Subgroups — M₁₆×#11924011 #33051692

Order 18688.

900 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22608235	C₂	1	2	yes	maximal, complemented
5	#22608233	C₂	1	2	yes	maximal, complemented
6	#22608221	C₂	1	1	yes	maximal, characteristic, complemented
7	#22608220	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608217	C₂	1	2	yes	maximal, complemented
9	M₁₆×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11924011	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₄	1	2	yes	—
13	C₂×M₁₆×D₇₃	C₄	1	2	yes	—
14	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	#17988643	C₄	1	2	yes	—
16	#17988641	C₄	1	2	yes	—
17	#17988640	C₂²	1	1	yes	characteristic
18	#17988638	C₂²	1	2	yes	—
19	#17988609	C₄	1	2	yes	—
20	#17988549	C₄	1	2	yes	—
21	C₄×#11924012	C₂²	1	1	yes	characteristic
22	#17988539	C₄	1	2	yes	—
23	M₁₆×Dic₇₃	C₄	1	2	yes	—
24	C₄×#11924011	C₄	1	2	yes	—
25	C₄×#11924011	C₄	1	2	yes	—
26	C₄×#11924011	C₂²	1	1	yes	characteristic
27	C₄×#11924011	C₂²	1	1	yes	characteristic
28	C₄×#11924011	C₂²	1	1	yes	characteristic
29	C₄×#11924011	C₂²	1	2	yes	—
30	C₄×#11924011	C₂²	1	2	yes	—
31	C₄×#11924011	C₂²	1	1	yes	characteristic
32	C₂×#14556501	C₄	1	2	yes	—
33	#97×D₇₃	C₄	1	2	yes	—
34	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₇₃	C₂²	1	2	yes	—
36	#17988309	C₂²	1	2	yes	complemented
37	#17988309	C₂²	1	2	yes	complemented
38	#17988308	C₂²	1	2	yes	complemented
39	#17988308	C₂²	1	2	yes	complemented
40	#17988308	C₂²	1	2	yes	complemented
41	C₈×#10596831	C₂²	1	2	yes	complemented
42	#431×C₇₃	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
45	#322×C₇₃	C₂²	1	2	yes	complemented
46	C₈²×C₇₃	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#11924012	C₂×C₄	1	2	yes	—
51	C₂×#11924011	—	2	8	no	—
52	C₂×#11924011	C₂×C₄	1	2	yes	—
53	C₂×#11924011	C₂×C₄	1	2	yes	—
54	C₂×#11924011	C₂×C₄	1	2	yes	—
55	C₂×#11924011	C₂×C₄	1	4	yes	—
56	C₂×#11924011	C₂×C₄	1	4	yes	—
57	C₂×#11924011	C₂×C₄	1	2	yes	—
58	M₁₆×D₇₃	—	2	8	no	—
59	C₂²×#10596831	C₂×C₄	1	2	yes	—
60	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₇₃	C₂³	1	1	yes	characteristic
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	C₄⋊#10596831	C₂×C₄	1	2	yes	—
73	#14556520	C₂×C₄	1	4	yes	—
74	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
75	#14556503	C₂×C₄	1	4	yes	—
76	#14556502	C₂×C₄	1	2	yes	—
77	#14556501	C₂×C₄	1	4	yes	—
78	#14556501	C₂×C₄	1	4	yes	—
79	#14556501	C₂×C₄	1	2	yes	—
80	#14556501	C₂×C₄	1	2	yes	—
81	#14556501	C₂×C₄	1	2	yes	—
82	#14556501	C₂×C₄	1	2	yes	—
83	C₄×#10596831	C₂×C₄	1	2	yes	—
84	C₄×#10596831	C₂³	1	2	yes	—
85	C₄×#10596831	C₂³	1	2	yes	—
86	C₄×#10596831	C₂³	1	1	yes	characteristic
87	C₄×#10596831	C₂³	1	1	yes	characteristic
88	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
89	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
90	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
94	#97×C₇₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₃	C₂³	1	2	yes	—
99	C₄×C₈×C₇₃	C₂³	1	2	yes	—
100	C₂³×D₇₃	C₄²	1	1	yes	characteristic
101	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
102	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₇₃	—	2	4	no	—
105	C₂×C₄×D₇₃	—	2	4	no	—
