Subgroups — #452×D₈₉ #26029457

Order 11392.

760 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151763	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151762	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151761	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151760	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151759	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151758	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151757	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×#13083574	—	2	1	no	—
18	C₂×#13083574	C₂²	1	1	yes	characteristic
19	C₂×#13083573	—	2	1	no	—
20	C₂×#13083573	C₂²	1	1	yes	characteristic
21	#41×D₈₉	—	2	4	no	—
22	#41×D₈₉	—	2	4	no	—
23	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₈₉	—	2	1	no	—
26	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₈₉	—	2	1	no	—
28	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
29	C₂×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
31	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
32	Q₁₆×D₈₉	—	2	4	no	—
33	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
36	SD₁₆×D₈₉	—	2	4	no	—
37	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
39	#15667992	C₂²	1	1	yes	characteristic, complemented
40	#15667991	C₂²	1	1	yes	characteristic, complemented
41	#15667990	—	2	1	no	—
42	#15667989	—	2	1	no	—
43	#15667988	C₂²	1	1	yes	characteristic, complemented
44	C₄⋊C₄×D₈₉	—	2	1	no	—
45	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
46	C₂²⋊C₄×D₈₉	—	2	1	no	—
47	#15667937	C₂²	1	1	yes	characteristic, complemented
48	#15667936	C₂²	1	1	yes	characteristic, complemented
49	#15667935	C₂²	1	1	yes	characteristic, complemented
50	#15667934	C₂²	1	1	yes	characteristic, complemented
51	#15667933	C₂²	1	1	yes	characteristic, complemented
52	#15667932	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
54	#15667924	C₂²	1	1	yes	characteristic, complemented
55	#15667924	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₈₉	—	2	1	no	—
64	C₂³×D₈₉	D₄	1	1	yes	characteristic
65	#13083575	—	2	2	no	—
66	#13083575	—	2	2	no	—
67	#13083574	—	2	8	no	—
68	#13083574	—	2	2	no	—
69	#13083574	—	2	2	no	—
70	#13083573	—	2	8	no	—
71	#13083573	—	2	2	no	—
72	#13083573	—	2	2	no	—
73	C₂×Dic₁₇₈	—	2	1	no	—
74	C₂×Dic₁₇₈	—	2	1	no	—
75	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
76	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
77	Q₈×D₈₉	—	2	2	no	—
78	Q₈×D₈₉	—	2	2	no	—
79	Q₈×D₈₉	—	2	2	no	—
80	Q₈×D₈₉	D₄	1	4	yes	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₈₉	—	2	1	no	—
84	C₂×C₂²⋊D₈₉	—	2	1	no	—
85	C₂×C₂²⋊D₈₉	—	2	1	no	—
86	D₄×D₈₉	—	2	8	no	—
