Subgroups — #33084564

Order 18688.

1014 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988707	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988702	C₂	1	1	yes	maximal, characteristic
3	#22618729	C₂	1	1	yes	maximal, characteristic
4	#22618356	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609838	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609816	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609811	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609777	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609773	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609770	C₂	1	1	yes	maximal, characteristic, complemented
11	#22609766	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#14556517	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14556518	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556611	C₂²	1	1	yes	characteristic
17	C₂×#14556597	C₂²	1	1	yes	characteristic
18	C₂×#14556597	C₂²	1	1	yes	characteristic
19	C₄×#11924028	C₂²	1	1	yes	characteristic
20	#17988707	C₄	1	8	yes	complemented
21	#17988702	C₄	1	8	yes	complemented
22	#17988697	C₄	1	2	yes	complemented
23	#17988692	C₄	1	2	yes	complemented
24	#17988687	C₄	1	2	yes	complemented
25	#17988685	C₄	1	2	yes	complemented
26	C₂×#14556526	C₂²	1	1	yes	characteristic
27	C₂×#14556526	C₂²	1	1	yes	characteristic
28	#17988623	C₂²	1	1	yes	characteristic
29	C₂×#14556518	C₂²	1	1	yes	characteristic
30	C₂×#14556518	C₂²	1	1	yes	characteristic
31	C₂×#14556517	C₂²	1	1	yes	characteristic
32	C₂×#14556517	C₂²	1	1	yes	characteristic
33	#17988583	C₂²	1	1	yes	characteristic
34	#17988581	C₂²	1	1	yes	characteristic
35	#17988544	—	2	1	no	—
36	#17988544	—	2	1	no	—
37	#17988542	C₂²	1	1	yes	characteristic
38	#17988542	C₂²	1	1	yes	characteristic
39	C₄×#11924012	C₂²	1	1	yes	characteristic
40	#17988539	—	2	1	no	—
41	C₂×#14556502	C₂²	1	1	yes	characteristic
42	C₂×#14556501	C₂²	1	1	yes	characteristic
43	C₂×#14556501	C₂²	1	1	yes	characteristic
44	#97×D₇₃	—	2	1	no	—
45	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
47	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
48	#17988351	C₂²	1	1	yes	characteristic
49	#17988351	C₂²	1	1	yes	characteristic
50	#17988348	C₂²	1	1	yes	characteristic
51	#17988348	C₂²	1	1	yes	characteristic
52	#17988346	C₂²	1	1	yes	characteristic
53	#17988346	C₂²	1	1	yes	characteristic
54	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
55	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
56	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
57	#405×C₇₃	—	2	1	no	—
58	#405×C₇₃	—	2	1	no	—
59	#405×C₇₃	C₂²	1	1	yes	characteristic
60	#405×C₇₃	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₇₃	—	2	1	no	—
62	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
63	C₂×#97×C₇₃	—	2	1	no	—
64	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
65	C₂×#11924028	C₂³	1	1	yes	characteristic
66	#14556611	C₂×C₄	1	4	yes	—
67	#14556611	C₂×C₄	1	4	yes	—
68	C₂×#11924018	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924016	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924015	C₂×C₄	1	1	yes	characteristic
71	C₂×#11924013	C₂×C₄	1	1	yes	characteristic
72	#14556597	—	2	2	no	—
73	#14556597	—	2	2	no	—
