Subgroups — #34021390

Order 18688.

810 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626409	C₂	1	2	yes	maximal
2	#22625869	C₂	1	2	yes	maximal, complemented
3	#22625853	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625852	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625809	C₂	1	2	yes	maximal
6	#22625808	C₂	1	1	yes	maximal, characteristic
7	#22625807	C₂	1	1	yes	maximal, characteristic
8	#22625745	C₂	1	2	yes	maximal, complemented
9	C₄×#14556660	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14556659	C₂	1	1	yes	maximal, characteristic, complemented
11	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556660	C₂²	1	2	yes	—
13	C₂×#14556660	C₂²	1	2	yes	—
14	C₂×#14556659	C₂²	1	2	yes	—
15	C₂×#14556659	C₂²	1	2	yes	—
16	#17989537	—	2	2	no	—
17	#17989537	—	2	2	no	—
18	#17989536	—	2	2	no	—
19	#17989536	—	2	2	no	—
20	#17989533	C₂²	1	2	yes	—
21	#17989531	C₂²	1	2	yes	—
22	#17989529	C₂²	1	2	yes	—
23	#17989529	C₂²	1	2	yes	—
24	C₄×C₄⋊#64408	C₂²	1	2	yes	—
25	C₄×C₄⋊#64408	C₂²	1	2	yes	—
26	#17989461	C₂²	1	1	yes	characteristic
27	#17989461	C₂²	1	1	yes	characteristic
28	#17989461	C₂²	1	1	yes	characteristic
29	#17989461	C₂²	1	1	yes	characteristic
30	#17989461	C₂²	1	2	yes	—
31	#17989461	C₂²	1	2	yes	—
32	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#117×D₇₃	C₂²	1	1	yes	characteristic
35	#17988545	C₄	1	1	yes	characteristic, complemented
36	#17988544	C₄	1	1	yes	characteristic, complemented
37	#17988544	C₄	1	1	yes	characteristic, complemented
38	#17988543	C₄	1	1	yes	characteristic, complemented
39	#17988542	C₄	1	1	yes	characteristic, complemented
40	#17988541	C₄	1	1	yes	characteristic, complemented
41	#17988541	C₄	1	1	yes	characteristic, complemented
42	#97×D₇₃	C₂²	1	1	yes	characteristic
43	#97×D₇₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
47	C₂×C₄⋊#64408	—	2	2	no	—
48	C₂×C₄⋊#64408	—	2	2	no	—
49	C₂×C₄⋊#64408	C₂³	1	2	yes	—
50	C₂×C₄⋊#64408	C₂³	1	2	yes	—
51	C₂×C₄⋊#64408	C₂³	1	2	yes	—
52	C₂×C₄⋊#64408	C₂³	1	2	yes	—
53	C₂×C₂²⋊#64408	—	2	2	no	—
54	C₂×C₂²⋊#64408	—	2	2	no	—
55	C₂×C₄×#64408	—	2	2	no	—
56	C₂×C₄×#64408	—	2	2	no	—
57	#14556660	—	2	4	no	—
58	#14556660	—	2	4	no	—
59	#14556659	—	2	4	no	—
60	#14556659	—	2	4	no	—
61	(C₂×#64408)⋊C₄	—	2	2	no	—
62	(C₂×#64408)⋊C₄	—	2	2	no	—
63	(C₂×#64408)⋊C₄	—	2	2	no	—
64	(C₂×#64408)⋊C₄	—	2	2	no	—
65	(C₂×#64408)⋊C₄	—	2	2	no	—
66	(C₂×#64408)⋊C₄	—	2	2	no	—
67	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
68	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
71	M₁₆×D₇₃	—	2	4	no	—
72	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₃	—	2	4	no	—
74	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
