₄	—	146	1	no	—
409	C₂²×C₄	#11924028	1	1	yes	characteristic
410	C₂²×C₄	#11924028	1	1	yes	characteristic
411	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
412	Q₁₆	—	146	4	no	—
413	SD₁₆	—	146	4	no	—
414	SD₁₆	—	146	4	no	—
415	D₈	—	146	4	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	4	4	no	—
420	M₁₆	—	292	4	no	—
421	M₁₆	—	146	2	no	—
422	M₁₆	—	146	2	no	—
423	M₁₆	D₄×D₇₃	1	2	yes	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	—	292	4	no	—
430	C₂×C₈	—	73	2	no	—
431	C₂×C₈	—	73	2	no	—
432	C₂×C₈	—	146	2	no	—
433	C₂×C₈	—	146	2	no	—
434	C₂×C₈	—	146	2	no	—
435	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
436	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	73	1	no	—
440	C₄⋊C₄	—	73	1	no	—
441	C₄⋊C₄	—	146	1	no	—
442	C₄⋊C₄	—	146	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	146	1	no	—
446	C₂²⋊C₄	—	146	1	no	—
447	C₂²⋊C₄	—	146	1	no	—
448	C₄²	—	292	2	no	—
449	C₄²	—	73	2	no	—
450	C₄²	—	146	4	no	—
451	C₄²	—	146	1	no	—
452	C₄²	—	146	1	no	—
453	C₄²	—	146	1	no	—
454	C₄²	—	146	1	no	—
455	C₄²	—	146	1	no	—
456	C₄²	—	146	1	no	—
457	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
458	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
459	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
460	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
461	C₂³	—	2	2	no	—
462	C₂³	—	146	1	no	—
463	C₂³	C₂×#11924028	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	73	2	no	—
467	Q₈	—	146	1	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	1	no	—
474	D₄	—	73	2	no	—
475	D₄	—	146	2	no	—
476	D₄	—	146	2	no	—
477	D₄	—	146	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	292	1	no	—
484	C₂×C₄	—	292	1	no	—
485	C₂×C₄	—	292	2	no	—
486	C₂×C₄	—	584	1	no	—
487	C₂×C₄	—	146	2	no	—
488	C₂×C₄	—	146	1	no	—
489	C₂×C₄	—	146	1	no	—
490	C₂×C₄	—	146	2	no	—
491	C₂×C₄	—	146	2	no	—
492	C₂×C₄	—	146	2	no	—
493	C₂×C₄	—	146	1	no	—
494	C₂×C₄	—	146	2	no	—
495	C₂×C₄	—	146	2	no	—
496	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
497	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
498	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
499	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
501	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
503	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
504	C₂×C₄	#14556636	1	1	yes	characteristic
505	C₂×C₄	#14556638	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	292	2	no	—
511	C₈	—	146	2	no	—
512	C₈	—	146	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	292	1	no	—
519	C₂²	—	292	1	no	—
520	C₂²	—	146	2	no	—
521	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
522	C₂²	#17989242	1	1	yes	characteristic
523	C₂²	#17989287	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	292	2	no	—
529	C₄	—	292	1	no	—
530	C₄	—	292	1	no	—
531	C₄	—	146	4	no	—
532	C₄	—	146	2	no	—
533	C₄	#17988702	1	2	yes	complemented
534	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
535	C₄	#17989066	1	1	yes	characteristic
536	C₄	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
537	C₄	#17989244	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	8	2	no	—
541	C₂	—	292	2	no	—
542	C₂	#22612943	1	1	yes	characteristic
543	C₂	C₂×#17988702	1	1	yes	characteristic
544	C₂	#22618838	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#2935	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#22619380	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#2935	D₇₃
hypocenter	C₇₃	#23015
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. C₂×#17988702	C₂	semidirect
3. #22618496	C₂	semidirect
4. #22610760	C₂	semidirect
5. #22610706	C₂	semidirect
6. #22610638	C₂	semidirect
7. #22610261	C₂	semidirect
8. #22610206	C₂	semidirect
9. C₄⋊C₈×Dic₇₃	C₂	semidirect
10. C₄×#14556517	C₂	semidirect
11. C₇₃×#2935	C₂	semidirect
15. #17988806	C₄	semidirect
16. #17988799	C₄	semidirect
17. #17988794	C₄	semidirect
18. #17988789	C₄	semidirect
19. #17988784	C₄	semidirect
20. #17988779	C₄	semidirect
85. #14556517	D₄	semidirect
255. C₄×C₇₃	#443	semidirect
275. #2935	D₇₃	semidirect
284. C₇₃	#23015	semidirect
533. C₄	#17988702	semidirect

Maximal subgroups

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

subgroup	index
#22619380	2
C₂×#17988702	2
#22618496	2
#22610760	2
#22610706	2
#22610638	2
#22610261	2
#22610206	2
C₄⋊C₈×Dic₇₃	2
C₄×#14556517	2
C₇₃×#2935	2
#23015	73