Subgroups — #36524031

Order 22784.

738 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	C₈×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668038	C₂	1	1	yes	maximal, characteristic
3	#26019128	C₂	1	2	yes	maximal, complemented
4	#26019114	C₂	1	2	yes	maximal, complemented
5	#26019093	C₂	1	2	yes	maximal, complemented
6	#26019079	C₂	1	2	yes	maximal, complemented
7	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018643	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018637	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#436×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668038	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
15	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
16	#19151708	C₄	1	2	yes	—
17	#19151698	C₄	1	2	yes	—
18	C₄×#13083562	C₂²	1	2	yes	—
19	C₄×#13083559	C₂²	1	2	yes	—
20	C₈×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
21	C₈×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
22	C₈×C₂²⋊D₈₉	—	2	1	no	—
23	C₈×C₂²⋊D₈₉	—	2	1	no	—
24	#19151651	C₂²	1	1	yes	characteristic
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151649	—	2	1	no	—
27	#19151638	C₄	1	1	yes	characteristic
28	#19151603	C₄	1	1	yes	characteristic
29	#19151597	C₄	1	1	yes	characteristic
30	C₄×#13083558	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	—	2	1	no	—
32	#19151350	C₂²	1	2	yes	complemented
33	#19151348	C₂²	1	2	yes	complemented
34	#19151328	C₂²	1	2	yes	complemented
35	D₄⋊#10623494	C₂²	1	2	yes	—
36	D₄⋊#10623494	C₂²	1	2	yes	—
37	#19151325	C₂²	1	2	yes	complemented
38	#19151320	C₂²	1	2	yes	complemented
39	#19151319	C₂²	1	2	yes	complemented
40	C₂²×M₁₆×C₈₉	—	2	1	no	—
41	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	#436×C₈₉	—	2	1	no	—
43	#436×C₈₉	—	2	1	no	—
44	#436×C₈₉	C₂²	1	2	yes	—
45	#436×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	#15668038	—	2	4	no	—
51	C₂×#13083562	C₂×C₄	1	2	yes	—
52	C₂×#13083559	C₂×C₄	1	2	yes	—
53	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	1	no	—
57	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
59	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
60	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
61	C₄×C₂²⋊D₈₉	—	2	1	no	—
62	C₄×C₂²⋊D₈₉	—	2	1	no	—
63	#15667971	C₂×C₄	1	1	yes	characteristic
64	#15667969	—	2	1	no	—
65	C₄²×D₈₉	—	2	1	no	—
66	#15667945	C₂×C₄	1	2	yes	—
67	#15667943	C₂×C₄	1	2	yes	—
68	C₄⋊#10623494	—	2	1	no	—
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667941	—	2	1	no	—
72	#15667941	—	2	1	no	—
73	#15667935	C₂×C₄	1	2	yes	—
74	#15667933	C₂×C₄	1	2	yes	—
75	#15667933	C₂×C₄	1	2	yes	—
76	#15667932	C₂×C₄	1	2	yes	—
77	C₂²⋊#10623494	—	2	1	no	—
78	C₂²⋊#10623494	—	2	1	no	—
79	#15667924	—	2	1	no	—
80	#15667924	—	2	1	no	—
81	#15667923	C₂×C₄	1	2	yes	—
82	C₄×#10623494	—	2	1	no	—
83	C₄×#10623494	C₂³	1	2	yes	—
84	C₄×#10623494	C₂³	1	2	yes	—
85	C₈×Dic₈₉	—	2	1	no	—
86	C₈×Dic₈₉	—	2	1	no	—
87	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	—	2	1	no	—
89	C₂×M₁₆×C₈₉	—	2	2	no	—
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂×M₁₆×C₈₉	—	4	4	no	—
92	C₂²×C₈×C₈₉	—	2	1	no	—
93	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₄×D₄×C₈₉	—	2	1	no	—
96	C₄×D₄×C₈₉	—	2	1	no	—
97	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	—	2	1	no	—
