Subgroups — #33239636

Order 18688.

452 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618863	C₂	1	1	yes	maximal, characteristic
2	#22611839	C₂	1	1	yes	maximal, characteristic, complemented
3	#22611838	C₂	1	1	yes	maximal, characteristic, complemented
4	#22611838	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611837	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611837	C₂	1	1	yes	maximal, characteristic, complemented
7	#22611836	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#22611833	C₂	1	1	yes	maximal, characteristic, complemented
10	#22611738	C₂	1	1	yes	maximal, characteristic
11	#22611735	C₂	1	1	yes	maximal, characteristic
12	#22611735	C₂	1	1	yes	maximal, characteristic
13	#22611731	C₂	1	1	yes	maximal, characteristic
14	#22611727	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2164	C₂	1	1	yes	maximal, characteristic
16	#17989140	C₄	1	1	yes	characteristic
17	#17988715	C₄	1	1	yes	characteristic
18	#17988715	C₄	1	1	yes	characteristic
19	#17988715	C₄	1	1	yes	characteristic
20	#17988715	C₄	1	1	yes	characteristic
21	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
25	#17988615	C₄	1	1	yes	characteristic
26	#17988614	C₄	1	1	yes	characteristic
27	#17988610	C₄	1	1	yes	characteristic
28	#17988542	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
30	C₄⋊#11924003	C₂²	1	1	yes	characteristic
31	C₄⋊#11924003	C₂²	1	1	yes	characteristic
32	#17988405	C₂²	1	1	yes	characteristic
33	#17988405	C₂²	1	1	yes	characteristic
34	#17988405	C₂²	1	1	yes	characteristic
35	#17988405	C₂²	1	1	yes	characteristic
36	#17988405	C₂²	1	1	yes	characteristic
37	#17988405	C₂²	1	1	yes	characteristic
38	#17988405	C₂²	1	1	yes	characteristic
39	#17988405	C₂²	1	1	yes	characteristic
40	C₂²⋊#11924003	C₂²	1	1	yes	characteristic
41	C₂²⋊#11924003	C₂²	1	1	yes	characteristic
42	#17988363	C₂²	1	1	yes	characteristic
43	#17988362	C₂²	1	1	yes	characteristic
44	#17988362	C₂²	1	1	yes	characteristic
45	#17988362	C₂²	1	1	yes	characteristic
46	#17988362	C₂²	1	1	yes	characteristic
47	C₄×#11924003	C₂²	1	1	yes	characteristic
48	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
49	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
52	#405×C₇₃	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
55	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
57	#346×C₇₃	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
59	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
60	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
61	#14556590	C₈	1	1	yes	characteristic
62	#14556590	C₈	1	1	yes	characteristic
63	#14556582	C₈	1	1	yes	characteristic
64	#14556582	C₈	1	1	yes	characteristic
65	#14556568	C₈	1	1	yes	characteristic
66	#14556568	C₈	1	1	yes	characteristic
67	#14556568	C₈	1	1	yes	characteristic
68	#14556568	C₈	1	1	yes	characteristic
69	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
73	#14556550	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×#11924003	C₂³	1	1	yes	characteristic
76	C₂×#11924003	C₂³	1	1	yes	characteristic
