Subgroups — #3483×D₇₃ #33993084

Order 18688.

8418 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623558	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623557	C₂	1	6	yes	maximal, complemented
3	#22623556	C₂	1	9	yes	maximal, complemented
4	#22623555	C₂	1	9	yes	maximal, complemented
5	#22623554	C₂	1	6	yes	maximal, complemented
6	Q₈²×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#555×D₇₃	C₂	1	9	yes	maximal, complemented
8	#550×D₇₃	C₂	1	6	yes	maximal, complemented
9	#532×D₇₃	C₂	1	9	yes	maximal, complemented
10	C₄×#41×D₇₃	C₂	1	6	yes	maximal, complemented
11	C₇₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₇₃	C₂²	1	6	yes	—
13	C₂×#41×D₇₃	C₂²	1	6	yes	—
14	Q₈×Dic₁₄₆	C₂²	1	6	yes	complemented
15	#17989317	C₂²	1	9	yes	complemented
16	#17989303	C₂²	1	9	yes	complemented
17	#17989302	C₂²	1	18	yes	complemented
18	#17989301	C₂²	1	36	yes	complemented
19	#17989300	C₂²	1	36	yes	complemented
20	#17989299	C₂²	1	36	yes	complemented
21	#17989259	C₂²	1	6	yes	complemented
22	#17989258	C₂²	1	18	yes	complemented
23	#17989257	C₂²	1	18	yes	complemented
24	#17989256	C₂²	1	12	yes	complemented
25	#17989255	C₂²	1	36	yes	complemented
26	#17989138	C₂²	1	9	yes	complemented
27	#17989137	C₂²	1	9	yes	complemented
28	#17989136	C₂²	1	18	yes	complemented
29	#17989135	C₂²	1	9	yes	complemented
30	#17989134	C₂²	1	36	yes	complemented
31	#17989133	C₂²	1	18	yes	complemented
32	#17989132	C₂²	1	36	yes	complemented
33	C₄⋊Q₈×D₇₃	C₂²	1	9	yes	—
34	#127×D₇₃	C₂²	1	9	yes	—
35	#124×D₇₃	C₂²	1	18	yes	—
36	#121×D₇₃	C₂²	1	36	yes	—
37	#41×Dic₇₃	C₂²	1	6	yes	complemented
38	C₄×#11924029	C₂²	1	6	yes	complemented
39	C₄×#11924029	C₂²	1	6	yes	complemented
40	C₄×#11924028	C₂²	1	18	yes	complemented
41	#17989055	C₂²	1	18	yes	complemented
42	C₄×#11924027	C₂²	1	18	yes	complemented
43	C₄×#11924027	C₂²	1	18	yes	complemented
44	C₄×Q₈×D₇₃	C₂²	1	6	yes	—
45	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
46	C₄×D₄×D₇₃	C₂²	1	18	yes	—
47	C₄×D₄×D₇₃	C₂²	1	18	yes	—
48	#117×D₇₃	C₂²	1	18	yes	—
49	C₂×C₄²×D₇₃	C₂²	1	9	yes	—
50	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#555×C₇₃	C₂²	1	9	yes	complemented
52	#550×C₇₃	C₂²	1	6	yes	complemented
53	#532×C₇₃	C₂²	1	9	yes	complemented
54	C₄×#41×C₇₃	C₂²	1	6	yes	complemented
55	C₂×#11924029	C₂³	1	6	yes	—
56	C₂×#11924029	C₂³	1	6	yes	—
