Subgroups — #33069822

Order 18688.

710 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620508	C₂	1	1	yes	maximal, characteristic
2	#22619398	C₂	1	2	yes	maximal, complemented
3	C₈×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22609374	C₂	1	2	yes	maximal, complemented
5	#22609373	C₂	1	2	yes	maximal, complemented
6	#22609326	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609325	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609288	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608688	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608605	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556620	—	2	2	no	—
13	#17989135	C₂²	1	2	yes	—
14	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
15	#17988992	C₂²	1	1	yes	characteristic
16	#17988933	C₂²	1	2	yes	—
17	#17988820	—	2	1	no	—
18	#17988820	—	2	1	no	—
19	#17988808	—	2	2	no	—
20	#17988807	—	2	2	no	—
21	#17988798	C₂²	1	2	yes	—
22	#17988797	C₂²	1	2	yes	—
23	#17988784	C₂²	1	2	yes	—
24	Q₈×#10596831	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₄₆	—	2	1	no	—
26	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	#17988711	—	2	1	no	—
28	#17988711	C₂²	1	1	yes	characteristic
29	D₈×Dic₇₃	—	2	1	no	—
30	D₈×Dic₇₃	—	2	1	no	—
31	#17988609	C₂²	1	2	yes	—
32	C₄⋊C₈×D₇₃	—	2	1	no	—
33	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#17988585	—	2	2	no	—
35	C₄×C₈×D₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988340	C₂²	1	1	yes	characteristic
38	#17988339	C₂²	1	2	yes	—
39	#17988334	C₂²	1	2	yes	—
40	#17988332	C₂²	1	2	yes	—
41	#17988331	C₂²	1	2	yes	—
42	#493×C₇₃	C₂²	1	1	yes	characteristic
43	#460×C₇₃	C₂²	1	2	yes	—
44	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#331×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924027	—	2	2	no	—
48	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
49	#14556620	—	4	8	no	—
50	C₂×Dic₂₉₂	—	2	2	no	—
51	C₂×#11924018	—	2	2	no	—
52	C₂×#11924016	—	2	2	no	—
53	C₂×#11924011	—	2	2	no	—
54	C₂×C₈×D₇₃	—	2	1	no	—
55	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
57	#14556591	C₂³	1	2	yes	—
58	#14556578	—	2	2	no	—
59	#14556562	—	2	2	no	—
60	#14556562	—	2	2	no	—
61	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
62	C₄×Dic₁₄₆	—	2	1	no	—
63	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
64	#14556556	—	2	1	no	—
65	#14556556	D₄	1	1	yes	characteristic
66	D₄×Dic₇₃	—	2	2	no	—
67	D₄×Dic₇₃	—	2	2	no	—
68	C₄⋊C₄×D₇₃	—	2	1	no	—
69	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
70	C₄²×D₇₃	—	2	1	no	—
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	#14556525	—	2	1	no	—
73	#14556525	—	2	1	no	—
74	C₄⋊#10596831	—	2	1	no	—
75	C₄⋊#10596831	C₂³	1	2	yes	—
76	C₄⋊#10596831	C₂³	1	1	yes	characteristic
77	#14556520	—	2	1	no	—
78	#14556520	—	2	2	no	—
79	#14556520	—	2	1	no	—
80	#14556520	—	2	1	no	—
81	#14556516	—	2	2	no	—
82	#14556514	—	2	2	no	—
83	#14556512	—	2	2	no	—
84	#14556512	—	2	2	no	—
85	#14556512	—	2	2	no	—
86	C₄×#10596831	—	2	1	no	—
87	C₄×#10596831	C₂³	1	1	yes	characteristic
88	C₈×Dic₇₃	—	2	1	no	—
89	C₈×Dic₇₃	—	2	1	no	—
90	C₈×Dic₇₃	D₄	1	1	yes	characteristic
91	C₈×Dic₇₃	D₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₇₃	—	2	2	no	—
93	C₂×D₈×C₇₃	—	2	1	no	—
94	C₂×D₈×C₇₃	—	2	1	no	—
95	#127×C₇₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	—	2	1	no	—
