Subgroups — C₈×#14556622 #33055409

Order 18688.

714 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11924028	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556622	C₂	1	1	yes	maximal, characteristic
3	#22608748	C₂	1	2	yes	maximal, complemented
4	#22608741	C₂	1	2	yes	maximal, complemented
5	C₈×#11924018	C₂	1	2	yes	maximal, complemented
6	C₈×#11924015	C₂	1	2	yes	maximal, complemented
7	#22608681	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608326	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608316	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556622	C₄	1	1	yes	characteristic
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
15	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
16	#17988692	C₄	1	2	yes	—
17	#17988685	C₄	1	2	yes	—
18	C₄×#11924018	C₂²	1	2	yes	—
19	C₄×#11924015	C₂²	1	2	yes	—
20	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
21	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₇₃	—	2	1	no	—
23	C₈×C₂²⋊D₇₃	—	2	1	no	—
24	#17988640	C₂²	1	1	yes	characteristic
25	#17988640	C₂²	1	1	yes	characteristic
26	#17988638	—	2	1	no	—
27	#17988627	C₄	1	1	yes	characteristic
28	#17988596	C₄	1	1	yes	characteristic
29	#17988586	C₄	1	1	yes	characteristic
30	C₄×#11924012	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₇₃	—	2	1	no	—
32	#17988339	C₂²	1	2	yes	—
33	#17988337	C₂²	1	2	yes	—
34	Q₈⋊#10596831	C₂²	1	2	yes	—
35	Q₈⋊#10596831	C₂²	1	2	yes	—
36	#17988317	C₂²	1	2	yes	—
37	#17988314	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	C₈×#10596831	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₇₃	—	2	1	no	—
42	C₈×Q₈×C₇₃	—	2	1	no	—
43	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
44	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₇₃	—	2	1	no	—
48	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
50	#14556622	C₈	1	8	yes	direct product factor
51	C₂×#11924018	C₂×C₄	1	2	yes	—
52	C₂×#11924015	C₂×C₄	1	2	yes	—
53	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
54	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇₃	—	2	1	no	—
56	C₂×C₈×D₇₃	—	2	1	no	—
57	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
59	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
60	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
61	C₄×C₂²⋊D₇₃	—	2	1	no	—
62	C₄×C₂²⋊D₇₃	—	2	1	no	—
63	#14556550	C₂×C₄	1	1	yes	characteristic
64	#14556548	—	2	1	no	—
65	C₄²×D₇₃	—	2	1	no	—
66	#14556524	C₂×C₄	1	2	yes	—
67	#14556522	C₂×C₄	1	2	yes	—
68	C₄⋊#10596831	—	2	1	no	—
69	C₄⋊#10596831	C₂³	1	1	yes	characteristic
70	C₄⋊#10596831	C₂³	1	1	yes	characteristic
71	#14556520	—	2	1	no	—
72	#14556520	—	2	1	no	—
73	#14556515	C₂×C₄	1	2	yes	—
74	#14556515	C₂×C₄	1	2	yes	—
75	#14556514	C₂×C₄	1	2	yes	—
76	#14556511	C₂×C₄	1	2	yes	—
77	C₂²⋊#10596831	—	2	1	no	—
78	C₂²⋊#10596831	—	2	1	no	—
79	#14556503	—	2	1	no	—
80	#14556503	—	2	1	no	—
81	#14556502	C₂×C₄	1	2	yes	—
82	C₄×#10596831	—	2	1	no	—
83	C₄×#10596831	C₂³	1	2	yes	—
84	C₄×#10596831	C₂³	1	2	yes	—
85	C₈×Dic₇₃	—	2	1	no	—
86	C₈×Dic₇₃	—	2	1	no	—
87	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	—	2	1	no	—
89	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₇₃	—	2	1	no	—
92	C₄×Q₈×C₇₃	—	2	1	no	—
93	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	—	2	1	no	—
