Subgroups — #33084050

Order 18688.

1218 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988628	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988626	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988539	C₂	1	1	yes	maximal, characteristic
4	C₄×#14556549	C₂	1	1	yes	maximal, characteristic
5	C₄×C₄⋊C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
6	#22609829	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609829	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609828	C₂	1	1	yes	maximal, characteristic, complemented
9	#107×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609823	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#22609819	C₂	1	1	yes	maximal, characteristic, complemented
13	#22609649	C₂	1	1	yes	maximal, characteristic
14	#22609649	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#11924011	C₂²	1	1	yes	characteristic
17	C₂²×#11924011	C₂²	1	1	yes	characteristic
18	C₂×#14556549	C₂²	1	1	yes	characteristic
19	C₂×#14556549	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₇₃	—	2	1	no	—
23	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
24	#17988628	C₄	1	8	yes	complemented
25	#17988626	C₄	1	8	yes	complemented
26	C₂×#14556525	C₂²	1	1	yes	characteristic
27	C₂×#14556524	C₂²	1	1	yes	characteristic
28	C₂×#14556524	C₂²	1	1	yes	characteristic
29	C₂×#14556523	C₂²	1	1	yes	characteristic
30	C₂×#14556522	C₂²	1	1	yes	characteristic
31	C₂×#14556522	C₂²	1	1	yes	characteristic
32	#17988539	C₄	1	8	yes	complemented
33	C₂×#14556502	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×Dic₇₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×Dic₇₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₇₃	C₂²	1	1	yes	characteristic
39	C₄⋊C₄×Dic₇₃	C₂²	1	1	yes	characteristic
40	C₄×#11924007	—	2	1	no	—
41	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
43	#17988438	—	2	1	no	—
44	C₄×#11924005	—	2	1	no	—
45	#17988434	—	2	1	no	—
46	#17988432	—	2	1	no	—
47	#95×D₇₃	—	2	1	no	—
48	C₄²×Dic₇₃	—	2	1	no	—
49	#17988350	C₂²	1	1	yes	characteristic
50	#17988350	C₂²	1	1	yes	characteristic
51	#17988349	C₂²	1	1	yes	characteristic
52	#17988349	C₂²	1	1	yes	characteristic
53	#17988349	C₂²	1	1	yes	characteristic
54	#17988349	C₂²	1	1	yes	characteristic
55	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
56	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
57	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
60	#340×C₇₃	C₂²	1	1	yes	characteristic
61	#340×C₇₃	C₂²	1	1	yes	characteristic
62	C₂²×C₄×D₇₃	—	2	1	no	—
63	C₂²×C₄×D₇₃	—	2	1	no	—
64	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
65	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
66	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
67	C₂×#11924011	—	2	2	no	—
68	C₂×#11924011	—	2	2	no	—
69	C₂×#11924011	C₂×C₄	1	4	yes	—
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	C₂²×#10596831	C₂³	1	1	yes	characteristic