80	#14556550	C₂×C₄	1	1	yes	characteristic
81	#14556549	Q₈	1	1	yes	characteristic
82	#14556549	Q₈	1	1	yes	characteristic
83	#14556548	C₂×C₄	1	1	yes	characteristic
84	#14556548	C₂×C₄	1	1	yes	characteristic
85	#14556547	Q₈	1	1	yes	characteristic
86	#14556547	Q₈	1	1	yes	characteristic
87	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
88	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
89	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
90	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
91	C₄²×D₇₃	C₂³	1	1	yes	characteristic
92	C₄²×D₇₃	C₂³	1	1	yes	characteristic
93	#14556502	C₂×C₄	1	1	yes	characteristic
94	#14556502	C₂×C₄	1	1	yes	characteristic
95	#14556501	C₂×C₄	1	1	yes	characteristic
96	#14556501	C₂×C₄	1	1	yes	characteristic
97	#14556501	C₂×C₄	1	1	yes	characteristic
98	#14556501	C₂×C₄	1	1	yes	characteristic
99	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
100	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
105	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
106	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
107	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
108	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
109	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
112	C₂²×#64408	—	2	2	no	—
113	C₂²×#64408	—	2	2	no	—
114	C₂²×#64408	—	2	2	no	—
115	C₂²×#64408	—	2	2	no	—
116	C₄⋊#64408	—	2	2	no	—
117	C₄⋊#64408	—	2	2	no	—
118	C₄⋊#64408	—	2	2	no	—
119	C₄⋊#64408	—	2	2	no	—
120	C₄⋊#64408	—	2	2	no	—
121	C₄⋊#64408	—	2	2	no	—
122	C₄⋊#64408	—	2	2	no	—
123	C₄⋊#64408	—	2	2	no	—
124	C₄⋊#64408	—	8	2	no	—
125	C₄⋊#64408	—	8	2	no	—
126	C₂²⋊#64408	—	8	2	no	—
127	C₂²⋊#64408	—	8	2	no	—
128	C₄×#64408	—	8	2	no	—
129	C₄×#64408	—	8	2	no	—
130	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
132	C₂×C₄×D₇₃	—	2	2	no	—
133	C₂×C₄×D₇₃	—	2	2	no	—
134	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
141	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
142	#11924012	—	2	2	no	—
143	#11924011	—	2	2	no	—
144	#11924011	—	2	2	no	—
145	C₂×#10596831	—	2	2	no	—
146	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
147	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
148	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
149	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
150	C₈×D₇₃	—	2	2	no	—
151	C₈×D₇₃	—	2	2	no	—
152	C₈×D₇₃	—	2	2	no	—
153	C₈×D₇₃	—	2	2	no	—
154	C₈×D₇₃	#41	1	4	yes	—
155	C₈×D₇₃	#41	1	4	yes	—
156	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
157	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
158	#11924007	C₄⋊C₄	1	1	yes	characteristic
159	#11924007	C₄⋊C₄	1	1	yes	characteristic
160	#11924007	C₄⋊C₄	1	1	yes	characteristic
