Subgroups — #33238688

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624642	C₂	1	1	yes	maximal, characteristic
2	#22623033	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17989003	C₂	1	1	yes	maximal, characteristic, complemented
4	#22611560	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611559	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611557	C₂	1	4	yes	maximal, complemented
7	C₂×#17988370	C₂	1	1	yes	maximal, characteristic, complemented
8	#350×D₇₃	C₂	1	4	yes	maximal, complemented
9	C₂×#350×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989423	C₄	1	1	yes	characteristic
11	#17989354	C₄	1	1	yes	characteristic
12	#17989353	—	2	2	no	—
13	#17989353	C₄	1	1	yes	characteristic
14	#17989353	C₄	1	1	yes	characteristic
15	#17989352	—	2	2	no	—
16	#17989352	C₄	1	4	yes	—
17	C₂×#14556597	—	2	2	no	—
18	C₂×#14556597	C₂²	1	1	yes	characteristic
19	C₂×#14556597	C₂²	1	1	yes	characteristic
20	#131×D₇₃	—	2	2	no	—
21	#131×D₇₃	C₂²	1	4	yes	—
22	#17989005	—	2	2	no	—
23	#17989003	—	2	2	no	—
24	#17989003	—	2	2	no	—
25	#17989003	—	2	2	no	—
26	C₂×#14556531	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14556531	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14556530	C₂²	1	2	yes	complemented
29	M₃₂×D₇₃	C₂²	1	4	yes	complemented
30	C₂×C₁₆×D₇₃	C₂²	1	2	yes	complemented
31	#17988372	C₂²	1	4	yes	complemented
32	#17988371	C₂²	1	4	yes	complemented
33	#17988370	C₂²	1	2	yes	complemented
34	#17988370	C₂²	1	2	yes	complemented
35	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#350×C₇₃	C₂²	1	2	yes	complemented
39	#350×C₇₃	C₂²	1	2	yes	complemented
40	#14556639	C₈	1	2	yes	—
41	#14556638	—	2	1	no	—
42	#14556638	C₈	1	2	yes	—
43	#14556637	—	2	1	no	—
44	#14556637	C₈	1	2	yes	—
45	#14556636	—	2	2	no	—
46	#14556636	C₈	1	2	yes	—
47	C₂×#11924028	—	2	2	no	—
48	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
49	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
50	#41×D₇₃	—	2	2	no	—
51	#41×D₇₃	C₂×C₄	1	4	yes	—
52	#14556599	—	2	2	no	—
53	#14556599	—	2	4	no	—
54	#14556599	—	2	4	no	—
55	#14556599	C₂×C₄	1	4	yes	—
56	#14556598	—	2	2	no	—
57	#14556598	C₂×C₄	1	4	yes	—
58	#14556597	—	2	2	no	—
59	#14556597	—	2	2	no	—
60	#14556597	—	2	4	no	—
61	#14556597	—	2	4	no	—
62	#14556597	—	2	1	no	—
63	#14556597	—	2	1	no	—
64	#14556597	C₂×C₄	1	2	yes	—
65	#14556597	D₄	1	2	yes	—
66	#14556597	D₄	1	2	yes	—
67	#14556597	D₄	1	2	yes	—
68	#14556597	D₄	1	2	yes	—
69	#14556597	C₂³	1	2	yes	—
70	C₂×#11924012	—	2	2	no	—
71	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
72	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
73	C₂×#11924011	—	2	4	no	—
74	C₂×#11924011	—	2	1	no	—
75	C₂×#11924011	C₂×C₄	1	2	yes	—
76	M₁₆×D₇₃	—	2	2	no	—
77	M₁₆×D₇₃	—	2	4	no	—
