Subgroups — #3291×D₇₃ #33962198

Order 18688.

2682 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#577×D₇₃	C₂	1	4	yes	maximal, complemented
2	#22621726	C₂	1	2	yes	maximal, complemented
3	#22621725	C₂	1	2	yes	maximal, complemented
4	#22621724	C₂	1	1	yes	maximal, characteristic, complemented
5	#22621723	C₂	1	4	yes	maximal, complemented
6	#22621722	C₂	1	4	yes	maximal, complemented
7	#22621721	C₂	1	2	yes	maximal, complemented
8	#492×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#471×D₇₃	C₂	1	4	yes	maximal, complemented
10	#456×D₇₃	C₂	1	2	yes	maximal, complemented
11	#453×D₇₃	C₂	1	2	yes	maximal, complemented
12	#443×D₇₃	C₂	1	2	yes	maximal, complemented
13	C₇₃×#3291	C₂	1	1	yes	maximal, characteristic, complemented
14	2₋¹⁺⁴×D₇₃	C₂²	1	2	yes	—
15	H(5,𝔽₂)×D₇₃	C₂²	1	2	yes	complemented
16	#17989399	C₂²	1	4	yes	complemented
17	#17989398	C₂²	1	4	yes	complemented
18	#17989397	—	2	4	no	—
19	#17989397	C₂²	1	4	yes	complemented
20	#17989396	—	2	4	no	—
21	#17989396	C₂²	1	4	yes	complemented
22	#17989395	C₂²	1	4	yes	complemented
23	#17989394	—	2	4	no	—
24	#17989394	C₂²	1	4	yes	complemented
25	#17989393	—	2	4	no	—
26	#17989393	C₂²	1	4	yes	complemented
27	#137×D₇₃	—	2	4	no	—
28	#137×D₇₃	C₂²	1	4	yes	complemented
29	AGL(1,ℤ/8)×D₇₃	—	2	4	no	—
30	AGL(1,ℤ/8)×D₇₃	C₂²	1	4	yes	—
31	#135×D₇₃	—	2	4	no	—
32	#135×D₇₃	C₂²	1	2	yes	—
33	C₂×SD₁₆×D₇₃	—	2	4	no	—
34	C₂×SD₁₆×D₇₃	C₂²	1	4	yes	complemented
35	#131×D₇₃	C₂²	1	4	yes	complemented
36	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
37	#127×D₇₃	C₂²	1	1	yes	characteristic
38	#17988961	C₂²	1	1	yes	characteristic, complemented
39	#17988960	C₂²	1	1	yes	characteristic, complemented
40	#17988959	C₂²	1	1	yes	characteristic, complemented
41	#17988958	C₂²	1	4	yes	complemented
42	#17988853	C₂²	1	4	yes	complemented
43	#17988852	C₂²	1	4	yes	complemented
44	#17988851	C₂²	1	4	yes	complemented
45	#17988850	C₂²	1	4	yes	complemented
46	#17988849	C₂²	1	4	yes	complemented
47	#17988848	C₂²	1	4	yes	complemented
48	#17988847	C₂²	1	4	yes	complemented
49	#17988772	C₂²	1	2	yes	complemented
50	#17988771	C₂²	1	4	yes	complemented
51	#17988770	C₂²	1	2	yes	complemented
52	#17988769	C₂²	1	2	yes	complemented
53	#17988768	C₂²	1	4	yes	complemented
54	#17988757	C₂²	1	2	yes	complemented
55	#17988756	C₂²	1	4	yes	complemented
56	#17988755	C₂²	1	2	yes	complemented
57	#17988754	C₂²	1	2	yes	complemented
58	#17988753	C₂²	1	4	yes	complemented
59	#17988705	C₂²	1	2	yes	complemented
60	#17988704	C₂²	1	2	yes	complemented
61	#17988703	C₂²	1	2	yes	complemented
62	#17988702	C₂²	1	4	yes	complemented
63	#17988701	C₂²	1	4	yes	complemented
64	#108×D₇₃	C₂²	1	2	yes	complemented
65	#104×D₇₃	C₂²	1	4	yes	complemented
66	#101×D₇₃	C₂²	1	2	yes	complemented
67	#100×D₇₃	C₂²	1	2	yes	complemented
68	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
69	#577×C₇₃	C₂²	1	4	yes	complemented
70	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
71	#471×C₇₃	C₂²	1	4	yes	complemented
72	#456×C₇₃	C₂²	1	2	yes	complemented
73	#453×C₇₃	C₂²	1	2	yes	complemented
74	#443×C₇₃	C₂²	1	2	yes	complemented
75	#14556639	—	2	4	no	—
76	#14556639	C₂³	1	2	yes	—
77	#14556638	—	2	4	no	—
78	#14556638	—	4	2	no	—
79	#14556638	C₂³	1	4	yes	—
80	#14556637	—	2	4	no	—
81	#14556637	C₂³	1	4	yes	complemented
82	#14556636	—	2	4	no	—
83	#14556636	—	4	2	no	—
84	#14556636	C₂³	1	2	yes	complemented
85	#41×D₇₃	—	2	4	no	—
86	#41×D₇₃	—	2	4	no	—
87	#41×D₇₃	—	4	2	no	—
88	#41×D₇₃	C₂³	1	4	yes	—
89	C₂×Q₈×D₇₃	—	2	4	no	—
90	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
