Subgroups — #33084007

Order 18688.

1042 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	C₂×#17988634	C₂	1	1	yes	maximal, characteristic
2	#22618519	C₂	1	1	yes	maximal, characteristic
3	#22618347	C₂	1	2	yes	maximal
4	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic
5	#22609818	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609817	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609816	C₂	1	2	yes	maximal, complemented
8	#22609810	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609809	C₂	1	2	yes	maximal, complemented
10	#339×D₇₃	C₂	1	2	yes	maximal
11	C₇₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	1	yes	characteristic
13	C₂²×#11924011	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
15	#117×D₇₃	C₂²	1	2	yes	—
16	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
17	#17988634	C₄	1	8	yes	complemented
18	C₂×#14556527	C₂²	1	1	yes	characteristic
19	C₂×#14556526	C₂²	1	2	yes	—
20	#17988628	C₄	1	4	yes	complemented
21	#17988626	C₄	1	4	yes	complemented
22	#17988625	C₂²	1	1	yes	characteristic
23	#17988623	C₂²	1	2	yes	—
24	#17988545	C₂²	1	2	yes	—
25	#17988544	—	2	2	no	—
26	#17988543	C₂²	1	2	yes	—
27	#17988542	C₂²	1	2	yes	—
28	#17988541	—	2	2	no	—
29	#17988539	—	2	2	no	—
30	C₄×#11924011	—	2	2	no	—
31	C₄×#11924011	C₄	1	8	yes	complemented
32	C₂×#14556501	C₂²	1	1	yes	characteristic
33	C₂×#14556501	C₂²	1	1	yes	characteristic
34	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
35	#17988348	C₂²	1	2	yes	—
36	#17988347	C₂²	1	2	yes	—
37	#17988346	C₂²	1	2	yes	—
38	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
39	#427×C₇₃	C₂²	1	1	yes	characteristic
40	#405×C₇₃	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
42	#339×C₇₃	C₂²	1	2	yes	—
43	C₂²×C₄×D₇₃	—	2	1	no	—
44	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
45	C₂×#11924012	C₂³	1	2	yes	—
46	C₂×#11924011	—	2	2	no	—
47	C₂×#11924011	C₂×C₄	1	2	yes	—
48	C₂×#11924011	C₂×C₄	1	2	yes	—
49	C₂×#11924011	C₂×C₄	1	4	yes	—
50	C₂×#11924011	C₂×C₄	1	4	yes	—
51	C₂×#11924011	C₂×C₄	1	4	yes	—
52	C₂×#11924011	D₄	1	2	yes	—
53	C₂×#11924011	D₄	1	2	yes	—
54	C₂×#11924011	Q₈	1	4	yes	—
55	M₁₆×D₇₃	—	2	4	no	—
56	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
57	C₂²×#10596831	C₂³	1	1	yes	characteristic
58	C₂²×#10596831	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₇₃	—	2	2	no	—
60	#14556550	C₂³	1	2	yes	—
61	#14556549	C₂×C₄	1	4	yes	—
62	#14556548	—	2	2	no	—
63	#14556547	—	2	2	no	—
64	C₄⋊C₄×D₇₃	C₂×C₄	1	4	yes	—
65	C₂²⋊C₄×D₇₃	—	2	2	no	—
66	C₂×C₄×Dic₇₃	—	2	1	no	—
67	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
68	C₄²×D₇₃	—	2	2	no	—
69	C₄²×D₇₃	—	2	2	no	—
70	C₄²×D₇₃	C₂×C₄	1	4	yes	—
71	#14556527	C₂×C₄	1	4	yes	complemented
72	#14556526	C₂×C₄	1	8	yes	complemented
73	#14556525	C₂×C₄	1	2	yes	complemented
74	#14556524	C₂×C₄	1	4	yes	complemented
75	#14556523	C₂×C₄	1	2	yes	complemented
76	#14556522	C₂×C₄	1	4	yes	complemented
77	#14556502	—	2	2	no	—
78	#14556501	—	2	2	no	—
79	#14556501	—	2	2	no	—
80	#14556501	C₂×C₄	1	4	yes	complemented
81	#14556501	C₂×C₄	1	4	yes	complemented
82	C₄×#10596831	—	2	2	no	—
83	C₄×#10596831	C₂×C₄	1	4	yes	complemented
84	C₈×Dic₇₃	—	2	2	no	—
85	C₈×Dic₇₃	—	2	2	no	—
86	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	#117×C₇₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	#108×C₇₃	C₂×C₄	1	4	yes	complemented
