Subgroups — #34020508

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#443	C₂	1	1	yes	maximal, characteristic
2	#135×#64408	C₂	1	1	yes	maximal, characteristic
3	#22626501	C₂	1	2	yes	maximal, complemented
4	#108×#64408	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625736	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625733	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625711	C₂	1	2	yes	maximal, complemented
8	#22625709	C₂	1	2	yes	maximal, complemented
9	#22625696	C₂	1	2	yes	maximal, complemented
10	#22625587	C₂	1	1	yes	maximal, characteristic, complemented
11	#443×D₇₃	C₂	1	1	yes	maximal, characteristic
12	D₇₃⋊#131	C₂²	1	2	yes	—
13	#41×#64408	C₂²	1	2	yes	—
14	#17989631	C₄	1	2	yes	complemented
15	#17989630	C₄	1	4	yes	complemented
16	#17989629	C₄	1	2	yes	complemented
17	Q₁₆×#64408	C₄	1	2	yes	complemented
18	SD₁₆×#64408	C₄	1	4	yes	complemented
19	D₈×#64408	C₄	1	2	yes	complemented
20	D₇₃⋊#108	C₂²	1	1	yes	characteristic
21	#17989597	C₂²	1	1	yes	characteristic
22	D₇₃⋊#104	C₂²	1	2	yes	—
23	#17989577	C₂²	1	2	yes	—
24	#17989553	—	2	2	no	—
25	#17989553	C₂²	1	2	yes	—
26	#17989550	—	2	2	no	—
27	#17989550	C₂²	1	2	yes	—
28	M₁₆×#64408	—	2	2	no	—
29	M₁₆×#64408	C₂²	1	2	yes	—
30	#17989546	C₂²	1	1	yes	characteristic
31	C₂×#14556645	—	2	2	no	—
32	C₂×#14556645	C₂²	1	1	yes	characteristic
33	C₂×#14556645	C₂²	1	1	yes	characteristic
34	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
35	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
36	#17989523	C₂²	1	1	yes	characteristic
37	#17989462	C₂²	1	2	yes	—
38	#17989459	C₂²	1	2	yes	—
39	#17989458	C₂²	1	2	yes	—
40	#135×D₇₃	C₂²	1	1	yes	characteristic
41	#131×D₇₃	C₂²	1	2	yes	—
42	#17988705	C₄	1	1	yes	characteristic, complemented
43	#17988704	C₄	1	1	yes	characteristic, complemented
44	#17988703	C₄	1	1	yes	characteristic, complemented
45	#17988702	C₄	1	2	yes	complemented
46	#17988701	C₄	1	2	yes	complemented
47	#108×D₇₃	C₂²	1	1	yes	characteristic
48	#104×D₇₃	C₂²	1	2	yes	—
49	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
50	#443×C₇₃	C₄	1	1	yes	characteristic, complemented
51	#14556679	C₂×C₄	1	4	yes	complemented
52	#14556678	—	2	4	no	—
53	#14556678	C₂×C₄	1	4	yes	complemented
54	D₇₃⋊M₁₆	—	2	2	no	—
55	D₇₃⋊M₁₆	C₂³	1	2	yes	—
56	C₂×#11924036	—	2	2	no	—
57	C₂×#11924036	C₂³	1	1	yes	characteristic
58	C₂×#11924036	C₂³	1	1	yes	characteristic
59	Q₈×#64408	C₂×C₄	1	4	yes	—
60	D₄×#64408	—	2	4	no	—
61	D₄×#64408	C₂×C₄	1	4	yes	—
62	#14556670	—	2	2	no	—
63	#14556670	C₂³	1	2	yes	—
64	C₂×C₄×#64408	—	2	2	no	—
65	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