91	C₂×D₄×D₇₃	—	2	4	no	—
92	C₂×D₄×D₇₃	—	4	1	no	—
93	C₂×D₄×D₇₃	—	4	2	no	—
94	C₂×D₄×D₇₃	C₂³	1	2	yes	—
95	#14556624	—	2	4	no	—
96	#14556624	C₂³	1	4	yes	complemented
97	#14556623	—	2	4	no	—
98	#14556623	—	2	4	no	—
99	#14556623	—	2	4	no	—
100	#14556622	—	2	4	no	—
101	#14556622	C₂³	1	4	yes	complemented
102	#14556621	—	2	4	no	—
103	#14556621	C₂³	1	4	yes	complemented
104	#14556620	—	2	4	no	—
105	#14556620	—	2	4	no	—
106	#14556620	—	2	4	no	—
107	#14556619	—	2	4	no	—
108	#14556619	C₂³	1	4	yes	—
109	#14556618	—	2	4	no	—
110	#14556618	—	2	4	no	—
111	#14556618	—	2	4	no	—
112	#14556617	—	2	4	no	—
113	#14556617	C₂³	1	4	yes	—
114	#14556616	—	2	4	no	—
115	#14556616	C₂³	1	4	yes	—
116	#14556615	—	2	4	no	—
117	#14556615	—	2	4	no	—
118	#14556615	—	2	4	no	—
119	#14556614	—	2	4	no	—
120	#14556614	D₄	1	2	yes	complemented
121	#14556613	—	2	4	no	—
122	#14556613	C₂³	1	2	yes	—
123	#14556612	—	2	4	no	—
124	#14556612	—	2	4	no	—
125	#14556612	D₄	1	4	yes	complemented
126	#14556611	—	2	4	no	—
127	#14556611	—	2	4	no	—
128	#14556611	C₂³	1	4	yes	—
129	#14556610	—	2	4	no	—
130	#14556610	D₄	1	2	yes	complemented
131	Q₁₆×D₇₃	—	2	4	no	—
132	Q₁₆×D₇₃	D₄	1	2	yes	complemented
133	C₂×#11924017	—	2	4	no	—
134	C₂×#11924017	C₂³	1	4	yes	complemented
135	C₂×#11924016	—	2	4	no	—
136	C₂×#11924016	C₂³	1	4	yes	complemented
137	C₂×#11924015	—	2	4	no	—
138	C₂×#11924015	C₂³	1	4	yes	complemented
139	SD₁₆×D₇₃	—	2	4	no	—
140	SD₁₆×D₇₃	—	2	4	no	—
141	SD₁₆×D₇₃	—	2	4	no	—
142	SD₁₆×D₇₃	—	2	4	no	—
143	SD₁₆×D₇₃	—	2	4	no	—
144	SD₁₆×D₇₃	—	2	4	no	—
145	SD₁₆×D₇₃	—	2	4	no	—
146	SD₁₆×D₇₃	—	2	4	no	—
147	SD₁₆×D₇₃	—	2	4	no	—
148	SD₁₆×D₇₃	—	2	4	no	—
149	SD₁₆×D₇₃	D₄	1	4	yes	complemented
150	D₈×D₇₃	—	2	4	no	—
151	D₈×D₇₃	D₄	1	2	yes	complemented
152	#14556599	—	2	4	no	—
153	#14556599	C₂³	1	4	yes	complemented
154	#14556598	C₂³	1	4	yes	complemented
155	#14556597	—	2	4	no	—
156	#14556597	C₂³	1	4	yes	complemented
157	M₁₆×D₇₃	—	2	4	no	—
158	M₁₆×D₇₃	C₂³	1	4	yes	—
159	C₂×C₈×D₇₃	—	2	4	no	—
160	C₂×C₈×D₇₃	C₂³	1	2	yes	—
161	#14556591	C₂³	1	1	yes	characteristic, complemented
162	#14556590	—	4	1	no	—
163	#14556589	C₂³	1	2	yes	complemented
164	#14556588	C₂³	1	1	yes	characteristic
165	#14556587	—	4	1	no	—
166	#14556587	C₂³	1	2	yes	—
167	C₄⋊C₄×D₇₃	—	4	1	no	—
168	C₄²×D₇₃	C₂³	1	1	yes	characteristic
169	#14556527	C₂³	1	2	yes	complemented
170	#14556526	C₂³	1	4	yes	complemented
171	#14556519	C₂³	1	4	yes	complemented
172	#14556518	C₂³	1	4	yes	complemented
173	#14556517	C₂³	1	4	yes	complemented
174	#14556510	C₂³	1	2	yes	complemented
175	#14556509	C₂³	1	4	yes	complemented
176	#14556508	C₂³	1	2	yes	complemented
177	#14556507	C₂³	1	4	yes	complemented
178	C₄×#10596831	C₂³	1	1	yes	characteristic, complemented
179	C₈×Dic₇₃	C₂³	1	2	yes	complemented
180	2₋¹⁺⁴×C₇₃	C₂³	1	2	yes	—
181	H(5,𝔽₂)×C₇₃	C₂³	1	2	yes	complemented
182	#137×C₇₃	—	2	4	no	—
183	#137×C₇₃	C₂³	1	4	yes	complemented
184	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
185	AGL(1,ℤ/8)×C₇₃	C₂³	1	4	yes	—
186	#135×C₇₃	—	2	4	no	—
187	#135×C₇₃	C₂³	1	2	yes	—
188	C₂×SD₁₆×C₇₃	—	2	4	no	—
189	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	complemented
190	#131×C₇₃	C₂³	1	4	yes	complemented
191	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic, complemented
192	#127×C₇₃	C₂³	1	1	yes	characteristic
193	#108×C₇₃	C₂³	1	2	yes	complemented
194	#104×C₇₃	C₂³	1	4	yes	complemented
195	#101×C₇₃	C₂³	1	2	yes	complemented
196	#100×C₇₃	C₂³	1	2	yes	complemented
197	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic, complemented
