Subgroups — #33962229

Order 18688.

2656 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624710	C₂	1	2	yes	maximal, complemented
2	C₂×#17989389	C₂	1	1	yes	maximal, characteristic, complemented
3	#22621728	C₂	1	4	yes	maximal, complemented
4	#22621717	C₂	1	4	yes	maximal, complemented
5	#22621693	C₂	1	8	yes	maximal, complemented
6	#22620418	C₂	1	1	yes	maximal, characteristic, complemented
7	#22619661	C₂	1	2	yes	maximal, complemented
8	#22619647	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17988857	C₂	1	1	yes	maximal, characteristic, complemented
10	#22619303	C₂	1	2	yes	maximal, complemented
11	#22619286	C₂	1	2	yes	maximal, complemented
12	#22618848	C₂	1	1	yes	maximal, characteristic, complemented
13	#22618832	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#14556637	C₂²	1	2	yes	complemented
16	#17989395	—	2	4	no	—
17	#17989395	C₂²	1	8	yes	complemented
18	#17989390	—	2	4	no	—
19	#17989390	C₂²	1	8	yes	complemented
20	#17989389	—	2	2	no	—
21	#17989389	—	2	2	no	—
22	#17989389	C₂²	1	4	yes	complemented
23	#17989389	C₂²	1	4	yes	complemented
24	#17989385	—	2	4	no	—
25	#17989385	C₂²	1	1	yes	characteristic
26	#17989385	C₂²	1	2	yes	complemented
27	C₂×#14556618	—	2	2	no	—
28	C₂×#14556616	—	2	4	no	—
29	C₂×#14556616	C₂²	1	2	yes	complemented
30	C₂×#14556616	C₂²	1	2	yes	complemented
31	C₂×#14556616	C₂²	1	2	yes	complemented
32	C₂×#14556614	—	2	1	no	—
33	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₈×D₇₃	—	2	1	no	—
35	#17989354	C₂²	1	2	yes	complemented
36	C₂×#14556597	C₂²	1	1	yes	characteristic, complemented
37	#17989151	C₂²	1	2	yes	complemented
38	#17988973	C₂²	1	4	yes	complemented
39	#17988972	C₂²	1	2	yes	complemented
40	#17988962	C₂²	1	2	yes	complemented
41	#17988859	C₂²	1	2	yes	complemented
42	#17988857	C₂²	1	4	yes	complemented
43	#17988857	C₂²	1	4	yes	complemented
44	#17988855	C₂²	1	8	yes	complemented
45	#17988854	C₂²	1	2	yes	complemented
46	#17988852	C₂²	1	8	yes	complemented
47	#17988847	C₂²	1	4	yes	complemented
48	#17988763	C₂²	1	8	yes	complemented
49	#17988760	C₂²	1	8	yes	complemented
50	#17988755	C₂²	1	8	yes	complemented
51	#17988753	C₂²	1	8	yes	complemented
52	#17988709	C₂²	1	4	yes	complemented
53	#17988707	C₂²	1	4	yes	complemented
54	#17988704	C₂²	1	4	yes	complemented
55	#17988702	C₂²	1	4	yes	complemented
56	#17988635	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14556527	C₂²	1	1	yes	characteristic, complemented
58	#17988604	C₂²	1	2	yes	complemented
59	#17988604	C₂²	1	1	yes	characteristic, complemented
60	#17988603	C₂²	1	1	yes	characteristic, complemented
61	#17988571	C₂²	1	2	yes	complemented
62	C₂×#14556507	C₂²	1	2	yes	complemented
63	#17988542	C₂²	1	1	yes	characteristic, complemented
64	#585×C₇₃	C₂²	1	2	yes	complemented
65	#578×C₇₃	—	2	1	no	—
66	#578×C₇₃	C₂²	1	2	yes	complemented
67	#577×C₇₃	—	2	2	no	—
68	#577×C₇₃	C₂²	1	4	yes	complemented
69	#576×C₇₃	—	2	1	no	—
70	#576×C₇₃	C₂²	1	2	yes	complemented
71	#575×C₇₃	—	2	2	no	—
72	#575×C₇₃	C₂²	1	2	yes	complemented
73	C₂×#135×C₇₃	—	2	2	no	—
74	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
75	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic, complemented
77	#14556637	—	2	4	no	—
78	#14556637	—	2	4	no	—
79	#14556637	—	4	2	no	—
80	#14556637	C₂³	1	8	yes	—
81	C₂×#11924029	—	2	2	no	—
82	C₂×#11924028	—	2	2	no	—
83	C₂×#11924028	C₂³	1	1	yes	characteristic
84	C₂²×D₂₉₂	—	2	2	no	—
85	C₂²×D₂₉₂	C₂³	1	2	yes	—
86	C₂×D₄×D₇₃	—	2	2	no	—
87	C₂×D₄×D₇₃	—	4	2	no	—
88	#14556622	—	2	8	no	—
89	#14556622	D₄	1	2	yes	complemented
90	#14556622	C₂³	1	4	yes	—
91	#14556621	—	2	2	no	—
92	#14556621	D₄	1	2	yes	complemented
93	#14556618	—	2	8	no	—
94	#14556618	—	2	8	no	—
