Subgroups — #33095638

Order 18688.

1200 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988611	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14556550	C₂	1	1	yes	maximal, characteristic, complemented
3	#22610909	C₂	1	2	yes	maximal, complemented
4	#22610760	C₂	1	2	yes	maximal, complemented
5	#22610234	C₂	1	4	yes	maximal, complemented
6	#22609951	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11924012	C₂²	1	2	yes	—
9	C₂×#14556550	—	2	1	no	—
10	#17988611	—	2	1	no	—
11	#17988611	—	2	1	no	—
12	#17988611	C₂²	1	2	yes	—
13	#17988611	C₂²	1	2	yes	—
14	C₂×C₄⋊#10596831	—	2	1	no	—
15	C₂×C₄⋊#10596831	—	2	1	no	—
16	C₂×#14556518	C₂²	1	8	yes	—
17	C₄×C₄⋊Dic₇₃	—	2	1	no	—
18	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	—
19	C₄×C₂²⋊Dic₇₃	—	2	1	no	—
20	C₄×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
21	#17988433	—	2	1	no	—
22	C₄²×Dic₇₃	C₂²	1	2	yes	—
23	#17988346	C₂²	1	8	yes	—
24	#533×C₇₃	C₄	1	1	yes	characteristic, complemented
25	#533×C₇₃	C₄	1	1	yes	characteristic, complemented
26	#533×C₇₃	C₂²	1	1	yes	characteristic
27	#532×C₇₃	C₄	1	1	yes	characteristic, complemented
28	#532×C₇₃	C₄	1	1	yes	characteristic, complemented
29	#532×C₇₃	C₂²	1	1	yes	characteristic
30	#529×C₇₃	—	2	1	no	—
31	#529×C₇₃	—	2	1	no	—
32	#529×C₇₃	—	2	1	no	—
33	#529×C₇₃	—	2	1	no	—
34	#529×C₇₃	C₄	1	2	yes	complemented
35	#529×C₇₃	C₄	1	2	yes	complemented
36	#525×C₇₃	—	2	1	no	—
37	#525×C₇₃	—	2	1	no	—
38	#525×C₇₃	C₂²	1	2	yes	—
39	C₄×#41×C₇₃	—	2	1	no	—
40	C₄×#41×C₇₃	—	2	1	no	—
41	C₄×#41×C₇₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#11924012	—	2	2	no	—
44	C₂×#11924012	—	4	4	no	—
45	C₂×#11924012	C₂³	1	4	yes	—
46	C₂²×#10596831	—	2	2	no	—
47	#14556550	—	2	8	no	—
48	C₂×C₄⋊Dic₇₃	—	2	2	no	—
49	C₂×C₂²⋊Dic₇₃	—	2	2	no	—
50	C₂×C₄×Dic₇₃	—	2	2	no	—
51	C₂×C₄×Dic₇₃	—	2	2	no	—
52	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
53	C₄⋊#10596831	—	2	2	no	—
54	C₄⋊#10596831	—	2	2	no	—
55	C₄⋊#10596831	—	2	2	no	—
56	C₄⋊#10596831	—	2	2	no	—
57	#14556518	—	4	8	no	—
58	#14556498	—	2	2	no	—
59	#14556498	—	2	2	no	—
60	C₂×#41×C₇₃	—	2	1	no	—
61	C₂×#41×C₇₃	—	2	1	no	—
62	C₂×#41×C₇₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
69	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
70	#126×C₇₃	—	2	2	no	—
71	#126×C₇₃	—	2	2	no	—
72	#125×C₇₃	—	2	1	no	—
73	#125×C₇₃	—	2	1	no	—
74	#125×C₇₃	C₂×C₄	1	2	yes	—
75	#124×C₇₃	—	2	1	no	—
76	#124×C₇₃	—	2	1	no	—
77	#124×C₇₃	C₂×C₄	1	2	yes	—
78	#123×C₇₃	—	2	2	no	—
79	#123×C₇₃	—	2	2	no	—
80	#123×C₇₃	—	2	2	no	—
81	C₂²⋊Q₈×C₇₃	—	2	1	no	—
82	C₂²⋊Q₈×C₇₃	—	2	1	no	—
83	C₂²⋊Q₈×C₇₃	—	2	1	no	—
84	C₂²⋊Q₈×C₇₃	—	2	1	no	—
85	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
86	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
87	#121×C₇₃	—	2	1	no	—
88	#121×C₇₃	—	2	1	no	—
89	#121×C₇₃	—	2	1	no	—
90	#121×C₇₃	—	2	1	no	—
91	#121×C₇₃	C₂×C₄	1	2	yes	—
92	#121×C₇₃	C₂×C₄	1	2	yes	—
93	#120×C₇₃	—	2	2	no	—
94	C₄×Q₈×C₇₃	—	2	1	no	—
95	C₄×Q₈×C₇₃	—	2	1	no	—
96	C₄×Q₈×C₇₃	—	2	1	no	—
97	C₄×Q₈×C₇₃	—	2	1	no	—
98	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
