Subgroups — #33099915

Order 18688.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620417	C₂	1	1	yes	maximal, characteristic
2	#22618849	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618784	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610841	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610829	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610462	C₂	1	2	yes	maximal, complemented
7	#22610457	C₂	1	2	yes	maximal, complemented
8	#22610419	C₂	1	2	yes	maximal, complemented
9	#22610412	C₂	1	2	yes	maximal, complemented
10	#22610055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556619	C₂²	1	2	yes	—
13	C₂×#14556613	C₂²	1	1	yes	characteristic
14	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic
15	#17989353	C₂²	1	2	yes	—
16	#17989156	C₂²	1	2	yes	—
17	#17989061	C₂²	1	2	yes	—
18	#17988976	C₄	1	4	yes	complemented
19	#17988971	C₄	1	2	yes	complemented
20	#17988964	C₄	1	2	yes	complemented
21	#17988710	—	2	2	no	—
22	#17988705	—	2	2	no	—
23	#17988700	—	2	2	no	—
24	C₄×D₅₈₄	—	2	2	no	—
25	C₂×#14556527	C₂²	1	1	yes	characteristic
26	#17988625	C₂²	1	1	yes	characteristic
27	#17988605	C₂²	1	2	yes	—
28	#17988603	C₂²	1	2	yes	—
29	#17988593	C₂²	1	2	yes	—
30	#17988591	C₂²	1	2	yes	—
31	C₂×#14556507	C₂²	1	2	yes	—
32	#17988560	C₂²	1	2	yes	—
33	#17988358	C₂²	1	2	yes	—
34	#17988343	C₂²	1	2	yes	—
35	#405×C₇₃	C₂²	1	1	yes	characteristic
36	#405×C₇₃	C₂²	1	1	yes	characteristic
37	#405×C₇₃	C₂²	1	1	yes	characteristic
38	#338×C₇₃	C₂²	1	1	yes	characteristic
39	H(3,ℤ/4)×C₇₃	C₂²	1	1	yes	characteristic
40	H(3,ℤ/4)×C₇₃	C₂²	1	1	yes	characteristic
41	H(3,ℤ/4)×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#11924028	C₂³	1	2	yes	—
43	C₂²×D₂₉₂	C₂³	1	2	yes	—
44	#14556619	—	4	2	no	—
45	#14556619	—	4	2	no	—
46	#14556613	—	2	1	no	—
47	#14556613	—	2	1	no	—
48	#14556613	—	2	1	no	—
49	#14556613	—	2	1	no	—
50	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#11924017	C₂×C₄	1	2	yes	complemented
52	C₂×#11924017	C₂×C₄	1	4	yes	complemented
53	C₂×D₅₈₄	—	2	1	no	—
54	C₂×D₅₈₄	—	2	1	no	—
55	C₂×D₅₈₄	—	2	1	no	—
56	C₂×D₅₈₄	—	2	1	no	—
57	C₂×D₅₈₄	C₂×C₄	1	2	yes	—
58	C₂×D₅₈₄	C₂×C₄	1	2	yes	—
59	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₅₈₄	C₂×C₄	1	4	yes	complemented
61	#14556599	—	4	2	no	—
62	#14556597	—	2	4	no	—
63	C₂×#11924012	C₂³	1	2	yes	—
64	M₁₆×D₇₃	—	4	2	no	—
65	#14556588	C₂×C₄	1	4	yes	complemented
66	#14556579	C₂×C₄	1	4	yes	complemented
67	#14556566	—	4	2	no	—
68	#14556561	—	4	2	no	—
69	C₄×D₂₉₂	—	2	4	no	—
70	#14556553	—	4	2	no	—
71	#14556550	C₂³	1	2	yes	—
72	C₂²⋊C₄×D₇₃	—	4	2	no	—
73	#14556527	—	2	1	no	—
74	#14556527	—	2	1	no	—
75	#14556525	—	2	1	no	—
76	#14556523	—	2	1	no	—
77	#14556519	—	2	4	no	—
