Subgroups — M₁₆×C₄⋊#64408 #34020219

Order 18688.

1242 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#423	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×#64408	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic
4	#22625729	C₂	1	4	yes	maximal, complemented
5	#22625725	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊#64408	C₂	1	2	yes	maximal, complemented
7	#22625593	C₂	1	2	yes	maximal
8	C₄×M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂²×C₄⋊#64408	C₄	1	2	yes	—
11	C₂²×C₄×#64408	C₂²	1	2	yes	—
12	#17989592	C₄	1	2	yes	complemented
13	#17989591	C₄	1	2	yes	complemented
14	#17989590	C₄	1	2	yes	complemented
15	#17989590	C₄	1	2	yes	complemented
16	#17989588	C₂²	1	2	yes	—
17	#17989588	C₂²	1	2	yes	—
18	M₁₆×#64408	—	2	8	no	—
19	C₂×#14556645	C₂²	1	4	yes	—
20	C₂×C₈×#64408	C₂²	1	4	yes	—
21	C₄×C₄⋊#64408	C₄	1	2	yes	—
22	C₄×C₄⋊#64408	C₄	1	2	yes	—
23	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊#64408	C₂²	1	2	yes	—
26	C₂×(C₂×#64408)⋊C₄	C₄	1	2	yes	—
27	#17989452	C₂²	1	4	yes	—
28	#17989452	C₂²	1	4	yes	—
29	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
30	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
32	C₄×#11924012	C₄	1	1	yes	characteristic, complemented
33	#17988539	C₄	1	2	yes	complemented
34	M₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
35	M₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
36	C₄×#11924011	C₄	1	2	yes	complemented
37	#97×D₇₃	C₂²	1	2	yes	—
38	C₄×C₈×D₇₃	C₂²	1	2	yes	—
39	C₄×M₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
40	C₂³×#64408	C₂×C₄	1	4	yes	—
41	C₂×#11924038	C₂×C₄	1	4	yes	—
42	D₇₃⋊M₁₆	—	2	4	no	—
43	D₇₃⋊M₁₆	—	2	4	no	—
44	C₂×#11924037	C₂×C₄	1	4	yes	—
45	C₂×#11924036	C₂³	1	4	yes	—
46	C₂×C₄⋊#64408	—	2	8	no	—
47	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
50	C₂×C₄×#64408	—	2	4	no	—
51	C₂×C₄×#64408	—	2	4	no	—
52	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
53	C₂×C₄×#64408	C₂³	1	2	yes	—
54	C₂×C₄×#64408	C₂³	1	2	yes	—
55	#14556658	C₂×C₄	1	4	yes	complemented
56	#14556658	C₂×C₄	1	4	yes	complemented
57	C₄⋊#10596833	C₂×C₄	1	4	yes	complemented
58	C₄⋊#10596833	C₂×C₄	1	4	yes	complemented
59	#14556645	—	2	8	no	—
60	C₈×#64408	—	2	8	no	—
61	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
62	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
63	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
64	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
67	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
68	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924011	C₂×C₄	1	2	yes	—
70	C₂×#11924011	C₂×C₄	1	2	yes	—
71	M₁₆×D₇₃	—	2	2	no	—
72	M₁₆×D₇₃	—	2	2	no	—
73	M₁₆×D₇₃	D₄	1	4	yes	—
74	M₁₆×D₇₃	Q₈	1	4	yes	—
75	C₂×C₈×D₇₃	C₂³	1	2	yes	—
76	C₂×C₈×D₇₃	C₂³	1	2	yes	—
77	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₇₃	C₂³	1	1	yes	characteristic
