Subgroups — #36523456

Order 22784.

756 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028884	C₂	1	1	yes	maximal, characteristic
2	#423×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#13083557	C₂	1	1	yes	maximal, characteristic
4	#26019018	C₂	1	4	yes	maximal, complemented
5	#26019010	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019008	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019007	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019003	C₂	1	4	yes	maximal, complemented
9	C₈₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13083557	C₄	1	2	yes	—
11	C₂×M₁₆×D₈₉	—	2	1	no	—
12	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
13	#19151654	—	2	1	no	—
14	#19151654	C₂²	1	2	yes	—
15	#19151650	—	2	1	no	—
16	#19151650	C₂²	1	2	yes	—
17	#19151622	C₂²	1	1	yes	characteristic
18	#19151622	C₂²	1	1	yes	characteristic
19	#19151621	—	2	1	no	—
20	#19151620	—	2	1	no	—
21	#19151620	C₂²	1	2	yes	—
22	C₄⋊C₈×D₈₉	—	2	1	no	—
23	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
24	#19151561	—	2	1	no	—
25	M₁₆×Dic₈₉	—	2	1	no	—
26	C₄×#13083557	C₄	1	1	yes	characteristic
27	C₄×#13083557	C₄	1	1	yes	characteristic
28	C₄×#13083557	C₄	1	1	yes	characteristic
29	C₄×#13083557	C₄	1	1	yes	characteristic
30	C₄×#13083557	C₂²	1	2	yes	—
31	C₄×#13083557	C₂²	1	2	yes	—
32	C₂×#15667922	C₄	1	2	yes	—
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	#19151350	C₂²	1	4	yes	complemented
35	#19151349	C₂²	1	4	yes	complemented
36	#19151348	C₂²	1	4	yes	complemented
37	#423×C₈₉	C₂²	1	1	yes	characteristic
38	#423×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	#335×C₈₉	C₂²	1	4	yes	complemented
41	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
43	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
44	C₂×#13083558	—	2	1	no	—
45	C₂×#13083558	—	2	1	no	—
46	C₂×#13083557	—	2	8	no	—
47	C₂×#13083557	—	2	2	no	—
48	C₂×#13083557	C₂×C₄	1	2	yes	—
49	C₂×#13083557	C₂×C₄	1	2	yes	—
50	C₂×#13083557	C₂×C₄	1	2	yes	—
51	C₂×#13083557	C₂×C₄	1	2	yes	—
52	M₁₆×D₈₉	—	4	4	no	—
53	C₂²×#10623494	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
58	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₈₉	D₄	1	1	yes	characteristic
61	C₄²×D₈₉	D₄	1	1	yes	characteristic
62	C₄²×D₈₉	Q₈	1	1	yes	characteristic
63	C₄²×D₈₉	Q₈	1	1	yes	characteristic
64	C₄²×D₈₉	C₂³	1	1	yes	characteristic
65	C₄²×D₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	—	2	1	no	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667941	—	2	2	no	—
71	#15667941	—	2	2	no	—
72	#15667924	—	2	2	no	—
73	#15667924	—	2	2	no	—
74	#15667922	—	2	2	no	—
75	#15667922	C₂×C₄	1	2	yes	—
76	#15667922	C₂×C₄	1	2	yes	—
77	#15667922	C₂×C₄	1	2	yes	—
78	#15667922	C₂×C₄	1	2	yes	—
79	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
80	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
81	C₄×#10623494	C₂³	1	2	yes	—
82	C₈×Dic₈₉	—	2	2	no	—
83	C₂×M₁₆×C₈₉	—	2	1	no	—
84	C₂×M₁₆×C₈₉	—	2	1	no	—
85	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	—	2	1	no	—
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