74	C₂²×#10596831	C₂³	1	1	yes	characteristic
75	#14556549	—	2	2	no	—
76	#14556549	—	2	2	no	—
77	#14556549	C₂×C₄	1	4	yes	—
78	#14556549	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
83	C₂×#11924007	—	2	1	no	—
84	C₂×#11924007	—	2	1	no	—
85	C₄⋊C₄×D₇₃	—	2	2	no	—
86	C₄⋊C₄×D₇₃	—	2	2	no	—
87	C₄⋊C₄×D₇₃	C₂×C₄	1	4	yes	—
88	C₄⋊C₄×D₇₃	C₂×C₄	1	4	yes	—
89	C₂×#11924005	—	2	1	no	—
90	C₂×#11924005	—	2	1	no	—
91	C₂×C₄×Dic₇₃	—	2	1	no	—
92	C₂×C₄×Dic₇₃	—	2	1	no	—
93	C₂×C₄×Dic₇₃	—	2	1	no	—
94	C₂×C₄×Dic₇₃	—	2	1	no	—
95	C₂×C₄×Dic₇₃	—	2	1	no	—
96	C₂×C₄×Dic₇₃	—	2	1	no	—
97	C₂×C₄×Dic₇₃	—	2	1	no	—
98	C₂×C₄×Dic₇₃	—	2	1	no	—
99	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
100	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
101	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
102	C₄²×D₇₃	—	4	4	no	—
103	C₄²×D₇₃	C₂×C₄	1	4	yes	—
104	C₄²×D₇₃	Q₈	1	4	yes	—
105	#14556525	C₂×C₄	1	4	yes	complemented
106	#14556524	C₂×C₄	1	4	yes	complemented
107	#14556524	C₂×C₄	1	4	yes	complemented
108	#14556523	C₂×C₄	1	4	yes	complemented
109	#14556522	C₂×C₄	1	4	yes	complemented
110	#14556522	C₂×C₄	1	4	yes	complemented
111	#14556502	C₂×C₄	1	4	yes	complemented
112	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
113	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
114	#14556498	—	2	1	no	—
115	#14556498	—	2	1	no	—
116	#14556498	—	2	1	no	—
117	#14556498	—	2	1	no	—
118	#14556498	—	2	1	no	—
119	#14556498	—	2	1	no	—
120	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₇₃	—	2	1	no	—
127	C₂×C₄²×C₇₃	—	2	1	no	—
128	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
129	#107×C₇₃	C₂×C₄	1	4	yes	complemented
130	#106×C₇₃	C₂×C₄	1	4	yes	complemented
131	#97×C₇₃	C₂×C₄	1	4	yes	complemented
132	#95×C₇₃	—	2	1	no	—
133	#95×C₇₃	—	2	1	no	—
134	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×Dic₇₃	—	2	1	no	—
136	C₂²×Dic₇₃	—	2	1	no	—
137	C₂²×Dic₇₃	—	2	1	no	—
138	C₂²×Dic₇₃	—	2	1	no	—
139	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×D₇₃	—	2	2	no	—
143	C₂×C₄×D₇₃	—	2	2	no	—
144	C₂×C₄×D₇₃	—	2	4	no	—
145	C₂×C₄×D₇₃	—	2	4	no	—
146	C₂×C₄×D₇₃	—	4	1	no	—
147	C₂×C₄×D₇₃	—	4	1	no	—
148	C₂×C₄×D₇₃	—	4	2	no	—
149	C₂×C₄×D₇₃	—	4	2	no	—
150	C₂×C₄×D₇₃	—	4	2	no	—
151	C₂×C₄×D₇₃	—	4	2	no	—
152	C₂×C₄×D₇₃	C₄⋊C₄	1	4	yes	—
153	C₂×C₄×D₇₃	C₄⋊C₄	1	4	yes	—
154	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
155	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
156	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
157	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
158	C₂×C₄×D₇₃	#41	1	2	yes	—
159	C₂×C₄×D₇₃	#41	1	2	yes	—
160	#11924011	—	2	8	no	—
161	#11924011	C₄²	1	16	yes	complemented
162	C₂×#10596831	—	2	1	no	—
163	C₂×#10596831	—	2	1	no	—
164	C₂×#10596831	C₂²×C₄	1	2	yes	—
165	C₂×#10596831	C₂²×C₄	1	2	yes	—
166	C₂×#10596831	C₂²×C₄	1	2	yes	—
167	C₂×#10596831	C₂²×C₄	1	2	yes	—
168	C₄⋊Dic₇₃	—	2	1	no	—
