Subgroups — #34015804

Order 18688.

814 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626742	C₂	1	2	yes	maximal
2	#22625155	C₂	1	1	yes	maximal, characteristic, complemented
3	#22625154	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625151	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625150	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625139	C₂	1	2	yes	maximal, complemented
7	#22625135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11924038	C₂	1	2	yes	maximal, complemented
9	C₈×#11924037	C₂	1	2	yes	maximal, complemented
10	C₈×#11924036	C₂	1	1	yes	maximal, characteristic, complemented
11	#22618353	C₂	1	1	yes	maximal, characteristic
12	#17989639	C₄	1	4	yes	—
13	#17989620	C₄	1	4	yes	—
14	#17989619	C₄	1	4	yes	—
15	#17989617	C₄	1	4	yes	—
16	#17989606	C₂²	1	2	yes	—
17	#17989605	C₂²	1	2	yes	—
18	#17989604	C₂²	1	2	yes	—
19	C₄×#11924038	C₂²	1	2	yes	—
20	C₄×#11924037	C₂²	1	2	yes	—
21	C₄×#11924036	C₂²	1	2	yes	—
22	#17989429	C₂²	1	2	yes	—
23	#17989429	C₂²	1	2	yes	—
24	#17989429	C₂²	1	2	yes	—
25	#17989429	C₂²	1	2	yes	—
26	#17989428	C₂²	1	1	yes	characteristic
27	#17989428	C₂²	1	1	yes	characteristic
28	C₈×#10596833	C₂²	1	2	yes	—
29	C₈×#10596833	C₂²	1	1	yes	characteristic
30	C₈×#10596833	C₂²	1	1	yes	characteristic
31	C₈×#10596833	C₂²	1	2	yes	—
32	C₂×#14556599	C₄	1	1	yes	characteristic
33	C₂×#14556597	C₄	1	1	yes	characteristic
34	#17989055	C₂²	1	1	yes	characteristic
35	#17988544	C₄	1	1	yes	characteristic
36	#17988544	C₄	1	1	yes	characteristic
37	#17988543	C₄	1	1	yes	characteristic
38	#17988541	C₄	1	1	yes	characteristic
39	#17988541	C₄	1	1	yes	characteristic
40	#17988539	C₂²	1	1	yes	characteristic
41	#17988539	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₄	1	1	yes	characteristic
47	C₂×#11924038	C₂×C₄	1	4	yes	—
48	C₂×#11924037	C₂×C₄	1	4	yes	—
49	C₂×#11924036	C₂×C₄	1	4	yes	—
50	#14556658	C₂×C₄	1	4	yes	—
51	#14556658	C₂×C₄	1	4	yes	—
52	C₄⋊#10596833	C₂×C₄	1	4	yes	—
53	#14556648	C₂×C₄	1	4	yes	—
54	#14556648	C₂×C₄	1	4	yes	—
55	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
56	#14556646	C₂×C₄	1	4	yes	—
57	#14556646	C₂×C₄	1	4	yes	—
58	C₄×#10596833	C₂×C₄	1	4	yes	—
59	C₄×#10596833	C₂³	1	2	yes	—
60	C₄×#10596833	C₂³	1	2	yes	—
61	C₄×#10596833	C₂³	1	2	yes	—
62	C₄×#10596833	C₂³	1	2	yes	—
63	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
64	#14556599	—	2	4	no	—
65	#14556597	—	2	4	no	—
66	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
67	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
68	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
71	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
76	#14556556	C₂×C₄	1	2	yes	—
77	#14556553	C₂×C₄	1	2	yes	—
78	#14556551	C₂×C₄	1	2	yes	—
79	#14556551	C₂×C₄	1	2	yes	—
80	#14556548	C₂×C₄	1	1	yes	characteristic
81	#14556548	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
83	C₄²×D₇₃	C₂³	1	1	yes	characteristic
84	C₄²×D₇₃	C₂³	1	1	yes	characteristic
85	#14556502	C₂×C₄	1	1	yes	characteristic
86	#14556502	C₂×C₄	1	1	yes	characteristic
87	#14556501	C₂×C₄	1	1	yes	characteristic
88	#14556501	C₂×C₄	1	1	yes	characteristic