66	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
67	#14556662	C₂×C₄	1	2	yes	complemented
68	#14556661	C₂×C₄	1	2	yes	complemented
69	#14556660	C₂×C₄	1	2	yes	—
70	#14556659	C₂×C₄	1	2	yes	—
71	#14556656	C₂×C₄	1	4	yes	complemented
72	#14556655	C₂×C₄	1	4	yes	complemented
73	#14556654	C₂×C₄	1	4	yes	—
74	#14556653	C₂×C₄	1	4	yes	—
75	#14556646	—	2	2	no	—
76	#14556645	—	2	2	no	—
77	#14556645	—	2	2	no	—
78	#14556645	—	2	2	no	—
79	#14556645	—	2	1	no	—
80	#14556645	—	2	1	no	—
81	#14556645	D₄	1	1	yes	characteristic
82	#14556645	D₄	1	1	yes	characteristic
83	#14556645	D₄	1	1	yes	characteristic
84	#14556645	D₄	1	1	yes	characteristic
85	C₈×#64408	—	2	2	no	—
86	C₈×#64408	—	2	2	no	—
87	C₈×#64408	—	2	2	no	—
88	C₈×#64408	C₂×C₄	1	2	yes	—
89	C₈×#64408	C₂×C₄	1	2	yes	—
90	C₈×#64408	C₂×C₄	1	2	yes	complemented
91	C₈×#64408	C₂×C₄	1	2	yes	complemented
92	(C₂×#64408)⋊C₄	—	2	2	no	—
93	#41×D₇₃	C₂³	1	2	yes	—
94	#14556614	C₂×C₄	1	1	yes	characteristic
95	#14556613	C₂×C₄	1	1	yes	characteristic
96	#14556612	C₂×C₄	1	2	yes	—
97	#14556611	C₂×C₄	1	2	yes	—
98	#14556610	C₂×C₄	1	1	yes	characteristic
99	Q₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
100	SD₁₆×D₇₃	C₂×C₄	1	2	yes	—
101	D₈×D₇₃	C₂×C₄	1	1	yes	characteristic
102	#14556599	—	2	2	no	—
103	#14556599	C₂×C₄	1	2	yes	complemented
104	#14556598	C₂×C₄	1	2	yes	complemented
105	#14556597	—	2	2	no	—
106	#14556597	C₂×C₄	1	2	yes	complemented
107	M₁₆×D₇₃	—	2	2	no	—
108	M₁₆×D₇₃	C₂³	1	2	yes	—
109	C₂×C₈×D₇₃	—	2	2	no	—
110	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
112	C₄²×D₇₃	C₂³	1	1	yes	characteristic
113	#14556527	C₂×C₄	1	1	yes	characteristic, complemented
114	#14556526	C₂×C₄	1	2	yes	complemented
115	#14556519	C₂×C₄	1	2	yes	complemented
116	#14556518	C₂×C₄	1	2	yes	complemented
117	#14556517	C₂×C₄	1	2	yes	complemented
118	C₄×#10596831	C₂×C₄	1	1	yes	characteristic, complemented
119	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
120	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
121	#135×C₇₃	C₂×C₄	1	1	yes	characteristic
122	#131×C₇₃	C₂×C₄	1	2	yes	complemented
123	#108×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
124	#104×C₇₃	C₂×C₄	1	2	yes	complemented
125	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂²×#64408	—	2	1	no	—
127	C₂²×#64408	—	2	4	no	—
128	C₂²×#64408	#41	1	2	yes	—
129	#11924038	—	2	4	no	—
130	#11924038	C₂²×C₄	1	4	yes	—
131	#11924037	—	2	2	no	—
132	#11924037	—	2	4	no	—
133	#11924036	—	2	2	no	—
134	#11924036	—	2	1	no	—
135	#11924036	—	2	4	no	—
136	#11924036	C₂²×C₄	1	2	yes	—
137	#11924036	C₂²×C₄	1	2	yes	—
138	#11924036	C₂×D₄	1	1	yes	characteristic