169	C₄⋊Dic₇₃	—	2	1	no	—
170	C₄⋊Dic₇₃	—	2	1	no	—
171	C₄⋊Dic₇₃	—	2	1	no	—
172	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
173	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
174	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
175	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
176	#11924007	—	2	4	no	—
177	#11924007	—	2	4	no	—
178	#11924005	—	2	4	no	—
179	#11924005	—	2	4	no	—
180	C₄×Dic₇₃	—	2	4	no	—
181	C₄×Dic₇₃	—	2	4	no	—
182	C₄×Dic₇₃	—	4	2	no	—
183	C₄×Dic₇₃	—	4	2	no	—
184	C₄×Dic₇₃	—	4	2	no	—
185	C₄×Dic₇₃	—	4	2	no	—
186	C₄×Dic₇₃	—	4	2	no	—
187	C₄×Dic₇₃	—	4	2	no	—
188	C₄×Dic₇₃	C₄⋊C₄	1	4	yes	—
189	C₄×Dic₇₃	C₄⋊C₄	1	4	yes	—
190	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
191	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
192	C₂²×C₄×C₇₃	—	2	1	no	—
193	C₂²×C₄×C₇₃	—	2	1	no	—
194	C₂²×C₄×C₇₃	—	2	1	no	—
195	C₂²×C₄×C₇₃	—	2	1	no	—
196	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₈×C₇₃	—	2	1	no	—
200	C₂×C₈×C₇₃	—	2	1	no	—
201	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
202	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
203	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
204	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₇₃	—	2	1	no	—
206	C₄⋊C₄×C₇₃	—	2	1	no	—
207	C₄⋊C₄×C₇₃	—	2	1	no	—
208	C₄⋊C₄×C₇₃	—	2	1	no	—
209	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
211	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
212	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
213	C₄²×C₇₃	—	4	2	no	—
214	C₄²×C₇₃	—	4	2	no	—
215	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
216	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
217	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
218	C₂²×D₇₃	—	2	1	no	—
219	C₂²×D₇₃	—	2	1	no	—
220	C₂²×D₇₃	—	2	1	no	—
221	C₂²×D₇₃	—	2	1	no	—
222	C₂²×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
223	C₂²×D₇₃	C₄×D₄	1	2	yes	—
224	C₂²×D₇₃	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₇₃	—	2	1	no	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	1	no	—
228	C₂×C₄×C₇₃	—	2	1	no	—
229	C₂×C₄×C₇₃	—	2	2	no	—
230	C₂×C₄×C₇₃	—	2	2	no	—
231	C₂×C₄×C₇₃	—	2	2	no	—
232	C₂×C₄×C₇₃	—	2	2	no	—
233	C₂×C₄×C₇₃	—	4	1	no	—
234	C₂×C₄×C₇₃	—	4	1	no	—
235	C₂×C₄×C₇₃	—	4	1	no	—
236	C₂×C₄×C₇₃	—	4	1	no	—
237	C₂×C₄×C₇₃	—	4	1	no	—
238	C₂×C₄×C₇₃	—	4	1	no	—
239	C₂×C₄×C₇₃	—	4	1	no	—
240	C₂×C₄×C₇₃	—	4	1	no	—
241	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
242	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
243	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
249	C₂×Dic₇₃	—	2	1	no	—
250	C₂×Dic₇₃	—	2	1	no	—
251	C₂×Dic₇₃	—	2	2	no	—
252	C₂×Dic₇₃	—	2	2	no	—
253	C₂×Dic₇₃	—	2	2	no	—
254	C₂×Dic₇₃	—	2	2	no	—
255	C₂×Dic₇₃	—	4	1	no	—
256	C₂×Dic₇₃	—	4	1	no	—
257	C₂×Dic₇₃	—	4	1	no	—
258	C₂×Dic₇₃	—	4	1	no	—
259	C₂×Dic₇₃	—	4	1	no	—
260	C₂×Dic₇₃	—	4	1	no	—
261	C₂×Dic₇₃	—	4	1	no	—
