Subgroups — #36523537

Order 22784.

692 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	#26028880	C₂	1	1	yes	maximal, characteristic
2	#431×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#423×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019043	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019041	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019025	C₂	1	2	yes	maximal, complemented
8	#26019021	C₂	1	2	yes	maximal, complemented
9	#26019003	C₂	1	2	yes	maximal, complemented
10	#26019001	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₈₉	—	2	1	no	—
13	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
14	#19151654	C₄	1	2	yes	—
15	#19151652	C₄	1	2	yes	—
16	#19151651	C₂²	1	1	yes	characteristic
17	#19151651	C₂²	1	1	yes	characteristic
18	#19151650	C₂²	1	1	yes	characteristic
19	#19151650	C₂²	1	1	yes	characteristic
20	#19151649	—	2	1	no	—
21	#19151649	C₂²	1	2	yes	—
22	#19151648	—	2	1	no	—
23	#19151622	C₂²	1	1	yes	characteristic
24	#19151621	—	2	1	no	—
25	#19151620	—	2	1	no	—
26	#19151620	C₄	1	2	yes	—
27	#19151620	C₂²	1	2	yes	—
28	C₄⋊C₈×D₈₉	—	2	1	no	—
29	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
30	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
31	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151560	C₄	1	2	yes	—
33	C₂²⋊C₈×D₈₉	—	2	1	no	—
34	C₄×#13083557	C₂²	1	2	yes	—
35	C₄×C₈×D₈₉	—	2	1	no	—
36	#19151351	C₂²	1	2	yes	complemented
37	#19151350	C₂²	1	2	yes	complemented
38	#19151350	C₂²	1	2	yes	complemented
39	#19151349	C₂²	1	2	yes	complemented
40	#19151348	C₂²	1	2	yes	complemented
41	#19151348	C₂²	1	2	yes	complemented
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	#431×C₈₉	C₂²	1	1	yes	characteristic
44	#423×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	2	yes	complemented
46	#334×C₈₉	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂×#13083557	C₂×C₄	1	4	yes	—
53	M₁₆×D₈₉	—	4	4	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₈×D₈₉	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	1	no	—
57	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
60	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₈₉	D₄	1	1	yes	characteristic
63	C₄²×D₈₉	D₄	1	1	yes	characteristic
64	C₄²×D₈₉	Q₈	1	1	yes	characteristic
65	C₄²×D₈₉	Q₈	1	1	yes	characteristic
66	C₄²×D₈₉	C₂³	1	1	yes	characteristic
67	C₄²×D₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	—	2	1	no	—
69	C₄⋊#10623494	C₂×C₄	1	2	yes	—
70	C₄⋊#10623494	C₂³	1	2	yes	—
71	C₄⋊#10623494	C₂³	1	1	yes	characteristic
72	C₄⋊#10623494	C₂³	1	1	yes	characteristic
73	#15667941	—	2	2	no	—
74	#15667941	—	2	2	no	—
75	#15667941	—	2	1	no	—
76	#15667941	—	2	1	no	—
77	#15667941	C₂×C₄	1	4	yes	—
78	C₂²⋊#10623494	—	2	1	no	—
79	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
80	#15667924	—	2	1	no	—
81	#15667924	—	2	1	no	—
82	#15667924	C₂×C₄	1	4	yes	—
83	#15667922	C₂×C₄	1	4	yes	—
84	C₄×#10623494	—	2	1	no	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₈×Dic₈₉	—	2	1	no	—
87	C₈×Dic₈₉	—	2	1	no	—
88	C₂×M₁₆×C₈₉	—	2	1	no	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
92	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₈₉	—	2	1	no	—
96	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	C₂³	1	2	yes	—
99	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	—	2	4	no	—
104	C₂×C₄×D₈₉	—	2	2	no	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	4	2	no	—
107	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