103	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₈₉	—	2	2	no	—
105	C₂²⋊C₈×C₈₉	—	2	2	no	—
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#13083574	—	2	2	no	—
111	#13083574	M₁₆	1	4	yes	complemented
112	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	#13083562	—	2	4	no	—
119	#13083559	—	2	4	no	—
120	#13083558	—	2	2	no	—
121	#13083558	—	2	2	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	C₂²×C₄	1	2	yes	—
126	C₂×#10623494	C₂²×C₄	1	2	yes	—
127	C₈×D₈₉	—	4	2	no	—
128	C₈×D₈₉	—	4	2	no	—
129	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	#13083553	—	2	1	no	—
132	#13083553	—	2	1	no	—
133	C₂²⋊Dic₈₉	—	2	1	no	—
134	#13083551	—	2	1	no	—
135	#13083551	—	2	1	no	—
136	C₄×Dic₈₉	—	2	1	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₂⁴×C₈₉	—	2	1	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	—	2	2	no	—
143	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	2	no	—
146	C₂²×C₄×C₈₉	—	2	2	no	—
147	C₂²×C₄×C₈₉	—	4	2	no	—
148	C₂²×C₄×C₈₉	—	4	2	no	—
149	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	M₁₆×C₈₉	—	4	4	no	—
153	M₁₆×C₈₉	—	4	4	no	—
154	C₂×C₈×C₈₉	—	2	2	no	—
155	C₂×C₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	4	1	no	—
157	C₂×C₈×C₈₉	—	4	2	no	—
158	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
164	C₂²⋊C₄×C₈₉	—	2	2	no	—
165	C₂²⋊C₄×C₈₉	—	2	2	no	—
166	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	#41	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	—	4	2	no	—
172	C₂³×C₈₉	—	4	2	no	—
173	C₂³×C₈₉	—	4	2	no	—
174	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂²×D₈₉	—	2	1	no	—
176	D₄×C₈₉	—	2	2	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	4	no	—
184	C₂×C₄×C₈₉	—	4	2	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₈₉	#131	1	2	yes	—
192	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
195	C₂²⋊D₈₉	—	2	4	no	—
196	C₂×Dic₈₉	—	2	1	no	—
197	C₂×Dic₈₉	—	2	1	no	—
198	C₂×Dic₈₉	—	2	1	no	—
199	D₃₅₆	—	2	1	no	—
200	D₃₅₆	C₂×M₁₆	1	2	yes	complemented
201	C₄×D₈₉	—	2	4	no	—
202	C₄×D₈₉	—	4	2	no	—
203	C₄×D₈₉	—	4	1	no	—
204	C₄×D₈₉	—	4	1	no	—
205	Dic₁₇₈	—	2	1	no	—
206	Dic₁₇₈	C₂×M₁₆	1	2	yes	complemented
207	C₈×C₈₉	—	2	1	no	—
208	C₈×C₈₉	—	2	1	no	—
209	C₈×C₈₉	—	2	1	no	—
210	C₈×C₈₉	—	4	2	no	—
211	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
212	#10623494	—	2	2	no	—
213	#10623494	—	2	2	no	—
214	#10623494	—	4	2	no	—
215	#10623494	—	4	1	no	—
216	#10623494	—	4	1	no	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	4	2	no	—
220	C₂²×C₈₉	—	4	2	no	—
221	C₂²×C₈₉	—	4	2	no	—
222	C₂²×C₈₉	—	8	4	no	—
223	C₂²×C₈₉	#435	1	2	yes	—
224	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂×D₈₉	—	2	2	no	—
226	C₂×D₈₉	—	4	1	no	—
227	C₂×D₈₉	—	4	1	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	4	2	no	—
232	C₄×C₈₉	#435	1	2	yes	—
233	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
235	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₈₉	#575	1	1	yes	characteristic
237	Dic₈₉	—	2	2	no	—
238	Dic₈₉	—	4	1	no	—
239	Dic₈₉	—	4	1	no	—
240	#17871	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	2	no	—
242	C₂×C₈₉	—	8	2	no	—
243	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
244	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₈₉	#2955	1	1	yes	characteristic
246	D₈₉	—	4	2	no	—
247	C₈×#41	—	89	1	no	—
248	C₄×AGL(1,ℤ/8)	—	89	1	no	—