100	C₄×D₄×C₇₃	—	2	2	no	—
101	C₄×D₄×C₇₃	—	2	2	no	—
102	C₄×D₄×C₇₃	—	2	2	no	—
103	C₄×D₄×C₇₃	—	2	2	no	—
104	C₄×D₄×C₇₃	—	2	2	no	—
105	C₄×D₄×C₇₃	—	2	2	no	—
106	C₄×D₄×C₇₃	—	2	1	no	—
107	C₄×D₄×C₇₃	—	2	1	no	—
108	C₄×D₄×C₇₃	—	2	1	no	—
109	C₄×D₄×C₇₃	—	2	1	no	—
110	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
111	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
112	#117×C₇₃	—	2	1	no	—
113	#117×C₇₃	—	2	1	no	—
114	#117×C₇₃	—	2	2	no	—
115	#117×C₇₃	—	2	2	no	—
116	#117×C₇₃	—	2	2	no	—
117	#117×C₇₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₇₃	—	2	2	no	—
119	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
131	C₂²×Dic₇₃	—	2	4	no	—
132	#11924012	—	2	8	no	—
133	#11924012	—	4	4	no	—
134	C₂×#10596831	—	2	4	no	—
135	C₂×#10596831	—	4	4	no	—
136	C₄⋊Dic₇₃	—	2	8	no	—
137	C₂²⋊Dic₇₃	—	2	8	no	—
138	C₄×Dic₇₃	—	2	8	no	—
139	C₄×Dic₇₃	—	2	4	no	—
140	C₄×Dic₇₃	—	2	4	no	—
141	C₄×Dic₇₃	—	4	4	no	—
142	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
143	#41×C₇₃	—	2	4	no	—
144	#41×C₇₃	—	2	4	no	—
145	#41×C₇₃	—	4	4	no	—
146	#41×C₇₃	—	4	4	no	—
147	C₂×Q₈×C₇₃	—	2	1	no	—
148	C₂×Q₈×C₇₃	—	2	1	no	—
149	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₇₃	—	2	2	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	—	2	2	no	—
153	C₂×D₄×C₇₃	—	2	1	no	—
154	C₂×D₄×C₇₃	—	2	1	no	—
155	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₇₃	—	2	4	no	—
157	C₂²×C₄×C₇₃	—	2	2	no	—
158	C₂²×C₄×C₇₃	—	2	2	no	—
159	C₂²×C₄×C₇₃	—	2	2	no	—
160	C₂²×C₄×C₇₃	—	2	2	no	—
161	C₂²×C₄×C₇₃	—	2	2	no	—
162	C₂²×C₄×C₇₃	—	4	2	no	—
163	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₇₃	—	2	1	no	—
182	C₄⋊C₄×C₇₃	—	2	1	no	—
183	C₄⋊C₄×C₇₃	—	2	1	no	—
184	C₄⋊C₄×C₇₃	—	2	1	no	—
185	C₄⋊C₄×C₇₃	—	2	2	no	—
186	C₄⋊C₄×C₇₃	—	2	2	no	—
187	C₄⋊C₄×C₇₃	—	2	2	no	—
188	C₄⋊C₄×C₇₃	—	2	2	no	—
189	C₄⋊C₄×C₇₃	—	2	2	no	—
190	C₄⋊C₄×C₇₃	—	2	2	no	—
191	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
192	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
193	C₂²⋊C₄×C₇₃	—	2	2	no	—
194	C₂²⋊C₄×C₇₃	—	2	2	no	—
195	C₂²⋊C₄×C₇₃	—	2	2	no	—
196	C₂²⋊C₄×C₇₃	—	2	2	no	—
197	C₂²⋊C₄×C₇₃	—	2	2	no	—
198	C₂²⋊C₄×C₇₃	—	2	2	no	—
199	C₂²⋊C₄×C₇₃	—	2	2	no	—
200	C₂²⋊C₄×C₇₃	—	2	2	no	—
201	C₂²⋊C₄×C₇₃	—	2	2	no	—
202	C₄²×C₇₃	—	2	2	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₄²×C₇₃	—	2	2	no	—
205	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₇₃	—	2	2	no	—
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	2	2	no	—
224	C₂³×C₇₃	—	4	1	no	—
225	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₇₃	—	2	4	no	—
229	Q₈×C₇₃	—	4	2	no	—
230	Q₈×C₇₃	—	4	2	no	—
231	D₄×C₇₃	—	2	4	no	—
232	D₄×C₇₃	—	4	4	no	—
233	D₄×C₇₃	—	4	4	no	—
234	D₄×C₇₃	—	4	4	no	—
235	D₄×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	2	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	—	2	2	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	2	1	no	—
242	C₂×C₄×C₇₃	—	2	1	no	—
243	C₂×C₄×C₇₃	—	2	1	no	—
244	C₂×C₄×C₇₃	—	2	1	no	—
245	C₂×C₄×C₇₃	—	2	2	no	—
246	C₂×C₄×C₇₃	—	2	2	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	2	no	—
249	C₂×C₄×C₇₃	—	2	2	no	—
250	C₂×C₄×C₇₃	—	2	2	no	—
