Subgroups — #33106853

Order 18688.

996 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619279	C₂	1	1	yes	maximal, characteristic
2	#22618838	C₂	1	2	yes	maximal, complemented
3	#22618477	C₂	1	2	yes	maximal, complemented
4	#22610764	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610603	C₂	1	2	yes	maximal, complemented
6	#22610429	C₂	1	2	yes	maximal, complemented
7	#22610172	C₂	1	2	yes	maximal, complemented
8	#22609740	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1884	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989423	C₂²	1	1	yes	characteristic
11	#17989385	C₂²	1	2	yes	—
12	#17989353	C₂²	1	2	yes	—
13	#17989055	C₂²	1	2	yes	—
14	#17988769	C₄	1	2	yes	complemented
15	#17988764	C₄	1	2	yes	complemented
16	#17988759	C₄	1	2	yes	complemented
17	#17988754	C₄	1	2	yes	complemented
18	#17988707	—	2	4	no	—
19	#17988702	—	2	4	no	—
20	#17988635	C₂²	1	2	yes	complemented
21	#17988611	C₂²	1	1	yes	characteristic, complemented
22	#17988605	C₂²	1	2	yes	—
23	#17988602	—	2	4	no	—
24	C₂×#14556519	C₂²	1	2	yes	—
25	C₂×#14556518	C₂²	1	2	yes	—
26	C₂×#14556518	C₂²	1	2	yes	complemented
27	C₂×#14556517	C₂²	1	2	yes	—
28	#104×D₇₃	—	2	4	no	—
29	#17988571	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₇₃	C₂²	1	2	yes	complemented
31	#17988433	C₂²	1	1	yes	characteristic, complemented
32	#17988357	C₂²	1	2	yes	complemented
33	#17988346	C₂²	1	2	yes	complemented
34	#568×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#532×C₇₃	C₂²	1	1	yes	characteristic
36	#421×C₇₃	C₂²	1	2	yes	—
37	#410×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#339×C₇₃	C₂²	1	2	yes	complemented
39	#14556639	C₂×C₄	1	2	yes	—
40	#14556638	—	2	2	no	—
41	#14556637	—	2	2	no	—
42	#14556636	—	4	1	no	—
43	#14556636	C₂×C₄	1	2	yes	—
44	C₂×#11924028	—	4	1	no	—
45	C₂×#11924028	C₂³	1	2	yes	—
46	#41×D₇₃	—	2	4	no	—
47	#14556622	C₂×C₄	1	4	yes	complemented
48	#14556621	—	2	2	no	—
49	#14556617	C₂×C₄	1	4	yes	complemented
50	#14556616	—	2	2	no	—
51	#14556611	—	2	4	no	—
52	#14556599	—	4	2	no	—
53	#14556597	—	2	4	no	—
54	C₂×#11924012	C₂³	1	2	yes	—
55	C₂×#11924012	C₂³	1	2	yes	—
56	M₁₆×D₇₃	—	2	4	no	—
57	#14556556	—	2	2	no	—
58	#14556553	—	2	2	no	—
59	#14556551	—	4	2	no	—
60	#14556548	—	2	2	no	—
61	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
62	C₄²×D₇₃	—	2	2	no	—
63	#14556526	—	2	4	no	—
64	C₄⋊#10596831	—	4	1	no	—
65	#14556519	—	2	4	no	—
66	#14556519	C₂×C₄	1	4	yes	complemented
67	#14556519	C₂×C₄	1	4	yes	complemented
68	#14556518	—	2	2	no	—
69	#14556518	—	2	2	no	—
70	#14556518	—	2	2	no	—
71	#14556518	—	2	2	no	—
72	#14556517	D₄	1	4	yes	complemented
73	#14556517	D₄	1	4	yes	complemented
74	#14556510	C₂×C₄	1	2	yes	complemented
75	#14556508	C₂×C₄	1	2	yes	complemented
76	#14556501	—	2	2	no	—
77	C₈×Dic₇₃	—	2	2	no	—
78	#14556498	—	4	1	no	—
79	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