57	C₂×#11924028	C₂³	1	18	yes	—
58	C₂×#11924028	C₂³	1	18	yes	—
59	C₂×#11924027	C₂³	1	18	yes	—
60	C₂×#11924027	C₂³	1	18	yes	—
61	#41×D₇₃	—	2	48	no	—
62	#41×D₇₃	—	4	24	no	—
63	C₂×Q₈×D₇₃	C₂³	1	6	yes	—
64	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
65	C₂×D₄×D₇₃	C₂³	1	18	yes	—
66	C₂×D₄×D₇₃	C₂³	1	18	yes	—
67	C₂²×C₄×D₇₃	C₂³	1	9	yes	—
68	C₂²×C₄×D₇₃	C₂³	1	18	yes	—
69	#14556591	C₂³	1	9	yes	—
70	#14556590	C₂³	1	36	yes	—
71	#14556589	C₂³	1	18	yes	—
72	#14556588	C₂³	1	9	yes	—
73	#14556587	C₂³	1	36	yes	—
74	#14556587	C₂³	1	18	yes	—
75	#14556580	C₂³	1	18	yes	—
76	#14556579	C₂³	1	18	yes	—
77	#14556578	C₂³	1	18	yes	—
78	#14556577	C₂³	1	72	yes	—
79	#14556566	C₂³	1	36	yes	—
80	#14556565	C₂³	1	36	yes	—
81	#14556564	C₂³	1	72	yes	—
82	#14556563	C₂³	1	72	yes	—
83	#14556562	C₂³	1	36	yes	—
84	Q₈×Dic₇₃	C₂³	1	6	yes	—
85	Q₈×Dic₇₃	C₂³	1	2	yes	—
86	C₄×Dic₁₄₆	C₂³	1	18	yes	—
87	C₄×Dic₁₄₆	C₂³	1	6	yes	—
88	#14556556	C₂³	1	18	yes	—
89	#14556556	C₂³	1	6	yes	—
90	C₄×D₂₉₂	C₂³	1	18	yes	—
91	C₄×D₂₉₂	C₂³	1	18	yes	—
92	D₄×Dic₇₃	C₂³	1	18	yes	—
93	D₄×Dic₇₃	C₂³	1	18	yes	—
94	#14556553	C₂³	1	18	yes	—
95	#14556553	C₂³	1	18	yes	—
96	C₄×C₂²⋊D₇₃	C₂³	1	36	yes	—
97	C₄×C₂²⋊D₇₃	C₂³	1	36	yes	—
98	#14556551	C₂³	1	36	yes	—
99	#14556551	C₂³	1	36	yes	—
100	#14556550	C₂³	1	18	yes	—
101	#14556549	C₂³	1	18	yes	—
102	#14556549	C₂³	1	18	yes	—
103	#14556548	C₂³	1	36	yes	—
104	#14556547	C₂³	1	36	yes	—
105	C₄⋊C₄×D₇₃	C₂³	1	18	yes	—
106	C₄⋊C₄×D₇₃	C₂³	1	6	yes	—
107	C₂²⋊C₄×D₇₃	C₂³	1	36	yes	—
108	C₂×C₄×Dic₇₃	C₂³	1	18	yes	—
109	C₂×C₄×Dic₇₃	C₂³	1	9	yes	—
110	C₄²×D₇₃	C₂³	1	9	yes	—
111	C₄²×D₇₃	C₂³	1	18	yes	—
112	C₄²×D₇₃	C₂³	1	9	yes	—
113	C₄²×D₇₃	C₂³	1	9	yes	—
114	C₄²×D₇₃	C₂³	1	6	yes	—
115	C₄²×D₇₃	C₂³	1	9	yes	—
116	C₂×#41×C₇₃	C₂³	1	6	yes	—
117	C₂×#41×C₇₃	C₂³	1	6	yes	—
118	C₄⋊Q₈×C₇₃	C₂³	1	9	yes	—
119	#127×C₇₃	C₂³	1	9	yes	—
120	#124×C₇₃	C₂³	1	18	yes	—
121	#121×C₇₃	C₂³	1	36	yes	—
122	C₄×Q₈×C₇₃	C₂³	1	6	yes	—
123	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
124	C₄×D₄×C₇₃	C₂³	1	18	yes	—
125	C₄×D₄×C₇₃	C₂³	1	18	yes	—
126	#117×C₇₃	C₂³	1	18	yes	—
127	C₂×C₄²×C₇₃	C₂³	1	9	yes	—
128	C₂³×D₇₃	C₂⁴	1	9	yes	—
129	#11924029	—	2	24	no	—
130	#11924029	—	4	12	no	—
131	#11924028	—	2	72	no	—
132	#11924028	—	4	36	no	—
133	#11924027	—	2	72	no	—
134	#11924027	—	4	36	no	—
135	C₂×Dic₁₄₆	C₂⁴	1	18	yes	—
136	C₂×Dic₁₄₆	C₂⁴	1	6	yes	—