74	#14556597	C₂×C₄	1	4	yes	complemented
75	#14556597	C₂×C₄	1	4	yes	complemented
76	C₂×#11924012	C₂³	1	1	yes	characteristic
77	C₂×#11924012	C₂³	1	1	yes	characteristic
78	C₂×#11924011	—	2	1	no	—
79	C₂×#11924011	—	2	1	no	—
80	C₂²×#10596831	C₂³	1	1	yes	characteristic
81	C₂²×#10596831	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₇₃	—	2	1	no	—
83	C₂×C₈×D₇₃	—	2	1	no	—
84	C₄×Dic₁₄₆	C₂×C₄	1	2	yes	—
85	C₄×D₂₉₂	C₂×C₄	1	2	yes	—
86	C₄×C₂²⋊D₇₃	—	2	2	no	—
87	#14556550	C₂³	1	1	yes	characteristic
88	#14556548	—	2	1	no	—
89	C₂×C₄×Dic₇₃	—	2	2	no	—
90	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
92	C₄²×D₇₃	—	2	1	no	—
93	#14556526	C₂×C₄	1	4	yes	complemented
94	#14556526	C₂×C₄	1	4	yes	complemented
95	#14556524	C₂×C₄	1	2	yes	—
96	#14556522	C₂×C₄	1	2	yes	—
97	#14556518	C₂×C₄	1	4	yes	complemented
98	#14556518	C₂×C₄	1	4	yes	complemented
99	#14556517	C₂×C₄	1	4	yes	complemented
100	#14556517	C₂×C₄	1	4	yes	complemented
101	#14556515	C₂×C₄	1	2	yes	—
102	#14556514	C₂×C₄	1	2	yes	—
103	#14556512	C₂×C₄	1	2	yes	—
104	#14556511	C₂×C₄	1	2	yes	—
105	#14556502	—	2	1	no	—
106	#14556502	C₂×C₄	1	2	yes	—
107	#14556502	C₂×C₄	1	2	yes	—
108	#14556501	—	2	1	no	—
109	#14556501	—	2	1	no	—
110	#14556501	—	2	2	no	—
111	#14556501	C₂×C₄	1	4	yes	complemented
112	C₄×#10596831	—	2	1	no	—
113	C₈×Dic₇₃	—	2	1	no	—
114	C₈×Dic₇₃	—	2	1	no	—
115	C₈×Dic₇₃	—	2	2	no	—
116	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
117	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
118	#131×C₇₃	—	2	2	no	—
119	#131×C₇₃	—	2	2	no	—
120	#131×C₇₃	C₂×C₄	1	4	yes	complemented
121	#131×C₇₃	C₂×C₄	1	4	yes	complemented
122	C₂×M₁₆×C₇₃	—	2	1	no	—
123	C₂×M₁₆×C₇₃	—	2	1	no	—
124	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₇₃	—	2	1	no	—
127	C₂²×C₈×C₇₃	—	2	1	no	—
128	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₇₃	—	2	2	no	—
132	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
133	#117×C₇₃	—	2	1	no	—
134	#117×C₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇₃	—	2	1	no	—
136	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
137	#97×C₇₃	—	2	1	no	—
138	#97×C₇₃	—	2	1	no	—
139	#97×C₇₃	—	2	1	no	—
140	#97×C₇₃	D₄	1	1	yes	characteristic
141	#97×C₇₃	D₄	1	1	yes	characteristic
142	#97×C₇₃	D₄	1	1	yes	characteristic
143	#97×C₇₃	D₄	1	1	yes	characteristic
144	C₄×C₈×C₇₃	—	2	1	no	—
145	C₄×C₈×C₇₃	—	2	1	no	—
146	C₄×C₈×C₇₃	—	2	1	no	—
147	#11924028	—	2	1	no	—
148	#11924028	—	2	1	no	—
149	#11924028	C₂²×C₄	1	2	yes	—
150	#11924028	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₇₃	—	2	1	no	—
154	C₂²×Dic₇₃	—	2	1	no	—
155	C₂²×Dic₇₃	—	2	1	no	—
156	C₂×C₄×D₇₃	—	2	1	no	—
157	C₂×C₄×D₇₃	—	2	2	no	—
158	#11924018	C₄²	1	4	yes	complemented
159	#11924016	C₄²	1	4	yes	complemented
160	#11924015	C₄²	1	4	yes	complemented
161	#11924013	C₄²	1	4	yes	complemented
162	#11924012	—	2	1	no	—
163	#11924012	—	2	1	no	—
164	#11924012	C₂²×C₄	1	2	yes	—
165	#11924012	C₂²×C₄	1	2	yes	—
166	#11924011	—	2	4	no	—
167	#11924011	—	2	4	no	—
168	C₂×#10596831	—	2	1	no	—
169	C₂×#10596831	—	2	1	no	—
170	C₂×#10596831	—	2	1	no	—
171	C₂×#10596831	—	2	1	no	—
172	C₂×#10596831	C₂²×C₄	1	2	yes	—
173	C₂×#10596831	C₂²×C₄	1	2	yes	—
174	C₂×#10596831	C₂²×C₄	1	2	yes	—