198	C₂³×D₇₃	—	2	2	no	—
199	C₂³×D₇₃	—	4	2	no	—
200	#11924029	—	2	4	no	—
201	#11924029	—	2	4	no	—
202	#11924029	—	4	2	no	—
203	#11924029	C₂×D₄	1	4	yes	—
204	#11924028	—	2	4	no	—
205	#11924028	—	2	4	no	—
206	#11924028	—	2	4	no	—
207	#11924028	—	4	4	no	—
208	#11924028	—	4	4	no	—
209	#11924028	—	4	4	no	—
210	#11924028	—	4	2	no	—
211	#11924028	C₂⁴	1	4	yes	—
212	#11924027	—	2	4	no	—
213	#11924027	—	2	4	no	—
214	#11924027	—	2	4	no	—
215	#11924027	—	4	4	no	—
216	#11924027	—	4	4	no	—
217	#11924027	—	4	4	no	—
218	#11924027	—	4	2	no	—
219	#11924027	C₂×D₄	1	4	yes	—
220	C₂×Dic₁₄₆	—	2	4	no	—
221	C₂×Dic₁₄₆	—	2	2	no	—
222	C₂×Dic₁₄₆	—	4	4	no	—
223	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
224	Q₈×D₇₃	—	2	4	no	—
225	Q₈×D₇₃	—	2	4	no	—
226	Q₈×D₇₃	—	2	4	no	—
227	Q₈×D₇₃	—	2	4	no	—
228	Q₈×D₇₃	—	4	4	no	—
229	Q₈×D₇₃	—	4	2	no	—
230	Q₈×D₇₃	C₂×D₄	1	4	yes	—
231	C₂×D₂₉₂	—	2	4	no	—
232	C₂×D₂₉₂	—	4	2	no	—
233	C₂×D₂₉₂	—	4	1	no	—
234	C₂×D₂₉₂	C₂⁴	1	2	yes	—
235	C₂×C₂²⋊D₇₃	—	2	2	no	—
236	C₂×C₂²⋊D₇₃	—	4	4	no	—
237	C₂×C₂²⋊D₇₃	—	4	2	no	—
238	C₂×C₂²⋊D₇₃	—	4	2	no	—
239	C₂×C₂²⋊D₇₃	—	4	2	no	—
240	D₄×D₇₃	—	2	4	no	—
241	D₄×D₇₃	—	2	4	no	—
242	D₄×D₇₃	—	2	4	no	—
243	D₄×D₇₃	—	2	4	no	—
244	D₄×D₇₃	—	2	4	no	—
245	D₄×D₇₃	—	4	4	no	—
246	D₄×D₇₃	—	4	4	no	—
247	D₄×D₇₃	—	4	4	no	—
248	D₄×D₇₃	—	4	4	no	—
249	D₄×D₇₃	—	4	2	no	—
250	D₄×D₇₃	—	8	4	no	—
251	D₄×D₇₃	C₂×D₄	1	4	yes	—
252	C₂×C₄×D₇₃	—	2	1	no	—
253	C₂×C₄×D₇₃	—	2	4	no	—
254	C₂×C₄×D₇₃	—	2	2	no	—
255	C₂×C₄×D₇₃	—	4	2	no	—
256	C₂×C₄×D₇₃	—	4	4	no	—
257	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
258	Dic₂₉₂	—	2	4	no	—
259	Dic₂₉₂	C₂×D₄	1	2	yes	complemented
260	#11924018	—	2	4	no	—
261	#11924018	—	2	4	no	—
262	#11924018	C₂×D₄	1	4	yes	complemented
263	#11924017	—	2	4	no	—
264	#11924017	—	2	4	no	—
265	#11924017	—	2	4	no	—
266	#11924017	—	2	4	no	—
267	#11924017	C₂×D₄	1	4	yes	complemented
268	#11924016	—	2	4	no	—
269	#11924016	—	2	4	no	—
270	#11924016	—	2	4	no	—
271	#11924016	—	2	4	no	—
272	#11924016	C₂×D₄	1	4	yes	complemented
273	#11924015	—	2	4	no	—
274	#11924015	—	2	4	no	—
275	#11924015	—	2	4	no	—
276	#11924015	—	2	4	no	—
277	#11924015	C₂×D₄	1	4	yes	complemented
278	D₅₈₄	—	2	4	no	—
279	D₅₈₄	C₂×D₄	1	2	yes	complemented
280	#11924013	—	2	4	no	—
281	#11924013	—	2	4	no	—
282	#11924013	C₂×D₄	1	4	yes	complemented
283	#11924012	—	2	4	no	—
284	#11924012	C₂⁴	1	4	yes	—
285	#11924011	—	2	4	no	—
286	#11924011	—	2	4	no	—
287	#11924011	—	2	4	no	—
288	C₂×#10596831	—	2	4	no	—
289	C₂×#10596831	C₂⁴	1	2	yes	—
290	C₈×D₇₃	—	2	4	no	—
291	C₈×D₇₃	—	2	4	no	—
292	C₈×D₇₃	—	2	4	no	—
293	C₈×D₇₃	C₂×D₄	1	2	yes	—
294	C₈×D₇₃	C₂×D₄	1	2	yes	—
295	C₈×D₇₃	C₂×D₄	1	2	yes	—
296	C₈×D₇₃	C₂×D₄	1	2	yes	—
297	C₄⋊Dic₇₃	—	4	1	no	—
298	#11924007	—	4	2	no	—
299	C₄×Dic₇₃	—	2	1	no	—
300	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
301	#41×C₇₃	—	2	4	no	—
302	#41×C₇₃	—	2	4	no	—
303	#41×C₇₃	—	4	2	no	—
304	#41×C₇₃	C₂⁴	1	4	yes	—
305	C₂×Q₈×C₇₃	—	2	4	no	—
306	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₇₃	—	2	4	no	—
308	C₂×D₄×C₇₃	—	4	1	no	—
309	C₂×D₄×C₇₃	—	4	2	no	—
310	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
311	Q₁₆×C₇₃	—	2	4	no	—
312	Q₁₆×C₇₃	C₂×D₄	1	2	yes	complemented
313	SD₁₆×C₇₃	—	2	4	no	—
314	SD₁₆×C₇₃	—	2	4	no	—
315	SD₁₆×C₇₃	—	2	4	no	—
316	SD₁₆×C₇₃	—	2	4	no	—
317	SD₁₆×C₇₃	C₂×D₄	1	4	yes	complemented
318	D₈×C₇₃	—	2	4	no	—
319	D₈×C₇₃	C₂×D₄	1	2	yes	complemented
320	M₁₆×C₇₃	—	2	4	no	—
321	M₁₆×C₇₃	C₂⁴	1	4	yes	—
322	C₂×C₈×C₇₃	—	2	4	no	—
323	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₇₃	—	4	1	no	—
