Subgroups — C₈×#14556616 #33055396

Order 18688.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14556616	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#22608753	C₂	1	2	yes	maximal, complemented
4	#22608741	C₂	1	2	yes	maximal, complemented
5	C₈×#11924015	C₂	1	2	yes	maximal, complemented
6	C₈×#11924013	C₂	1	2	yes	maximal, complemented
7	#22608684	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608321	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608318	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556616	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₇₃	—	2	1	no	—
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	#17988697	C₄	1	2	yes	—
16	#17988685	C₄	1	2	yes	—
17	C₄×#11924015	C₂²	1	2	yes	—
18	C₄×#11924013	C₂²	1	2	yes	—
19	C₈×D₂₉₂	—	2	1	no	—
20	C₈×D₂₉₂	—	2	1	no	—
21	C₈×D₂₉₂	C₂²	1	2	yes	—
22	C₈×D₂₉₂	C₂²	1	2	yes	—
23	#17988640	C₂²	1	1	yes	characteristic
24	#17988630	C₄	1	1	yes	characteristic
25	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
26	#17988591	C₄	1	1	yes	characteristic
27	#17988588	C₄	1	1	yes	characteristic
28	C₂×#14556503	—	2	1	no	—
29	C₄×#11924012	C₂²	1	1	yes	characteristic
30	#17988339	C₂²	1	2	yes	complemented
31	#17988337	C₂²	1	2	yes	complemented
32	Q₈⋊#10596831	C₂²	1	2	yes	complemented
33	D₄⋊#10596831	C₂²	1	2	yes	complemented
34	#17988314	C₂²	1	2	yes	—
35	#17988314	C₂²	1	2	yes	—
36	#17988309	C₂²	1	2	yes	complemented
37	C₈×#10596831	C₂²	1	2	yes	complemented
38	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
39	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₈×D₄×C₇₃	—	2	1	no	—
42	C₈×D₄×C₇₃	—	2	1	no	—
43	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#431×C₇₃	—	2	1	no	—
46	#431×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	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₇₃	—	2	1	no	—
51	#14556616	C₈	1	8	yes	direct product factor
52	C₂×#11924015	C₂×C₄	1	2	yes	—
53	C₂×#11924013	C₂×C₄	1	2	yes	—
54	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
55	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
56	C₂²×#10596831	—	2	1	no	—
57	C₂×C₈×D₇₃	—	2	2	no	—
58	C₂×C₈×D₇₃	—	2	2	no	—
59	C₂×C₈×D₇₃	—	4	4	no	—
60	C₄×D₂₉₂	—	2	1	no	—
61	C₄×D₂₉₂	—	2	1	no	—
62	C₄×D₂₉₂	C₂×C₄	1	2	yes	—
63	C₄×D₂₉₂	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂×#11924005	—	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	—	2	1	no	—
70	C₄⋊#10596831	C₂³	1	2	yes	—
71	#14556515	C₂×C₄	1	2	yes	—
72	#14556512	C₂×C₄	1	2	yes	—
73	#14556511	C₂×C₄	1	2	yes	—
74	#14556511	C₂×C₄	1	2	yes	—
75	C₂²⋊#10596831	—	2	1	no	—
76	#14556503	—	2	2	no	—
77	#14556503	—	2	2	no	—
78	#14556502	C₂×C₄	1	2	yes	—
79	C₄×#10596831	C₂³	1	2	yes	—
80	C₄×#10596831	C₂³	1	2	yes	—
81	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	—	2	1	no	—
83	C₂²×C₈×C₇₃	—	2	1	no	—
84	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₇₃	—	2	1	no	—