78	#14556517	—	4	2	no	—
79	#14556513	—	2	4	no	—
80	#14556511	—	4	2	no	—
81	#14556507	—	4	2	no	—
82	#14556505	—	4	2	no	—
83	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
87	#117×C₇₃	C₂³	1	1	yes	characteristic
88	#117×C₇₃	C₂³	1	1	yes	characteristic
89	#117×C₇₃	C₂³	1	1	yes	characteristic
90	#97×C₇₃	—	2	1	no	—
91	#97×C₇₃	C₂×C₄	1	2	yes	complemented
92	#97×C₇₃	D₄	1	2	yes	complemented
93	C₄×C₈×C₇₃	—	2	1	no	—
94	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₇₃	D₄	1	2	yes	complemented
96	C₂³×D₇₃	—	2	2	no	—
97	#11924028	—	2	2	no	—
98	#11924028	—	2	2	no	—
99	#11924028	—	2	2	no	—
100	#11924028	—	2	2	no	—
101	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
102	C₂×D₂₉₂	—	2	2	no	—
103	C₂×D₂₉₂	—	2	2	no	—
104	C₂×D₂₉₂	—	2	2	no	—
105	C₂×D₂₉₂	—	2	2	no	—
106	C₂×D₂₉₂	—	2	2	no	—
107	C₂×D₂₉₂	—	4	4	no	—
108	C₂×D₂₉₂	C₂²×C₄	1	4	yes	—
109	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
110	C₂×C₂²⋊D₇₃	—	2	2	no	—
111	C₂×C₄×D₇₃	—	2	2	no	—
112	C₂×C₄×D₇₃	—	4	4	no	—
113	Dic₂₉₂	—	2	1	no	—
114	Dic₂₉₂	—	2	1	no	—
115	#11924017	—	2	2	no	—
116	#11924017	—	2	2	no	—
117	#11924017	—	4	4	no	—
118	D₅₈₄	—	2	2	no	—
119	D₅₈₄	—	2	2	no	—
120	D₅₈₄	—	2	2	no	—
121	D₅₈₄	—	2	2	no	—
122	D₅₈₄	—	2	1	no	—
123	D₅₈₄	—	2	1	no	—
124	D₅₈₄	—	4	4	no	—
125	#11924012	—	2	2	no	—
126	#11924012	—	2	2	no	—
127	#11924011	—	4	4	no	—
128	C₂×#10596831	—	2	2	no	—
129	C₈×D₇₃	—	4	4	no	—
130	C₄⋊Dic₇₃	—	2	2	no	—
131	C₂²⋊Dic₇₃	—	2	2	no	—
132	#11924005	—	4	4	no	—
133	#11924005	—	4	4	no	—
134	C₄×Dic₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₇₃	—	2	1	no	—
137	M₁₆×C₇₃	—	2	1	no	—
138	M₁₆×C₇₃	—	2	1	no	—
139	M₁₆×C₇₃	—	2	1	no	—
140	M₁₆×C₇₃	—	2	1	no	—
141	M₁₆×C₇₃	—	2	1	no	—
142	C₂×C₈×C₇₃	—	2	1	no	—
143	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
150	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	1	no	—
153	C₄⋊C₄×C₇₃	—	2	1	no	—
154	C₂²⋊C₄×C₇₃	—	2	1	no	—
155	C₂²⋊C₄×C₇₃	—	2	1	no	—
156	C₂²⋊C₄×C₇₃	—	2	1	no	—
157	C₄²×C₇₃	—	2	1	no	—
158	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
159	C₄²×C₇₃	C₂×D₄	1	2	yes	—
160	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₇₃	—	2	4	no	—
162	C₂²×D₇₃	—	2	2	no	—
163	C₂²×D₇₃	—	4	2	no	—
164	C₂²×D₇₃	—	4	2	no	—
165	C₂²×D₇₃	—	16	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	C₂³×C₄	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	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²⋊D₇₃	—	4	2	no	—
176	C₂²⋊D₇₃	—	4	2	no	—
177	C₂×Dic₇₃	—	2	2	no	—
178	C₂×Dic₇₃	—	4	2	no	—
179	D₂₉₂	—	2	4	no	—
180	D₂₉₂	—	2	2	no	—
181	D₂₉₂	—	2	2	no	—
182	D₂₉₂	—	2	4	no	—
183	D₂₉₂	—	4	2	no	—
184	D₂₉₂	—	4	2	no	—
185	D₂₉₂	—	16	4	no	—
186	C₄×D₇₃	—	4	2	no	—
187	C₄×D₇₃	—	4	2	no	—
188	C₄×D₇₃	—	16	4	no	—
