Subgroups — C₂²×C₂²⋊C₈×D₇₃ #33949409

Order 18688.

7646 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈×D₇₃	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊#10596831	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#14556503	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊C₈×D₇₃	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₇₃	C₄	1	1	yes	characteristic
8	C₂⁴×Dic₇₃	C₄	1	1	yes	characteristic
9	C₂³×C₄×D₇₃	—	2	16	no	—
10	C₂³×C₄×D₇₃	C₄	1	1	yes	characteristic
11	C₂³×C₄×D₇₃	C₄	1	1	yes	characteristic
12	C₂³×C₄×D₇₃	C₄	1	12	yes	—
13	C₂³×C₄×D₇₃	C₂²	1	12	yes	—
14	C₂³×C₄×D₇₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×D₇₃	C₂²	1	1	yes	characteristic
16	C₂³×#10596831	C₂²	1	2	yes	complemented
17	C₂²×C₈×D₇₃	—	2	16	no	—
18	C₂²×C₈×D₇₃	C₂²	1	24	yes	complemented
19	C₂×C₂²⋊#10596831	C₂²	1	12	yes	complemented
20	C₂×#14556503	C₂²	1	24	yes	complemented
21	C₂²⋊C₈×D₇₃	C₂²	1	64	yes	direct product factor
22	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₇₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊C₈×C₇₃	C₂²	1	12	yes	complemented
25	C₂⁴×D₇₃	—	2	8	no	—
26	C₂⁴×D₇₃	—	2	8	no	—
27	C₂⁴×D₇₃	C₈	1	16	yes	complemented
28	C₂⁴×D₇₃	C₂×C₄	1	12	yes	—
29	C₂⁴×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂⁴×D₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×Dic₇₃	—	2	8	no	—
32	C₂³×Dic₇₃	C₂×C₄	1	12	yes	—
33	C₂³×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×Dic₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₃	—	2	8	no	—
36	C₂²×C₄×D₇₃	—	2	8	no	—
37	C₂²×C₄×D₇₃	—	2	96	no	—
38	C₂²×C₄×D₇₃	—	2	96	no	—
39	C₂²×C₄×D₇₃	—	2	8	no	—
40	C₂²×C₄×D₇₃	C₂×C₄	1	12	yes	—
41	C₂²×C₄×D₇₃	C₂×C₄	1	12	yes	—
42	C₂²×C₄×D₇₃	C₂×C₄	1	48	yes	—
43	C₂²×C₄×D₇₃	C₂×C₄	1	6	yes	—
44	C₂²×C₄×D₇₃	C₂×C₄	1	6	yes	—
45	C₂²×C₄×D₇₃	D₄	1	16	yes	—
46	C₂²×C₄×D₇₃	C₂³	1	16	yes	—
47	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
48	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
49	C₂²×#10596831	—	2	8	no	—
50	C₂²×#10596831	C₂³	1	12	yes	complemented
51	C₂×C₈×D₇₃	—	2	96	no	—
52	C₂×C₈×D₇₃	C₂³	1	32	yes	complemented
53	C₂²⋊#10596831	C₂³	1	16	yes	complemented
54	#14556503	C₂³	1	32	yes	complemented
55	C₂⁵×C₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₃	—	2	8	no	—
57	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₃	C₂×C₄	1	6	yes	—