175	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
176	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
177	C₈×D₇₃	—	2	4	no	—
178	C₈×D₇₃	—	2	4	no	—
179	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
180	#11924007	—	2	2	no	—
181	C₂²⋊Dic₇₃	—	2	1	no	—
182	#11924005	—	2	2	no	—
183	C₄×Dic₇₃	—	2	2	no	—
184	C₄×Dic₇₃	—	2	1	no	—
185	C₄×Dic₇₃	—	2	1	no	—
186	C₄×Dic₇₃	—	2	1	no	—
187	C₄×Dic₇₃	—	4	4	no	—
188	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
189	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
190	#41×C₇₃	—	2	1	no	—
191	#41×C₇₃	—	2	1	no	—
192	#41×C₇₃	C₂²×C₄	1	2	yes	—
193	#41×C₇₃	C₂²×C₄	1	2	yes	—
194	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₇₃	—	2	1	no	—
196	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	—	2	1	no	—
198	C₂²×C₄×C₇₃	—	2	2	no	—
199	C₂²×C₄×C₇₃	#41	1	2	yes	—
200	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
201	M₁₆×C₇₃	—	2	1	no	—
202	M₁₆×C₇₃	—	2	1	no	—
203	M₁₆×C₇₃	—	2	4	no	—
204	M₁₆×C₇₃	—	2	4	no	—
205	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
206	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
207	C₂×C₈×C₇₃	—	2	1	no	—
208	C₂×C₈×C₇₃	—	2	1	no	—
209	C₂×C₈×C₇₃	—	2	4	no	—
210	C₂×C₈×C₇₃	—	2	4	no	—
211	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
213	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
217	C₂×C₈×C₇₃	#41	1	2	yes	—
218	C₂×C₈×C₇₃	#41	1	2	yes	—
219	C₄⋊C₄×C₇₃	—	2	2	no	—
220	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
221	C₂²⋊C₄×C₇₃	—	2	1	no	—
222	C₂²⋊C₄×C₇₃	—	2	2	no	—
223	C₄²×C₇₃	—	2	2	no	—
224	C₄²×C₇₃	—	2	1	no	—
225	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
226	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₇₃	—	2	1	no	—
229	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
230	C₂²×D₇₃	—	2	1	no	—
231	Q₈×C₇₃	—	2	1	no	—
232	Q₈×C₇₃	C₂×C₄²	1	2	yes	—
233	D₄×C₇₃	—	2	2	no	—
234	D₄×C₇₃	—	2	2	no	—
235	D₄×C₇₃	—	2	1	no	—
236	D₄×C₇₃	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₇₃	—	2	1	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	—	4	2	no	—
242	C₂×C₄×C₇₃	—	8	2	no	—
243	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₇₃	—	2	2	no	—
252	C₂²⋊D₇₃	—	2	2	no	—
253	C₂×Dic₇₃	—	2	4	no	—
254	C₂×Dic₇₃	—	2	1	no	—
255	C₂×Dic₇₃	—	2	2	no	—
256	C₂×Dic₇₃	—	2	2	no	—
257	C₂×Dic₇₃	—	2	2	no	—
258	C₂×Dic₇₃	—	4	2	no	—
259	D₂₉₂	—	2	1	no	—
260	D₂₉₂	C₂×C₄²	1	2	yes	—
261	C₄×D₇₃	—	2	2	no	—
262	C₄×D₇₃	—	2	2	no	—
263	C₄×D₇₃	—	8	2	no	—
264	Dic₁₄₆	—	2	1	no	—
265	Dic₁₄₆	C₂×C₄²	1	2	yes	—
266	C₈×C₇₃	—	2	2	no	—
267	C₈×C₇₃	—	2	2	no	—
268	C₈×C₇₃	C₄×D₄	1	2	yes	—
269	C₈×C₇₃	C₄×D₄	1	2	yes	—
270	C₈×C₇₃	C₄×D₄	1	2	yes	—
271	C₈×C₇₃	C₄×D₄	1	2	yes	—
272	#10596831	—	2	2	no	—
273	#10596831	—	2	2	no	—
274	#10596831	—	2	2	no	—
275	#10596831	C₂×C₄²	1	2	yes	—
276	#10596831	C₂×C₄²	1	2	yes	—
277	C₂²×C₇₃	—	2	2	no	—
278	C₂²×C₇₃	—	2	2	no	—
279	C₂²×C₇₃	—	4	2	no	—
280	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
282	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
283	C₂×D₇₃	—	2	2	no	—
284	C₂×D₇₃	—	4	2	no	—
285	C₄×C₇₃	—	2	2	no	—
286	C₄×C₇₃	—	2	2	no	—
287	C₄×C₇₃	—	2	2	no	—
288	C₄×C₇₃	—	4	2	no	—
289	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
290	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
