Subgroups — #3391×D₇₃ #33966873

Order 18688.

2582 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#550×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22622906	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622905	C₂	1	3	yes	maximal, complemented
4	#22622904	C₂	1	3	yes	maximal, complemented
5	#22622903	C₂	1	2	yes	maximal, complemented
6	#22622902	C₂	1	6	yes	maximal, complemented
7	#493×D₇₃	C₂	1	3	yes	maximal, complemented
8	#459×D₇₃	C₂	1	6	yes	maximal, complemented
9	C₈×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×D₈×D₇₃	C₂	1	3	yes	maximal, complemented
11	C₇₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₇₃	—	2	2	no	—
13	C₂×D₈×D₇₃	C₂²	1	3	yes	—
14	C₂×D₈×D₇₃	C₂²	1	6	yes	—
15	#17989259	C₂²	1	2	yes	complemented
16	#17989258	C₂²	1	6	yes	complemented
17	#17989257	C₂²	1	6	yes	complemented
18	#17989256	—	2	2	no	—
19	#17989255	—	2	6	no	—
20	#127×D₇₃	C₂²	1	6	yes	—
21	#121×D₇₃	—	2	6	no	—
22	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
23	C₄×D₄×D₇₃	C₂²	1	6	yes	—
24	#17988964	C₂²	1	3	yes	complemented
25	#17988963	C₂²	1	6	yes	complemented
26	#17988962	C₂²	1	6	yes	complemented
27	#17988962	C₂²	1	6	yes	complemented
28	#17988783	C₂²	1	6	yes	complemented
29	#17988782	C₂²	1	6	yes	complemented
30	#17988781	C₂²	1	12	yes	complemented
31	#17988780	C₂²	1	12	yes	complemented
32	#17988779	C₂²	1	6	yes	complemented
33	Q₈×#10596831	C₂²	1	1	yes	characteristic, complemented
34	C₈×Dic₁₄₆	C₂²	1	3	yes	complemented
35	#17988711	C₂²	1	3	yes	complemented
36	C₄×D₅₈₄	C₂²	1	3	yes	complemented
37	D₈×Dic₇₃	C₂²	1	3	yes	complemented
38	#17988669	C₂²	1	3	yes	complemented
39	C₄×#11924013	C₂²	1	6	yes	complemented
40	#17988667	C₂²	1	6	yes	complemented
41	#107×D₇₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₇₃	C₂²	1	3	yes	—
43	#102×D₇₃	C₂²	1	6	yes	—
44	C₄×C₈×D₇₃	C₂²	1	3	yes	—
45	#550×C₇₃	C₂²	1	2	yes	complemented
46	#493×C₇₃	C₂²	1	3	yes	complemented
47	#459×C₇₃	C₂²	1	6	yes	complemented
48	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₈×C₇₃	C₂²	1	3	yes	complemented
50	C₂×#11924029	—	2	2	no	—
51	C₂×#11924028	—	2	6	no	—
52	C₂×#11924027	—	2	6	no	—
53	#41×D₇₃	—	4	16	no	—
54	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
55	C₂×D₄×D₇₃	—	2	6	no	—
56	C₂×D₄×D₇₃	—	2	6	no	—
57	C₂×D₄×D₇₃	C₂³	1	6	yes	—
58	C₂²×C₄×D₇₃	—	2	6	no	—
59	C₂×D₅₈₄	C₂³	1	3	yes	—
60	C₂×D₅₈₄	C₂³	1	6	yes	—
61	C₂×#11924013	C₂³	1	6	yes	—
62	C₂×#11924013	C₂³	1	12	yes	—
63	D₈×D₇₃	—	2	12	no	—
64	D₈×D₇₃	—	4	12	no	—
65	C₂×C₈×D₇₃	C₂³	1	3	yes	—
66	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