59	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
60	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₇₃	—	2	8	no	—
62	C₂²×C₈×C₇₃	C₂³	1	12	yes	complemented
63	C₂²⋊C₈×C₇₃	C₂³	1	16	yes	complemented
64	C₂³×D₇₃	—	2	4	no	—
65	C₂³×D₇₃	—	2	4	no	—
66	C₂³×D₇₃	—	2	128	no	—
67	C₂³×D₇₃	—	2	48	no	—
68	C₂³×D₇₃	—	2	48	no	—
69	C₂³×D₇₃	C₂²⋊C₄	1	8	yes	—
70	C₂³×D₇₃	C₂×C₈	1	8	yes	—
71	C₂³×D₇₃	C₂×C₈	1	96	yes	complemented
72	C₂³×D₇₃	C₂×C₈	1	8	yes	complemented
73	C₂³×D₇₃	M₁₆	1	8	yes	—
74	C₂³×D₇₃	C₂²×C₄	1	6	yes	—
75	C₂³×D₇₃	C₂²×C₄	1	16	yes	—
76	C₂³×D₇₃	C₂²×C₄	1	6	yes	—
77	C₂²×Dic₇₃	—	2	4	no	—
78	C₂²×Dic₇₃	—	2	48	no	—
79	C₂²×Dic₇₃	C₂²⋊C₄	1	8	yes	—
80	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
81	C₂²×Dic₇₃	C₂²×C₄	1	16	yes	—
82	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
83	C₂×C₄×D₇₃	—	2	48	no	—
84	C₂×C₄×D₇₃	—	2	24	no	—
85	C₂×C₄×D₇₃	—	2	24	no	—
86	C₂×C₄×D₇₃	—	2	48	no	—
87	C₂×C₄×D₇₃	—	2	192	no	—
88	C₂×C₄×D₇₃	—	2	64	no	—
89	C₂×C₄×D₇₃	C₂²⋊C₄	1	48	yes	—
90	C₂×C₄×D₇₃	C₂²×C₄	1	16	yes	—
91	C₂×C₄×D₇₃	C₂²×C₄	1	12	yes	—
92	C₂×C₄×D₇₃	C₂²×C₄	1	16	yes	—
93	C₂×C₄×D₇₃	C₂²×C₄	1	12	yes	—
94	C₂×C₄×D₇₃	C₂×D₄	1	48	yes	—
95	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
96	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
97	C₂×#10596831	—	2	24	no	—
98	C₂×#10596831	C₂⁴	1	8	yes	complemented
99	C₈×D₇₃	—	2	64	no	—
100	C₂⁴×C₇₃	—	2	4	no	—
101	C₂⁴×C₇₃	—	2	4	no	—
102	C₂⁴×C₇₃	C₂×C₈	1	8	yes	complemented
103	C₂⁴×C₇₃	C₂²×C₄	1	6	yes	—
104	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₃	—	2	4	no	—
106	C₂²×C₄×C₇₃	—	2	24	no	—
107	C₂²×C₄×C₇₃	—	2	24	no	—
108	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
109	C₂²×C₄×C₇₃	C₂²×C₄	1	12	yes	—
110	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
111	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
114	C₂×C₈×C₇₃	—	2	24	no	—
115	C₂×C₈×C₇₃	C₂⁴	1	8	yes	complemented
116	C₂³×C₇₃	—	2	12	no	—
117	C₂³×C₇₃	—	2	12	no	—
118	C₂³×C₇₃	—	2	32	no	—
119	C₂³×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
120	C₂³×C₇₃	C₂²×C₈	1	4	yes	—
121	C₂³×C₇₃	C₂²×C₈	1	24	yes	complemented
122	C₂³×C₇₃	C₂×M₁₆	1	4	yes	—
123	C₂³×C₇₃	C₂³×C₄	1	4	yes	—
124	C₂³×C₇₃	C₂³×C₄	1	3	yes	—
125	C₂²×D₇₃	—	2	12	no	—
126	C₂²×D₇₃	—	2	12	no	—
127	C₂²×D₇₃	—	2	32	no	—
128	C₂²×D₇₃	—	2	32	no	—
129	C₂²×D₇₃	—	2	32	no	—
130	C₂²×D₇₃	—	2	384	no	—
131	C₂²×D₇₃	C₂²⋊C₈	1	64	yes	direct product factor