137	Q₈×D₇₃	—	4	12	no	—
138	Q₈×D₇₃	#41	1	16	yes	complemented
139	C₂×D₂₉₂	C₂⁴	1	18	yes	—
140	C₂×D₂₉₂	C₂⁴	1	18	yes	—
141	C₂×C₂²⋊D₇₃	C₂⁴	1	36	yes	—
142	C₂×C₂²⋊D₇₃	C₂⁴	1	36	yes	—
143	D₄×D₇₃	—	2	72	no	—
144	D₄×D₇₃	—	4	36	no	—
145	C₂²×Dic₇₃	C₂⁴	1	18	yes	—
146	C₂²×Dic₇₃	C₂⁴	1	9	yes	—
147	C₂×C₄×D₇₃	—	2	72	no	—
148	C₂×C₄×D₇₃	—	2	36	no	—
149	C₂×C₄×D₇₃	C₂⁴	1	6	yes	—
150	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
151	C₂×C₄×D₇₃	C₂⁴	1	18	yes	—
152	C₂×C₄×D₇₃	C₂⁴	1	18	yes	—
153	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
154	C₂×C₄×D₇₃	C₂⁴	1	9	yes	—
155	C₂×C₄×D₇₃	C₂⁴	1	6	yes	—
156	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
157	C₄⋊Dic₇₃	C₂⁴	1	6	yes	—
158	C₄⋊Dic₇₃	C₂⁴	1	18	yes	—
159	#11924007	C₂⁴	1	12	yes	—
160	#11924007	C₂⁴	1	36	yes	—
161	C₂²⋊Dic₇₃	C₂⁴	1	36	yes	—
162	#11924005	C₂⁴	1	36	yes	—
163	#11924005	C₂⁴	1	36	yes	—
164	C₄×Dic₇₃	C₂⁴	1	6	yes	—
165	C₄×Dic₇₃	C₂⁴	1	6	yes	—
166	C₄×Dic₇₃	C₂⁴	1	6	yes	—
167	C₄×Dic₇₃	C₂⁴	1	9	yes	—
168	C₄×Dic₇₃	C₂⁴	1	18	yes	—
169	C₄×Dic₇₃	C₂⁴	1	9	yes	—
170	C₄×Dic₇₃	C₂⁴	1	18	yes	—
171	#41×C₇₃	—	2	24	no	—
172	#41×C₇₃	—	4	12	no	—
173	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
174	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
175	C₂×D₄×C₇₃	C₂⁴	1	18	yes	—
176	C₂×D₄×C₇₃	C₂⁴	1	18	yes	—
177	C₂²×C₄×C₇₃	C₂⁴	1	18	yes	—
178	C₂²×C₄×C₇₃	C₂⁴	1	9	yes	—
179	C₄⋊C₄×C₇₃	C₂⁴	1	6	yes	—
180	C₄⋊C₄×C₇₃	C₂⁴	1	18	yes	—
181	C₂²⋊C₄×C₇₃	C₂⁴	1	36	yes	—
182	C₄²×C₇₃	C₂⁴	1	6	yes	—
183	C₄²×C₇₃	C₂⁴	1	9	yes	—
184	C₄²×C₇₃	C₂⁴	1	9	yes	—
185	C₂³×C₇₃	C₂⁵	1	9	yes	—
186	C₂²×D₇₃	—	2	36	no	—
187	C₂²×D₇₃	—	2	18	no	—
188	C₂²×D₇₃	C₂⁵	1	9	yes	—
189	C₂²×D₇₃	C₂⁵	1	1	yes	characteristic
190	Q₈×C₇₃	—	4	6	no	—
191	Q₈×C₇₃	C₂×#41	1	8	yes	complemented
192	D₄×C₇₃	—	2	36	no	—
193	D₄×C₇₃	—	4	18	no	—
194	C₂×C₄×C₇₃	—	2	36	no	—
195	C₂×C₄×C₇₃	—	2	18	no	—
196	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
197	C₂×C₄×C₇₃	C₂⁵	1	9	yes	—
198	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
199	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
200	C₂²⋊D₇₃	—	2	72	no	—
201	C₂²⋊D₇₃	—	4	36	no	—
202	C₂×Dic₇₃	—	2	36	no	—
203	C₂×Dic₇₃	—	2	18	no	—
204	C₂×Dic₇₃	C₂⁵	1	6	yes	—
205	C₂×Dic₇₃	C₂⁵	1	9	yes	—
206	C₂×Dic₇₃	C₂⁵	1	6	yes	—
207	C₂×Dic₇₃	C₂⁵	1	1	yes	characteristic
208	D₂₉₂	—	2	36	no	—
209	D₂₉₂	—	4	18	no	—
210	C₄×D₇₃	—	2	12	no	—
211	C₄×D₇₃	—	2	18	no	—