78	M₁₆×D₇₃	—	2	4	no	—
79	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
80	C₂×C₈×D₇₃	—	2	4	no	—
81	C₂×C₈×D₇₃	—	2	1	no	—
82	C₂×C₈×D₇₃	C₂³	1	2	yes	—
83	#14556531	—	2	1	no	—
84	#14556531	—	2	1	no	—
85	#14556531	—	2	1	no	—
86	#14556531	C₂³	1	2	yes	—
87	#14556530	—	2	4	no	—
88	#14556530	—	2	4	no	—
89	C₂×#11924003	—	2	1	no	—
90	C₂×#11924003	C₂³	1	2	yes	—
91	C₁₆×D₇₃	—	2	4	no	—
92	C₁₆×D₇₃	—	2	4	no	—
93	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
94	#131×C₇₃	—	2	1	no	—
95	#131×C₇₃	—	2	1	no	—
96	#131×C₇₃	C₂×C₄	1	2	yes	—
97	#131×C₇₃	C₂³	1	2	yes	—
98	C₂×M₁₆×C₇₃	—	2	1	no	—
99	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	—	2	1	no	—
101	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	M₃₂×C₇₃	—	2	1	no	—
103	M₃₂×C₇₃	C₂³	1	2	yes	—
104	C₂×C₁₆×C₇₃	—	2	1	no	—
105	C₂×C₁₆×C₇₃	—	2	1	no	—
106	C₂×C₁₆×C₇₃	—	2	1	no	—
107	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
109	#11924029	—	2	2	no	—
110	#11924029	C₂×C₈	1	4	yes	—
111	#11924028	—	2	1	no	—
112	#11924028	—	2	1	no	—
113	#11924028	—	2	4	no	—
114	#11924028	—	2	2	no	—
115	#11924028	—	2	4	no	—
116	#11924028	—	2	2	no	—
117	#11924028	C₂²⋊C₄	1	2	yes	—
118	#11924028	C₂²⋊C₄	1	2	yes	—
119	#11924028	C₂×C₈	1	2	yes	—
120	#11924028	C₂×C₈	1	2	yes	—
121	#11924028	C₂×C₈	1	2	yes	—
122	#11924028	C₂²×C₄	1	2	yes	—
123	#11924027	—	2	4	no	—
124	#11924027	—	2	4	no	—
125	#11924027	—	2	2	no	—
126	#11924027	C₂×C₈	1	4	yes	—
127	C₂×Dic₁₄₆	—	2	2	no	—
128	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
129	C₂×Dic₁₄₆	M₁₆	1	1	yes	characteristic
130	Q₈×D₇₃	—	2	2	no	—
131	Q₈×D₇₃	C₂×C₈	1	4	yes	—
132	C₂×D₂₉₂	—	2	2	no	—
133	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
134	C₂×D₂₉₂	M₁₆	1	1	yes	characteristic
135	C₂×C₂²⋊D₇₃	—	2	1	no	—
136	C₂×C₂²⋊D₇₃	—	2	4	no	—
137	C₂×C₂²⋊D₇₃	M₁₆	1	2	yes	—
138	D₄×D₇₃	—	2	4	no	—
139	D₄×D₇₃	—	2	4	no	—
140	D₄×D₇₃	—	2	2	no	—
141	D₄×D₇₃	C₂×C₈	1	4	yes	—
142	C₂×C₄×D₇₃	—	2	1	no	—
143	C₂×C₄×D₇₃	—	2	4	no	—
144	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
145	#11924012	—	2	1	no	—
146	#11924012	—	2	4	no	—
147	#11924012	C₂²⋊C₄	1	2	yes	—
148	#11924012	C₂²⋊C₄	1	2	yes	—
149	#11924012	C₂²×C₄	1	2	yes	—
150	#11924011	—	2	4	no	—
151	#11924011	—	2	2	no	—
152	#11924011	—	2	2	no	—
153	#11924011	—	2	4	no	—
154	#11924011	C₂²⋊C₄	1	4	yes	—
155	#11924011	C₂²⋊C₄	1	4	yes	—
156	C₂×#10596831	—	2	1	no	—
157	C₂×#10596831	—	2	4	no	—
158	C₂×#10596831	C₂²×C₄	1	2	yes	—
159	C₈×D₇₃	—	2	4	no	—
160	C₈×D₇₃	—	2	2	no	—
161	C₈×D₇₃	—	2	2	no	—
162	C₈×D₇₃	—	2	4	no	—
163	C₈×D₇₃	C₂×D₄	1	4	yes	—
164	C₈×D₇₃	C₂×D₄	1	4	yes	—
165	#11924003	—	2	2	no	—
166	#11924003	—	2	2	no	—
167	#41×C₇₃	—	2	1	no	—
168	#41×C₇₃	—	2	1	no	—
169	#41×C₇₃	C₂×C₈	1	2	yes	—
170	#41×C₇₃	C₂²×C₄	1	2	yes	—
171	C₂×Q₈×C₇₃	C₂×C₈	1	1	yes	characteristic