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	—	2	2	no	—
100	C₄⋊C₈×C₇₃	—	2	2	no	—
101	C₄⋊C₈×C₇₃	—	2	1	no	—
102	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
103	C₄×C₈×C₇₃	—	2	2	no	—
104	C₄×C₈×C₇₃	—	2	2	no	—
105	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	#11924028	—	2	2	no	—
110	#11924028	C₂×C₈	1	4	yes	—
111	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	#11924018	C₂×C₈	1	8	yes	complemented
118	#11924015	C₂×C₈	1	8	yes	complemented
119	#11924012	—	2	2	no	—
120	#11924012	C₂×C₈	1	4	yes	complemented
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	1	no	—
123	C₂×#10596831	—	2	2	no	—
124	C₂×#10596831	C₂²×C₄	1	2	yes	—
125	C₂×#10596831	C₂²×C₄	1	2	yes	—
126	C₈×D₇₃	—	4	2	no	—
127	C₈×D₇₃	—	4	2	no	—
128	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
130	#11924007	—	2	1	no	—
131	#11924007	—	2	1	no	—
132	C₂²⋊Dic₇₃	—	2	1	no	—
133	#11924005	—	2	1	no	—
134	#11924005	—	2	1	no	—
135	C₄×Dic₇₃	—	2	1	no	—
136	C₄×Dic₇₃	—	2	1	no	—
137	C₄×Dic₇₃	—	2	1	no	—
138	C₂×Q₈×C₇₃	—	2	1	no	—
139	C₂×Q₈×C₇₃	—	2	2	no	—
140	C₂×Q₈×C₇₃	C₂×C₈	1	4	yes	complemented
141	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₇₃	—	2	1	no	—
143	C₂²×C₄×C₇₃	—	2	1	no	—
144	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	4	1	no	—
150	C₂×C₈×C₇₃	—	4	2	no	—
151	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	2	2	no	—
158	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇₃	#41	1	1	yes	characteristic
164	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
165	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₇₃	—	2	1	no	—
167	Q₈×C₇₃	—	2	2	no	—
168	Q₈×C₇₃	—	2	4	no	—
169	Q₈×C₇₃	C₂²×C₈	1	4	yes	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	4	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	4	1	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
181	C₂×C₄×C₇₃	#131	1	2	yes	—
182	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₇₃	—	2	4	no	—
186	C₂×Dic₇₃	—	2	1	no	—
187	C₂×Dic₇₃	—	2	1	no	—
188	C₂×Dic₇₃	—	2	1	no	—
189	D₂₉₂	—	2	1	no	—
190	D₂₉₂	C₂²×C₈	1	2	yes	—
191	C₄×D₇₃	—	2	4	no	—
192	C₄×D₇₃	—	4	2	no	—
193	C₄×D₇₃	—	4	1	no	—
194	C₄×D₇₃	—	4	1	no	—
195	Dic₁₄₆	—	2	1	no	—
196	Dic₁₄₆	C₂²×C₈	1	2	yes	—
197	C₈×C₇₃	—	2	1	no	—
198	C₈×C₇₃	—	2	1	no	—
199	C₈×C₇₃	—	2	1	no	—
200	C₈×C₇₃	—	4	2	no	—
201	C₈×C₇₃	#137	1	2	yes	complemented
202	#10596831	—	2	2	no	—
203	#10596831	—	4	2	no	—
204	#10596831	—	4	1	no	—
205	#10596831	—	4	1	no	—
206	#10596831	C₂²×C₈	1	4	yes	—
207	C₂²×C₇₃	—	2	1	no	—
208	C₂²×C₇₃	—	2	1	no	—
209	C₂²×C₇₃	C₈×D₄	1	2	yes	—
210	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₇₃	—	2	2	no	—
212	C₂×D₇₃	—	4	1	no	—
213	C₂×D₇₃	—	4	1	no	—
214	C₄×C₇₃	—	2	4	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	—	2	1	no	—
217	C₄×C₇₃	—	2	1	no	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	C₈×D₄	1	2	yes	—
220	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
221	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
222	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
223	C₄×C₇₃	#575	1	1	yes	characteristic
224	Dic₇₃	—	2	2	no	—
225	Dic₇₃	—	4	1	no	—
226	Dic₇₃	—	4	1	no	—
227	C₈×#137	—	73	1	no	maximal, Sylow
228	C₂×C₇₃	—	2	2	no	—
229	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
230	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