262	C₂×Dic₇₃	—	4	1	no	—
263	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
264	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
265	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
266	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
267	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
268	C₂×Dic₇₃	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×Dic₇₃	#137	1	2	yes	—
270	C₄×D₇₃	—	2	8	no	—
271	C₄×D₇₃	—	4	4	no	—
272	C₄×D₇₃	—	4	8	no	—
273	C₄×D₇₃	—	4	8	no	—
274	C₄×D₇₃	C₂×C₄²	1	4	yes	—
275	C₄×D₇₃	#117	1	4	yes	—
276	C₄×D₇₃	C₄×Q₈	1	4	yes	—
277	C₄×D₇₃	C₄×Q₈	1	4	yes	—
278	C₈×C₇₃	—	2	2	no	—
279	C₈×C₇₃	C₂×C₄²	1	4	yes	complemented
280	#10596831	—	2	2	no	—
281	#10596831	C₂×C₄²	1	4	yes	complemented
282	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
287	C₂²×C₇₃	#575	1	1	yes	characteristic
288	C₂²×C₇₃	#575	1	1	yes	characteristic
289	C₂×D₇₃	—	2	2	no	—
290	C₂×D₇₃	—	2	2	no	—
291	C₂×D₇₃	—	2	2	no	—
292	C₂×D₇₃	—	2	2	no	—
293	C₂×D₇₃	—	2	2	no	—
294	C₂×D₇₃	—	2	2	no	—
295	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
296	C₄×C₇₃	—	2	2	no	—
297	C₄×C₇₃	—	2	2	no	—
298	C₄×C₇₃	—	4	2	no	—
299	C₄×C₇₃	—	4	2	no	—
300	C₄×C₇₃	—	4	2	no	—
301	C₄×C₇₃	—	4	2	no	—
302	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
303	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
304	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
305	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
306	Dic₇₃	—	2	2	no	—
307	Dic₇₃	—	4	2	no	—
308	Dic₇₃	—	4	2	no	—
309	Dic₇₃	—	4	2	no	—
310	Dic₇₃	—	4	2	no	—
311	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
312	Dic₇₃	#428	1	4	yes	complemented
313	C₄×#428	—	73	1	no	maximal, Sylow
314	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
315	C₂×C₇₃	C₂×#428	1	1	yes	characteristic
316	C₂×C₇₃	#2911	1	1	yes	characteristic
317	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
320	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
321	D₇₃	—	2	4	no	—
322	C₂×#428	—	73	1	no	—
323	C₂×#428	—	73	1	no	—
324	C₂×C₄×M₁₆	—	73	1	no	—
325	C₄×#117	—	73	1	no	—
326	C₂×C₄×C₄⋊C₄	—	73	1	no	—
327	#1776	—	73	1	no	—
328	#1776	—	73	1	no	—
329	#1776	—	73	1	no	—
330	#1776	D₇₃	1	1	yes	characteristic, complemented
331	C₄×#107	—	73	1	no	—
332	C₄×#107	—	73	1	no	—
333	C₄×#106	—	73	1	no	—
334	C₄×#106	—	73	1	no	—
335	#1736	—	73	1	no	—
336	#1736	—	73	1	no	—
337	C₇₃	C₄×#428	1	1	yes	characteristic, complemented, Sylow
338	C₂²×M₁₆	—	73	1	no	—
339	C₂²×M₁₆	—	73	1	no	—
340	C₂×#117	—	73	1	no	—
341	C₂×#117	—	73	1	no	—
342	C₂²×C₄⋊C₄	—	73	1	no	—
343	C₂²×C₄⋊C₄	—	73	1	no	—
344	C₂²×C₄²	—	73	1	no	—
345	C₂²×C₄²	—	146	1	no	—
346	#428	—	73	8	no	—
347	#428	—	73	8	no	—
348	C₂×#107	—	73	1	no	—
349	C₂×#107	—	73	1	no	—
350	C₂×#107	—	73	1	no	—
351	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
352	C₂×#106	—	73	1	no	—
353	C₂×#106	—	73	1	no	—
354	C₂×#106	—	73	1	no	—