172	C₂×D₄×C₇₃	—	2	1	no	—
173	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	—	2	1	no	—
175	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
176	M₁₆×C₇₃	—	2	1	no	—
177	M₁₆×C₇₃	—	2	2	no	—
178	M₁₆×C₇₃	—	2	2	no	—
179	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₇₃	—	2	1	no	—
181	C₂×C₈×C₇₃	—	2	2	no	—
182	C₂×C₈×C₇₃	—	2	2	no	—
183	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
189	C₁₆×C₇₃	—	2	1	no	—
190	C₁₆×C₇₃	—	2	1	no	—
191	C₁₆×C₇₃	—	2	2	no	—
192	C₂³×C₇₃	—	2	1	no	—
193	C₂³×C₇₃	C₂×M₁₆	1	1	yes	characteristic
194	C₂²×D₇₃	—	2	1	no	—
195	C₂²×D₇₃	—	2	4	no	—
196	C₂²×D₇₃	C₂×M₁₆	1	2	yes	—
197	Q₈×C₇₃	—	2	1	no	—
198	Q₈×C₇₃	C₂²×C₈	1	2	yes	—
199	D₄×C₇₃	—	2	2	no	—
200	D₄×C₇₃	—	2	2	no	—
201	D₄×C₇₃	—	2	1	no	—
202	D₄×C₇₃	C₂²×C₈	1	2	yes	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
211	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
212	C₂²⋊D₇₃	—	2	2	no	—
213	C₂²⋊D₇₃	—	2	2	no	—
214	C₂²⋊D₇₃	—	2	4	no	—
215	C₂²⋊D₇₃	—	2	4	no	—
216	C₂²⋊D₇₃	C₂²⋊C₈	1	4	yes	—
217	C₂²⋊D₇₃	C₂²⋊C₈	1	4	yes	—
218	C₂×Dic₇₃	—	2	1	no	—
219	C₂×Dic₇₃	—	2	4	no	—
220	C₂×Dic₇₃	C₂×M₁₆	1	2	yes	—
221	D₂₉₂	—	2	4	no	—
222	D₂₉₂	—	2	1	no	—
223	D₂₉₂	C₂²⋊C₈	1	2	yes	—
224	D₂₉₂	C₂²⋊C₈	1	2	yes	—
225	D₂₉₂	C₂²×C₈	1	2	yes	—
226	C₄×D₇₃	—	2	4	no	—
227	C₄×D₇₃	—	2	2	no	—
228	C₄×D₇₃	—	2	2	no	—
229	C₄×D₇₃	—	2	4	no	—
230	C₄×D₇₃	C₂×C₂²⋊C₄	1	4	yes	—
231	C₄×D₇₃	C₂²×C₈	1	4	yes	—
232	Dic₁₄₆	—	2	1	no	—
233	Dic₁₄₆	—	2	4	no	—
234	Dic₁₄₆	C₂²⋊C₈	1	2	yes	—
235	Dic₁₄₆	C₂²⋊C₈	1	2	yes	—
236	Dic₁₄₆	C₂²×C₈	1	2	yes	—
237	C₈×C₇₃	—	2	2	no	—
238	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
241	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
242	#10596831	—	2	2	no	—
243	#10596831	C₂×C₂²⋊C₄	1	4	yes	—
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	—	4	1	no	—
246	C₂²×C₇₃	—	8	1	no	—
247	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
248	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
249	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
250	C₂×D₇₃	—	2	2	no	—
251	C₂×D₇₃	—	4	2	no	—
252	C₂×D₇₃	—	8	4	no	—
253	C₂×D₇₃	—	8	1	no	—
254	C₂×D₇₃	C₂×C₂²⋊C₈	1	4	yes	—
255	C₄×C₇₃	—	2	2	no	—
256	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
257	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
258	C₄×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
259	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
260	Dic₇₃	—	2	2	no	—
261	Dic₇₃	C₂×C₂²⋊C₈	1	4	yes	—
262	#33340	—	73	1	no	maximal, Sylow
263	C₂×C₇₃	—	2	1	no	—
264	C₂×C₇₃	—	2	1	no	—
265	C₂×C₇₃	—	2	1	no	—
266	C₂×C₇₃	—	4	2	no	—
267	C₂×C₇₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
268	D₇₃	—	2	4	no	—
269	D₇₃	—	4	2	no	—
270	#3573	—	73	1	no	—
271	#3407	—	73	1	no	—
272	C₂×#504	—	73	1	no	—
273	#2117	—	73	1	no	—