293	Dic₇₃	—	2	4	no	—
294	Dic₇₃	—	2	2	no	—
295	Dic₇₃	—	4	2	no	—
296	Dic₇₃	—	4	2	no	—
297	#20512	—	73	1	no	maximal, Sylow
298	C₂×C₇₃	—	2	1	no	—
299	C₂×C₇₃	—	2	1	no	—
300	C₂×C₇₃	—	4	2	no	—
301	C₂×C₇₃	C₄²×D₄	1	1	yes	characteristic
302	C₂×C₇₃	#2956	1	2	yes	—
303	D₇₃	—	4	2	no	—
304	C₂×#444	—	73	1	no	—
305	C₂×#443	—	73	1	no	—
306	#2943	—	73	1	no	—
307	#2875	—	73	1	no	—
308	#2875	D₇₃	1	1	yes	characteristic, complemented
309	#1778	—	73	1	no	—
310	#1773	—	73	1	no	—
311	#1772	—	73	1	no	—
312	#1765	—	73	1	no	—
313	#1765	—	73	1	no	—
314	#1764	—	73	1	no	—
315	#1764	—	73	1	no	—
316	C₄×#104	—	73	1	no	—
317	C₄×#104	—	73	1	no	—
318	C₄×#97	—	73	1	no	—
319	C₇₃	#20512	1	1	yes	characteristic, complemented, Sylow
320	C₂×#135	—	73	1	no	—
321	C₂×#131	—	73	1	no	—
322	C₂×#131	—	73	1	no	—
323	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
324	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
325	C₄×#41	—	73	1	no	—
326	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
327	#444	—	73	8	no	—
328	#443	—	73	8	no	—
329	#442	—	73	2	no	—
330	#441	—	73	2	no	—
331	#440	—	73	2	no	—
332	#440	—	73	2	no	—
333	C₂×#108	—	73	1	no	—
334	C₂×#108	—	73	1	no	—
335	#427	—	73	1	no	—
336	C₂×#104	—	73	1	no	—
337	C₂×#104	—	73	1	no	—
338	C₂×#104	—	73	1	no	—
339	C₂×#104	—	73	1	no	—
340	#416	—	73	1	no	—
341	#416	—	73	1	no	—
342	#405	—	2	1	no	—
343	#405	—	2	1	no	—
344	#405	—	73	1	no	—
345	#405	—	73	1	no	—
346	#405	—	146	1	no	—
347	#405	—	146	1	no	—
348	#405	C₂×D₇₃	1	1	yes	characteristic
349	#405	C₂×D₇₃	1	1	yes	characteristic
350	C₄×M₁₆	—	2	1	no	—
351	C₄×M₁₆	—	73	1	no	—
352	C₄×M₁₆	—	146	1	no	—
353	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
354	C₂×#97	—	2	1	no	—
355	C₂×#97	—	73	1	no	—
356	C₂×#97	—	73	1	no	—
357	C₂×#97	—	73	1	no	—
358	C₂×#97	—	146	1	no	—
359	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
360	C₂×C₄×C₈	—	73	1	no	—
361	C₂×C₄×C₈	—	73	1	no	—
362	C₄³	—	73	1	no	—
363	#341	—	73	1	no	—
364	#341	—	73	1	no	—
365	#339	—	73	1	no	—
366	#339	—	73	1	no	—
367	#339	—	73	1	no	—
368	#339	—	73	1	no	—
369	C₂×#41	—	73	1	no	—
370	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
371	#135	—	73	4	no	—
372	#135	—	73	4	no	—
373	C₂×Q₁₆	—	73	1	no	—
374	C₂×SD₁₆	—	73	1	no	—
375	C₂×SD₁₆	—	73	1	no	—
376	C₂×D₈	—	73	1	no	—
377	#131	—	2	2	no	—
378	#131	—	2	2	no	—
379	#131	—	73	4	no	—
380	#131	—	73	4	no	—
381	#131	—	146	2	no	—
382	#131	—	146	2	no	—
383	#131	C₄×D₇₃	1	4	yes	complemented
384	#131	C₄×D₇₃	1	4	yes	complemented
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	73	1	no	—
388	C₂×M₁₆	—	73	1	no	—
389	C₂×M₁₆	—	146	1	no	—
390	C₂×M₁₆	—	146	1	no	—
391	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
392	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	73	1	no	—
396	C₂²×C₈	—	73	1	no	—
397	C₂²×C₈	—	146	1	no	—
398	C₂²×C₈	—	146	1	no	—
399	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
401	C₄×Q₈	—	73	2	no	—
402	C₄×Q₈	C₄×D₇₃	1	2	yes	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	73	2	no	—
405	C₄×D₄	—	146	2	no	—
406	C₄×D₄	C₄×D₇₃	1	2	yes	—
407	#117	—	2	1	no	—
408	#117	—	73	1	no	—
409	#117	—	146	1	no	—
410	#117	C₂²×D₇₃	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	73	1	no	—
413	C₂×C₄²	—	73	1	no	—