355	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
356	C₄×M₁₆	—	73	8	no	—
357	C₂×#97	—	73	1	no	—
358	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
359	C₂×C₄×C₈	—	73	1	no	—
360	C₂×C₄×C₈	—	73	1	no	—
361	C₄×C₄⋊C₄	—	73	1	no	—
362	C₄×C₄⋊C₄	—	73	1	no	—
363	C₄×C₄⋊C₄	—	73	1	no	—
364	C₄×C₄⋊C₄	—	73	1	no	—
365	C₄×C₄⋊C₄	—	73	1	no	—
366	C₄×C₄⋊C₄	—	73	1	no	—
367	C₄×C₄⋊C₄	—	146	1	no	—
368	C₄×C₄⋊C₄	—	146	1	no	—
369	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	—	146	1	no	—
372	C₄×C₂²⋊C₄	—	146	1	no	—
373	#376	—	146	1	no	—
374	C₂×#95	—	146	1	no	—
375	C₄³	—	146	1	no	—
376	#340	—	73	1	no	—
377	#340	—	73	1	no	—
378	#340	—	73	1	no	—
379	#340	—	73	1	no	—
380	#340	—	73	1	no	—
381	#340	—	73	1	no	—
382	#340	C₂×D₇₃	1	1	yes	characteristic
383	#340	C₂×D₇₃	1	1	yes	characteristic
384	C₂³×C₄	—	73	1	no	—
385	C₂³×C₄	—	73	1	no	—
386	C₂³×C₄	—	73	1	no	—
387	C₂³×C₄	—	146	1	no	—
388	C₂³×C₄	—	146	1	no	—
389	C₂×M₁₆	—	73	4	no	—
390	C₂×M₁₆	—	73	4	no	—
391	C₂×M₁₆	—	73	4	no	—
392	C₂×M₁₆	—	73	4	no	—
393	C₂×M₁₆	—	146	2	no	—
394	C₂×M₁₆	—	146	2	no	—
395	C₂²×C₈	—	73	1	no	—
396	C₂²×C₈	—	73	1	no	—
397	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
399	#117	—	73	4	no	—
400	#117	—	73	4	no	—
401	#117	—	146	2	no	—
402	#117	—	146	2	no	—
403	C₂×C₄⋊C₄	—	73	1	no	—
404	C₂×C₄⋊C₄	—	73	1	no	—
405	C₂×C₄⋊C₄	—	73	1	no	—
406	C₂×C₄⋊C₄	—	73	1	no	—
407	C₂×C₄⋊C₄	—	73	4	no	—
408	C₂×C₄⋊C₄	—	73	4	no	—
409	C₂×C₄⋊C₄	—	146	2	no	—
410	C₂×C₄⋊C₄	—	146	2	no	—
411	C₂×C₄⋊C₄	—	146	1	no	—
412	C₂×C₄⋊C₄	—	146	1	no	—
413	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	146	1	no	—
418	C₂×C₂²⋊C₄	—	146	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	292	4	no	—
422	C₂×C₄²	—	73	1	no	—
423	C₂×C₄²	—	73	1	no	—
424	C₂×C₄²	—	73	1	no	—
425	C₂×C₄²	—	73	4	no	—
426	C₂×C₄²	—	73	4	no	—
427	C₂×C₄²	—	146	1	no	—
428	C₂×C₄²	—	146	1	no	—
429	C₂×C₄²	—	146	1	no	—
430	C₂×C₄²	—	146	1	no	—
431	C₂×C₄²	—	146	1	no	—
432	C₂×C₄²	—	146	1	no	—
433	C₂×C₄²	—	146	1	no	—
434	C₂×C₄²	—	146	1	no	—
435	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
436	#107	—	73	4	no	—
437	#107	—	73	4	no	—
438	#107	—	73	4	no	—
439	#107	C₄×D₇₃	1	4	yes	complemented
440	#106	—	73	4	no	—
441	#106	—	73	4	no	—
442	#106	—	73	4	no	—
443	#106	C₄×D₇₃	1	4	yes	complemented
444	#97	—	73	4	no	—
445	#97	C₄×D₇₃	1	4	yes	complemented
446	C₄×C₈	—	73	4	no	—
447	C₄×C₈	—	73	4	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	146	1	no	—
451	#95	—	146	1	no	—
452	#95	—	146	1	no	—
453	#95	—	146	1	no	—
454	#95	—	146	1	no	—
455	#95	—	146	1	no	—
456	C₂⁴	—	73	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	292	1	no	—
462	C₂²×C₄	—	292	1	no	—
463	C₂²×C₄	—	292	2	no	—
464	C₂²×C₄	—	292	2	no	—
465	C₂²×C₄	—	292	2	no	—
466	C₂²×C₄	—	292	2	no	—
467	C₂²×C₄	—	73	4	no	—
468	C₂²×C₄	—	73	1	no	—
469	C₂²×C₄	—	73	1	no	—
470	C₂²×C₄	—	73	2	no	—
471	C₂²×C₄	—	73	2	no	—
472	C₂²×C₄	—	73	2	no	—
473	C₂²×C₄	—	73	2	no	—
474	C₂²×C₄	—	73	2	no	—