87	C₄²×D₇₃	C₂³	1	1	yes	characteristic
88	#14556502	C₂×C₄	1	2	yes	complemented
89	#14556501	C₂×C₄	1	2	yes	complemented
90	#14556501	C₂×C₄	1	2	yes	complemented
91	C₄×#10596831	C₂×C₄	1	2	yes	complemented
92	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
93	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
94	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
97	#97×C₇₃	C₂×C₄	1	2	yes	complemented
98	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
99	C₂²×#64408	—	2	8	no	—
100	C₂²×#64408	—	2	8	no	—
101	C₂²×#64408	—	4	4	no	—
102	C₂²×#64408	C₂²×C₄	1	4	yes	—
103	C₂²×#64408	C₂²×C₄	1	4	yes	—
104	#11924038	—	2	8	no	—
105	#11924037	—	2	8	no	—
106	#11924036	—	2	4	no	—
107	#11924036	—	2	4	no	—
108	C₂×#10596833	C₂²×C₄	1	8	yes	—
109	C₄⋊#64408	—	2	8	no	—
110	C₄⋊#64408	—	2	4	no	—
111	C₄⋊#64408	M₁₆	1	8	yes	direct product factor
112	C₄×#64408	—	2	8	no	—
113	C₄×#64408	—	2	2	no	—
114	C₄×#64408	—	2	2	no	—
115	C₄×#64408	—	2	2	no	—
116	C₄×#64408	—	2	2	no	—
117	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
119	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
120	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	—	2	4	no	—
122	C₂×C₄×D₇₃	—	4	2	no	—
123	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
127	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
135	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
136	C₂×C₄×D₇₃	#41	1	2	yes	—
137	C₂×C₄×D₇₃	#41	1	2	yes	—
138	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
139	#11924012	—	2	2	no	—
140	#11924012	C₄⋊C₄	1	4	yes	complemented
141	#11924011	—	2	4	no	—
142	#11924011	C₄⋊C₄	1	8	yes	complemented
143	C₂×#10596831	C₂²×C₄	1	2	yes	—
144	C₂×#10596831	C₂²×C₄	1	2	yes	—
145	C₈×D₇₃	—	2	2	no	—
146	C₈×D₇₃	—	2	2	no	—
147	C₈×D₇₃	C₂×D₄	1	4	yes	—
148	C₈×D₇₃	C₂×Q₈	1	4	yes	—
149	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
150	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
151	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
152	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
153	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
154	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
155	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
163	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
164	M₁₆×C₇₃	—	2	2	no	—
165	M₁₆×C₇₃	C₄⋊C₄	1	4	yes	complemented
166	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
168	C₄²×C₇₃	C₄²	1	1	yes	characteristic
169	C₄²×C₇₃	C₄²	1	1	yes	characteristic
170	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₂²×D₇₃	—	2	2	no	—
174	C₂²×D₇₃	—	2	2	no	—
175	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
176	C₂²×D₇₃	C₄×D₄	1	2	yes	—
177	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
178	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×#64408	—	2	4	no	—
180	C₂×#64408	—	2	4	no	—