249	C₂×#436	D₈₉	1	1	yes	characteristic, complemented
250	#1588	—	89	2	no	—
251	#1586	—	89	2	no	—
252	#1583	—	89	2	no	—
253	#1581	—	89	2	no	—
254	#1565	—	89	1	no	—
255	#1478	—	89	1	no	—
256	#1477	—	89	1	no	—
257	#1451	—	89	1	no	—
258	C₈₉	#17871	1	1	yes	characteristic, complemented, Sylow
259	C₂×AGL(1,ℤ/8)	—	89	1	no	—
260	C₂²×M₁₆	—	2	1	no	—
261	C₄×#41	—	89	1	no	—
262	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
263	C₈×Q₈	—	89	1	no	—
264	C₈×Q₈	—	89	1	no	—
265	#442	—	89	2	no	—
266	#440	—	89	2	no	—
267	C₄×SD₁₆	—	89	2	no	—
268	C₄×D₈	—	89	2	no	—
269	#436	—	2	1	no	—
270	#436	—	2	1	no	—
271	#436	C₂×D₈₉	1	2	yes	—
272	#436	C₂×D₈₉	1	2	yes	—
273	C₈×D₄	—	89	1	no	—
274	C₈×D₄	—	89	1	no	—
275	C₈×D₄	—	178	1	no	—
276	C₈×D₄	—	178	1	no	—
277	#431	—	89	1	no	—
278	#431	—	89	1	no	—
279	#431	—	178	1	no	—
280	#428	—	89	1	no	—
281	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
282	#418	—	89	1	no	—
283	#417	—	89	1	no	—
284	C₂×C₂²⋊C₈	—	2	1	no	—
285	C₄×M₁₆	—	89	1	no	—
286	C₂×C₄×C₈	—	178	1	no	—
287	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
288	#335	—	89	2	no	—
289	#334	—	89	2	no	—
290	Q₈⋊C₈	—	89	2	no	—
291	D₄⋊C₈	—	89	2	no	—
292	D₄⋊C₈	—	89	2	no	—
293	D₄⋊C₈	—	89	2	no	—
294	#322	—	89	2	no	—
295	#322	—	89	2	no	—
296	C₂×#41	—	89	1	no	—
297	C₂²×D₄	C₄×D₈₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	—	178	4	no	—
300	C₂×SD₁₆	—	89	2	no	—
301	C₂×D₈	—	89	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	4	4	no	—
305	C₂×M₁₆	—	89	1	no	—
306	C₂×M₁₆	—	89	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	178	1	no	—
309	C₂²×C₈	—	178	1	no	—
310	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
311	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
312	C₄×Q₈	—	89	1	no	—
313	C₄×Q₈	—	89	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	C₄×D₄	C₄×D₈₉	1	2	yes	—
321	C₄×D₄	C₂²×D₈₉	1	2	yes	—
322	#117	—	89	1	no	—
323	#117	—	178	1	no	—
324	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	178	1	no	—
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	#107	—	89	2	no	—
329	#106	—	89	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	89	1	no	—
332	C₄⋊C₈	—	89	1	no	—
333	C₄⋊C₈	—	178	1	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
337	#103	—	89	2	no	—
338	#102	—	89	2	no	—
339	#102	—	89	2	no	—
340	#102	—	89	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	178	1	no	—
344	C₂²⋊C₈	—	178	1	no	—
345	C₂²⋊C₈	—	178	1	no	—
346	C₂²⋊C₈	—	178	1	no	—
347	#97	—	89	2	no	—
348	C₄×C₈	—	89	2	no	—
349	C₄×C₈	—	89	2	no	—
350	C₄×C₈	—	178	1	no	—
351	C₄×C₈	—	178	1	no	—
352	C₄×C₈	—	178	1	no	—
353	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
354	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	#41	—	89	4	no	—
359	#41	—	178	2	no	—
360	C₂×Q₈	—	89	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	89	1	no	—
365	C₂×D₄	—	178	1	no	—
366	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	178	1	no	—
373	C₂²×C₄	—	178	1	no	—
374	C₂²×C₄	—	178	1	no	—
375	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
377	C₂²×C₄	#13083574	1	1	yes	characteristic
378	SD₁₆	—	178	4	no	—
379	D₈	—	178	4	no	—
380	M₁₆	—	4	4	no	—
381	M₁₆	—	4	4	no	—
382	M₁₆	—	178	2	no	—
383	M₁₆	—	178	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	89	2	no	—
389	C₂×C₈	—	89	2	no	—
390	C₂×C₈	—	356	2	no	—
