Subgroups — #33090680

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22612405	C₂	1	1	yes	maximal, characteristic
2	#22610867	C₂	1	1	yes	maximal, characteristic
3	#22610866	C₂	1	1	yes	maximal, characteristic
4	#22610650	C₂	1	1	yes	maximal, characteristic
5	#22610491	C₂	1	2	yes	maximal
6	#22610485	C₂	1	2	yes	maximal
7	#22609790	C₂	1	2	yes	maximal
8	#22609786	C₂	1	1	yes	maximal, characteristic
9	#22609681	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
14	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	C₂×#14556501	C₂²	1	2	yes	—
16	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
21	#17988492	C₄	1	1	yes	characteristic
22	#17988492	C₄	1	1	yes	characteristic
23	#17988483	C₄	1	1	yes	characteristic
24	#17988483	C₄	1	1	yes	characteristic
25	#17988469	C₄	1	2	yes	—
26	#17988469	C₄	1	2	yes	—
27	C₄×#11924007	C₂²	1	2	yes	—
28	#17988433	C₂²	1	2	yes	—
29	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
30	#17988342	C₂²	1	2	yes	—
31	#17988341	C₂²	1	2	yes	—
32	#17988341	C₂²	1	2	yes	—
33	#17988341	C₂²	1	2	yes	—
34	#17988341	C₂²	1	2	yes	—
35	#17988341	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
37	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
40	#336×C₇₃	C₂²	1	2	yes	—
41	C₂²×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
42	C₂²×#10596831	C₂³	1	2	yes	—
43	C₂²×#10596831	C₂³	1	1	yes	characteristic
44	C₂²×#10596831	C₂³	1	1	yes	characteristic
45	C₄×Dic₁₄₆	—	2	2	no	—
46	C₄×Dic₁₄₆	—	2	2	no	—
47	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂×#11924007	C₂×C₄	1	2	yes	—
49	C₂×#11924007	C₂×C₄	1	2	yes	—
50	C₂×#11924007	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
57	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
58	C₄⋊#10596831	—	2	4	no	—
59	C₄⋊#10596831	—	2	2	no	—
60	#14556501	—	2	4	no	—
61	C₄×#10596831	—	2	2	no	—
62	C₈×Dic₇₃	—	2	2	no	—
63	C₈×Dic₇₃	—	2	2	no	—
64	C₈×Dic₇₃	—	2	2	no	—
65	C₈×Dic₇₃	Q₈	1	4	yes	complemented
66	#14556498	C₂×C₄	1	2	yes	—
67	#14556498	C₂×C₄	1	2	yes	—
68	#14556498	C₂×C₄	1	2	yes	—
69	#14556498	C₂×C₄	1	2	yes	—
70	#14556498	C₂×C₄	1	2	yes	—
71	#14556498	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₇₃	—	2	4	no	—
80	C₄⋊C₈×C₇₃	—	2	2	no	—
81	C₄×C₈×C₇₃	—	2	2	no	—
82	#95×C₇₃	C₂×C₄	1	2	yes	—
83	C₂×Dic₁₄₆	—	2	2	no	—
84	C₂×Dic₁₄₆	—	2	2	no	—
85	C₂×Dic₁₄₆	—	2	2	no	—
86	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
87	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
88	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×#10596831	—	2	1	no	—
93	C₂×#10596831	—	2	1	no	—
94	C₂×#10596831	—	2	1	no	—
95	C₂×#10596831	—	2	1	no	—
96	C₂×#10596831	—	2	2	no	—
97	C₂×#10596831	—	2	2	no	—
98	C₂×#10596831	—	2	2	no	—
99	C₂×#10596831	C₂×Q₈	1	2	yes	—
100	C₂×#10596831	#41	1	2	yes	—
101	C₄⋊Dic₇₃	—	2	2	no	—
102	#11924007	—	2	4	no	—
103	#11924007	—	2	4	no	—
104	#11924007	—	2	4	no	—
