Subgroups — #33083974

Order 18688.

1242 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988539	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988539	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic
5	C₄×C₄⋊C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
6	#22609808	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609806	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609803	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609799	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11924007	C₂	1	1	yes	maximal, characteristic, complemented
12	#22609792	C₂	1	1	yes	maximal, characteristic, complemented
13	#22609623	C₂	1	1	yes	maximal, characteristic
14	#22609623	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#11924011	C₂²	1	1	yes	characteristic
17	C₂²×#11924011	C₂²	1	1	yes	characteristic
18	C₂²×#11924011	C₂²	1	1	yes	characteristic
19	C₂²×#11924011	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₇₃	C₄	1	2	yes	—
21	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
24	#17988609	C₄	1	8	yes	complemented
25	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
26	C₂×#14556520	C₂²	1	1	yes	characteristic
27	C₂×#14556520	C₂²	1	1	yes	characteristic
28	#17988539	—	2	4	no	—
29	#17988539	C₄	1	8	yes	complemented
30	C₄×#11924011	—	2	4	no	—
31	C₂×#14556502	C₂²	1	1	yes	characteristic
32	C₂×#14556502	C₂²	1	1	yes	characteristic
33	C₂×#14556501	C₂²	1	1	yes	characteristic
34	C₂×#14556501	C₂²	1	1	yes	characteristic
35	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×Dic₇₃	C₄	1	2	yes	—
41	C₄×#11924007	C₂²	1	1	yes	characteristic
42	C₄×#11924007	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
44	#17988438	C₄	1	2	yes	—
45	#95×D₇₃	C₄	1	2	yes	—
46	#17988342	C₂²	1	1	yes	characteristic
47	#17988342	C₂²	1	1	yes	characteristic
48	#17988341	C₂²	1	1	yes	characteristic
49	#17988341	C₂²	1	1	yes	characteristic
50	#17988341	C₂²	1	1	yes	characteristic
51	#17988341	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
54	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
57	#336×C₇₃	C₂²	1	1	yes	characteristic
58	#336×C₇₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
64	C₂×#11924011	—	2	2	no	—
65	C₂×#11924011	—	2	2	no	—
66	C₂×#11924011	—	2	2	no	—
67	C₂×#11924011	—	2	2	no	—
68	C₂×#11924011	—	2	2	no	—
69	C₂×#11924011	—	2	2	no	—
70	C₂×#11924011	C₂×C₄	1	4	yes	—
71	C₂×#11924011	C₂×C₄	1	4	yes	—
72	C₂×#11924011	C₂×C₄	1	4	yes	—
73	C₂×#11924011	C₂×C₄	1	4	yes	—
74	C₂×#11924011	D₄	1	4	yes	—
75	C₂×#11924011	Q₈	1	4	yes	—
76	C₂²×#10596831	C₂³	1	1	yes	characteristic
77	C₂²×#10596831	C₂³	1	1	yes	characteristic
78	C₂²×#10596831	C₂³	1	1	yes	characteristic
79	C₂²×#10596831	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
81	C₂×#11924007	C₂×C₄	1	2	yes	—
82	C₂×#11924007	C₂×C₄	1	2	yes	—