325	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
326	C₂³×C₇₃	—	2	2	no	—
327	C₂³×C₇₃	—	4	2	no	—
328	C₂²×D₇₃	—	2	4	no	—
329	C₂²×D₇₃	—	2	2	no	—
330	C₂²×D₇₃	—	4	2	no	—
331	C₂²×D₇₃	—	4	4	no	—
332	C₂²×D₇₃	—	4	2	no	—
333	C₂²×D₇₃	—	4	2	no	—
334	C₂²×D₇₃	—	8	4	no	—
335	C₂²×D₇₃	—	16	4	no	—
336	C₂²×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
337	Q₈×C₇₃	—	2	4	no	—
338	Q₈×C₇₃	—	4	2	no	—
339	Q₈×C₇₃	C₂²×D₄	1	4	yes	—
340	D₄×C₇₃	—	2	4	no	—
341	D₄×C₇₃	—	2	4	no	—
342	D₄×C₇₃	—	4	4	no	—
343	D₄×C₇₃	—	4	2	no	—
344	D₄×C₇₃	—	8	2	no	—
345	D₄×C₇₃	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₇₃	—	2	1	no	—
347	C₂×C₄×C₇₃	—	2	4	no	—
348	C₂×C₄×C₇₃	—	2	2	no	—
349	C₂×C₄×C₇₃	—	4	2	no	—
350	C₂×C₄×C₇₃	—	4	4	no	—
351	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
352	C₂²⋊D₇₃	—	2	4	no	—
353	C₂²⋊D₇₃	—	2	4	no	—
354	C₂²⋊D₇₃	—	2	4	no	—
355	C₂²⋊D₇₃	—	4	4	no	—
356	C₂²⋊D₇₃	—	4	4	no	—
357	C₂²⋊D₇₃	—	4	4	no	—
358	C₂²⋊D₇₃	—	4	4	no	—
359	C₂²⋊D₇₃	—	8	4	no	—
360	C₂×Dic₇₃	—	2	1	no	—
361	C₂×Dic₇₃	—	2	4	no	—
362	C₂×Dic₇₃	—	2	2	no	—
363	C₂×Dic₇₃	—	4	2	no	—
364	C₂×Dic₇₃	—	4	4	no	—
365	C₂×Dic₇₃	H(5,𝔽₂)	1	1	yes	characteristic
366	D₂₉₂	—	2	4	no	—
367	D₂₉₂	—	2	4	no	—
368	D₂₉₂	—	4	4	no	—
369	D₂₉₂	—	4	2	no	—
370	D₂₉₂	—	8	2	no	—
371	D₂₉₂	C₂²×D₄	1	4	yes	—
372	C₄×D₇₃	—	2	4	no	—
373	C₄×D₇₃	—	2	4	no	—
374	C₄×D₇₃	—	2	4	no	—
375	C₄×D₇₃	—	2	4	no	—
376	C₄×D₇₃	—	4	4	no	—
377	C₄×D₇₃	—	4	4	no	—
378	C₄×D₇₃	—	4	4	no	—
379	C₄×D₇₃	—	4	2	no	—
380	C₄×D₇₃	—	4	2	no	—
381	C₄×D₇₃	C₂²×D₄	1	2	yes	—
382	C₄×D₇₃	C₂²×D₄	1	2	yes	—
383	Dic₁₄₆	—	2	4	no	—
384	Dic₁₄₆	—	2	4	no	—
385	Dic₁₄₆	—	4	2	no	—
386	Dic₁₄₆	—	4	4	no	—
387	Dic₁₄₆	—	4	4	no	—
388	Dic₁₄₆	C₂²×D₄	1	4	yes	—
389	C₈×C₇₃	—	2	4	no	—
390	C₈×C₇₃	C₂²×D₄	1	2	yes	—
391	C₈×C₇₃	C₂²×D₄	1	2	yes	—
392	#10596831	—	2	4	no	—
393	#10596831	C₂²×D₄	1	2	yes	—
394	#10596831	C₂²×D₄	1	2	yes	—
395	C₂²×C₇₃	—	2	4	no	—
396	C₂²×C₇₃	—	4	2	no	—
397	C₂²×C₇₃	—	8	2	no	—
398	C₂²×C₇₃	—	16	2	no	—
399	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×D₇₃	—	2	2	no	—
401	C₂×D₇₃	—	2	4	no	—
402	C₂×D₇₃	—	4	8	no	—
403	C₂×D₇₃	—	4	2	no	—
404	C₂×D₇₃	—	8	4	no	—
405	C₂×D₇₃	—	8	2	no	—
406	C₂×D₇₃	—	16	2	no	—
407	C₂×D₇₃	—	16	2	no	—
408	C₂×D₇₃	—	16	4	no	—
409	C₂×D₇₃	D₄²	1	1	yes	characteristic
410	C₂×D₇₃	D₄²	1	1	yes	characteristic
411	C₄×C₇₃	—	2	2	no	—
412	C₄×C₇₃	—	2	4	no	—
413	C₄×C₇₃	—	4	2	no	—
414	C₄×C₇₃	C₂³×D₄	1	2	yes	—
415	Dic₇₃	—	2	2	no	—
416	Dic₇₃	—	2	4	no	—
417	Dic₇₃	—	4	2	no	—
418	Dic₇₃	D₄²	1	2	yes	—
419	C₂×#3291	—	73	1	no	maximal, Sylow
420	C₂×C₇₃	—	2	1	no	—
421	C₂×C₇₃	—	4	4	no	—
422	C₂×C₇₃	—	8	2	no	—
423	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
424	D₇₃	—	2	1	no	—
425	D₇₃	—	4	4	no	—
426	D₇₃	—	8	2	no	—
427	D₇₃	#3291	1	2	yes	direct product factor
428	C₂×#577	—	73	4	no	—
429	#3291	—	73	1	no	—
430	#3291	—	73	4	no	—
431	#3291	—	73	2	no	—
432	#3291	—	73	2	no	—
433	#3291	—	73	2	no	—
434	#3291	—	73	4	no	—
435	#3291	D₇₃	1	1	yes	characteristic, direct product factor
436	C₂×#492	—	73	1	no	—
437	C₂×#471	—	73	4	no	—
438	C₂×#456	—	73	2	no	—
439	C₂×#453	—	73	2	no	—
440	C₂×#443	—	73	2	no	—
441	C₇₃	C₂×#3291	1	1	yes	characteristic, complemented, Sylow
442	C₂×2₋¹⁺⁴	—	73	2	no	—
443	C₂×H(5,𝔽₂)	—	73	2	no	—
444	#577	—	73	4	no	—
445	#577	—	73	4	no	—
446	#577	—	73	4	no	—
447	#577	—	73	4	no	—
448	#577	—	73	4	no	—
449	#577	—	73	4	no	—
450	#577	—	73	4	no	—
451	#577	—	146	4	no	—
452	#577	—	146	4	no	—
453	#577	—	146	4	no	—
454	#577	—	146	4	no	—
455	#577	C₂×D₇₃	1	4	yes	complemented
456	C₂×#137	—	73	4	no	—