132	C₂²×D₇₃	C₂×C₂²⋊C₄	1	24	yes	—
133	C₂²×D₇₃	C₂²×C₈	1	24	yes	—
134	C₂²×D₇₃	C₂²×C₈	1	64	yes	complemented
135	C₂²×D₇₃	C₂²×C₈	1	24	yes	complemented
136	C₂²×D₇₃	C₂×M₁₆	1	24	yes	—
137	C₂²×D₇₃	C₂³×C₄	1	4	yes	—
138	C₂²×D₇₃	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₇₃	—	2	12	no	—
140	C₂×C₄×C₇₃	—	2	24	no	—
141	C₂×C₄×C₇₃	—	2	8	no	—
142	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	12	yes	—
143	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
145	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
146	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
147	C₂×Dic₇₃	—	2	12	no	—
148	C₂×Dic₇₃	—	2	32	no	—
149	C₂×Dic₇₃	C₂×C₂²⋊C₄	1	24	yes	—
150	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
151	C₂×Dic₇₃	C₂³×C₄	1	4	yes	—
152	C₄×D₇₃	—	2	32	no	—
153	C₄×D₇₃	—	2	24	no	—
154	C₄×D₇₃	—	2	8	no	—
155	C₄×D₇₃	—	2	32	no	—
156	C₄×D₇₃	C₂×C₂²⋊C₄	1	48	yes	—
157	C₄×D₇₃	C₂²×D₄	1	16	yes	—
158	C₈×C₇₃	—	2	8	no	—
159	#10596831	—	2	8	no	—
160	C₂²×C₇₃	—	2	48	no	—
161	C₂²×C₇₃	—	2	4	no	—
162	C₂²×C₇₃	—	2	4	no	—
163	C₂²×C₇₃	C₂×C₂²⋊C₈	1	16	yes	complemented
164	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	6	yes	—
165	C₂²×C₇₃	C₂³×C₈	1	6	yes	—
166	C₂²×C₇₃	C₂³×C₈	1	8	yes	complemented
167	C₂²×C₇₃	C₂²×M₁₆	1	6	yes	—
168	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
169	C₂×D₇₃	—	2	48	no	—
170	C₂×D₇₃	—	2	4	no	—
171	C₂×D₇₃	—	2	4	no	—
172	C₂×D₇₃	—	2	128	no	—
173	C₂×D₇₃	C₂×C₂²⋊C₈	1	96	yes	direct product factor
174	C₂×D₇₃	C₂²×C₂²⋊C₄	1	8	yes	—
175	C₂×D₇₃	C₂³×C₈	1	8	yes	—
176	C₂×D₇₃	C₂³×C₈	1	8	yes	complemented
177	C₂×D₇₃	C₂²×M₁₆	1	8	yes	—
178	C₄×C₇₃	—	2	4	no	—
179	C₄×C₇₃	C₂²×C₂²⋊C₄	1	6	yes	—
180	C₄×C₇₃	C₂³×D₄	1	2	yes	—
181	Dic₇₃	—	2	4	no	—
182	Dic₇₃	C₂²×C₂²⋊C₄	1	8	yes	—
183	C₂³×C₂²⋊C₈	—	73	1	no	maximal, Sylow
184	C₂×C₇₃	—	2	8	no	—
185	C₂×C₇₃	C₂²×C₂²⋊C₈	1	12	yes	complemented
186	C₂×C₇₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₇₃	C₂⁴×C₈	1	1	yes	characteristic
188	C₂×C₇₃	C₂³×M₁₆	1	1	yes	characteristic
189	D₇₃	—	2	8	no	—
190	D₇₃	C₂²×C₂²⋊C₈	1	16	yes	direct product factor
191	C₂⁵×C₄	—	73	1	no	—
192	C₂⁴×C₈	—	73	2	no	—
193	C₂²×C₂²⋊C₈	—	73	24	no	—
194	C₂²×C₂²⋊C₈	—	73	1	no	—
195	C₂²×C₂²⋊C₈	—	73	2	no	—
196	C₂²×C₂²⋊C₈	D₇₃	1	1	yes	characteristic, direct product factor
197	C₇₃	C₂³×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
198	C₂⁶	—	73	1	no	—