161	#11924007	C₄⋊C₄	1	1	yes	characteristic
162	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
163	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
164	#11924005	C₄⋊C₄	1	1	yes	characteristic
165	#11924005	C₄⋊C₄	1	1	yes	characteristic
166	#11924005	C₄⋊C₄	1	1	yes	characteristic
167	#11924005	C₄⋊C₄	1	1	yes	characteristic
168	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
171	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
172	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
173	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
175	M₁₆×C₇₃	—	2	2	no	—
176	C₂×C₈×C₇₃	—	2	2	no	—
177	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
185	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
187	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×D₇₃	—	2	2	no	—
189	C₂²×D₇₃	—	2	1	no	—
190	C₂²×D₇₃	—	2	2	no	—
191	C₂²×D₇₃	—	2	1	no	—
192	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×#64408	—	4	2	no	—
195	C₂×#64408	—	4	2	no	—
196	C₂×#64408	—	4	2	no	—
197	C₂×#64408	—	4	2	no	—
198	C₂×#64408	—	4	2	no	—
199	C₂×#64408	—	4	2	no	—
200	C₂×#64408	—	4	2	no	—
201	C₂×#64408	—	4	2	no	—
202	C₂×#64408	—	4	2	no	—
203	C₂×#64408	—	4	2	no	—
204	C₂×#64408	—	4	2	no	—
205	C₂×#64408	—	4	2	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
214	C₂×Dic₇₃	—	2	2	no	—
215	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
221	C₄×D₇₃	—	2	2	no	—
222	C₄×D₇₃	—	2	1	no	—
223	C₄×D₇₃	—	2	1	no	—
224	C₄×D₇₃	—	2	2	no	—
225	C₄×D₇₃	—	2	2	no	—
226	C₄×D₇₃	—	2	1	no	—
227	C₄×D₇₃	—	2	1	no	—
228	C₄×D₇₃	—	2	1	no	—
229	C₄×D₇₃	—	2	1	no	—
230	C₄×D₇₃	—	2	2	no	—
231	C₄×D₇₃	C₂×#41	1	2	yes	—
232	C₄×D₇₃	C₂×#41	1	2	yes	—
233	C₈×C₇₃	—	2	1	no	—
234	C₈×C₇₃	—	2	1	no	—
235	C₈×C₇₃	#117	1	2	yes	—
236	C₈×C₇₃	#117	1	2	yes	—
237	#10596831	—	2	1	no	—
238	#10596831	—	2	1	no	—
239	#10596831	#117	1	2	yes	—
240	#10596831	#117	1	2	yes	—
241	C₂²×C₇₃	—	2	1	no	—
242	C₂²×C₇₃	—	2	1	no	—
243	C₂²×C₇₃	—	2	1	no	—
244	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
245	C₂×D₇₃	—	2	1	no	—
246	C₂×D₇₃	—	2	1	no	—
247	C₂×D₇₃	—	2	1	no	—
248	C₂×D₇₃	—	4	2	no	—
249	C₂×D₇₃	—	4	2	no	—
250	C₂×D₇₃	#532	1	2	yes	—
251	C₂×D₇₃	#576	1	1	yes	characteristic
252	C₂×D₇₃	#577	1	2	yes	—
253	C₂×D₇₃	#578	1	1	yes	characteristic
254	#64408	—	8	2	no	—
255	#64408	—	8	2	no	—
256	#64408	—	8	2	no	—
257	#64408	—	8	2	no	—
258	C₄×C₇₃	—	2	1	no	—
259	C₄×C₇₃	—	2	1	no	—
260	C₄×C₇₃	—	2	1	no	—
261	C₄×C₇₃	—	2	1	no	—
262	C₄×C₇₃	—	2	1	no	—
263	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
264	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
265	Dic₇₃	—	2	1	no	—
266	Dic₇₃	—	2	1	no	—
267	Dic₇₃	—	2	1	no	—
268	Dic₇₃	—	2	1	no	—
269	Dic₇₃	—	2	1	no	—
270	Dic₇₃	#533	1	2	yes	—