95	#14556617	—	2	8	no	—
96	#14556617	D₄	1	2	yes	complemented
97	#14556617	C₂³	1	4	yes	—
98	#14556616	—	2	2	no	—
99	#14556616	—	2	8	no	—
100	#14556616	—	2	8	no	—
101	#14556616	—	2	4	no	—
102	#14556616	—	2	4	no	—
103	#14556616	—	2	4	no	—
104	#14556616	—	2	4	no	—
105	#14556616	D₄	1	2	yes	complemented
106	#14556616	C₂³	1	8	yes	—
107	#14556616	C₂³	1	8	yes	complemented
108	#14556614	—	2	4	no	—
109	#14556614	—	2	4	no	—
110	#14556611	—	2	4	no	—
111	#14556611	—	2	8	no	—
112	#14556611	—	2	8	no	—
113	#14556611	C₂³	1	4	yes	—
114	C₂×#11924015	—	2	8	no	—
115	C₂×#11924015	—	2	2	no	—
116	C₂×#11924015	—	2	2	no	—
117	C₂×#11924015	C₂³	1	4	yes	complemented
118	C₂×D₅₈₄	—	2	1	no	—
119	C₂×D₅₈₄	—	2	1	no	—
120	C₂×D₅₈₄	—	2	1	no	—
121	C₂×D₅₈₄	—	2	1	no	—
122	C₂×D₅₈₄	C₂³	1	2	yes	—
123	C₂×D₅₈₄	C₂³	1	2	yes	—
124	C₂×#11924013	—	2	8	no	—
125	C₂×#11924013	—	2	2	no	—
126	C₂×#11924013	—	2	2	no	—
127	C₂×#11924013	C₂³	1	4	yes	complemented
128	D₈×D₇₃	—	2	4	no	—
129	D₈×D₇₃	—	2	4	no	—
130	#14556598	—	2	4	no	—
131	#14556598	C₂³	1	8	yes	complemented
132	#14556597	—	2	1	no	—
133	#14556597	—	2	1	no	—
134	#14556597	C₂³	1	2	yes	—
135	#14556597	C₂³	1	2	yes	—
136	C₂×#11924012	—	2	4	no	—
137	C₂×#11924012	C₂³	1	2	yes	—
138	C₂×#11924012	C₂³	1	1	yes	characteristic
139	C₂×#11924012	C₂³	1	1	yes	characteristic
140	C₂×#11924011	—	2	1	no	—
141	C₂×C₈×D₇₃	—	2	1	no	—
142	#14556587	C₂³	1	4	yes	complemented
143	#14556580	C₂³	1	4	yes	complemented
144	#14556565	—	4	2	no	—
145	#14556559	—	4	2	no	—
146	#14556550	C₂³	1	1	yes	characteristic
147	#14556527	C₂³	1	2	yes	complemented
148	#14556527	C₂³	1	2	yes	complemented
149	#14556526	C₂³	1	4	yes	complemented
150	#14556518	C₂³	1	4	yes	complemented
151	#14556518	C₂³	1	8	yes	complemented
152	#14556517	C₂³	1	4	yes	—
153	#14556510	C₂³	1	4	yes	complemented
154	#14556508	C₂³	1	4	yes	complemented
155	#14556507	C₂³	1	8	yes	complemented
156	#14556501	C₂³	1	2	yes	complemented
157	C₈×Dic₇₃	C₂³	1	2	yes	complemented
158	2₋¹⁺⁴×C₇₃	—	2	2	no	—
159	2₋¹⁺⁴×C₇₃	—	2	2	no	—
160	2₋¹⁺⁴×C₇₃	C₂³	1	4	yes	complemented
161	H(5,𝔽₂)×C₇₃	—	2	2	no	—
162	H(5,𝔽₂)×C₇₃	—	2	2	no	—
163	H(5,𝔽₂)×C₇₃	—	4	2	no	—
164	H(5,𝔽₂)×C₇₃	C₂³	1	4	yes	complemented
165	C₂×#41×C₇₃	—	2	4	no	—
166	C₂×#41×C₇₃	—	2	4	no	—
167	C₂×#41×C₇₃	—	4	2	no	—
168	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×#41×C₇₃	C₂³	1	2	yes	—
170	C₂×#41×C₇₃	C₂³	1	2	yes	—
171	#137×C₇₃	—	2	2	no	—
172	#137×C₇₃	—	2	4	no	—
173	#137×C₇₃	—	2	4	no	—
174	#137×C₇₃	C₂³	1	4	yes	complemented
175	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
176	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
177	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
178	AGL(1,ℤ/8)×C₇₃	C₂³	1	4	yes	complemented
179	#135×C₇₃	—	2	4	no	—
180	#135×C₇₃	—	2	2	no	—
181	#135×C₇₃	—	2	4	no	—
182	#135×C₇₃	—	2	2	no	—
183	#135×C₇₃	—	2	1	no	—
184	#135×C₇₃	—	2	1	no	—
185	#135×C₇₃	—	2	1	no	—
186	#135×C₇₃	—	2	1	no	—
187	#135×C₇₃	D₄	1	2	yes	complemented
188	#135×C₇₃	D₄	1	2	yes	complemented
189	#135×C₇₃	C₂³	1	2	yes	—
190	#135×C₇₃	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₇₃	—	2	2	no	—
192	C₂×Q₁₆×C₇₃	D₄	1	1	yes	characteristic, complemented
193	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic, complemented
194	C₂×SD₁₆×C₇₃	—	2	4	no	—
195	C₂×SD₁₆×C₇₃	D₄	1	2	yes	complemented
196	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	complemented
197	C₂×D₈×C₇₃	—	2	2	no	—
198	C₂×D₈×C₇₃	D₄	1	1	yes	characteristic, complemented
199	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic, complemented
200	#131×C₇₃	—	2	1	no	—
201	#131×C₇₃	—	2	1	no	—
202	#131×C₇₃	C₂³	1	2	yes	complemented
203	#131×C₇₃	C₂³	1	2	yes	complemented
204	C₂×M₁₆×C₇₃	—	2	1	no	—
