Subgroups — #2208×D₇₃ #33240210

Order 18688.

766 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₇₃	C₂	1	2	yes	maximal
2	#494×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22611977	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611976	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611975	C₂	1	2	yes	maximal, complemented
7	#22611974	C₂	1	2	yes	maximal, complemented
8	#22611973	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#358×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₃	—	2	1	no	—
13	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	—
14	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×D₇₃	—	2	1	no	—
16	C₄×D₄×D₇₃	—	2	1	no	—
17	C₂×#14556536	C₂²	1	2	yes	—
18	C₂×#14556535	C₂²	1	2	yes	—
19	C₂×#14556534	C₂²	1	2	yes	—
20	SD₃₂×D₇₃	—	2	8	no	—
21	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
22	#17988967	C₂²	1	1	yes	characteristic, complemented
23	#17988966	—	2	1	no	—
24	#17988965	—	2	1	no	—
25	#17988965	C₂²	1	2	yes	complemented
26	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
27	D₈×Dic₇₃	C₂²	1	1	yes	characteristic
28	#17988669	C₂²	1	1	yes	characteristic
29	C₄×#11924013	—	2	1	no	—
30	#17988667	—	2	1	no	—
31	#107×D₇₃	C₂²	1	1	yes	characteristic
32	#102×D₇₃	—	2	1	no	—
33	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	C₄⋊#11924003	C₂²	1	1	yes	characteristic, complemented
35	#17988405	C₂²	1	2	yes	complemented
36	#17988392	C₂²	1	2	yes	complemented
37	#17988391	C₂²	1	2	yes	complemented
38	#17988390	C₂²	1	2	yes	complemented
39	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	—
40	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#358×C₇₃	C₂²	1	2	yes	complemented
44	C₂×Q₈×D₇₃	—	2	2	no	—
45	C₂×D₄×D₇₃	—	2	1	no	—
46	C₂²×C₄×D₇₃	—	4	1	no	—
47	C₂×Dic₂₉₂	—	2	1	no	—
48	C₂×Dic₂₉₂	C₂³	1	2	yes	—
49	C₂×#11924018	—	2	2	no	—
50	C₂×#11924018	—	2	2	no	—
51	Q₁₆×D₇₃	—	2	4	no	—
52	Q₁₆×D₇₃	—	2	4	no	—
53	Q₁₆×D₇₃	—	4	4	no	—
54	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
55	C₂×#11924013	—	2	1	no	—
56	D₈×D₇₃	—	2	2	no	—
57	D₈×D₇₃	D₄	1	4	yes	—
58	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
60	#14556591	—	2	1	no	—
61	#14556590	—	4	1	no	—
62	#14556590	—	4	1	no	—
63	#14556589	—	2	2	no	—
64	C₄×D₂₉₂	—	2	1	no	—
65	D₄×Dic₇₃	—	2	1	no	—
66	#14556553	—	2	1	no	—
67	C₄×C₂²⋊D₇₃	—	4	1	no	—
68	#14556551	—	4	1	no	—
69	C₄⋊C₄×D₇₃	—	2	1	no	—
70	C₄⋊C₄×D₇₃	—	4	1	no	—
71	C₄⋊C₄×D₇₃	—	4	1	no	—
72	C₂²⋊C₄×D₇₃	—	4	1	no	—
73	C₄²×D₇₃	D₄	1	1	yes	characteristic
74	#14556536	—	2	4	no	—
75	#14556535	—	2	4	no	—
76	#14556534	—	2	4	no	—
77	C₂×#11924003	C₂³	1	2	yes	—
78	C₁₆×D₇₃	—	2	4	no	—
79	#14556525	C₂³	1	1	yes	characteristic
80	#14556524	—	2	1	no	—
81	#14556513	—	2	1	no	—
82	#14556512	—	2	1	no	—
83	#14556511	—	2	1	no	—
84	C₄×#10596831	D₄	1	1	yes	characteristic