106	C₂×C₄×D₇₃	—	4	2	no	—
107	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	#11924012	—	2	4	no	—
120	#11924011	—	2	4	no	—
121	#11924011	—	2	8	no	—
122	#11924011	—	2	4	no	—
123	#11924011	—	2	4	no	—
124	#11924011	—	4	4	no	—
125	#11924011	M₁₆	1	8	yes	direct product factor
126	C₂×#10596831	—	2	4	no	—
127	C₂×#10596831	C₂²×C₄	1	4	yes	—
128	C₂×#10596831	C₂²×C₄	1	2	yes	—
129	C₂×#10596831	C₂²×C₄	1	4	yes	—
130	C₂×#10596831	C₂²×C₄	1	2	yes	—
131	C₈×D₇₃	—	2	8	no	—
132	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	M₁₆×C₇₃	M₁₆	1	8	yes	complemented
148	C₂×C₈×C₇₃	—	2	4	no	—
149	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
151	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
153	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₇₃	—	2	2	no	—
159	C₂²×D₇₃	—	2	2	no	—
160	C₂²×D₇₃	—	4	1	no	—
161	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×Dic₇₃	—	2	2	no	—
173	C₂×Dic₇₃	—	2	2	no	—
174	C₂×Dic₇₃	—	4	1	no	—
175	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	2	2	no	—
184	C₄×D₇₃	—	2	2	no	—
185	C₄×D₇₃	—	2	2	no	—
186	C₄×D₇₃	—	2	2	no	—
187	C₄×D₇₃	—	2	2	no	—
188	C₄×D₇₃	—	2	2	no	—
189	C₄×D₇₃	—	2	2	no	—
190	C₄×D₇₃	—	4	1	no	—
191	C₄×D₇₃	—	4	1	no	—
192	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
193	C₈×C₇₃	—	2	2	no	—
194	C₈×C₇₃	—	2	4	no	—
195	C₈×C₇₃	C₂×M₁₆	1	4	yes	complemented
196	C₈×C₇₃	C₂×M₁₆	1	8	yes	complemented
197	#10596831	—	2	4	no	—
198	#10596831	—	2	2	no	—
199	#10596831	—	2	4	no	—
200	#10596831	C₂×M₁₆	1	4	yes	complemented
201	C₂²×C₇₃	—	2	1	no	—
202	C₂²×C₇₃	—	2	1	no	—
203	C₂²×C₇₃	C₄×M₁₆	1	2	yes	—
204	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
205	C₂×D₇₃	—	2	1	no	—
206	C₂×D₇₃	—	2	1	no	—
207	C₂×D₇₃	—	2	1	no	—
208	C₂×D₇₃	—	2	1	no	—
209	C₂×D₇₃	—	2	1	no	—
210	C₂×D₇₃	—	4	4	no	—
211	C₂×D₇₃	C₄×M₁₆	1	2	yes	—
212	C₄×C₇₃	—	2	1	no	—
213	C₄×C₇₃	—	2	1	no	—
214	C₄×C₇₃	C₄×M₁₆	1	2	yes	—
215	C₄×C₇₃	C₂²×M₁₆	1	2	yes	—
216	C₄×C₇₃	C₂²×M₁₆	1	2	yes	—
217	C₄×C₇₃	#568	1	2	yes	—
218	Dic₇₃	—	2	1	no	—
219	Dic₇₃	—	2	1	no	—
220	Dic₇₃	—	2	1	no	—
221	Dic₇₃	—	2	1	no	—
222	Dic₇₃	—	2	1	no	—
223	Dic₇₃	C₄×M₁₆	1	2	yes	—
224	M₁₆²	—	73	1	no	maximal, Sylow
225	C₂×C₇₃	—	2	2	no	—
226	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
227	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
228	C₂×C₇₃	#2873	1	1	yes	characteristic
229	D₇₃	—	2	2	no	—
230	D₇₃	—	4	1	no	—
231	#2920	—	73	1	no	—
232	C₂×C₄×M₁₆	—	73	1	no	—
233	C₂×C₄×M₁₆	—	73	1	no	—
234	#1455	—	73	2	no	—
235	#1455	—	73	2	no	—
236	#1451	—	73	1	no	—
237	#1451	—	73	1	no	—
238	#1451	—	73	2	no	—
239	C₈×M₁₆	—	73	1	no	—
240	C₈×M₁₆	—	73	2	no	—
241	C₈×M₁₆	D₇₃	1	1	yes	characteristic, complemented
242	C₇₃	M₁₆²	1	1	yes	characteristic, complemented, Sylow
243	C₂²×M₁₆	—	73	2	no	—
244	C₂²×M₁₆	—	73	2	no	—
245	C₂²×C₄²	—	73	1	no	—
246	#432	—	73	2	no	—
247	#432	—	73	2	no	—
248	#431	—	73	1	no	—
249	#431	—	73	2	no	—
250	#431	C₂×D₇₃	1	1	yes	characteristic
251	#423	—	73	2	no	—
252	#407	—	73	2	no	—
253	C₄×M₁₆	—	73	2	no	—
254	C₄×M₁₆	—	73	1	no	—
255	C₄×M₁₆	—	73	2	no	—
256	C₄×M₁₆	—	73	2	no	—
257	C₄×M₁₆	—	73	2	no	—
258	C₄×M₁₆	—	73	1	no	—
259	C₄×M₁₆	—	73	1	no	—
260	C₄×M₁₆	—	73	1	no	—
261	C₄×M₁₆	—	73	2	no	—
262	C₄×M₁₆	—	73	1	no	—