139	#11924036	C₂×D₄	1	1	yes	characteristic
140	C₂×#10596833	—	2	1	no	—
141	C₂×#10596833	—	2	4	no	—
142	C₂×#10596833	#41	1	2	yes	—
143	C₄⋊#64408	—	2	4	no	—
144	C₄⋊#64408	C₂²×C₄	1	4	yes	—
145	C₂²⋊#64408	—	2	2	no	—
146	C₂²⋊#64408	—	2	4	no	—
147	C₄×#64408	—	2	4	no	—
148	C₄×#64408	—	2	2	no	—
149	C₄×#64408	—	2	1	no	—
150	C₄×#64408	C₂²×C₄	1	2	yes	—
151	C₄×#64408	C₂²×C₄	1	2	yes	—
152	C₄×#64408	C₂×D₄	1	1	yes	characteristic
153	C₄×#64408	C₂×D₄	1	1	yes	characteristic
154	#11924029	C₂²×C₄	1	2	yes	—
155	#11924028	—	2	2	no	—
156	#11924028	C₂²×C₄	1	2	yes	—
157	#11924027	—	2	2	no	—
158	#11924027	C₂²×C₄	1	2	yes	—
159	Q₈×D₇₃	C₂²×C₄	1	2	yes	—
160	D₄×D₇₃	—	2	2	no	—
161	D₄×D₇₃	C₂²×C₄	1	2	yes	—
162	C₂×C₄×D₇₃	—	2	2	no	—
163	C₂×C₄×D₇₃	—	2	1	no	—
164	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
165	Dic₂₉₂	C₄²	1	1	yes	characteristic
166	#11924018	C₄²	1	2	yes	—
167	#11924017	C₄²	1	2	yes	—
168	#11924016	C₄²	1	2	yes	—
169	#11924015	C₄²	1	2	yes	—
170	D₅₈₄	C₄²	1	1	yes	characteristic
171	#11924013	C₄²	1	2	yes	—
172	#11924012	—	2	2	no	—
173	#11924012	C₂²×C₄	1	2	yes	—
174	#11924011	—	2	2	no	—
175	#11924011	—	2	2	no	—
176	#11924011	—	2	2	no	—
177	C₂×#10596831	—	2	2	no	—
178	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
179	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
180	C₈×D₇₃	—	2	2	no	—
181	C₈×D₇₃	—	2	2	no	—
182	C₈×D₇₃	—	2	2	no	—
183	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
184	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
185	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
187	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
188	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
189	C₈×D₇₃	#41	1	1	yes	characteristic
190	C₈×D₇₃	#41	1	1	yes	characteristic
191	C₄×Dic₇₃	—	2	1	no	—
192	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
193	#41×C₇₃	C₂²×C₄	1	2	yes	—
194	Q₁₆×C₇₃	C₄²	1	1	yes	characteristic
195	SD₁₆×C₇₃	C₄²	1	2	yes	—
196	D₈×C₇₃	C₄²	1	1	yes	characteristic
197	M₁₆×C₇₃	—	2	2	no	—
198	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
199	C₂×C₈×C₇₃	—	2	2	no	—
200	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×D₇₃	—	2	2	no	—
204	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
205	C₂×#64408	—	2	4	no	—
206	C₂×#64408	—	2	2	no	—
207	C₂×#64408	—	4	2	no	—
208	C₂×#64408	—	4	2	no	—
209	C₂×#64408	—	8	4	no	—
210	C₂×#64408	C₄×D₄	1	2	yes	—
211	C₂×#64408	C₄×D₄	1	2	yes	—
212	Q₈×C₇₃	C₂×C₄²	1	2	yes	—
213	D₄×C₇₃	—	2	2	no	—
214	D₄×C₇₃	C₂×C₄²	1	2	yes	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
218	C₂²⋊D₇₃	—	2	2	no	—
219	C₂²⋊D₇₃	—	2	2	no	—
220	C₂²⋊D₇₃	—	2	2	no	—
221	C₂×Dic₇₃	—	2	2	no	—