92	#107×C₇₃	C₂×C₄	1	2	yes	complemented
93	#106×C₇₃	C₂×C₄	1	2	yes	complemented
94	#97×C₇₃	—	2	2	no	—
95	C₄×C₈×C₇₃	—	2	2	no	—
96	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
97	C₂³×D₇₃	#41	1	1	yes	characteristic
98	C₂²×Dic₇₃	—	2	1	no	—
99	C₂²×Dic₇₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₇₃	—	2	4	no	—
101	C₂×C₄×D₇₃	—	2	4	no	—
102	C₂×C₄×D₇₃	—	4	4	no	—
103	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
107	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
108	C₂×C₄×D₇₃	#41	1	2	yes	—
109	#11924012	—	2	2	no	—
110	#11924012	C₂²×C₄	1	4	yes	—
111	#11924011	—	2	8	no	—
112	#11924011	C₄²	1	8	yes	—
113	#11924011	C₄²	1	8	yes	—
114	#11924011	C₄⋊C₄	1	8	yes	—
115	#11924011	C₄⋊C₄	1	8	yes	—
116	C₂×#10596831	—	2	2	no	—
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂²×C₄	1	2	yes	—
119	C₂×#10596831	C₂²×C₄	1	2	yes	—
120	C₂×#10596831	C₂²×C₄	1	2	yes	—
121	C₂×#10596831	C₂×D₄	1	2	yes	—
122	C₂×#10596831	C₂×Q₈	1	2	yes	—
123	C₈×D₇₃	—	2	8	no	—
124	C₄⋊Dic₇₃	C₂²×C₄	1	4	yes	—
125	#11924007	—	2	4	no	—
126	C₂²⋊Dic₇₃	—	2	2	no	—
127	#11924005	—	2	4	no	—
128	C₄×Dic₇₃	—	2	2	no	—
129	C₄×Dic₇₃	—	2	1	no	—
130	C₄×Dic₇₃	—	2	4	no	—
131	C₄×Dic₇₃	—	2	4	no	—
132	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₇₃	—	2	2	no	—
136	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
146	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	1	no	—
150	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
151	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
152	C₂²×D₇₃	—	4	2	no	—
153	C₂²×D₇₃	#117	1	2	yes	—
154	C₂²×D₇₃	C₄×D₄	1	2	yes	—
155	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	—	2	4	no	—
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₇₃	—	2	2	no	—
166	C₂×Dic₇₃	—	2	4	no	—
167	C₂×Dic₇₃	—	4	2	no	—
168	C₂×Dic₇₃	#117	1	2	yes	—
169	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
170	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
171	C₄×D₇₃	—	4	8	no	—
172	C₄×D₇₃	—	8	4	no	—
173	C₄×D₇₃	C₂×C₄²	1	4	yes	—
174	C₄×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
175	C₄×D₇₃	C₄×D₄	1	4	yes	—
176	C₄×D₇₃	C₄×Q₈	1	4	yes	—
177	C₈×C₇₃	—	2	4	no	—
178	C₈×C₇₃	C₂×C₄²	1	2	yes	—
179	C₈×C₇₃	C₂×C₄²	1	2	yes	—
180	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
181	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
182	#10596831	—	2	4	no	—
183	#10596831	C₂×C₄²	1	4	yes	—
184	#10596831	C₂×C₄⋊C₄	1	4	yes	—
185	C₂²×C₇₃	—	2	2	no	—
186	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
187	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
189	C₂×D₇₃	—	2	4	no	—
190	C₂×D₇₃	—	4	2	no	—
191	C₂×D₇₃	—	4	2	no	—
192	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
193	C₄×C₇₃	—	2	4	no	—
194	C₄×C₇₃	—	4	4	no	—
195	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
196	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
199	Dic₇₃	—	4	2	no	—
200	Dic₇₃	—	4	4	no	—
201	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
202	#20445	—	73	1	no	maximal, Sylow
203	C₂×C₇₃	—	2	1	no	—
204	C₂×C₇₃	—	2	1	no	—
205	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₇₃	#2956	1	2	yes	—
207	D₇₃	—	2	4	no	—
208	C₂×#430	—	73	1	no	—
209	#2911	—	73	1	no	—
210	#2873	—	73	2	no	—
211	C₂×C₄×M₁₆	—	73	1	no	—
212	#1773	—	73	1	no	—
213	#1773	—	73	1	no	—