181	C₂×#64408	—	2	4	no	—
182	C₂×#64408	—	2	4	no	—
183	C₂×#64408	—	2	4	no	—
184	C₂×#64408	—	4	16	no	—
185	C₂×#64408	C₂×M₁₆	1	8	yes	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
194	C₂×C₄×C₇₃	#117	1	2	yes	—
195	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×Dic₇₃	—	2	2	no	—
197	C₂×Dic₇₃	—	4	1	no	—
198	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
200	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
202	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
203	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
204	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
205	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
206	C₄×D₇₃	—	2	2	no	—
207	C₄×D₇₃	—	2	2	no	—
208	C₄×D₇₃	—	2	2	no	—
209	C₄×D₇₃	—	2	2	no	—
210	C₄×D₇₃	—	2	2	no	—
211	C₄×D₇₃	—	4	1	no	—
212	C₄×D₇₃	—	4	1	no	—
213	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
214	C₄×D₇₃	#117	1	2	yes	—
215	C₄×D₇₃	C₄×D₄	1	2	yes	—
216	C₄×D₇₃	C₄×D₄	1	2	yes	—
217	C₄×D₇₃	C₄×Q₈	1	2	yes	—
218	C₄×D₇₃	C₄×Q₈	1	2	yes	—
219	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
220	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
221	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
222	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
223	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
224	#10596833	—	2	8	no	—
225	C₈×C₇₃	—	2	2	no	—
226	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	complemented
227	#10596831	—	2	2	no	—
228	#10596831	C₂×C₄⋊C₄	1	4	yes	complemented
229	C₂²×C₇₃	—	2	1	no	—
230	C₂²×C₇₃	—	2	1	no	—
231	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
232	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
233	C₂×D₇₃	—	2	1	no	—
234	C₂×D₇₃	—	2	1	no	—
235	C₂×D₇₃	—	2	4	no	—
236	C₂×D₇₃	—	2	4	no	—
237	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
238	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
240	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
241	C₂×D₇₃	#568	1	2	yes	—
242	#64408	—	2	8	no	—
243	#64408	—	4	4	no	—
244	C₄×C₇₃	—	2	1	no	—
245	C₄×C₇₃	—	2	1	no	—
246	C₄×C₇₃	—	2	1	no	—
247	C₄×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
248	C₄×C₇₃	C₄×M₁₆	1	2	yes	complemented
249	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
250	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
251	Dic₇₃	—	2	1	no	—
252	Dic₇₃	—	2	1	no	—
253	Dic₇₃	—	2	1	no	—
254	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
255	Dic₇₃	C₄×M₁₆	1	2	yes	complemented
256	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
257	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
258	C₄⋊C₄×M₁₆	—	73	1	no	maximal, Sylow
259	C₂×C₇₃	—	2	2	no	—
260	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
262	C₂×C₇₃	#2873	1	1	yes	characteristic
263	D₇₃	—	2	2	no	—
264	D₇₃	D₄×M₁₆	1	2	yes	—
265	D₇₃	Q₈×M₁₆	1	2	yes	—