85	C₈×Dic₇₃	D₄	1	1	yes	characteristic
86	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₇₃	—	2	1	no	—
88	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
89	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₃	—	2	1	no	—
91	C₄×D₄×C₇₃	—	2	1	no	—
92	SD₃₂×C₇₃	—	2	4	no	—
93	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
94	#107×C₇₃	C₂³	1	1	yes	characteristic
95	#102×C₇₃	—	2	1	no	—
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₂³×D₇₃	—	4	1	no	—
98	C₂×Dic₁₄₆	—	2	2	no	—
99	C₂×Dic₁₄₆	—	4	2	no	—
100	Q₈×D₇₃	—	4	4	no	—
101	Q₈×D₇₃	—	4	4	no	—
102	C₂×D₂₉₂	—	2	1	no	—
103	C₂×C₂²⋊D₇₃	—	4	1	no	—
104	D₄×D₇₃	—	2	4	no	—
105	D₄×D₇₃	—	4	2	no	—
106	C₂²×Dic₇₃	—	4	1	no	—
107	C₂×C₄×D₇₃	—	4	1	no	—
108	C₂×C₄×D₇₃	—	4	2	no	—
109	C₂×C₄×D₇₃	—	4	1	no	—
110	C₂×C₄×D₇₃	—	4	1	no	—
111	C₂×C₄×D₇₃	—	8	4	no	—
112	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
113	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
115	Dic₂₉₂	—	2	2	no	—
116	Dic₂₉₂	—	2	2	no	—
117	Dic₂₉₂	—	4	2	no	—
118	#11924018	—	4	4	no	—
119	#11924018	—	4	4	no	—
120	D₅₈₄	—	2	1	no	—
121	D₅₈₄	C₂×D₄	1	2	yes	—
122	#11924013	—	2	4	no	—
123	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
124	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
125	C₈×D₇₃	—	2	2	no	—
126	C₈×D₇₃	C₂×D₄	1	2	yes	—
127	C₈×D₇₃	#41	1	2	yes	—
128	C₄⋊Dic₇₃	—	2	1	no	—
129	C₄⋊Dic₇₃	—	4	1	no	—
130	C₄⋊Dic₇₃	—	4	1	no	—
131	#11924007	—	4	1	no	—
132	#11924007	—	4	2	no	—
133	#11924007	—	4	2	no	—
134	C₂²⋊Dic₇₃	—	4	1	no	—
135	#11924005	—	4	1	no	—
136	#11924005	—	4	1	no	—
137	C₄×Dic₇₃	D₈	1	1	yes	characteristic
138	C₄×Dic₇₃	D₈	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
140	#11924003	—	2	2	no	—
141	C₂×Q₈×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	2	1	no	—
143	C₂²×C₄×C₇₃	—	4	1	no	—
144	Q₁₆×C₇₃	—	2	2	no	—
145	Q₁₆×C₇₃	—	2	2	no	—
146	Q₁₆×C₇₃	—	4	2	no	—
147	D₈×C₇₃	—	2	1	no	—
148	D₈×C₇₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	4	1	no	—
153	C₄⋊C₄×C₇₃	—	4	1	no	—
154	C₂²⋊C₄×C₇₃	—	4	1	no	—
155	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₇₃	—	2	2	no	—
157	C₂³×C₇₃	—	4	1	no	—
158	C₂²×D₇₃	—	4	1	no	—
159	C₂²×D₇₃	—	4	4	no	—
160	C₂²×D₇₃	—	8	2	no	—
161	C₂²×D₇₃	—	8	2	no	—
162	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
163	Q₈×C₇₃	—	4	2	no	—
164	Q₈×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	2	2	no	—
166	D₄×C₇₃	—	4	1	no	—
167	C₂×C₄×C₇₃	—	4	1	no	—
168	C₂×C₄×C₇₃	—	4	2	no	—
169	C₂×C₄×C₇₃	—	8	2	no	—
170	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²⋊D₇₃	—	4	4	no	—
174	C₂×Dic₇₃	—	4	1	no	—
175	C₂×Dic₇₃	—	4	2	no	—
176	C₂×Dic₇₃	—	8	2	no	—
177	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
178	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
180	D₂₉₂	—	2	2	no	—
181	D₂₉₂	—	4	1	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	8	4	no	—