81	#131×C₇₃	—	2	4	no	—
82	C₂×M₁₆×C₇₃	—	4	1	no	—
83	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
84	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
85	#127×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
86	#124×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
87	#124×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
88	#121×C₇₃	—	4	1	no	—
89	C₄×D₄×C₇₃	—	4	1	no	—
90	#117×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
92	#104×C₇₃	—	2	4	no	—
93	#99×C₇₃	—	4	1	no	—
94	#11924029	—	2	4	no	—
95	#11924028	—	2	2	no	—
96	#11924028	—	2	2	no	—
97	#11924028	—	4	2	no	—
98	#11924028	—	4	2	no	—
99	#11924028	—	4	2	no	—
100	#11924028	C₂²×C₄	1	4	yes	—
101	#11924028	C₂×D₄	1	4	yes	—
102	#11924027	—	2	4	no	—
103	#11924027	—	4	4	no	—
104	C₂×Dic₁₄₆	—	4	1	no	—
105	C₂×Dic₁₄₆	#41	1	2	yes	—
106	Q₈×D₇₃	—	2	4	no	—
107	C₂×D₂₉₂	—	4	1	no	—
108	C₂×D₂₉₂	#41	1	2	yes	—
109	C₂×C₂²⋊D₇₃	—	2	2	no	—
110	C₂×C₂²⋊D₇₃	—	4	2	no	—
111	D₄×D₇₃	—	2	4	no	—
112	D₄×D₇₃	—	4	4	no	—
113	C₂²×Dic₇₃	—	2	2	no	—
114	C₂×C₄×D₇₃	—	2	2	no	—
115	C₂×C₄×D₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	4	2	no	—
117	#11924018	—	2	4	no	—
118	#11924016	—	2	4	no	—
119	#11924015	—	2	4	no	—
120	#11924013	—	2	4	no	—
121	#11924012	—	2	2	no	—
122	#11924012	—	2	2	no	—
123	#11924012	—	2	2	no	—
124	#11924012	C₂²×C₄	1	4	yes	—
125	#11924011	—	4	4	no	—
126	C₂×#10596831	—	2	2	no	—
127	C₂×#10596831	—	2	2	no	—
128	C₈×D₇₃	—	4	4	no	—
129	#11924007	—	4	2	no	—
130	#11924005	—	4	2	no	—
131	C₄×Dic₇₃	—	2	2	no	—
132	C₄×Dic₇₃	—	4	2	no	—
133	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
134	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
135	#41×C₇₃	—	2	2	no	—
136	#41×C₇₃	—	2	2	no	—
137	#41×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×D₄×C₇₃	—	2	1	no	—
142	C₂×D₄×C₇₃	—	2	1	no	—
143	C₂×D₄×C₇₃	—	4	1	no	—
144	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	—	2	1	no	—
147	C₂²×C₄×C₇₃	—	2	1	no	—
148	C₂²×C₄×C₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₇₃	—	2	2	no	—
151	M₁₆×C₇₃	—	4	2	no	—
152	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	4	2	no	—
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	4	1	no	—
157	C₂²⋊C₄×C₇₃	—	2	2	no	—
158	C₂²⋊C₄×C₇₃	—	4	1	no	—
159	C₂²⋊C₄×C₇₃	—	4	1	no	—
160	C₄²×C₇₃	—	2	1	no	—
161	C₄²×C₇₃	—	2	2	no	—
162	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
164	C₂³×C₇₃	—	2	1	no	—
165	C₂³×C₇₃	—	2	1	no	—
166	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×D₇₃	—	2	2	no	—
168	C₂²×D₇₃	—	4	2	no	—
169	Q₈×C₇₃	—	2	2	no	—
170	Q₈×C₇₃	—	2	2	no	—
171	D₄×C₇₃	—	2	2	no	—
172	D₄×C₇₃	—	2	2	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	4	2	no	—
175	D₄×C₇₃	—	8	2	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	4	1	no	—
181	C₂×C₄×C₇₃	—	4	1	no	—
182	C₂×C₄×C₇₃	—	4	1	no	—
183	C₂×C₄×C₇₃	—	4	1	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	8	1	no	—