205	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
206	C₂²×C₈×C₇₃	—	2	1	no	—
207	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
208	C₂³×D₇₃	—	2	2	no	—
209	C₂³×D₇₃	—	4	2	no	—
210	#11924029	—	2	8	no	—
211	#11924029	—	4	4	no	—
212	#11924028	—	2	1	no	—
213	#11924028	—	2	1	no	—
214	#11924028	—	2	8	no	—
215	#11924028	—	4	4	no	—
216	#11924028	C₂×D₄	1	2	yes	—
217	#11924028	C₂⁴	1	2	yes	—
218	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
219	C₂×D₂₉₂	—	2	2	no	—
220	C₂×D₂₉₂	—	2	2	no	—
221	C₂×D₂₉₂	—	2	2	no	—
222	C₂×D₂₉₂	—	2	2	no	—
223	C₂×D₂₉₂	—	2	8	no	—
224	C₂×D₂₉₂	—	2	2	no	—
225	C₂×D₂₉₂	—	4	4	no	—
226	C₂×D₂₉₂	—	4	2	no	—
227	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
228	C₂×D₂₉₂	C₂⁴	1	4	yes	—
229	C₂×C₂²⋊D₇₃	—	2	1	no	—
230	C₂×C₂²⋊D₇₃	—	4	2	no	—
231	C₂×C₂²⋊D₇₃	—	4	4	no	—
232	D₄×D₇₃	—	2	8	no	—
233	D₄×D₇₃	—	4	4	no	—
234	D₄×D₇₃	—	4	8	no	—
235	D₄×D₇₃	—	4	8	no	—
236	C₂×C₄×D₇₃	—	2	1	no	—
237	C₂×C₄×D₇₃	—	4	2	no	—
238	#11924018	—	2	4	no	—
239	#11924018	C₂×D₄	1	4	yes	—
240	#11924016	—	2	4	no	—
241	#11924016	C₂×D₄	1	4	yes	—
242	#11924015	—	2	8	no	—
243	#11924015	—	2	8	no	—
244	#11924015	—	2	4	no	—
245	#11924015	—	2	8	no	—
246	#11924015	C₂×D₄	1	4	yes	—
247	D₅₈₄	—	2	2	no	—
248	D₅₈₄	—	2	2	no	—
249	D₅₈₄	—	2	2	no	—
250	D₅₈₄	—	2	2	no	—
251	#11924013	—	2	8	no	—
252	#11924013	—	2	8	no	—
253	#11924013	—	2	4	no	—
254	#11924013	—	2	8	no	—
255	#11924013	C₂×D₄	1	4	yes	—
256	#11924012	—	2	2	no	—
257	#11924012	—	2	1	no	—
258	#11924012	—	2	8	no	—
259	#11924012	C₂×D₄	1	2	yes	—
260	#11924012	C₂×D₄	1	2	yes	—
261	#11924012	C₂⁴	1	4	yes	—
262	#11924012	C₂⁴	1	2	yes	—
263	#11924011	—	2	2	no	—
264	#11924011	—	2	2	no	—
265	C₂×#10596831	—	2	1	no	—
266	C₂×#10596831	—	2	2	no	—
267	C₂×#10596831	—	2	8	no	—
268	C₂×#10596831	C₂⁴	1	2	yes	—
269	C₈×D₇₃	—	2	2	no	—
270	C₈×D₇₃	—	2	2	no	—
271	C₄⋊Dic₇₃	—	2	1	no	—
272	C₂²⋊Dic₇₃	—	2	1	no	—
273	#11924005	—	4	4	no	—
274	C₄×Dic₇₃	C₂⁴	1	2	yes	—
275	#41×C₇₃	—	2	1	no	—
276	#41×C₇₃	—	2	2	no	—
277	#41×C₇₃	—	2	1	no	—
278	#41×C₇₃	—	2	2	no	—
279	#41×C₇₃	—	2	4	no	—
280	#41×C₇₃	—	2	4	no	—
281	#41×C₇₃	—	2	4	no	—
282	#41×C₇₃	—	2	4	no	—
283	#41×C₇₃	—	2	2	no	—
284	#41×C₇₃	—	2	2	no	—
285	#41×C₇₃	—	2	2	no	—
286	#41×C₇₃	—	2	2	no	—
287	#41×C₇₃	—	4	4	no	—
288	#41×C₇₃	—	4	4	no	—
289	#41×C₇₃	—	4	4	no	—
290	#41×C₇₃	—	4	4	no	—
291	#41×C₇₃	—	4	2	no	—
292	#41×C₇₃	—	4	2	no	—
293	#41×C₇₃	C₂×D₄	1	2	yes	—
294	#41×C₇₃	C₂×D₄	1	4	yes	—
295	#41×C₇₃	C₂⁴	1	2	yes	—
296	#41×C₇₃	C₂⁴	1	4	yes	—
297	C₂×Q₈×C₇₃	—	2	4	no	—
298	C₂×Q₈×C₇₃	—	2	4	no	—
299	C₂×Q₈×C₇₃	—	4	2	no	—
300	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
302	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
303	C₂×D₄×C₇₃	—	2	1	no	—
304	C₂×D₄×C₇₃	—	2	2	no	—
305	C₂×D₄×C₇₃	—	2	4	no	—
306	C₂×D₄×C₇₃	—	2	4	no	—
307	C₂×D₄×C₇₃	—	2	2	no	—
308	C₂×D₄×C₇₃	—	4	4	no	—
309	C₂×D₄×C₇₃	—	4	2	no	—
310	C₂×D₄×C₇₃	—	4	4	no	—
311	C₂×D₄×C₇₃	—	4	4	no	—
312	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇₃	—	2	1	no	—
316	C₂²×C₄×C₇₃	—	2	2	no	—
317	C₂²×C₄×C₇₃	—	2	2	no	—
318	C₂²×C₄×C₇₃	—	4	4	no	—
319	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
320	Q₁₆×C₇₃	—	2	4	no	—
321	Q₁₆×C₇₃	—	2	1	no	—
322	Q₁₆×C₇₃	—	2	1	no	—
323	Q₁₆×C₇₃	C₂×D₄	1	2	yes	—
324	Q₁₆×C₇₃	C₂×D₄	1	2	yes	—
325	SD₁₆×C₇₃	—	2	4	no	—
326	SD₁₆×C₇₃	—	2	4	no	—
327	SD₁₆×C₇₃	—	2	2	no	—
328	SD₁₆×C₇₃	—	2	2	no	—
329	SD₁₆×C₇₃	C₂×D₄	1	4	yes	—
330	SD₁₆×C₇₃	C₂×D₄	1	4	yes	—
331	D₈×C₇₃	—	2	4	no	—
332	D₈×C₇₃	—	2	1	no	—
333	D₈×C₇₃	—	2	1	no	—
334	D₈×C₇₃	C₂×D₄	1	2	yes	—
335	D₈×C₇₃	C₂×D₄	1	2	yes	—
336	M₁₆×C₇₃	—	2	1	no	—
337	M₁₆×C₇₃	—	2	2	no	—
338	M₁₆×C₇₃	—	2	2	no	—
339	M₁₆×C₇₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₇₃	—	2	1	no	—
341	C₂×C₈×C₇₃	—	2	2	no	—