105	C₄×Dic₇₃	—	2	2	no	—
106	C₄×Dic₇₃	—	2	2	no	—
107	C₄×Dic₇₃	—	2	1	no	—
108	C₄×Dic₇₃	—	2	1	no	—
109	C₄×Dic₇₃	—	2	2	no	—
110	C₄×Dic₇₃	—	2	2	no	—
111	C₄×Dic₇₃	—	2	2	no	—
112	C₄×Dic₇₃	—	2	2	no	—
113	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
114	C₄×Dic₇₃	#41	1	2	yes	—
115	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₇₃	—	2	1	no	—
121	C₂×C₈×C₇₃	—	2	1	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	—	2	1	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₇₃	#41	1	2	yes	—
129	C₄⋊C₄×C₇₃	—	2	2	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄²×C₇₃	—	2	2	no	—
132	C₄²×C₇₃	—	2	2	no	—
133	C₄²×C₇₃	#41	1	2	yes	—
134	C₄²×C₇₃	#41	1	2	yes	—
135	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₇₃	—	2	1	no	—
137	C₂×C₄×C₇₃	—	2	1	no	—
138	C₂×C₄×C₇₃	—	2	2	no	—
139	C₂×C₄×C₇₃	—	2	2	no	—
140	C₂×C₄×C₇₃	—	2	2	no	—
141	C₂×C₄×C₇₃	—	2	2	no	—
142	C₂×C₄×C₇₃	—	2	2	no	—
143	C₂×C₄×C₇₃	—	2	2	no	—
144	C₂×C₄×C₇₃	#117	1	2	yes	—
145	C₂×C₄×C₇₃	#117	1	2	yes	—
146	C₂×C₄×C₇₃	#131	1	2	yes	—
147	C₂×C₄×C₇₃	#131	1	2	yes	—
148	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
154	C₂×Dic₇₃	—	2	1	no	—
155	C₂×Dic₇₃	—	2	1	no	—
156	C₂×Dic₇₃	—	2	1	no	—
157	C₂×Dic₇₃	—	2	1	no	—
158	C₂×Dic₇₃	—	2	1	no	—
159	C₂×Dic₇₃	—	2	1	no	—
160	C₂×Dic₇₃	—	2	1	no	—
161	C₂×Dic₇₃	—	2	1	no	—
162	C₂×Dic₇₃	—	2	2	no	—
163	C₂×Dic₇₃	—	2	2	no	—
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	—	2	2	no	—
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	2	no	—
168	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
169	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
170	C₂×Dic₇₃	#131	1	2	yes	—
171	C₂×Dic₇₃	#131	1	2	yes	—
172	Dic₁₄₆	—	4	4	no	—
173	C₈×C₇₃	—	2	2	no	—
174	C₈×C₇₃	—	2	2	no	—
175	C₈×C₇₃	—	4	2	no	—
176	#10596831	—	2	2	no	—
177	#10596831	—	2	2	no	—
178	#10596831	—	4	2	no	—
179	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
180	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
181	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
182	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
183	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
184	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
185	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
186	C₄×C₇₃	—	2	2	no	—
187	C₄×C₇₃	—	4	2	no	—
188	C₄×C₇₃	—	4	2	no	—
189	C₄×C₇₃	#433	1	4	yes	—
190	C₄×C₇₃	#529	1	1	yes	characteristic
191	C₄×C₇₃	#529	1	1	yes	characteristic
192	C₄×C₇₃	#533	1	1	yes	characteristic
193	C₄×C₇₃	#533	1	1	yes	characteristic
194	Dic₇₃	—	2	2	no	—
195	Dic₇₃	—	2	2	no	—
196	Dic₇₃	—	2	2	no	—
197	Dic₇₃	—	2	2	no	—
198	Dic₇₃	—	4	2	no	—
199	Dic₇₃	—	4	2	no	—
200	#21341	—	73	1	no	maximal, Sylow
201	C₂×C₇₃	#2295	1	1	yes	characteristic
202	C₂×C₇₃	C₂×#433	1	1	yes	characteristic
203	C₂×C₇₃	#2922	1	1	yes	characteristic
204	C₂×C₇₃	#2960	1	1	yes	characteristic
205	C₂×C₇₃	#2960	1	1	yes	characteristic
