Subgroups — D₄×C₁₆×D₇₃ #33239130

Order 18688.

806 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×#11924003	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611750	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×C₂²⋊D₇₃	C₂	1	2	yes	maximal, complemented
7	#22611748	C₂	1	2	yes	maximal, complemented
8	C₄⋊C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²⋊C₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
13	C₄×D₄×D₇₃	C₄	1	1	yes	characteristic
14	C₂²×#11924003	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₇₃	—	2	8	no	—
16	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
17	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₇₃	C₂²	1	2	yes	complemented
20	C₂×C₁₆×D₇₃	C₂²	1	2	yes	complemented
21	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
22	D₄×#10596831	C₄	1	1	yes	characteristic
23	#17988652	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	—
25	#17988650	C₄	1	2	yes	—
26	C₄⋊C₈×D₇₃	C₄	1	1	yes	characteristic
27	C₂²⋊C₈×D₇₃	C₄	1	2	yes	—
28	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₄⋊#11924003	C₂²	1	1	yes	characteristic, complemented
30	#17988405	C₂²	1	2	yes	complemented
31	C₂²⋊#11924003	C₂²	1	2	yes	complemented
32	#17988366	C₂²	1	2	yes	complemented
33	#17988366	C₂²	1	2	yes	complemented
34	C₄×#11924003	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₇₃	C₂²	1	2	yes	complemented
38	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊C₁₆×C₇₃	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₇₃	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
44	C₂²×#10596831	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₇₃	—	2	4	no	—
46	C₂×C₈×D₇₃	—	2	4	no	—
47	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₇₃	C₂³	1	2	yes	—
51	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
52	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₇₃	C₈	1	1	yes	characteristic
54	#14556553	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
56	#14556551	C₈	1	2	yes	—
57	C₄⋊C₄×D₇₃	C₈	1	1	yes	characteristic
58	C₂²⋊C₄×D₇₃	C₈	1	2	yes	—
59	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#11924003	—	2	4	no	—
61	C₂×#11924003	C₂³	1	1	yes	characteristic
62	C₂×#11924003	C₂³	1	2	yes	—
63	C₂×#11924003	C₂³	1	1	yes	characteristic
64	C₁₆×D₇₃	—	2	4	no	—
65	C₁₆×D₇₃	—	2	2	no	—
66	C₁₆×D₇₃	—	2	4	no	—
67	C₁₆×D₇₃	—	2	4	no	—
68	C₁₆×D₇₃	D₄	1	4	yes	direct product factor
69	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
70	#14556520	C₂×C₄	1	2	yes	—
71	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
72	#14556503	C₂×C₄	1	2	yes	—
73	#14556503	C₂×C₄	1	2	yes	—
74	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