212	C₄×D₇₃	—	2	36	no	—
213	C₄×D₇₃	—	2	18	no	—
214	C₄×D₇₃	—	2	36	no	—
215	C₄×D₇₃	—	2	18	no	—
216	C₄×D₇₃	C₂×#41	1	24	yes	—
217	C₄×D₇₃	H(5,𝔽₂)	1	4	yes	—
218	Dic₁₄₆	—	4	18	no	—
219	Dic₁₄₆	C₂×#41	1	24	yes	complemented
220	C₂²×C₇₃	—	2	18	no	—
221	C₂²×C₇₃	—	2	9	no	—
222	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
223	C₂×D₇₃	—	2	18	no	—
224	C₂×D₇₃	—	2	9	no	—
225	C₂×D₇₃	—	4	36	no	—
226	C₂×D₇₃	C₂²×#41	1	4	yes	—
227	C₂×D₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
228	C₄×C₇₃	—	2	6	no	—
229	C₄×C₇₃	—	2	9	no	—
230	C₄×C₇₃	C₂²×#41	1	12	yes	—
231	C₄×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
232	Dic₇₃	—	2	6	no	—
233	Dic₇₃	—	2	9	no	—
234	Dic₇₃	C₂²×#41	1	12	yes	—
235	Dic₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
236	C₂×#3483	—	73	1	no	maximal, Sylow
237	C₂×C₇₃	—	4	9	no	—
238	C₂×C₇₃	C₂³×#41	1	2	yes	—
239	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
240	D₇₃	—	4	9	no	—
241	D₇₃	#3483	1	4	yes	direct product factor
242	#3483	—	73	1	no	—
243	#3483	—	73	9	no	—
244	#3483	—	73	6	no	—
245	#3483	—	73	9	no	—
246	#3483	—	73	6	no	—
247	#3483	D₇₃	1	1	yes	characteristic, direct product factor
248	C₂×Q₈²	—	73	1	no	—
249	C₂×#555	—	73	9	no	—
250	C₂×#550	—	73	6	no	—
251	C₂×#532	—	73	9	no	—
252	C₂×C₄×#41	—	73	6	no	—
253	C₇₃	C₂×#3483	1	1	yes	characteristic, complemented, Sylow
254	C₂²×#41	—	73	6	no	—
255	C₂²×#41	—	73	6	no	—
256	Q₈²	—	73	9	no	—
257	Q₈²	—	73	6	no	—
258	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
259	#555	—	73	9	no	—
260	#555	—	73	36	no	—
261	#555	—	73	36	no	—
262	#555	—	73	18	no	—
263	#555	—	73	36	no	—
264	#555	C₂×D₇₃	1	9	yes	complemented
265	#550	—	73	12	no	—
266	#550	—	73	18	no	—
267	#550	—	73	36	no	—
268	#550	—	73	6	no	—
269	#550	—	73	18	no	—
270	#550	C₂×D₇₃	1	6	yes	complemented
271	#532	—	73	18	no	—
272	#532	—	73	9	no	—
273	#532	—	73	9	no	—
274	#532	—	73	18	no	—
275	#532	—	73	36	no	—
276	#532	—	73	36	no	—
277	#532	—	73	9	no	—
278	#532	C₂×D₇₃	1	9	yes	complemented
279	C₂×C₄⋊Q₈	—	73	9	no	—
280	C₂×#127	—	73	9	no	—
281	C₂×#124	—	73	18	no	—
282	C₂×#121	—	73	36	no	—
283	C₄×#41	—	73	6	no	—
284	C₄×#41	—	73	6	no	—
285	C₄×#41	—	73	6	no	—
286	C₄×#41	—	73	18	no	—
287	C₄×#41	—	73	18	no	—
288	C₄×#41	—	73	18	no	—
289	C₄×#41	—	73	18	no	—
290	C₄×#41	C₂×D₇₃	1	6	yes	complemented
291	C₂×C₄×Q₈	—	73	2	no	—