199	C₂⁴×C₄	—	73	1	no	—
200	C₂⁴×C₄	—	73	1	no	—
201	C₂⁴×C₄	—	73	1	no	—
202	C₂⁴×C₄	—	73	12	no	—
203	C₂⁴×C₄	—	73	1	no	—
204	C₂⁴×C₄	—	73	12	no	—
205	C₂⁴×C₄	—	73	1	no	—
206	C₂⁴×C₄	—	146	16	no	—
207	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
208	C₂³×C₈	—	73	2	no	—
209	C₂³×C₈	—	73	24	no	—
210	C₂³×C₈	—	146	16	no	—
211	C₂³×C₈	C₂×D₇₃	1	2	yes	complemented
212	C₂×C₂²⋊C₈	—	73	12	no	—
213	C₂×C₂²⋊C₈	—	73	24	no	—
214	C₂×C₂²⋊C₈	—	73	64	no	—
215	C₂×C₂²⋊C₈	C₂×D₇₃	1	12	yes	direct product factor
216	C₂⁵	—	73	1	no	—
217	C₂⁵	—	73	16	no	—
218	C₂⁵	—	73	12	no	—
219	C₂⁵	—	73	1	no	—
220	C₂⁵	—	146	8	no	—
221	C₂⁵	—	146	8	no	—
222	C₂⁵	C₄×D₇₃	1	1	yes	characteristic
223	C₂³×C₄	—	2	8	no	—
224	C₂³×C₄	—	73	1	no	—
225	C₂³×C₄	—	73	6	no	—
226	C₂³×C₄	—	73	16	no	—
227	C₂³×C₄	—	73	6	no	—
228	C₂³×C₄	—	73	12	no	—
229	C₂³×C₄	—	73	1	no	—
230	C₂³×C₄	—	73	12	no	—
231	C₂³×C₄	—	73	48	no	—
232	C₂³×C₄	—	73	12	no	—
233	C₂³×C₄	—	73	6	no	—
234	C₂³×C₄	—	73	16	no	—
235	C₂³×C₄	—	73	6	no	—
236	C₂³×C₄	—	146	8	no	—
237	C₂³×C₄	—	146	96	no	—
238	C₂³×C₄	—	146	96	no	—
239	C₂³×C₄	—	146	8	no	—
240	C₂³×C₄	—	146	8	no	—
241	C₂³×C₄	—	146	8	no	—
242	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
243	C₂³×C₄	C₄×D₇₃	1	6	yes	—
244	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
245	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
246	C₂²×C₈	—	2	8	no	—
247	C₂²×C₈	—	73	12	no	—
248	C₂²×C₈	—	73	32	no	—
249	C₂²×C₈	—	146	96	no	—
250	C₂²×C₈	—	146	8	no	—
251	C₂²×C₈	C₂²×D₇₃	1	12	yes	complemented
252	C₂²⋊C₈	—	73	16	no	—
253	C₂²⋊C₈	—	73	32	no	—
254	C₂²⋊C₈	C₂²×D₇₃	1	16	yes	direct product factor
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	73	8	no	—
258	C₂⁴	—	73	8	no	—
259	C₂⁴	—	73	8	no	—
260	C₂⁴	—	73	6	no	—
261	C₂⁴	—	73	8	no	—
262	C₂⁴	—	73	96	no	—
263	C₂⁴	—	73	16	no	—
264	C₂⁴	—	73	6	no	—
265	C₂⁴	—	146	48	no	—
266	C₂⁴	—	146	128	no	—
267	C₂⁴	—	146	48	no	—
268	C₂⁴	—	146	4	no	—
269	C₂⁴	—	146	4	no	—
270	C₂⁴	C₈×D₇₃	1	8	yes	complemented
271	C₂⁴	C₂×C₄×D₇₃	1	6	yes	—
272	C₂⁴	C₂×C₄×D₇₃	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	24	no	—
275	C₂²×C₄	—	2	24	no	—
276	C₂²×C₄	—	73	8	no	—
277	C₂²×C₄	—	73	6	no	—
278	C₂²×C₄	—	73	48	no	—
279	C₂²×C₄	—	73	12	no	—
280	C₂²×C₄	—	73	48	no	—
281	C₂²×C₄	—	73	4	no	—
282	C₂²×C₄	—	73	16	no	—
283	C₂²×C₄	—	73	6	no	—
284	C₂²×C₄	—	73	16	no	—
285	C₂²×C₄	—	73	16	no	—
286	C₂²×C₄	—	73	12	no	—