87	D₄×D₈₉	—	2	2	no	—
88	D₄×D₈₉	D₄	1	4	yes	—
89	C₂²×Dic₈₉	—	2	1	no	—
90	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
91	C₂×C₄×D₈₉	—	2	8	no	—
92	C₂×C₄×D₈₉	—	2	1	no	—
93	C₂×C₄×D₈₉	—	2	1	no	—
94	C₂×C₄×D₈₉	—	2	1	no	—
95	C₂×C₄×D₈₉	—	2	2	no	—
96	C₂×C₄×D₈₉	—	2	2	no	—
97	C₂×C₄×D₈₉	—	2	1	no	—
98	C₂×C₄×D₈₉	—	2	1	no	—
99	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
100	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
103	Dic₃₅₆	—	2	2	no	—
104	#13083564	—	2	2	no	—
105	#13083564	—	2	2	no	—
106	#13083563	—	2	2	no	—
107	#13083562	—	2	2	no	—
108	#13083561	—	2	2	no	—
109	C₂×#10623494	C₂³	1	1	yes	characteristic
110	C₂×#10623494	C₂³	1	1	yes	characteristic
111	C₈×D₈₉	—	2	2	no	—
112	C₈×D₈₉	—	2	2	no	—
113	C₄⋊Dic₈₉	—	2	1	no	—
114	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
115	#13083553	—	2	1	no	—
116	#13083553	—	2	1	no	—
117	#13083553	—	2	1	no	—
118	C₂²⋊Dic₈₉	—	2	1	no	—
119	#13083551	—	2	1	no	—
120	#13083551	—	2	1	no	—
121	#41×C₈₉	—	2	2	no	—
122	#41×C₈₉	—	2	2	no	—
123	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
129	Q₁₆×C₈₉	—	2	2	no	—
130	SD₁₆×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂³×C₈₉	—	2	1	no	—
137	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₈₉	—	2	1	no	—
139	C₂²×D₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	2	4	no	—
141	C₂²×D₈₉	—	2	2	no	—
142	C₂²×D₈₉	—	2	2	no	—
143	C₂²×D₈₉	—	4	2	no	—
144	C₂²×D₈₉	—	4	2	no	—
145	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
147	Q₈×C₈₉	—	2	1	no	—
148	Q₈×C₈₉	—	2	1	no	—
149	Q₈×C₈₉	—	2	1	no	—
150	Q₈×C₈₉	C₂×D₄	1	2	yes	—
151	D₄×C₈₉	—	2	4	no	—
152	D₄×C₈₉	—	2	1	no	—
153	D₄×C₈₉	C₂×D₄	1	2	yes	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	C₂²⋊D₈₉	—	2	4	no	—
163	C₂²⋊D₈₉	—	2	4	no	—
164	C₂²⋊D₈₉	—	2	4	no	—
165	C₂×Dic₈₉	—	2	4	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
172	D₃₅₆	—	2	4	no	—
173	D₃₅₆	—	2	1	no	—
174	D₃₅₆	C₂×D₄	1	2	yes	—
175	C₄×D₈₉	—	2	4	no	—
176	C₄×D₈₉	—	2	4	no	—
177	C₄×D₈₉	—	2	2	no	—
178	C₄×D₈₉	—	2	4	no	—
179	C₄×D₈₉	—	2	1	no	—
180	C₄×D₈₉	—	2	1	no	—
181	C₄×D₈₉	—	2	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₄×D₈₉	C₂×D₄	1	2	yes	—
185	C₄×D₈₉	C₂×D₄	1	2	yes	—
186	Dic₁₇₈	—	2	1	no	—
187	Dic₁₇₈	—	2	4	no	—
188	Dic₁₇₈	—	2	1	no	—
189	Dic₁₇₈	—	2	1	no	—
190	Dic₁₇₈	—	4	2	no	—
191	Dic₁₇₈	C₂×D₄	1	2	yes	—
192	C₈×C₈₉	—	2	1	no	—
193	C₈×C₈₉	—	2	1	no	—
194	#10623494	—	2	1	no	—
195	#10623494	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×D₈₉	—	2	1	no	—
204	C₂×D₈₉	—	2	2	no	—
205	C₂×D₈₉	—	2	1	no	—
206	C₂×D₈₉	—	2	1	no	—
207	C₂×D₈₉	—	4	1	no	—
208	C₂×D₈₉	—	4	1	no	—
209	C₂×D₈₉	—	4	4	no	—
210	C₂×D₈₉	—	4	8	no	—