342	C₂×C₈×C₇₃	—	2	2	no	—
343	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
344	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
345	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
346	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
347	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₇₃	—	2	1	no	—
350	C₂³×C₇₃	—	2	2	no	—
351	C₂³×C₇₃	—	2	2	no	—
352	C₂³×C₇₃	—	4	4	no	—
353	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×D₇₃	—	2	1	no	—
355	C₂²×D₇₃	—	2	4	no	—
356	C₂²×D₇₃	—	4	8	no	—
357	C₂²×D₇₃	—	4	2	no	—
358	C₂²×D₇₃	—	4	2	no	—
359	C₂²×D₇₃	—	16	4	no	—
360	C₂²×D₇₃	—	16	2	no	—
361	Q₈×C₇₃	—	2	1	no	—
362	Q₈×C₇₃	—	2	2	no	—
363	Q₈×C₇₃	—	2	2	no	—
364	Q₈×C₇₃	—	2	2	no	—
365	Q₈×C₇₃	—	4	4	no	—
366	Q₈×C₇₃	C₂²×D₄	1	2	yes	—
367	Q₈×C₇₃	C₂²×D₄	1	4	yes	—
368	D₄×C₇₃	—	2	2	no	—
369	D₄×C₇₃	—	2	4	no	—
370	D₄×C₇₃	—	2	2	no	—
371	D₄×C₇₃	—	2	4	no	—
372	D₄×C₇₃	—	2	1	no	—
373	D₄×C₇₃	—	2	2	no	—
374	D₄×C₇₃	—	2	2	no	—
375	D₄×C₇₃	—	2	2	no	—
376	D₄×C₇₃	—	4	4	no	—
377	D₄×C₇₃	—	4	4	no	—
378	D₄×C₇₃	—	4	4	no	—
379	D₄×C₇₃	—	4	2	no	—
380	D₄×C₇₃	—	4	2	no	—
381	D₄×C₇₃	C₂²×D₄	1	2	yes	—
382	D₄×C₇₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	2	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	4	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	4	no	—
389	C₂×C₄×C₇₃	—	2	2	no	—
390	C₂×C₄×C₇₃	—	4	4	no	—
391	C₂×C₄×C₇₃	—	4	4	no	—
392	C₂×C₄×C₇₃	—	4	4	no	—
393	C₂×C₄×C₇₃	—	4	2	no	—
394	C₂×C₄×C₇₃	—	4	2	no	—
395	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
401	C₂²⋊D₇₃	—	2	2	no	—
402	C₂²⋊D₇₃	—	2	2	no	—
403	C₂²⋊D₇₃	—	4	8	no	—
404	C₂²⋊D₇₃	—	16	4	no	—
405	C₂×Dic₇₃	—	2	1	no	—
406	C₂×Dic₇₃	—	2	2	no	—
407	D₂₉₂	—	2	1	no	—
408	D₂₉₂	—	2	4	no	—
409	D₂₉₂	—	2	4	no	—
410	D₂₉₂	—	4	8	no	—
411	D₂₉₂	—	4	2	no	—
412	D₂₉₂	—	4	2	no	—
413	D₂₉₂	C₂²×D₄	1	2	yes	—
414	C₄×D₇₃	—	2	2	no	—
415	C₄×D₇₃	—	2	2	no	—
416	C₄×D₇₃	—	4	8	no	—
417	Dic₁₄₆	—	2	1	no	—
418	Dic₁₄₆	C₂²×D₄	1	2	yes	—
419	C₈×C₇₃	—	2	2	no	—
420	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
421	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
422	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
423	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
424	#10596831	—	2	2	no	—
425	#10596831	—	2	4	no	—
426	#10596831	C₂²×D₄	1	4	yes	—
427	C₂²×C₇₃	—	2	4	no	—
428	C₂²×C₇₃	—	2	2	no	—
429	C₂²×C₇₃	—	4	1	no	—
430	C₂²×C₇₃	—	4	2	no	—
431	C₂²×C₇₃	—	8	2	no	—
432	C₂²×C₇₃	—	8	1	no	—
433	C₂²×C₇₃	—	8	2	no	—
434	C₂²×C₇₃	—	16	4	no	—
435	C₂²×C₇₃	D₄²	1	1	yes	characteristic
436	C₂²×C₇₃	D₄²	1	1	yes	characteristic
437	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×D₇₃	—	2	2	no	—
439	C₂×D₇₃	—	4	2	no	—
440	C₂×D₇₃	—	4	4	no	—
441	C₂×D₇₃	—	8	4	no	—
442	C₂×D₇₃	—	8	4	no	—
443	C₂×D₇₃	—	16	8	no	—
444	C₂×D₇₃	—	16	2	no	—
445	C₄×C₇₃	—	2	4	no	—
446	C₄×C₇₃	—	2	2	no	—
447	C₄×C₇₃	—	4	2	no	—
448	C₄×C₇₃	D₄²	1	1	yes	characteristic
449	C₄×C₇₃	D₄²	1	1	yes	characteristic
450	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
452	Dic₇₃	—	2	2	no	—
453	Dic₇₃	—	4	2	no	—
454	#61106	—	73	1	no	maximal, Sylow
455	C₂×C₇₃	—	2	1	no	—
456	C₂×C₇₃	—	2	1	no	—
457	C₂×C₇₃	—	2	1	no	—
458	C₂×C₇₃	—	4	4	no	—
459	C₂×C₇₃	—	4	2	no	—
460	C₂×C₇₃	—	8	2	no	—
461	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
462	D₇₃	—	4	2	no	—
463	D₇₃	—	8	4	no	—
464	#3585	—	73	2	no	—
465	#3584	D₇₃	1	1	yes	characteristic, complemented
466	C₂×#576	—	73	1	no	—
467	#3292	—	73	4	no	—
468	#3290	—	73	4	no	—
469	#3288	—	73	8	no	—
470	#3155	—	73	1	no	—
471	#3068	—	73	2	no	—
472	#3067	—	73	1	no	—
473	C₂×#472	—	73	1	no	—
474	#3021	—	73	2	no	—
475	#3019	—	73	2	no	—
476	#2957	—	73	1	no	—
477	#2955	—	73	1	no	—
478	C₇₃	#61106	1	1	yes	characteristic, complemented, Sylow
