Subgroups — #32975682

Order 18688.

550 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618562	C₂	1	1	yes	maximal, characteristic
2	#22618559	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988639	C₂	1	1	yes	maximal, characteristic
4	#22607782	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607781	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607780	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
9	#17988643	—	2	1	no	—
10	#17988642	—	2	1	no	—
11	#17988642	—	2	1	no	—
12	#17988641	C₄	1	2	yes	—
13	#17988640	C₂²	1	1	yes	characteristic
14	#17988639	—	2	1	no	—
15	#17988639	—	2	1	no	—
16	#17988639	—	2	1	no	—
17	#17988639	—	2	1	no	—
18	#17988638	—	2	1	no	—
19	#17988638	—	2	1	no	—
20	#17988638	—	2	1	no	—
21	#17988610	C₄	1	2	yes	—
22	#17988609	—	2	1	no	—
23	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
24	#17988550	C₄	1	2	yes	—
25	#17988549	C₄	1	2	yes	—
26	C₂×#14556503	C₄	1	2	yes	—
27	C₄×#11924012	C₂²	1	1	yes	characteristic
28	C₄×#11924011	—	2	1	no	—
29	C₂×C₈×Dic₇₃	C₄	1	2	yes	—
30	#431×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂×#11924012	C₂×C₄	1	2	yes	—
37	C₂×#11924011	—	2	2	no	—
38	C₂²×#10596831	C₂×C₄	1	2	yes	—
39	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
42	C₄²×D₇₃	D₄	1	1	yes	characteristic
43	C₄²×D₇₃	D₄	1	1	yes	characteristic
44	C₄²×D₇₃	D₄	1	1	yes	characteristic
45	C₄²×D₇₃	D₄	1	1	yes	characteristic
46	C₄²×D₇₃	D₄	1	1	yes	characteristic
47	C₄²×D₇₃	D₄	1	1	yes	characteristic
48	C₄²×D₇₃	Q₈	1	1	yes	characteristic
49	C₄²×D₇₃	Q₈	1	1	yes	characteristic
50	C₄⋊#10596831	—	2	1	no	—
51	C₄⋊#10596831	—	2	1	no	—
52	C₄⋊#10596831	—	2	1	no	—
53	#14556520	—	2	2	no	—
54	#14556520	—	2	2	no	—
55	#14556520	—	2	2	no	—
56	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
57	#14556503	—	2	2	no	—
58	#14556503	—	2	2	no	—
59	#14556503	—	2	2	no	—
60	#14556503	—	2	2	no	—
61	#14556503	—	2	2	no	—
62	#14556502	—	2	1	no	—
63	#14556501	—	2	2	no	—
64	C₄×#10596831	—	2	1	no	—
65	C₄×#10596831	—	2	1	no	—
66	C₈×Dic₇₃	—	2	2	no	—
67	C₈×Dic₇₃	—	2	2	no	—
68	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₇₃	—	2	1	no	—
72	C₄⋊C₈×C₇₃	—	2	1	no	—
73	C₄⋊C₈×C₇₃	—	2	1	no	—
74	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
75	#97×C₇₃	—	2	1	no	—
76	C₄×C₈×C₇₃	—	2	1	no	—
77	C₄×C₈×C₇₃	—	2	1	no	—
78	C₂³×D₇₃	C₄²	1	1	yes	characteristic
79	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
80	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
81	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
82	C₂×C₄×D₇₃	—	2	2	no	—
83	C₂×C₄×D₇₃	—	2	2	no	—
84	C₂×C₄×D₇₃	—	4	2	no	—
85	C₂×C₄×D₇₃	—	4	1	no	—
86	C₂×C₄×D₇₃	—	4	1	no	—
87	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
99	#11924012	—	2	2	no	—
100	#11924012	—	2	2	no	—