67	#14556588	C₂³	1	6	yes	—
68	#14556587	—	2	6	no	—
69	#14556587	—	2	6	no	—
70	#14556587	C₂³	1	12	yes	—
71	#14556566	—	2	6	no	—
72	#14556565	—	2	6	no	—
73	#14556564	—	2	12	no	—
74	#14556563	—	2	12	no	—
75	#14556562	—	2	6	no	—
76	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
77	C₄×Dic₁₄₆	C₂³	1	3	yes	—
78	#14556556	D₄	1	3	yes	—
79	C₄×D₂₉₂	C₂³	1	6	yes	—
80	D₄×Dic₇₃	C₂³	1	6	yes	—
81	#14556553	C₂³	1	6	yes	—
82	C₄×C₂²⋊D₇₃	—	2	6	no	—
83	#14556551	—	2	6	no	—
84	C₄⋊C₄×D₇₃	D₄	1	3	yes	—
85	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
86	C₂²⋊C₄×D₇₃	—	2	6	no	—
87	C₄²×D₇₃	C₂³	1	3	yes	—
88	#14556525	C₂³	1	1	yes	characteristic
89	#14556524	C₂³	1	2	yes	—
90	C₄⋊#10596831	C₂³	1	3	yes	—
91	#14556520	C₂³	1	6	yes	—
92	#14556513	C₂³	1	6	yes	—
93	#14556512	C₂³	1	6	yes	—
94	#14556511	C₂³	1	6	yes	—
95	C₄×#10596831	C₂³	1	3	yes	—
96	C₈×Dic₇₃	C₂³	1	3	yes	—
97	C₈×Dic₇₃	C₂³	1	3	yes	—
98	C₂×#41×C₇₃	—	2	2	no	—
99	C₂×D₈×C₇₃	C₂³	1	3	yes	—
100	C₂×D₈×C₇₃	C₂³	1	6	yes	—
101	#127×C₇₃	C₂³	1	6	yes	—
102	#121×C₇₃	—	2	6	no	—
103	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₇₃	C₂³	1	6	yes	—
105	#107×C₇₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₇₃	C₂³	1	3	yes	—
107	#102×C₇₃	C₂³	1	6	yes	—
108	C₄×C₈×C₇₃	C₂³	1	3	yes	—
109	C₂³×D₇₃	—	2	6	no	—
110	#11924029	—	4	8	no	—
111	#11924028	—	4	24	no	—
112	#11924027	—	4	24	no	—
113	C₂×Dic₁₄₆	C₂×D₄	1	3	yes	—
114	Q₈×D₇₃	D₈	1	8	yes	complemented
115	C₂×D₂₉₂	—	2	6	no	—
116	C₂×D₂₉₂	—	2	6	no	—
117	C₂×D₂₉₂	C₂⁴	1	6	yes	—
118	C₂×C₂²⋊D₇₃	—	2	6	no	—
119	C₂×C₂²⋊D₇₃	—	2	12	no	—
120	C₂×C₂²⋊D₇₃	—	2	12	no	—
121	D₄×D₇₃	—	2	12	no	—
122	D₄×D₇₃	—	2	12	no	—
123	D₄×D₇₃	—	4	24	no	—
124	D₄×D₇₃	—	8	12	no	—
125	C₂²×Dic₇₃	—	2	6	no	—
126	C₂×C₄×D₇₃	—	2	2	no	—
127	C₂×C₄×D₇₃	—	2	6	no	—
128	C₂×C₄×D₇₃	—	2	6	no	—
129	C₂×C₄×D₇₃	—	4	24	no	—
130	C₂×C₄×D₇₃	C₂×D₄	1	3	yes	—
131	C₂×C₄×D₇₃	C₂×D₄	1	3	yes	—
132	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
133	D₅₈₄	—	2	6	no	—
134	D₅₈₄	—	4	6	no	—
135	#11924013	—	2	12	no	—
136	#11924013	—	4	12	no	—
137	C₂×#10596831	C₂⁴	1	3	yes	—
138	C₂×#10596831	C₂⁴	1	1	yes	characteristic
139	C₈×D₇₃	—	2	6	no	—
140	C₈×D₇₃	#41	1	4	yes	complemented
141	C₄⋊Dic₇₃	C₂×D₄	1	3	yes	—
142	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
143	#11924007	—	2	2	no	—
144	#11924007	C₂×D₄	1	6	yes	—
145	C₂²⋊Dic₇₃	—	2	6	no	—
146	#11924005	—	2	6	no	—
147	#11924005	—	2	6	no	—
148	C₄×Dic₇₃	C₂×D₄	1	3	yes	—
149	C₄×Dic₇₃	C₂×D₄	1	3	yes	—
150	C₄×Dic₇₃	C₂⁴	1	3	yes	—
151	#41×C₇₃	—	4	8	no	—
152	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₇₃	—	2	6	no	—
154	C₂×D₄×C₇₃	—	2	6	no	—