186	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²⋊D₇₃	—	2	4	no	—
191	C₂²⋊D₇₃	—	2	4	no	—
192	C₂²⋊D₇₃	—	4	4	no	—
193	C₂×Dic₇₃	—	2	2	no	—
194	C₂×Dic₇₃	—	2	2	no	—
195	C₂×Dic₇₃	—	2	2	no	—
196	C₂×Dic₇₃	—	4	2	no	—
197	C₂×Dic₇₃	—	8	2	no	—
198	D₂₉₂	—	2	2	no	—
199	D₂₉₂	—	4	2	no	—
200	D₂₉₂	C₄×D₄	1	4	yes	—
201	C₄×D₇₃	—	2	4	no	—
202	C₄×D₇₃	—	2	4	no	—
203	C₄×D₇₃	—	4	4	no	—
204	C₄×D₇₃	—	8	4	no	—
205	Dic₁₄₆	—	2	2	no	—
206	Dic₁₄₆	—	4	2	no	—
207	Dic₁₄₆	C₄×D₄	1	4	yes	—
208	C₈×C₇₃	—	2	4	no	—
209	#10596831	—	2	4	no	—
210	#10596831	—	4	2	no	—
211	C₂²×C₇₃	—	4	1	no	—
212	C₂²×C₇₃	—	4	1	no	—
213	C₂²×C₇₃	—	4	1	no	—
214	C₂²×C₇₃	—	8	1	no	—
215	C₂²×C₇₃	—	8	1	no	—
216	C₂²×C₇₃	#518	1	1	yes	characteristic
217	C₂²×C₇₃	#546	1	2	yes	—
218	C₂×D₇₃	—	2	4	no	—
219	C₂×D₇₃	—	8	2	no	—
220	C₂×D₇₃	—	16	2	no	—
221	C₄×C₇₃	—	4	1	no	—
222	C₄×C₇₃	—	4	1	no	—
223	C₄×C₇₃	—	4	1	no	—
224	C₄×C₇₃	—	4	1	no	—
225	C₄×C₇₃	—	8	2	no	—
226	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
227	C₄×C₇₃	D₄²	1	1	yes	characteristic
228	C₄×C₇₃	#551	1	1	yes	characteristic
229	Dic₇₃	—	2	4	no	—
230	Dic₇₃	—	4	2	no	—
231	Dic₇₃	—	4	2	no	—
232	#22898	—	73	1	no	maximal, Sylow
233	C₂×C₇₃	—	2	2	no	—
234	C₂×C₇₃	—	2	1	no	—
235	C₂×C₇₃	—	8	1	no	—
236	C₂×C₇₃	—	8	1	no	—
237	C₂×C₇₃	#2358	1	1	yes	characteristic
238	D₇₃	—	4	4	no	—
239	#3018	—	73	1	no	—
240	#2956	—	73	2	no	—
241	#2901	—	73	2	no	—
242	#1963	—	73	1	no	—
243	#1932	—	73	2	no	—
244	#1906	—	73	2	no	—
245	#1884	D₇₃	1	1	yes	characteristic, complemented
246	#1861	—	73	2	no	—
247	#1759	—	73	2	no	—
248	C₇₃	#22898	1	1	yes	characteristic, complemented, Sylow
249	#585	—	73	1	no	—
250	#575	—	73	2	no	—
251	#568	—	73	2	no	—
252	#568	C₂×D₇₃	1	1	yes	characteristic, complemented
253	#532	C₂×D₇₃	1	1	yes	characteristic
254	C₄×#41	—	73	2	no	—
255	#456	—	73	2	no	—
256	#455	—	73	2	no	—
257	#454	—	73	2	no	—
258	#453	—	73	2	no	—
259	#444	—	146	4	no	—
260	#443	—	146	4	no	—
261	#430	—	73	2	no	—
262	#423	—	73	1	no	—
263	#421	—	73	2	no	—
264	#421	—	146	4	no	—
265	#421	C₂×D₇₃	1	2	yes	—
266	C₂×#104	—	73	2	no	—
267	C₂×#104	—	73	2	no	—
268	C₂×#104	—	73	2	no	—
269	C₂×#104	—	73	2	no	—
270	C₂×#104	—	146	4	no	—
271	#413	—	73	1	no	—
272	#410	C₂×D₇₃	1	1	yes	characteristic, complemented
273	C₄×M₁₆	—	73	2	no	—
274	#376	—	73	1	no	—
275	#344	—	73	2	no	—
276	#339	—	73	2	no	—
277	#339	C₂×D₇₃	1	2	yes	complemented
278	2₋¹⁺⁴	—	73	2	no	—
279	2₋¹⁺⁴	—	146	2	no	—
280	H(5,𝔽₂)	—	292	1	no	—
281	H(5,𝔽₂)	—	73	2	no	—
282	H(5,𝔽₂)	—	146	2	no	—
283	C₂×#41	—	292	1	no	—
284	C₂×#41	—	73	2	no	—
285	C₂×#41	—	146	4	no	—
286	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
287	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
288	#137	—	73	4	no	—
289	#137	—	146	2	no	—
290	AGL(1,ℤ/8)	—	73	4	no	—
291	AGL(1,ℤ/8)	—	146	2	no	—
292	#135	—	146	4	no	—
293	#131	—	2	4	no	—
294	#131	—	292	2	no	—
295	#131	—	146	4	no	—