475	C₂²×C₄	—	73	2	no	—
476	C₂²×C₄	—	73	1	no	—
477	C₂²×C₄	—	73	4	no	—
478	C₂²×C₄	—	146	4	no	—
479	C₂²×C₄	—	146	4	no	—
480	C₂²×C₄	—	146	2	no	—
481	C₂²×C₄	—	146	2	no	—
482	C₂²×C₄	—	146	1	no	—
483	C₂²×C₄	—	146	1	no	—
484	C₂²×C₄	—	146	1	no	—
485	C₂²×C₄	—	146	1	no	—
486	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
488	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
489	M₁₆	—	73	16	no	—
490	M₁₆	—	146	8	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	73	2	no	—
494	C₂×C₈	—	73	2	no	—
495	C₂×C₈	—	73	2	no	—
496	C₂×C₈	—	73	2	no	—
497	C₂×C₈	—	146	1	no	—
498	C₂×C₈	—	146	1	no	—
499	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
500	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
501	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
502	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	73	2	no	—
508	C₄⋊C₄	—	73	2	no	—
509	C₄⋊C₄	—	73	2	no	—
510	C₄⋊C₄	—	73	2	no	—
511	C₄⋊C₄	—	146	4	no	—
512	C₄⋊C₄	—	146	4	no	—
513	C₄⋊C₄	—	146	1	no	—
514	C₄⋊C₄	—	146	1	no	—
515	C₄⋊C₄	—	146	1	no	—
516	C₄⋊C₄	—	146	1	no	—
517	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
518	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
519	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
520	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
521	C₂²⋊C₄	—	146	4	no	—
522	C₂²⋊C₄	—	146	4	no	—
523	C₄²	—	4	2	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	292	2	no	—
526	C₄²	—	292	2	no	—
527	C₄²	—	292	2	no	—
528	C₄²	—	292	2	no	—
529	C₄²	—	292	2	no	—
530	C₄²	—	292	2	no	—
531	C₄²	—	73	4	no	—
532	C₄²	—	73	4	no	—
533	C₄²	—	73	2	no	—
534	C₄²	—	73	2	no	—
535	C₄²	—	146	4	no	—
536	C₄²	—	146	4	no	—
537	C₄²	C₂×C₄×D₇₃	1	2	yes	—
538	C₄²	Q₈×D₇₃	1	2	yes	—
539	C₂³	—	73	2	no	—
540	C₂³	—	73	2	no	—
541	C₂³	—	73	2	no	—
542	C₂³	—	146	1	no	—
543	C₂³	—	146	1	no	—
544	C₂³	—	146	1	no	—
545	C₂³	—	146	1	no	—
546	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	292	4	no	—
564	C₂×C₄	—	292	8	no	—
565	C₂×C₄	—	292	8	no	—
566	C₂×C₄	—	292	1	no	—
567	C₂×C₄	—	292	1	no	—
568	C₂×C₄	—	292	1	no	—
569	C₂×C₄	—	292	1	no	—
570	C₂×C₄	—	292	1	no	—
571	C₂×C₄	—	292	1	no	—
572	C₂×C₄	—	292	1	no	—
573	C₂×C₄	—	292	1	no	—
574	C₂×C₄	—	73	2	no	—
575	C₂×C₄	—	73	2	no	—
576	C₂×C₄	—	73	2	no	—
577	C₂×C₄	—	73	2	no	—
578	C₂×C₄	—	73	2	no	—
579	C₂×C₄	—	73	2	no	—
580	C₂×C₄	—	73	4	no	—
581	C₂×C₄	—	73	4	no	—
582	C₂×C₄	—	73	4	no	—
583	C₂×C₄	—	73	4	no	—
584	C₂×C₄	—	73	2	no	—
585	C₂×C₄	—	146	8	no	—
586	C₂×C₄	—	146	2	no	—
587	C₂×C₄	—	146	2	no	—
588	C₂×C₄	—	146	2	no	—
589	C₂×C₄	—	146	2	no	—
590	C₂×C₄	—	146	1	no	—
591	C₂×C₄	—	146	1	no	—
592	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
593	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
594	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
596	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
597	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