155	C₂×D₄×C₇₃	C₂⁴	1	6	yes	—
156	C₂²×C₄×C₇₃	—	2	6	no	—
157	D₈×C₇₃	—	2	6	no	—
158	D₈×C₇₃	—	4	6	no	—
159	C₂×C₈×C₇₃	C₂⁴	1	3	yes	—
160	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₇₃	C₂×D₄	1	3	yes	—
162	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
163	C₂²⋊C₄×C₇₃	—	2	6	no	—
164	C₄²×C₇₃	C₂⁴	1	3	yes	—
165	C₂³×C₇₃	—	2	6	no	—
166	C₂²×D₇₃	—	2	6	no	—
167	C₂²×D₇₃	—	4	12	no	—
168	C₂²×D₇₃	—	4	12	no	—
169	C₂²×D₇₃	—	4	12	no	—
170	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₇₃	C₂×D₈	1	4	yes	complemented
172	D₄×C₇₃	—	2	6	no	—
173	D₄×C₇₃	—	2	6	no	—
174	D₄×C₇₃	—	4	12	no	—
175	D₄×C₇₃	—	8	6	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	4	12	no	—
178	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	4	12	no	—
182	C₂²⋊D₇₃	—	4	24	no	—
183	C₂²⋊D₇₃	—	8	12	no	—
184	C₂×Dic₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	4	12	no	—
186	C₂×Dic₇₃	C₂²×D₄	1	3	yes	—
187	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×Dic₇₃	C₂²×D₄	1	3	yes	—
189	D₂₉₂	—	2	6	no	—
190	D₂₉₂	—	2	6	no	—
191	D₂₉₂	—	4	12	no	—
192	D₂₉₂	—	8	6	no	—
193	C₄×D₇₃	—	2	6	no	—
194	C₄×D₇₃	—	4	4	no	—
195	C₄×D₇₃	—	4	12	no	—
196	C₄×D₇₃	—	4	12	no	—
197	C₄×D₇₃	C₂×D₈	1	12	yes	—
198	C₄×D₇₃	C₂×#41	1	2	yes	—
199	C₄×D₇₃	H(5,𝔽₂)	1	2	yes	—
200	Dic₁₄₆	C₂×D₈	1	12	yes	complemented
201	C₈×C₇₃	—	2	3	no	—
202	C₈×C₇₃	C₂×#41	1	2	yes	complemented
203	#10596831	—	2	3	no	—
204	#10596831	C₂×#41	1	2	yes	complemented
205	C₂²×C₇₃	—	4	6	no	—
206	C₂²×C₇₃	—	4	6	no	—
207	C₂²×C₇₃	—	4	6	no	—
208	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
209	C₂×D₇₃	—	4	6	no	—
210	C₂×D₇₃	—	4	6	no	—
211	C₂×D₇₃	—	4	6	no	—
212	C₂×D₇₃	—	8	24	no	—
213	C₂×D₇₃	#550	1	2	yes	—
214	C₂×D₇₃	C₂²×D₈	1	2	yes	—
215	C₂×D₇₃	#576	1	2	yes	—
216	C₄×C₇₃	—	2	3	no	—
217	C₄×C₇₃	—	4	2	no	—
218	C₄×C₇₃	C₂²×D₈	1	6	yes	—
219	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
220	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
221	Dic₇₃	—	2	3	no	—
222	Dic₇₃	—	4	2	no	—
223	Dic₇₃	#550	1	2	yes	—
224	Dic₇₃	C₂²×D₈	1	6	yes	—
225	C₂×#3391	—	73	1	no	maximal, Sylow
226	C₂×C₇₃	—	8	6	no	—
227	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
228	C₂×C₇₃	C₂³×D₈	1	1	yes	characteristic
229	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
230	D₇₃	—	8	6	no	—
231	D₇₃	#3391	1	4	yes	direct product factor
232	C₂×#550	—	73	2	no	—
233	#3391	—	73	3	no	—
234	#3391	—	73	6	no	—
235	#3391	—	73	1	no	—
236	#3391	—	73	3	no	—
237	#3391	—	73	2	no	—
238	#3391	D₇₃	1	1	yes	characteristic, direct product factor
239	C₂×#493	—	73	3	no	—
240	C₂×#459	—	73	6	no	—
241	C₂×C₈×Q₈	—	73	1	no	—