266	C₂×#423	—	73	1	no	—
267	C₂×C₄×M₁₆	—	73	1	no	—
268	C₂×C₄×M₁₆	—	73	2	no	—
269	C₂×C₄×C₄⋊C₄	—	73	1	no	—
270	#1771	—	73	4	no	—
271	#1770	—	73	2	no	—
272	C₈×C₄⋊C₄	—	73	2	no	—
273	#1728	—	73	2	no	—
274	C₇₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
275	C₂²×M₁₆	—	73	1	no	—
276	C₂²×M₁₆	—	73	2	no	—
277	C₂²×M₁₆	—	73	1	no	—
278	C₂²×C₄⋊C₄	—	73	2	no	—
279	C₂²×C₄²	—	73	1	no	—
280	C₂²×C₄²	—	73	2	no	—
281	#423	—	73	2	no	—
282	#423	—	73	2	no	—
283	#423	—	73	2	no	—
284	#423	—	73	2	no	—
285	C₂×C₄⋊C₈	—	73	2	no	—
286	C₂×C₄⋊C₈	—	73	2	no	—
287	C₄×M₁₆	—	73	1	no	—
288	C₄×M₁₆	—	73	1	no	—
289	C₄×M₁₆	—	73	1	no	—
290	C₄×M₁₆	—	73	2	no	—
291	C₄×M₁₆	—	73	2	no	—
292	C₄×M₁₆	—	146	8	no	—
293	C₄×M₁₆	#64408	1	1	yes	characteristic, complemented
294	C₂×#97	—	73	2	no	—
295	C₂×#97	—	73	4	no	—
296	C₂×C₄×C₈	—	73	2	no	—
297	C₂×C₄×C₈	—	73	4	no	—
298	C₄×C₄⋊C₄	—	73	2	no	—
299	C₄×C₄⋊C₄	—	73	2	no	—
300	C₄×C₄⋊C₄	—	73	1	no	—
301	C₄×C₄⋊C₄	—	73	1	no	—
302	C₄×C₄⋊C₄	—	73	2	no	—
303	C₂×#95	—	73	2	no	—
304	#336	—	73	4	no	—
305	#336	—	73	4	no	—
306	C₂³×C₄	—	73	1	no	—
307	C₂³×C₄	—	73	4	no	—
308	C₂³×C₄	—	73	1	no	—
309	C₂³×C₄	—	73	1	no	—
310	C₂×M₁₆	—	73	1	no	—
311	C₂×M₁₆	—	73	4	no	—
312	C₂×M₁₆	—	73	4	no	—
313	C₂×M₁₆	—	73	4	no	—
314	C₂×M₁₆	—	73	4	no	—
315	C₂×M₁₆	—	73	1	no	—
316	C₂×M₁₆	—	73	2	no	—
317	C₂×M₁₆	—	73	2	no	—
318	C₂×M₁₆	—	146	2	no	—
319	C₂×M₁₆	—	146	2	no	—
320	C₂×M₁₆	—	146	4	no	—
321	C₂×M₁₆	—	146	4	no	—
322	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
323	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
324	C₂²×C₈	—	73	2	no	—
325	C₂²×C₈	—	73	4	no	—
326	C₂²×C₈	—	73	2	no	—
327	C₂×C₄⋊C₄	—	73	2	no	—
328	C₂×C₄⋊C₄	—	73	2	no	—
329	C₂×C₄⋊C₄	—	73	4	no	—
330	C₂×C₄⋊C₄	—	146	8	no	—
331	C₂×C₄²	—	73	1	no	—
332	C₂×C₄²	—	73	1	no	—
333	C₂×C₄²	—	73	1	no	—
334	C₂×C₄²	—	73	1	no	—
335	C₂×C₄²	—	73	1	no	—
336	C₂×C₄²	—	73	1	no	—
337	C₂×C₄²	—	73	1	no	—
338	C₂×C₄²	—	73	1	no	—
339	C₂×C₄²	—	73	1	no	—
340	C₂×C₄²	—	73	1	no	—
341	C₂×C₄²	—	73	1	no	—
342	C₂×C₄²	—	73	2	no	—
343	C₂×C₄²	—	73	2	no	—
344	C₂×C₄²	—	73	4	no	—
345	C₂×C₄²	—	146	4	no	—
346	C₂×C₄²	—	146	4	no	—
347	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
348	C₄⋊C₈	—	73	4	no	—
349	C₄⋊C₈	—	73	4	no	—
350	C₄⋊C₈	—	73	4	no	—
351	C₄⋊C₈	—	73	4	no	—
352	#97	—	73	2	no	—
353	#97	—	73	2	no	—
354	#97	—	73	2	no	—
355	#97	—	146	8	no	—
356	#97	C₂×#64408	1	2	yes	complemented
357	C₄×C₈	—	73	2	no	—
358	C₄×C₈	—	73	2	no	—
359	C₄×C₈	—	73	2	no	—
360	C₄×C₈	—	146	8	no	—
361	C₄×C₈	C₂×#64408	1	2	yes	complemented
362	#95	—	73	2	no	—
363	#95	—	73	4	no	—
364	#95	—	73	2	no	—
365	C₂⁴	—	73	1	no	—
366	C₂²×C₄	—	292	2	no	—
367	C₂²×C₄	—	292	4	no	—
368	C₂²×C₄	—	73	1	no	—
369	C₂²×C₄	—	73	1	no	—
370	C₂²×C₄	—	73	1	no	—
371	C₂²×C₄	—	73	1	no	—
372	C₂²×C₄	—	73	1	no	—
373	C₂²×C₄	—	73	1	no	—
374	C₂²×C₄	—	73	1	no	—
375	C₂²×C₄	—	73	1	no	—
376	C₂²×C₄	—	73	1	no	—
377	C₂²×C₄	—	73	2	no	—