77	C₂×#11924003	C₂³	1	1	yes	characteristic
78	C₂×#11924003	C₂³	1	1	yes	characteristic
79	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
80	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
81	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
83	#14556520	C₂×C₄	1	1	yes	characteristic
84	#14556520	C₂×C₄	1	1	yes	characteristic
85	#14556520	C₂×C₄	1	1	yes	characteristic
86	#14556520	C₂×C₄	1	1	yes	characteristic
87	#14556520	C₂×C₄	1	1	yes	characteristic
88	#14556520	C₂×C₄	1	1	yes	characteristic
89	#14556520	C₂×C₄	1	1	yes	characteristic
90	#14556520	C₂×C₄	1	1	yes	characteristic
91	#14556501	C₂×C₄	1	1	yes	characteristic
92	#14556501	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
106	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
107	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
111	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
112	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
113	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
114	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
115	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
116	#11924012	—	4	1	no	—
117	C₂×#10596831	—	4	1	no	—
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
123	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
128	#11924007	C₂×C₈	1	1	yes	characteristic
129	#11924007	C₂×C₈	1	1	yes	characteristic
130	#11924007	C₂×C₈	1	1	yes	characteristic
131	#11924007	C₂×C₈	1	1	yes	characteristic
132	#11924007	C₂×C₈	1	1	yes	characteristic
133	#11924007	C₂×C₈	1	1	yes	characteristic
134	#11924007	C₂×C₈	1	1	yes	characteristic
135	#11924007	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
144	#11924003	—	2	1	no	—
145	#11924003	—	2	1	no	—
146	#11924003	—	2	1	no	—
147	#11924003	—	2	1	no	—
148	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	M₁₆×C₇₃	—	4	1	no	—
150	C₂×C₈×C₇₃	—	2	1	no	—
151	C₂×C₈×C₇₃	—	2	1	no	—
152	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
157	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
158	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
159	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
160	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₁₆×C₇₃	—	2	1	no	—
163	C₁₆×C₇₃	—	2	1	no	—
164	C₁₆×C₇₃	—	2	1	no	—
165	C₁₆×C₇₃	—	2	1	no	—
166	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	—	4	1	no	—
177	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
185	Dic₁₄₆	—	2	2	no	—
186	Dic₁₄₆	—	2	2	no	—
187	Dic₁₄₆	—	4	1	no	—
188	Dic₁₄₆	—	4	1	no	—
189	C₈×C₇₃	—	2	1	no	—
190	C₈×C₇₃	—	2	1	no	—
191	C₈×C₇₃	—	2	1	no	—
192	C₈×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
194	#10596831	—	2	1	no	—
195	#10596831	—	2	1	no	—
196	#10596831	—	2	1	no	—
197	#10596831	—	2	1	no	—
198	C₂²×C₇₃	—	2	1	no	—
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
202	C₄×C₇₃	—	2	1	no	—
203	C₄×C₇₃	—	2	1	no	—
204	C₄×C₇₃	—	2	1	no	—
205	C₄×C₇₃	—	2	1	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	#519	1	1	yes	characteristic
208	C₄×C₇₃	#568	1	1	yes	characteristic
209	Dic₇₃	—	2	1	no	—