242	C₂×C₄×D₈	—	73	3	no	—
243	C₇₃	C₂×#3391	1	1	yes	characteristic, complemented, Sylow
244	C₂²×#41	—	146	2	no	—
245	C₂²×D₈	—	73	6	no	—
246	C₂²×D₈	—	73	3	no	—
247	#550	—	73	6	no	—
248	#550	—	73	2	no	—
249	#550	—	73	6	no	—
250	#550	—	146	6	no	—
251	#550	—	146	2	no	—
252	#550	C₂×D₇₃	1	2	yes	complemented
253	C₂×#127	—	73	6	no	—
254	C₂×#121	—	146	6	no	—
255	C₂×C₄×Q₈	—	73	1	no	—
256	C₂×C₄×D₄	—	73	6	no	—
257	#493	—	73	6	no	—
258	#493	—	73	6	no	—
259	#493	—	73	6	no	—
260	#493	—	73	3	no	—
261	#493	C₂×D₇₃	1	3	yes	complemented
262	#459	—	73	12	no	—
263	#459	—	73	6	no	—
264	#459	—	73	6	no	—
265	#459	—	73	6	no	—
266	#459	—	73	12	no	—
267	#459	C₂×D₇₃	1	6	yes	complemented
268	C₈×Q₈	—	73	1	no	—
269	C₈×Q₈	—	73	3	no	—
270	C₈×Q₈	—	73	3	no	—
271	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
272	C₄×D₈	—	73	3	no	—
273	C₄×D₈	—	73	6	no	—
274	C₄×D₈	—	73	3	no	—
275	C₄×D₈	—	73	6	no	—
276	C₄×D₈	—	73	3	no	—
277	C₄×D₈	C₂×D₇₃	1	3	yes	complemented
278	C₂×#107	—	73	1	no	—
279	C₂×C₄⋊C₈	—	73	3	no	—
280	C₂×#102	—	73	6	no	—
281	C₂×C₄×C₈	—	73	3	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	292	16	no	—
284	C₂×#41	—	146	6	no	—
285	C₂×#41	—	146	6	no	—
286	C₂×#41	—	146	2	no	—
287	C₂²×Q₈	—	73	1	no	—
288	C₂²×D₄	—	73	6	no	—
289	C₂²×D₄	—	146	6	no	—
290	C₂²×D₄	—	146	6	no	—
291	C₂³×C₄	—	146	6	no	—
292	C₂×D₈	—	292	12	no	—
293	C₂×D₈	—	73	12	no	—
294	C₂×D₈	—	73	6	no	—
295	C₂×D₈	—	73	6	no	—
296	C₂×D₈	—	73	3	no	—
297	C₂×D₈	—	146	12	no	—
298	C₂×D₈	C₂²×D₇₃	1	3	yes	—
299	C₂×D₈	C₂²×D₇₃	1	6	yes	—
300	C₂²×C₈	—	73	1	no	—
301	C₂²×C₈	—	73	3	no	—
302	#127	—	73	12	no	—
303	#127	—	73	6	no	—
304	#127	—	146	6	no	—
305	#127	—	146	6	no	—
306	#127	C₂²×D₇₃	1	6	yes	—
307	#121	—	2	6	no	—
308	#121	—	146	12	no	—
309	#121	—	146	6	no	—
310	#121	—	146	6	no	—
311	#121	—	146	12	no	—
312	#121	—	146	6	no	—
313	C₄×Q₈	—	73	1	no	—
314	C₄×Q₈	—	73	3	no	—
315	C₄×Q₈	—	73	3	no	—
316	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
317	C₄×D₄	—	73	6	no	—
318	C₄×D₄	—	73	6	no	—
319	C₄×D₄	—	73	6	no	—
320	C₄×D₄	—	146	6	no	—
321	C₄×D₄	—	146	6	no	—
322	C₄×D₄	C₂²×D₇₃	1	6	yes	—
323	C₂×C₄⋊C₄	—	73	3	no	—
324	C₂×C₄⋊C₄	—	73	2	no	—
325	C₂×C₂²⋊C₄	—	146	6	no	—
326	C₂×C₄²	—	73	3	no	—
327	#107	—	73	1	no	—
328	#107	—	73	2	no	—
329	#107	C₂²×D₇₃	1	1	yes	characteristic
330	C₄⋊C₈	—	73	6	no	—
331	C₄⋊C₈	—	73	3	no	—
332	C₄⋊C₈	C₂²×D₇₃	1	3	yes	—
333	#102	—	73	6	no	—
334	#102	—	73	6	no	—
335	#102	—	73	6	no	—
336	#102	C₂²×D₇₃	1	6	yes	—
337	C₄×C₈	—	73	3	no	—
338	C₄×C₈	—	73	3	no	—
339	C₄×C₈	—	73	3	no	—
340	C₄×C₈	C₂²×D₇₃	1	3	yes	—
341	C₂⁴	—	146	6	no	—
342	#41	—	4	8	no	—