378	C₂²×C₄	—	73	2	no	—
379	C₂²×C₄	—	73	2	no	—
380	C₂²×C₄	—	73	2	no	—
381	C₂²×C₄	—	73	4	no	—
382	C₂²×C₄	—	73	1	no	—
383	C₂²×C₄	—	73	1	no	—
384	C₂²×C₄	—	73	1	no	—
385	C₂²×C₄	—	73	1	no	—
386	C₂²×C₄	—	73	1	no	—
387	C₂²×C₄	—	73	1	no	—
388	C₂²×C₄	—	73	4	no	—
389	C₂²×C₄	—	146	4	no	—
390	C₂²×C₄	—	146	8	no	—
391	C₂²×C₄	—	146	8	no	—
392	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
393	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
394	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
395	M₁₆	—	2	2	no	—
396	M₁₆	—	73	4	no	—
397	M₁₆	—	73	8	no	—
398	M₁₆	—	146	4	no	—
399	M₁₆	—	146	8	no	—
400	M₁₆	—	146	8	no	—
401	M₁₆	—	146	2	no	—
402	M₁₆	C₄⋊#64408	1	4	yes	direct product factor
403	C₂×C₈	—	73	2	no	—
404	C₂×C₈	—	73	4	no	—
405	C₂×C₈	—	73	4	no	—
406	C₂×C₈	—	73	8	no	—
407	C₂×C₈	—	73	2	no	—
408	C₂×C₈	—	146	2	no	—
409	C₂×C₈	—	146	2	no	—
410	C₂×C₈	—	146	4	no	—
411	C₂×C₈	—	146	4	no	—
412	C₂×C₈	C₂²×#64408	1	2	yes	—
413	C₂×C₈	C₂²×#64408	1	2	yes	—
414	C₄⋊C₄	—	73	8	no	—
415	C₄⋊C₄	—	146	4	no	—
416	C₄⋊C₄	—	146	8	no	—
417	C₄²	—	73	1	no	—
418	C₄²	—	73	1	no	—
419	C₄²	—	73	1	no	—
420	C₄²	—	73	1	no	—
421	C₄²	—	73	1	no	—
422	C₄²	—	73	1	no	—
423	C₄²	—	73	1	no	—
424	C₄²	—	73	1	no	—
425	C₄²	—	73	1	no	—
426	C₄²	—	73	1	no	—
427	C₄²	—	73	1	no	—
428	C₄²	—	73	1	no	—
429	C₄²	—	146	2	no	—
430	C₄²	—	146	2	no	—
431	C₄²	—	146	2	no	—
432	C₄²	—	146	2	no	—
433	C₄²	—	146	8	no	—
434	C₄²	C₄×#64408	1	1	yes	characteristic
435	C₄²	C₄×#64408	1	1	yes	characteristic
436	C₄²	C₂²×#64408	1	1	yes	characteristic
437	C₄²	C₂²×#64408	1	1	yes	characteristic
438	C₂³	—	73	1	no	—
439	C₂³	—	73	1	no	—
440	C₂³	—	73	2	no	—
441	C₂³	—	73	2	no	—
442	C₂³	—	146	2	no	—
443	C₂³	—	146	2	no	—
444	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	292	1	no	—
448	C₂×C₄	—	292	1	no	—
449	C₂×C₄	—	292	16	no	—
450	C₂×C₄	—	292	1	no	—
451	C₂×C₄	—	73	1	no	—
452	C₂×C₄	—	73	1	no	—
453	C₂×C₄	—	73	1	no	—
454	C₂×C₄	—	73	2	no	—
455	C₂×C₄	—	73	2	no	—
456	C₂×C₄	—	73	1	no	—
457	C₂×C₄	—	73	1	no	—
458	C₂×C₄	—	73	2	no	—
459	C₂×C₄	—	73	1	no	—
460	C₂×C₄	—	73	1	no	—
461	C₂×C₄	—	73	2	no	—
462	C₂×C₄	—	73	2	no	—
463	C₂×C₄	—	73	2	no	—
464	C₂×C₄	—	73	2	no	—
465	C₂×C₄	—	73	2	no	—
466	C₂×C₄	—	73	4	no	—
467	C₂×C₄	—	73	8	no	—
468	C₂×C₄	—	73	1	no	—
469	C₂×C₄	—	73	1	no	—
470	C₂×C₄	—	73	1	no	—
471	C₂×C₄	—	146	2	no	—
472	C₂×C₄	—	146	2	no	—
473	C₂×C₄	—	146	2	no	—
474	C₂×C₄	—	146	2	no	—
475	C₂×C₄	—	146	4	no	—
476	C₂×C₄	—	146	4	no	—
477	C₂×C₄	—	146	4	no	—
478	C₂×C₄	—	146	2	no	—
479	C₂×C₄	—	146	4	no	—
480	C₂×C₄	—	146	4	no	—
481	C₂×C₄	—	146	2	no	—
482	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
483	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
484	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
485	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
486	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