457	C₂×#137	—	146	4	no	—
458	C₂×AGL(1,ℤ/8)	—	73	4	no	—
459	C₂×AGL(1,ℤ/8)	—	146	4	no	—
460	C₂×#135	—	73	2	no	—
461	C₂×#135	—	146	4	no	—
462	C₂²×SD₁₆	—	73	4	no	—
463	C₂²×SD₁₆	—	146	4	no	—
464	C₂×#131	—	73	4	no	—
465	C₂×C₄⋊Q₈	—	73	1	no	—
466	C₂×#127	—	73	1	no	—
467	#492	—	73	4	no	—
468	#492	—	73	1	no	—
469	#492	—	73	1	no	—
470	#492	—	73	1	no	—
471	#492	C₂×D₇₃	1	1	yes	characteristic, complemented
472	#471	—	73	4	no	—
473	#471	—	73	4	no	—
474	#471	—	73	4	no	—
475	#471	—	73	4	no	—
476	#471	—	73	4	no	—
477	#471	—	73	4	no	—
478	#471	—	73	4	no	—
479	#471	C₂×D₇₃	1	4	yes	complemented
480	#456	—	73	2	no	—
481	#456	—	73	4	no	—
482	#456	—	73	2	no	—
483	#456	—	73	4	no	—
484	#456	—	73	2	no	—
485	#456	C₂×D₇₃	1	2	yes	complemented
486	#453	—	73	2	no	—
487	#453	—	73	4	no	—
488	#453	—	73	2	no	—
489	#453	—	73	4	no	—
490	#453	—	73	2	no	—
491	#453	C₂×D₇₃	1	2	yes	complemented
492	#443	—	73	2	no	—
493	#443	—	73	4	no	—
494	#443	—	73	2	no	—
495	#443	—	73	4	no	—
496	#443	—	73	2	no	—
497	#443	C₂×D₇₃	1	2	yes	complemented
498	C₂×#108	—	73	2	no	—
499	C₂×#104	—	73	4	no	—
500	C₂×#101	—	73	2	no	—
501	C₂×#100	—	73	2	no	—
502	C₂×C₄×C₈	—	73	1	no	—
503	2₋¹⁺⁴	—	292	2	no	—
504	2₋¹⁺⁴	—	73	4	no	—
505	2₋¹⁺⁴	—	73	2	no	—
506	2₋¹⁺⁴	—	146	4	no	—
507	2₋¹⁺⁴	—	146	4	no	—
508	2₋¹⁺⁴	C₂²×D₇₃	1	2	yes	—
509	H(5,𝔽₂)	—	292	2	no	—
510	H(5,𝔽₂)	—	73	4	no	—
511	H(5,𝔽₂)	—	73	2	no	—
512	H(5,𝔽₂)	—	146	4	no	—
513	H(5,𝔽₂)	—	146	4	no	—
514	H(5,𝔽₂)	C₂²×D₇₃	1	2	yes	complemented
515	C₂×#41	—	292	2	no	—
516	C₂×#41	—	73	4	no	—
517	C₂×#41	—	146	4	no	—
518	C₂×#41	—	146	4	no	—
519	C₂²×Q₈	—	73	2	no	—
520	C₂²×Q₈	—	146	4	no	—
521	C₂²×D₄	—	292	2	no	—
522	C₂²×D₄	—	292	1	no	—
523	C₂²×D₄	—	73	2	no	—
524	C₂²×D₄	—	146	4	no	—
525	#137	—	2	4	no	—
526	#137	—	73	4	no	—
527	#137	—	73	4	no	—
528	#137	—	73	4	no	—
529	#137	—	146	4	no	—
530	#137	—	146	4	no	—
531	#137	—	146	4	no	—
532	#137	—	146	4	no	—
533	#137	—	146	4	no	—
534	#137	—	146	4	no	—
535	#137	—	146	4	no	—
536	#137	—	146	4	no	—
537	#137	—	146	4	no	—
538	#137	C₂²×D₇₃	1	4	yes	complemented
539	AGL(1,ℤ/8)	—	2	4	no	—
540	AGL(1,ℤ/8)	—	73	4	no	—
541	AGL(1,ℤ/8)	—	73	4	no	—
542	AGL(1,ℤ/8)	—	73	4	no	—
543	AGL(1,ℤ/8)	—	146	4	no	—
544	AGL(1,ℤ/8)	—	146	4	no	—
545	AGL(1,ℤ/8)	—	146	4	no	—
546	AGL(1,ℤ/8)	—	146	4	no	—
547	AGL(1,ℤ/8)	—	146	4	no	—
548	AGL(1,ℤ/8)	—	146	4	no	—
549	AGL(1,ℤ/8)	—	146	4	no	—
550	AGL(1,ℤ/8)	—	146	4	no	—
551	AGL(1,ℤ/8)	—	146	4	no	—
552	AGL(1,ℤ/8)	C₂²×D₇₃	1	4	yes	—
553	#135	—	2	4	no	—
554	#135	—	73	4	no	—
555	#135	—	73	2	no	—
556	#135	—	73	4	no	—
557	#135	—	73	2	no	—
558	#135	—	73	2	no	—
559	#135	—	146	4	no	—
560	#135	—	146	4	no	—
561	#135	—	146	4	no	—
562	#135	—	146	4	no	—
563	#135	—	146	4	no	—
564	#135	—	146	4	no	—
565	#135	—	146	4	no	—
566	#135	C₂²×D₇₃	1	2	yes	—
567	C₂×Q₁₆	—	73	2	no	—
568	C₂×Q₁₆	—	146	4	no	—
569	C₂×SD₁₆	—	2	4	no	—
570	C₂×SD₁₆	—	73	4	no	—
571	C₂×SD₁₆	—	73	4	no	—
572	C₂×SD₁₆	—	73	4	no	—
573	C₂×SD₁₆	—	73	4	no	—
574	C₂×SD₁₆	—	146	4	no	—
575	C₂×SD₁₆	—	146	4	no	—
576	C₂×SD₁₆	—	146	4	no	—
577	C₂×SD₁₆	—	146	4	no	—
578	C₂×SD₁₆	—	146	4	no	—
579	C₂×SD₁₆	—	146	4	no	—
580	C₂×SD₁₆	—	146	4	no	—
581	C₂×SD₁₆	—	146	4	no	—
582	C₂×SD₁₆	—	146	4	no	—
583	C₂×SD₁₆	—	146	4	no	—
584	C₂×SD₁₆	—	146	4	no	—
585	C₂×SD₁₆	—	146	4	no	—
586	C₂×SD₁₆	—	146	4	no	—
587	C₂×SD₁₆	C₂²×D₇₃	1	4	yes	complemented
588	C₂×D₈	—	73	2	no	—
589	C₂×D₈	—	146	4	no	—
590	#131	—	73	4	no	—
591	#131	—	73	4	no	—
592	#131	—	73	4	no	—
593	#131	—	146	4	no	—
594	#131	—	146	4	no	—
595	#131	C₂²×D₇₃	1	4	yes	complemented
596	C₂×M₁₆	—	73	4	no	—