251	C₂×C₄×C₇₃	—	2	2	no	—
252	C₂×C₄×C₇₃	—	2	2	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	2	2	no	—
255	C₂×C₄×C₇₃	—	4	1	no	—
256	C₂×C₄×C₇₃	—	4	1	no	—
257	C₂×C₄×C₇₃	—	4	1	no	—
258	C₂×C₄×C₇₃	—	4	4	no	—
259	C₂×C₄×C₇₃	—	4	2	no	—
260	C₂×C₄×C₇₃	—	4	2	no	—
261	C₂×C₄×C₇₃	—	4	4	no	—
262	C₂×C₄×C₇₃	#104	1	4	yes	complemented
263	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
276	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
277	C₂×Dic₇₃	—	2	8	no	—
278	C₂×Dic₇₃	—	4	4	no	—
279	C₂×Dic₇₃	—	4	4	no	—
280	#10596831	—	4	4	no	—
281	C₂²×C₇₃	—	2	1	no	—
282	C₂²×C₇₃	—	2	1	no	—
283	C₂²×C₇₃	—	2	1	no	—
284	C₂²×C₇₃	—	2	1	no	—
285	C₂²×C₇₃	—	2	1	no	—
286	C₂²×C₇₃	—	2	1	no	—
287	C₂²×C₇₃	—	2	1	no	—
288	C₂²×C₇₃	—	4	4	no	—
289	C₂²×C₇₃	—	4	2	no	—
290	C₂²×C₇₃	—	4	2	no	—
291	C₂²×C₇₃	—	4	2	no	—
292	C₂²×C₇₃	C₂×#104	1	2	yes	—
293	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₇₃	#537	1	2	yes	—
295	C₄×C₇₃	—	2	1	no	—
296	C₄×C₇₃	—	2	1	no	—
297	C₄×C₇₃	—	2	1	no	—
298	C₄×C₇₃	—	2	1	no	—
299	C₄×C₇₃	—	2	1	no	—
300	C₄×C₇₃	—	2	1	no	—
301	C₄×C₇₃	—	2	1	no	—
302	C₄×C₇₃	—	4	2	no	—
303	C₄×C₇₃	—	4	2	no	—
304	C₄×C₇₃	—	4	2	no	—
305	C₄×C₇₃	C₂×#104	1	2	yes	—
306	C₄×C₇₃	C₂×#104	1	2	yes	—
307	C₄×C₇₃	#421	1	2	yes	—
308	C₄×C₇₃	#520	1	2	yes	—
309	C₄×C₇₃	#535	1	1	yes	characteristic
310	C₄×C₇₃	#536	1	1	yes	characteristic
311	Dic₇₃	—	4	8	no	—
312	#21856	—	73	1	no	maximal, Sylow
313	C₂×C₇₃	—	2	2	no	—
314	C₂×C₇₃	—	2	2	no	—
315	C₂×C₇₃	—	4	1	no	—
316	C₂×C₇₃	—	8	2	no	—
317	C₂×C₇₃	#2311	1	1	yes	characteristic
318	C₂×C₇₃	C₂²×#104	1	1	yes	characteristic
319	C₂×C₇₃	C₂×#421	1	1	yes	characteristic
320	#3444	D₇₃	1	1	yes	characteristic
321	C₂×#423	—	73	1	no	—
322	C₄×#117	—	73	1	no	—
323	#1994	—	73	2	no	—
324	#1962	—	73	2	no	—
325	#1871	—	73	4	no	—
326	#1806	—	73	4	no	—
327	C₇₃	#21856	1	1	yes	characteristic, complemented, Sylow
328	C₂²×M₁₆	—	73	2	no	—
329	#533	Dic₇₃	1	1	yes	characteristic, complemented
330	#533	Dic₇₃	1	1	yes	characteristic, complemented
331	#533	C₂×D₇₃	1	1	yes	characteristic
332	#532	Dic₇₃	1	1	yes	characteristic, complemented
333	#532	Dic₇₃	1	1	yes	characteristic, complemented
334	#532	C₂×D₇₃	1	1	yes	characteristic
335	#529	—	2	1	no	—
336	#529	—	2	1	no	—
337	#529	—	2	1	no	—
338	#529	—	2	1	no	—
339	#529	Dic₇₃	1	2	yes	complemented
340	#529	Dic₇₃	1	2	yes	complemented
341	#525	—	2	1	no	—
342	#525	—	2	1	no	—
343	#525	C₂×D₇₃	1	2	yes	—
344	C₄×#41	—	2	1	no	—
345	C₄×#41	—	2	1	no	—
346	C₄×#41	C₂×D₇₃	1	2	yes	—
347	C₂×#117	—	146	1	no	—
348	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
349	#423	—	73	2	no	—
350	#423	—	73	2	no	—
351	#423	—	146	1	no	—
352	#423	—	146	1	no	—
353	C₂×C₄⋊C₈	—	146	1	no	—
354	C₂×C₄⋊C₈	—	146	1	no	—
355	C₂×#104	—	73	8	no	—
356	C₄×C₄⋊C₄	—	73	2	no	—
357	C₄×C₄⋊C₄	—	146	1	no	—
358	C₄×C₂²⋊C₄	—	73	2	no	—
359	C₄×C₂²⋊C₄	—	146	1	no	—
360	#376	—	146	1	no	—
361	C₄³	—	73	2	no	—
362	#339	—	73	8	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂²×D₇₃	1	2	yes	—
366	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
367	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