214	#1773	—	73	2	no	—
215	#1772	—	73	1	no	—
216	#1772	—	73	2	no	—
217	#1772	D₇₃	1	1	yes	characteristic, complemented
218	C₂×#339	—	73	2	no	—
219	C₇₃	#20445	1	1	yes	characteristic, complemented, Sylow
220	C₂²×M₁₆	—	73	1	no	—
221	C₂²×M₁₆	—	73	1	no	—
222	C₂²×M₁₆	—	73	2	no	—
223	C₂×#117	—	73	2	no	—
224	C₂²×C₄²	—	73	1	no	—
225	#430	—	73	8	no	—
226	C₂×#108	—	73	2	no	—
227	C₂×#108	—	73	1	no	—
228	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
229	#428	—	73	4	no	—
230	#428	—	73	4	no	—
231	#427	—	73	1	no	—
232	#427	—	73	2	no	—
233	#427	C₂×D₇₃	1	1	yes	characteristic
234	#405	—	73	2	no	—
235	#405	—	73	2	no	—
236	#405	—	73	2	no	—
237	#405	—	146	2	no	—
238	#405	—	146	2	no	—
239	#405	C₂×D₇₃	1	2	yes	—
240	C₄×M₁₆	—	73	8	no	—
241	C₄×M₁₆	—	146	2	no	—
242	C₄×M₁₆	—	146	2	no	—
243	C₂×#97	—	73	1	no	—
244	C₂×#97	—	73	1	no	—
245	C₂×C₄×C₈	—	73	1	no	—
246	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
247	#339	—	73	2	no	—
248	#339	—	73	2	no	—
249	#339	—	73	2	no	—
250	#339	C₂×D₇₃	1	2	yes	—
251	C₂³×C₄	—	73	1	no	—
252	C₂³×C₄	—	146	1	no	—
253	C₂×M₁₆	—	73	4	no	—
254	C₂×M₁₆	—	73	4	no	—
255	C₂×M₁₆	—	73	2	no	—
256	C₂×M₁₆	—	73	2	no	—
257	C₂×M₁₆	—	73	4	no	—
258	C₂×M₁₆	—	73	2	no	—
259	C₂×M₁₆	—	73	2	no	—
260	C₂×M₁₆	—	73	4	no	—
261	C₂×M₁₆	—	73	2	no	—
262	C₂×M₁₆	—	73	8	no	—
263	C₂×M₁₆	—	146	2	no	—
264	C₂×M₁₆	—	146	4	no	—
265	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
266	C₂²×C₈	—	73	1	no	—
267	C₂²×C₈	—	73	1	no	—
268	C₂²×C₈	—	146	2	no	—
269	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
271	#117	—	73	2	no	—
272	#117	—	73	4	no	—
273	#117	—	146	2	no	—
274	#117	—	146	2	no	—
275	#117	C₂²×D₇₃	1	2	yes	—
276	C₂×C₄⋊C₄	—	73	4	no	—
277	C₂×C₂²⋊C₄	—	146	2	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	4	no	—
280	C₂×C₄²	—	146	2	no	—
281	C₂×C₄²	—	146	2	no	—
282	C₂×C₄²	—	146	1	no	—
283	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
284	#108	—	73	8	no	—
285	#108	—	73	4	no	—
286	#108	C₄×D₇₃	1	4	yes	complemented
287	#107	—	73	2	no	—
288	#107	—	73	4	no	—
289	#107	C₄×D₇₃	1	2	yes	complemented
290	#106	—	73	2	no	—
291	#106	—	73	4	no	—
292	#106	C₄×D₇₃	1	2	yes	complemented
293	#97	—	2	2	no	—
294	#97	—	73	4	no	—
295	#97	—	73	4	no	—
296	#97	—	146	2	no	—
297	#97	—	146	2	no	—
298	#97	—	146	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	73	4	no	—
301	C₄×C₈	—	146	2	no	—
302	C₄×C₈	—	146	2	no	—
303	C₄×C₈	—	146	2	no	—
304	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
305	C₂⁴	—	73	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	292	4	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	2	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	—	73	2	no	—
312	C₂²×C₄	—	73	2	no	—
313	C₂²×C₄	—	73	2	no	—
314	C₂²×C₄	—	73	2	no	—
315	C₂²×C₄	—	146	4	no	—
316	C₂²×C₄	—	146	4	no	—
317	C₂²×C₄	—	146	1	no	—
318	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
319	M₁₆	—	2	2	no	—
320	M₁₆	—	73	8	no	—
321	M₁₆	—	73	8	no	—
322	M₁₆	—	73	8	no	—
323	M₁₆	—	73	8	no	—
324	M₁₆	—	73	4	no	—
325	M₁₆	—	146	8	no	—
326	M₁₆	—	146	2	no	—
327	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	73	2	no	—
330	C₂×C₈	—	73	2	no	—
331	C₂×C₈	—	73	2	no	—
332	C₂×C₈	—	73	2	no	—
333	C₂×C₈	—	73	2	no	—
334	C₂×C₈	—	73	2	no	—
335	C₂×C₈	—	146	8	no	—
336	C₂×C₈	—	146	2	no	—
337	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