222	C₂×Dic₇₃	—	2	1	no	—
223	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
224	D₂₉₂	—	2	2	no	—
225	D₂₉₂	C₂×C₄²	1	2	yes	—
226	C₄×D₇₃	—	2	2	no	—
227	C₄×D₇₃	—	2	2	no	—
228	C₄×D₇₃	—	2	2	no	—
229	C₄×D₇₃	—	4	2	no	—
230	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
231	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
232	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
233	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
234	Dic₁₄₆	—	2	2	no	—
235	Dic₁₄₆	C₂×C₄²	1	2	yes	—
236	#10596833	—	2	4	no	—
237	#10596833	—	2	2	no	—
238	#10596833	C₄×D₄	1	2	yes	—
239	#10596833	C₄×D₄	1	2	yes	—
240	C₈×C₇₃	—	2	2	no	—
241	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
242	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
243	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
244	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
245	#10596831	—	2	2	no	—
246	#10596831	C₂×C₄²	1	1	yes	characteristic
247	#10596831	C₂×C₄²	1	1	yes	characteristic
248	#10596831	C₄×D₄	1	1	yes	characteristic
249	#10596831	C₄×D₄	1	1	yes	characteristic
250	C₂²×C₇₃	—	2	2	no	—
251	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
252	C₂×D₇₃	—	2	2	no	—
253	C₂×D₇₃	—	2	2	no	—
254	C₂×D₇₃	—	4	4	no	—
255	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂×D₇₃	C₄×#41	1	1	yes	characteristic
257	#64408	—	2	2	no	—
258	#64408	—	2	2	no	—
259	#64408	—	4	2	no	—
260	#64408	—	4	4	no	—
261	C₄×C₇₃	—	2	2	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
264	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
265	Dic₇₃	—	2	2	no	—
266	Dic₇₃	—	4	1	no	—
267	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
268	Dic₇₃	C₄×#41	1	1	yes	characteristic
269	#20514	—	73	1	no	maximal, Sylow
270	C₂×C₇₃	—	2	1	no	—
271	C₂×C₇₃	—	4	2	no	—
272	C₂×C₇₃	C₄²×D₄	1	1	yes	characteristic
273	D₇₃	—	2	1	no	—
274	D₇₃	—	4	2	no	—
275	D₇₃	#2957	1	2	yes	—
276	C₂×#443	—	73	1	no	—
277	C₂×#443	—	73	1	no	—
278	C₄×#135	—	73	1	no	—
279	#2875	—	73	2	no	—
280	C₄×#108	—	73	1	no	—
281	#1772	—	73	1	no	—
282	#1772	—	73	1	no	—
283	#1765	—	73	2	no	—
284	#1765	—	73	2	no	—
285	#1759	—	73	2	no	—
286	#1726	—	73	1	no	—
287	C₇₃	#20514	1	1	yes	characteristic, complemented, Sylow
288	C₂×#135	—	73	1	no	—
289	C₂×#131	—	73	2	no	—
290	C₂×#131	—	73	2	no	—
291	C₄×#41	—	73	2	no	—
292	#443	—	73	2	no	—
293	#443	—	73	4	no	—
294	#443	—	73	2	no	—
295	#443	—	73	1	no	—
296	#443	—	73	2	no	—
297	#443	—	73	1	no	—
298	#443	—	73	2	no	—
299	#443	—	73	1	no	—
300	#443	#64408	1	1	yes	characteristic, complemented
301	C₄×Q₁₆	—	73	2	no	—
302	C₄×SD₁₆	—	73	4	no	—
303	C₄×D₈	—	73	2	no	—
304	C₂×#108	—	73	1	no	—
