Subgroups — #36524444

Order 22784.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019089	C₂	1	2	yes	maximal, complemented
4	#26019082	C₂	1	2	yes	maximal, complemented
5	#26019076	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#10623494	C₂	1	2	yes	maximal, complemented
7	#26019037	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018695	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018665	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3105	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10623494	—	2	1	no	—
13	#19151729	C₂²	1	1	yes	characteristic, complemented
14	Q₈×#10623494	C₂²	1	1	yes	characteristic, complemented
15	#19151676	C₂²	1	1	yes	characteristic, complemented
16	#19151670	—	2	1	no	—
17	D₄×#10623494	—	2	1	no	—
18	D₄×#10623494	—	2	1	no	—
19	D₄×#10623494	—	2	1	no	—
20	D₄×#10623494	C₂²	1	2	yes	—
21	D₄×#10623494	C₂²	1	2	yes	—
22	D₄×#10623494	C₂²	1	1	yes	characteristic, complemented
23	#19151659	—	2	1	no	—
24	#19151655	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#10623494	—	2	1	no	—
27	#19151554	—	2	1	no	—
28	C₄×#13083558	C₂²	1	1	yes	characteristic
29	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	2	yes	complemented
31	#19151349	C₂²	1	2	yes	complemented
32	Q₈⋊#10623494	C₂²	1	2	yes	complemented
33	D₄⋊#10623494	C₂²	1	2	yes	—
34	D₄⋊#10623494	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	complemented
36	#19151320	C₂²	1	2	yes	complemented
37	#19151319	C₂²	1	2	yes	complemented
38	#529×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	#484×C₈₉	C₄	1	1	yes	characteristic
41	#481×C₈₉	C₄	1	1	yes	characteristic
42	#478×C₈₉	C₄	1	2	yes	—
43	#463×C₈₉	C₄	1	2	yes	—
44	#450×C₈₉	C₄	1	1	yes	characteristic
45	#447×C₈₉	C₄	1	1	yes	characteristic
46	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
47	C₄×D₈×C₈₉	C₂²	1	2	yes	—
48	#431×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂²×#10623494	—	2	2	no	—
52	C₂²×#10623494	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂²×#10623494	—	4	4	no	—
56	C₂²×#10623494	D₄	1	1	yes	characteristic
57	C₂²×#10623494	D₄	1	1	yes	characteristic
58	C₄⋊#10623494	—	2	1	no	—
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	—	2	1	no	—
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₄⋊#10623494	C₂³	1	1	yes	characteristic
63	C₄⋊#10623494	C₂³	1	1	yes	characteristic
64	C₂²⋊#10623494	—	2	1	no	—
65	C₂²⋊#10623494	—	2	1	no	—
66	C₂²⋊#10623494	—	2	2	no	—
67	C₂²⋊#10623494	—	2	2	no	—
68	C₂²⋊#10623494	—	2	1	no	—
69	#15667923	—	2	1	no	—
70	#15667923	—	2	1	no	—
71	#15667923	—	2	1	no	—
72	C₄×#10623494	—	2	1	no	—
73	C₄×#10623494	D₄	1	1	yes	characteristic
74	C₄×#10623494	D₄	1	1	yes	characteristic
75	C₄×#10623494	C₂³	1	2	yes	—
76	C₄×#10623494	C₂³	1	1	yes	characteristic
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	—	2	1	no	—
80	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
82	#126×C₈₉	—	2	1	no	—
83	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
84	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
85	#123×C₈₉	—	2	1	no	—
86	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	—	2	1	no	—
92	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₈₉	C₂³	1	2	yes	—
94	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
95	#117×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	#107×C₈₉	C₂×C₄	1	2	yes	—
100	#106×C₈₉	C₂×C₄	1	2	yes	—
101	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
102	#103×C₈₉	C₂×C₄	1	2	yes	—
103	#102×C₈₉	C₂×C₄	1	2	yes	—
104	#102×C₈₉	C₂×C₄	1	2	yes	—
105	#102×C₈₉	C₂×C₄	1	2	yes	—
106	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	2	yes	—
109	#13083558	—	4	2	no	—
110	#13083558	—	4	2	no	—
111	C₂×#10623494	—	2	2	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₂×#10623494	—	4	1	no	—
117	C₂×#10623494	—	4	2	no	—
118	C₂×#10623494	—	4	4	no	—
119	C₂×#10623494	—	4	2	no	—