479	#585	C₂×D₇₃	1	2	yes	complemented
480	C₂×H(5,𝔽₂)	—	73	2	no	—
481	#578	—	2	1	no	—
482	#578	C₂×D₇₃	1	2	yes	complemented
483	#577	—	2	2	no	—
484	#577	—	73	8	no	—
485	#577	—	146	4	no	—
486	#577	C₂×D₇₃	1	4	yes	complemented
487	#576	—	2	1	no	—
488	#576	—	73	8	no	—
489	#576	—	73	4	no	—
490	#576	—	73	4	no	—
491	#576	—	146	4	no	—
492	#576	—	146	2	no	—
493	#576	—	146	2	no	—
494	#576	C₂×D₇₃	1	2	yes	complemented
495	#575	—	2	2	no	—
496	#575	—	73	1	no	—
497	#575	—	73	2	no	—
498	#575	—	146	4	no	—
499	#575	C₂×D₇₃	1	2	yes	complemented
500	C₂×AGL(1,ℤ/8)	—	73	2	no	—
501	C₂×AGL(1,ℤ/8)	—	73	2	no	—
502	C₂×AGL(1,ℤ/8)	—	73	2	no	—
503	C₂×AGL(1,ℤ/8)	—	146	4	no	—
504	C₂×AGL(1,ℤ/8)	—	146	2	no	—
505	C₂×#135	—	2	2	no	—
506	C₂×#135	—	146	1	no	—
507	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
508	C₂×#135	C₂×D₇₃	1	1	yes	characteristic, complemented
509	C₂²×D₈	—	73	1	no	—
510	C₂²×D₈	—	146	1	no	—
511	#568	—	73	2	no	—
512	C₂×#131	—	73	1	no	—
513	C₂×#131	C₂×D₇₃	1	1	yes	characteristic, complemented
514	#535	—	73	2	no	—
515	#496	—	73	4	no	—
516	#495	—	73	2	no	—
517	#493	—	73	2	no	—
518	#473	—	73	2	no	—
519	#472	—	73	8	no	—
520	#472	—	73	2	no	—
521	#472	—	73	4	no	—
522	#472	—	73	4	no	—
523	#471	—	73	8	no	—
524	#471	—	73	4	no	—
525	#455	—	73	8	no	—
526	#454	—	73	8	no	—
527	#453	—	73	8	no	—
528	#453	—	73	8	no	—
529	#444	—	73	4	no	—
530	#444	—	73	4	no	—
531	#443	—	73	4	no	—
532	#443	—	73	4	no	—
533	#430	—	73	1	no	—
534	C₂×#108	—	73	1	no	—
535	#421	—	73	1	no	—
536	#421	—	73	2	no	—
537	#421	—	73	1	no	—
538	#413	—	73	2	no	—
539	C₂×#100	—	73	2	no	—
540	#405	—	73	1	no	—
541	2₋¹⁺⁴	—	2	2	no	—
542	2₋¹⁺⁴	—	2	2	no	—
543	2₋¹⁺⁴	C₂²×D₇₃	1	4	yes	complemented
544	H(5,𝔽₂)	—	2	2	no	—
545	H(5,𝔽₂)	—	2	2	no	—
546	H(5,𝔽₂)	—	4	2	no	—
547	H(5,𝔽₂)	—	292	2	no	—
548	H(5,𝔽₂)	—	73	8	no	—
549	H(5,𝔽₂)	—	146	4	no	—
550	H(5,𝔽₂)	—	146	4	no	—
551	H(5,𝔽₂)	C₂²×D₇₃	1	4	yes	complemented
552	C₂×#41	—	2	4	no	—
553	C₂×#41	—	2	4	no	—
554	C₂×#41	—	4	2	no	—
555	C₂×#41	—	73	1	no	—
556	C₂×#41	—	146	2	no	—
557	C₂×#41	—	146	2	no	—
558	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
559	C₂×#41	C₂²×D₇₃	1	2	yes	—
560	C₂×#41	C₂²×D₇₃	1	2	yes	—
561	C₂²×D₄	—	292	2	no	—
562	C₂²×D₄	—	73	2	no	—
563	C₂²×D₄	—	146	2	no	—
564	C₂²×D₄	—	146	2	no	—
565	#137	—	2	2	no	—
566	#137	—	2	4	no	—
567	#137	—	2	4	no	—
568	#137	—	73	2	no	—
569	#137	—	73	2	no	—
570	#137	—	73	4	no	—
571	#137	—	146	8	no	—
572	#137	—	146	2	no	—
573	#137	C₂²×D₇₃	1	4	yes	complemented
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	—	2	4	no	—
576	AGL(1,ℤ/8)	—	2	4	no	—
577	AGL(1,ℤ/8)	—	73	2	no	—
578	AGL(1,ℤ/8)	—	73	2	no	—
579	AGL(1,ℤ/8)	—	73	8	no	—
580	AGL(1,ℤ/8)	—	73	8	no	—
581	AGL(1,ℤ/8)	—	73	4	no	—
582	AGL(1,ℤ/8)	—	146	4	no	—
583	AGL(1,ℤ/8)	—	146	4	no	—
584	AGL(1,ℤ/8)	—	146	8	no	—
585	AGL(1,ℤ/8)	—	146	8	no	—
586	AGL(1,ℤ/8)	—	146	8	no	—
587	AGL(1,ℤ/8)	—	146	2	no	—
588	AGL(1,ℤ/8)	—	146	4	no	—
589	AGL(1,ℤ/8)	—	146	4	no	—
590	AGL(1,ℤ/8)	—	146	8	no	—
591	AGL(1,ℤ/8)	—	146	8	no	—
592	AGL(1,ℤ/8)	C₂²×D₇₃	1	4	yes	complemented
593	#135	—	2	4	no	—
594	#135	—	2	2	no	—
595	#135	—	2	4	no	—
596	#135	—	2	2	no	—
597	#135	—	2	1	no	—
598	#135	—	2	1	no	—
599	#135	—	2	1	no	—
600	#135	—	2	1	no	—
601	#135	—	73	4	no	—
602	#135	—	146	8	no	—
603	#135	—	146	8	no	—
604	#135	—	146	4	no	—
605	#135	—	146	4	no	—
606	#135	—	146	4	no	—
607	#135	C₂²⋊D₇₃	1	2	yes	complemented
608	#135	C₂²⋊D₇₃	1	2	yes	complemented
609	#135	C₂²×D₇₃	1	2	yes	—
610	#135	C₂²×D₇₃	1	2	yes	—
611	C₂×Q₁₆	—	2	2	no	—
612	C₂×Q₁₆	C₂²⋊D₇₃	1	1	yes	characteristic, complemented
613	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic, complemented
614	C₂×SD₁₆	—	2	4	no	—
615	C₂×SD₁₆	—	73	4	no	—