287	C₂²×C₄	—	73	4	no	—
288	C₂²×C₄	—	146	48	no	—
289	C₂²×C₄	—	146	64	no	—
290	C₂²×C₄	—	146	192	no	—
291	C₂²×C₄	—	146	48	no	—
292	C₂²×C₄	—	146	48	no	—
293	C₂²×C₄	—	146	4	no	—
294	C₂²×C₄	—	146	24	no	—
295	C₂²×C₄	—	146	24	no	—
296	C₂²×C₄	C₂×C₄×D₇₃	1	6	yes	—
297	C₂²×C₄	C₂×C₄×D₇₃	1	12	yes	—
298	C₂²×C₄	C₂×C₄×D₇₃	1	3	yes	—
299	C₂²×C₄	D₄×D₇₃	1	8	yes	—
300	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
301	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
302	C₂×C₈	—	2	24	no	—
303	C₂×C₈	—	73	8	no	—
304	C₂×C₈	—	146	64	no	—
305	C₂×C₈	—	146	24	no	—
306	C₂×C₈	C₂³×D₇₃	1	8	yes	complemented
307	C₂³	—	2	12	no	—
308	C₂³	—	2	32	no	—
309	C₂³	—	2	12	no	—
310	C₂³	—	73	4	no	—
311	C₂³	—	73	24	no	—
312	C₂³	—	73	64	no	—
313	C₂³	—	73	24	no	—
314	C₂³	—	73	24	no	—
315	C₂³	—	73	4	no	—
316	C₂³	—	73	24	no	—
317	C₂³	—	73	64	no	—
318	C₂³	—	146	32	no	—
319	C₂³	—	146	32	no	—
320	C₂³	—	146	384	no	—
321	C₂³	—	146	12	no	—
322	C₂³	—	146	32	no	—
323	C₂³	—	146	12	no	—
324	C₂³	C₂²⋊C₄×D₇₃	1	4	yes	—
325	C₂³	C₂×C₈×D₇₃	1	4	yes	—
326	C₂³	C₂×C₈×D₇₃	1	24	yes	complemented
327	C₂³	M₁₆×D₇₃	1	4	yes	—
328	C₂³	C₂²×C₄×D₇₃	1	4	yes	—
329	C₂³	C₂²×C₄×D₇₃	1	3	yes	—
330	C₂×C₄	—	2	12	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	24	no	—
333	C₂×C₄	—	73	4	no	—
334	C₂×C₄	—	73	24	no	—
335	C₂×C₄	—	73	16	no	—
336	C₂×C₄	—	73	48	no	—
337	C₂×C₄	—	73	4	no	—
338	C₂×C₄	—	146	32	no	—
339	C₂×C₄	—	146	32	no	—
340	C₂×C₄	—	146	32	no	—
341	C₂×C₄	—	146	12	no	—
342	C₂×C₄	—	146	8	no	—
343	C₂×C₄	—	146	24	no	—
344	C₂×C₄	C₂²⋊C₄×D₇₃	1	12	yes	—
345	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
346	C₂×C₄	C₂²×C₄×D₇₃	1	3	yes	—
347	C₂×C₄	C₂×D₄×D₇₃	1	12	yes	—
348	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
349	C₈	—	2	8	no	—
350	C₈	—	146	8	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	48	no	—
354	C₂²	—	73	8	no	—
355	C₂²	—	73	8	no	—
356	C₂²	—	73	8	no	—
357	C₂²	—	73	96	no	—
358	C₂²	—	73	8	no	—
359	C₂²	—	146	128	no	—
360	C₂²	—	146	4	no	—
361	C₂²	—	146	4	no	—
362	C₂²	—	146	48	no	—
363	C₂²	C₂²⋊C₈×D₇₃	1	16	yes	direct product factor
364	C₂²	C₂×C₂²⋊C₄×D₇₃	1	6	yes	—
365	C₂²	C₂²×C₈×D₇₃	1	6	yes	—
366	C₂²	C₂²×C₈×D₇₃	1	8	yes	complemented
367	C₂²	C₂×M₁₆×D₇₃	1	6	yes	—
368	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	73	8	no	—
371	C₄	—	146	4	no	—
372	C₄	C₂×C₂²⋊C₄×D₇₃	1	6	yes	—
373	C₄	C₂²×D₄×D₇₃	1	2	yes	—