120	C₂×#10623494	—	4	4	no	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂⁴×C₈₉	—	2	1	no	—
126	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₈₉	—	2	4	no	—
128	C₂×D₄×C₈₉	—	2	1	no	—
129	C₂×D₄×C₈₉	—	2	1	no	—
130	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	—	4	2	no	—
137	C₂²×C₄×C₈₉	—	4	2	no	—
138	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
141	SD₁₆×C₈₉	—	2	4	no	—
142	D₈×C₈₉	—	2	4	no	—
143	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₂²⋊C₄×C₈₉	—	2	2	no	—
155	C₂²⋊C₄×C₈₉	—	2	1	no	—
156	C₂²⋊C₄×C₈₉	—	2	1	no	—
157	C₂²⋊C₄×C₈₉	—	2	1	no	—
158	C₂²⋊C₄×C₈₉	—	2	2	no	—
159	C₂²⋊C₄×C₈₉	—	2	1	no	—
160	C₄²×C₈₉	—	2	1	no	—
161	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	#41	1	1	yes	characteristic
164	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂³×C₈₉	—	2	4	no	—
166	C₂³×C₈₉	—	2	2	no	—
167	C₂³×C₈₉	—	2	1	no	—
168	C₂³×C₈₉	—	4	2	no	—
169	C₂³×C₈₉	—	4	2	no	—
170	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
171	Q₈×C₈₉	—	2	2	no	—
172	D₄×C₈₉	—	2	4	no	—
173	D₄×C₈₉	—	2	2	no	—
174	D₄×C₈₉	—	2	2	no	—
175	D₄×C₈₉	—	4	2	no	—
176	D₄×C₈₉	#131	1	4	yes	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	4	4	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	2	2	no	—
199	#10623494	—	2	1	no	—
200	#10623494	—	2	1	no	—
201	#10623494	—	2	1	no	—
202	#10623494	—	4	2	no	—
203	#10623494	—	4	2	no	—
204	#10623494	—	4	1	no	—
205	#10623494	—	4	1	no	—
206	#10623494	AGL(1,ℤ/8)	1	2	yes	—
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	2	4	no	—
210	C₂²×C₈₉	—	4	8	no	—
211	C₂²×C₈₉	—	4	2	no	—
212	C₂²×C₈₉	—	4	2	no	—
213	C₂²×C₈₉	—	4	1	no	—
214	C₂²×C₈₉	—	4	1	no	—
215	C₂²×C₈₉	—	4	1	no	—
216	C₂²×C₈₉	#444	1	2	yes	—
217	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	2	1	no	—
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	—	4	1	no	—
223	C₄×C₈₉	—	4	1	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	—	4	1	no	—
226	C₄×C₈₉	C₂×#131	1	2	yes	—
227	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₈₉	#575	1	1	yes	characteristic
229	#17914	—	89	1	no	maximal, Sylow
230	C₂×C₈₉	—	2	2	no	—
231	C₂×C₈₉	—	4	4	no	—
232	C₂×C₈₉	—	8	1	no	—
233	C₂×C₈₉	#2929	1	1	yes	characteristic
234	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
236	#3105	D₈₉	1	1	yes	characteristic
237	#2966	—	89	1	no	—
238	C₂×C₈×D₄	—	89	1	no	—
239	#1582	—	89	2	no	—
240	#1581	—	89	2	no	—
241	#1580	—	89	2	no	—
242	SD₁₆⋊C₈	—	89	2	no	—
243	#1573	—	89	1	no	—
244	#1490	—	89	1	no	—
245	#1483	—	89	1	no	—
246	#1451	—	89	1	no	—
247	C₈₉	#17914	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₈	—	178	1	no	—
249	#529	C₂×D₈₉	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
251	#484	Dic₈₉	1	1	yes	characteristic
252	#481	Dic₈₉	1	1	yes	characteristic
253	#478	Dic₈₉	1	2	yes	—
254	#463	Dic₈₉	1	2	yes	—
255	#450	Dic₈₉	1	1	yes	characteristic
256	#447	Dic₈₉	1	1	yes	characteristic
257	#446	—	89	1	no	—
258	C₈×Q₈	—	89	1	no	—
259	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
260	C₄×D₈	C₂×D₈₉	1	2	yes	—
261	#436	—	89	1	no	—
262	#435	—	178	1	no	—
263	C₈×D₄	—	89	2	no	—
264	C₈×D₄	—	89	1	no	—
265	C₈×D₄	—	89	2	no	—
266	C₈×D₄	—	178	1	no	—
267	C₈×D₄	—	178	1	no	—
268	C₈×D₄	—	178	1	no	—
269	#433	—	178	1	no	—
270	#432	—	89	1	no	—
271	#431	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	89	1	no	—
273	C₂×C₂²⋊C₈	—	178	1	no	—
274	#405	—	178	1	no	—
275	C₄×M₁₆	—	89	1	no	—
276	C₂×C₄×C₈	—	89	1	no	—
277	#335	—	89	2	no	—
278	#334	—	89	2	no	—
279	Q₈⋊C₈	—	89	2	no	—
280	D₄⋊C₈	—	89	2	no	—
281	D₄⋊C₈	—	89	2	no	—
282	D₄⋊C₈	—	89	2	no	—
283	#322	—	89	2	no	—
284	#322	—	89	2	no	—
285	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
288	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
289	C₂×M₁₆	—	178	1	no	—
290	C₂×M₁₆	—	178	1	no	—
291	C₂²×C₈	—	89	1	no	—
292	C₂²×C₈	—	89	1	no	—
293	C₂²×C₈	—	356	4	no	—
294	C₂²×C₈	—	178	2	no	—
295	C₂²×C₈	—	178	2	no	—
296	C₂²×C₈	—	178	1	no	—
297	C₂²×C₈	—	178	1	no	—