263	C₄×M₁₆	—	73	2	no	—
264	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
265	C₂×#97	—	73	2	no	—
266	C₂×#97	—	73	2	no	—
267	C₂×C₄×C₈	—	73	1	no	—
268	C₂×C₄×C₈	—	73	2	no	—
269	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
270	#322	—	73	2	no	—
271	#322	—	73	2	no	—
272	#322	—	73	2	no	—
273	#322	—	73	2	no	—
274	#322	—	73	2	no	—
275	#322	C₂×D₇₃	1	2	yes	complemented
276	C₈²	—	73	2	no	—
277	C₈²	C₂×D₇₃	1	2	yes	complemented
278	C₂³×C₄	—	73	1	no	—
279	C₂³×C₄	—	73	1	no	—
280	C₂³×C₄	—	73	1	no	—
281	C₂×M₁₆	—	73	2	no	—
282	C₂×M₁₆	—	73	4	no	—
283	C₂×M₁₆	—	73	2	no	—
284	C₂×M₁₆	—	73	2	no	—
285	C₂×M₁₆	—	73	2	no	—
286	C₂×M₁₆	—	73	2	no	—
287	C₂×M₁₆	—	73	4	no	—
288	C₂×M₁₆	—	146	8	no	—
289	C₂×M₁₆	—	146	8	no	—
290	C₂×M₁₆	C₄×D₇₃	1	2	yes	—
291	C₂²×C₈	—	73	2	no	—
292	C₂²×C₈	—	73	4	no	—
293	C₂²×C₈	C₄×D₇₃	1	2	yes	—
294	C₂×C₄²	—	73	1	no	—
295	C₂×C₄²	—	73	1	no	—
296	C₂×C₄²	—	73	1	no	—
297	C₂×C₄²	—	73	1	no	—
298	C₂×C₄²	—	73	1	no	—
299	C₂×C₄²	—	73	1	no	—
300	C₂×C₄²	—	73	1	no	—
301	C₂×C₄²	—	73	1	no	—
302	C₂×C₄²	—	73	1	no	—
303	C₂×C₄²	—	73	1	no	—
304	C₂×C₄²	—	73	1	no	—
305	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
306	C₄⋊C₈	—	73	4	no	—
307	C₄⋊C₈	—	73	2	no	—
308	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
309	C₂²⋊C₈	—	73	2	no	—
310	C₂²⋊C₈	—	73	4	no	—
311	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
312	#97	—	73	2	no	—
313	#97	—	73	2	no	—
314	#97	—	73	2	no	—
315	#97	—	73	2	no	—
316	#97	—	73	4	no	—
317	#97	—	73	4	no	—
318	#97	—	73	2	no	—
319	#97	C₄×D₇₃	1	2	yes	—
320	C₄×C₈	—	73	4	no	—
321	C₄×C₈	—	73	2	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	—	73	2	no	—
324	C₄×C₈	—	73	1	no	—
325	C₄×C₈	—	73	2	no	—
326	C₄×C₈	C₄×D₇₃	1	2	yes	—
327	C₄×C₈	C₂²×D₇₃	1	2	yes	—
328	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₇₃	1	2	yes	—
330	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
331	C₂⁴	—	73	1	no	—
332	C₂²×C₄	—	292	2	no	—
333	C₂²×C₄	—	73	1	no	—
334	C₂²×C₄	—	73	1	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	73	1	no	—
347	C₂²×C₄	—	73	1	no	—
348	C₂²×C₄	—	146	4	no	—
349	C₂²×C₄	—	146	4	no	—
350	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
353	M₁₆	—	292	4	no	—
354	M₁₆	—	73	8	no	—
355	M₁₆	—	146	4	no	—
356	M₁₆	—	146	4	no	—
357	M₁₆	—	146	4	no	—
358	M₁₆	—	146	4	no	—
359	M₁₆	—	146	8	no	—
360	M₁₆	#11924011	1	8	yes	direct product factor
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	73	2	no	—
363	C₂×C₈	—	73	2	no	—
364	C₂×C₈	—	73	4	no	—
365	C₂×C₈	—	73	4	no	—
366	C₂×C₈	—	146	4	no	—
367	C₂×C₈	—	146	8	no	—
368	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
369	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
370	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
371	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
372	C₄²	—	73	1	no	—
373	C₄²	—	73	1	no	—
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	—	73	1	no	—
377	C₄²	—	73	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	—	73	1	no	—
384	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
385	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
386	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
387	C₄²	C₂³×D₇₃	1	1	yes	characteristic