231	C₂×C₇₃	#2955	1	1	yes	characteristic
232	D₇₃	—	4	2	no	—
233	C₈×#41	—	73	1	no	—
234	C₂×C₈×Q₈	D₇₃	1	1	yes	characteristic, complemented
235	C₄×#137	—	73	1	no	—
236	#1579	—	73	2	no	—
237	SD₁₆⋊C₈	—	73	2	no	—
238	C₈×Q₁₆	—	73	2	no	—
239	C₈×SD₁₆	—	73	2	no	—
240	#1565	—	73	1	no	—
241	#1479	—	73	1	no	—
242	#1477	—	73	1	no	—
243	C₈×M₁₆	—	73	1	no	—
244	C₇₃	C₈×#137	1	1	yes	characteristic, complemented, Sylow
245	C₂×#137	—	73	1	no	—
246	C₄×#41	—	73	1	no	—
247	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
248	C₈×Q₈	—	2	1	no	—
249	C₈×Q₈	—	2	1	no	—
250	C₈×Q₈	—	73	1	no	—
251	C₈×Q₈	—	73	1	no	—
252	C₈×Q₈	C₂×D₇₃	1	2	yes	—
253	C₈×Q₈	C₂×D₇₃	1	2	yes	—
254	#441	—	73	2	no	—
255	#440	—	73	2	no	—
256	C₄×Q₁₆	—	73	2	no	—
257	C₄×SD₁₆	—	73	2	no	—
258	C₈×D₄	—	73	1	no	—
259	C₈×D₄	—	73	1	no	—
260	C₈×D₄	—	146	1	no	—
261	C₈×D₄	—	146	1	no	—
262	#431	—	73	1	no	—
263	#431	—	73	1	no	—
264	#431	—	146	1	no	—
265	#428	—	73	1	no	—
266	C₂×C₄⋊C₈	—	2	1	no	—
267	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
268	#419	—	73	1	no	—
269	#417	—	73	1	no	—
270	C₄×M₁₆	—	73	1	no	—
271	C₂×C₄×C₈	—	2	1	no	—
272	C₂×C₄×C₈	—	146	1	no	—
273	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
274	#335	—	73	2	no	—
275	#334	—	73	2	no	—
276	Q₈⋊C₈	—	73	2	no	—
277	Q₈⋊C₈	—	73	2	no	—
278	Q₈⋊C₈	—	73	2	no	—
279	D₄⋊C₈	—	73	2	no	—
280	#322	—	73	2	no	—
281	C₈²	—	73	2	no	—
282	C₂×#41	—	73	1	no	—
283	C₂²×Q₈	C₄×D₇₃	1	1	yes	characteristic
284	#137	—	73	8	no	—
285	C₂×Q₁₆	—	73	2	no	—
286	C₂×SD₁₆	—	73	2	no	—
287	C₂×M₁₆	—	73	1	no	—
288	C₂×M₁₆	—	73	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	146	1	no	—
291	C₂²×C₈	—	146	1	no	—
292	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	73	1	no	—
297	C₄×Q₈	—	73	1	no	—
298	C₄×Q₈	C₄×D₇₃	1	2	yes	—
299	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
300	C₄×D₄	—	73	1	no	—
301	C₄×D₄	—	73	1	no	—
302	C₄×D₄	—	146	1	no	—
303	C₄×D₄	—	146	1	no	—
304	#117	—	73	1	no	—
305	#117	—	146	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	146	1	no	—
310	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
311	#107	—	73	2	no	—
312	#106	—	73	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	73	1	no	—
317	C₄⋊C₈	—	73	1	no	—
318	C₄⋊C₈	—	146	1	no	—
319	C₄⋊C₈	—	146	1	no	—
320	C₄⋊C₈	—	146	1	no	—
321	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
322	#103	—	73	2	no	—
323	#103	—	73	2	no	—
324	#103	—	73	2	no	—
325	#102	—	73	2	no	—
326	C₂²⋊C₈	—	146	1	no	—
327	C₂²⋊C₈	—	146	1	no	—
328	C₂²⋊C₈	—	146	1	no	—
329	C₂²⋊C₈	—	146	1	no	—
330	#97	—	73	2	no	—
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	73	2	no	—
334	C₄×C₈	—	73	2	no	—
335	C₄×C₈	—	146	1	no	—
336	C₄×C₈	—	146	1	no	—
337	C₄×C₈	—	146	1	no	—
338	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
339	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
342	#41	—	73	4	no	—
343	#41	—	146	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	73	1	no	—
347	C₂×Q₈	C₈×D₇₃	1	4	yes	complemented
348	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
349	C₂×D₄	—	73	1	no	—
350	C₂×D₄	—	146	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	146	1	no	—
354	C₂²×C₄	—	146	1	no	—
355	C₂²×C₄	—	146	1	no	—
356	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
358	C₂²×C₄	#11924028	1	1	yes	characteristic
359	Q₁₆	—	73	8	no	—
360	SD₁₆	—	73	8	no	—