391	C₂×C₈	—	356	2	no	—
392	C₂×C₈	—	178	1	no	—
393	C₂×C₈	—	178	1	no	—
394	C₂×C₈	—	178	2	no	—
395	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	89	1	no	—
401	C₄⋊C₄	—	89	1	no	—
402	C₄⋊C₄	—	178	1	no	—
403	C₄⋊C₄	—	178	1	no	—
404	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	178	1	no	—
408	C₂²⋊C₄	—	178	1	no	—
409	C₂²⋊C₄	—	178	1	no	—
410	C₄²	—	178	1	no	—
411	C₄²	—	178	1	no	—
412	C₄²	—	178	1	no	—
413	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
415	C₄²	#13083574	1	1	yes	characteristic
416	C₄²	C₂³×D₈₉	1	1	yes	characteristic
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	178	1	no	—
422	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
423	Q₈	—	89	2	no	—
424	Q₈	—	178	1	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	89	2	no	—
429	D₄	—	178	4	no	—
430	D₄	—	178	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	356	2	no	—
440	C₂×C₄	—	356	1	no	—
441	C₂×C₄	—	356	1	no	—
442	C₂×C₄	—	178	1	no	—
443	C₂×C₄	—	178	1	no	—
444	C₂×C₄	—	178	1	no	—
445	C₂×C₄	—	178	4	no	—
446	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
447	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
450	C₂×C₄	#15668020	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	2	no	—
458	C₈	—	356	2	no	—
459	C₈	—	356	1	no	—
460	C₈	—	356	1	no	—
461	C₈	—	178	2	no	—
462	C₈	—	178	2	no	—
463	C₈	#15668038	1	2	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	356	1	no	—
471	C₂²	—	356	1	no	—
472	C₂²	—	178	2	no	—
473	C₂²	#19151667	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	356	1	no	—
480	C₄	—	356	1	no	—
481	C₄	—	178	2	no	—
482	C₄	#19151667	1	2	yes	—
483	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
484	C₄	C₂×#15668020	1	1	yes	characteristic
485	C₄	C₂×#15668038	1	1	yes	characteristic
486	C₄	#19152396	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	2	no	—
489	C₂	—	356	2	no	—
490	C₂	C₂×#19151667	1	1	yes	characteristic
491	C₂	C₄×#15668038	1	1	yes	characteristic
492	C₂	#26029153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#436×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668038	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#436	D₈₉
hypocenter	C₈₉	#17871
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. C₈×#13083574	C₂	semidirect
3. #26019128	C₂	semidirect
4. #26019114	C₂	semidirect
5. #26019093	C₂	semidirect
6. #26019079	C₂	semidirect
7. #26019002	C₂	semidirect
8. #26018643	C₂	semidirect
9. #26018637	C₂	semidirect
10. #26018541	C₂	semidirect
11. C₂×#436×C₈₉	C₂	semidirect
14. C₈×Dic₁₇₈	C₂²	semidirect
15. C₈×Dic₁₇₈	C₂²	semidirect
20. C₈×D₃₅₆	C₂²	semidirect
21. C₈×D₃₅₆	C₂²	semidirect
32. #19151350	C₂²	semidirect
33. #19151348	C₂²	semidirect
34. #19151328	C₂²	semidirect
37. #19151325	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. #19151319	C₂²	semidirect
111. #13083574	M₁₆	semidirect
200. D₃₅₆	C₂×M₁₆	semidirect
206. Dic₁₇₈	C₂×M₁₆	semidirect
211. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
249. C₂×#436	D₈₉	semidirect
258. C₈₉	#17871	semidirect
463. C₈	#15668038	semidirect

Maximal subgroups

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

subgroup	index
C₈×#13083574	2
C₄×#15668038	2
#26019128	2
#26019114	2
#26019093	2
#26019079	2
#26019002	2
#26018643	2
#26018637	2
#26018541	2
C₂×#436×C₈₉	2
#17871	89