91	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	2	yes	—
94	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₈₉	—	2	2	no	—
99	C₂×C₄×D₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	4	no	—
101	C₂×C₄×D₈₉	—	4	2	no	—
102	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
114	#13083558	—	4	2	no	—
115	#13083558	—	4	2	no	—
116	#13083557	—	2	4	no	—
117	#13083557	—	2	4	no	—
118	#13083557	—	2	4	no	—
119	#13083557	—	4	4	no	—
120	#13083557	M₁₆	1	8	yes	complemented
121	C₂×#10623494	—	2	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₂×#10623494	C₂²×C₄	1	2	yes	—
126	C₈×D₈₉	—	4	4	no	—
127	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
142	M₁₆×C₈₉	—	4	2	no	—
143	M₁₆×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	—	2	4	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
149	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
152	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂²×D₈₉	—	2	2	no	—
155	C₂²×D₈₉	—	2	2	no	—
156	C₂²×D₈₉	—	4	1	no	—
157	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₈₉	#137	1	2	yes	—
166	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	4	1	no	—
172	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₄×D₈₉	—	2	2	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	—	2	1	no	—
181	C₄×D₈₉	—	2	1	no	—
182	C₄×D₈₉	—	2	1	no	—
183	C₄×D₈₉	—	2	1	no	—
184	C₄×D₈₉	—	2	2	no	—
185	C₄×D₈₉	—	2	2	no	—
186	C₄×D₈₉	—	2	2	no	—
187	C₄×D₈₉	—	2	2	no	—
188	C₄×D₈₉	—	2	2	no	—
189	C₄×D₈₉	—	4	1	no	—
190	C₄×D₈₉	—	4	1	no	—
191	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
192	C₈×C₈₉	—	2	2	no	—
193	C₈×C₈₉	—	4	2	no	—
194	C₈×C₈₉	—	4	2	no	—
195	C₈×C₈₉	C₂×M₁₆	1	4	yes	complemented
196	#10623494	—	2	2	no	—
197	#10623494	—	4	2	no	—
198	#10623494	—	4	2	no	—
199	#10623494	C₂×M₁₆	1	4	yes	complemented
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	#428	1	2	yes	—
203	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
204	C₂×D₈₉	—	2	1	no	—
205	C₂×D₈₉	—	2	1	no	—
206	C₂×D₈₉	—	2	1	no	—
207	C₂×D₈₉	—	2	1	no	—
208	C₂×D₈₉	—	2	1	no	—
209	C₂×D₈₉	—	4	4	no	—
210	C₂×D₈₉	#423	1	2	yes	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	#428	1	2	yes	—
214	C₄×C₈₉	#430	1	2	yes	—
215	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
216	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
218	Dic₈₉	—	2	1	no	—
219	Dic₈₉	—	2	1	no	—
220	Dic₈₉	—	2	1	no	—
221	Dic₈₉	—	2	1	no	—
222	Dic₈₉	—	2	1	no	—
223	Dic₈₉	#423	1	2	yes	—
224	#17796	—	89	1	no	maximal, Sylow
225	C₂×C₈₉	—	2	2	no	—
226	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
227	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
228	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
229	D₈₉	—	2	2	no	—
230	D₈₉	—	4	1	no	—
231	#2920	—	89	1	no	—
232	C₂×#423	—	89	1	no	—
233	C₂×C₄×M₁₆	—	89	1	no	—
234	#1569	—	89	4	no	—
235	#1567	—	89	1	no	—
236	#1567	D₈₉	1	1	yes	characteristic, complemented
237	#1566	—	89	1	no	—
238	#1566	—	89	1	no	—
239	#1565	—	89	4	no	—
240	C₈₉	#17796	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	89	2	no	—