89	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
90	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
94	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
99	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
100	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
101	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
104	#11924038	—	2	8	no	—
105	#11924037	—	2	8	no	—
106	#11924036	—	2	8	no	—
107	C₂×#10596833	C₂²×C₄	1	4	yes	—
108	C₂×#10596833	C₂²×C₄	1	4	yes	—
109	C₂×#10596833	C₂²×C₄	1	4	yes	—
110	C₂×#10596833	C₂²×C₄	1	4	yes	—
111	#11924028	—	2	2	no	—
112	#11924028	—	2	2	no	—
113	C₂×Dic₁₄₆	C₄²	1	1	yes	characteristic
114	C₂×D₂₉₂	C₄²	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
116	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
117	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
121	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	#11924012	—	2	2	no	—
123	#11924011	—	2	2	no	—
124	#11924011	—	2	2	no	—
125	#11924011	—	2	2	no	—
126	#11924011	—	2	2	no	—
127	C₂×#10596831	—	2	2	no	—
128	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
129	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
130	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₇₃	—	2	2	no	—
133	C₈×D₇₃	—	2	2	no	—
134	C₈×D₇₃	M₁₆	1	4	yes	complemented
135	C₈×D₇₃	M₁₆	1	4	yes	complemented
136	#11924007	C₄²	1	2	yes	—
137	#11924007	C₄²	1	2	yes	—
138	#11924005	C₄²	1	2	yes	—
139	#11924005	C₄²	1	2	yes	—
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
142	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
143	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
144	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	M₁₆×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₇₃	C₄²	1	2	yes	—
153	C₂²⋊C₄×C₇₃	C₄²	1	2	yes	—
154	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₇₃	—	2	1	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
162	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₇₃	—	2	2	no	—
166	C₂²⋊D₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	4	no	—
168	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
169	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
172	D₂₉₂	—	2	2	no	—
173	C₄×D₇₃	—	2	1	no	—
174	C₄×D₇₃	—	2	1	no	—
175	C₄×D₇₃	—	2	4	no	—
176	C₄×D₇₃	—	2	4	no	—
177	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
178	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
179	Dic₁₄₆	—	2	2	no	—
180	#10596833	—	2	4	no	—
181	#10596833	—	2	4	no	—
182	#10596833	—	2	4	no	—
183	#10596833	#131	1	8	yes	complemented
184	C₈×C₇₃	—	2	1	no	—
185	C₈×C₇₃	—	2	1	no	—
186	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
187	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
188	#10596831	—	2	1	no	—
189	#10596831	—	2	1	no	—
190	#10596831	C₂×M₁₆	1	2	yes	—
191	#10596831	C₂×M₁₆	1	2	yes	—
192	C₂²×C₇₃	—	2	1	no	—
193	C₂²×C₇₃	—	2	2	no	—
194	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	1	no	—
197	C₂×D₇₃	—	2	2	no	—
198	C₂×D₇₃	C₄×M₁₆	1	2	yes	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	2	2	no	—
201	C₄×C₇₃	—	2	2	no	—
202	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