298	#126	—	2	1	no	—
299	#125	C₂×Dic₈₉	1	1	yes	characteristic
300	#124	C₂×Dic₈₉	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
303	#121	C₂×Dic₈₉	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
309	C₄×D₄	C₂²×D₈₉	1	2	yes	—
310	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
315	#107	C₂×Dic₈₉	1	2	yes	—
316	#106	C₂×Dic₈₉	1	2	yes	—
317	C₄⋊C₈	—	89	1	no	—
318	C₄⋊C₈	—	89	1	no	—
319	C₄⋊C₈	—	89	2	no	—
320	C₄⋊C₈	—	178	1	no	—
321	C₄⋊C₈	—	178	1	no	—
322	C₄⋊C₈	—	178	1	no	—
323	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
324	#103	C₂×Dic₈₉	1	2	yes	—
325	#102	C₂×Dic₈₉	1	2	yes	—
326	#102	C₂×Dic₈₉	1	2	yes	—
327	#102	C₂×Dic₈₉	1	2	yes	—
328	C₂²⋊C₈	—	178	2	no	—
329	C₂²⋊C₈	—	178	2	no	—
330	C₂²⋊C₈	—	178	1	no	—
331	C₂²⋊C₈	—	178	1	no	—
332	C₂²⋊C₈	—	178	1	no	—
333	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
334	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
335	#97	—	178	1	no	—
336	#97	—	178	1	no	—
337	#97	—	178	1	no	—
338	C₄×C₈	—	89	1	no	—
339	C₄×C₈	—	89	1	no	—
340	C₄×C₈	—	89	1	no	—
341	C₄×C₈	—	89	1	no	—
342	C₄×C₈	—	89	2	no	—
343	C₄×C₈	—	178	1	no	—
344	C₄×C₈	C₂²×D₈₉	1	2	yes	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
351	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₄	#13083573	1	1	yes	characteristic
361	SD₁₆	—	2	4	no	—
362	D₈	—	2	4	no	—
363	M₁₆	—	356	2	no	—
364	M₁₆	—	356	2	no	—
365	C₂×C₈	—	89	1	no	—
366	C₂×C₈	—	89	1	no	—
367	C₂×C₈	—	89	1	no	—
368	C₂×C₈	—	89	1	no	—
369	C₂×C₈	—	356	4	no	—
370	C₂×C₈	—	356	2	no	—
371	C₂×C₈	—	356	4	no	—
372	C₂×C₈	—	356	2	no	—
373	C₂×C₈	—	356	1	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	—	178	1	no	—
376	C₂×C₈	—	178	1	no	—
377	C₂×C₈	—	178	2	no	—
378	C₂×C₈	—	178	2	no	—
379	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
380	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
398	C₄²	D₄×D₈₉	1	1	yes	characteristic
399	C₄²	#13083573	1	1	yes	characteristic
400	C₄²	C₂³×D₈₉	1	1	yes	characteristic
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	#15668019	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
428	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
429	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	89	2	no	—
436	C₈	—	356	2	no	—
437	C₈	—	356	1	no	—
438	C₈	—	356	2	no	—
439	C₈	—	356	1	no	—
440	C₈	—	178	1	no	—
441	C₈	—	178	1	no	—
442	C₈	—	178	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	#19151720	1	2	yes	—
453	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	C₂×#15668019	1	2	yes	—
463	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
464	C₄	#19152394	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	4	no	—
467	C₂	—	8	1	no	—
468	C₂	#26028947	1	1	yes	characteristic
469	C₂	AGL(1,ℤ/8)×Dic₈₉	1	1	yes	characteristic
470	C₂	C₂×#19151720	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3105	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#447×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3105	D₈₉
hypocenter	C₈₉	#17914
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #26029228	C₂	semidirect
2. C₂×D₄×#10623494	C₂	semidirect
3. #26019089	C₂	semidirect
4. #26019082	C₂	semidirect
5. #26019076	C₂	semidirect
6. SD₁₆⋊#10623494	C₂	semidirect
7. #26019037	C₂	semidirect
8. #26018695	C₂	semidirect
9. #26018665	C₂	semidirect
10. #26018542	C₂	semidirect
13. #19151729	C₂²	semidirect
14. Q₈×#10623494	C₂²	semidirect
15. #19151676	C₂²	semidirect
22. D₄×#10623494	C₂²	semidirect
30. #19151351	C₂²	semidirect
31. #19151349	C₂²	semidirect
32. Q₈⋊#10623494	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151320	C₂²	semidirect
37. #19151319	C₂²	semidirect
247. C₈₉	#17914	semidirect

Maximal subgroups

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

subgroup	index
#26029228	2
C₂×D₄×#10623494	2
#26019089	2
#26019082	2
#26019076	2
SD₁₆⋊#10623494	2
#26019037	2
#26018695	2
#26018665	2
#26018542	2
C₈₉×#3105	2
#17914	89