83	C₄⋊C₄×D₇₃	—	2	8	no	—
84	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
85	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
86	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
91	C₄²×D₇₃	—	2	2	no	—
92	C₄²×D₇₃	—	2	2	no	—
93	C₄²×D₇₃	—	2	2	no	—
94	C₄²×D₇₃	—	2	2	no	—
95	C₄²×D₇₃	C₂×C₄	1	4	yes	—
96	C₄²×D₇₃	C₂×C₄	1	4	yes	—
97	C₄⋊#10596831	C₂×C₄	1	4	yes	complemented
98	#14556520	C₂×C₄	1	4	yes	complemented
99	#14556520	C₂×C₄	1	4	yes	complemented
100	#14556502	—	2	2	no	—
101	#14556502	C₂×C₄	1	4	yes	complemented
102	#14556501	—	2	2	no	—
103	#14556501	—	2	2	no	—
104	C₄×#10596831	—	2	2	no	—
105	C₈×Dic₇₃	—	2	2	no	—
106	C₈×Dic₇₃	—	2	2	no	—
107	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
108	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
109	#14556498	C₂×C₄	1	2	yes	—
110	#14556498	C₂×C₄	1	2	yes	—
111	#14556498	C₂×C₄	1	2	yes	—
112	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
117	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₇₃	C₂×C₄	1	4	yes	complemented
121	#97×C₇₃	—	2	2	no	—
122	#97×C₇₃	C₂×C₄	1	4	yes	complemented
123	C₄×C₈×C₇₃	—	2	2	no	—
124	#95×C₇₃	C₂×C₄	1	2	yes	—
125	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
127	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₇₃	—	2	4	no	—
132	C₂×C₄×D₇₃	—	2	4	no	—
133	C₂×C₄×D₇₃	—	2	4	no	—
134	C₂×C₄×D₇₃	—	2	4	no	—
135	C₂×C₄×D₇₃	—	2	4	no	—
136	C₂×C₄×D₇₃	—	4	2	no	—
137	C₂×C₄×D₇₃	—	4	2	no	—
138	C₂×C₄×D₇₃	—	4	2	no	—
139	C₂×C₄×D₇₃	C₄²	1	4	yes	—
140	C₂×C₄×D₇₃	C₄²	1	4	yes	—
141	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
142	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
143	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
144	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
145	C₂×C₄×D₇₃	#41	1	2	yes	—
146	C₂×C₄×D₇₃	#41	1	2	yes	—
147	#11924011	—	2	8	no	—
148	#11924011	—	2	8	no	—
149	#11924011	—	2	8	no	—
150	#11924011	C₄⋊C₄	1	16	yes	complemented
151	C₂×#10596831	—	2	1	no	—
152	C₂×#10596831	—	2	1	no	—
153	C₂×#10596831	—	2	1	no	—
154	C₂×#10596831	—	2	1	no	—
155	C₂×#10596831	—	2	1	no	—
156	C₂×#10596831	—	2	1	no	—
157	C₂×#10596831	C₂²×C₄	1	2	yes	—
158	C₂×#10596831	C₂²×C₄	1	2	yes	—
159	C₂×#10596831	C₂²×C₄	1	2	yes	—
160	C₂×#10596831	C₂²×C₄	1	2	yes	—
161	C₂×#10596831	C₂×D₄	1	2	yes	—
162	C₂×#10596831	C₂×Q₈	1	2	yes	—
163	C₄⋊Dic₇₃	—	2	4	no	—
164	#11924007	—	2	4	no	—
165	#11924007	M₁₆	1	8	yes	complemented
166	C₄×Dic₇₃	—	2	1	no	—
167	C₄×Dic₇₃	—	2	1	no	—
168	C₄×Dic₇₃	—	2	1	no	—
169	C₄×Dic₇₃	—	2	1	no	—
170	C₄×Dic₇₃	—	2	4	no	—
171	C₄×Dic₇₃	—	2	4	no	—
172	C₄×Dic₇₃	C₄²	1	4	yes	—
173	C₄×Dic₇₃	C₄²	1	4	yes	—
174	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
175	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₇₃	—	2	1	no	—
182	C₂×C₈×C₇₃	—	2	1	no	—
183	C₂×C₈×C₇₃	—	2	1	no	—