189	Dic₁₄₆	—	2	2	no	—
190	Dic₁₄₆	—	2	2	no	—
191	C₈×C₇₃	—	2	2	no	—
192	C₈×C₇₃	—	2	2	no	—
193	C₈×C₇₃	—	4	1	no	—
194	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
196	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
197	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
198	#10596831	—	4	2	no	—
199	C₂²×C₇₃	—	4	1	no	—
200	C₂²×C₇₃	#518	1	1	yes	characteristic
201	C₂²×C₇₃	#535	1	1	yes	characteristic
202	C₂²×C₇₃	#540	1	1	yes	characteristic
203	C₂×D₇₃	—	4	2	no	—
204	C₂×D₇₃	—	4	4	no	—
205	C₂×D₇₃	—	8	4	no	—
206	C₂×D₇₃	—	8	2	no	—
207	C₂×D₇₃	—	8	4	no	—
208	C₂×D₇₃	—	16	2	no	—
209	C₄×C₇₃	—	4	2	no	—
210	C₄×C₇₃	—	4	2	no	—
211	C₄×C₇₃	—	8	1	no	—
212	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₇₃	#518	1	1	yes	characteristic
214	C₄×C₇₃	#535	1	1	yes	characteristic
215	C₄×C₇₃	#540	1	1	yes	characteristic
216	Dic₇₃	—	4	2	no	—
217	Dic₇₃	—	8	2	no	—
218	#22286	—	73	1	no	maximal, Sylow
219	C₂×C₇₃	—	2	1	no	—
220	C₂×C₇₃	—	2	1	no	—
221	C₂×C₇₃	—	2	1	no	—
222	C₂×C₇₃	#2328	1	1	yes	characteristic
223	D₇₃	—	8	2	no	—
224	D₇₃	—	8	4	no	—
225	#3155	—	73	1	no	—
226	#2957	—	73	1	no	—
227	#2948	—	73	1	no	—
228	#1978	—	73	1	no	—
229	#1976	—	73	1	no	—
230	#1911	—	73	2	no	—
231	#1910	—	73	2	no	—
232	#1904	—	73	2	no	—
233	#1903	—	73	2	no	—
234	#1833	—	73	1	no	—
235	#1747	D₇₃	1	1	yes	characteristic, complemented
236	C₇₃	#22286	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	73	2	no	—
238	C₂×#135	—	73	1	no	—
239	C₂²×D₈	—	73	1	no	—
240	#568	—	73	2	no	—
241	#535	—	73	2	no	—
242	#518	—	73	2	no	—
243	#496	—	73	4	no	—
244	#495	—	73	2	no	—
245	#493	—	73	2	no	—
246	#444	—	146	2	no	—
247	#443	—	146	2	no	—
248	#442	—	146	2	no	—
249	C₄×D₈	—	146	2	no	—
250	C₂×#108	—	73	1	no	—
251	#427	—	73	1	no	—
252	#421	—	73	2	no	—
253	#421	—	73	2	no	—
254	#418	—	73	2	no	—
255	#418	—	73	2	no	—
256	C₂×#100	—	73	2	no	—
257	#410	—	73	2	no	—
258	#405	C₂×D₇₃	1	1	yes	characteristic
259	#405	C₂×D₇₃	1	1	yes	characteristic
260	#405	C₂×D₇₃	1	1	yes	characteristic
261	#344	—	73	2	no	—
262	#338	C₂×D₇₃	1	1	yes	characteristic
263	H(3,ℤ/4)	—	73	2	no	—
264	H(3,ℤ/4)	C₂×D₇₃	1	1	yes	characteristic
265	H(3,ℤ/4)	C₂×D₇₃	1	1	yes	characteristic
266	H(3,ℤ/4)	C₂×D₇₃	1	1	yes	characteristic
267	C₂×#41	—	73	2	no	—
268	C₂²×D₄	—	73	2	no	—
269	AGL(1,ℤ/8)	—	292	2	no	—
270	AGL(1,ℤ/8)	—	292	2	no	—
271	#135	—	146	1	no	—
272	#135	—	146	1	no	—
273	#135	—	146	1	no	—
274	#135	—	146	1	no	—
275	C₂×Q₁₆	—	73	1	no	—
276	C₂×SD₁₆	—	73	4	no	—
277	C₂×SD₁₆	—	73	2	no	—
278	C₂×D₈	—	73	4	no	—
279	C₂×D₈	—	73	2	no	—
280	C₂×D₈	—	73	2	no	—
281	C₂×D₈	—	73	1	no	—
282	C₂×D₈	—	146	1	no	—
283	C₂×D₈	—	146	1	no	—
284	C₂×D₈	—	146	1	no	—
285	C₂×D₈	—	146	1	no	—
286	#131	—	292	2	no	—
287	#131	—	146	4	no	—