616	C₂×SD₁₆	—	146	8	no	—
617	C₂×SD₁₆	—	146	2	no	—
618	C₂×SD₁₆	—	146	2	no	—
619	C₂×SD₁₆	C₂²⋊D₇₃	1	2	yes	complemented
620	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	complemented
621	C₂×D₈	—	2	2	no	—
622	C₂×D₈	—	73	4	no	—
623	C₂×D₈	—	73	2	no	—
624	C₂×D₈	—	73	2	no	—
625	C₂×D₈	—	146	8	no	—
626	C₂×D₈	—	146	2	no	—
627	C₂×D₈	—	146	2	no	—
628	C₂×D₈	—	146	4	no	—
629	C₂×D₈	—	146	4	no	—
630	C₂×D₈	—	146	1	no	—
631	C₂×D₈	—	146	1	no	—
632	C₂×D₈	—	146	1	no	—
633	C₂×D₈	—	146	1	no	—
634	C₂×D₈	C₂²⋊D₇₃	1	1	yes	characteristic, complemented
635	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic, complemented
636	#131	—	2	1	no	—
637	#131	—	2	1	no	—
638	#131	—	73	8	no	—
639	#131	—	73	2	no	—
640	#131	—	73	2	no	—
641	#131	—	146	4	no	—
642	#131	—	146	1	no	—
643	#131	—	146	1	no	—
644	#131	C₂²×D₇₃	1	2	yes	complemented
645	#131	C₂²×D₇₃	1	2	yes	complemented
646	C₂×M₁₆	—	2	1	no	—
647	C₂×M₁₆	—	73	1	no	—
648	C₂×M₁₆	—	73	1	no	—
649	C₂×M₁₆	—	73	2	no	—
650	C₂×M₁₆	—	146	4	no	—
651	C₂×M₁₆	—	146	1	no	—
652	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
653	C₂²×C₈	—	2	1	no	—
654	C₂²×C₈	—	146	1	no	—
655	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
656	#127	—	73	4	no	—
657	#124	—	73	4	no	—
658	#121	—	292	2	no	—
659	#120	—	292	2	no	—
660	#117	—	73	1	no	—
661	#108	—	73	4	no	—
662	#108	—	73	2	no	—
663	#108	—	73	2	no	—
664	#104	—	73	4	no	—
665	#104	—	73	8	no	—
666	#104	—	73	4	no	—
667	#101	—	73	4	no	—
668	#100	—	73	4	no	—
669	#100	—	73	8	no	—
670	#97	—	73	2	no	—
671	C₄×C₈	—	73	2	no	—
672	C₂⁴	—	292	2	no	—
673	C₂⁴	—	146	2	no	—
674	#41	—	2	2	no	—
675	#41	—	2	1	no	—
676	#41	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	2	4	no	—
679	#41	—	2	4	no	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	2	no	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	2	2	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	#41	—	4	2	no	—
691	#41	—	4	2	no	—
692	#41	—	292	4	no	—
693	#41	—	292	4	no	—
694	#41	—	73	2	no	—
695	#41	—	73	2	no	—
696	#41	—	146	8	no	—
697	#41	—	146	8	no	—
698	#41	—	146	1	no	—
699	#41	—	146	1	no	—
700	#41	D₄×D₇₃	1	2	yes	—
701	#41	C₂×C₂²⋊D₇₃	1	4	yes	—
702	#41	C₂³×D₇₃	1	2	yes	—
703	#41	C₂³×D₇₃	1	4	yes	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	—	73	1	no	—
708	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
709	C₂×Q₈	C₂×C₂²⋊D₇₃	1	2	yes	—
710	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	292	2	no	—
721	C₂×D₄	—	292	4	no	—
722	C₂×D₄	—	292	8	no	—
723	C₂×D₄	—	292	8	no	—
724	C₂×D₄	—	292	4	no	—
725	C₂×D₄	—	292	2	no	—
726	C₂×D₄	—	292	4	no	—
727	C₂×D₄	—	73	1	no	—
728	C₂×D₄	—	73	4	no	—
729	C₂×D₄	—	146	8	no	—
730	C₂×D₄	—	146	8	no	—
731	C₂×D₄	—	146	1	no	—
732	C₂×D₄	—	146	2	no	—
733	C₂×D₄	—	146	2	no	—
734	C₂×D₄	—	146	2	no	—
735	C₂×D₄	—	146	2	no	—
736	C₂×D₄	—	146	2	no	—
737	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
738	C₂×D₄	C₂×C₂²⋊D₇₃	1	2	yes	—
739	C₂×D₄	C₂³×D₇₃	1	2	yes	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	4	4	no	—
744	C₂²×C₄	—	292	2	no	—
745	C₂²×C₄	—	146	1	no	—
746	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
747	Q₁₆	—	2	4	no	—
748	Q₁₆	—	2	1	no	—
749	Q₁₆	—	2	1	no	—
750	Q₁₆	—	73	4	no	—
751	Q₁₆	—	146	4	no	—
752	Q₁₆	C₂×C₂²⋊D₇₃	1	2	yes	—
753	Q₁₆	C₂×C₂²⋊D₇₃	1	2	yes	—
754	SD₁₆	—	2	4	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	2	2	no	—
757	SD₁₆	—	2	2	no	—
758	SD₁₆	—	73	4	no	—
759	SD₁₆	—	73	4	no	—
760	SD₁₆	—	146	8	no	—
761	SD₁₆	—	146	4	no	—
762	SD₁₆	—	146	4	no	—
763	SD₁₆	—	146	8	no	—
764	SD₁₆	—	146	8	no	—
765	SD₁₆	C₂×C₂²⋊D₇₃	1	4	yes	—
766	SD₁₆	C₂×C₂²⋊D₇₃	1	4	yes	—
767	D₈	—	2	4	no	—
768	D₈	—	2	1	no	—
769	D₈	—	2	1	no	—
770	D₈	—	73	4	no	—
771	D₈	—	146	8	no	—
772	D₈	—	146	4	no	—