361	M₁₆	—	73	4	no	—
362	M₁₆	—	146	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	292	2	no	—
368	C₂×C₈	—	292	2	no	—
369	C₂×C₈	—	73	2	no	—
370	C₂×C₈	—	73	2	no	—
371	C₂×C₈	—	146	1	no	—
372	C₂×C₈	—	146	1	no	—
373	C₂×C₈	—	146	2	no	—
374	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
377	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	73	1	no	—
382	C₄⋊C₄	—	73	1	no	—
383	C₄⋊C₄	—	146	1	no	—
384	C₄⋊C₄	—	146	1	no	—
385	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
386	C₂²⋊C₄	—	146	1	no	—
387	C₂²⋊C₄	—	146	1	no	—
388	C₂²⋊C₄	—	146	1	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	146	1	no	—
392	C₄²	—	146	1	no	—
393	C₄²	—	146	1	no	—
394	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
395	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
396	C₄²	#11924028	1	1	yes	characteristic
397	C₄²	C₂³×D₇₃	1	1	yes	characteristic
398	C₂³	—	146	1	no	—
399	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	73	2	no	—
403	Q₈	—	146	1	no	—
404	Q₈	C₂×C₈×D₇₃	1	4	yes	—
405	D₄	—	73	2	no	—
406	D₄	—	146	4	no	—
407	D₄	—	146	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	292	2	no	—
416	C₂×C₄	—	292	1	no	—
417	C₂×C₄	—	292	1	no	—
418	C₂×C₄	—	146	1	no	—
419	C₂×C₄	—	146	1	no	—
420	C₂×C₄	—	146	1	no	—
421	C₂×C₄	—	146	4	no	—
422	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
423	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
426	C₂×C₄	#14556597	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	292	2	no	—
435	C₈	—	292	1	no	—
436	C₈	—	292	1	no	—
437	C₈	—	73	4	no	—
438	C₈	—	146	2	no	—
439	C₈	#14556622	1	2	yes	direct product factor
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	292	1	no	—
443	C₂²	—	292	1	no	—
444	C₂²	—	146	2	no	—
445	C₂²	C₈×C₂²⋊D₇₃	1	2	yes	—
446	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	292	1	no	—
453	C₄	—	292	1	no	—
454	C₄	—	146	2	no	—
455	C₄	C₈×C₂²⋊D₇₃	1	2	yes	—
456	C₄	C₂²×C₈×D₇₃	1	1	yes	characteristic
457	C₄	C₂×#14556597	1	1	yes	characteristic
458	C₄	C₂×#14556622	1	1	yes	characteristic
459	C₄	#17989385	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	292	2	no	—
462	C₂	C₂×C₈×C₂²⋊D₇₃	1	1	yes	characteristic
463	C₂	C₄×#14556622	1	1	yes	characteristic
464	C₂	#22618832	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×C₈×Q₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₂×C₈×Q₈	D₇₃
hypocenter	C₇₃	C₈×#137
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. #22608748	C₂	semidirect
4. #22608741	C₂	semidirect
5. C₈×#11924018	C₂	semidirect
6. C₈×#11924015	C₂	semidirect
7. #22608681	C₂	semidirect
8. #22608326	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₂×C₈×Q₈×C₇₃	C₂	semidirect
50. #14556622	C₈	direct (N × H)
117. #11924018	C₂×C₈	semidirect
118. #11924015	C₂×C₈	semidirect
120. #11924012	C₂×C₈	semidirect
140. C₂×Q₈×C₇₃	C₂×C₈	semidirect
201. C₈×C₇₃	#137	semidirect
234. C₂×C₈×Q₈	D₇₃	semidirect
244. C₇₃	C₈×#137	semidirect
347. C₂×Q₈	C₈×D₇₃	semidirect
439. C₈	#14556622	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#11924028	2
C₄×#14556622	2
#22608748	2
#22608741	2
C₈×#11924018	2
C₈×#11924015	2
#22608681	2
#22608326	2
#22608316	2
C₈×#11924012	2
C₂×C₈×Q₈×C₇₃	2
C₈×#137	73

Subgroups — C8×#14556622 #33055409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14556622 #33055409