89	C₄×D₄×C₇₃	—	2	1	no	—
90	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
92	#117×C₇₃	—	2	1	no	—
93	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₃	—	2	1	no	—
97	C₄⋊C₈×C₇₃	—	2	1	no	—
98	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₇₃	—	2	1	no	—
101	C₂²⋊C₈×C₇₃	—	2	1	no	—
102	C₂²⋊C₈×C₇₃	—	2	1	no	—
103	C₄×C₈×C₇₃	—	2	1	no	—
104	C₄×C₈×C₇₃	—	2	1	no	—
105	C₄×C₈×C₇₃	—	2	1	no	—
106	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₂³×D₇₃	—	2	1	no	—
111	C₂×D₂₉₂	—	2	1	no	—
112	C₂×D₂₉₂	—	2	2	no	—
113	C₂×D₂₉₂	C₂×C₈	1	4	yes	complemented
114	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	2	2	no	—
117	C₂×C₄×D₇₃	—	2	2	no	—
118	C₂×C₄×D₇₃	—	4	2	no	—
119	C₂×C₄×D₇₃	—	4	2	no	—
120	#11924015	C₂×C₈	1	8	yes	complemented
121	#11924013	C₂×C₈	1	8	yes	complemented
122	#11924012	—	2	2	no	—
123	#11924012	C₂×C₈	1	4	yes	complemented
124	C₂×#10596831	—	2	2	no	—
125	C₂×#10596831	—	2	2	no	—
126	C₂×#10596831	—	4	2	no	—
127	C₂×#10596831	C₂²×C₄	1	2	yes	—
128	C₂×#10596831	C₂²×C₄	1	2	yes	—
129	C₈×D₇₃	—	4	4	no	—
130	C₈×D₇₃	—	4	4	no	—
131	C₄⋊Dic₇₃	—	2	1	no	—
132	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
133	#11924005	—	2	2	no	—
134	#11924005	—	2	2	no	—
135	#41×C₇₃	—	2	2	no	—
136	#41×C₇₃	C₂×C₈	1	4	yes	complemented
137	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×D₄×C₇₃	—	2	1	no	—
139	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	—	2	1	no	—
141	C₂²×C₄×C₇₃	—	2	1	no	—
142	C₂²×C₄×C₇₃	—	2	1	no	—
143	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	2	1	no	—
149	C₂×C₈×C₇₃	—	4	1	no	—
150	C₂×C₈×C₇₃	—	4	2	no	—
151	C₂×C₈×C₇₃	—	4	2	no	—
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	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	2	1	no	—
158	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₇₃	—	2	1	no	—
161	C₂²⋊C₄×C₇₃	—	2	1	no	—
162	C₂²⋊C₄×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	—	2	1	no	—
164	C₄²×C₇₃	—	2	1	no	—
165	C₄²×C₇₃	—	2	1	no	—
166	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇₃	#41	1	1	yes	characteristic
169	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
170	C₂³×C₇₃	—	2	1	no	—
171	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
172	C₂²×D₇₃	—	2	2	no	—
173	C₂²×D₇₃	—	2	4	no	—
174	C₂²×D₇₃	—	4	2	no	—
175	C₂²×D₇₃	—	4	2	no	—
176	Q₈×C₇₃	—	2	1	no	—
177	Q₈×C₇₃	C₂²×C₈	1	2	yes	complemented
178	D₄×C₇₃	—	2	4	no	—
179	D₄×C₇₃	—	2	1	no	—
180	D₄×C₇₃	C₂²×C₈	1	2	yes	complemented
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	1	no	—
184	C₂×C₄×C₇₃	—	2	4	no	—
185	C₂×C₄×C₇₃	—	2	1	no	—
186	C₂×C₄×C₇₃	—	2	1	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	1	no	—
190	C₂×C₄×C₇₃	—	4	1	no	—
191	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
195	C₂×C₄×C₇₃	#131	1	2	yes	—
196	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₇₃	—	2	2	no	—
200	C₂×Dic₇₃	—	4	2	no	—
201	D₂₉₂	—	2	2	no	—