338	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
341	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
342	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
343	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
344	C₂×C₈	Q₈×D₇₃	1	2	yes	—
345	C₄⋊C₄	—	73	4	no	—
346	C₄⋊C₄	—	146	4	no	—
347	C₄⋊C₄	C₂×C₄×D₇₃	1	4	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	146	4	no	—
350	C₂²⋊C₄	—	146	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	73	2	no	—
354	C₄²	—	146	4	no	—
355	C₄²	—	146	4	no	—
356	C₄²	—	146	2	no	—
357	C₄²	—	146	1	no	—
358	C₄²	C₂×C₄×D₇₃	1	2	yes	—
359	C₂³	—	292	2	no	—
360	C₂³	—	73	2	no	—
361	C₂³	—	73	2	no	—
362	C₂³	—	73	2	no	—
363	C₂³	#41×D₇₃	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	292	8	no	—
368	C₂×C₄	—	292	2	no	—
369	C₂×C₄	—	584	4	no	—
370	C₂×C₄	—	73	2	no	—
371	C₂×C₄	—	73	2	no	—
372	C₂×C₄	—	73	2	no	—
373	C₂×C₄	—	73	4	no	—
374	C₂×C₄	—	73	4	no	—
375	C₂×C₄	—	73	4	no	—
376	C₂×C₄	—	73	4	no	—
377	C₂×C₄	—	146	2	no	—
378	C₂×C₄	—	146	4	no	—
379	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
383	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
384	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	73	4	no	—
387	C₈	—	73	4	no	—
388	C₈	—	146	4	no	—
389	C₈	C₄²×D₇₃	1	2	yes	—
390	C₈	C₄²×D₇₃	1	2	yes	—
391	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
392	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	292	2	no	—
395	C₂²	—	292	2	no	—
396	C₂²	—	73	4	no	—
397	C₂²	—	146	4	no	—
398	C₂²	#117×D₇₃	1	1	yes	characteristic
399	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
400	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	4	4	no	—
403	C₄	—	292	2	no	—
404	C₄	—	292	4	no	—
405	C₄	—	73	4	no	—
406	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
407	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
408	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
409	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	146	4	no	—
413	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
414	C₂	#22618836	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1772	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1772	D₇₃
hypocenter	C₇₃	#20445
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #22609818	C₂	semidirect
6. #22609817	C₂	semidirect
7. #22609816	C₂	semidirect
8. #22609810	C₂	semidirect
9. #22609809	C₂	semidirect
11. C₇₃×#1772	C₂	semidirect
17. #17988634	C₄	semidirect
20. #17988628	C₄	semidirect
21. #17988626	C₄	semidirect
31. C₄×#11924011	C₄	semidirect
71. #14556527	C₂×C₄	semidirect
72. #14556526	C₂×C₄	semidirect
73. #14556525	C₂×C₄	semidirect
74. #14556524	C₂×C₄	semidirect
75. #14556523	C₂×C₄	semidirect
76. #14556522	C₂×C₄	semidirect
80. #14556501	C₂×C₄	semidirect
81. #14556501	C₂×C₄	semidirect
83. C₄×#10596831	C₂×C₄	semidirect
91. #108×C₇₃	C₂×C₄	semidirect
92. #107×C₇₃	C₂×C₄	semidirect
93. #106×C₇₃	C₂×C₄	semidirect
96. C₄×C₈×C₇₃	C₂×C₄	semidirect
217. #1772	D₇₃	semidirect
219. C₇₃	#20445	semidirect
286. #108	C₄×D₇₃	semidirect
289. #107	C₄×D₇₃	semidirect
292. #106	C₄×D₇₃	semidirect
304. C₄×C₈	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988634	2
#22618519	2
#22618347	2
C₂×C₄×#11924011	2
#22609818	2
#22609817	2
#22609816	2
#22609810	2
#22609809	2
#339×D₇₃	2
C₇₃×#1772	2
#20445	73