292	C₂×C₄×Q₈	—	73	6	no	—
293	C₂×C₄×D₄	—	73	18	no	—
294	C₂×C₄×D₄	—	73	18	no	—
295	C₂×#117	—	73	18	no	—
296	C₂²×C₄²	—	73	9	no	—
297	C₂×#41	—	292	24	no	—
298	C₂×#41	—	73	6	no	—
299	C₂×#41	—	73	6	no	—
300	C₂×#41	—	73	18	no	—
301	C₂×#41	—	73	18	no	—
302	C₂×#41	—	73	18	no	—
303	C₂×#41	—	73	18	no	—
304	C₂×#41	—	146	48	no	—
305	C₂×#41	C₂²×D₇₃	1	6	yes	—
306	C₂×#41	C₂²×D₇₃	1	6	yes	—
307	C₂²×Q₈	—	73	6	no	—
308	C₂²×Q₈	—	73	2	no	—
309	C₂²×D₄	—	73	18	no	—
310	C₂²×D₄	—	73	18	no	—
311	C₂³×C₄	—	73	18	no	—
312	C₂³×C₄	—	73	9	no	—
313	C₄⋊Q₈	—	73	18	no	—
314	C₄⋊Q₈	—	73	36	no	—
315	C₄⋊Q₈	—	73	9	no	—
316	C₄⋊Q₈	C₂²×D₇₃	1	9	yes	—
317	#127	—	73	36	no	—
318	#127	—	73	18	no	—
319	#127	—	73	9	no	—
320	#127	C₂²×D₇₃	1	9	yes	—
321	#124	—	73	18	no	—
322	#124	—	73	18	no	—
323	#124	—	73	72	no	—
324	#124	—	73	18	no	—
325	#124	C₂²×D₇₃	1	18	yes	—
326	#121	—	73	36	no	—
327	#121	—	73	72	no	—
328	#121	—	73	36	no	—
329	#121	—	73	36	no	—
330	#121	—	73	72	no	—
331	#121	C₂²×D₇₃	1	36	yes	—
332	C₄×Q₈	—	73	2	no	—
333	C₄×Q₈	—	73	6	no	—
334	C₄×Q₈	—	73	6	no	—
335	C₄×Q₈	—	73	18	no	—
336	C₄×Q₈	—	73	6	no	—
337	C₄×Q₈	—	73	18	no	—
338	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
339	C₄×Q₈	C₂²×D₇₃	1	6	yes	—
340	C₄×D₄	—	73	18	no	—
341	C₄×D₄	—	73	18	no	—
342	C₄×D₄	—	73	36	no	—
343	C₄×D₄	—	73	36	no	—
344	C₄×D₄	—	73	18	no	—
345	C₄×D₄	—	73	18	no	—
346	C₄×D₄	—	73	36	no	—
347	C₄×D₄	—	73	36	no	—
348	C₄×D₄	—	73	18	no	—
349	C₄×D₄	—	73	18	no	—
350	C₄×D₄	C₂²×D₇₃	1	18	yes	—
351	C₄×D₄	C₂²×D₇₃	1	18	yes	—
352	#117	—	73	18	no	—
353	#117	—	73	18	no	—
354	#117	—	73	18	no	—
355	#117	—	73	36	no	—
356	#117	—	73	36	no	—
357	#117	C₂²×D₇₃	1	18	yes	—
358	C₂×C₄⋊C₄	—	73	6	no	—
359	C₂×C₄⋊C₄	—	73	18	no	—
360	C₂×C₂²⋊C₄	—	73	36	no	—
361	C₂×C₄²	—	73	18	no	—
362	C₂×C₄²	—	73	9	no	—
363	C₂×C₄²	—	73	9	no	—
364	C₂×C₄²	—	73	6	no	—
365	C₂×C₄²	—	73	9	no	—
366	C₂×C₄²	—	73	9	no	—
367	C₂×C₄²	—	73	9	no	—
368	C₂×C₄²	—	73	18	no	—
369	C₂×C₄²	C₂²×D₇₃	1	9	yes	—
370	C₂⁴	—	73	9	no	—
371	#41	—	2	24	no	—
372	#41	—	4	12	no	—
373	#41	—	292	36	no	—
374	#41	—	292	36	no	—
375	#41	—	292	12	no	—
376	#41	—	146	72	no	—
377	#41	—	146	72	no	—
378	#41	—	146	24	no	—
379	C₂×Q₈	—	292	12	no	—
380	C₂×Q₈	—	73	16	no	—
381	C₂×Q₈	—	73	18	no	—
382	C₂×Q₈	—	73	6	no	—
383	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
384	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