296	C₂×M₁₆	—	4	1	no	—
297	C₂×M₁₆	—	73	2	no	—
298	C₂×M₁₆	—	73	2	no	—
299	C₂×M₁₆	—	146	4	no	—
300	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
301	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic, complemented
302	#127	C₄×D₇₃	1	1	yes	characteristic, complemented
303	#124	C₄×D₇₃	1	1	yes	characteristic, complemented
304	#124	C₄×D₇₃	1	1	yes	characteristic, complemented
305	#121	—	4	1	no	—
306	C₄×Q₈	—	146	2	no	—
307	C₄×D₄	—	4	1	no	—
308	C₄×D₄	—	292	2	no	—
309	C₄×D₄	—	146	2	no	—
310	#117	—	146	2	no	—
311	#117	C₂²×D₇₃	1	2	yes	—
312	C₂×C₄²	—	73	2	no	—
313	C₂×C₄²	—	146	2	no	—
314	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
315	#108	—	146	4	no	—
316	C₄⋊C₈	—	292	1	no	—
317	#104	—	2	4	no	—
318	#104	—	73	4	no	—
319	#104	—	73	4	no	—
320	#104	—	73	4	no	—
321	#104	—	73	4	no	—
322	#104	—	146	4	no	—
323	#104	—	146	2	no	—
324	#104	—	146	2	no	—
325	#104	—	146	2	no	—
326	#104	—	146	2	no	—
327	#101	—	73	2	no	—
328	#100	—	73	2	no	—
329	#99	—	4	1	no	—
330	#97	—	146	2	no	—
331	C₄×C₈	—	146	2	no	—
332	#95	—	292	1	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	#41	—	292	2	no	—
338	#41	—	292	2	no	—
339	#41	—	292	2	no	—
340	#41	—	292	4	no	—
341	#41	—	73	4	no	—
342	#41	—	73	4	no	—
343	#41	—	146	4	no	—
344	#41	—	146	4	no	—
345	#41	—	146	2	no	—
346	#41	—	146	2	no	—
347	C₂×Q₈	—	292	1	no	—
348	C₂×Q₈	—	73	2	no	—
349	C₂×Q₈	—	146	4	no	—
350	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
351	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	292	1	no	—
356	C₂×D₄	—	292	4	no	—
357	C₂×D₄	—	292	2	no	—
358	C₂×D₄	—	73	2	no	—
359	C₂×D₄	—	146	4	no	—
360	C₂×D₄	—	146	2	no	—
361	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
362	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	292	2	no	—
367	C₂²×C₄	—	292	2	no	—
368	C₂²×C₄	—	146	2	no	—
369	C₂²×C₄	—	146	2	no	—
370	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
371	Q₁₆	—	146	4	no	—
372	SD₁₆	—	146	4	no	—
373	SD₁₆	—	146	4	no	—
374	D₈	—	146	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	2	no	—
377	M₁₆	—	292	4	no	—
378	M₁₆	—	73	4	no	—
379	M₁₆	—	146	2	no	—
380	M₁₆	—	146	2	no	—
381	M₁₆	—	146	2	no	—
382	M₁₆	D₄×D₇₃	1	4	yes	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	292	4	no	—
386	C₂×C₈	—	146	2	no	—
387	C₂×C₈	—	146	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	292	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	292	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	292	2	no	—
398	C₄²	—	73	2	no	—
399	C₄²	—	73	2	no	—
400	C₄²	—	146	2	no	—
401	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
402	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	292	2	no	—
406	C₂³	—	146	2	no	—
407	C₂³	#14556636	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	292	2	no	—
411	Q₈	—	73	4	no	—
412	Q₈	—	146	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	292	2	no	—