202	D₂₉₂	—	2	4	no	—
203	D₂₉₂	C₂²×C₈	1	4	yes	—
204	C₄×D₇₃	—	4	4	no	—
205	C₄×D₇₃	—	4	2	no	—
206	C₄×D₇₃	—	4	2	no	—
207	C₈×C₇₃	—	2	1	no	—
208	C₈×C₇₃	—	2	1	no	—
209	C₈×C₇₃	—	2	1	no	—
210	C₈×C₇₃	—	4	1	no	—
211	C₈×C₇₃	—	4	1	no	—
212	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
213	#10596831	—	2	2	no	—
214	#10596831	—	4	2	no	—
215	#10596831	—	4	2	no	—
216	#10596831	C₂²×C₈	1	4	yes	complemented
217	C₂²×C₇₃	—	2	1	no	—
218	C₂²×C₇₃	—	2	1	no	—
219	C₂²×C₇₃	—	2	2	no	—
220	C₂²×C₇₃	—	4	1	no	—
221	C₂²×C₇₃	—	4	1	no	—
222	C₂²×C₇₃	C₈×D₄	1	2	yes	—
223	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂×D₇₃	—	2	4	no	—
225	C₂×D₇₃	—	4	8	no	—
226	C₂×D₇₃	—	4	2	no	—
227	C₂×D₇₃	—	4	2	no	—
228	C₄×C₇₃	—	2	2	no	—
229	C₄×C₇₃	—	2	1	no	—
230	C₄×C₇₃	—	2	1	no	—
231	C₄×C₇₃	—	2	1	no	—
232	C₄×C₇₃	—	4	1	no	—
233	C₄×C₇₃	—	4	1	no	—
234	C₄×C₇₃	C₈×D₄	1	2	yes	—
235	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
236	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
237	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₄×C₇₃	#575	1	1	yes	characteristic
239	Dic₇₃	—	4	2	no	—
240	C₈×AGL(1,ℤ/8)	—	73	1	no	maximal, Sylow
241	C₂×C₇₃	—	2	2	no	—
242	C₂×C₇₃	—	4	2	no	—
243	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
244	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₇₃	#2955	1	1	yes	characteristic
246	D₇₃	—	4	4	no	—
247	C₈×#41	D₇₃	1	1	yes	characteristic, complemented
248	C₄×AGL(1,ℤ/8)	—	73	1	no	—
249	C₂×C₈×D₄	—	73	1	no	—
250	#1580	—	73	2	no	—
251	SD₁₆⋊C₈	—	73	2	no	—
252	C₈×SD₁₆	—	73	2	no	—
253	C₈×D₈	—	73	2	no	—
254	#1565	—	73	1	no	—
255	#1478	—	73	1	no	—
256	#1477	—	73	1	no	—
257	C₈×M₁₆	—	73	1	no	—
258	C₇₃	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
259	C₂×AGL(1,ℤ/8)	—	73	1	no	—
260	C₂³×C₈	—	146	1	no	—
261	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
262	C₂×C₄×D₄	—	73	1	no	—
263	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
264	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
265	#442	—	73	2	no	—
266	#440	—	73	2	no	—
267	C₄×SD₁₆	—	73	2	no	—
268	C₄×D₈	—	73	2	no	—
269	C₈×D₄	—	2	1	no	—
270	C₈×D₄	—	2	1	no	—
271	C₈×D₄	—	73	2	no	—
272	C₈×D₄	—	73	2	no	—
273	C₈×D₄	—	146	1	no	—
274	C₈×D₄	—	146	1	no	—
275	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
276	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
277	#431	—	2	1	no	—
278	#431	—	73	1	no	—
279	#431	C₂×D₇₃	1	1	yes	characteristic
280	#428	—	73	1	no	—
281	C₂×C₄⋊C₈	—	73	1	no	—
282	#418	—	73	1	no	—
283	#417	—	73	1	no	—
284	C₂×C₂²⋊C₈	—	146	1	no	—
285	C₄×M₁₆	—	73	1	no	—
286	C₂×C₄×C₈	—	2	1	no	—
287	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
288	#335	—	73	2	no	—
289	#334	—	73	2	no	—
290	Q₈⋊C₈	—	73	2	no	—
291	D₄⋊C₈	—	73	2	no	—
292	D₄⋊C₈	—	73	2	no	—
293	D₄⋊C₈	—	73	2	no	—
294	#322	—	73	2	no	—
295	C₈²	—	73	2	no	—
296	C₂×#41	C₄×D₇₃	1	1	yes	characteristic
297	C₂²×D₄	—	73	1	no	—