210	Dic₇₃	—	2	1	no	—
211	Dic₇₃	—	2	1	no	—
212	Dic₇₃	—	2	1	no	—
213	Dic₇₃	—	2	1	no	—
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	#504	1	2	yes	—
217	#33499	—	73	1	no	maximal, Sylow
218	C₂×C₇₃	—	4	1	no	—
219	C₂×C₇₃	#2982	1	1	yes	characteristic
220	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
221	C₂×C₇₃	#3407	1	1	yes	characteristic
222	#2960	—	73	1	no	—
223	#2183	—	73	1	no	—
224	#2183	—	73	1	no	—
225	#2183	—	73	1	no	—
226	#2183	—	73	1	no	—
227	#2183	—	73	1	no	—
228	#2183	—	73	1	no	—
229	Q₈×C₁₆	—	73	1	no	—
230	Q₈×C₁₆	—	73	1	no	—
231	#2164	—	73	1	no	—
232	#2164	—	73	1	no	—
233	#2164	—	73	1	no	—
234	#2164	D₇₃	1	1	yes	characteristic
235	#2163	—	73	1	no	—
236	#2162	—	73	1	no	—
237	C₇₃	#33499	1	1	yes	characteristic, complemented, Sylow
238	#533	—	73	1	no	—
239	#446	—	73	1	no	—
240	#446	—	73	1	no	—
241	#446	—	73	1	no	—
242	#446	—	73	1	no	—
243	C₈×Q₈	—	73	1	no	—
244	C₈×Q₈	—	73	1	no	—
245	C₈×Q₈	—	73	1	no	—
246	C₈×Q₈	—	73	1	no	—
247	#424	—	73	1	no	—
248	#424	—	73	1	no	—
249	#423	—	73	1	no	—
250	#405	—	73	1	no	—
251	#405	C₂×D₇₃	1	1	yes	characteristic
252	C₂×C₄×C₈	—	73	1	no	—
253	C₄⋊C₁₆	—	73	1	no	—
254	C₄⋊C₁₆	—	73	1	no	—
255	C₄⋊C₁₆	—	73	1	no	—
256	C₄⋊C₁₆	—	73	1	no	—
257	C₄⋊C₁₆	—	73	1	no	—
258	C₄⋊C₁₆	—	73	1	no	—
259	C₄⋊C₁₆	—	73	1	no	—
260	C₄⋊C₁₆	—	73	1	no	—
261	C₄⋊C₁₆	—	73	1	no	—
262	C₄⋊C₁₆	—	73	1	no	—
263	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
264	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
265	C₂²⋊C₁₆	—	73	1	no	—
266	C₂²⋊C₁₆	—	73	1	no	—
267	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
268	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
269	#346	—	73	1	no	—
270	#346	—	73	1	no	—
271	#346	—	73	1	no	—
272	#346	—	73	1	no	—
273	#346	—	73	1	no	—
274	#346	C₂×D₇₃	1	1	yes	characteristic
275	C₄×C₁₆	—	73	1	no	—
276	C₄×C₁₆	—	73	1	no	—
277	C₄×C₁₆	—	73	1	no	—
278	C₄×C₁₆	—	73	1	no	—
279	C₄×C₁₆	—	73	1	no	—
280	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
281	C₂×M₁₆	—	73	1	no	—
282	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
283	C₂²×C₈	—	73	1	no	—
284	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
285	C₄⋊Q₈	—	73	1	no	—
286	C₄⋊Q₈	—	73	1	no	—
287	#125	—	73	1	no	—
288	#125	—	73	1	no	—
289	C₂²⋊Q₈	—	73	1	no	—
290	C₂²⋊Q₈	—	73	1	no	—
291	C₂²⋊Q₈	—	73	1	no	—
292	C₂²⋊Q₈	—	73	1	no	—
293	C₄×Q₈	—	73	1	no	—
294	C₄×Q₈	—	73	1	no	—
295	C₄×Q₈	—	73	1	no	—
296	C₄×Q₈	—	73	1	no	—
297	#117	—	73	1	no	—
298	#117	C₄×D₇₃	1	1	yes	characteristic
299	C₂×C₄²	—	73	1	no	—
300	C₂×C₁₆	—	73	1	no	—
301	C₂×C₁₆	—	73	1	no	—
302	C₂×C₁₆	—	73	1	no	—
303	C₂×C₁₆	—	73	1	no	—
304	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
306	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
307	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
308	C₄⋊C₈	—	73	1	no	—
309	C₄⋊C₈	—	73	1	no	—
310	C₄⋊C₈	—	73	1	no	—
311	C₄⋊C₈	—	73	1	no	—
312	C₄⋊C₈	—	73	1	no	—
313	C₄⋊C₈	—	73	1	no	—
314	C₄⋊C₈	—	73	1	no	—
315	C₄⋊C₈	—	73	1	no	—
316	C₄⋊C₈	—	73	1	no	—
317	C₄⋊C₈	—	73	1	no	—
318	C₄⋊C₈	—	73	1	no	—
319	C₄⋊C₈	—	73	1	no	—
320	#97	—	73	1	no	—