773	D₈	—	146	8	no	—
774	D₈	—	146	8	no	—
775	D₈	—	146	2	no	—
776	D₈	—	146	2	no	—
777	D₈	—	146	2	no	—
778	D₈	—	146	2	no	—
779	D₈	C₂×C₂²⋊D₇₃	1	2	yes	—
780	D₈	C₂×C₂²⋊D₇₃	1	2	yes	—
781	M₁₆	—	2	1	no	—
782	M₁₆	—	2	2	no	—
783	M₁₆	—	2	2	no	—
784	M₁₆	—	73	2	no	—
785	M₁₆	—	73	2	no	—
786	M₁₆	—	73	4	no	—
787	M₁₆	—	73	2	no	—
788	M₁₆	—	146	8	no	—
789	M₁₆	—	146	2	no	—
790	M₁₆	—	146	1	no	—
791	M₁₆	—	146	2	no	—
792	M₁₆	—	146	2	no	—
793	M₁₆	C₂³×D₇₃	1	2	yes	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	73	2	no	—
798	C₂×C₈	—	146	8	no	—
799	C₂×C₈	—	146	2	no	—
800	C₂×C₈	—	146	1	no	—
801	C₂×C₈	—	146	2	no	—
802	C₂×C₈	—	146	2	no	—
803	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
804	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
805	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
806	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
807	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
808	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
809	C₄⋊C₄	—	146	1	no	—
810	C₂²⋊C₄	—	292	4	no	—
811	C₂²⋊C₄	—	146	1	no	—
812	C₄²	—	73	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	292	8	no	—
818	C₂³	—	292	2	no	—
819	C₂³	—	292	2	no	—
820	C₂³	—	1168	2	no	—
821	C₂³	—	1168	4	no	—
822	C₂³	—	146	1	no	—
823	C₂³	—	146	4	no	—
824	C₂³	#14556636	1	1	yes	characteristic
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	4	4	no	—
830	Q₈	—	73	2	no	—
831	Q₈	—	146	1	no	—
832	Q₈	C₂×D₄×D₇₃	1	2	yes	—
833	Q₈	C₂²×C₂²⋊D₇₃	1	4	yes	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	292	8	no	—
848	D₄	—	292	8	no	—
849	D₄	—	292	2	no	—
850	D₄	—	292	2	no	—
851	D₄	—	73	2	no	—
852	D₄	—	1168	4	no	—
853	D₄	—	146	2	no	—
854	D₄	—	146	2	no	—
855	D₄	—	146	4	no	—
856	D₄	—	146	4	no	—
857	D₄	—	146	1	no	—
858	D₄	C₂×D₄×D₇₃	1	2	yes	—
859	D₄	C₂²×C₂²⋊D₇₃	1	4	yes	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	292	8	no	—
873	C₂×C₄	—	146	2	no	—
874	C₂×C₄	—	146	1	no	—
875	C₂×C₄	—	146	2	no	—
876	C₂×C₄	—	146	2	no	—
877	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
878	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
881	C₂×C₄	#14556636	1	1	yes	characteristic
882	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	73	4	no	—
885	C₈	—	146	4	no	—
886	C₈	—	146	2	no	—
887	C₈	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
888	C₈	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
889	C₈	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
890	C₈	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	8	2	no	—
896	C₂²	—	8	1	no	—
897	C₂²	—	8	2	no	—
898	C₂²	—	16	4	no	—
899	C₂²	—	292	2	no	—
900	C₂²	—	292	4	no	—
901	C₂²	—	584	4	no	—
902	C₂²	—	584	4	no	—
903	C₂²	—	1168	2	no	—
904	C₂²	—	1168	8	no	—
905	C₂²	—	146	2	no	—
906	C₂²	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
907	C₂²	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
908	C₂²	C₂×#14556636	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	292	2	no	—
913	C₄	—	146	2	no	—
914	C₄	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
915	C₄	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
916	C₄	C₂²×D₄×D₇₃	1	1	yes	characteristic
917	C₄	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
918	C₂	—	2	1	no	—
919	C₂	—	2	1	no	—
920	C₂	—	2	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	8	2	no	—
924	C₂	—	292	2	no	—
925	C₂	—	584	4	no	—
926	C₂	C₂×D₄×C₂²⋊D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₂²⋊D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3584	C₂
socle	C₂×C₇₃	C₂×D₄²
hypercenter	#3584	D₇₃
hypocenter	C₇₃	#61106
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #22624710	C₂	semidirect
2. C₂×#17989389	C₂	semidirect
3. #22621728	C₂	semidirect