184	C₄×D₇₃	—	8	2	no	—
185	C₄×D₇₃	—	8	2	no	—
186	C₄×D₇₃	—	8	2	no	—
187	C₄×D₇₃	SD₃₂	1	4	yes	complemented
188	C₄×D₇₃	#121	1	2	yes	—
189	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
190	Dic₁₄₆	—	4	2	no	—
191	Dic₁₄₆	—	4	2	no	—
192	Dic₁₄₆	—	8	4	no	—
193	C₈×C₇₃	—	2	1	no	—
194	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
196	#10596831	—	2	1	no	—
197	#10596831	#121	1	2	yes	—
198	C₂²×C₇₃	—	4	2	no	—
199	C₂²×C₇₃	—	8	1	no	—
200	C₂²×C₇₃	—	8	1	no	—
201	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
202	C₂×D₇₃	—	4	2	no	—
203	C₂×D₇₃	—	8	1	no	—
204	C₂×D₇₃	—	8	1	no	—
205	C₂×D₇₃	—	8	8	no	—
206	C₂×D₇₃	#459	1	2	yes	—
207	C₂×D₇₃	C₂×SD₃₂	1	2	yes	—
208	C₂×D₇₃	#510	1	2	yes	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	8	1	no	—
211	C₄×C₇₃	—	8	2	no	—
212	C₄×C₇₃	C₂×SD₃₂	1	2	yes	complemented
213	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
214	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	8	1	no	—
217	Dic₇₃	—	8	2	no	—
218	Dic₇₃	#459	1	2	yes	—
219	Dic₇₃	C₂×SD₃₂	1	2	yes	complemented
220	C₂×#2208	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	8	2	no	—
222	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
223	C₂×C₇₃	C₂²×SD₃₂	1	1	yes	characteristic
224	C₂×C₇₃	C₂×#510	1	1	yes	characteristic
225	D₇₃	—	8	2	no	—
226	D₇₃	#2208	1	4	yes	direct product factor
227	C₂²×SD₃₂	—	73	2	no	—
228	C₂×#494	—	73	1	no	—
229	C₂×C₄×D₈	—	73	1	no	—
230	#2208	—	73	2	no	—
231	#2208	—	73	1	no	—
232	#2208	—	73	1	no	—
233	#2208	—	73	1	no	—
234	#2208	—	73	2	no	—
235	#2208	D₇₃	1	1	yes	characteristic, direct product factor
236	C₂×C₄⋊C₁₆	—	73	1	no	—
237	C₂×#358	—	73	2	no	—
238	C₇₃	C₂×#2208	1	1	yes	characteristic, complemented, Sylow
239	C₂²×Q₁₆	—	73	2	no	—
240	C₂²×Q₁₆	—	146	1	no	—
241	C₂²×D₈	—	73	1	no	—
242	C₂×C₄⋊Q₈	—	146	1	no	—
243	C₂×C₄×D₄	—	146	1	no	—
244	C₂×SD₃₂	—	73	2	no	—
245	C₂×SD₃₂	—	73	2	no	—
246	C₂×SD₃₂	—	73	2	no	—
247	C₂×SD₃₂	—	146	8	no	—
248	C₂×SD₃₂	C₂×D₇₃	1	2	yes	—
249	C₂²×C₁₆	—	73	2	no	—
250	#494	—	73	2	no	—
251	#494	—	73	1	no	—
252	#494	—	146	1	no	—
253	#494	—	146	1	no	—
254	#494	C₂×D₇₃	1	1	yes	characteristic, complemented
255	C₄×D₈	—	73	1	no	—
256	C₄×D₈	—	73	1	no	—
257	C₄×D₈	—	73	1	no	—
258	C₄×D₈	—	146	1	no	—
259	C₄×D₈	—	146	1	no	—
260	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
261	C₂×#107	—	73	1	no	—
262	C₂×#102	—	146	1	no	—
263	C₂×C₄×C₈	—	73	1	no	—
264	C₄⋊C₁₆	—	73	2	no	—
265	C₄⋊C₁₆	—	73	1	no	—
266	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
267	#358	—	73	2	no	—
268	#358	—	73	2	no	—
269	#358	—	73	2	no	—
270	#358	C₂×D₇₃	1	2	yes	complemented
271	C₂²×Q₈	—	146	2	no	—
272	C₂²×D₄	—	146	1	no	—
273	C₂³×C₄	—	292	1	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	292	4	no	—
276	C₂×Q₁₆	—	73	2	no	—
277	C₂×Q₁₆	—	146	4	no	—
278	C₂×Q₁₆	—	146	4	no	—