305	C₂×#108	—	73	1	no	—
306	#427	—	73	1	no	—
307	C₂×#104	—	73	2	no	—
308	C₂×#104	—	73	2	no	—
309	#416	—	73	2	no	—
310	#405	—	73	2	no	—
311	#405	—	73	2	no	—
312	#405	—	146	2	no	—
313	#405	—	146	2	no	—
314	C₄×M₁₆	—	73	2	no	—
315	C₄×M₁₆	—	146	2	no	—
316	C₂×#97	—	73	1	no	—
317	C₂×#97	—	73	1	no	—
318	C₂×#97	—	73	1	no	—
319	C₂×#97	—	146	2	no	—
320	C₂×C₄×C₈	—	73	1	no	—
321	C₂×C₄×C₈	—	73	1	no	—
322	C₂×C₄×C₈	—	73	1	no	—
323	#376	—	73	1	no	—
324	#341	—	73	2	no	—
325	#339	—	73	2	no	—
326	#339	—	73	2	no	—
327	C₂×#41	—	73	2	no	—
328	#135	—	73	2	no	—
329	#135	—	73	1	no	—
330	#135	—	73	2	no	—
331	#135	—	73	1	no	—
332	#135	—	73	1	no	—
333	#135	C₂×#64408	1	1	yes	characteristic
334	C₂×Q₁₆	—	73	1	no	—
335	C₂×SD₁₆	—	73	2	no	—
336	C₂×D₈	—	73	1	no	—
337	#131	—	73	4	no	—
338	#131	—	73	4	no	—
339	#131	—	73	2	no	—
340	#131	—	73	2	no	—
341	#131	—	73	2	no	—
342	#131	—	146	2	no	—
343	#131	—	146	2	no	—
344	#131	—	146	4	no	—
345	#131	C₂×#64408	1	2	yes	complemented
346	C₂×M₁₆	—	73	2	no	—
347	C₂×M₁₆	—	73	2	no	—
348	C₂×M₁₆	—	146	2	no	—
349	C₂×M₁₆	—	146	2	no	—
350	C₂²×C₈	—	73	1	no	—
351	C₂²×C₈	—	73	1	no	—
352	C₂²×C₈	—	73	1	no	—
353	C₂²×C₈	—	73	1	no	—
354	C₂²×C₈	—	146	2	no	—
355	C₂²×C₈	—	146	2	no	—
356	C₄×Q₈	—	73	4	no	—
357	C₄×D₄	—	73	4	no	—
358	C₄×D₄	—	146	4	no	—
359	#117	—	73	2	no	—
360	#117	—	146	2	no	—
361	C₂×C₄²	—	73	1	no	—
362	C₂×C₄²	—	73	1	no	—
363	C₂×C₄²	—	73	1	no	—
364	C₂×C₄²	—	146	2	no	—
365	#108	—	73	2	no	—
366	#108	—	73	2	no	—
367	#108	—	73	2	no	—
368	#108	—	73	1	no	—
369	#108	C₂×#64408	1	1	yes	characteristic, complemented
370	#107	—	73	2	no	—
371	#106	—	73	2	no	—
372	#104	—	73	4	no	—
373	#104	—	73	4	no	—
374	#104	—	73	2	no	—
375	#104	—	73	2	no	—
376	#104	—	73	2	no	—
377	#104	C₂×#64408	1	2	yes	complemented
378	#103	—	73	4	no	—
379	#102	—	73	4	no	—
380	#97	—	73	1	no	—
381	#97	—	73	1	no	—
382	#97	—	73	1	no	—
383	#97	—	73	1	no	—
384	#97	—	146	2	no	—
385	#97	—	146	1	no	—
386	#97	—	146	1	no	—
387	#97	—	146	2	no	—
388	#97	—	146	2	no	—
389	#97	—	146	2	no	—
390	C₄×C₈	—	73	2	no	—
391	C₄×C₈	—	73	2	no	—
392	C₄×C₈	—	73	2	no	—
393	C₄×C₈	—	73	2	no	—
394	C₄×C₈	—	73	1	no	—
395	C₄×C₈	—	73	1	no	—
396	C₄×C₈	—	73	1	no	—
397	C₄×C₈	—	146	2	no	—
398	C₄×C₈	—	146	2	no	—
399	C₄×C₈	—	146	2	no	—
400	C₄×C₈	C₂×#64408	1	1	yes	characteristic, complemented
401	#95	—	146	2	no	—
402	#41	—	73	2	no	—
403	#41	—	73	2	no	—
404	#41	—	73	2	no	—
405	#41	—	146	2	no	—
406	#41	—	146	2	no	—
407	#41	C₂²×#64408	1	2	yes	—
408	C₂×Q₈	—	73	2	no	—
409	C₂×D₄	—	73	2	no	—
410	C₂×D₄	—	146	2	no	—
411	C₂²×C₄	—	73	2	no	—
412	C₂²×C₄	—	73	1	no	—
413	C₂²×C₄	—	146	1	no	—
414	C₂²×C₄	—	146	2	no	—