4. #22621717	C₂	semidirect
5. #22621693	C₂	semidirect
6. #22620418	C₂	semidirect
7. #22619661	C₂	semidirect
8. #22619647	C₂	semidirect
9. C₂×#17988857	C₂	semidirect
10. #22619303	C₂	semidirect
11. #22619286	C₂	semidirect
12. #22618848	C₂	semidirect
13. #22618832	C₂	semidirect
14. C₇₃×#3584	C₂	semidirect
15. C₂×#14556637	C₂²	semidirect
17. #17989395	C₂²	semidirect
19. #17989390	C₂²	semidirect
22. #17989389	C₂²	semidirect
23. #17989389	C₂²	semidirect
26. #17989385	C₂²	semidirect
29. C₂×#14556616	C₂²	semidirect
30. C₂×#14556616	C₂²	semidirect
31. C₂×#14556616	C₂²	semidirect
33. C₂²×D₅₈₄	C₂²	semidirect
35. #17989354	C₂²	semidirect
36. C₂×#14556597	C₂²	semidirect
37. #17989151	C₂²	semidirect
38. #17988973	C₂²	semidirect
39. #17988972	C₂²	semidirect
40. #17988962	C₂²	semidirect
41. #17988859	C₂²	semidirect
42. #17988857	C₂²	semidirect
43. #17988857	C₂²	semidirect
44. #17988855	C₂²	semidirect
45. #17988854	C₂²	semidirect
46. #17988852	C₂²	semidirect
47. #17988847	C₂²	semidirect
48. #17988763	C₂²	semidirect
49. #17988760	C₂²	semidirect
50. #17988755	C₂²	semidirect
51. #17988753	C₂²	semidirect
52. #17988709	C₂²	semidirect
53. #17988707	C₂²	semidirect
54. #17988704	C₂²	semidirect
55. #17988702	C₂²	semidirect
56. #17988635	C₂²	semidirect
57. C₂×#14556527	C₂²	semidirect
58. #17988604	C₂²	semidirect
59. #17988604	C₂²	semidirect
60. #17988603	C₂²	semidirect
61. #17988571	C₂²	semidirect
62. C₂×#14556507	C₂²	semidirect
63. #17988542	C₂²	semidirect
64. #585×C₇₃	C₂²	semidirect
66. #578×C₇₃	C₂²	semidirect
68. #577×C₇₃	C₂²	semidirect
70. #576×C₇₃	C₂²	semidirect
72. #575×C₇₃	C₂²	semidirect
75. C₂×#135×C₇₃	C₂²	semidirect
76. C₂×#131×C₇₃	C₂²	semidirect
89. #14556622	D₄	semidirect
92. #14556621	D₄	semidirect
96. #14556617	D₄	semidirect
105. #14556616	D₄	semidirect
107. #14556616	C₂³	semidirect
117. C₂×#11924015	C₂³	semidirect
127. C₂×#11924013	C₂³	semidirect
131. #14556598	C₂³	semidirect
142. #14556587	C₂³	semidirect
143. #14556580	C₂³	semidirect
147. #14556527	C₂³	semidirect
148. #14556527	C₂³	semidirect
149. #14556526	C₂³	semidirect
150. #14556518	C₂³	semidirect
151. #14556518	C₂³	semidirect
153. #14556510	C₂³	semidirect
154. #14556508	C₂³	semidirect
155. #14556507	C₂³	semidirect
156. #14556501	C₂³	semidirect
157. C₈×Dic₇₃	C₂³	semidirect
160. 2₋¹⁺⁴×C₇₃	C₂³	semidirect
164. H(5,𝔽₂)×C₇₃	C₂³	semidirect
174. #137×C₇₃	C₂³	semidirect
178. AGL(1,ℤ/8)×C₇₃	C₂³	semidirect
187. #135×C₇₃	D₄	semidirect
188. #135×C₇₃	D₄	semidirect
192. C₂×Q₁₆×C₇₃	D₄	semidirect
193. C₂×Q₁₆×C₇₃	C₂³	semidirect
195. C₂×SD₁₆×C₇₃	D₄	semidirect
196. C₂×SD₁₆×C₇₃	C₂³	semidirect
198. C₂×D₈×C₇₃	D₄	semidirect
199. C₂×D₈×C₇₃	C₂³	semidirect
202. #131×C₇₃	C₂³	semidirect
203. #131×C₇₃	C₂³	semidirect
465. #3584	D₇₃	semidirect
478. C₇₃	#61106	semidirect
479. #585	C₂×D₇₃	semidirect
482. #578	C₂×D₇₃	semidirect
486. #577	C₂×D₇₃	semidirect
494. #576	C₂×D₇₃	semidirect
499. #575	C₂×D₇₃	semidirect
508. C₂×#135	C₂×D₇₃	semidirect
513. C₂×#131	C₂×D₇₃	semidirect
543. 2₋¹⁺⁴	C₂²×D₇₃	semidirect
551. H(5,𝔽₂)	C₂²×D₇₃	semidirect
573. #137	C₂²×D₇₃	semidirect
592. AGL(1,ℤ/8)	C₂²×D₇₃	semidirect
607. #135	C₂²⋊D₇₃	semidirect
608. #135	C₂²⋊D₇₃	semidirect
612. C₂×Q₁₆	C₂²⋊D₇₃	semidirect
613. C₂×Q₁₆	C₂²×D₇₃	semidirect
619. C₂×SD₁₆	C₂²⋊D₇₃	semidirect
620. C₂×SD₁₆	C₂²×D₇₃	semidirect
634. C₂×D₈	C₂²⋊D₇₃	semidirect
635. C₂×D₈	C₂²×D₇₃	semidirect
644. #131	C₂²×D₇₃	semidirect
645. #131	C₂²×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22624710	2
C₂×#17989389	2
#22621728	2
#22621717	2
#22621693	2
#22620418	2
#22619661	2
#22619647	2
C₂×#17988857	2
#22619303	2
#22619286	2
#22618848	2
#22618832	2
C₇₃×#3584	2
#61106	73