206	C₂×C₇₃	#2966	1	1	yes	characteristic
207	C₂×C₇₃	#2966	1	1	yes	characteristic
208	#2295	—	73	1	no	—
209	#1984	—	73	1	no	—
210	#1984	—	73	1	no	—
211	#1939	—	73	1	no	—
212	#1939	D₇₃	1	1	yes	characteristic
213	#1916	—	73	2	no	—
214	#1916	—	73	2	no	—
215	#1768	—	73	2	no	—
216	#1767	—	73	1	no	—
217	#1746	—	73	2	no	—
218	C₄²×C₈	—	73	1	no	—
219	C₇₃	#21341	1	1	yes	characteristic, complemented, Sylow
220	C₂×C₄×Q₈	—	73	1	no	—
221	C₂×C₄⋊C₈	—	73	2	no	—
222	C₂×C₄⋊C₈	—	73	1	no	—
223	C₂×C₄⋊C₈	C₂×D₇₃	1	2	yes	—
224	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
225	C₂×#97	—	73	2	no	—
226	C₂×C₄×C₈	—	73	1	no	—
227	C₂×C₄×C₈	—	73	1	no	—
228	C₂×C₄×C₈	—	73	1	no	—
229	C₂×C₄×C₈	—	73	1	no	—
230	C₂×C₄×C₈	—	73	1	no	—
231	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
232	#391	—	73	1	no	—
233	#391	—	73	1	no	—
234	#389	—	73	1	no	—
235	#389	—	73	1	no	—
236	#387	—	73	2	no	—
237	#387	—	73	2	no	—
238	C₄×C₄⋊C₄	—	73	2	no	—
239	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
240	#376	—	73	2	no	—
241	C₄³	—	73	1	no	—
242	#336	—	73	2	no	—
243	#336	—	73	2	no	—
244	#336	—	73	2	no	—
245	#336	—	73	2	no	—
246	#336	—	73	2	no	—
247	#336	—	73	2	no	—
248	#336	C₂×D₇₃	1	2	yes	—
249	C₂²×Q₈	—	73	1	no	—
250	C₂²×C₈	—	73	1	no	—
251	C₂²×C₈	—	73	1	no	—
252	C₂²×C₈	—	73	2	no	—
253	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
254	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
256	C₄×Q₈	—	146	2	no	—
257	C₄×Q₈	—	146	2	no	—
258	C₂×C₄⋊C₄	—	73	2	no	—
259	C₂×C₄⋊C₄	—	73	1	no	—
260	C₂×C₄⋊C₄	—	73	2	no	—
261	C₂×C₄⋊C₄	—	73	2	no	—
262	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
264	C₂×C₄²	—	73	1	no	—
265	C₂×C₄²	—	73	1	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	73	1	no	—
268	C₂×C₄²	—	73	1	no	—
269	C₂×C₄²	—	73	2	no	—
270	C₂×C₄²	—	73	1	no	—
271	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
272	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	146	4	no	—
276	C₄⋊C₈	—	146	2	no	—
277	#97	—	146	4	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	73	4	no	—
280	C₄×C₈	—	146	2	no	—
281	C₄×C₈	—	146	2	no	—
282	C₄×C₈	—	146	2	no	—
283	C₄×C₈	—	146	2	no	—
284	#95	—	73	2	no	—
285	#95	—	73	2	no	—
286	#95	—	73	2	no	—
287	#95	—	73	2	no	—
288	#95	—	73	2	no	—
289	#95	—	73	2	no	—
290	#95	C₄×D₇₃	1	2	yes	—
291	C₂×Q₈	—	146	2	no	—
292	C₂×Q₈	—	146	2	no	—
293	C₂×Q₈	—	146	2	no	—
294	C₂²×C₄	—	73	1	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	2	no	—
299	C₂²×C₄	—	73	2	no	—
300	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
301	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	73	2	no	—
313	C₂×C₈	—	73	2	no	—
314	C₂×C₈	—	146	2	no	—
315	C₂×C₈	—	146	2	no	—
316	C₂×C₈	—	146	2	no	—
317	C₂×C₈	—	146	1	no	—
318	C₂×C₈	—	146	1	no	—
319	C₂×C₈	—	146	1	no	—
320	C₂×C₈	—	146	1	no	—
321	C₂×C₈	Q₈×D₇₃	1	2	yes	—
322	C₂×C₈	#11924027	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	146	4	no	—