279	C₂×Q₁₆	—	146	2	no	—
280	C₂×Q₁₆	—	146	2	no	—
281	C₂×Q₁₆	—	146	1	no	—
282	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	—
283	C₂×D₈	—	73	4	no	—
284	C₂×D₈	—	73	1	no	—
285	C₂×D₈	—	146	2	no	—
286	C₂×D₈	—	146	1	no	—
287	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
288	C₂²×C₈	—	73	1	no	—
289	C₂²×C₈	—	73	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	292	1	no	—
292	C₄⋊Q₈	—	292	1	no	—
293	C₄⋊Q₈	—	146	2	no	—
294	C₄⋊Q₈	—	146	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	292	1	no	—
297	C₄×D₄	—	292	1	no	—
298	C₄×D₄	—	146	1	no	—
299	C₄×D₄	—	146	1	no	—
300	C₄×D₄	—	146	1	no	—
301	C₂×C₄⋊C₄	—	292	1	no	—
302	C₂×C₄⋊C₄	—	292	1	no	—
303	C₂×C₄⋊C₄	—	146	1	no	—
304	C₂×C₂²⋊C₄	—	292	1	no	—
305	C₂×C₄²	—	73	1	no	—
306	SD₃₂	—	2	4	no	—
307	SD₃₂	—	146	4	no	—
308	SD₃₂	—	146	4	no	—
309	SD₃₂	—	146	4	no	—
310	C₂×C₁₆	—	73	2	no	—
311	C₂×C₁₆	—	146	4	no	—
312	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
313	#107	—	73	1	no	—
314	#107	—	146	1	no	—
315	#107	C₂²×D₇₃	1	1	yes	characteristic
316	#102	—	2	1	no	—
317	#102	—	146	1	no	—
318	#102	—	146	1	no	—
319	#102	—	146	1	no	—
320	C₄×C₈	—	73	1	no	—
321	C₄×C₈	—	73	1	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
324	C₂⁴	—	292	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	292	2	no	—
327	C₂×Q₈	—	292	4	no	—
328	C₂×Q₈	—	292	4	no	—
329	C₂×Q₈	—	146	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	292	2	no	—
332	C₂×D₄	—	292	1	no	—
333	C₂×D₄	—	146	4	no	—
334	C₂×D₄	—	146	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	292	1	no	—
337	C₂²×C₄	—	292	2	no	—
338	C₂²×C₄	—	292	1	no	—
339	C₂²×C₄	—	292	1	no	—
340	C₂²×C₄	—	292	1	no	—
341	C₂²×C₄	—	584	4	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	2	2	no	—
347	Q₁₆	—	4	2	no	—
348	Q₁₆	—	292	2	no	—
349	Q₁₆	—	292	4	no	—
350	Q₁₆	—	292	4	no	—
351	Q₁₆	—	146	2	no	—
352	Q₁₆	—	146	2	no	—
353	D₈	—	2	1	no	—
354	D₈	—	73	2	no	—
355	D₈	—	146	4	no	—
356	D₈	—	146	1	no	—
357	D₈	D₄×D₇₃	1	2	yes	—
358	C₂×C₈	—	73	1	no	—
359	C₂×C₈	—	73	2	no	—
360	C₂×C₈	—	73	2	no	—
361	C₂×C₈	—	73	1	no	—
362	C₂×C₈	—	146	2	no	—
363	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
364	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	292	2	no	—
369	C₄⋊C₄	—	292	2	no	—
370	C₄⋊C₄	—	292	1	no	—
371	C₄⋊C₄	—	292	1	no	—
372	C₄⋊C₄	—	292	1	no	—
373	C₄⋊C₄	—	146	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	292	1	no	—
376	C₂²⋊C₄	—	292	1	no	—
377	C₂²⋊C₄	—	292	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	73	1	no	—
381	C₄²	D₄×D₇₃	1	1	yes	characteristic
382	C₁₆	—	2	2	no	—
383	C₁₆	—	146	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	292	4	no	—
386	C₂³	—	292	1	no	—
387	C₂³	—	584	2	no	—
388	C₂³	—	584	2	no	—
389	C₂³	—	73	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	292	2	no	—
393	Q₈	—	292	2	no	—