119	#13083558	—	4	2	no	—
120	#13083557	—	2	8	no	—
121	#13083557	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	1	no	—
125	C₂×#10623494	C₂²×C₄	1	4	yes	—
126	C₈×D₈₉	—	4	4	no	—
127	C₈×D₈₉	—	4	2	no	—
128	C₈×D₈₉	—	4	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
144	M₁₆×C₈₉	—	4	2	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	4	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	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	2	no	—
181	C₄×D₈₉	—	2	1	no	—
182	C₄×D₈₉	—	2	1	no	—
183	C₄×D₈₉	—	2	2	no	—
184	C₄×D₈₉	—	2	2	no	—
185	C₄×D₈₉	—	2	2	no	—
186	C₄×D₈₉	—	2	2	no	—
187	C₄×D₈₉	—	4	1	no	—
188	C₄×D₈₉	—	4	1	no	—
189	C₄×D₈₉	#131	1	4	yes	—
190	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
191	C₄×D₈₉	#137	1	2	yes	—
192	C₈×C₈₉	—	2	4	no	—
193	C₈×C₈₉	—	4	2	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	—	4	1	no	—
196	#10623494	—	2	4	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	2	no	—
199	#10623494	—	4	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	2	1	no	—
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	—	4	4	no	—
209	C₂×D₈₉	#424	1	2	yes	—
210	C₂×D₈₉	#428	1	2	yes	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	#430	1	2	yes	—
215	C₄×C₈₉	C₂×#131	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	#424	1	2	yes	—
223	Dic₈₉	#428	1	2	yes	—
224	#17809	—	89	1	no	maximal, Sylow
225	C₂×C₈₉	—	4	1	no	—
226	C₂×C₈₉	C₂×#424	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	—	2	2	no	—
231	#2920	—	89	1	no	—
232	C₂×#431	—	89	1	no	—
233	C₂×#423	—	89	1	no	—
234	#1574	—	89	1	no	—
235	#1574	—	89	1	no	—
236	#1574	—	89	1	no	—
237	#1574	D₈₉	1	1	yes	characteristic, complemented
238	#1571	—	89	2	no	—
239	#1570	—	89	2	no	—
240	#1565	—	89	2	no	—
241	#1565	—	89	2	no	—
242	C₈₉	#17809	1	1	yes	characteristic, complemented, Sylow
243	C₂²×M₁₆	—	178	1	no	—
244	C₂²×C₄²	—	89	1	no	—
245	#432	—	89	2	no	—
246	#432	—	89	2	no	—
247	#431	—	89	1	no	—
248	#431	—	89	2	no	—
249	#431	—	89	1	no	—
250	#431	—	89	1	no	—
251	#431	—	89	1	no	—
252	#431	—	178	1	no	—
253	#431	—	178	1	no	—
254	#431	C₂×D₈₉	1	1	yes	characteristic
255	#431	C₂×D₈₉	1	1	yes	characteristic
256	#423	—	89	2	no	—
257	#423	—	89	1	no	—
258	#423	—	89	2	no	—
259	#423	—	178	1	no	—
260	#423	—	178	1	no	—
261	#423	C₂×D₈₉	1	1	yes	characteristic
262	C₂×C₄⋊C₈	—	89	2	no	—
263	C₂×C₄⋊C₈	—	89	1	no	—
264	C₂×C₄⋊C₈	—	89	1	no	—
265	C₂×C₄⋊C₈	—	178	1	no	—
266	#407	—	89	2	no	—
267	C₂×C₂²⋊C₈	—	178	1	no	—
268	C₄×M₁₆	—	89	2	no	—
269	C₂×C₄×C₈	—	178	1	no	—
270	#335	—	89	2	no	—
271	#335	—	89	2	no	—
272	#335	—	89	2	no	—
273	#335	C₂×D₈₉	1	2	yes	complemented
274	#334	—	89	2	no	—
275	#334	—	89	2	no	—
276	#334	—	89	2	no	—
277	#334	C₂×D₈₉	1	2	yes	complemented
278	C₂³×C₄	—	89	1	no	—
279	C₂³×C₄	—	89	1	no	—
280	C₂³×C₄	—	89	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	89	4	no	—
283	C₂×M₁₆	—	356	4	no	—
284	C₂×M₁₆	—	178	2	no	—
285	C₂×M₁₆	—	178	1	no	—
286	C₂²×C₈	—	178	2	no	—
287	C₂²×C₈	—	178	1	no	—
288	C₂²×C₈	—	178	1	no	—
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	—	89	4	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	—	89	1	no	—
305	C₄⋊C₈	—	89	2	no	—
306	C₄⋊C₈	—	89	1	no	—
307	C₄⋊C₈	—	178	2	no	—
308	C₄⋊C₈	—	178	1	no	—
309	C₄⋊C₈	—	178	1	no	—
310	C₄⋊C₈	—	178	2	no	—
311	C₄⋊C₈	—	178	1	no	—
312	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
313	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