271	#20822	—	73	1	no	maximal, Sylow
272	C₂×C₇₃	—	4	1	no	—
273	C₂×C₇₃	#2285	1	1	yes	characteristic
274	C₂×C₇₃	#2912	1	1	yes	characteristic
275	C₂×C₇₃	#2913	1	1	yes	characteristic
276	D₇₃	—	4	1	no	—
277	D₇₃	#3178	1	2	yes	—
278	D₇₃	#3179	1	2	yes	—
279	C₂×#405	—	73	1	no	—
280	#2314	—	73	2	no	—
281	#1847	—	73	2	no	—
282	#1835	—	73	1	no	—
283	#1834	—	73	1	no	—
284	#1809	—	73	2	no	—
285	#1808	—	73	1	no	—
286	#1807	—	73	1	no	—
287	#1776	—	73	2	no	—
288	C₄×#107	—	73	1	no	—
289	C₄×#106	—	73	1	no	—
290	C₇₃	#20822	1	1	yes	characteristic, complemented, Sylow
291	C₂²×M₁₆	—	73	1	no	—
292	C₂³×C₈	—	73	1	no	—
293	C₂×#117	—	73	1	no	—
294	C₂×#107	—	73	2	no	—
295	C₂×#107	—	73	2	no	—
296	C₂×#106	—	73	2	no	—
297	C₂×#106	—	73	2	no	—
298	#405	—	73	1	no	—
299	#405	—	73	1	no	—
300	#405	—	73	1	no	—
301	#405	—	73	1	no	—
302	#405	—	73	1	no	—
303	#405	—	73	1	no	—
304	#405	—	73	1	no	—
305	#405	#64408	1	1	yes	characteristic, complemented
306	C₂×#97	—	73	1	no	—
307	C₂×#97	—	73	1	no	—
308	C₂×C₄×C₈	—	73	1	no	—
309	C₂×C₄×C₈	—	73	1	no	—
310	#388	—	146	2	no	—
311	#388	—	146	2	no	—
312	#387	—	146	2	no	—
313	#387	—	146	2	no	—
314	#384	—	73	2	no	—
315	#382	—	73	2	no	—
316	#380	—	73	2	no	—
317	#380	—	73	2	no	—
318	C₄×C₄⋊C₄	—	73	2	no	—
319	C₄×C₄⋊C₄	—	73	2	no	—
320	#340	—	73	1	no	—
321	#340	—	73	1	no	—
322	#340	—	73	1	no	—
323	#340	—	73	1	no	—
324	#340	—	73	2	no	—
325	#340	—	73	2	no	—
326	C₂³×C₄	—	73	1	no	—
327	C₂×M₁₆	—	73	1	no	—
328	C₂×M₁₆	—	73	1	no	—
329	C₂×M₁₆	—	73	1	no	—
330	C₂×M₁₆	—	146	4	no	—
331	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
332	C₂²×C₈	—	73	1	no	—
333	C₂²×C₈	—	73	1	no	—
334	C₂²×C₈	—	73	1	no	—
335	C₂²×C₈	—	73	1	no	—
336	C₂²×C₈	—	73	1	no	—
337	C₂²×C₈	—	73	1	no	—
338	C₂²×C₈	—	73	1	no	—
339	C₂²×C₈	—	146	4	no	—
340	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
341	#117	—	73	1	no	—
342	#117	—	73	1	no	—
343	#117	—	73	1	no	—
344	#117	—	73	1	no	—
345	#117	—	73	1	no	—
346	#117	—	73	1	no	—
347	#117	—	73	1	no	—
348	#117	C₂×#64408	1	1	yes	characteristic
349	C₂×C₄⋊C₄	—	73	1	no	—
350	C₂×C₄⋊C₄	—	73	1	no	—
351	C₂×C₄⋊C₄	—	73	2	no	—
352	C₂×C₄⋊C₄	—	73	2	no	—
353	C₂×C₄⋊C₄	—	73	2	no	—
354	C₂×C₄⋊C₄	—	73	2	no	—
355	C₂×C₄⋊C₄	—	146	2	no	—
356	C₂×C₄⋊C₄	—	146	2	no	—
357	C₂×C₂²⋊C₄	—	73	1	no	—
358	C₂×C₂²⋊C₄	—	73	1	no	—
359	C₂×C₂²⋊C₄	—	146	2	no	—
360	C₂×C₂²⋊C₄	—	146	2	no	—
361	C₂×C₄²	—	73	1	no	—
362	C₂×C₄²	—	73	1	no	—
363	C₂×C₄²	—	146	2	no	—
364	C₂×C₄²	—	146	2	no	—
365	#107	—	146	4	no	—
366	#107	—	146	4	no	—
367	#106	—	146	4	no	—
368	#106	—	146	4	no	—
369	#97	—	73	1	no	—
370	#97	—	73	1	no	—
371	#97	—	73	1	no	—
372	#97	—	73	1	no	—
373	#97	—	73	1	no	—
374	#97	—	73	1	no	—
375	#97	C₂×#64408	1	1	yes	characteristic