487	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
488	C₂×C₄	#14556670	1	2	yes	—
489	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	73	4	no	—
492	C₈	—	146	8	no	—
493	C₈	—	146	2	no	—
494	C₈	C₂×C₄⋊#64408	1	4	yes	complemented
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	73	1	no	—
498	C₂²	—	73	1	no	—
499	C₂²	—	73	2	no	—
500	C₂²	—	73	2	no	—
501	C₂²	—	73	2	no	—
502	C₂²	—	146	4	no	—
503	C₂²	—	146	4	no	—
504	C₂²	—	146	1	no	—
505	C₂²	—	146	1	no	—
506	C₂²	C₄×C₄⋊#64408	1	2	yes	—
507	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	292	4	no	—
512	C₄	—	73	1	no	—
513	C₄	—	73	1	no	—
514	C₄	—	73	2	no	—
515	C₄	—	73	2	no	—
516	C₄	—	146	8	no	—
517	C₄	—	146	1	no	—
518	C₄	—	146	1	no	—
519	C₄	—	146	1	no	—
520	C₄	C₄×C₄⋊#64408	1	2	yes	—
521	C₄	M₁₆×#64408	1	2	yes	complemented
522	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
523	C₄	C₂×#14556670	1	1	yes	characteristic
524	C₂	—	2	2	no	—
525	C₂	—	73	2	no	—
526	C₂	—	73	2	no	—
527	C₂	—	146	2	no	—
528	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic
529	C₂	C₂×M₁₆×#64408	1	1	yes	characteristic
530	C₂	#22626494	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	C₄×M₁₆×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₄×M₁₆	#64408
hypocenter	C₇₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #22625729	C₂	semidirect
5. #22625725	C₂	semidirect
6. C₈×C₄⋊#64408	C₂	semidirect
12. #17989592	C₄	semidirect
13. #17989591	C₄	semidirect
14. #17989590	C₄	semidirect
15. #17989590	C₄	semidirect
32. C₄×#11924012	C₄	semidirect
33. #17988539	C₄	semidirect
34. M₁₆×Dic₇₃	C₄	semidirect
35. M₁₆×Dic₇₃	C₄	semidirect
36. C₄×#11924011	C₄	semidirect
39. C₄×M₁₆×C₇₃	C₄	semidirect
55. #14556658	C₂×C₄	semidirect
56. #14556658	C₂×C₄	semidirect
57. C₄⋊#10596833	C₂×C₄	semidirect
58. C₄⋊#10596833	C₂×C₄	semidirect
88. #14556502	C₂×C₄	semidirect
89. #14556501	C₂×C₄	semidirect
90. #14556501	C₂×C₄	semidirect
91. C₄×#10596831	C₂×C₄	semidirect
92. C₈×Dic₇₃	C₂×C₄	semidirect
93. C₈×Dic₇₃	C₂×C₄	semidirect
97. #97×C₇₃	C₂×C₄	semidirect
98. C₄×C₈×C₇₃	C₂×C₄	semidirect
111. C₄⋊#64408	M₁₆	direct (N × H)
140. #11924012	C₄⋊C₄	semidirect
142. #11924011	C₄⋊C₄	semidirect
165. M₁₆×C₇₃	C₄⋊C₄	semidirect
226. C₈×C₇₃	C₂×C₄⋊C₄	semidirect
228. #10596831	C₂×C₄⋊C₄	semidirect
248. C₄×C₇₃	C₄×M₁₆	semidirect
255. Dic₇₃	C₄×M₁₆	semidirect
274. C₇₃	C₄⋊C₄×M₁₆	semidirect
293. C₄×M₁₆	#64408	semidirect
356. #97	C₂×#64408	semidirect
361. C₄×C₈	C₂×#64408	semidirect
402. M₁₆	C₄⋊#64408	direct (N × H)
494. C₈	C₂×C₄⋊#64408	semidirect
521. C₄	M₁₆×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#423	2
C₂×M₁₆×#64408	2
C₂×C₄×C₄⋊#64408	2
#22625729	2
#22625725	2
C₈×C₄⋊#64408	2
#22625593	2
C₄×M₁₆×D₇₃	2
C₄⋊C₄×M₁₆	73

Subgroups — M16×C4⋊#64408 #34020219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×C₄⋊#64408 #34020219