394	Q₈	—	584	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	292	4	no	—
398	D₄	—	292	1	no	—
399	D₄	—	146	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	292	1	no	—
404	C₂×C₄	—	292	2	no	—
405	C₂×C₄	—	584	2	no	—
406	C₂×C₄	—	584	4	no	—
407	C₂×C₄	—	584	2	no	—
408	C₂×C₄	—	584	2	no	—
409	C₂×C₄	—	584	2	no	—
410	C₂×C₄	—	73	1	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	73	4	no	—
413	C₂×C₄	—	73	2	no	—
414	C₂×C₄	—	73	2	no	—
415	C₂×C₄	—	73	1	no	—
416	C₂×C₄	—	146	2	no	—
417	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
418	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	73	2	no	—
422	C₈	—	146	1	no	—
423	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
424	C₈	#41×D₇₃	1	1	yes	characteristic
425	C₂²	—	4	2	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	292	2	no	—
429	C₂²	—	584	8	no	—
430	C₂²	—	584	1	no	—
431	C₂²	—	584	1	no	—
432	C₂²	—	73	2	no	—
433	C₂²	—	73	2	no	—
434	C₂²	—	73	2	no	—
435	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	584	1	no	—
440	C₄	—	584	2	no	—
441	C₄	—	73	2	no	—
442	C₄	—	73	2	no	—
443	C₄	—	146	1	no	—
444	C₄	SD₃₂×D₇₃	1	2	yes	complemented
445	C₄	#121×D₇₃	1	1	yes	characteristic
446	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
447	C₂	—	8	2	no	—
448	C₂	—	584	2	no	—
449	C₂	—	73	4	no	—
450	C₂	#459×D₇₃	1	1	yes	characteristic
451	C₂	C₂×SD₃₂×D₇₃	1	1	yes	characteristic
452	C₂	#510×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2208	C₂
socle	C₂²×C₇₃	C₂²×D₈
prime radical	C₂×D₈×D₇₃	C₂²
hypercenter	#2208	D₇₃
hypocenter	C₇₃	C₂×#2208
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2208

Complements

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

N	H ≅ G/N	type
2. #494×D₇₃	C₂	semidirect
4. #22611977	C₂	semidirect
5. #22611976	C₂	semidirect
6. #22611975	C₂	semidirect
7. #22611974	C₂	semidirect
8. #22611973	C₂	semidirect
9. C₄⋊C₁₆×D₇₃	C₂	semidirect
10. #358×D₇₃	C₂	semidirect
11. C₇₃×#2208	C₂	semidirect
22. #17988967	C₂²	semidirect
25. #17988965	C₂²	semidirect
34. C₄⋊#11924003	C₂²	semidirect
35. #17988405	C₂²	semidirect
36. #17988392	C₂²	semidirect
37. #17988391	C₂²	semidirect
38. #17988390	C₂²	semidirect
40. #494×C₇₃	C₂²	semidirect
42. C₄⋊C₁₆×C₇₃	C₂²	semidirect
43. #358×C₇₃	C₂²	semidirect
187. C₄×D₇₃	SD₃₂	semidirect
212. C₄×C₇₃	C₂×SD₃₂	semidirect
219. Dic₇₃	C₂×SD₃₂	semidirect
226. D₇₃	#2208	direct (N × H)
235. #2208	D₇₃	direct (N × H)
238. C₇₃	C₂×#2208	semidirect
254. #494	C₂×D₇₃	semidirect
266. C₄⋊C₁₆	C₂×D₇₃	semidirect
270. #358	C₂×D₇₃	semidirect
444. C₄	SD₃₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₇₃	2
#494×D₇₃	2
C₄×D₈×D₇₃	2
#22611977	2
#22611976	2
#22611975	2
#22611974	2
#22611973	2
C₄⋊C₁₆×D₇₃	2
#358×D₇₃	2
C₇₃×#2208	2
C₂×#2208	73

Subgroups — #2208×D73 #33240210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2208×D₇₃ #33240210