184	C₂×C₈×C₇₃	—	2	1	no	—
185	C₂×C₈×C₇₃	—	2	1	no	—
186	C₂×C₈×C₇₃	—	2	1	no	—
187	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
189	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
193	C₄⋊C₄×C₇₃	—	2	4	no	—
194	C₄²×C₇₃	—	2	1	no	—
195	C₄²×C₇₃	—	2	1	no	—
196	C₄²×C₇₃	—	2	1	no	—
197	C₄²×C₇₃	—	2	1	no	—
198	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
199	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
200	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
201	C₂²×D₇₃	—	2	2	no	—
202	C₂²×D₇₃	—	2	2	no	—
203	C₂²×D₇₃	C₂×C₄²	1	2	yes	—
204	C₂²×D₇₃	C₄×D₄	1	2	yes	—
205	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
214	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
215	C₂×C₄×C₇₃	C₂×M₁₆	1	4	yes	—
216	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₇₃	—	2	2	no	—
223	C₂×Dic₇₃	—	2	2	no	—
224	C₂×Dic₇₃	—	2	2	no	—
225	C₂×Dic₇₃	—	2	2	no	—
226	C₂×Dic₇₃	—	2	2	no	—
227	C₂×Dic₇₃	—	2	2	no	—
228	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
229	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
230	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
231	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
232	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
233	C₂×Dic₇₃	C₂×M₁₆	1	4	yes	—
234	C₂×Dic₇₃	C₂×M₁₆	1	4	yes	—
235	C₄×D₇₃	—	2	8	no	—
236	C₄×D₇₃	—	4	4	no	—
237	C₄×D₇₃	—	4	8	no	—
238	C₄×D₇₃	—	4	8	no	—
239	C₄×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
240	C₄×D₇₃	#117	1	4	yes	—
241	C₄×D₇₃	C₄×D₄	1	4	yes	—
242	C₄×D₇₃	C₄×Q₈	1	4	yes	—
243	C₈×C₇₃	—	2	2	no	—
244	C₈×C₇₃	—	2	2	no	—
245	C₈×C₇₃	—	2	2	no	—
246	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	complemented
247	#10596831	—	2	2	no	—
248	#10596831	—	2	2	no	—
249	#10596831	—	2	2	no	—
250	#10596831	C₂×C₄⋊C₄	1	4	yes	complemented
251	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
252	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
254	C₂²×C₇₃	C₂²×M₁₆	1	2	yes	—
255	C₂²×C₇₃	#568	1	2	yes	—
256	C₂×D₇₃	—	2	2	no	—
257	C₂×D₇₃	—	2	2	no	—
258	C₂×D₇₃	—	2	4	no	—
259	C₂×D₇₃	—	2	4	no	—
260	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
261	C₄×C₇₃	—	2	2	no	—
262	C₄×C₇₃	—	2	2	no	—
263	C₄×C₇₃	—	2	4	no	—
264	C₄×C₇₃	—	4	2	no	—
265	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
267	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
269	Dic₇₃	—	2	2	no	—
270	Dic₇₃	—	2	4	no	—
271	Dic₇₃	—	4	2	no	—
272	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
273	Dic₇₃	C₄×M₁₆	1	4	yes	complemented
274	C₄⋊C₄×M₁₆	—	73	1	no	maximal, Sylow
275	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
277	C₂×C₇₃	#2873	1	1	yes	characteristic
278	C₂×C₇₃	D₄×M₁₆	1	2	yes	—
279	C₂×C₇₃	Q₈×M₁₆	1	2	yes	—
280	D₇₃	—	2	4	no	—
281	C₂×#423	—	73	1	no	—
282	C₂×C₄×M₁₆	—	73	1	no	—
283	C₂×C₄×M₁₆	—	73	1	no	—
284	C₂×C₄×M₁₆	—	73	1	no	—