419	D₄	—	292	4	no	—
420	D₄	—	73	4	no	—
421	D₄	—	146	4	no	—
422	D₄	—	146	4	no	—
423	D₄	—	146	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	292	4	no	—
435	C₂×C₄	—	292	2	no	—
436	C₂×C₄	—	584	4	no	—
437	C₂×C₄	—	584	2	no	—
438	C₂×C₄	—	146	2	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	2	no	—
441	C₂×C₄	—	146	4	no	—
442	C₂×C₄	—	146	4	no	—
443	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
445	C₂×C₄	#41×D₇₃	1	2	yes	—
446	C₂×C₄	#14556636	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	292	2	no	—
449	C₈	—	146	4	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	584	2	no	—
456	C₂²	—	1168	2	no	—
457	C₂²	—	146	4	no	—
458	C₂²	#17989060	1	1	yes	characteristic
459	C₂²	#17989234	1	2	yes	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	292	2	no	—
466	C₄	—	292	2	no	—
467	C₄	—	146	4	no	—
468	C₄	C₄×D₄×D₇₃	1	2	yes	—
469	C₄	#17989219	1	1	yes	characteristic
470	C₄	#17989265	1	1	yes	characteristic
471	C₂	—	2	1	no	—
472	C₂	—	2	2	no	—
473	C₂	—	8	1	no	—
474	C₂	—	8	1	no	—
475	C₂	—	292	4	no	—
476	C₂	#22612914	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17989219
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1884	C₂
socle	C₂×C₇₃	#2358
prime radical	#22619279	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1884	D₇₃
hypocenter	C₇₃	#22898
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1884

Complements

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

N	H ≅ G/N	type
2. #22618838	C₂	semidirect
3. #22618477	C₂	semidirect
4. #22610764	C₂	semidirect
5. #22610603	C₂	semidirect
6. #22610429	C₂	semidirect
7. #22610172	C₂	semidirect
8. #22609740	C₂	semidirect
9. C₇₃×#1884	C₂	semidirect
14. #17988769	C₄	semidirect
15. #17988764	C₄	semidirect
16. #17988759	C₄	semidirect
17. #17988754	C₄	semidirect
20. #17988635	C₂²	semidirect
21. #17988611	C₂²	semidirect
26. C₂×#14556518	C₂²	semidirect
30. M₁₆×Dic₇₃	C₂²	semidirect
31. #17988433	C₂²	semidirect
32. #17988357	C₂²	semidirect
33. #17988346	C₂²	semidirect
34. #568×C₇₃	C₂²	semidirect
37. #410×C₇₃	C₂²	semidirect
38. #339×C₇₃	C₂²	semidirect
47. #14556622	C₂×C₄	semidirect
49. #14556617	C₂×C₄	semidirect
66. #14556519	C₂×C₄	semidirect
67. #14556519	C₂×C₄	semidirect
72. #14556517	D₄	semidirect
73. #14556517	D₄	semidirect
74. #14556510	C₂×C₄	semidirect
75. #14556508	C₂×C₄	semidirect
84. C₄⋊Q₈×C₇₃	C₂×C₄	semidirect
85. #127×C₇₃	C₂×C₄	semidirect
86. #124×C₇₃	C₂×C₄	semidirect
87. #124×C₇₃	C₂×C₄	semidirect
245. #1884	D₇₃	semidirect
248. C₇₃	#22898	semidirect
252. #568	C₂×D₇₃	semidirect
272. #410	C₂×D₇₃	semidirect
277. #339	C₂×D₇₃	semidirect
301. C₄⋊Q₈	C₄×D₇₃	semidirect
302. #127	C₄×D₇₃	semidirect
303. #124	C₄×D₇₃	semidirect
304. #124	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22619279	2
#22618838	2
#22618477	2
#22610764	2
#22610603	2
#22610429	2
#22610172	2
#22609740	2
C₇₃×#1884	2
#22898	73