98	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
99	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
100	#102×C₇₃	—	2	2	no	—
101	C₄×C₈×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	#11924027	—	4	4	no	—
104	#11924027	—	4	4	no	—
105	C₂×Dic₁₄₆	—	2	1	no	—
106	C₂×Dic₁₄₆	—	2	2	no	—
107	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₇₃	—	2	2	no	—
109	Q₈×D₇₃	D₈	1	4	yes	complemented
110	C₂×C₂²⋊D₇₃	—	4	2	no	—
111	C₂²×Dic₇₃	—	4	2	no	—
112	C₂×C₄×D₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
117	Dic₂₉₂	—	4	4	no	—
118	#11924018	—	4	4	no	—
119	#11924016	—	4	4	no	—
120	#11924011	—	4	4	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	2	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	—	4	1	no	—
127	C₈×D₇₃	—	4	2	no	—
128	C₄⋊Dic₇₃	—	2	1	no	—
129	C₄⋊Dic₇₃	—	2	2	no	—
130	C₄⋊Dic₇₃	—	2	2	no	—
131	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
132	#11924007	—	2	1	no	—
133	#11924007	—	2	1	no	—
134	#11924007	—	2	1	no	—
135	C₂²⋊Dic₇₃	—	4	2	no	—
136	C₂²⋊Dic₇₃	—	4	2	no	—
137	C₄×Dic₇₃	—	2	1	no	—
138	C₄×Dic₇₃	—	2	1	no	—
139	C₄×Dic₇₃	—	2	1	no	—
140	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₇₃	#41	1	1	yes	characteristic
143	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₇₃	—	2	2	no	—
145	C₂×D₄×C₇₃	—	2	2	no	—
146	C₂×D₄×C₇₃	—	2	2	no	—
147	SD₁₆×C₇₃	—	4	4	no	—
148	D₈×C₇₃	—	4	2	no	—
149	D₈×C₇₃	—	4	2	no	—
150	C₂×C₈×C₇₃	—	2	1	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₄⋊C₄×C₇₃	—	2	1	no	—
155	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₇₃	—	2	1	no	—
157	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
158	C₂³×C₇₃	—	4	2	no	—
159	C₂²×D₇₃	#121	1	1	yes	characteristic
160	Q₈×C₇₃	—	2	1	no	—
161	Q₈×C₇₃	C₂×D₈	1	2	yes	—
162	D₄×C₇₃	—	4	2	no	—
163	D₄×C₇₃	—	4	2	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	4	2	no	—
166	D₄×C₇₃	—	8	2	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₇₃	—	8	4	no	—
173	C₂×Dic₇₃	—	2	1	no	—
174	C₂×Dic₇₃	—	2	1	no	—
175	C₂×Dic₇₃	—	4	2	no	—
176	C₂×Dic₇₃	—	8	4	no	—
177	C₂×Dic₇₃	#121	1	1	yes	characteristic
178	C₂×Dic₇₃	#121	1	1	yes	characteristic
179	C₂×Dic₇₃	#121	1	1	yes	characteristic
180	C₄×D₇₃	—	2	4	no	—
181	C₄×D₇₃	—	2	1	no	—
182	C₄×D₇₃	—	2	1	no	—
183	C₄×D₇₃	—	4	1	no	—
184	C₄×D₇₃	—	4	2	no	—
185	C₄×D₇₃	C₂×D₈	1	2	yes	—
186	C₄×D₇₃	#135	1	2	yes	—
187	Dic₁₄₆	—	2	1	no	—
188	Dic₁₄₆	—	2	4	no	—
189	Dic₁₄₆	—	4	2	no	—
190	Dic₁₄₆	—	4	2	no	—
191	Dic₁₄₆	C₂×D₈	1	2	yes	—
192	C₈×C₇₃	—	2	1	no	—
193	C₈×C₇₃	—	4	2	no	—
194	C₈×C₇₃	—	4	1	no	—
195	C₈×C₇₃	#137	1	2	yes	complemented
196	#10596831	—	2	1	no	—
197	#10596831	—	2	1	no	—
198	#10596831	—	4	2	no	—
199	#10596831	—	4	1	no	—
200	C₂²×C₇₃	—	8	2	no	—
201	C₂²×C₇₃	—	8	2	no	—
202	C₂²×C₇₃	—	8	2	no	—
203	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
204	C₂×D₇₃	—	2	1	no	—
205	C₂×D₇₃	—	2	1	no	—
206	C₂×D₇₃	#466	1	2	yes	—
207	C₄×C₇₃	—	2	2	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	4	1	no	—
210	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
212	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
213	C₄×C₇₃	#575	1	1	yes	characteristic
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	2	no	—
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	—	4	1	no	—
218	Dic₇₃	—	8	2	no	—
219	Dic₇₃	#466	1	2	yes	—