78	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₆×C₇₃	—	2	4	no	—
80	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
82	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
86	C₂³×D₇₃	C₂×C₈	1	2	yes	—
87	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
88	C₂×C₂²⋊D₇₃	C₂×C₈	1	2	yes	—
89	D₄×D₇₃	C₁₆	1	8	yes	direct product factor
90	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₇₃	—	2	4	no	—
92	C₂×C₄×D₇₃	—	2	4	no	—
93	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
98	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×#10596831	—	2	4	no	—
100	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
101	C₂×#10596831	C₂²×C₄	1	2	yes	—
102	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
103	C₈×D₇₃	—	2	4	no	—
104	C₈×D₇₃	—	2	2	no	—
105	C₈×D₇₃	—	2	2	no	—
106	C₈×D₇₃	—	2	2	no	—
107	C₈×D₇₃	—	2	4	no	—
108	C₈×D₇₃	C₂×D₄	1	2	yes	—
109	C₈×D₇₃	#41	1	2	yes	—
110	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
111	#11924007	C₂×C₈	1	2	yes	—
112	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
113	#11924005	C₂×C₈	1	2	yes	—
114	#11924005	C₂×C₈	1	2	yes	—
115	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
118	#11924003	—	2	2	no	—
119	#11924003	—	2	1	no	—
120	#11924003	C₂×D₄	1	2	yes	complemented
121	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
129	C₂²⋊C₄×C₇₃	C₂×C₈	1	2	yes	—
130	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₁₆×C₇₃	—	2	2	no	—
132	C₁₆×C₇₃	—	2	1	no	—
133	C₁₆×C₇₃	C₂×D₄	1	2	yes	complemented
134	C₂³×C₇₃	C₂²×C₈	1	2	yes	—
135	C₂²×D₇₃	—	2	4	no	—
136	C₂²×D₇₃	—	2	4	no	—
137	C₂²×D₇₃	C₂×C₁₆	1	8	yes	complemented
138	C₂²×D₇₃	C₂²×C₈	1	2	yes	—
139	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
140	D₄×C₇₃	C₂×C₁₆	1	4	yes	complemented
141	C₂×C₄×C₇₃	—	2	2	no	—
142	C₂×C₄×C₇₃	—	2	2	no	—
143	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
145	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
147	C₂²⋊D₇₃	C₂×C₁₆	1	8	yes	complemented
148	C₂×Dic₇₃	—	2	4	no	—
149	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
151	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
153	D₂₉₂	C₂×C₁₆	1	4	yes	complemented
154	C₄×D₇₃	—	2	4	no	—
155	C₄×D₇₃	—	2	2	no	—
156	C₄×D₇₃	—	2	2	no	—
157	C₄×D₇₃	—	2	2	no	—
158	C₄×D₇₃	—	2	4	no	—
159	C₄×D₇₃	C₂×C₁₆	1	4	yes	complemented
160	C₄×D₇₃	C₄×D₄	1	2	yes	—
161	C₄×D₇₃	#131	1	2	yes	—
162	C₈×C₇₃	—	2	2	no	—
163	C₈×C₇₃	—	2	1	no	—
164	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
166	#10596831	—	2	2	no	—
167	#10596831	—	2	1	no	—
168	#10596831	C₄×D₄	1	2	yes	—
169	C₂²×C₇₃	—	2	2	no	—
170	C₂²×C₇₃	—	2	2	no	—
171	C₂²×C₇₃	C₂²×C₁₆	1	4	yes	complemented
172	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
173	C₂×D₇₃	—	2	2	no	—
174	C₂×D₇₃	—	2	2	no	—