368	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
369	C₂×M₁₆	—	292	4	no	—
370	C₂×M₁₆	—	73	4	no	—
371	C₂×M₁₆	—	146	2	no	—
372	C₂²×C₈	—	146	2	no	—
373	C₄⋊Q₈	C₂×Dic₇₃	1	1	yes	characteristic
374	C₄⋊Q₈	C₂×Dic₇₃	1	1	yes	characteristic
375	C₄⋊Q₈	C₂×Dic₇₃	1	1	yes	characteristic
376	#127	C₂×Dic₇₃	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	C₂×Dic₇₃	1	2	yes	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	C₂×Dic₇₃	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	C₂×Dic₇₃	1	2	yes	—
393	C₂²⋊Q₈	C₂×Dic₇₃	1	2	yes	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	C₂×Dic₇₃	1	2	yes	—
399	#121	C₂×Dic₇₃	1	2	yes	—
400	#120	—	2	2	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	C₂×Dic₇₃	1	2	yes	—
406	C₄×Q₈	C₂×Dic₇₃	1	2	yes	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂×Dic₇₃	1	2	yes	—
418	C₄×D₄	C₂×Dic₇₃	1	2	yes	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	146	8	no	—
425	#117	C₂²×D₇₃	1	2	yes	—
426	C₂×C₄⋊C₄	—	146	2	no	—
427	C₂×C₂²⋊C₄	—	146	2	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	73	4	no	—
430	C₂×C₄²	—	146	2	no	—
431	C₂×C₄²	—	146	2	no	—
432	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
433	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
434	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
435	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
436	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
437	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
438	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
439	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
440	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
441	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
442	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
443	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
444	C₄⋊C₈	—	146	2	no	—
445	C₄⋊C₈	—	146	2	no	—
446	C₄⋊C₈	—	146	2	no	—
447	C₄⋊C₈	—	146	2	no	—
448	#104	—	292	8	no	—
449	#95	—	146	2	no	—
450	#95	—	146	2	no	—
451	C₂⁴	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	—	4	4	no	—
455	#41	—	4	4	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	C₂²×Dic₇₃	1	2	yes	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	C₂²×Dic₇₃	1	2	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	146	4	no	—
473	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
479	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
490	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
491	M₁₆	—	292	4	no	—
492	M₁₆	—	146	8	no	—
493	C₂×C₈	—	292	4	no	—
494	C₂×C₈	—	146	4	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	146	8	no	—
506	C₄⋊C₄	C₂²×Dic₇₃	1	2	yes	—
507	C₄⋊C₄	C₂²×Dic₇₃	1	2	yes	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	146	8	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	292	4	no	—
522	C₄²	—	146	8	no	—
523	C₄²	—	146	4	no	—
524	C₄²	—	146	4	no	—
525	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
526	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
527	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