211	C₂×D₈₉	#120	1	2	yes	—
212	C₂×D₈₉	#135	1	2	yes	—
213	C₂×D₈₉	#137	1	2	yes	—
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	4	1	no	—
217	C₄×C₈₉	—	4	1	no	—
218	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
219	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
220	Dic₈₉	—	2	2	no	—
221	Dic₈₉	—	2	1	no	—
222	Dic₈₉	—	4	1	no	—
223	Dic₈₉	—	4	1	no	—
224	Dic₈₉	#120	1	2	yes	—
225	C₂×C₈₉	—	4	1	no	—
226	C₂×C₈₉	—	4	2	no	—
227	C₂×C₈₉	C₂×#120	1	1	yes	characteristic
228	C₂×C₈₉	C₂×#135	1	1	yes	characteristic
229	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
230	D₈₉	—	4	1	no	—
231	D₈₉	—	4	2	no	—
232	D₈₉	#452	1	4	yes	direct product factor
233	C₂×#452	—	89	1	no	maximal, Sylow
234	C₈₉	C₂×#452	1	1	yes	characteristic, complemented, Sylow
235	C₂²×#41	—	89	1	no	—
236	C₂²×Q₁₆	—	89	1	no	—
237	C₂²×SD₁₆	—	89	1	no	—
238	C₂×C₂²⋊Q₈	—	89	1	no	—
239	#452	—	89	1	no	—
240	#452	—	89	1	no	—
241	#452	—	89	1	no	—
242	#452	—	89	1	no	—
243	#452	—	89	1	no	—
244	#452	—	89	1	no	—
245	#452	—	89	1	no	—
246	#452	D₈₉	1	1	yes	characteristic, direct product factor
247	C₂×#103	—	89	1	no	—
248	C₂×#102	—	89	1	no	—
249	C₂×C₂²⋊C₈	—	89	1	no	—
250	C₂×#41	—	89	1	no	—
251	C₂×#41	—	89	1	no	—
252	C₂×#41	—	89	1	no	—
253	C₂×#41	—	178	1	no	—
254	C₂×#41	—	178	1	no	—
255	C₂×#41	—	178	4	no	—
256	C₂×#41	—	178	4	no	—
257	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
258	C₂²×Q₈	—	89	1	no	—
259	C₂²×Q₈	—	89	1	no	—
260	C₂²×D₄	—	89	1	no	—
261	C₂²×D₄	—	178	1	no	—
262	C₂³×C₄	—	89	1	no	—
263	C₂³×C₄	—	178	1	no	—
264	C₂×Q₁₆	—	89	1	no	—
265	C₂×Q₁₆	—	89	1	no	—
266	C₂×Q₁₆	—	89	1	no	—
267	C₂×Q₁₆	—	178	4	no	—
268	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	—	89	1	no	—
270	C₂×SD₁₆	—	89	1	no	—
271	C₂×SD₁₆	—	89	1	no	—
272	C₂×SD₁₆	—	178	4	no	—
273	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
274	C₂²×C₈	—	89	1	no	—
275	C₂²×C₈	—	89	1	no	—
276	C₂²⋊Q₈	—	89	1	no	—
277	C₂²⋊Q₈	—	89	1	no	—
278	C₂²⋊Q₈	—	89	1	no	—
279	C₂²⋊Q₈	—	178	1	no	—
280	C₂²⋊Q₈	—	178	1	no	—
281	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
282	C₂×C₄⋊C₄	—	89	1	no	—
283	C₂×C₄⋊C₄	—	178	1	no	—
284	C₂×C₂²⋊C₄	—	178	1	no	—
285	#103	—	89	1	no	—
286	#103	—	89	1	no	—
287	#103	—	89	1	no	—
288	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
289	#102	—	89	1	no	—
290	#102	—	89	1	no	—
291	#102	—	89	1	no	—
292	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
293	C₂²⋊C₈	—	89	1	no	—
294	C₂²⋊C₈	—	89	1	no	—
295	C₂²⋊C₈	—	89	1	no	—
296	C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
297	C₂⁴	—	89	1	no	—
298	C₂⁴	—	178	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	178	2	no	—
302	#41	—	178	2	no	—