414	C₂×C₄²	—	146	2	no	—
415	C₂×C₄²	—	146	1	no	—
416	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
417	#108	—	73	4	no	—
418	#108	—	73	4	no	—
419	#107	—	73	2	no	—
420	#106	—	73	2	no	—
421	#104	—	73	4	no	—
422	#104	—	73	4	no	—
423	#104	—	73	4	no	—
424	#104	—	73	4	no	—
425	#103	—	73	2	no	—
426	#103	—	73	2	no	—
427	#102	—	73	2	no	—
428	#102	—	73	2	no	—
429	#97	—	2	1	no	—
430	#97	—	2	1	no	—
431	#97	—	2	1	no	—
432	#97	—	73	4	no	—
433	#97	—	73	2	no	—
434	#97	—	73	2	no	—
435	#97	—	146	1	no	—
436	#97	—	146	1	no	—
437	#97	—	146	2	no	—
438	#97	—	146	1	no	—
439	#97	C₂²⋊D₇₃	1	1	yes	characteristic
440	#97	C₂²⋊D₇₃	1	1	yes	characteristic
441	#97	C₂²⋊D₇₃	1	1	yes	characteristic
442	#97	C₂²⋊D₇₃	1	1	yes	characteristic
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	—	73	4	no	—
447	C₄×C₈	—	146	1	no	—
448	C₄×C₈	—	146	1	no	—
449	C₄×C₈	—	146	2	no	—
450	C₄×C₈	—	146	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	73	2	no	—
454	#41	—	73	2	no	—
455	#41	—	146	1	no	—
456	#41	—	146	1	no	—
457	#41	C₂×C₄×D₇₃	1	2	yes	—
458	#41	C₂×C₄×D₇₃	1	2	yes	—
459	C₂×Q₈	—	73	1	no	—
460	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	73	1	no	—
463	C₂×D₄	—	146	1	no	—
464	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	146	1	no	—
468	C₂²×C₄	—	146	2	no	—
469	C₂²×C₄	—	146	1	no	—
470	C₂²×C₄	—	146	1	no	—
471	C₂²×C₄	#11924028	1	2	yes	—
472	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
473	Q₁₆	—	73	4	no	—
474	SD₁₆	—	73	4	no	—
475	SD₁₆	—	73	4	no	—
476	D₈	—	73	4	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	2	4	no	—
481	M₁₆	—	73	2	no	—
482	M₁₆	—	73	2	no	—
483	M₁₆	—	146	1	no	—
484	M₁₆	—	146	1	no	—
485	M₁₆	—	146	4	no	—
486	M₁₆	—	146	4	no	—
487	M₁₆	C₂×C₄×D₇₃	1	2	yes	—
488	M₁₆	C₂×C₄×D₇₃	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	73	2	no	—
494	C₂×C₈	—	73	1	no	—
495	C₂×C₈	—	73	1	no	—
496	C₂×C₈	—	73	2	no	—
497	C₂×C₈	—	73	2	no	—
498	C₂×C₈	—	146	1	no	—
499	C₂×C₈	—	146	1	no	—
500	C₂×C₈	—	146	1	no	—
501	C₂×C₈	—	146	1	no	—
502	C₂×C₈	—	146	4	no	—
503	C₂×C₈	—	146	4	no	—
504	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
505	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
506	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
507	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
508	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
509	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
510	C₂×C₈	#11924028	1	2	yes	—
511	C₂×C₈	#11924028	1	2	yes	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	73	2	no	—
514	C₄⋊C₄	—	146	2	no	—
515	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	146	1	no	—
519	C₂²⋊C₄	—	146	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	292	4	no	—
523	C₄²	—	73	2	no	—
524	C₄²	—	73	2	no	—
525	C₄²	—	146	2	no	—
526	C₄²	—	146	1	no	—
527	C₄²	—	146	1	no	—
528	C₄²	—	146	1	no	—
529	C₄²	C₂×C₄×D₇₃	1	2	yes	—
530	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
531	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	146	1	no	—
534	C₂³	C₂×#11924028	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	73	2	no	—
537	Q₈	—	146	1	no	—
538	Q₈	C₄²×D₇₃	1	2	yes	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	73	2	no	—
543	D₄	—	146	2	no	—
544	D₄	—	146	2	no	—