220	#19261	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	16	2	no	—
222	C₂×C₇₃	#3037	1	1	yes	characteristic
223	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
224	C₂×C₇₃	#3067	1	1	yes	characteristic
225	D₇₃	—	2	2	no	—
226	#3169	—	73	1	no	—
227	#3037	—	73	2	no	—
228	C₂×C₈×Q₈	—	73	1	no	—
229	#1682	—	73	2	no	—
230	#1682	—	73	2	no	—
231	#1674	—	73	1	no	—
232	#1674	—	73	1	no	—
233	#1668	—	73	1	no	—
234	#1668	D₇₃	1	1	yes	characteristic, complemented
235	#1567	—	73	1	no	—
236	#1547	—	73	2	no	—
237	C₇₃	#19261	1	1	yes	characteristic, complemented, Sylow
238	C₂×#137	—	146	2	no	—
239	#532	—	73	2	no	—
240	C₂×C₄×Q₈	—	73	1	no	—
241	#500	—	73	1	no	—
242	#493	C₂×D₇₃	1	1	yes	characteristic
243	#486	—	73	2	no	—
244	#466	—	146	1	no	—
245	#466	—	146	1	no	—
246	#464	—	146	2	no	—
247	#464	—	146	2	no	—
248	#462	—	73	2	no	—
249	#462	—	73	2	no	—
250	#460	—	73	2	no	—
251	#460	C₂×D₇₃	1	2	yes	—
252	C₈×Q₈	—	73	1	no	—
253	C₈×Q₈	—	73	1	no	—
254	C₈×Q₈	—	73	1	no	—
255	C₈×Q₈	—	146	1	no	—
256	C₈×Q₈	—	146	1	no	—
257	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic
258	C₄×D₈	—	146	1	no	—
259	C₄×D₈	—	146	1	no	—
260	#423	—	73	2	no	—
261	C₂×C₄⋊C₈	—	73	1	no	—
262	C₂×C₄⋊C₈	—	146	1	no	—
263	#417	—	146	2	no	—
264	C₂×C₄×C₈	—	73	1	no	—
265	C₂×C₄×C₈	—	146	1	no	—
266	#335	—	73	2	no	—
267	#335	—	73	1	no	—
268	#335	C₂×D₇₃	1	1	yes	characteristic
269	#332	—	73	2	no	—
270	#332	—	73	2	no	—
271	#331	—	73	2	no	—
272	#331	C₂×D₇₃	1	2	yes	—
273	C₂×#41	—	146	2	no	—
274	C₂²×Q₈	—	73	1	no	—
275	#137	—	292	8	no	—
276	C₂×Q₁₆	—	146	2	no	—
277	C₂×Q₁₆	—	146	2	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×SD₁₆	—	146	2	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×M₁₆	—	146	2	no	—
283	C₂²×C₈	—	73	1	no	—
284	C₂²×C₈	—	73	1	no	—
285	C₂²×C₈	—	146	1	no	—
286	C₄⋊Q₈	—	73	2	no	—
287	#127	C₂²×D₇₃	1	2	yes	—
288	#124	—	146	2	no	—
289	#121	—	146	2	no	—
290	#121	—	146	2	no	—
291	C₄×Q₈	—	73	1	no	—
292	C₄×Q₈	—	73	1	no	—
293	C₄×Q₈	—	73	1	no	—
294	C₄×Q₈	—	146	1	no	—
295	C₄×Q₈	—	146	1	no	—
296	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
297	C₄×D₄	—	146	2	no	—
298	C₄×D₄	—	146	2	no	—
299	C₂×C₄⋊C₄	—	73	1	no	—
300	C₂×C₄⋊C₄	—	146	1	no	—
301	C₂×C₄²	—	73	1	no	—
302	C₂×C₄²	—	146	1	no	—
303	#107	—	146	1	no	—
304	#107	—	146	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	73	1	no	—
307	C₄⋊C₈	—	73	2	no	—
308	C₄⋊C₈	—	146	1	no	—
309	C₄⋊C₈	—	146	1	no	—
310	C₄⋊C₈	—	146	2	no	—
311	C₄⋊C₈	—	146	1	no	—
312	C₄⋊C₈	—	146	1	no	—
313	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
315	#103	—	146	2	no	—
316	#103	—	146	2	no	—
317	#102	—	2	2	no	—
318	#102	—	146	2	no	—
319	#102	—	146	2	no	—
320	#102	—	146	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	—	73	1	no	—
324	C₄×C₈	—	73	1	no	—
325	C₄×C₈	—	146	1	no	—
326	C₄×C₈	—	146	1	no	—
327	C₄×C₈	—	146	1	no	—
328	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
329	#41	—	292	4	no	—
330	#41	—	292	4	no	—
331	C₂×Q₈	—	73	4	no	—
332	C₂×Q₈	—	73	1	no	—
333	C₂×Q₈	—	146	1	no	—
334	C₂×Q₈	—	146	2	no	—
335	C₂×Q₈	—	146	2	no	—
336	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	292	2	no	—
341	C₂²×C₄	—	292	2	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	146	1	no	—
346	C₂²×C₄	—	146	1	no	—
347	Q₁₆	—	292	4	no	—
348	Q₁₆	—	292	4	no	—
349	SD₁₆	—	4	4	no	—
350	SD₁₆	—	292	4	no	—
351	D₈	—	4	2	no	—
352	D₈	—	4	2	no	—