597	C₂×M₁₆	—	146	4	no	—
598	C₂²×C₈	—	73	2	no	—
599	C₂²×C₈	—	146	4	no	—
600	C₄⋊Q₈	—	292	1	no	—
601	C₄⋊Q₈	—	73	2	no	—
602	C₄⋊Q₈	—	73	1	no	—
603	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic, complemented
604	#127	—	292	1	no	—
605	#127	—	73	2	no	—
606	#127	—	73	1	no	—
607	#127	C₂²×D₇₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	—	292	1	no	—
609	C₂×C₄²	—	73	1	no	—
610	#108	—	73	4	no	—
611	#108	—	73	2	no	—
612	#108	C₂²×D₇₃	1	2	yes	complemented
613	#104	—	73	4	no	—
614	#104	—	73	4	no	—
615	#104	—	73	4	no	—
616	#104	C₂²×D₇₃	1	4	yes	complemented
617	#101	—	73	2	no	—
618	#101	—	73	4	no	—
619	#101	C₂²×D₇₃	1	2	yes	complemented
620	#100	—	73	2	no	—
621	#100	—	73	4	no	—
622	#100	C₂²×D₇₃	1	2	yes	complemented
623	C₄×C₈	—	73	2	no	—
624	C₄×C₈	—	73	1	no	—
625	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic, complemented
626	C₂⁴	—	292	2	no	—
627	C₂⁴	—	146	2	no	—
628	#41	—	2	4	no	—
629	#41	—	2	4	no	—
630	#41	—	4	2	no	—
631	#41	—	292	2	no	—
632	#41	—	292	4	no	—
633	#41	—	292	4	no	—
634	#41	—	292	4	no	—
635	#41	—	292	2	no	—
636	#41	—	292	2	no	—
637	#41	—	292	4	no	—
638	#41	—	292	4	no	—
639	#41	—	292	4	no	—
640	#41	—	73	4	no	—
641	#41	—	73	4	no	—
642	#41	—	73	4	no	—
643	#41	—	146	4	no	—
644	#41	—	146	4	no	—
645	#41	—	146	4	no	—
646	#41	—	146	4	no	—
647	#41	—	146	4	no	—
648	#41	—	146	4	no	—
649	#41	—	146	4	no	—
650	#41	—	146	4	no	—
651	#41	C₂³×D₇₃	1	4	yes	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	292	4	no	—
654	C₂×Q₈	—	292	4	no	—
655	C₂×Q₈	—	292	2	no	—
656	C₂×Q₈	—	73	4	no	—
657	C₂×Q₈	—	73	2	no	—
658	C₂×Q₈	—	146	4	no	—
659	C₂×Q₈	—	146	2	no	—
660	C₂×Q₈	—	146	4	no	—
661	C₂×Q₈	—	146	4	no	—
662	C₂×Q₈	—	146	4	no	—
663	C₂×Q₈	—	146	4	no	—
664	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	292	1	no	—
669	C₂×D₄	—	292	2	no	—
670	C₂×D₄	—	292	4	no	—
671	C₂×D₄	—	292	2	no	—
672	C₂×D₄	—	292	4	no	—
673	C₂×D₄	—	292	2	no	—
674	C₂×D₄	—	292	2	no	—
675	C₂×D₄	—	292	4	no	—
676	C₂×D₄	—	292	4	no	—
677	C₂×D₄	—	292	4	no	—
678	C₂×D₄	—	292	2	no	—
679	C₂×D₄	—	584	4	no	—
680	C₂×D₄	—	73	4	no	—
681	C₂×D₄	—	73	2	no	—
682	C₂×D₄	—	146	4	no	—
683	C₂×D₄	—	146	4	no	—
684	C₂×D₄	—	146	4	no	—
685	C₂×D₄	—	146	2	no	—
686	C₂×D₄	—	146	4	no	—
687	C₂×D₄	—	146	4	no	—
688	C₂×D₄	—	146	4	no	—
689	C₂×D₄	C₂³×D₇₃	1	2	yes	—
690	C₂²×C₄	—	292	4	no	—
691	C₂²×C₄	—	292	2	no	—
692	C₂²×C₄	—	73	1	no	—
693	C₂²×C₄	—	146	2	no	—
694	C₂²×C₄	—	146	4	no	—
695	C₂²×C₄	—	146	1	no	—
696	Q₁₆	—	2	4	no	—
697	Q₁₆	—	73	4	no	—
698	Q₁₆	—	73	2	no	—
699	Q₁₆	—	146	4	no	—
700	Q₁₆	—	146	4	no	—
701	Q₁₆	—	146	4	no	—
702	Q₁₆	D₄×D₇₃	1	2	yes	complemented
703	SD₁₆	—	2	4	no	—
704	SD₁₆	—	2	4	no	—
705	SD₁₆	—	2	4	no	—
706	SD₁₆	—	2	4	no	—
707	SD₁₆	—	73	4	no	—
708	SD₁₆	—	73	4	no	—
709	SD₁₆	—	73	4	no	—
710	SD₁₆	—	146	4	no	—
711	SD₁₆	—	146	4	no	—
712	SD₁₆	—	146	4	no	—
713	SD₁₆	—	146	4	no	—
714	SD₁₆	—	146	4	no	—
715	SD₁₆	—	146	4	no	—
716	SD₁₆	—	146	4	no	—
717	SD₁₆	—	146	4	no	—
718	SD₁₆	—	146	4	no	—
719	SD₁₆	—	146	4	no	—
720	SD₁₆	—	146	4	no	—
721	SD₁₆	—	146	4	no	—
722	SD₁₆	D₄×D₇₃	1	4	yes	complemented
723	D₈	—	2	4	no	—
724	D₈	—	73	4	no	—
725	D₈	—	73	2	no	—
726	D₈	—	146	4	no	—
727	D₈	—	146	4	no	—
728	D₈	—	146	4	no	—
729	D₈	D₄×D₇₃	1	2	yes	complemented
730	M₁₆	—	2	4	no	—
731	M₁₆	—	73	4	no	—
732	M₁₆	—	146	4	no	—
733	M₁₆	—	146	4	no	—
734	M₁₆	—	146	4	no	—
735	M₁₆	—	146	4	no	—
736	M₁₆	C₂³×D₇₃	1	4	yes	—
737	C₂×C₈	—	2	4	no	—
738	C₂×C₈	—	73	2	no	—
739	C₂×C₈	—	73	2	no	—
740	C₂×C₈	—	73	2	no	—
741	C₂×C₈	—	73	2	no	—
742	C₂×C₈	—	73	2	no	—
743	C₂×C₈	—	146	4	no	—
744	C₂×C₈	—	146	4	no	—
