Subgroups — #33070003

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620515	C₂	1	1	yes	maximal, characteristic, complemented
2	#22619723	C₂	1	2	yes	maximal
3	#436×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22609505	C₂	1	2	yes	maximal, complemented
5	#22609504	C₂	1	2	yes	maximal, complemented
6	#22609455	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609454	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609417	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608685	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608620	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	—	2	1	no	—
13	#17989142	C₂²	1	2	yes	—
14	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
15	#17988992	C₂²	1	1	yes	characteristic, complemented
16	#17988937	C₂²	1	2	yes	complemented
17	#17988890	—	2	2	no	—
18	#17988889	—	2	2	no	—
19	#17988878	C₂²	1	2	yes	—
20	#17988877	C₂²	1	2	yes	—
21	#17988864	C₂²	1	2	yes	—
22	#17988825	—	2	1	no	—
23	#17988825	—	2	1	no	—
24	Q₁₆×Dic₇₃	—	2	1	no	—
25	Q₁₆×Dic₇₃	—	2	1	no	—
26	#17988666	C₂²	1	1	yes	characteristic
27	#17988665	C₂²	1	1	yes	characteristic
28	#17988664	C₂²	1	1	yes	characteristic
29	#17988663	—	2	1	no	—
30	#17988662	—	2	1	no	—
31	#17988628	—	2	2	no	—
32	#17988609	C₂²	1	2	yes	—
33	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#17988590	—	2	2	no	—
35	C₂²⋊C₈×D₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988338	C₂²	1	1	yes	characteristic, complemented
38	#17988337	C₂²	1	2	yes	complemented
39	#17988335	C₂²	1	2	yes	complemented
40	#17988335	C₂²	1	2	yes	complemented
41	#17988333	C₂²	1	2	yes	complemented
42	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#474×C₇₃	C₂²	1	2	yes	—
44	#436×C₇₃	C₂²	1	1	yes	characteristic
45	#334×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#332×C₇₃	C₂²	1	2	yes	complemented
47	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₃	—	2	1	no	—
49	C₂×#11924012	—	2	1	no	—
50	C₂×#11924011	—	2	2	no	—
51	C₂×#11924011	—	2	1	no	—
52	C₂×#11924011	—	2	1	no	—
53	M₁₆×D₇₃	—	4	4	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	#14556582	—	2	2	no	—
59	#14556571	—	2	2	no	—
60	#14556567	—	2	2	no	—
61	Q₈×Dic₇₃	—	2	2	no	—
62	#14556556	—	2	2	no	—
63	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
64	D₄×Dic₇₃	D₄	1	1	yes	characteristic
65	#14556553	D₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	#14556551	—	2	1	no	—
68	#14556549	—	2	2	no	—
69	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
70	C₂²⋊C₄×D₇₃	—	2	1	no	—
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	#14556525	—	2	1	no	—
73	#14556525	—	2	1	no	—
74	#14556524	—	2	2	no	—
75	#14556523	—	2	2	no	—
76	#14556522	—	2	2	no	—
77	C₄⋊#10596831	C₂³	1	2	yes	—
78	C₄⋊#10596831	C₂³	1	1	yes	characteristic
79	#14556520	—	2	2	no	—
80	#14556520	—	2	1	no	—
81	#14556515	—	2	2	no	—
82	#14556515	—	2	2	no	—
83	#14556513	—	2	2	no	—
84	#14556512	—	2	2	no	—
85	#14556511	—	2	2	no	—
86	C₂²⋊#10596831	—	2	1	no	—
87	#14556503	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	C₄×#10596831	C₂³	1	1	yes	characteristic
90	C₈×Dic₇₃	D₄	1	1	yes	characteristic
91	C₈×Dic₇₃	D₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₇₃	—	2	1	no	—
93	C₂×Q₁₆×C₇₃	—	2	1	no	—