203	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
204	Dic₇₃	—	2	1	no	—
205	Dic₇₃	—	2	2	no	—
206	Dic₇₃	C₄×M₁₆	1	2	yes	—
207	Dic₇₃	C₂×#131	1	4	yes	—
208	#17335	—	73	1	no	maximal, Sylow
209	C₂×C₇₃	—	4	1	no	—
210	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
211	C₂×C₇₃	C₄×#131	1	2	yes	—
212	D₇₃	—	2	2	no	—
213	D₇₃	—	4	1	no	—
214	#2965	—	73	2	no	—
215	C₄×#131	—	73	1	no	—
216	#1455	—	73	1	no	—
217	#1455	—	73	1	no	—
218	#1453	—	73	1	no	—
219	#1453	—	73	1	no	—
220	#1451	—	73	2	no	—
221	#1450	—	73	1	no	—
222	C₈×M₁₆	—	73	2	no	—
223	C₈×M₁₆	—	73	2	no	—
224	C₂×C₈²	—	73	1	no	—
225	C₇₃	#17335	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	73	1	no	—
227	C₂×#131	—	73	1	no	—
228	C₄×#41	—	73	1	no	—
229	#446	—	73	4	no	—
230	#436	—	73	4	no	—
231	#435	—	73	4	no	—
232	#435	—	73	4	no	—
233	#431	—	73	2	no	—
234	#431	—	73	2	no	—
235	#431	—	73	2	no	—
236	#405	—	73	1	no	—
237	#405	—	73	1	no	—
238	#405	—	73	1	no	—
239	#405	—	73	1	no	—
240	#405	—	73	1	no	—
241	#405	#64408	1	1	yes	characteristic
242	C₄×M₁₆	—	73	2	no	—
243	C₄×M₁₆	—	73	2	no	—
244	C₄×M₁₆	—	73	1	no	—
245	C₄×M₁₆	—	73	1	no	—
246	C₄×M₁₆	—	73	1	no	—
247	C₂×C₄×C₈	—	73	2	no	—
248	C₂×C₄×C₈	—	73	1	no	—
249	C₂×C₄×C₈	—	73	1	no	—
250	C₂×C₄×C₈	—	73	1	no	—
251	#322	—	73	1	no	—
252	#322	—	73	1	no	—
253	#322	—	73	2	no	—
254	#322	—	73	2	no	—
255	#322	—	73	2	no	—
256	#322	—	73	2	no	—
257	C₈²	—	73	2	no	—
258	C₈²	—	73	1	no	—
259	C₈²	—	73	1	no	—
260	C₈²	—	73	2	no	—
261	C₂×#41	—	73	1	no	—
262	#131	—	146	4	no	—
263	#131	—	146	4	no	—
264	C₂×M₁₆	—	73	4	no	—
265	C₂×M₁₆	—	73	4	no	—
266	C₂×M₁₆	—	73	1	no	—
267	C₂×M₁₆	—	73	1	no	—
268	C₂×M₁₆	—	73	1	no	—
269	C₂×M₁₆	—	73	1	no	—
270	C₂×M₁₆	—	73	1	no	—
271	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
272	C₂²×C₈	—	73	1	no	—
273	C₂²×C₈	—	73	1	no	—
274	C₂²×C₈	—	73	4	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂²×C₈	—	73	1	no	—
278	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
279	C₄×Q₈	—	73	2	no	—
280	C₄×D₄	—	73	2	no	—
281	C₄×D₄	—	73	2	no	—
282	C₄×D₄	—	73	2	no	—
283	#117	—	73	1	no	—
284	#117	—	73	1	no	—
285	#117	C₂×#64408	1	1	yes	characteristic
286	C₂×C₄²	—	73	1	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	—	73	1	no	—
289	C₄⋊C₈	—	73	4	no	—
290	C₄⋊C₈	—	73	4	no	—
291	C₄⋊C₈	—	73	4	no	—
292	C₂²⋊C₈	—	73	4	no	—
293	C₂²⋊C₈	—	73	4	no	—
294	C₂²⋊C₈	—	73	4	no	—
295	#97	—	73	4	no	—
296	#97	—	73	4	no	—
297	#97	—	73	1	no	—
298	#97	—	73	1	no	—
299	#97	—	73	1	no	—
300	#97	—	73	1	no	—
301	#97	C₂×#64408	1	1	yes	characteristic
302	#97	C₂×#64408	1	1	yes	characteristic
303	C₄×C₈	—	73	2	no	—
304	C₄×C₈	—	73	2	no	—
305	C₄×C₈	—	73	2	no	—
306	C₄×C₈	—	73	2	no	—
307	C₄×C₈	—	73	4	no	—
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	C₂×#64408	1	1	yes	characteristic
317	C₄×C₈	C₂×#64408	1	1	yes	characteristic
318	#41	—	146	2	no	—
319	#41	—	146	2	no	—
320	C₂×Q₈	—	73	1	no	—
321	C₂×D₄	—	73	1	no	—
322	C₂×D₄	—	73	1	no	—
323	C₂×D₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	2	no	—
326	C₂²×C₄	—	73	1	no	—
327	C₂²×C₄	—	73	2	no	—
328	C₂²×C₄	—	73	2	no	—
329	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	146	2	no	—