376	#97	C₂×#64408	1	1	yes	characteristic
377	C₄×C₈	—	73	1	no	—
378	C₄×C₈	—	73	1	no	—
379	C₄×C₈	—	73	1	no	—
380	C₄×C₈	—	73	1	no	—
381	C₄×C₈	—	73	1	no	—
382	C₄×C₈	—	73	1	no	—
383	C₄×C₈	C₂×#64408	1	1	yes	characteristic
384	C₄×C₈	C₂×#64408	1	1	yes	characteristic
385	#95	—	146	2	no	—
386	#95	—	146	2	no	—
387	#95	—	146	2	no	—
388	#95	—	146	2	no	—
389	#95	—	146	2	no	—
390	#95	—	146	2	no	—
391	C₂⁴	—	73	1	no	—
392	C₂²×C₄	—	73	1	no	—
393	C₂²×C₄	—	73	1	no	—
394	C₂²×C₄	—	73	1	no	—
395	C₂²×C₄	—	73	1	no	—
396	C₂²×C₄	—	73	1	no	—
397	C₂²×C₄	—	73	1	no	—
398	C₂²×C₄	—	73	1	no	—
399	C₂²×C₄	—	73	1	no	—
400	C₂²×C₄	—	73	1	no	—
401	C₂²×C₄	—	146	2	no	—
402	C₂²×C₄	—	146	2	no	—
403	C₂²×C₄	—	146	2	no	—
404	C₂²×C₄	—	146	2	no	—
405	C₂²×C₄	—	146	2	no	—
406	C₂²×C₄	—	146	2	no	—
407	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
408	M₁₆	—	2	2	no	—
409	M₁₆	—	146	2	no	—
410	M₁₆	—	146	2	no	—
411	M₁₆	—	146	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	73	1	no	—
414	C₂×C₈	—	73	1	no	—
415	C₂×C₈	—	73	4	no	—
416	C₂×C₈	—	73	4	no	—
417	C₂×C₈	—	73	1	no	—
418	C₂×C₈	—	73	1	no	—
419	C₂×C₈	—	146	2	no	—
420	C₂×C₈	—	146	2	no	—
421	C₂×C₈	—	146	2	no	—
422	C₂×C₈	—	146	2	no	—
423	C₂×C₈	—	146	2	no	—
424	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
425	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
426	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
427	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
428	C₄⋊C₄	—	584	2	no	—
429	C₄⋊C₄	—	584	2	no	—
430	C₄⋊C₄	—	73	1	no	—
431	C₄⋊C₄	—	73	1	no	—
432	C₄⋊C₄	—	73	1	no	—
433	C₄⋊C₄	—	73	1	no	—
434	C₄⋊C₄	—	73	1	no	—
435	C₄⋊C₄	—	73	1	no	—
436	C₄⋊C₄	—	146	2	no	—
437	C₄⋊C₄	—	146	2	no	—
438	C₄⋊C₄	—	146	2	no	—
439	C₄⋊C₄	—	146	2	no	—
440	C₄⋊C₄	—	146	2	no	—
441	C₄⋊C₄	—	146	2	no	—
442	C₄⋊C₄	—	146	2	no	—
443	C₄⋊C₄	—	146	2	no	—
444	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
445	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
446	C₂²⋊C₄	—	584	2	no	—
447	C₂²⋊C₄	—	584	2	no	—
448	C₂²⋊C₄	—	73	1	no	—
449	C₂²⋊C₄	—	73	1	no	—
450	C₂²⋊C₄	—	73	1	no	—
451	C₂²⋊C₄	—	73	1	no	—
452	C₂²⋊C₄	—	73	1	no	—
453	C₂²⋊C₄	—	73	1	no	—
454	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
455	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
456	C₄²	—	584	2	no	—
457	C₄²	—	584	2	no	—
458	C₄²	—	73	1	no	—
459	C₄²	—	73	1	no	—
460	C₄²	—	73	1	no	—
461	C₄²	—	73	1	no	—
462	C₄²	—	73	1	no	—
463	C₄²	—	73	1	no	—
464	C₄²	C₂²×#64408	1	1	yes	characteristic
465	C₄²	C₂²×#64408	1	1	yes	characteristic
466	C₂³	—	73	1	no	—
467	C₂³	—	73	1	no	—
468	C₂³	—	146	1	no	—
469	C₂³	—	146	2	no	—
470	C₂³	—	146	2	no	—
471	C₂³	—	146	1	no	—
472	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	292	2	no	—