353	M₁₆	—	292	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	292	1	no	—
357	C₂×C₈	—	292	2	no	—
358	C₂×C₈	—	73	1	no	—
359	C₂×C₈	—	73	1	no	—
360	C₂×C₈	—	146	1	no	—
361	C₂×C₈	—	146	2	no	—
362	C₂×C₈	—	146	2	no	—
363	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
364	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	73	1	no	—
367	C₄⋊C₄	—	146	1	no	—
368	C₄⋊C₄	—	146	1	no	—
369	C₄⋊C₄	—	146	1	no	—
370	C₄⋊C₄	—	146	2	no	—
371	C₄⋊C₄	—	146	2	no	—
372	C₄⋊C₄	—	146	1	no	—
373	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
374	C₂²⋊C₄	—	292	2	no	—
375	C₂²⋊C₄	—	292	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	73	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	146	1	no	—
381	C₄²	—	146	1	no	—
382	C₄²	—	146	1	no	—
383	C₄²	C₂³×D₇₃	1	1	yes	characteristic
384	C₂³	—	4	2	no	—
385	C₂³	—	73	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	292	2	no	—
388	Q₈	—	292	2	no	—
389	Q₈	—	73	2	no	—
390	Q₈	—	146	4	no	—
391	Q₈	—	146	1	no	—
392	Q₈	D₈×D₇₃	1	2	yes	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	584	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	292	1	no	—
402	C₂×C₄	—	292	2	no	—
403	C₂×C₄	—	292	2	no	—
404	C₂×C₄	—	584	4	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	73	2	no	—
407	C₂×C₄	—	73	2	no	—
408	C₂×C₄	—	73	1	no	—
409	C₂×C₄	—	73	1	no	—
410	C₂×C₄	—	146	4	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	—	146	1	no	—
413	C₂×C₄	—	146	1	no	—
414	C₂×C₄	—	146	1	no	—
415	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
417	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	2	no	—
421	C₈	—	292	1	no	—
422	C₈	—	292	2	no	—
423	C₈	—	146	1	no	—
424	C₈	—	146	1	no	—
425	C₈	#14556620	1	2	yes	complemented
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	73	2	no	—
430	C₂²	—	146	1	no	—
431	C₂²	—	146	1	no	—
432	C₂²	#121×D₇₃	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	292	1	no	—
437	C₄	—	584	2	no	—
438	C₄	—	73	2	no	—
439	C₄	—	146	1	no	—
440	C₄	—	146	1	no	—
441	C₄	—	146	2	no	—
442	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
443	C₄	#135×D₇₃	1	1	yes	characteristic
444	C₄	C₂×#14556620	1	1	yes	characteristic
445	C₄	#17989383	1	1	yes	characteristic
446	C₂	—	16	2	no	—
447	C₂	—	146	2	no	—
448	C₂	#22619398	1	1	yes	characteristic
449	C₂	#466×D₇₃	1	1	yes	characteristic
450	C₂	#22619649	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1668	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	#22620508	C₂
hypercenter	#1668	D₇₃
hypocenter	C₇₃	#19261
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1668

Complements

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

N	H ≅ G/N	type
2. #22619398	C₂	semidirect
3. C₈×Q₈×D₇₃	C₂	semidirect
4. #22609374	C₂	semidirect
5. #22609373	C₂	semidirect
6. #22609326	C₂	semidirect
7. #22609325	C₂	semidirect
8. #22609288	C₂	semidirect
9. #22608688	C₂	semidirect
10. #22608605	C₂	semidirect
11. C₇₃×#1668	C₂	semidirect
109. Q₈×D₇₃	D₈	semidirect
195. C₈×C₇₃	#137	semidirect
234. #1668	D₇₃	semidirect
237. C₇₃	#19261	semidirect
425. C₈	#14556620	semidirect

Maximal subgroups

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

subgroup	index
#22620508	2
#22619398	2
C₈×Q₈×D₇₃	2
#22609374	2
#22609373	2
#22609326	2
#22609325	2
#22609288	2
#22608688	2
#22608605	2
C₇₃×#1668	2
#19261	73