94	C₂×M₁₆×C₇₃	—	2	1	no	—
95	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
96	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
97	#107×C₇₃	—	2	2	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	C₂²⋊C₈×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	C₂³×D₇₃	—	2	1	no	—
104	C₂×Dic₁₄₆	—	2	2	no	—
105	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₃	—	2	1	no	—
107	D₄×D₇₃	—	2	4	no	—
108	C₂²×Dic₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	C₂×C₄×D₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	1	no	—
112	C₂×C₄×D₇₃	—	4	2	no	—
113	C₂×C₄×D₇₃	—	4	2	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	#11924012	—	4	2	no	—
118	#11924011	—	4	2	no	—
119	#11924011	—	4	4	no	—
120	#11924011	—	4	2	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	2	no	—
129	C₄⋊Dic₇₃	—	2	2	no	—
130	C₄⋊Dic₇₃	—	4	2	no	—
131	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
132	#11924007	—	2	1	no	—
133	#11924007	—	4	2	no	—
134	C₂²⋊Dic₇₃	—	2	1	no	—
135	#11924005	—	2	1	no	—
136	#11924005	—	2	1	no	—
137	#11924005	—	4	2	no	—
138	C₄×Dic₇₃	—	4	2	no	—
139	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₇₃	#41	1	1	yes	characteristic
142	C₂×Q₈×C₇₃	—	2	2	no	—
143	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	—	2	1	no	—
145	Q₁₆×C₇₃	—	4	2	no	—
146	Q₁₆×C₇₃	—	4	2	no	—
147	M₁₆×C₇₃	—	4	2	no	—
148	C₂×C₈×C₇₃	—	2	1	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₇₃	—	2	1	no	—
156	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₃	—	2	1	no	—
158	C₂²×D₇₃	—	2	1	no	—
159	C₂²×D₇₃	—	4	2	no	—
160	C₂²×D₇₃	—	4	2	no	—
161	C₂²×D₇₃	—	4	2	no	—
162	C₂²×D₇₃	#121	1	1	yes	characteristic
163	Q₈×C₇₃	—	4	2	no	—
164	Q₈×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	4	1	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	—	4	2	no	—
170	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₇₃	—	4	2	no	—
174	C₂×Dic₇₃	—	2	1	no	—
175	C₂×Dic₇₃	—	4	2	no	—
176	C₂×Dic₇₃	—	4	2	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	D₂₉₂	—	2	2	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	—	4	2	no	—
186	C₄×D₇₃	—	4	1	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	#137	1	4	yes	—
189	Dic₁₄₆	—	8	2	no	—
190	C₈×C₇₃	—	2	1	no	—
191	C₈×C₇₃	—	4	1	no	—
192	C₈×C₇₃	—	4	2	no	—
193	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
194	#10596831	—	2	1	no	—
195	#10596831	—	2	1	no	—
196	#10596831	—	4	1	no	—
197	#10596831	—	4	2	no	—
198	C₂²×C₇₃	—	4	1	no	—
199	C₂²×C₇₃	—	4	1	no	—
200	C₂²×C₇₃	—	4	1	no	—
201	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
202	C₂×D₇₃	—	2	1	no	—
203	C₂×D₇₃	—	2	1	no	—
204	C₂×D₇₃	—	4	1	no	—
205	C₂×D₇₃	—	4	1	no	—
206	C₂×D₇₃	—	4	1	no	—
207	C₂×D₇₃	—	8	4	no	—
208	C₂×D₇₃	#470	1	2	yes	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	4	1	no	—
211	C₄×C₇₃	—	8	2	no	—
212	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₄×C₇₃	C₂×#137	1	2	yes	—
214	C₄×C₇₃	#575	1	1	yes	characteristic
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	—	4	1	no	—
218	Dic₇₃	—	8	2	no	—
219	Dic₇₃	#470	1	2	yes	—
220	#19281	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	8	1	no	—
222	C₂×C₇₃	#3036	1	1	yes	characteristic
223	C₂×C₇₃	C₂×#470	1	1	yes	characteristic
224	C₂×C₇₃	#3067	1	1	yes	characteristic