343	#41	—	292	24	no	—
344	#41	—	292	24	no	—
345	#41	—	292	8	no	—
346	C₂×Q₈	—	73	8	no	—
347	C₂×Q₈	—	73	3	no	—
348	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	6	no	—
351	C₂×D₄	—	292	24	no	—
352	C₂×D₄	—	584	12	no	—
353	C₂×D₄	—	73	6	no	—
354	C₂×D₄	—	146	12	no	—
355	C₂×D₄	—	146	12	no	—
356	C₂×D₄	—	146	6	no	—
357	C₂×D₄	—	146	12	no	—
358	C₂×D₄	—	146	12	no	—
359	C₂×D₄	—	146	6	no	—
360	C₂×D₄	—	146	6	no	—
361	C₂×D₄	C₂³×D₇₃	1	6	yes	—
362	C₂²×C₄	—	2	6	no	—
363	C₂²×C₄	—	292	24	no	—
364	C₂²×C₄	—	73	3	no	—
365	C₂²×C₄	—	73	1	no	—
366	C₂²×C₄	—	73	3	no	—
367	C₂²×C₄	—	146	6	no	—
368	C₂²×C₄	—	146	2	no	—
369	C₂²×C₄	—	146	6	no	—
370	C₂²×C₄	—	146	6	no	—
371	D₈	—	2	6	no	—
372	D₈	—	4	6	no	—
373	D₈	—	292	6	no	—
374	D₈	—	292	12	no	—
375	D₈	—	146	12	no	—
376	D₈	—	146	6	no	—
377	C₂×C₈	—	73	1	no	—
378	C₂×C₈	—	73	4	no	—
379	C₂×C₈	—	73	3	no	—
380	C₂×C₈	—	146	6	no	—
381	C₂×C₈	C₂³×D₇₃	1	3	yes	—
382	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
383	C₄⋊C₄	—	73	6	no	—
384	C₄⋊C₄	—	73	3	no	—
385	C₄⋊C₄	—	73	2	no	—
386	C₄⋊C₄	—	146	2	no	—
387	C₄⋊C₄	D₄×D₇₃	1	3	yes	—
388	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
389	C₂²⋊C₄	—	2	6	no	—
390	C₂²⋊C₄	—	146	6	no	—
391	C₂²⋊C₄	—	146	6	no	—
392	C₂²⋊C₄	—	146	6	no	—
393	C₄²	—	73	3	no	—
394	C₄²	—	73	3	no	—
395	C₄²	—	73	3	no	—
396	C₄²	C₂³×D₇₃	1	3	yes	—
397	C₂³	—	2	6	no	—
398	C₂³	—	292	12	no	—
399	C₂³	—	292	12	no	—
400	C₂³	—	292	12	no	—
401	C₂³	—	73	1	no	—
402	C₂³	—	146	6	no	—
403	Q₈	—	73	12	no	—
404	Q₈	D₈×D₇₃	1	4	yes	complemented
405	D₄	—	2	6	no	—
406	D₄	—	2	6	no	—
407	D₄	—	4	12	no	—
408	D₄	—	8	6	no	—
409	D₄	—	292	24	no	—
410	D₄	—	292	12	no	—
411	D₄	—	292	12	no	—
412	D₄	—	584	6	no	—
413	D₄	—	584	12	no	—
414	D₄	—	146	6	no	—
415	D₄	—	146	6	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	12	no	—
418	C₂×C₄	—	292	4	no	—
419	C₂×C₄	—	292	12	no	—
420	C₂×C₄	—	292	12	no	—
421	C₂×C₄	—	292	12	no	—
422	C₂×C₄	—	73	1	no	—
423	C₂×C₄	—	73	3	no	—
424	C₂×C₄	—	73	2	no	—
425	C₂×C₄	—	73	2	no	—
426	C₂×C₄	—	73	12	no	—
427	C₂×C₄	—	73	3	no	—
428	C₂×C₄	—	146	6	no	—
429	C₂×C₄	—	146	2	no	—
430	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
431	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
432	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
433	C₈	—	2	3	no	—
434	C₈	—	73	2	no	—
435	C₈	—	146	3	no	—
436	C₈	#41×D₇₃	1	2	yes	complemented
437	C₂²	—	4	6	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	6	no	—
440	C₂²	—	292	6	no	—
441	C₂²	—	292	6	no	—
442	C₂²	—	292	6	no	—
443	C₂²	—	584	24	no	—
444	C₂²	—	73	2	no	—
445	C₂²	—	73	2	no	—
446	C₂²	—	73	2	no	—