745	C₂×C₈	—	146	4	no	—
746	C₂×C₈	—	146	4	no	—
747	C₂×C₈	C₂³×D₇₃	1	2	yes	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	292	2	no	—
750	C₄⋊C₄	—	292	1	no	—
751	C₄²	—	73	1	no	—
752	C₄²	—	146	1	no	—
753	C₄²	C₂³×D₇₃	1	1	yes	characteristic
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	292	4	no	—
757	C₂³	—	292	2	no	—
758	C₂³	—	292	2	no	—
759	C₂³	—	292	2	no	—
760	C₂³	—	584	4	no	—
761	C₂³	—	73	1	no	—
762	C₂³	—	1168	4	no	—
763	C₂³	—	146	4	no	—
764	C₂³	—	146	2	no	—
765	Q₈	—	2	4	no	—
766	Q₈	—	4	2	no	—
767	Q₈	—	292	4	no	—
768	Q₈	—	292	4	no	—
769	Q₈	—	292	2	no	—
770	Q₈	—	73	4	no	—
771	Q₈	—	146	4	no	—
772	Q₈	—	146	4	no	—
773	Q₈	C₂×D₄×D₇₃	1	4	yes	—
774	D₄	—	2	4	no	—
775	D₄	—	2	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	2	no	—
779	D₄	—	292	4	no	—
780	D₄	—	292	2	no	—
781	D₄	—	292	4	no	—
782	D₄	—	292	4	no	—
783	D₄	—	292	4	no	—
784	D₄	—	292	4	no	—
785	D₄	—	584	2	no	—
786	D₄	—	584	4	no	—
787	D₄	—	73	4	no	—
788	D₄	—	146	4	no	—
789	D₄	—	146	4	no	—
790	D₄	—	146	4	no	—
791	D₄	—	146	4	no	—
792	D₄	—	146	4	no	—
793	D₄	C₂×D₄×D₇₃	1	4	yes	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	292	4	no	—
800	C₂×C₄	—	292	4	no	—
801	C₂×C₄	—	292	2	no	—
802	C₂×C₄	—	292	2	no	—
803	C₂×C₄	—	292	4	no	—
804	C₂×C₄	—	292	4	no	—
805	C₂×C₄	—	292	2	no	—
806	C₂×C₄	—	73	1	no	—
807	C₂×C₄	—	73	2	no	—
808	C₂×C₄	—	73	2	no	—
809	C₂×C₄	—	146	4	no	—
810	C₂×C₄	—	146	4	no	—
811	C₂×C₄	—	146	4	no	—
812	C₂×C₄	—	146	2	no	—
813	C₂×C₄	—	146	4	no	—
814	C₂×C₄	—	146	1	no	—
815	C₂×C₄	—	146	4	no	—
816	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
817	C₈	—	2	4	no	—
818	C₈	—	73	2	no	—
819	C₈	—	73	2	no	—
820	C₈	—	146	4	no	—
821	C₈	C₂×D₄×D₇₃	1	2	yes	—
822	C₈	C₂×D₄×D₇₃	1	2	yes	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	8	2	no	—
826	C₂²	—	16	2	no	—
827	C₂²	—	292	8	no	—
828	C₂²	—	292	2	no	—
829	C₂²	—	584	2	no	—
830	C₂²	—	584	4	no	—
831	C₂²	—	73	1	no	—
832	C₂²	—	73	1	no	—
833	C₂²	—	1168	4	no	—
834	C₂²	—	1168	2	no	—
835	C₂²	—	1168	2	no	—
836	C₂²	—	146	2	no	—
837	C₂²	—	146	4	no	—
838	C₂²	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
839	C₄	—	2	2	no	—
840	C₄	—	2	4	no	—
841	C₄	—	4	2	no	—
842	C₄	—	292	2	no	—
843	C₄	—	73	2	no	—
844	C₄	—	146	2	no	—
845	C₄	—	146	4	no	—
846	C₄	C₂²×D₄×D₇₃	1	2	yes	—
847	C₂	—	2	1	no	—
848	C₂	—	4	4	no	—
849	C₂	—	8	2	no	—
850	C₂	—	292	4	no	—
851	C₂	—	584	2	no	—
852	C₂	—	73	2	no	—
853	C₂	—	146	1	no	—
854	C₂	D₄²×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄²×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3291	C₂
socle	C₂×C₇₃	C₂×D₄²
hypercenter	#3291	D₇₃
hypocenter	C₇₃	C₂×#3291
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3291

Complements

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

N	H ≅ G/N	type
1. #577×D₇₃	C₂	semidirect
2. #22621726	C₂	semidirect
3. #22621725	C₂	semidirect
4. #22621724	C₂	semidirect
5. #22621723	C₂	semidirect
6. #22621722	C₂	semidirect
7. #22621721	C₂	semidirect
8. #492×D₇₃	C₂	semidirect
9. #471×D₇₃	C₂	semidirect
10. #456×D₇₃	C₂	semidirect
11. #453×D₇₃	C₂	semidirect
12. #443×D₇₃	C₂	semidirect
13. C₇₃×#3291	C₂	semidirect
15. H(5,𝔽₂)×D₇₃	C₂²	semidirect
16. #17989399	C₂²	semidirect
17. #17989398	C₂²	semidirect
19. #17989397	C₂²	semidirect
21. #17989396	C₂²	semidirect
22. #17989395	C₂²	semidirect
24. #17989394	C₂²	semidirect
26. #17989393	C₂²	semidirect
28. #137×D₇₃	C₂²	semidirect
34. C₂×SD₁₆×D₇₃	C₂²	semidirect
35. #131×D₇₃	C₂²	semidirect
36. C₄⋊Q₈×D₇₃	C₂²	semidirect
38. #17988961	C₂²	semidirect
39. #17988960	C₂²	semidirect