303	#41	—	178	8	no	—
304	#41	—	178	2	no	—
305	#41	—	178	8	no	—
306	#41	—	178	2	no	—
307	#41	—	178	2	no	—
308	#41	—	178	2	no	—
309	C₂×Q₈	—	89	4	no	—
310	C₂×Q₈	—	89	1	no	—
311	C₂×Q₈	—	89	1	no	—
312	C₂×Q₈	—	178	1	no	—
313	C₂×Q₈	—	178	1	no	—
314	C₂×Q₈	—	178	2	no	—
315	C₂×Q₈	—	178	2	no	—
316	C₂×Q₈	—	178	2	no	—
317	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	89	4	no	—
321	C₂×D₄	—	89	1	no	—
322	C₂×D₄	—	178	1	no	—
323	C₂×D₄	—	178	2	no	—
324	C₂×D₄	—	178	1	no	—
325	C₂×D₄	—	178	8	no	—
326	C₂×D₄	—	178	1	no	—
327	C₂×D₄	—	178	1	no	—
328	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	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	—	178	2	no	—
336	C₂²×C₄	—	178	2	no	—
337	C₂²×C₄	—	178	1	no	—
338	C₂²×C₄	—	178	1	no	—
339	C₂²×C₄	—	178	1	no	—
340	C₂²×C₄	—	178	1	no	—
341	C₂²×C₄	—	178	8	no	—
342	C₂²×C₄	—	178	1	no	—
343	C₂²×C₄	—	178	1	no	—
344	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	178	2	no	—
347	Q₁₆	—	178	2	no	—
348	Q₁₆	—	178	2	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	178	2	no	—
351	SD₁₆	—	178	2	no	—
352	SD₁₆	—	178	2	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
358	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	89	1	no	—
361	C₄⋊C₄	—	178	1	no	—
362	C₄⋊C₄	—	178	1	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₄⋊C₄	—	178	1	no	—
365	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	178	1	no	—
368	C₂²⋊C₄	—	178	1	no	—
369	C₂²⋊C₄	—	178	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	89	1	no	—
372	C₂³	—	89	1	no	—
373	C₂³	—	356	2	no	—
374	C₂³	—	356	2	no	—
375	C₂³	—	178	4	no	—
376	C₂³	—	178	2	no	—
377	C₂³	—	178	2	no	—
378	C₂³	—	178	2	no	—
379	C₂³	—	178	1	no	—
380	C₂³	D₄×D₈₉	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	89	2	no	—
385	Q₈	—	356	2	no	—
386	Q₈	—	178	4	no	—
387	Q₈	—	178	1	no	—
388	Q₈	—	178	1	no	—
389	Q₈	—	178	1	no	—
390	Q₈	D₄×D₈₉	1	2	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	89	2	no	—
394	D₄	—	178	4	no	—
395	D₄	—	178	4	no	—
396	D₄	—	178	4	no	—
397	D₄	—	178	4	no	—
398	D₄	—	178	1	no	—
399	D₄	D₄×D₈₉	1	2	yes	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	89	1	no	—
407	C₂×C₄	—	89	2	no	—
408	C₂×C₄	—	89	2	no	—
409	C₂×C₄	—	89	1	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	356	2	no	—
412	C₂×C₄	—	178	2	no	—
413	C₂×C₄	—	178	2	no	—
414	C₂×C₄	—	178	4	no	—
415	C₂×C₄	—	178	4	no	—
416	C₂×C₄	—	178	4	no	—
417	C₂×C₄	—	178	2	no	—
418	C₂×C₄	—	178	1	no	—
419	C₂×C₄	—	178	1	no	—
420	C₂×C₄	—	178	4	no	—
421	C₂×C₄	—	178	1	no	—
422	C₂×C₄	—	178	1	no	—
423	C₂×C₄	—	178	1	no	—
424	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	178	1	no	—