385	C₂×D₄	—	292	36	no	—
386	C₂×D₄	—	73	36	no	—
387	C₂×D₄	—	73	36	no	—
388	C₂×D₄	—	73	18	no	—
389	C₂×D₄	—	73	18	no	—
390	C₂×D₄	—	146	72	no	—
391	C₂×D₄	C₂³×D₇₃	1	18	yes	—
392	C₂×D₄	C₂³×D₇₃	1	18	yes	—
393	C₂²×C₄	—	73	6	no	—
394	C₂²×C₄	—	73	1	no	—
395	C₂²×C₄	—	73	18	no	—
396	C₂²×C₄	—	73	9	no	—
397	C₂²×C₄	—	73	6	no	—
398	C₂²×C₄	—	73	9	no	—
399	C₂²×C₄	—	73	18	no	—
400	C₂²×C₄	—	73	18	no	—
401	C₂²×C₄	—	73	9	no	—
402	C₂²×C₄	—	73	9	no	—
403	C₂²×C₄	—	146	36	no	—
404	C₂²×C₄	—	146	72	no	—
405	C₂²×C₄	C₂³×D₇₃	1	18	yes	—
406	C₂²×C₄	C₂³×D₇₃	1	9	yes	—
407	C₄⋊C₄	—	73	12	no	—
408	C₄⋊C₄	—	73	36	no	—
409	C₄⋊C₄	—	73	6	no	—
410	C₄⋊C₄	—	73	18	no	—
411	C₄⋊C₄	C₂³×D₇₃	1	6	yes	—
412	C₄⋊C₄	C₂³×D₇₃	1	18	yes	—
413	C₂²⋊C₄	—	73	36	no	—
414	C₂²⋊C₄	—	73	36	no	—
415	C₂²⋊C₄	—	73	36	no	—
416	C₂²⋊C₄	C₂³×D₇₃	1	36	yes	—
417	C₄²	—	73	6	no	—
418	C₄²	—	73	6	no	—
419	C₄²	—	73	9	no	—
420	C₄²	—	73	18	no	—
421	C₄²	—	73	9	no	—
422	C₄²	—	73	18	no	—
423	C₄²	—	73	6	no	—
424	C₄²	C₂³×D₇₃	1	9	yes	—
425	C₄²	C₂³×D₇₃	1	9	yes	—
426	C₄²	C₂³×D₇₃	1	6	yes	—
427	C₂³	—	73	1	no	—
428	C₂³	—	73	9	no	—
429	C₂³	—	146	18	no	—
430	C₂³	—	146	36	no	—
431	C₂³	C₂⁴×D₇₃	1	9	yes	—
432	Q₈	—	4	6	no	—
433	Q₈	—	292	18	no	—
434	Q₈	—	73	24	no	—
435	Q₈	#41×D₇₃	1	8	yes	complemented
436	D₄	—	2	36	no	—
437	D₄	—	4	18	no	—
438	D₄	—	292	18	no	—
439	D₄	—	292	36	no	—
440	D₄	—	146	72	no	—
441	D₄	—	146	36	no	—
442	C₂×C₄	—	2	36	no	—
443	C₂×C₄	—	2	18	no	—
444	C₂×C₄	—	73	1	no	—
445	C₂×C₄	—	73	6	no	—
446	C₂×C₄	—	73	24	no	—
447	C₂×C₄	—	73	4	no	—
448	C₂×C₄	—	73	6	no	—
449	C₂×C₄	—	73	9	no	—
450	C₂×C₄	—	146	18	no	—
451	C₂×C₄	—	146	36	no	—
452	C₂×C₄	—	146	12	no	—
453	C₂×C₄	—	146	18	no	—
454	C₂×C₄	—	146	18	no	—
455	C₂×C₄	—	146	36	no	—
456	C₂×C₄	—	146	36	no	—
457	C₂×C₄	—	146	18	no	—
458	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
459	C₂×C₄	C₂⁴×D₇₃	1	9	yes	—
460	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
461	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
462	C₂²	—	2	18	no	—
463	C₂²	—	2	9	no	—
464	C₂²	—	292	36	no	—
465	C₂²	—	73	4	no	—
466	C₂²	—	73	2	no	—
467	C₂²	—	146	18	no	—
468	C₂²	—	146	9	no	—
469	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
470	C₄	—	2	6	no	—
471	C₄	—	2	9	no	—
472	C₄	—	73	12	no	—
473	C₄	—	73	2	no	—
474	C₄	—	146	6	no	—
475	C₄	—	146	9	no	—
476	C₄	C₂×#41×D₇₃	1	12	yes	—