40. #17988959	C₂²	semidirect
41. #17988958	C₂²	semidirect
42. #17988853	C₂²	semidirect
43. #17988852	C₂²	semidirect
44. #17988851	C₂²	semidirect
45. #17988850	C₂²	semidirect
46. #17988849	C₂²	semidirect
47. #17988848	C₂²	semidirect
48. #17988847	C₂²	semidirect
49. #17988772	C₂²	semidirect
50. #17988771	C₂²	semidirect
51. #17988770	C₂²	semidirect
52. #17988769	C₂²	semidirect
53. #17988768	C₂²	semidirect
54. #17988757	C₂²	semidirect
55. #17988756	C₂²	semidirect
56. #17988755	C₂²	semidirect
57. #17988754	C₂²	semidirect
58. #17988753	C₂²	semidirect
59. #17988705	C₂²	semidirect
60. #17988704	C₂²	semidirect
61. #17988703	C₂²	semidirect
62. #17988702	C₂²	semidirect
63. #17988701	C₂²	semidirect
64. #108×D₇₃	C₂²	semidirect
65. #104×D₇₃	C₂²	semidirect
66. #101×D₇₃	C₂²	semidirect
67. #100×D₇₃	C₂²	semidirect
68. C₄×C₈×D₇₃	C₂²	semidirect
69. #577×C₇₃	C₂²	semidirect
70. #492×C₇₃	C₂²	semidirect
71. #471×C₇₃	C₂²	semidirect
72. #456×C₇₃	C₂²	semidirect
73. #453×C₇₃	C₂²	semidirect
74. #443×C₇₃	C₂²	semidirect
81. #14556637	C₂³	semidirect
84. #14556636	C₂³	semidirect
96. #14556624	C₂³	semidirect
101. #14556622	C₂³	semidirect
103. #14556621	C₂³	semidirect
120. #14556614	D₄	semidirect
125. #14556612	D₄	semidirect
130. #14556610	D₄	semidirect
132. Q₁₆×D₇₃	D₄	semidirect
134. C₂×#11924017	C₂³	semidirect
136. C₂×#11924016	C₂³	semidirect
138. C₂×#11924015	C₂³	semidirect
149. SD₁₆×D₇₃	D₄	semidirect
151. D₈×D₇₃	D₄	semidirect
153. #14556599	C₂³	semidirect
154. #14556598	C₂³	semidirect
156. #14556597	C₂³	semidirect
161. #14556591	C₂³	semidirect
163. #14556589	C₂³	semidirect
169. #14556527	C₂³	semidirect
170. #14556526	C₂³	semidirect
171. #14556519	C₂³	semidirect
172. #14556518	C₂³	semidirect
173. #14556517	C₂³	semidirect
174. #14556510	C₂³	semidirect
175. #14556509	C₂³	semidirect
176. #14556508	C₂³	semidirect
177. #14556507	C₂³	semidirect
178. C₄×#10596831	C₂³	semidirect
179. C₈×Dic₇₃	C₂³	semidirect
181. H(5,𝔽₂)×C₇₃	C₂³	semidirect
183. #137×C₇₃	C₂³	semidirect
189. C₂×SD₁₆×C₇₃	C₂³	semidirect
190. #131×C₇₃	C₂³	semidirect
191. C₄⋊Q₈×C₇₃	C₂³	semidirect
193. #108×C₇₃	C₂³	semidirect
194. #104×C₇₃	C₂³	semidirect
195. #101×C₇₃	C₂³	semidirect
196. #100×C₇₃	C₂³	semidirect
197. C₄×C₈×C₇₃	C₂³	semidirect
259. Dic₂₉₂	C₂×D₄	semidirect
262. #11924018	C₂×D₄	semidirect
267. #11924017	C₂×D₄	semidirect
272. #11924016	C₂×D₄	semidirect
277. #11924015	C₂×D₄	semidirect
279. D₅₈₄	C₂×D₄	semidirect
282. #11924013	C₂×D₄	semidirect
312. Q₁₆×C₇₃	C₂×D₄	semidirect
317. SD₁₆×C₇₃	C₂×D₄	semidirect
319. D₈×C₇₃	C₂×D₄	semidirect
427. D₇₃	#3291	direct (N × H)
435. #3291	D₇₃	direct (N × H)
441. C₇₃	C₂×#3291	semidirect
455. #577	C₂×D₇₃	semidirect
471. #492	C₂×D₇₃	semidirect
479. #471	C₂×D₇₃	semidirect
485. #456	C₂×D₇₃	semidirect
491. #453	C₂×D₇₃	semidirect
497. #443	C₂×D₇₃	semidirect
514. H(5,𝔽₂)	C₂²×D₇₃	semidirect
538. #137	C₂²×D₇₃	semidirect
587. C₂×SD₁₆	C₂²×D₇₃	semidirect
595. #131	C₂²×D₇₃	semidirect
603. C₄⋊Q₈	C₂²×D₇₃	semidirect
612. #108	C₂²×D₇₃	semidirect
616. #104	C₂²×D₇₃	semidirect
619. #101	C₂²×D₇₃	semidirect
622. #100	C₂²×D₇₃	semidirect
625. C₄×C₈	C₂²×D₇₃	semidirect
702. Q₁₆	D₄×D₇₃	semidirect
722. SD₁₆	D₄×D₇₃	semidirect
729. D₈	D₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#577×D₇₃	2
#22621726	2
#22621725	2
#22621724	2
#22621723	2
#22621722	2
#22621721	2
#492×D₇₃	2
#471×D₇₃	2
#456×D₇₃	2
#453×D₇₃	2
#443×D₇₃	2
C₇₃×#3291	2
C₂×#3291	73

Subgroups — #3291×D73 #33962198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3291×D₇₃ #33962198