447	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
448	C₄	—	2	3	no	—
449	C₄	—	4	2	no	—
450	C₄	—	292	2	no	—
451	C₄	—	73	6	no	—
452	C₄	—	73	2	no	—
453	C₄	—	146	3	no	—
454	C₄	C₂×D₈×D₇₃	1	6	yes	—
455	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
456	C₄	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
457	C₂	—	8	6	no	—
458	C₂	—	584	6	no	—
459	C₂	—	73	4	no	—
460	C₂	#550×D₇₃	1	1	yes	characteristic
461	C₂	C₂²×D₈×D₇₃	1	1	yes	characteristic
462	C₂	#576×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3391	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3391	D₇₃
hypocenter	C₇₃	C₂×#3391
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3391

Complements

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

N	H ≅ G/N	type
1. #550×D₇₃	C₂	semidirect
2. #22622906	C₂	semidirect
3. #22622905	C₂	semidirect
4. #22622904	C₂	semidirect
5. #22622903	C₂	semidirect
6. #22622902	C₂	semidirect
7. #493×D₇₃	C₂	semidirect
8. #459×D₇₃	C₂	semidirect
9. C₈×Q₈×D₇₃	C₂	semidirect
10. C₄×D₈×D₇₃	C₂	semidirect
11. C₇₃×#3391	C₂	semidirect
15. #17989259	C₂²	semidirect
16. #17989258	C₂²	semidirect
17. #17989257	C₂²	semidirect
24. #17988964	C₂²	semidirect
25. #17988963	C₂²	semidirect
26. #17988962	C₂²	semidirect
27. #17988962	C₂²	semidirect
28. #17988783	C₂²	semidirect
29. #17988782	C₂²	semidirect
30. #17988781	C₂²	semidirect
31. #17988780	C₂²	semidirect
32. #17988779	C₂²	semidirect
33. Q₈×#10596831	C₂²	semidirect
34. C₈×Dic₁₄₆	C₂²	semidirect
35. #17988711	C₂²	semidirect
36. C₄×D₅₈₄	C₂²	semidirect
37. D₈×Dic₇₃	C₂²	semidirect
38. #17988669	C₂²	semidirect
39. C₄×#11924013	C₂²	semidirect
40. #17988667	C₂²	semidirect
45. #550×C₇₃	C₂²	semidirect
46. #493×C₇₃	C₂²	semidirect
47. #459×C₇₃	C₂²	semidirect
48. C₈×Q₈×C₇₃	C₂²	semidirect
49. C₄×D₈×C₇₃	C₂²	semidirect
114. Q₈×D₇₃	D₈	semidirect
140. C₈×D₇₃	#41	semidirect
171. Q₈×C₇₃	C₂×D₈	semidirect
200. Dic₁₄₆	C₂×D₈	semidirect
202. C₈×C₇₃	C₂×#41	semidirect
204. #10596831	C₂×#41	semidirect
231. D₇₃	#3391	direct (N × H)
238. #3391	D₇₃	direct (N × H)
243. C₇₃	C₂×#3391	semidirect
252. #550	C₂×D₇₃	semidirect
261. #493	C₂×D₇₃	semidirect
267. #459	C₂×D₇₃	semidirect
271. C₈×Q₈	C₂×D₇₃	semidirect
277. C₄×D₈	C₂×D₇₃	semidirect
404. Q₈	D₈×D₇₃	semidirect
436. C₈	#41×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#550×D₇₃	2
#22622906	2
#22622905	2
#22622904	2
#22622903	2
#22622902	2
#493×D₇₃	2
#459×D₇₃	2
C₈×Q₈×D₇₃	2
C₄×D₈×D₇₃	2
C₇₃×#3391	2
C₂×#3391	73

Subgroups — #3391×D73 #33966873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3391×D₇₃ #33966873