285	C₂×C₄×C₄⋊C₄	—	73	1	no	—
286	#1771	—	73	1	no	—
287	#1771	—	73	1	no	—
288	#1771	—	73	1	no	—
289	#1771	D₇₃	1	1	yes	characteristic, complemented
290	#1770	—	73	1	no	—
291	#1770	—	73	1	no	—
292	C₈×C₄⋊C₄	—	73	1	no	—
293	C₈×C₄⋊C₄	—	73	1	no	—
294	#1728	—	73	1	no	—
295	#1728	—	73	1	no	—
296	C₇₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
297	C₂²×M₁₆	—	73	1	no	—
298	C₂²×M₁₆	—	73	1	no	—
299	C₂²×M₁₆	—	73	1	no	—
300	C₂²×M₁₆	—	73	1	no	—
301	C₂²×C₄⋊C₄	—	73	2	no	—
302	C₂²×C₄²	—	73	1	no	—
303	C₂²×C₄²	—	73	1	no	—
304	C₂²×C₄²	—	73	1	no	—
305	#423	—	73	8	no	—
306	C₂×C₄⋊C₈	—	73	1	no	—
307	C₂×C₄⋊C₈	—	73	1	no	—
308	C₂×C₄⋊C₈	—	73	1	no	—
309	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
310	C₄×M₁₆	—	73	8	no	—
311	C₄×M₁₆	—	146	4	no	—
312	C₄×M₁₆	—	146	4	no	—
313	C₂×#97	—	73	1	no	—
314	C₂×#97	—	73	1	no	—
315	C₂×#97	—	73	1	no	—
316	C₂×#97	—	73	1	no	—
317	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
318	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
319	C₂×C₄×C₈	—	73	1	no	—
320	C₂×C₄×C₈	—	73	1	no	—
321	C₂×C₄×C₈	—	73	1	no	—
322	C₂×C₄×C₈	—	73	1	no	—
323	C₂×C₄×C₈	—	73	1	no	—
324	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
325	C₄×C₄⋊C₄	—	73	2	no	—
326	C₄×C₄⋊C₄	—	73	1	no	—
327	C₄×C₄⋊C₄	—	73	1	no	—
328	C₄×C₄⋊C₄	—	73	1	no	—
329	C₄×C₄⋊C₄	—	73	2	no	—
330	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
331	C₂×#95	—	73	2	no	—
332	#336	—	73	1	no	—
333	#336	—	73	1	no	—
334	#336	—	73	1	no	—
335	#336	—	73	1	no	—
336	#336	—	73	1	no	—
337	#336	—	73	1	no	—
338	#336	C₂×D₇₃	1	1	yes	characteristic
339	#336	C₂×D₇₃	1	1	yes	characteristic
340	C₂³×C₄	—	73	1	no	—
341	C₂³×C₄	—	73	2	no	—
342	C₂³×C₄	—	73	2	no	—
343	C₂³×C₄	—	73	1	no	—
344	C₂³×C₄	—	73	1	no	—
345	C₂×M₁₆	—	73	4	no	—
346	C₂×M₁₆	—	73	4	no	—
347	C₂×M₁₆	—	73	4	no	—
348	C₂×M₁₆	—	73	4	no	—
349	C₂×M₁₆	—	73	4	no	—
350	C₂×M₁₆	—	73	4	no	—
351	C₂×M₁₆	—	146	2	no	—
352	C₂×M₁₆	—	146	2	no	—
353	C₂×M₁₆	—	146	2	no	—
354	C₂×M₁₆	—	146	2	no	—
355	C₂×M₁₆	—	146	2	no	—
356	C₂×M₁₆	—	146	2	no	—
357	C₂²×C₈	—	73	1	no	—
358	C₂²×C₈	—	73	1	no	—
359	C₂²×C₈	—	73	1	no	—
360	C₂²×C₈	—	73	1	no	—
361	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
362	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	—	73	2	no	—
366	C₂×C₄⋊C₄	—	73	2	no	—
367	C₂×C₄⋊C₄	—	73	2	no	—
368	C₂×C₄⋊C₄	—	146	8	no	—
369	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
370	C₂×C₄²	—	73	1	no	—
371	C₂×C₄²	—	73	1	no	—
372	C₂×C₄²	—	73	1	no	—
373	C₂×C₄²	—	73	4	no	—
374	C₂×C₄²	—	73	4	no	—
375	C₂×C₄²	—	73	2	no	—
376	C₂×C₄²	—	73	2	no	—
377	C₂×C₄²	—	73	1	no	—
378	C₂×C₄²	—	73	1	no	—
379	C₂×C₄²	—	146	2	no	—
380	C₂×C₄²	—	146	2	no	—
381	C₂×C₄²	—	146	2	no	—
382	C₂×C₄²	—	146	2	no	—
383	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
385	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