598	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
599	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
600	C₈	—	2	2	no	—
601	C₈	—	73	4	no	—
602	C₈	—	146	2	no	—
603	C₈	C₄²×D₇₃	1	4	yes	complemented
604	C₂²	—	73	4	no	—
605	C₂²	—	146	2	no	—
606	C₂²	—	146	2	no	—
607	C₂²	—	146	2	no	—
608	C₂²	—	146	2	no	—
609	C₂²	—	146	2	no	—
610	C₂²	—	146	2	no	—
611	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
612	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
613	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
614	C₂²	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
615	C₂²	#137×D₇₃	1	1	yes	characteristic
616	C₂²	#17989383	1	1	yes	characteristic
617	C₂²	#17989386	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	292	2	no	—
625	C₄	—	292	2	no	—
626	C₄	—	292	2	no	—
627	C₄	—	292	2	no	—
628	C₄	—	73	4	no	—
629	C₄	—	73	4	no	—
630	C₄	—	146	2	no	—
631	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
632	C₄	#117×D₇₃	1	1	yes	characteristic
633	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
634	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
635	C₂	—	146	4	no	—
636	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
637	C₂	#428×D₇₃	1	1	yes	characteristic
638	C₂	#22618518	1	1	yes	characteristic
639	C₂	#22618736	1	1	yes	characteristic
640	C₂	#22618742	1	1	yes	characteristic
641	C₂	#22618747	1	1	yes	characteristic
642	C₂	#22618753	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1776	C₂
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1776	D₇₃
hypocenter	C₇₃	C₄×#428
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1776

Complements

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

N	H ≅ G/N	type
6. #22609829	C₂	semidirect
7. #22609829	C₂	semidirect
8. #22609828	C₂	semidirect
9. #107×Dic₇₃	C₂	semidirect
10. #22609823	C₂	semidirect
11. #106×Dic₇₃	C₂	semidirect
12. #22609819	C₂	semidirect
15. C₇₃×#1776	C₂	semidirect
24. #17988628	C₄	semidirect
25. #17988626	C₄	semidirect
32. #17988539	C₄	semidirect
105. #14556525	C₂×C₄	semidirect
106. #14556524	C₂×C₄	semidirect
107. #14556524	C₂×C₄	semidirect
108. #14556523	C₂×C₄	semidirect
109. #14556522	C₂×C₄	semidirect
110. #14556522	C₂×C₄	semidirect
111. #14556502	C₂×C₄	semidirect
112. C₈×Dic₇₃	C₂×C₄	semidirect
113. C₈×Dic₇₃	C₂×C₄	semidirect
129. #107×C₇₃	C₂×C₄	semidirect
130. #106×C₇₃	C₂×C₄	semidirect
131. #97×C₇₃	C₂×C₄	semidirect
161. #11924011	C₄²	semidirect
279. C₈×C₇₃	C₂×C₄²	semidirect
281. #10596831	C₂×C₄²	semidirect
312. Dic₇₃	#428	semidirect
330. #1776	D₇₃	semidirect
337. C₇₃	C₄×#428	semidirect
439. #107	C₄×D₇₃	semidirect
443. #106	C₄×D₇₃	semidirect
445. #97	C₄×D₇₃	semidirect
603. C₈	C₄²×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988628	2
C₂×#17988626	2
C₂×#17988539	2
C₄×#14556549	2
C₄×C₄⋊C₄×D₇₃	2
#22609829	2
#22609828	2
#107×Dic₇₃	2
#22609823	2
#106×Dic₇₃	2
#22609819	2
#22609649	2
C₇₃×#1776	2
C₄×#428	73