101	#11924011	—	4	4	no	—
102	C₂×#10596831	—	2	2	no	—
103	C₂×#10596831	—	2	2	no	—
104	C₂×#10596831	—	2	2	no	—
105	C₂×#10596831	—	4	2	no	—
106	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₇₃	—	2	2	no	—
122	M₁₆×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	—	4	2	no	—
127	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
131	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
132	C₂²×D₇₃	—	2	1	no	—
133	C₂²×D₇₃	—	2	1	no	—
134	C₂²×D₇₃	—	4	1	no	—
135	C₂²×D₇₃	—	4	1	no	—
136	C₂²×D₇₃	#95	1	1	yes	characteristic
137	C₂²×D₇₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₇₃	—	2	1	no	—
139	C₂×C₄×C₇₃	—	2	1	no	—
140	C₂×C₄×C₇₃	—	4	1	no	—
141	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₃	#131	1	2	yes	—
148	C₂×C₄×C₇₃	#131	1	2	yes	—
149	C₂×Dic₇₃	—	2	1	no	—
150	C₂×Dic₇₃	—	2	1	no	—
151	C₂×Dic₇₃	—	2	2	no	—
152	C₂×Dic₇₃	—	4	1	no	—
153	C₂×Dic₇₃	#95	1	1	yes	characteristic
154	C₂×Dic₇₃	#95	1	1	yes	characteristic
155	C₂×Dic₇₃	#95	1	1	yes	characteristic
156	C₂×Dic₇₃	#95	1	1	yes	characteristic
157	C₂×Dic₇₃	#95	1	1	yes	characteristic
158	C₂×Dic₇₃	#95	1	1	yes	characteristic
159	C₄×D₇₃	—	2	2	no	—
160	C₄×D₇₃	—	2	2	no	—
161	C₄×D₇₃	—	2	1	no	—
162	C₄×D₇₃	—	2	1	no	—
163	C₄×D₇₃	—	2	1	no	—
164	C₄×D₇₃	—	2	1	no	—
165	C₄×D₇₃	—	2	2	no	—
166	C₄×D₇₃	—	2	2	no	—
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	—	2	2	no	—
169	C₄×D₇₃	—	4	1	no	—
170	C₄×D₇₃	—	4	1	no	—
171	C₄×D₇₃	—	4	1	no	—
172	C₄×D₇₃	—	4	1	no	—
173	C₈×C₇₃	—	4	2	no	—
174	C₈×C₇₃	—	4	2	no	—
175	C₈×C₇₃	—	4	2	no	—
176	#10596831	—	4	2	no	—
177	#10596831	—	4	2	no	—
178	#10596831	—	4	2	no	—
179	C₂²×C₇₃	—	2	1	no	—
180	C₂²×C₇₃	—	2	1	no	—
181	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
182	C₂²×C₇₃	#405	1	1	yes	characteristic
183	C₂²×C₇₃	#405	1	1	yes	characteristic
184	C₂×D₇₃	—	2	1	no	—
185	C₂×D₇₃	—	2	1	no	—
186	C₂×D₇₃	—	2	1	no	—
187	C₂×D₇₃	—	2	1	no	—
188	C₂×D₇₃	—	2	1	no	—
189	C₂×D₇₃	—	2	1	no	—
190	C₂×D₇₃	—	4	2	no	—
191	C₂×D₇₃	—	4	2	no	—
192	C₄×C₇₃	—	2	1	no	—
193	C₄×C₇₃	—	2	1	no	—
194	C₄×C₇₃	—	2	1	no	—
195	C₄×C₇₃	#408	1	2	yes	—
196	C₄×C₇₃	#413	1	1	yes	characteristic
197	C₄×C₇₃	#413	1	1	yes	characteristic
198	C₄×C₇₃	#424	1	2	yes	—
199	Dic₇₃	—	2	1	no	—
200	Dic₇₃	—	2	1	no	—
201	Dic₇₃	—	2	1	no	—
202	Dic₇₃	—	2	1	no	—
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	#344	1	2	yes	—
205	#7936	—	73	1	no	maximal, Sylow
206	C₂×C₇₃	—	2	1	no	—
207	C₂×C₇₃	—	2	1	no	—
208	C₂×C₇₃	#1729	1	1	yes	characteristic
209	C₂×C₇₃	#1742	1	1	yes	characteristic
210	C₂×C₇₃	C₂×#344	1	1	yes	characteristic
211	D₇₃	—	4	1	no	—
212	D₇₃	—	4	1	no	—
213	#2920	—	73	1	no	—
214	#2920	—	73	1	no	—
215	C₂×#431	—	73	1	no	—
216	#1283	—	73	1	no	—
217	#1283	—	73	1	no	—
218	#1283	—	73	1	no	—