476	C₂×C₄	—	292	2	no	—
477	C₂×C₄	—	292	2	no	—
478	C₂×C₄	—	292	2	no	—
479	C₂×C₄	—	292	2	no	—
480	C₂×C₄	—	292	2	no	—
481	C₂×C₄	—	292	2	no	—
482	C₂×C₄	—	292	2	no	—
483	C₂×C₄	—	292	2	no	—
484	C₂×C₄	—	292	2	no	—
485	C₂×C₄	—	292	2	no	—
486	C₂×C₄	—	292	2	no	—
487	C₂×C₄	—	73	1	no	—
488	C₂×C₄	—	73	2	no	—
489	C₂×C₄	—	73	2	no	—
490	C₂×C₄	—	73	1	no	—
491	C₂×C₄	—	73	1	no	—
492	C₂×C₄	—	73	1	no	—
493	C₂×C₄	—	73	1	no	—
494	C₂×C₄	—	73	1	no	—
495	C₂×C₄	—	146	2	no	—
496	C₂×C₄	—	146	1	no	—
497	C₂×C₄	—	146	2	no	—
498	C₂×C₄	—	146	1	no	—
499	C₂×C₄	—	146	2	no	—
500	C₂×C₄	—	146	2	no	—
501	C₂×C₄	—	146	1	no	—
502	C₂×C₄	—	146	1	no	—
503	C₂×C₄	—	146	2	no	—
504	C₂×C₄	—	146	1	no	—
505	C₂×C₄	—	146	1	no	—
506	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
507	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
508	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
509	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
510	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
511	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	73	2	no	—
515	C₈	—	73	2	no	—
516	C₈	—	146	1	no	—
517	C₈	—	146	1	no	—
518	C₈	#14556670	1	2	yes	—
519	C₈	#14556670	1	2	yes	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	292	2	no	—
524	C₂²	—	292	2	no	—
525	C₂²	—	73	2	no	—
526	C₂²	—	73	1	no	—
527	C₂²	—	73	1	no	—
528	C₂²	—	73	2	no	—
529	C₂²	—	146	1	no	—
530	C₂²	—	146	1	no	—
531	C₂²	—	146	1	no	—
532	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	584	2	no	—
539	C₄	—	584	2	no	—
540	C₄	—	584	2	no	—
541	C₄	—	584	2	no	—
542	C₄	—	73	2	no	—
543	C₄	—	146	1	no	—
544	C₄	—	146	1	no	—
545	C₄	—	146	1	no	—
546	C₄	—	146	1	no	—
547	C₄	—	146	1	no	—
548	C₄	C₂×#14556670	1	1	yes	characteristic
549	C₄	C₂×#14556670	1	1	yes	characteristic
550	C₂	—	4	1	no	—
551	C₂	—	292	1	no	—
552	C₂	—	73	2	no	—
553	C₂	—	73	2	no	—
554	C₂	#22626380	1	1	yes	characteristic
555	C₂	#22626585	1	1	yes	characteristic
556	C₂	#22626586	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20822
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #22625869	C₂	semidirect
3. #22625853	C₂	semidirect
4. #22625852	C₂	semidirect
8. #22625745	C₂	semidirect
9. C₄×#14556660	C₂	semidirect
10. C₄×#14556659	C₂	semidirect
35. #17988545	C₄	semidirect
36. #17988544	C₄	semidirect
37. #17988544	C₄	semidirect
38. #17988543	C₄	semidirect
39. #17988542	C₄	semidirect
40. #17988541	C₄	semidirect
41. #17988541	C₄	semidirect
46. #405×C₇₃	C₄	semidirect
290. C₇₃	#20822	semidirect
305. #405	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22626409	2
#22625869	2
#22625853	2
#22625852	2
#22625809	2
#22625808	2
#22625807	2
#22625745	2
C₄×#14556660	2
C₄×#14556659	2
#405×D₇₃	2
#20822	73