386	C₄⋊C₈	—	73	4	no	—
387	C₄⋊C₈	—	73	4	no	—
388	C₄⋊C₈	—	73	4	no	—
389	C₄⋊C₈	C₄×D₇₃	1	4	yes	complemented
390	#97	—	2	2	no	—
391	#97	—	73	4	no	—
392	#97	—	146	2	no	—
393	#97	—	146	2	no	—
394	#97	—	146	2	no	—
395	#97	C₄×D₇₃	1	4	yes	complemented
396	C₄×C₈	—	2	2	no	—
397	C₄×C₈	—	73	4	no	—
398	C₄×C₈	—	73	4	no	—
399	C₄×C₈	—	146	2	no	—
400	C₄×C₈	—	146	2	no	—
401	C₄×C₈	—	146	2	no	—
402	#95	—	73	2	no	—
403	#95	—	73	2	no	—
404	#95	—	73	2	no	—
405	#95	C₄×D₇₃	1	2	yes	—
406	C₂⁴	—	73	1	no	—
407	C₂²×C₄	—	292	2	no	—
408	C₂²×C₄	—	292	2	no	—
409	C₂²×C₄	—	292	2	no	—
410	C₂²×C₄	—	73	4	no	—
411	C₂²×C₄	—	73	1	no	—
412	C₂²×C₄	—	73	1	no	—
413	C₂²×C₄	—	73	2	no	—
414	C₂²×C₄	—	73	2	no	—
415	C₂²×C₄	—	73	2	no	—
416	C₂²×C₄	—	73	2	no	—
417	C₂²×C₄	—	73	2	no	—
418	C₂²×C₄	—	73	2	no	—
419	C₂²×C₄	—	73	1	no	—
420	C₂²×C₄	—	73	2	no	—
421	C₂²×C₄	—	73	4	no	—
422	C₂²×C₄	—	73	2	no	—
423	C₂²×C₄	—	146	4	no	—
424	C₂²×C₄	—	146	4	no	—
425	C₂²×C₄	—	146	4	no	—
426	C₂²×C₄	—	146	4	no	—
427	C₂²×C₄	—	146	4	no	—
428	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
429	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
432	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
433	M₁₆	—	73	16	no	—
434	M₁₆	—	146	8	no	—
435	M₁₆	—	146	8	no	—
436	M₁₆	—	146	8	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	73	2	no	—
444	C₂×C₈	—	73	2	no	—
445	C₂×C₈	—	73	2	no	—
446	C₂×C₈	—	73	2	no	—
447	C₂×C₈	—	73	2	no	—
448	C₂×C₈	—	73	2	no	—
449	C₂×C₈	—	146	1	no	—
450	C₂×C₈	—	146	1	no	—
451	C₂×C₈	—	146	1	no	—
452	C₂×C₈	—	146	1	no	—
453	C₂×C₈	—	146	1	no	—
454	C₂×C₈	—	146	1	no	—
455	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
456	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
457	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
458	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
459	C₂×C₈	D₄×D₇₃	1	2	yes	—
460	C₂×C₈	Q₈×D₇₃	1	2	yes	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	73	8	no	—
463	C₄⋊C₄	—	146	4	no	—
464	C₄⋊C₄	—	146	4	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	73	4	no	—
470	C₄²	—	73	4	no	—
471	C₄²	—	73	2	no	—
472	C₄²	—	73	2	no	—
473	C₄²	—	146	4	no	—
474	C₄²	—	146	4	no	—
475	C₄²	—	146	1	no	—
476	C₄²	—	146	1	no	—
477	C₄²	—	146	1	no	—
478	C₄²	—	146	1	no	—
479	C₄²	C₂×C₄×D₇₃	1	2	yes	—
480	C₄²	C₂×C₄×D₇₃	1	2	yes	—
481	C₂³	—	73	2	no	—
482	C₂³	—	73	2	no	—
483	C₂³	—	73	2	no	—
484	C₂³	—	146	2	no	—
485	C₂³	—	146	2	no	—
486	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	292	8	no	—
495	C₂×C₄	—	292	4	no	—
496	C₂×C₄	—	292	8	no	—
497	C₂×C₄	—	73	2	no	—
498	C₂×C₄	—	73	2	no	—
499	C₂×C₄	—	73	2	no	—
500	C₂×C₄	—	73	2	no	—
501	C₂×C₄	—	73	4	no	—
502	C₂×C₄	—	73	4	no	—
503	C₂×C₄	—	73	4	no	—
504	C₂×C₄	—	73	4	no	—
505	C₂×C₄	—	73	4	no	—
506	C₂×C₄	—	73	2	no	—
507	C₂×C₄	—	73	4	no	—
508	C₂×C₄	—	146	8	no	—
509	C₂×C₄	—	146	2	no	—