219	#1283	D₇₃	1	1	yes	characteristic, complemented
220	C₇₃	#7936	1	1	yes	characteristic, complemented, Sylow
221	C₂²×C₄²	—	73	1	no	—
222	#432	—	73	2	no	—
223	#432	—	146	1	no	—
224	#432	—	146	1	no	—
225	#432	—	146	1	no	—
226	#431	—	73	1	no	—
227	#431	—	146	1	no	—
228	#431	—	146	1	no	—
229	#431	—	146	1	no	—
230	#431	—	146	1	no	—
231	#431	—	146	1	no	—
232	#431	—	146	1	no	—
233	#431	—	146	1	no	—
234	#431	C₂×D₇₃	1	1	yes	characteristic
235	#423	—	73	2	no	—
236	#423	—	146	1	no	—
237	C₂×C₄⋊C₈	—	73	1	no	—
238	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
239	#407	—	73	2	no	—
240	#407	—	73	2	no	—
241	C₂×C₂²⋊C₈	—	73	2	no	—
242	C₄×M₁₆	—	73	1	no	—
243	C₄×M₁₆	—	146	1	no	—
244	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
245	C₂×C₄×C₈	—	73	2	no	—
246	C₂³×C₄	—	73	1	no	—
247	C₂³×C₄	—	73	1	no	—
248	C₂³×C₄	—	73	1	no	—
249	C₂×M₁₆	—	73	2	no	—
250	C₂×M₁₆	—	146	2	no	—
251	C₂×M₁₆	C₄×D₇₃	1	2	yes	—
252	C₂²×C₈	—	73	2	no	—
253	C₂²×C₈	C₄×D₇₃	1	2	yes	—
254	C₂×C₄²	—	73	1	no	—
255	C₂×C₄²	—	73	1	no	—
256	C₂×C₄²	—	73	1	no	—
257	C₂×C₄²	—	73	1	no	—
258	C₂×C₄²	—	73	1	no	—
259	C₂×C₄²	—	73	1	no	—
260	C₂×C₄²	—	73	1	no	—
261	C₂×C₄²	—	73	1	no	—
262	C₂×C₄²	—	73	1	no	—
263	C₂×C₄²	—	73	1	no	—
264	C₂×C₄²	—	73	1	no	—
265	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	146	2	no	—
270	C₄⋊C₈	—	146	2	no	—
271	C₄⋊C₈	—	146	2	no	—
272	C₄⋊C₈	—	146	1	no	—
273	C₄⋊C₈	—	146	1	no	—
274	C₄⋊C₈	—	146	1	no	—
275	C₂²⋊C₈	—	73	2	no	—
276	C₂²⋊C₈	—	146	2	no	—
277	C₂²⋊C₈	—	146	2	no	—
278	C₂²⋊C₈	—	146	2	no	—
279	C₂²⋊C₈	—	146	2	no	—
280	C₂²⋊C₈	—	146	2	no	—
281	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
282	#97	—	2	1	no	—
283	#97	—	146	2	no	—
284	#97	—	146	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	146	2	no	—
288	C₄×C₈	—	146	2	no	—
289	C₄×C₈	—	146	1	no	—
290	C₄×C₈	—	146	1	no	—
291	C₂⁴	—	73	1	no	—
292	C₂²×C₄	—	292	1	no	—
293	C₂²×C₄	—	292	1	no	—
294	C₂²×C₄	—	292	2	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	146	2	no	—
311	C₂²×C₄	—	146	2	no	—
312	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	292	4	no	—
318	M₁₆	—	146	2	no	—
319	M₁₆	—	146	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	292	2	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	—	146	2	no	—
328	C₄²	—	73	1	no	—
329	C₄²	—	73	1	no	—
330	C₄²	—	73	1	no	—
331	C₄²	—	73	1	no	—
332	C₄²	—	73	1	no	—
333	C₄²	—	73	1	no	—
334	C₄²	—	73	1	no	—
335	C₄²	—	73	1	no	—
336	C₄²	—	73	1	no	—
337	C₄²	—	73	1	no	—
338	C₄²	—	73	1	no	—
339	C₄²	—	73	1	no	—
340	C₄²	D₄×D₇₃	1	1	yes	characteristic
341	C₄²	D₄×D₇₃	1	1	yes	characteristic
342	C₄²	D₄×D₇₃	1	1	yes	characteristic
343	C₄²	Q₈×D₇₃	1	1	yes	characteristic
344	C₂³	—	292	1	no	—
345	C₂³	—	292	1	no	—
346	C₂³	—	73	1	no	—
347	C₂³	—	73	1	no	—
348	C₂³	—	146	1	no	—