225	D₇₃	—	2	2	no	—
226	D₇₃	—	8	1	no	—
227	#3170	—	73	1	no	—
228	#3077	—	73	2	no	—
229	C₂×#436	—	73	1	no	—
230	#1703	—	73	2	no	—
231	#1703	—	73	2	no	—
232	#1695	—	73	1	no	—
233	#1695	—	73	1	no	—
234	#1689	—	73	1	no	—
235	#1689	D₇₃	1	1	yes	characteristic, complemented
236	#1566	—	73	1	no	—
237	#1550	—	73	2	no	—
238	C₇₃	#19281	1	1	yes	characteristic, complemented, Sylow
239	C₂²×M₁₆	—	146	1	no	—
240	#533	—	73	2	no	—
241	C₂×C₄×D₄	—	73	1	no	—
242	#500	—	73	1	no	—
243	#494	C₂×D₇₃	1	1	yes	characteristic, complemented
244	#487	—	73	2	no	—
245	#478	—	146	2	no	—
246	#478	—	146	2	no	—
247	#476	—	73	2	no	—
248	#476	—	73	2	no	—
249	#474	—	73	2	no	—
250	#474	C₂×D₇₃	1	2	yes	—
251	#467	—	146	1	no	—
252	#467	—	146	1	no	—
253	C₄×Q₁₆	—	146	1	no	—
254	C₄×Q₁₆	—	146	1	no	—
255	#436	—	73	1	no	—
256	#436	—	73	1	no	—
257	#436	—	73	1	no	—
258	#436	—	146	1	no	—
259	#436	—	146	1	no	—
260	#436	C₂×D₇₃	1	1	yes	characteristic
261	#428	—	146	2	no	—
262	#423	—	73	2	no	—
263	C₂×C₄⋊C₈	—	73	1	no	—
264	#418	—	146	2	no	—
265	C₂×C₂²⋊C₈	—	146	1	no	—
266	C₂×C₄×C₈	—	73	1	no	—
267	#334	—	73	2	no	—
268	#334	—	73	1	no	—
269	#334	C₂×D₇₃	1	1	yes	characteristic, complemented
270	#333	—	73	2	no	—
271	#333	—	73	2	no	—
272	#332	—	73	2	no	—
273	#332	C₂×D₇₃	1	2	yes	complemented
274	C₂²×D₄	—	73	1	no	—
275	C₂³×C₄	—	146	1	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	292	4	no	—
280	C₂×M₁₆	—	146	1	no	—
281	C₂×M₁₆	—	146	2	no	—
282	C₂×M₁₆	—	146	1	no	—
283	C₂×M₁₆	—	146	1	no	—
284	C₂²×C₈	—	73	1	no	—
285	C₂²×C₈	—	73	1	no	—
286	C₂²×C₈	—	146	1	no	—
287	C₄⋊Q₈	—	73	2	no	—
288	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
289	#125	—	146	2	no	—
290	C₂²⋊Q₈	—	146	2	no	—
291	C₂²⋊Q₈	—	146	2	no	—
292	C₄×Q₈	—	146	2	no	—
293	C₄×Q₈	—	146	2	no	—
294	C₄×D₄	—	73	1	no	—
295	C₄×D₄	—	73	1	no	—
296	C₄×D₄	—	73	1	no	—
297	C₄×D₄	—	146	1	no	—
298	C₄×D₄	—	146	1	no	—
299	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
300	#117	—	146	2	no	—
301	C₂×C₄⋊C₄	—	73	1	no	—
302	C₂×C₂²⋊C₄	—	146	1	no	—
303	C₂×C₄²	—	73	1	no	—
304	#107	—	2	2	no	—
305	#107	—	146	2	no	—
306	#107	—	146	1	no	—
307	#107	—	146	1	no	—
308	#106	—	146	2	no	—
309	#106	—	146	2	no	—
310	C₄⋊C₈	—	73	1	no	—
311	C₄⋊C₈	—	73	2	no	—
312	C₄⋊C₈	—	146	1	no	—
313	C₄⋊C₈	—	146	2	no	—
314	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
315	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
316	#103	—	146	2	no	—
317	#103	—	146	2	no	—
318	#102	—	2	2	no	—
319	#102	—	146	2	no	—
320	#102	—	146	2	no	—
321	#102	—	146	2	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	146	1	no	—
324	C₂²⋊C₈	—	146	1	no	—
325	C₂²⋊C₈	—	146	1	no	—
326	C₄×C₈	—	73	1	no	—
327	C₄×C₈	—	73	1	no	—
328	C₄×C₈	—	73	1	no	—
329	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₂⁴	—	146	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	146	2	no	—
333	C₂×D₄	—	73	1	no	—
334	C₂×D₄	—	146	4	no	—
335	C₂×D₄	—	146	1	no	—
336	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	292	2	no	—
339	C₂²×C₄	—	292	2	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	146	1	no	—
344	C₂²×C₄	—	146	1	no	—
345	C₂²×C₄	—	146	1	no	—
346	C₂²×C₄	—	146	1	no	—
347	Q₁₆	—	4	2	no	—
348	Q₁₆	—	4	2	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	292	4	no	—