477	C₄	H(5,𝔽₂)×D₇₃	1	2	yes	—
478	C₂	—	4	9	no	—
479	C₂	—	292	9	no	—
480	C₂	—	73	4	no	—
481	C₂	C₂²×#41×D₇₃	1	2	yes	—
482	C₂	C₂×H(5,𝔽₂)×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₇₃
commutator, socle, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₇₃×#3483	C₂
hypercenter	#3483	D₇₃
hypocenter	C₇₃	C₂×#3483
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #3483

Complements

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

N	H ≅ G/N	type
1. #22623558	C₂	semidirect
2. #22623557	C₂	semidirect
3. #22623556	C₂	semidirect
4. #22623555	C₂	semidirect
5. #22623554	C₂	semidirect
6. Q₈²×D₇₃	C₂	semidirect
7. #555×D₇₃	C₂	semidirect
8. #550×D₇₃	C₂	semidirect
9. #532×D₇₃	C₂	semidirect
10. C₄×#41×D₇₃	C₂	semidirect
11. C₇₃×#3483	C₂	semidirect
14. Q₈×Dic₁₄₆	C₂²	semidirect
15. #17989317	C₂²	semidirect
16. #17989303	C₂²	semidirect
17. #17989302	C₂²	semidirect
18. #17989301	C₂²	semidirect
19. #17989300	C₂²	semidirect
20. #17989299	C₂²	semidirect
21. #17989259	C₂²	semidirect
22. #17989258	C₂²	semidirect
23. #17989257	C₂²	semidirect
24. #17989256	C₂²	semidirect
25. #17989255	C₂²	semidirect
26. #17989138	C₂²	semidirect
27. #17989137	C₂²	semidirect
28. #17989136	C₂²	semidirect
29. #17989135	C₂²	semidirect
30. #17989134	C₂²	semidirect
31. #17989133	C₂²	semidirect
32. #17989132	C₂²	semidirect
37. #41×Dic₇₃	C₂²	semidirect
38. C₄×#11924029	C₂²	semidirect
39. C₄×#11924029	C₂²	semidirect
40. C₄×#11924028	C₂²	semidirect
41. #17989055	C₂²	semidirect
42. C₄×#11924027	C₂²	semidirect
43. C₄×#11924027	C₂²	semidirect
50. Q₈²×C₇₃	C₂²	semidirect
51. #555×C₇₃	C₂²	semidirect
52. #550×C₇₃	C₂²	semidirect
53. #532×C₇₃	C₂²	semidirect
54. C₄×#41×C₇₃	C₂²	semidirect
138. Q₈×D₇₃	#41	semidirect
191. Q₈×C₇₃	C₂×#41	semidirect
219. Dic₁₄₆	C₂×#41	semidirect
241. D₇₃	#3483	direct (N × H)
247. #3483	D₇₃	direct (N × H)
253. C₇₃	C₂×#3483	semidirect
258. Q₈²	C₂×D₇₃	semidirect
264. #555	C₂×D₇₃	semidirect
270. #550	C₂×D₇₃	semidirect
278. #532	C₂×D₇₃	semidirect
290. C₄×#41	C₂×D₇₃	semidirect
435. Q₈	#41×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623558	2
#22623557	2
#22623556	2
#22623555	2
#22623554	2
Q₈²×D₇₃	2
#555×D₇₃	2
#550×D₇₃	2
#532×D₇₃	2
C₄×#41×D₇₃	2
C₇₃×#3483	2
C₂×#3483	73

Subgroups — #3483×D73 #33993084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3483×D₇₃ #33993084