388	C₂³	—	292	1	no	—
389	C₂³	—	73	1	no	—
390	C₂³	—	73	1	no	—
391	C₂³	—	146	2	no	—
392	C₂³	—	146	2	no	—
393	C₂³	C₄²×D₇₃	1	1	yes	characteristic
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	292	1	no	—
397	C₂×C₄	—	292	1	no	—
398	C₂×C₄	—	292	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	4	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	—	146	2	no	—
408	C₂×C₄	—	146	2	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	—	146	2	no	—
411	C₂×C₄	—	146	2	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	—	146	2	no	—
414	C₂×C₄	—	146	2	no	—
415	C₂×C₄	—	146	2	no	—
416	C₂×C₄	—	146	2	no	—
417	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
418	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
419	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#11924011	1	4	yes	—
421	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	—	73	4	no	—
427	C₈	—	146	2	no	—
428	C₈	—	146	4	no	—
429	C₈	—	146	4	no	—
430	C₈	M₁₆×D₇₃	1	4	yes	complemented
431	C₈	C₂×#11924011	1	8	yes	complemented
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	292	4	no	—
435	C₂²	—	73	2	no	—
436	C₂²	—	146	1	no	—
437	C₂²	—	146	1	no	—
438	C₂²	—	146	1	no	—
439	C₂²	—	146	1	no	—
440	C₂²	—	146	1	no	—
441	C₂²	C₄×#11924011	1	2	yes	—
442	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	73	2	no	—
446	C₄	—	146	1	no	—
447	C₄	—	146	1	no	—
448	C₄	—	146	1	no	—
449	C₄	—	146	1	no	—
450	C₄	—	146	1	no	—
451	C₄	C₄×#11924011	1	2	yes	—
452	C₄	C₂×M₁₆×D₇₃	1	2	yes	—
453	C₄	C₂²×#11924011	1	2	yes	—
454	C₄	#17989352	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	292	1	no	—
457	C₂	—	146	2	no	—
458	C₂	C₄×M₁₆×D₇₃	1	1	yes	characteristic
459	C₂	C₂×C₄×#11924011	1	1	yes	characteristic
460	C₂	#22618347	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	C₈×M₁₆×C₇₃	C₂
prime radical	C₂³×D₇₃	C₄²
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₈×M₁₆	D₇₃
hypocenter	C₇₃	M₁₆²
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #22608235	C₂	semidirect
5. #22608233	C₂	semidirect
6. #22608221	C₂	semidirect
7. #22608220	C₂	semidirect
8. #22608217	C₂	semidirect
9. M₁₆×#10596831	C₂	semidirect
10. C₈×#11924011	C₂	semidirect
11. C₈×M₁₆×C₇₃	C₂	semidirect
36. #17988309	C₂²	semidirect
37. #17988309	C₂²	semidirect
38. #17988308	C₂²	semidirect
39. #17988308	C₂²	semidirect
40. #17988308	C₂²	semidirect
41. C₈×#10596831	C₂²	semidirect
45. #322×C₇₃	C₂²	semidirect
46. C₈²×C₇₃	C₂²	semidirect
125. #11924011	M₁₆	direct (N × H)
147. M₁₆×C₇₃	M₁₆	semidirect
195. C₈×C₇₃	C₂×M₁₆	semidirect
196. C₈×C₇₃	C₂×M₁₆	semidirect
200. #10596831	C₂×M₁₆	semidirect
241. C₈×M₁₆	D₇₃	semidirect
242. C₇₃	M₁₆²	semidirect
275. #322	C₂×D₇₃	semidirect
277. C₈²	C₂×D₇₃	semidirect
360. M₁₆	#11924011	direct (N × H)
430. C₈	M₁₆×D₇₃	semidirect
431. C₈	C₂×#11924011	semidirect

Maximal subgroups

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

subgroup	index
#22618559	2
C₂×C₄×#11924011	2
C₄×M₁₆×D₇₃	2
#22608235	2
#22608233	2
#22608221	2
#22608220	2
#22608217	2
M₁₆×#10596831	2
C₈×#11924011	2
C₈×M₁₆×C₇₃	2
M₁₆²	73

Subgroups — M16×#11924011 #33051692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#11924011 #33051692