274	#2117	—	73	4	no	—
275	#2117	—	73	1	no	—
276	C₂×#350	—	73	1	no	—
277	C₂×#350	—	73	4	no	—
278	C₂×#350	D₇₃	1	1	yes	characteristic, complemented
279	C₇₃	#33340	1	1	yes	characteristic, complemented, Sylow
280	#585	—	73	1	no	—
281	#568	—	73	1	no	—
282	#568	—	73	1	no	—
283	#568	—	73	4	no	—
284	#568	—	73	1	no	—
285	#568	—	146	2	no	—
286	#568	—	146	2	no	—
287	C₂×#131	—	73	1	no	—
288	C₂×#131	—	73	4	no	—
289	C₂×#131	—	73	1	no	—
290	C₂×#131	—	146	2	no	—
291	C₂×#131	—	146	2	no	—
292	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
293	#504	—	146	2	no	—
294	#504	—	146	2	no	—
295	#504	—	146	2	no	—
296	#504	—	146	2	no	—
297	C₂×M₃₂	—	73	1	no	—
298	C₂×M₃₂	—	73	2	no	—
299	C₂×M₃₂	—	73	1	no	—
300	C₂×M₃₂	—	73	4	no	—
301	C₂×M₃₂	C₂×D₇₃	1	1	yes	characteristic, complemented
302	C₂²×C₁₆	—	73	2	no	—
303	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
304	#350	—	73	4	no	—
305	#350	—	73	4	no	—
306	#350	—	73	2	no	—
307	#350	—	73	2	no	—
308	#350	C₂×D₇₃	1	2	yes	complemented
309	#350	C₂×D₇₃	1	2	yes	complemented
310	2₋¹⁺⁴	—	73	2	no	—
311	2₋¹⁺⁴	—	73	2	no	—
312	2₋¹⁺⁴	—	146	1	no	—
313	H(5,𝔽₂)	—	73	2	no	—
314	H(5,𝔽₂)	—	73	2	no	—
315	H(5,𝔽₂)	—	146	2	no	—
316	H(5,𝔽₂)	—	146	1	no	—
317	C₂×#41	—	73	1	no	—
318	C₂×#41	—	73	4	no	—
319	C₂×#41	—	73	1	no	—
320	C₂×#41	—	146	2	no	—
321	C₂×#41	—	146	2	no	—
322	C₂×#41	C₄×D₇₃	1	1	yes	characteristic
323	#131	—	2	1	no	—
324	#131	—	2	1	no	—
325	#131	—	73	2	no	—
326	#131	—	73	2	no	—
327	#131	—	73	2	no	—
328	#131	—	73	2	no	—
329	#131	—	73	4	no	—
330	#131	—	73	4	no	—
331	#131	—	73	2	no	—
332	#131	—	73	2	no	—
333	#131	—	146	4	no	—
334	#131	—	146	2	no	—
335	#131	—	146	4	no	—
336	#131	—	146	2	no	—
337	#131	—	146	4	no	—
338	#131	—	146	4	no	—
339	#131	—	146	2	no	—
340	#131	—	146	2	no	—
341	#131	—	146	1	no	—
342	#131	—	146	1	no	—
343	#131	C₄×D₇₃	1	2	yes	—
344	#131	C₂²×D₇₃	1	2	yes	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	73	1	no	—
347	C₂×M₁₆	—	73	2	no	—
348	C₂×M₁₆	—	73	1	no	—
349	C₂×M₁₆	—	73	4	no	—
350	C₂×M₁₆	—	146	4	no	—
351	C₂×M₁₆	—	146	4	no	—
352	C₂×M₁₆	—	146	2	no	—
353	C₂×M₁₆	—	146	4	no	—
354	C₂×M₁₆	—	146	2	no	—
355	C₂×M₁₆	—	146	1	no	—
356	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	73	2	no	—
359	C₂²×C₈	—	146	4	no	—
360	C₂²×C₈	—	146	1	no	—
361	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
362	M₃₂	—	2	1	no	—
363	M₃₂	—	73	2	no	—
364	M₃₂	—	146	4	no	—
365	M₃₂	—	146	4	no	—
366	M₃₂	—	146	1	no	—
367	M₃₂	—	146	1	no	—
368	M₃₂	—	146	1	no	—
369	M₃₂	C₂²×D₇₃	1	2	yes	—
370	C₂×C₁₆	—	2	1	no	—
371	C₂×C₁₆	—	2	1	no	—
372	C₂×C₁₆	—	2	1	no	—
373	C₂×C₁₆	—	73	2	no	—
374	C₂×C₁₆	—	146	4	no	—
375	C₂×C₁₆	—	146	4	no	—
376	C₂×C₁₆	—	146	1	no	—
377	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