242	C₂²×M₁₆	—	178	1	no	—
243	C₂²×C₄²	—	89	1	no	—
244	#432	—	89	2	no	—
245	#432	—	178	1	no	—
246	#431	—	89	2	no	—
247	#431	—	178	1	no	—
248	#423	—	89	1	no	—
249	#423	—	89	1	no	—
250	#423	—	89	2	no	—
251	#423	—	178	1	no	—
252	#423	—	178	1	no	—
253	#423	C₂×D₈₉	1	1	yes	characteristic
254	#423	C₂×D₈₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	—	89	2	no	—
256	C₂×C₄⋊C₈	—	178	1	no	—
257	#407	—	178	1	no	—
258	C₄×M₁₆	—	89	1	no	—
259	C₄×M₁₆	—	89	1	no	—
260	C₄×M₁₆	—	89	1	no	—
261	C₄×M₁₆	—	89	1	no	—
262	C₄×M₁₆	—	89	2	no	—
263	C₄×M₁₆	—	89	2	no	—
264	C₄×M₁₆	—	178	1	no	—
265	C₂×#97	—	89	2	no	—
266	C₂×C₄×C₈	—	89	1	no	—
267	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
268	#335	—	89	4	no	—
269	#335	C₂×D₈₉	1	4	yes	complemented
270	#334	—	89	4	no	—
271	#334	—	89	4	no	—
272	C₂³×C₄	—	89	1	no	—
273	C₂³×C₄	—	89	1	no	—
274	C₂³×C₄	—	89	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	89	2	no	—
278	C₂×M₁₆	—	89	2	no	—
279	C₂×M₁₆	—	89	2	no	—
280	C₂×M₁₆	—	89	2	no	—
281	C₂×M₁₆	—	356	4	no	—
282	C₂×M₁₆	—	178	8	no	—
283	C₂×M₁₆	—	178	2	no	—
284	C₂×M₁₆	—	178	1	no	—
285	C₂×M₁₆	—	178	1	no	—
286	C₂²×C₈	—	89	2	no	—
287	C₂²×C₈	—	178	2	no	—
288	C₂²×C₈	C₄×D₈₉	1	2	yes	—
289	C₂×C₄²	—	89	1	no	—
290	C₂×C₄²	—	89	1	no	—
291	C₂×C₄²	—	89	1	no	—
292	C₂×C₄²	—	89	1	no	—
293	C₂×C₄²	—	89	1	no	—
294	C₂×C₄²	—	89	1	no	—
295	C₂×C₄²	—	89	1	no	—
296	C₂×C₄²	—	89	1	no	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	89	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	—	89	2	no	—
305	C₄⋊C₈	—	178	2	no	—
306	C₄⋊C₈	—	178	2	no	—
307	C₄⋊C₈	—	178	1	no	—
308	C₄⋊C₈	—	178	1	no	—
309	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
310	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
311	C₂²⋊C₈	—	178	2	no	—
312	C₂²⋊C₈	—	178	2	no	—
313	#97	—	89	2	no	—
314	#97	—	89	2	no	—
315	#97	—	89	2	no	—
316	#97	—	89	2	no	—
317	#97	—	178	2	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	2	no	—
321	C₄×C₈	—	178	2	no	—
322	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
323	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₈₉	1	2	yes	—
325	C₂⁴	—	89	1	no	—
326	C₂²×C₄	—	89	1	no	—
327	C₂²×C₄	—	89	1	no	—
328	C₂²×C₄	—	89	1	no	—
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	89	1	no	—
331	C₂²×C₄	—	89	1	no	—
332	C₂²×C₄	—	89	1	no	—
333	C₂²×C₄	—	89	1	no	—
334	C₂²×C₄	—	89	1	no	—
335	C₂²×C₄	—	89	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	C₂²×C₄	—	89	1	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	—	356	2	no	—
342	C₂²×C₄	—	178	4	no	—
343	C₂²×C₄	—	178	2	no	—
344	C₂²×C₄	—	178	2	no	—
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
348	M₁₆	—	4	2	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	89	8	no	—
351	M₁₆	—	356	4	no	—
352	M₁₆	—	356	2	no	—
353	M₁₆	—	356	2	no	—
354	M₁₆	—	178	4	no	—
355	M₁₆	—	178	4	no	—
356	M₁₆	—	178	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	89	2	no	—
361	C₂×C₈	—	89	2	no	—
362	C₂×C₈	—	356	4	no	—
363	C₂×C₈	—	178	4	no	—
364	C₂×C₈	—	178	2	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