288	C₂×M₁₆	—	292	2	no	—
289	C₂×M₁₆	—	73	2	no	—
290	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
291	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
292	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
294	#127	—	73	4	no	—
295	#124	—	73	4	no	—
296	#121	—	292	2	no	—
297	#120	—	292	2	no	—
298	C₄×D₄	—	292	2	no	—
299	C₄×D₄	—	146	4	no	—
300	#117	—	73	2	no	—
301	#117	C₂²×D₇₃	1	1	yes	characteristic
302	#117	C₂²×D₇₃	1	1	yes	characteristic
303	#117	C₂²×D₇₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	292	2	no	—
305	#108	—	146	1	no	—
306	#108	—	146	1	no	—
307	#107	—	146	1	no	—
308	#106	—	146	1	no	—
309	#104	—	292	2	no	—
310	#104	—	146	4	no	—
311	#102	—	292	2	no	—
312	#102	—	146	4	no	—
313	#100	—	292	2	no	—
314	#99	—	292	2	no	—
315	#97	—	2	1	no	—
316	#97	C₄×D₇₃	1	2	yes	complemented
317	#97	D₂₉₂	1	2	yes	complemented
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	C₄×D₇₃	1	2	yes	complemented
320	C₄×C₈	D₂₉₂	1	2	yes	complemented
321	C₂⁴	—	146	2	no	—
322	#41	—	146	2	no	—
323	#41	—	146	2	no	—
324	#41	—	146	2	no	—
325	#41	—	146	2	no	—
326	C₂×Q₈	—	73	2	no	—
327	C₂×D₄	—	292	4	no	—
328	C₂×D₄	—	73	4	no	—
329	C₂×D₄	—	73	2	no	—
330	C₂×D₄	—	146	2	no	—
331	C₂×D₄	—	146	2	no	—
332	C₂×D₄	—	146	2	no	—
333	C₂×D₄	—	146	2	no	—
334	C₂×D₄	—	146	2	no	—
335	C₂×D₄	—	146	2	no	—
336	C₂²×C₄	—	292	4	no	—
337	C₂²×C₄	—	146	2	no	—
338	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
339	Q₁₆	—	146	1	no	—
340	Q₁₆	—	146	1	no	—
341	SD₁₆	—	292	4	no	—
342	SD₁₆	—	146	2	no	—
343	SD₁₆	—	146	2	no	—
344	D₈	—	292	4	no	—
345	D₈	—	146	2	no	—
346	D₈	—	146	2	no	—
347	D₈	—	146	2	no	—
348	D₈	—	146	2	no	—
349	D₈	—	146	1	no	—
350	D₈	—	146	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	292	4	no	—
358	M₁₆	—	146	2	no	—
359	M₁₆	—	146	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	292	4	no	—
362	C₂×C₈	—	146	2	no	—
363	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
366	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
367	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
368	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
369	C₂×C₈	#11924028	1	1	yes	characteristic
370	C₂×C₈	#11924028	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	146	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	292	4	no	—
379	C₂²⋊C₄	—	292	4	no	—
380	C₂²⋊C₄	—	146	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	146	2	no	—
383	C₄²	C₂×C₄×D₇₃	1	2	yes	—
384	C₄²	C₂×D₂₉₂	1	2	yes	—
385	C₂³	—	292	2	no	—
386	C₂³	—	292	2	no	—
387	C₂³	—	1168	2	no	—
388	C₂³	—	146	4	no	—
389	C₂³	—	146	2	no	—
390	C₂³	#14556637	1	1	yes	characteristic
391	Q₈	—	146	2	no	—
392	Q₈	—	146	2	no	—
393	D₄	—	292	2	no	—
394	D₄	—	292	2	no	—
395	D₄	—	292	2	no	—