374	C₂	—	2	8	no	—
375	C₂	—	73	16	no	—
376	C₂	—	146	8	no	—
377	C₂	C₂×C₂²⋊C₈×D₇₃	1	12	yes	direct product factor
378	C₂	C₂²×C₂²⋊C₄×D₇₃	1	1	yes	characteristic
379	C₂	C₂³×C₈×D₇₃	1	1	yes	characteristic
380	C₂	C₂²×M₁₆×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₇₃
commutator	C₂×C₇₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂²×C₂²⋊C₈×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂²×C₄
prime radical	C₂⁵×D₇₃	C₄
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂²×C₂²⋊C₈	D₇₃
hypocenter	C₇₃	C₂³×C₂²⋊C₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂³×C₈×D₇₃	C₂	semidirect
3. C₂²×C₂²⋊#10596831	C₂	semidirect
4. C₂²×#14556503	C₂	semidirect
5. C₂×C₂²⋊C₈×D₇₃	C₂	direct (N × H)
6. C₂²×C₂²⋊C₈×C₇₃	C₂	semidirect
16. C₂³×#10596831	C₂²	semidirect
18. C₂²×C₈×D₇₃	C₂²	semidirect
19. C₂×C₂²⋊#10596831	C₂²	semidirect
20. C₂×#14556503	C₂²	semidirect
21. C₂²⋊C₈×D₇₃	C₂²	direct (N × H)
23. C₂³×C₈×C₇₃	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
27. C₂⁴×D₇₃	C₈	semidirect
50. C₂²×#10596831	C₂³	semidirect
52. C₂×C₈×D₇₃	C₂³	semidirect
53. C₂²⋊#10596831	C₂³	semidirect
54. #14556503	C₂³	semidirect
62. C₂²×C₈×C₇₃	C₂³	semidirect
63. C₂²⋊C₈×C₇₃	C₂³	semidirect
71. C₂³×D₇₃	C₂×C₈	semidirect
72. C₂³×D₇₃	C₂×C₈	semidirect
98. C₂×#10596831	C₂⁴	semidirect
102. C₂⁴×C₇₃	C₂×C₈	semidirect
115. C₂×C₈×C₇₃	C₂⁴	semidirect
121. C₂³×C₇₃	C₂²×C₈	semidirect
131. C₂²×D₇₃	C₂²⋊C₈	direct (N × H)
134. C₂²×D₇₃	C₂²×C₈	semidirect
135. C₂²×D₇₃	C₂²×C₈	semidirect
163. C₂²×C₇₃	C₂×C₂²⋊C₈	semidirect
166. C₂²×C₇₃	C₂³×C₈	semidirect
173. C₂×D₇₃	C₂×C₂²⋊C₈	direct (N × H)
176. C₂×D₇₃	C₂³×C₈	semidirect
185. C₂×C₇₃	C₂²×C₂²⋊C₈	semidirect
190. D₇₃	C₂²×C₂²⋊C₈	direct (N × H)
196. C₂²×C₂²⋊C₈	D₇₃	direct (N × H)
197. C₇₃	C₂³×C₂²⋊C₈	semidirect
211. C₂³×C₈	C₂×D₇₃	semidirect
215. C₂×C₂²⋊C₈	C₂×D₇₃	direct (N × H)
251. C₂²×C₈	C₂²×D₇₃	semidirect
254. C₂²⋊C₈	C₂²×D₇₃	direct (N × H)
270. C₂⁴	C₈×D₇₃	semidirect
306. C₂×C₈	C₂³×D₇₃	semidirect
326. C₂³	C₂×C₈×D₇₃	semidirect
363. C₂²	C₂²⋊C₈×D₇₃	direct (N × H)
366. C₂²	C₂²×C₈×D₇₃	semidirect
377. C₂	C₂×C₂²⋊C₈×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×D₇₃	2
C₂³×C₈×D₇₃	2
C₂²×C₂²⋊#10596831	2
C₂²×#14556503	2
C₂×C₂²⋊C₈×D₇₃	2
C₂²×C₂²⋊C₈×C₇₃	2
C₂³×C₂²⋊C₈	73

Subgroups — C22×C22⋊C8×D73 #33949409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊C₈×D₇₃ #33949409