545	D₄	—	146	1	no	—
546	D₄	C₄²×D₇₃	1	2	yes	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	292	2	no	—
554	C₂×C₄	—	584	2	no	—
555	C₂×C₄	—	146	2	no	—
556	C₂×C₄	—	146	2	no	—
557	C₂×C₄	—	146	4	no	—
558	C₂×C₄	—	146	1	no	—
559	C₂×C₄	—	146	2	no	—
560	C₂×C₄	—	146	2	no	—
561	C₂×C₄	—	146	2	no	—
562	C₂×C₄	C₄×C₂²⋊D₇₃	1	2	yes	—
563	C₂×C₄	C₄×C₂²⋊D₇₃	1	2	yes	—
564	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
568	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
569	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	73	2	no	—
573	C₈	—	73	2	no	—
574	C₈	—	146	2	no	—
575	C₈	—	146	2	no	—
576	C₈	—	146	2	no	—
577	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
578	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
579	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
580	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	292	2	no	—
585	C₂²	—	146	2	no	—
586	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
587	C₂²	C₄×#11924028	1	1	yes	characteristic
588	C₂²	C₄×#11924028	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	292	2	no	—
594	C₄	—	292	2	no	—
595	C₄	—	146	4	no	—
596	C₄	—	146	2	no	—
597	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
598	C₄	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
599	C₄	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
600	C₄	C₄×#11924028	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	292	2	no	—
605	C₂	C₄²×C₂²⋊D₇₃	1	1	yes	characteristic
606	C₂	#22618838	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#2875	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#14556611	C₂²
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#2875	D₇₃
hypocenter	C₇₃	#20512
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2875

Complements

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

N	H ≅ G/N	type
4. #22618356	C₂	semidirect
5. #22609838	C₂	semidirect
6. #22609816	C₂	semidirect
7. #22609811	C₂	semidirect
8. #22609777	C₂	semidirect
9. #22609773	C₂	semidirect
10. #22609770	C₂	semidirect
11. #22609766	C₂	semidirect
12. C₄×#14556517	C₂	semidirect
13. C₄×#14556518	C₂	semidirect
14. #97×Dic₇₃	C₂	semidirect
15. C₇₃×#2875	C₂	semidirect
20. #17988707	C₄	semidirect
21. #17988702	C₄	semidirect
22. #17988697	C₄	semidirect
23. #17988692	C₄	semidirect
24. #17988687	C₄	semidirect
25. #17988685	C₄	semidirect
74. #14556597	C₂×C₄	semidirect
75. #14556597	C₂×C₄	semidirect
93. #14556526	C₂×C₄	semidirect
94. #14556526	C₂×C₄	semidirect
97. #14556518	C₂×C₄	semidirect
98. #14556518	C₂×C₄	semidirect
99. #14556517	C₂×C₄	semidirect
100. #14556517	C₂×C₄	semidirect
111. #14556501	C₂×C₄	semidirect
116. C₈×Dic₇₃	C₂×C₄	semidirect
120. #131×C₇₃	C₂×C₄	semidirect
121. #131×C₇₃	C₂×C₄	semidirect
158. #11924018	C₄²	semidirect
159. #11924016	C₄²	semidirect
160. #11924015	C₄²	semidirect
161. #11924013	C₄²	semidirect
308. #2875	D₇₃	semidirect
319. C₇₃	#20512	semidirect
383. #131	C₄×D₇₃	semidirect
384. #131	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×#17988707	2
C₂×#17988702	2
#22618729	2
#22618356	2
#22609838	2
#22609816	2
#22609811	2
#22609777	2
#22609773	2
#22609770	2
#22609766	2
C₄×#14556517	2
C₄×#14556518	2
#97×Dic₇₃	2
C₇₃×#2875	2
#20512	73