378	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
379	#41	—	2	1	no	—
380	#41	—	2	1	no	—
381	#41	—	73	2	no	—
382	#41	—	73	2	no	—
383	#41	—	73	2	no	—
384	#41	—	73	2	no	—
385	#41	—	73	4	no	—
386	#41	—	73	4	no	—
387	#41	—	73	2	no	—
388	#41	—	73	2	no	—
389	#41	—	146	4	no	—
390	#41	—	146	4	no	—
391	#41	—	146	2	no	—
392	#41	—	146	2	no	—
393	#41	—	146	4	no	—
394	#41	—	146	4	no	—
395	#41	—	146	2	no	—
396	#41	—	146	2	no	—
397	#41	—	146	1	no	—
398	#41	—	146	1	no	—
399	#41	C₈×D₇₃	1	2	yes	—
400	#41	C₂×C₄×D₇₃	1	2	yes	—
401	C₂×Q₈	—	73	1	no	—
402	C₂×Q₈	—	73	4	no	—
403	C₂×Q₈	—	73	1	no	—
404	C₂×Q₈	—	146	2	no	—
405	C₂×Q₈	—	146	2	no	—
406	C₂×Q₈	C₈×D₇₃	1	1	yes	characteristic
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	73	2	no	—
409	C₂×D₄	—	73	4	no	—
410	C₂×D₄	—	73	1	no	—
411	C₂×D₄	—	73	1	no	—
412	C₂×D₄	—	146	2	no	—
413	C₂×D₄	—	146	4	no	—
414	C₂×D₄	—	146	2	no	—
415	C₂×D₄	—	146	4	no	—
416	C₂×D₄	—	146	4	no	—
417	C₂×D₄	—	146	1	no	—
418	C₂×D₄	C₈×D₇₃	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	73	2	no	—
421	C₂²×C₄	—	146	4	no	—
422	C₂²×C₄	—	146	1	no	—
423	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	73	2	no	—
428	M₁₆	—	73	2	no	—
429	M₁₆	—	73	4	no	—
430	M₁₆	—	73	4	no	—
431	M₁₆	—	73	2	no	—
432	M₁₆	—	146	4	no	—
433	M₁₆	—	146	4	no	—
434	M₁₆	—	146	4	no	—
435	M₁₆	—	146	1	no	—
436	M₁₆	—	146	2	no	—
437	M₁₆	—	146	2	no	—
438	M₁₆	C₂×C₄×D₇₃	1	2	yes	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	73	2	no	—
443	C₂×C₈	—	73	4	no	—
444	C₂×C₈	—	73	4	no	—
445	C₂×C₈	—	146	4	no	—
446	C₂×C₈	—	146	4	no	—
447	C₂×C₈	—	146	4	no	—
448	C₂×C₈	—	146	1	no	—
449	C₂×C₈	—	146	2	no	—
450	C₂×C₈	—	146	2	no	—
451	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
452	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
453	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
454	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
455	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
456	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
457	C₁₆	—	2	1	no	—
458	C₁₆	—	2	1	no	—
459	C₁₆	—	2	2	no	—
460	C₁₆	—	146	2	no	—
461	C₁₆	—	146	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	73	2	no	—
464	C₂³	—	146	4	no	—
465	C₂³	—	146	1	no	—
466	C₂³	M₁₆×D₇₃	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	73	2	no	—
469	Q₈	—	73	2	no	—
470	Q₈	—	73	2	no	—
471	Q₈	—	146	4	no	—
472	Q₈	—	146	1	no	—
473	Q₈	C₂×C₈×D₇₃	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	73	4	no	—
478	D₄	—	73	4	no	—
479	D₄	—	73	2	no	—
480	D₄	—	73	2	no	—
481	D₄	—	73	2	no	—
482	D₄	—	146	4	no	—
483	D₄	—	146	4	no	—
484	D₄	—	146	4	no	—
485	D₄	—	146	2	no	—
486	D₄	—	146	2	no	—
487	D₄	—	146	1	no	—
488	D₄	C₂×C₈×D₇₃	1	2	yes	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	73	2	no	—
493	C₂×C₄	—	73	4	no	—