429	C₈	—	178	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	89	2	no	—
437	C₂²	—	89	2	no	—
438	C₂²	—	89	2	no	—
439	C₂²	—	356	8	no	—
440	C₂²	—	356	4	no	—
441	C₂²	—	356	1	no	—
442	C₂²	—	356	1	no	—
443	C₂²	—	178	1	no	—
444	C₂²	—	178	2	no	—
445	C₂²	—	178	1	no	—
446	C₂²	—	178	1	no	—
447	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	89	2	no	—
453	C₄	—	356	1	no	—
454	C₄	—	356	1	no	—
455	C₄	—	178	1	no	—
456	C₄	—	178	2	no	—
457	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
458	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	89	4	no	—
462	C₂	—	356	2	no	—
463	C₂	—	356	1	no	—
464	C₂	#120×D₈₉	1	1	yes	characteristic
465	C₂	#135×D₈₉	1	1	yes	characteristic
466	C₂	#137×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#452×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×#41×D₈₉	C₂
hypercenter	#452	D₈₉
hypocenter	C₈₉	C₂×#452
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×D₈₉	C₂	semidirect
3. C₂×SD₁₆×D₈₉	C₂	semidirect
4. C₂²⋊Q₈×D₈₉	C₂	semidirect
5. #19151763	C₂	semidirect
6. #19151762	C₂	semidirect
7. #19151761	C₂	semidirect
8. #19151760	C₂	semidirect
9. #19151759	C₂	semidirect
10. #19151758	C₂	semidirect
11. #19151757	C₂	semidirect
12. #103×D₈₉	C₂	semidirect
13. #102×D₈₉	C₂	semidirect
14. C₂²⋊C₈×D₈₉	C₂	semidirect
15. #452×C₈₉	C₂	semidirect
29. C₂×Dic₃₅₆	C₂²	semidirect
30. C₂×#13083564	C₂²	semidirect
31. C₂×#13083564	C₂²	semidirect
33. C₂×#13083563	C₂²	semidirect
34. C₂×#13083562	C₂²	semidirect
35. C₂×#13083561	C₂²	semidirect
39. #15667992	C₂²	semidirect
40. #15667991	C₂²	semidirect
43. #15667988	C₂²	semidirect
47. #15667937	C₂²	semidirect
48. #15667936	C₂²	semidirect
49. #15667935	C₂²	semidirect
50. #15667934	C₂²	semidirect
51. #15667933	C₂²	semidirect
52. #15667932	C₂²	semidirect
53. C₂²⋊#10623494	C₂²	semidirect
54. #15667924	C₂²	semidirect
55. #15667924	C₂²	semidirect
57. C₂×Q₁₆×C₈₉	C₂²	semidirect
58. C₂×SD₁₆×C₈₉	C₂²	semidirect
59. C₂²⋊Q₈×C₈₉	C₂²	semidirect
60. #103×C₈₉	C₂²	semidirect
61. #102×C₈₉	C₂²	semidirect
62. C₂²⋊C₈×C₈₉	C₂²	semidirect
232. D₈₉	#452	direct (N × H)
234. C₈₉	C₂×#452	semidirect
246. #452	D₈₉	direct (N × H)
268. C₂×Q₁₆	C₂×D₈₉	semidirect
273. C₂×SD₁₆	C₂×D₈₉	semidirect
281. C₂²⋊Q₈	C₂×D₈₉	semidirect
288. #103	C₂×D₈₉	semidirect
292. #102	C₂×D₈₉	semidirect
296. C₂²⋊C₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₈₉	2
C₂×Q₁₆×D₈₉	2
C₂×SD₁₆×D₈₉	2
C₂²⋊Q₈×D₈₉	2
#19151763	2
#19151762	2
#19151761	2
#19151760	2
#19151759	2
#19151758	2
#19151757	2
#103×D₈₉	2
#102×D₈₉	2
C₂²⋊C₈×D₈₉	2
#452×C₈₉	2
C₂×#452	89

Subgroups — #452×D89 #26029457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #452×D₈₉ #26029457