321	#97	—	73	1	no	—
322	#97	C₄×D₇₃	1	1	yes	characteristic
323	#97	C₄×D₇₃	1	1	yes	characteristic
324	C₄×C₈	—	73	1	no	—
325	C₄×C₈	—	73	1	no	—
326	C₄×C₈	—	73	1	no	—
327	C₄×C₈	—	73	1	no	—
328	C₄×C₈	—	73	1	no	—
329	C₄×C₈	—	73	1	no	—
330	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
332	C₂×Q₈	—	73	1	no	—
333	C₂×Q₈	—	73	1	no	—
334	C₂×Q₈	—	73	1	no	—
335	C₂×Q₈	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
339	M₁₆	—	4	1	no	—
340	M₁₆	—	292	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	292	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
352	C₄⋊C₄	—	73	1	no	—
353	C₄⋊C₄	—	73	1	no	—
354	C₄⋊C₄	—	73	1	no	—
355	C₄⋊C₄	—	73	1	no	—
356	C₄⋊C₄	—	73	1	no	—
357	C₄⋊C₄	—	73	1	no	—
358	C₄⋊C₄	—	73	1	no	—
359	C₄⋊C₄	—	73	1	no	—
360	C₄⋊C₄	—	73	1	no	—
361	C₄⋊C₄	—	73	1	no	—
362	C₄⋊C₄	—	73	1	no	—
363	C₄⋊C₄	—	73	1	no	—
364	C₄⋊C₄	—	73	1	no	—
365	C₄⋊C₄	—	73	1	no	—
366	C₄⋊C₄	C₈×D₇₃	1	1	yes	characteristic
367	C₄⋊C₄	C₈×D₇₃	1	1	yes	characteristic
368	C₂²⋊C₄	—	73	1	no	—
369	C₂²⋊C₄	—	73	1	no	—
370	C₂²⋊C₄	C₈×D₇₃	1	1	yes	characteristic
371	C₂²⋊C₄	C₈×D₇₃	1	1	yes	characteristic
372	C₄²	—	73	1	no	—
373	C₄²	—	73	1	no	—
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	—	73	1	no	—
377	C₄²	—	73	1	no	—
378	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	2	1	no	—
384	C₁₆	—	146	1	no	—
385	C₁₆	—	146	1	no	—
386	C₁₆	—	146	1	no	—
387	C₁₆	—	146	1	no	—
388	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
389	Q₈	—	292	1	no	—
390	Q₈	—	292	1	no	—
391	Q₈	—	146	2	no	—
392	Q₈	—	146	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	292	1	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	146	2	no	—
405	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	146	1	no	—
415	C₈	—	146	1	no	—
416	C₈	—	146	1	no	—
417	C₈	—	146	1	no	—
418	C₈	#14556638	1	1	yes	characteristic
419	C₈	#14556638	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	C₂²×C₈×D₇₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	73	2	no	—
430	C₄	—	146	1	no	—
431	C₄	—	146	1	no	—
432	C₄	—	146	1	no	—
433	C₄	—	146	1	no	—
434	C₄	—	146	1	no	—
435	C₄	—	146	1	no	—
436	C₄	—	146	1	no	—
437	C₄	#17989064	1	1	yes	characteristic
438	C₄	#17989353	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	#22619011	1	1	yes	characteristic
441	C₂	#504×D₇₃	1	1	yes	characteristic
442	C₂	#22623032	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	C₇₃×#2164	C₂
prime radical	C₂³×C₇₃	C₂²×C₈
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	#2164	D₇₃
hypocenter	C₇₃	#33499
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #22611839	C₂	semidirect
3. #22611838	C₂	semidirect
4. #22611838	C₂	semidirect
5. #22611837	C₂	semidirect
6. #22611837	C₂	semidirect
7. #22611836	C₂	semidirect
8. C₁₆×Dic₁₄₆	C₂	semidirect
9. #22611833	C₂	semidirect
237. C₇₃	#33499	semidirect

Maximal subgroups

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

subgroup	index
#22618863	2
#22611839	2
#22611838	2
#22611837	2
#22611836	2
C₁₆×Dic₁₄₆	2
#22611833	2
#22611738	2
#22611735	2
#22611731	2
#22611727	2
C₇₃×#2164	2
#33499	73