349	C₂³	—	146	1	no	—
350	C₂³	C₄²×D₇₃	1	1	yes	characteristic
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	292	1	no	—
355	C₂×C₄	—	292	1	no	—
356	C₂×C₄	—	292	1	no	—
357	C₂×C₄	—	292	1	no	—
358	C₂×C₄	—	292	1	no	—
359	C₂×C₄	—	73	1	no	—
360	C₂×C₄	—	73	1	no	—
361	C₂×C₄	—	73	1	no	—
362	C₂×C₄	—	73	1	no	—
363	C₂×C₄	—	73	1	no	—
364	C₂×C₄	—	73	1	no	—
365	C₂×C₄	—	146	2	no	—
366	C₂×C₄	—	146	2	no	—
367	C₂×C₄	—	146	2	no	—
368	C₂×C₄	—	146	1	no	—
369	C₂×C₄	—	146	1	no	—
370	C₂×C₄	—	146	2	no	—
371	C₂×C₄	—	146	2	no	—
372	C₂×C₄	—	146	2	no	—
373	C₂×C₄	—	146	2	no	—
374	C₂×C₄	—	146	1	no	—
375	C₂×C₄	—	146	1	no	—
376	C₂×C₄	—	146	1	no	—
377	C₂×C₄	—	146	1	no	—
378	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
379	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
380	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
381	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
382	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
383	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
384	C₂×C₄	#14556597	1	2	yes	—
385	C₂×C₄	#14556599	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	292	2	no	—
390	C₈	—	292	2	no	—
391	C₈	—	292	2	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	292	2	no	—
395	C₂²	—	292	2	no	—
396	C₂²	—	146	1	no	—
397	C₂²	—	146	1	no	—
398	C₂²	—	146	1	no	—
399	C₂²	—	146	1	no	—
400	C₂²	—	146	1	no	—
401	C₂²	—	146	1	no	—
402	C₂²	#95×D₇₃	1	1	yes	characteristic
403	C₂²	#17988541	1	1	yes	characteristic
404	C₂²	#17988544	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	73	2	no	—
409	C₄	—	146	1	no	—
410	C₄	—	146	1	no	—
411	C₄	—	146	1	no	—
412	C₄	—	146	1	no	—
413	C₄	—	146	1	no	—
414	C₄	#17988552	1	2	yes	—
415	C₄	#17988568	1	1	yes	characteristic
416	C₄	#17988570	1	1	yes	characteristic
417	C₄	#17988612	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	292	1	no	—
421	C₂	—	292	1	no	—
422	C₂	#22609626	1	1	yes	characteristic
423	C₂	#22609668	1	1	yes	characteristic
424	C₂	#344×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₃
commutator	C₂³×C₇₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1283	C₂
socle	C₂²×C₇₃	C₂×#95
prime radical	C₂³×D₇₃	C₄²
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1283	D₇₃
hypocenter	C₇₃	#7936
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1283

Complements

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

N	H ≅ G/N	type
4. #22607782	C₂	semidirect
5. #22607781	C₂	semidirect
6. #22607780	C₂	semidirect
7. C₇₃×#1283	C₂	semidirect
219. #1283	D₇₃	semidirect
220. C₇₃	#7936	semidirect

Maximal subgroups

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

subgroup	index
#22618562	2
#22618559	2
C₂×#17988639	2
#22607782	2
#22607781	2
#22607780	2
C₇₃×#1283	2
#7936	73