415	C₂²×C₄	—	146	1	no	—
416	C₂²×C₄	—	146	4	no	—
417	Q₁₆	—	73	2	no	—
418	Q₁₆	—	73	1	no	—
419	Q₁₆	C₄×#64408	1	1	yes	characteristic
420	SD₁₆	—	73	2	no	—
421	SD₁₆	—	73	2	no	—
422	SD₁₆	—	73	2	no	—
423	SD₁₆	C₄×#64408	1	2	yes	—
424	D₈	—	73	2	no	—
425	D₈	—	73	1	no	—
426	D₈	C₄×#64408	1	1	yes	characteristic
427	M₁₆	—	2	2	no	—
428	M₁₆	—	73	4	no	—
429	M₁₆	—	73	2	no	—
430	M₁₆	—	146	2	no	—
431	M₁₆	—	146	2	no	—
432	M₁₆	—	146	2	no	—
433	M₁₆	—	146	4	no	—
434	M₁₆	—	146	4	no	—
435	M₁₆	—	146	2	no	—
436	M₁₆	—	146	2	no	—
437	M₁₆	C₂²×#64408	1	2	yes	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	73	2	no	—
440	C₂×C₈	—	73	2	no	—
441	C₂×C₈	—	73	1	no	—
442	C₂×C₈	—	73	1	no	—
443	C₂×C₈	—	73	1	no	—
444	C₂×C₈	—	73	1	no	—
445	C₂×C₈	—	73	1	no	—
446	C₂×C₈	—	73	1	no	—
447	C₂×C₈	—	73	1	no	—
448	C₂×C₈	—	73	1	no	—
449	C₂×C₈	—	73	1	no	—
450	C₂×C₈	—	73	1	no	—
451	C₂×C₈	—	73	1	no	—
452	C₂×C₈	—	73	1	no	—
453	C₂×C₈	—	73	2	no	—
454	C₂×C₈	—	146	2	no	—
455	C₂×C₈	—	146	2	no	—
456	C₂×C₈	—	146	2	no	—
457	C₂×C₈	—	146	4	no	—
458	C₂×C₈	—	146	4	no	—
459	C₂×C₈	—	146	1	no	—
460	C₂×C₈	—	146	2	no	—
461	C₂×C₈	—	146	1	no	—
462	C₂×C₈	—	146	2	no	—
463	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
464	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
465	C₄⋊C₄	—	73	4	no	—
466	C₄⋊C₄	—	146	4	no	—
467	C₂²⋊C₄	—	146	4	no	—
468	C₂²⋊C₄	—	146	2	no	—
469	C₄²	—	73	2	no	—
470	C₄²	—	73	1	no	—
471	C₄²	—	73	1	no	—
472	C₄²	—	73	2	no	—
473	C₄²	—	73	1	no	—
474	C₄²	—	146	1	no	—
475	C₄²	—	146	2	no	—
476	C₄²	—	146	1	no	—
477	C₄²	—	146	4	no	—
478	C₄²	C₂²×#64408	1	1	yes	characteristic
479	C₂³	—	73	1	no	—
480	C₂³	—	146	2	no	—
481	Q₈	—	73	2	no	—
482	Q₈	—	146	2	no	—
483	Q₈	C₂×C₄×#64408	1	2	yes	—
484	D₄	—	2	2	no	—
485	D₄	—	73	2	no	—
486	D₄	—	146	2	no	—
487	D₄	—	146	2	no	—
488	D₄	—	146	2	no	—
489	D₄	—	146	2	no	—
490	D₄	C₂×C₄×#64408	1	2	yes	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	292	2	no	—
494	C₂×C₄	—	292	2	no	—
495	C₂×C₄	—	292	2	no	—
496	C₂×C₄	—	584	4	no	—
497	C₂×C₄	—	73	1	no	—
498	C₂×C₄	—	73	1	no	—
499	C₂×C₄	—	73	1	no	—
500	C₂×C₄	—	73	1	no	—
501	C₂×C₄	—	73	1	no	—
502	C₂×C₄	—	73	2	no	—
503	C₂×C₄	—	73	2	no	—
504	C₂×C₄	—	146	2	no	—
505	C₂×C₄	—	146	2	no	—
506	C₂×C₄	—	146	2	no	—
507	C₂×C₄	—	146	4	no	—
508	C₂×C₄	—	146	1	no	—
509	C₂×C₄	—	146	2	no	—
510	C₂×C₄	—	146	2	no	—
511	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	73	2	no	—
514	C₈	—	73	2	no	—
515	C₈	—	73	1	no	—
516	C₈	—	73	1	no	—
517	C₈	—	73	1	no	—
518	C₈	—	73	1	no	—
519	C₈	—	146	2	no	—
520	C₈	—	146	4	no	—
521	C₈	—	146	2	no	—
522	C₈	C₂×C₄×#64408	1	1	yes	characteristic
523	C₈	C₂×C₄×#64408	1	1	yes	characteristic