332	M₁₆	—	146	2	no	—
333	M₁₆	—	146	2	no	—
334	M₁₆	—	146	2	no	—
335	M₁₆	—	146	8	no	—
336	M₁₆	—	146	8	no	—
337	M₁₆	—	146	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	73	4	no	—
340	C₂×C₈	—	73	1	no	—
341	C₂×C₈	—	73	1	no	—
342	C₂×C₈	—	73	4	no	—
343	C₂×C₈	—	73	4	no	—
344	C₂×C₈	—	73	4	no	—
345	C₂×C₈	—	73	4	no	—
346	C₂×C₈	—	73	4	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	1	no	—
349	C₂×C₈	—	146	2	no	—
350	C₂×C₈	—	146	2	no	—
351	C₂×C₈	—	146	8	no	—
352	C₂×C₈	—	146	2	no	—
353	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
354	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
355	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
356	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
357	C₄⋊C₄	—	73	2	no	—
358	C₄⋊C₄	—	73	2	no	—
359	C₄⋊C₄	C₄×#64408	1	2	yes	—
360	C₂²⋊C₄	—	73	2	no	—
361	C₂²⋊C₄	—	73	2	no	—
362	C₂²⋊C₄	C₄×#64408	1	2	yes	—
363	C₄²	—	73	1	no	—
364	C₄²	—	73	1	no	—
365	C₄²	—	73	2	no	—
366	C₄²	—	73	2	no	—
367	C₄²	—	73	2	no	—
368	C₄²	C₂²×#64408	1	1	yes	characteristic
369	C₄²	C₂²×#64408	1	1	yes	characteristic
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
373	Q₈	—	146	2	no	—
374	D₄	—	146	2	no	—
375	D₄	—	146	2	no	—
376	D₄	—	146	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	73	2	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	2	no	—
382	C₂×C₄	—	73	2	no	—
383	C₂×C₄	—	73	2	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	146	4	no	—
386	C₂×C₄	—	146	4	no	—
387	C₂×C₄	—	146	4	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	—	146	1	no	—
390	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
392	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
393	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	73	8	no	—
397	C₈	—	73	2	no	—
398	C₈	—	73	2	no	—
399	C₈	—	146	4	no	—
400	C₈	—	146	4	no	—
401	C₈	—	146	4	no	—
402	C₈	—	146	1	no	—
403	C₈	—	146	1	no	—
404	C₈	D₇₃⋊M₁₆	1	2	yes	—
405	C₈	D₇₃⋊M₁₆	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	73	2	no	—
409	C₂²	—	146	1	no	—
410	C₂²	—	146	2	no	—
411	C₂²	—	146	2	no	—
412	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	73	2	no	—
417	C₄	—	73	4	no	—
418	C₄	—	146	1	no	—
419	C₄	—	146	2	no	—
420	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
421	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	292	1	no	—
424	C₂	—	146	2	no	—
425	C₂	C₄×D₇₃⋊M₁₆	1	1	yes	characteristic
426	C₂	#131×#64408	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#17335
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #22625155	C₂	semidirect
3. #22625154	C₂	semidirect
4. #22625151	C₂	semidirect
5. #22625150	C₂	semidirect
6. #22625139	C₂	semidirect
7. #22625135	C₂	semidirect
8. C₈×#11924038	C₂	semidirect
9. C₈×#11924037	C₂	semidirect
10. C₈×#11924036	C₂	semidirect
134. C₈×D₇₃	M₁₆	semidirect
135. C₈×D₇₃	M₁₆	semidirect
183. #10596833	#131	semidirect
225. C₇₃	#17335	semidirect

Maximal subgroups

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

subgroup	index
#22626742	2
#22625155	2
#22625154	2
#22625151	2
#22625150	2
#22625139	2
#22625135	2
C₈×#11924038	2
C₈×#11924037	2
C₈×#11924036	2
#22618353	2
#17335	73