175	C₂×D₇₃	—	2	16	no	—
176	C₂×D₇₃	C₈×D₄	1	2	yes	—
177	C₂×D₇₃	C₂²×C₁₆	1	2	yes	—
178	C₂×D₇₃	C₂²×C₁₆	1	4	yes	complemented
179	C₂×D₇₃	#504	1	2	yes	—
180	C₄×C₇₃	—	2	1	no	—
181	C₄×C₇₃	—	2	2	no	—
182	C₄×C₇₃	C₂²×C₁₆	1	2	yes	complemented
183	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
185	Dic₇₃	—	2	1	no	—
186	Dic₇₃	—	2	2	no	—
187	Dic₇₃	C₈×D₄	1	2	yes	—
188	Dic₇₃	C₂²×C₁₆	1	2	yes	complemented
189	C₂×D₄×C₁₆	—	73	1	no	maximal, Sylow
190	C₂×C₇₃	—	2	4	no	—
191	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
192	C₂×C₇₃	C₂³×C₁₆	1	1	yes	characteristic
193	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
194	D₇₃	—	2	4	no	—
195	D₇₃	D₄×C₁₆	1	4	yes	direct product factor
196	C₂³×C₁₆	—	73	2	no	—
197	C₂×C₈×D₄	—	73	1	no	—
198	D₄×C₁₆	—	73	2	no	—
199	D₄×C₁₆	—	73	1	no	—
200	D₄×C₁₆	—	73	1	no	—
201	D₄×C₁₆	—	73	2	no	—
202	D₄×C₁₆	—	73	1	no	—
203	D₄×C₁₆	D₇₃	1	1	yes	characteristic, direct product factor
204	C₂×C₄⋊C₁₆	—	73	1	no	—
205	C₂×C₂²⋊C₁₆	—	73	2	no	—
206	C₂×C₄×C₁₆	—	73	1	no	—
207	C₇₃	C₂×D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₈	—	73	2	no	—
209	C₂×C₄×D₄	—	73	1	no	—
210	C₂²×C₁₆	—	73	1	no	—
211	C₂²×C₁₆	—	73	2	no	—
212	C₂²×C₁₆	—	73	1	no	—
213	C₂²×C₁₆	—	73	2	no	—
214	C₂²×C₁₆	—	73	2	no	—
215	C₂²×C₁₆	—	73	2	no	—
216	C₂²×C₁₆	—	146	8	no	—
217	C₂²×C₁₆	C₂×D₇₃	1	2	yes	complemented
218	C₈×D₄	—	73	2	no	—
219	C₈×D₄	—	73	1	no	—
220	C₈×D₄	—	73	1	no	—
221	C₈×D₄	—	73	2	no	—
222	C₈×D₄	—	73	1	no	—
223	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
224	C₂×C₄⋊C₈	—	73	1	no	—
225	C₂×C₂²⋊C₈	—	73	2	no	—
226	C₂×C₄×C₈	—	73	1	no	—
227	C₄⋊C₁₆	—	73	2	no	—
228	C₄⋊C₁₆	—	73	1	no	—
229	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
230	C₂²⋊C₁₆	—	73	2	no	—
231	C₂²⋊C₁₆	—	73	2	no	—
232	C₂²⋊C₁₆	—	73	2	no	—
233	C₂²⋊C₁₆	C₂×D₇₃	1	2	yes	complemented
234	C₄×C₁₆	—	73	1	no	—
235	C₄×C₁₆	—	73	1	no	—
236	C₄×C₁₆	—	73	1	no	—
237	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
238	C₂²×D₄	—	73	1	no	—
239	C₂³×C₄	—	73	2	no	—
240	C₂²×C₈	—	73	1	no	—
241	C₂²×C₈	—	73	2	no	—
242	C₂²×C₈	—	73	2	no	—
243	C₂²×C₈	—	73	2	no	—
244	C₂²×C₈	—	73	1	no	—
245	C₂²×C₈	—	73	2	no	—
246	C₂²×C₈	—	146	4	no	—
247	C₂²×C₈	—	146	4	no	—
248	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
249	C₄×D₄	—	73	1	no	—
250	C₄×D₄	—	73	2	no	—
251	C₄×D₄	—	73	1	no	—
252	C₄×D₄	—	73	2	no	—
253	C₄×D₄	—	73	1	no	—
254	C₄×D₄	C₄×D₇₃	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	73	1	no	—
256	C₂×C₂²⋊C₄	—	73	2	no	—
257	C₂×C₄²	—	73	1	no	—
258	C₂×C₁₆	—	2	4	no	—
259	C₂×C₁₆	—	73	1	no	—
260	C₂×C₁₆	—	73	4	no	—
261	C₂×C₁₆	—	73	1	no	—
262	C₂×C₁₆	—	73	2	no	—
263	C₂×C₁₆	—	146	4	no	—
264	C₂×C₁₆	—	146	2	no	—
265	C₂×C₁₆	—	146	4	no	—
266	C₂×C₁₆	—	146	4	no	—
267	C₂×C₁₆	—	146	4	no	—