528	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
529	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
530	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
531	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
532	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
533	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
534	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
535	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
536	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
537	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
538	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
539	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
540	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
546	C₂³	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
547	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
548	Q₈	—	2	4	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	2	no	—
551	D₄	—	2	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	292	4	no	—
583	C₂×C₄	—	292	4	no	—
584	C₂×C₄	—	146	8	no	—
585	C₂×C₄	#14556518	1	4	yes	complemented
586	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
587	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
588	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
590	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
594	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
598	C₂×C₄	#14556637	1	2	yes	—
599	C₂×C₄	#14556638	1	2	yes	—
600	C₈	—	292	4	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	C₂×#14556518	1	2	yes	—
613	C₂²	C₂²×C₂²⋊Dic₇₃	1	1	yes	characteristic
614	C₂²	#17989165	1	2	yes	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	292	8	no	—
626	C₄	C₂×#14556518	1	2	yes	—
627	C₄	C₂×#14556518	1	2	yes	—
628	C₄	#17988604	1	2	yes	—
629	C₄	#17989070	1	2	yes	—
630	C₄	#17989151	1	1	yes	characteristic
631	C₄	#17989158	1	1	yes	characteristic
632	C₂	—	2	2	no	—
633	C₂	—	2	2	no	—
634	C₂	—	4	1	no	—
635	C₂	—	8	2	no	—
636	C₂	#22612523	1	1	yes	characteristic
637	C₂	C₂²×#14556518	1	1	yes	characteristic
638	C₂	C₂×#17988604	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting, prime radical	C₇₃×#3444	C₂
socle	C₂²×C₇₃	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#3444	D₇₃
hypocenter	C₇₃	#21856
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂×#17988611	C₂	semidirect
2. C₄×#14556550	C₂	semidirect
3. #22610909	C₂	semidirect
4. #22610760	C₂	semidirect
5. #22610234	C₂	semidirect
6. #22609951	C₂	semidirect
24. #533×C₇₃	C₄	semidirect
25. #533×C₇₃	C₄	semidirect
27. #532×C₇₃	C₄	semidirect
28. #532×C₇₃	C₄	semidirect
34. #529×C₇₃	C₄	semidirect
35. #529×C₇₃	C₄	semidirect
262. C₂×C₄×C₇₃	#104	semidirect
327. C₇₃	#21856	semidirect
329. #533	Dic₇₃	semidirect
330. #533	Dic₇₃	semidirect
332. #532	Dic₇₃	semidirect
333. #532	Dic₇₃	semidirect
339. #529	Dic₇₃	semidirect
340. #529	Dic₇₃	semidirect
585. C₂×C₄	#14556518	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988611	2
C₄×#14556550	2
#22610909	2
#22610760	2
#22610234	2
#22609951	2
C₇₃×#3444	2
#21856	73