510	C₂×C₄	—	146	2	no	—
511	C₂×C₄	—	146	2	no	—
512	C₂×C₄	—	146	2	no	—
513	C₂×C₄	—	146	2	no	—
514	C₂×C₄	—	146	2	no	—
515	C₂×C₄	C₄²×D₇₃	1	2	yes	—
516	C₂×C₄	C₄²×D₇₃	1	2	yes	—
517	C₂×C₄	M₁₆×D₇₃	1	4	yes	—
518	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
521	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
522	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
523	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	73	4	no	—
528	C₈	—	146	2	no	—
529	C₈	—	146	2	no	—
530	C₈	—	146	2	no	—
531	C₈	C₄⋊C₄×D₇₃	1	4	yes	complemented
532	C₂²	—	73	4	no	—
533	C₂²	—	146	4	no	—
534	C₂²	—	146	4	no	—
535	C₂²	—	146	2	no	—
536	C₂²	—	146	2	no	—
537	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
538	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
539	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
540	C₂²	C₂×M₁₆×D₇₃	1	2	yes	—
541	C₂²	#17989352	1	2	yes	—
542	C₄	—	2	4	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	292	2	no	—
547	C₄	—	73	4	no	—
548	C₄	—	73	4	no	—
549	C₄	—	146	4	no	—
550	C₄	—	146	2	no	—
551	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
552	C₄	#117×D₇₃	1	1	yes	characteristic
553	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
554	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
555	C₂	—	146	4	no	—
556	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
557	C₂	C₄×M₁₆×D₇₃	1	1	yes	characteristic
558	C₂	#22618347	1	1	yes	characteristic
559	C₂	#22618664	1	2	yes	—
560	C₂	#22618883	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂²×C₄²
Fitting	C₇₃×#1771	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1771	D₇₃
hypocenter	C₇₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
6. #22609808	C₂	semidirect
7. #22609806	C₂	semidirect
8. #22609803	C₂	semidirect
9. #22609799	C₂	semidirect
10. #22609797	C₂	semidirect
11. C₈×#11924007	C₂	semidirect
12. #22609792	C₂	semidirect
15. C₇₃×#1771	C₂	semidirect
24. #17988609	C₄	semidirect
29. #17988539	C₄	semidirect
97. C₄⋊#10596831	C₂×C₄	semidirect
98. #14556520	C₂×C₄	semidirect
99. #14556520	C₂×C₄	semidirect
101. #14556502	C₂×C₄	semidirect
107. C₈×Dic₇₃	C₂×C₄	semidirect
108. C₈×Dic₇₃	C₂×C₄	semidirect
120. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
122. #97×C₇₃	C₂×C₄	semidirect
150. #11924011	C₄⋊C₄	semidirect
165. #11924007	M₁₆	semidirect
246. C₈×C₇₃	C₂×C₄⋊C₄	semidirect
250. #10596831	C₂×C₄⋊C₄	semidirect
273. Dic₇₃	C₄×M₁₆	semidirect
289. #1771	D₇₃	semidirect
296. C₇₃	C₄⋊C₄×M₁₆	semidirect
389. C₄⋊C₈	C₄×D₇₃	semidirect
395. #97	C₄×D₇₃	semidirect
531. C₈	C₄⋊C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988609	2
C₂×#17988539	2
C₂×C₄×#11924011	2
C₄×C₄⋊C₄×D₇₃	2
#22609808	2
#22609806	2
#22609803	2
#22609799	2
#22609797	2
C₈×#11924007	2
#22609792	2
#22609623	2
C₇₃×#1771	2
C₄⋊C₄×M₁₆	73