268	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
269	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
270	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
271	C₄⋊C₈	—	73	2	no	—
272	C₄⋊C₈	—	73	1	no	—
273	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
274	C₂²⋊C₈	—	73	2	no	—
275	C₂²⋊C₈	—	73	2	no	—
276	C₂²⋊C₈	—	73	2	no	—
277	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
278	C₄×C₈	—	73	1	no	—
279	C₄×C₈	—	73	1	no	—
280	C₄×C₈	—	73	1	no	—
281	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
282	C₂⁴	—	73	2	no	—
283	C₂×D₄	—	73	2	no	—
284	C₂×D₄	—	73	8	no	—
285	C₂×D₄	—	73	1	no	—
286	C₂×D₄	C₈×D₇₃	1	1	yes	characteristic
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	1	no	—
289	C₂²×C₄	—	73	2	no	—
290	C₂²×C₄	—	73	1	no	—
291	C₂²×C₄	—	73	2	no	—
292	C₂²×C₄	—	73	2	no	—
293	C₂²×C₄	—	73	2	no	—
294	C₂²×C₄	—	146	4	no	—
295	C₂²×C₄	—	146	4	no	—
296	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	73	1	no	—
300	C₂×C₈	—	73	2	no	—
301	C₂×C₈	—	73	2	no	—
302	C₂×C₈	—	73	1	no	—
303	C₂×C₈	—	73	2	no	—
304	C₂×C₈	—	146	4	no	—
305	C₂×C₈	—	146	2	no	—
306	C₂×C₈	—	146	4	no	—
307	C₂×C₈	—	146	4	no	—
308	C₂×C₈	—	146	2	no	—
309	C₂×C₈	—	146	2	no	—
310	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
312	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
313	C₄⋊C₄	—	73	2	no	—
314	C₄⋊C₄	—	73	1	no	—
315	C₄⋊C₄	C₈×D₇₃	1	1	yes	characteristic
316	C₂²⋊C₄	—	73	2	no	—
317	C₂²⋊C₄	—	73	2	no	—
318	C₂²⋊C₄	—	73	2	no	—
319	C₂²⋊C₄	C₈×D₇₃	1	2	yes	—
320	C₄²	—	73	1	no	—
321	C₄²	—	73	1	no	—
322	C₄²	—	73	1	no	—
323	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
324	C₁₆	—	2	2	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	73	2	no	—
327	C₁₆	—	146	2	no	—
328	C₁₆	—	146	1	no	—
329	C₁₆	D₄×D₇₃	1	2	yes	direct product factor
330	C₂³	—	73	1	no	—
331	C₂³	—	73	8	no	—
332	C₂³	—	73	2	no	—
333	C₂³	—	146	4	no	—
334	C₂³	—	146	4	no	—
335	C₂³	C₂×C₈×D₇₃	1	2	yes	—
336	D₄	—	73	8	no	—
337	D₄	—	73	4	no	—
338	D₄	C₁₆×D₇₃	1	4	yes	direct product factor
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	73	1	no	—
342	C₂×C₄	—	73	1	no	—
343	C₂×C₄	—	73	4	no	—
344	C₂×C₄	—	73	2	no	—
345	C₂×C₄	—	73	2	no	—
346	C₂×C₄	—	73	1	no	—
347	C₂×C₄	—	73	2	no	—
348	C₂×C₄	—	146	4	no	—
349	C₂×C₄	—	146	4	no	—
350	C₂×C₄	—	146	2	no	—
351	C₂×C₄	—	146	4	no	—
352	C₂×C₄	—	146	2	no	—
353	C₂×C₄	—	146	2	no	—
354	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	1	no	—
360	C₈	—	73	2	no	—
361	C₈	—	146	2	no	—
362	C₈	—	146	1	no	—
363	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
364	C₈	#41×D₇₃	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	73	2	no	—
368	C₂²	—	73	2	no	—
369	C₂²	—	73	2	no	—
370	C₂²	—	73	4	no	—