298	C₂³×C₄	—	146	1	no	—
299	AGL(1,ℤ/8)	—	73	8	no	—
300	C₂×SD₁₆	—	73	2	no	—
301	C₂×D₈	—	73	2	no	—
302	C₂×M₁₆	—	73	1	no	—
303	C₂×M₁₆	—	73	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	292	4	no	—
307	C₂²×C₈	—	146	1	no	—
308	C₂²×C₈	—	146	2	no	—
309	C₂²×C₈	—	146	2	no	—
310	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
311	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
312	C₄×Q₈	C₄×D₇₃	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	73	2	no	—
317	C₄×D₄	—	73	2	no	—
318	C₄×D₄	—	146	1	no	—
319	C₄×D₄	—	146	1	no	—
320	C₄×D₄	C₄×D₇₃	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₄×D₇₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	—	73	1	no	—
325	C₂×C₂²⋊C₄	—	146	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
328	#107	—	73	2	no	—
329	#106	—	73	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	73	2	no	—
333	C₄⋊C₈	—	146	1	no	—
334	C₄⋊C₈	—	146	1	no	—
335	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
337	#103	—	73	2	no	—
338	#102	—	73	2	no	—
339	#102	—	73	2	no	—
340	#102	—	73	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	146	1	no	—
345	C₂²⋊C₈	—	146	2	no	—
346	C₂²⋊C₈	—	146	2	no	—
347	#97	—	73	2	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	73	2	no	—
352	C₄×C₈	—	73	2	no	—
353	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
354	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
357	C₂⁴	—	146	1	no	—
358	#41	—	2	2	no	—
359	#41	C₈×D₇₃	1	4	yes	complemented
360	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	73	4	no	—
363	C₂×D₄	—	73	2	no	—
364	C₂×D₄	—	146	1	no	—
365	C₂×D₄	—	146	2	no	—
366	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	292	2	no	—
371	C₂²×C₄	—	292	2	no	—
372	C₂²×C₄	—	146	1	no	—
373	C₂²×C₄	—	146	2	no	—
374	C₂²×C₄	—	146	2	no	—
375	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
377	C₂²×C₄	#11924028	1	1	yes	characteristic
378	SD₁₆	—	73	8	no	—
379	D₈	—	73	8	no	—
380	M₁₆	—	73	4	no	—
381	M₁₆	—	146	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	292	4	no	—
389	C₂×C₈	—	292	2	no	—
390	C₂×C₈	—	292	4	no	—
391	C₂×C₈	—	73	2	no	—
392	C₂×C₈	—	73	2	no	—
393	C₂×C₈	—	146	2	no	—
394	C₂×C₈	—	146	2	no	—
395	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	73	2	no	—
402	C₄⋊C₄	—	146	1	no	—
403	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
404	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	146	2	no	—
409	C₂²⋊C₄	—	146	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
414	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
415	C₄²	#11924028	1	1	yes	characteristic
416	C₄²	C₂³×D₇₃	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	292	2	no	—
419	C₂³	—	292	2	no	—
420	C₂³	—	146	4	no	—
421	C₂³	—	146	2	no	—
422	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂×C₈×D₇₃	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	1	no	—
427	D₄	—	73	4	no	—