367	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
368	C₄²	—	89	1	no	—
369	C₄²	—	89	1	no	—
370	C₄²	—	89	1	no	—
371	C₄²	—	89	1	no	—
372	C₄²	—	89	1	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	89	1	no	—
375	C₄²	—	89	1	no	—
376	C₄²	—	89	1	no	—
377	C₄²	—	89	1	no	—
378	C₄²	—	89	1	no	—
379	C₄²	—	89	1	no	—
380	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₄²	D₄×D₈₉	1	1	yes	characteristic
382	C₄²	Q₈×D₈₉	1	1	yes	characteristic
383	C₄²	C₂³×D₈₉	1	1	yes	characteristic
384	C₂³	—	89	1	no	—
385	C₂³	—	89	1	no	—
386	C₂³	—	356	1	no	—
387	C₂³	—	178	2	no	—
388	C₂³	—	178	2	no	—
389	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	89	1	no	—
393	C₂×C₄	—	89	4	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	89	1	no	—
398	C₂×C₄	—	89	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	1	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	178	2	no	—
405	C₂×C₄	—	178	2	no	—
406	C₂×C₄	—	178	1	no	—
407	C₂×C₄	—	178	1	no	—
408	C₂×C₄	—	178	2	no	—
409	C₂×C₄	—	178	2	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	—	178	2	no	—
412	C₂×C₄	—	178	2	no	—
413	C₂×C₄	—	178	1	no	—
414	C₂×C₄	—	178	1	no	—
415	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
418	C₂×C₄	#15668036	1	2	yes	—
419	C₂×C₄	#15668044	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	89	4	no	—
427	C₈	—	356	2	no	—
428	C₈	—	356	2	no	—
429	C₈	—	178	2	no	—
430	C₈	M₁₆×D₈₉	1	4	yes	complemented
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	89	2	no	—
434	C₂²	—	356	4	no	—
435	C₂²	—	178	1	no	—
436	C₂²	—	178	1	no	—
437	C₂²	—	178	1	no	—
438	C₂²	—	178	1	no	—
439	C₂²	—	178	1	no	—
440	C₂²	#19151639	1	2	yes	—
441	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	89	2	no	—
445	C₄	—	178	1	no	—
446	C₄	—	178	1	no	—
447	C₄	—	178	1	no	—
448	C₄	—	178	1	no	—
449	C₄	—	178	1	no	—
450	C₄	#19151639	1	2	yes	—
451	C₄	#19151645	1	2	yes	—
452	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
453	C₄	C₂×#15668036	1	1	yes	characteristic
454	C₄	C₂×#15668044	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	356	1	no	—
457	C₂	—	178	2	no	—
458	C₂	#423×D₈₉	1	1	yes	characteristic
459	C₂	C₂×#19151639	1	1	yes	characteristic
460	C₂	C₂×#19151645	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×#1567	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1567	D₈₉
hypocenter	C₈₉	#17796
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #26019018	C₂	semidirect
5. #26019010	C₂	semidirect
6. #26019008	C₂	semidirect
7. #26019007	C₂	semidirect
8. #26019003	C₂	semidirect
9. C₈₉×#1567	C₂	semidirect
34. #19151350	C₂²	semidirect
35. #19151349	C₂²	semidirect
36. #19151348	C₂²	semidirect
40. #335×C₈₉	C₂²	semidirect
120. #13083557	M₁₆	semidirect
195. C₈×C₈₉	C₂×M₁₆	semidirect
199. #10623494	C₂×M₁₆	semidirect
236. #1567	D₈₉	semidirect
240. C₈₉	#17796	semidirect
269. #335	C₂×D₈₉	semidirect
430. C₈	M₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028884	2
#423×D₈₉	2
C₂×C₄×#13083557	2
#26019018	2
#26019010	2
#26019008	2
#26019007	2
#26019003	2
C₈₉×#1567	2
#17796	89