396	D₄	—	292	2	no	—
397	D₄	—	1168	4	no	—
398	D₄	—	146	4	no	—
399	D₄	—	146	2	no	—
400	D₄	—	146	2	no	—
401	D₄	—	146	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	292	2	no	—
406	C₂×C₄	—	292	2	no	—
407	C₂×C₄	—	292	2	no	—
408	C₂×C₄	—	1168	4	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
412	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
413	C₂×C₄	#14556637	1	1	yes	characteristic
414	C₂×C₄	#14556637	1	1	yes	characteristic
415	C₂×C₄	#14556637	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	292	2	no	—
420	C₈	C₄×D₂₉₂	1	1	yes	characteristic
421	C₈	C₄×D₂₉₂	1	1	yes	characteristic
422	C₈	C₄×D₂₉₂	1	1	yes	characteristic
423	C₈	C₄×D₂₉₂	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	292	2	no	—
426	C₂²	—	292	4	no	—
427	C₂²	—	584	2	no	—
428	C₂²	—	584	4	no	—
429	C₂²	—	584	4	no	—
430	C₂²	—	1168	2	no	—
431	C₂²	#17989061	1	1	yes	characteristic
432	C₂²	#17989156	1	1	yes	characteristic
433	C₂²	#17989192	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	292	2	no	—
438	C₄	—	584	2	no	—
439	C₄	C₂×C₄×D₂₉₂	1	1	yes	characteristic
440	C₄	#17989061	1	1	yes	characteristic
441	C₄	#17989156	1	1	yes	characteristic
442	C₄	#17989192	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	584	4	no	—
447	C₂	—	584	2	no	—
448	C₂	#22612656	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22612656
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1747	C₂
socle	C₂×C₇₃	#2328
prime radical	#22620417	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1747	D₇₃
hypocenter	C₇₃	#22286
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
2. #22618849	C₂	semidirect
3. #22618784	C₂	semidirect
4. #22610841	C₂	semidirect
5. #22610829	C₂	semidirect
6. #22610462	C₂	semidirect
7. #22610457	C₂	semidirect
8. #22610419	C₂	semidirect
9. #22610412	C₂	semidirect
10. #22610055	C₂	semidirect
11. C₇₃×#1747	C₂	semidirect
18. #17988976	C₄	semidirect
19. #17988971	C₄	semidirect
20. #17988964	C₄	semidirect
50. C₂×Dic₂₉₂	C₂×C₄	semidirect
51. C₂×#11924017	C₂×C₄	semidirect
52. C₂×#11924017	C₂×C₄	semidirect
59. C₂×D₅₈₄	C₂×C₄	semidirect
60. C₂×D₅₈₄	C₂×C₄	semidirect
65. #14556588	C₂×C₄	semidirect
66. #14556579	C₂×C₄	semidirect
91. #97×C₇₃	C₂×C₄	semidirect
92. #97×C₇₃	D₄	semidirect
94. C₄×C₈×C₇₃	C₂×C₄	semidirect
95. C₄×C₈×C₇₃	D₄	semidirect
235. #1747	D₇₃	semidirect
236. C₇₃	#22286	semidirect
316. #97	C₄×D₇₃	semidirect
317. #97	D₂₉₂	semidirect
319. C₄×C₈	C₄×D₇₃	semidirect
320. C₄×C₈	D₂₉₂	semidirect

Maximal subgroups

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

subgroup	index
#22620417	2
#22618849	2
#22618784	2
#22610841	2
#22610829	2
#22610462	2
#22610457	2
#22610419	2
#22610412	2
#22610055	2
C₇₃×#1747	2
#22286	73