326	C₄⋊C₄	—	146	4	no	—
327	C₄⋊C₄	—	146	4	no	—
328	C₄⋊C₄	—	146	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	73	2	no	—
332	C₄²	—	73	2	no	—
333	C₄²	—	146	2	no	—
334	C₄²	—	146	2	no	—
335	C₄²	—	146	2	no	—
336	C₄²	—	146	2	no	—
337	C₄²	—	146	1	no	—
338	C₄²	—	146	1	no	—
339	C₄²	—	146	2	no	—
340	C₄²	—	146	2	no	—
341	C₄²	#11924027	1	2	yes	—
342	C₄²	#11924029	1	2	yes	—
343	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
344	Q₈	—	292	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	73	2	no	—
354	C₂×C₄	—	73	2	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	2	no	—
357	C₂×C₄	—	146	2	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	—	146	2	no	—
360	C₂×C₄	—	146	2	no	—
361	C₂×C₄	—	146	2	no	—
362	C₂×C₄	—	146	2	no	—
363	C₂×C₄	—	146	1	no	—
364	C₂×C₄	—	146	1	no	—
365	C₂×C₄	—	146	1	no	—
366	C₂×C₄	—	146	1	no	—
367	C₂×C₄	—	146	1	no	—
368	C₂×C₄	—	146	1	no	—
369	C₂×C₄	—	146	1	no	—
370	C₂×C₄	—	146	1	no	—
371	C₂×C₄	#14556549	1	2	yes	—
372	C₂×C₄	#14556549	1	2	yes	—
373	C₂×C₄	#14556597	1	2	yes	—
374	C₂×C₄	#14556599	1	2	yes	—
375	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
376	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
379	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
380	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	292	2	no	—
385	C₈	—	146	2	no	—
386	C₈	—	146	2	no	—
387	C₂²	C₂×#14556549	1	1	yes	characteristic
388	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
389	C₂²	C₄×#11924027	1	1	yes	characteristic
390	C₂²	#131×D₇₃	1	1	yes	characteristic
391	C₂²	#131×D₇₃	1	1	yes	characteristic
392	C₂²	C₂×#14556597	1	1	yes	characteristic
393	C₂²	C₂×#14556599	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	292	2	no	—
398	C₄	—	292	2	no	—
399	C₄	—	146	2	no	—
400	C₄	—	146	2	no	—
401	C₄	—	146	2	no	—
402	C₄	—	146	2	no	—
403	C₄	#17988647	1	4	yes	—
404	C₄	#17989118	1	1	yes	characteristic
405	C₄	#17989122	1	1	yes	characteristic
406	C₄	#17989139	1	1	yes	characteristic
407	C₄	#17989142	1	1	yes	characteristic
408	C₂	#22612402	1	1	yes	characteristic
409	C₂	C₂×#17988647	1	1	yes	characteristic
410	C₂	#22618574	1	1	yes	characteristic
411	C₂	#22618860	1	1	yes	characteristic
412	C₂	#22618862	1	1	yes	characteristic
413	C₂	#22618903	1	1	yes	characteristic
414	C₂	#22618909	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle, prime radical	C₂³×C₇₃	C₂³×C₄
Fitting	C₇₃×#1939	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1939	D₇₃
hypocenter	C₇₃	#21341
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
65. C₈×Dic₇₃	Q₈	semidirect
219. C₇₃	#21341	semidirect

Maximal subgroups

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

subgroup	index
#22612405	2
#22610867	2
#22610866	2
#22610650	2
#22610491	2
#22610485	2
#22609790	2
#22609786	2
#22609681	2
C₄×C₈×Dic₇₃	2
C₇₃×#1939	2
#21341	73