428	D₄	—	146	4	no	—
429	D₄	—	146	2	no	—
430	D₄	C₂×C₈×D₇₃	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	292	4	no	—
442	C₂×C₄	—	292	2	no	—
443	C₂×C₄	—	292	2	no	—
444	C₂×C₄	—	292	2	no	—
445	C₂×C₄	—	146	2	no	—
446	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
447	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
450	C₂×C₄	#14556597	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	292	2	no	—
460	C₈	—	292	2	no	—
461	C₈	—	73	4	no	—
462	C₈	—	146	2	no	—
463	C₈	#14556616	1	2	yes	direct product factor
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	292	8	no	—
470	C₂²	—	292	2	no	—
471	C₂²	—	292	2	no	—
472	C₂²	—	146	4	no	—
473	C₂²	C₈×C₂²⋊D₇₃	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	292	2	no	—
482	C₄	C₈×C₂²⋊D₇₃	1	2	yes	—
483	C₄	C₂²×C₈×D₇₃	1	1	yes	characteristic
484	C₄	C₂×#14556597	1	1	yes	characteristic
485	C₄	C₂×#14556616	1	1	yes	characteristic
486	C₄	#17989385	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	292	4	no	—
490	C₂	C₂×C₈×C₂²⋊D₇₃	1	1	yes	characteristic
491	C₂	C₄×#14556616	1	1	yes	characteristic
492	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	C₈×#41×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#14556616	C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₈×#41	D₇₃
hypocenter	C₇₃	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₂₉₂	C₂	semidirect
3. #22608753	C₂	semidirect
4. #22608741	C₂	semidirect
5. C₈×#11924015	C₂	semidirect
6. C₈×#11924013	C₂	semidirect
7. #22608684	C₂	semidirect
8. #22608321	C₂	semidirect
9. #22608318	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₈×#41×C₇₃	C₂	semidirect
30. #17988339	C₂²	semidirect
31. #17988337	C₂²	semidirect
32. Q₈⋊#10596831	C₂²	semidirect
33. D₄⋊#10596831	C₂²	semidirect
36. #17988309	C₂²	semidirect
37. C₈×#10596831	C₂²	semidirect
39. C₈×Q₈×C₇₃	C₂²	semidirect
40. C₈×Q₈×C₇₃	C₂²	semidirect
43. C₈×D₄×C₇₃	C₂²	semidirect
44. C₈×D₄×C₇₃	C₂²	semidirect
51. #14556616	C₈	direct (N × H)
113. C₂×D₂₉₂	C₂×C₈	semidirect
120. #11924015	C₂×C₈	semidirect
121. #11924013	C₂×C₈	semidirect
123. #11924012	C₂×C₈	semidirect
136. #41×C₇₃	C₂×C₈	semidirect
177. Q₈×C₇₃	C₂²×C₈	semidirect
180. D₄×C₇₃	C₂²×C₈	semidirect
212. C₈×C₇₃	AGL(1,ℤ/8)	semidirect
216. #10596831	C₂²×C₈	semidirect
247. C₈×#41	D₇₃	semidirect
258. C₇₃	C₈×AGL(1,ℤ/8)	semidirect
263. C₈×Q₈	C₂×D₇₃	semidirect
264. C₈×Q₈	C₂×D₇₃	semidirect
275. C₈×D₄	C₂×D₇₃	semidirect
276. C₈×D₄	C₂×D₇₃	semidirect
359. #41	C₈×D₇₃	semidirect
424. Q₈	C₂×C₈×D₇₃	semidirect
430. D₄	C₂×C₈×D₇₃	semidirect
463. C₈	#14556616	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#14556616	2
C₂×C₈×D₂₉₂	2
#22608753	2
#22608741	2
C₈×#11924015	2
C₈×#11924013	2
#22608684	2
#22608321	2
#22608318	2
C₈×#11924012	2
C₈×#41×C₇₃	2
C₈×AGL(1,ℤ/8)	73

Subgroups — C8×#14556616 #33055396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14556616 #33055396