315	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	89	2	no	—
318	C₂²⋊C₈	—	89	4	no	—
319	C₂²⋊C₈	—	178	1	no	—
320	C₂²⋊C₈	—	178	1	no	—
321	C₂²⋊C₈	—	178	1	no	—
322	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
323	#97	—	89	4	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	89	2	no	—
326	C₄×C₈	—	178	1	no	—
327	C₄×C₈	—	178	1	no	—
328	C₄×C₈	—	178	1	no	—
329	C₄×C₈	C₂²×D₈₉	1	2	yes	—
330	C₂⁴	—	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	—	89	1	no	—
342	C₂²×C₄	—	89	1	no	—
343	C₂²×C₄	—	89	1	no	—
344	C₂²×C₄	—	89	1	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	356	2	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	—	178	2	no	—
349	C₂²×C₄	—	178	4	no	—
350	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
353	M₁₆	—	4	2	no	—
354	M₁₆	—	356	4	no	—
355	M₁₆	—	356	2	no	—
356	M₁₆	—	178	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	89	4	no	—
361	C₂×C₈	—	356	2	no	—
362	C₂×C₈	—	356	2	no	—
363	C₂×C₈	—	356	4	no	—
364	C₂×C₈	—	178	1	no	—
365	C₂×C₈	—	178	1	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	C₂×C₄×D₈₉	1	4	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	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	2	no	—
397	C₂×C₄	—	89	4	no	—
398	C₂×C₄	—	89	2	no	—
399	C₂×C₄	—	89	1	no	—
400	C₂×C₄	—	89	1	no	—
401	C₂×C₄	—	89	1	no	—
402	C₂×C₄	—	89	1	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	1	no	—
405	C₂×C₄	—	356	1	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	—	178	2	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	1	no	—
413	C₂×C₄	—	178	2	no	—
414	C₂×C₄	—	178	2	no	—
415	C₂×C₄	—	178	2	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
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	4	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	—	356	1	no	—
428	C₈	—	356	1	no	—
429	C₈	—	356	2	no	—
430	C₈	—	178	4	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	89	2	no	—
435	C₂²	—	89	2	no	—
436	C₂²	—	356	4	no	—
437	C₂²	—	178	1	no	—
438	C₂²	—	178	1	no	—
439	C₂²	—	178	1	no	—
440	C₂²	—	178	1	no	—
441	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	89	2	no	—
446	C₄	—	89	2	no	—
447	C₄	—	178	1	no	—
448	C₄	—	178	1	no	—
449	C₄	—	178	1	no	—
450	C₄	—	178	1	no	—
451	C₄	#19151645	1	2	yes	—
452	C₄	#131×D₈₉	1	2	yes	—
453	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
454	C₄	#137×D₈₉	1	1	yes	characteristic
455	C₂	—	4	1	no	—
456	C₂	—	178	2	no	—
457	C₂	—	178	2	no	—
458	C₂	#424×D₈₉	1	1	yes	characteristic
459	C₂	#428×D₈₉	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×#1574	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1574	D₈₉
hypocenter	C₈₉	#17809
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
4. #26019043	C₂	semidirect
5. #26019041	C₂	semidirect
6. #26019040	C₂	semidirect
7. #26019025	C₂	semidirect
8. #26019021	C₂	semidirect
9. #26019003	C₂	semidirect
10. #26019001	C₂	semidirect
11. C₈₉×#1574	C₂	semidirect
36. #19151351	C₂²	semidirect
37. #19151350	C₂²	semidirect
38. #19151350	C₂²	semidirect
39. #19151349	C₂²	semidirect
40. #19151348	C₂²	semidirect
41. #19151348	C₂²	semidirect
45. #335×C₈₉	C₂²	semidirect
46. #334×C₈₉	C₂²	semidirect
237. #1574	D₈₉	semidirect
242. C₈₉	#17809	semidirect
273. #335	C₂×D₈₉	semidirect
277. #334	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028880	2
#431×D₈₉	2
#423×D₈₉	2
#26019043	2
#26019041	2
#26019040	2
#26019025	2
#26019021	2
#26019003	2
#26019001	2
C₈₉×#1574	2
#17809	89