494	C₂×C₄	—	73	4	no	—
495	C₂×C₄	—	146	4	no	—
496	C₂×C₄	—	146	4	no	—
497	C₂×C₄	—	146	4	no	—
498	C₂×C₄	—	146	1	no	—
499	C₂×C₄	—	146	2	no	—
500	C₂×C₄	—	146	2	no	—
501	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
502	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
503	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
504	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
505	C₂×C₄	M₁₆×D₇₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	73	4	no	—
509	C₈	—	146	2	no	—
510	C₈	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
511	C₈	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
512	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
513	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	292	2	no	—
518	C₂²	—	584	1	no	—
519	C₂²	—	584	4	no	—
520	C₂²	—	73	4	no	—
521	C₂²	—	146	2	no	—
522	C₂²	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
523	C₂²	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
524	C₂²	C₂×M₁₆×D₇₃	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	73	4	no	—
527	C₄	—	146	2	no	—
528	C₄	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
529	C₄	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
530	C₄	C₂×C₂²⋊C₄×D₇₃	1	1	yes	characteristic
531	C₄	C₂²×C₈×D₇₃	1	1	yes	characteristic
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	1	no	—
535	C₂	—	4	2	no	—
536	C₂	—	292	2	no	—
537	C₂	—	146	4	no	—
538	C₂	C₂×C₂²⋊C₈×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₂×#350×C₇₃	C₂
socle	C₂×C₇₃	C₂²×C₂²⋊C₈
prime radical	#17989423	C₄
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	C₂×#350	D₇₃
hypocenter	C₇₃	#33340
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#350

Complements

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

N	H ≅ G/N	type
2. #22623033	C₂	semidirect
3. C₂×#17989003	C₂	semidirect
4. #22611560	C₂	semidirect
5. #22611559	C₂	semidirect
6. #22611557	C₂	semidirect
7. C₂×#17988370	C₂	semidirect
8. #350×D₇₃	C₂	semidirect
9. C₂×#350×C₇₃	C₂	semidirect
26. C₂×#14556531	C₂²	semidirect
27. C₂×#14556531	C₂²	semidirect
28. C₂×#14556530	C₂²	semidirect
29. M₃₂×D₇₃	C₂²	semidirect
30. C₂×C₁₆×D₇₃	C₂²	semidirect
31. #17988372	C₂²	semidirect
32. #17988371	C₂²	semidirect
33. #17988370	C₂²	semidirect
34. #17988370	C₂²	semidirect
36. C₂×M₃₂×C₇₃	C₂²	semidirect
37. C₂²×C₁₆×C₇₃	C₂²	semidirect
38. #350×C₇₃	C₂²	semidirect
39. #350×C₇₃	C₂²	semidirect
278. C₂×#350	D₇₃	semidirect
279. C₇₃	#33340	semidirect
301. C₂×M₃₂	C₂×D₇₃	semidirect
303. C₂²×C₁₆	C₂×D₇₃	semidirect
308. #350	C₂×D₇₃	semidirect
309. #350	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22624642	2
#22623033	2
C₂×#17989003	2
#22611560	2
#22611559	2
#22611557	2
C₂×#17988370	2
#350×D₇₃	2
C₂×#350×C₇₃	2
#33340	73