371	C₂²	—	146	16	no	—
372	C₂²	—	146	2	no	—
373	C₂²	—	146	2	no	—
374	C₂²	C₂×C₁₆×D₇₃	1	4	yes	complemented
375	C₂²	C₂²×C₈×D₇₃	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	73	2	no	—
379	C₄	—	73	2	no	—
380	C₄	—	146	1	no	—
381	C₄	—	146	2	no	—
382	C₄	C₂×C₁₆×D₇₃	1	2	yes	complemented
383	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
384	C₄	#131×D₇₃	1	1	yes	characteristic
385	C₂	—	2	4	no	—
386	C₂	—	73	4	no	—
387	C₂	—	146	4	no	—
388	C₂	C₈×D₄×D₇₃	1	1	yes	characteristic
389	C₂	C₂²×C₁₆×D₇₃	1	1	yes	characteristic
390	C₂	#504×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₇₃
commutator	C₂×C₇₃	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	D₄×C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×C₈
prime radical	C₂×D₄×D₇₃	C₈
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	D₄×C₁₆	D₇₃
hypocenter	C₇₃	C₂×D₄×C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₆×D₇₃	C₂	semidirect
3. C₁₆×D₂₉₂	C₂	semidirect
4. D₄×#11924003	C₂	semidirect
5. #22611750	C₂	semidirect
6. C₁₆×C₂²⋊D₇₃	C₂	semidirect
7. #22611748	C₂	semidirect
8. C₄⋊C₁₆×D₇₃	C₂	semidirect
9. C₂²⋊C₁₆×D₇₃	C₂	semidirect
10. C₄×C₁₆×D₇₃	C₂	semidirect
11. D₄×C₁₆×C₇₃	C₂	semidirect
14. C₂²×#11924003	C₂²	semidirect
19. C₂×C₁₆×D₇₃	C₂²	semidirect
20. C₂×C₁₆×D₇₃	C₂²	semidirect
29. C₄⋊#11924003	C₂²	semidirect
30. #17988405	C₂²	semidirect
31. C₂²⋊#11924003	C₂²	semidirect
32. #17988366	C₂²	semidirect
33. #17988366	C₂²	semidirect
34. C₄×#11924003	C₂²	semidirect
35. C₁₆×Dic₇₃	C₂²	semidirect
36. C₁₆×Dic₇₃	C₂²	semidirect
37. C₂²×C₁₆×C₇₃	C₂²	semidirect
39. C₄⋊C₁₆×C₇₃	C₂²	semidirect
40. C₂²⋊C₁₆×C₇₃	C₂²	semidirect
41. C₄×C₁₆×C₇₃	C₂²	semidirect
68. C₁₆×D₇₃	D₄	direct (N × H)
89. D₄×D₇₃	C₁₆	direct (N × H)
120. #11924003	C₂×D₄	semidirect
133. C₁₆×C₇₃	C₂×D₄	semidirect
137. C₂²×D₇₃	C₂×C₁₆	semidirect
140. D₄×C₇₃	C₂×C₁₆	semidirect
147. C₂²⋊D₇₃	C₂×C₁₆	semidirect
153. D₂₉₂	C₂×C₁₆	semidirect
159. C₄×D₇₃	C₂×C₁₆	semidirect
171. C₂²×C₇₃	C₂²×C₁₆	semidirect
178. C₂×D₇₃	C₂²×C₁₆	semidirect
182. C₄×C₇₃	C₂²×C₁₆	semidirect
188. Dic₇₃	C₂²×C₁₆	semidirect
195. D₇₃	D₄×C₁₆	direct (N × H)
203. D₄×C₁₆	D₇₃	direct (N × H)
207. C₇₃	C₂×D₄×C₁₆	semidirect
217. C₂²×C₁₆	C₂×D₇₃	semidirect
229. C₄⋊C₁₆	C₂×D₇₃	semidirect
233. C₂²⋊C₁₆	C₂×D₇₃	semidirect
237. C₄×C₁₆	C₂×D₇₃	semidirect
329. C₁₆	D₄×D₇₃	direct (N × H)
338. D₄	C₁₆×D₇₃	direct (N × H)
374. C₂²	C₂×C₁₆×D₇₃	semidirect
382. C₄	C₂×C₁₆×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×D₇₃	2
C₈×D₄×D₇₃	2
C₁₆×D₂₉₂	2
D₄×#11924003	2
#22611750	2
C₁₆×C₂²⋊D₇₃	2
#22611748	2
C₄⋊C₁₆×D₇₃	2
C₂²⋊C₁₆×D₇₃	2
C₄×C₁₆×D₇₃	2
D₄×C₁₆×C₇₃	2
C₂×D₄×C₁₆	73

Subgroups — D4×C16×D73 #33239130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₆×D₇₃ #33239130