524	C₈	D₄×#64408	1	1	yes	characteristic
525	C₈	D₄×#64408	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	292	4	no	—
528	C₂²	—	73	1	no	—
529	C₂²	—	73	1	no	—
530	C₂²	—	146	2	no	—
531	C₂²	—	146	2	no	—
532	C₂²	#41×#64408	1	1	yes	characteristic
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	292	1	no	—
536	C₄	—	292	4	no	—
537	C₄	—	292	2	no	—
538	C₄	—	73	1	no	—
539	C₄	—	73	1	no	—
540	C₄	—	146	2	no	—
541	C₄	—	146	2	no	—
542	C₄	—	146	2	no	—
543	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
544	C₄	C₂×D₄×#64408	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	4	2	no	—
547	C₂	—	292	2	no	—
548	C₂	—	73	2	no	—
549	C₂	—	146	1	no	—
550	C₂	C₄×D₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#443×C₇₃	C₄
socle	C₂×C₇₃	C₄²×D₄
prime radical	#135×D₇₃	C₂²
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#443	#64408
hypocenter	C₇₃	#20514
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #22626501	C₂	semidirect
4. #108×#64408	C₂	semidirect
5. #22625736	C₂	semidirect
6. #22625733	C₂	semidirect
7. #22625711	C₂	semidirect
8. #22625709	C₂	semidirect
9. #22625696	C₂	semidirect
10. #22625587	C₂	semidirect
14. #17989631	C₄	semidirect
15. #17989630	C₄	semidirect
16. #17989629	C₄	semidirect
17. Q₁₆×#64408	C₄	semidirect
18. SD₁₆×#64408	C₄	semidirect
19. D₈×#64408	C₄	semidirect
42. #17988705	C₄	semidirect
43. #17988704	C₄	semidirect
44. #17988703	C₄	semidirect
45. #17988702	C₄	semidirect
46. #17988701	C₄	semidirect
50. #443×C₇₃	C₄	semidirect
51. #14556679	C₂×C₄	semidirect
53. #14556678	C₂×C₄	semidirect
67. #14556662	C₂×C₄	semidirect
68. #14556661	C₂×C₄	semidirect
71. #14556656	C₂×C₄	semidirect
72. #14556655	C₂×C₄	semidirect
90. C₈×#64408	C₂×C₄	semidirect
91. C₈×#64408	C₂×C₄	semidirect
103. #14556599	C₂×C₄	semidirect
104. #14556598	C₂×C₄	semidirect
106. #14556597	C₂×C₄	semidirect
113. #14556527	C₂×C₄	semidirect
114. #14556526	C₂×C₄	semidirect
115. #14556519	C₂×C₄	semidirect
116. #14556518	C₂×C₄	semidirect
117. #14556517	C₂×C₄	semidirect
118. C₄×#10596831	C₂×C₄	semidirect
119. C₈×Dic₇₃	C₂×C₄	semidirect
120. C₈×Dic₇₃	C₂×C₄	semidirect
122. #131×C₇₃	C₂×C₄	semidirect
123. #108×C₇₃	C₂×C₄	semidirect
124. #104×C₇₃	C₂×C₄	semidirect
125. C₄×C₈×C₇₃	C₂×C₄	semidirect
287. C₇₃	#20514	semidirect
300. #443	#64408	semidirect
345. #131	C₂×#64408	semidirect
369. #108	C₂×#64408	semidirect
377. #104	C₂×#64408	semidirect
400. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#443	2
#135×#64408	2
#22626501	2
#108×#64408	2
#22625736	2
#22625733	2
#22625711	2
#22625709	2
#22625696	2
#22625587	2
#443×D₇₃	2
#20514	73