351	M₁₆	—	292	2	no	—
352	M₁₆	—	292	2	no	—
353	M₁₆	—	292	2	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	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	292	2	no	—
368	C₄⋊C₄	—	292	2	no	—
369	C₄⋊C₄	—	73	1	no	—
370	C₄⋊C₄	—	146	1	no	—
371	C₄⋊C₄	—	146	2	no	—
372	C₄⋊C₄	—	146	2	no	—
373	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	292	2	no	—
376	C₂²⋊C₄	—	146	1	no	—
377	C₂²⋊C₄	—	146	1	no	—
378	C₂²⋊C₄	—	146	1	no	—
379	C₄²	—	292	2	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	C₂³×D₇₃	1	1	yes	characteristic
384	C₂³	—	2	1	no	—
385	C₂³	—	292	2	no	—
386	C₂³	—	292	2	no	—
387	C₂³	—	292	2	no	—
388	C₂³	—	73	1	no	—
389	C₂³	—	146	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	584	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	292	2	no	—
395	D₄	—	146	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	292	1	no	—
401	C₂×C₄	—	292	2	no	—
402	C₂×C₄	—	292	2	no	—
403	C₂×C₄	—	292	2	no	—
404	C₂×C₄	—	292	1	no	—
405	C₂×C₄	—	292	1	no	—
406	C₂×C₄	—	292	2	no	—
407	C₂×C₄	—	73	1	no	—
408	C₂×C₄	—	73	4	no	—
409	C₂×C₄	—	73	1	no	—
410	C₂×C₄	—	73	1	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	—	146	1	no	—
413	C₂×C₄	—	146	1	no	—
414	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
417	C₈	—	2	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	292	2	no	—
421	C₈	—	292	1	no	—
422	C₈	—	146	1	no	—
423	C₈	—	146	1	no	—
424	C₈	#14556615	1	2	yes	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	292	1	no	—
429	C₂²	—	292	1	no	—
430	C₂²	—	292	1	no	—
431	C₂²	—	584	4	no	—
432	C₂²	—	73	2	no	—
433	C₂²	—	146	1	no	—
434	C₂²	—	146	1	no	—
435	C₂²	#121×D₇₃	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	292	1	no	—
440	C₄	—	584	2	no	—
441	C₄	—	73	2	no	—
442	C₄	—	146	1	no	—
443	C₄	—	146	1	no	—
444	C₄	C₂×#14556615	1	1	yes	characteristic
445	C₄	#137×D₇₃	1	2	yes	—
446	C₄	#17989383	1	1	yes	characteristic
447	C₂	—	8	1	no	—
448	C₂	—	584	1	no	—
449	C₂	—	146	2	no	—
450	C₂	#22619390	1	1	yes	characteristic
451	C₂	#470×D₇₃	1	1	yes	characteristic
452	C₂	#22619653	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1689	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×D₄×D₇₃	D₄
hypercenter	#1689	D₇₃
hypocenter	C₇₃	#19281
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1689

Complements

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

N	H ≅ G/N	type
1. #22620515	C₂	semidirect
4. #22609505	C₂	semidirect
5. #22609504	C₂	semidirect
6. #22609455	C₂	semidirect
7. #22609454	C₂	semidirect
8. #22609417	C₂	semidirect
9. #22608685	C₂	semidirect
10. #22608620	C₂	semidirect
11. C₇₃×#1689	C₂	semidirect
15. #17988992	C₂²	semidirect
16. #17988937	C₂²	semidirect
37. #17988338	C₂²	semidirect
38. #17988337	C₂²	semidirect
39. #17988335	C₂²	semidirect
40. #17988335	C₂²	semidirect
41. #17988333	C₂²	semidirect
42. #494×C₇₃	C₂²	semidirect
45. #334×C₇₃	C₂²	semidirect
46. #332×C₇₃	C₂²	semidirect
235. #1689	D₇₃	semidirect
238. C₇₃	#19281	semidirect
243. #494	C₂×D₇₃	semidirect
269. #334	C₂×D₇₃	semidirect
273. #332	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22620515	2
#22619723	2
#436×D₇₃	2
#22609505	2
#22609504	2
#22609455	2
#22609454	2
#22609417	2
#22608685	2
#22608620	2
C₇₃×#1689	2
#19281	73