Subgroups — #36561261

Order 22784.

938 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151715	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028956	C₂	1	2	yes	maximal, complemented
3	C₂×M₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021146	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021006	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020958	C₂	1	2	yes	maximal, complemented
7	#26020696	C₂	1	2	yes	maximal, complemented
8	#26020294	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020099	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	C₂²×#13083558	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
15	#19151715	—	2	4	no	—
16	#19151676	—	2	4	no	—
17	#19151670	—	2	4	no	—
18	C₂×#15667948	C₂²	1	1	yes	characteristic
19	C₂×#15667948	C₂²	1	1	yes	characteristic
20	#19151625	C₂²	1	2	yes	—
21	C₂×#15667939	C₂²	1	2	yes	—
22	C₂×#15667939	C₂²	1	2	yes	—
23	#19151565	C₂²	1	2	yes	—
24	#19151562	C₂²	1	2	yes	—
25	#19151554	C₂²	1	2	yes	—
26	M₁₆×Dic₈₉	—	2	4	no	—
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×#15667922	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151363	C₂²	1	2	yes	—
32	#19151357	C₂²	1	2	yes	—
33	#19151357	C₂²	1	2	yes	—
34	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
36	#525×C₈₉	C₂²	1	2	yes	—
37	#470×C₈₉	C₄	1	2	yes	complemented
38	#469×C₈₉	C₄	1	2	yes	complemented
39	#468×C₈₉	C₄	1	4	yes	complemented
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#416×C₈₉	C₂²	1	2	yes	—
42	C₂³×Dic₈₉	—	2	1	no	—
43	#15668019	—	2	4	no	—
44	#15668019	—	2	4	no	—
45	C₂×#13083558	—	2	2	no	—
46	C₂×#13083558	—	2	2	no	—
47	C₂×#13083558	—	2	2	no	—
48	C₂×#13083558	D₄	1	2	yes	—
49	C₂×#13083558	D₄	1	2	yes	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083558	C₂³	1	2	yes	—
52	C₂²×#10623494	—	2	2	no	—
53	C₂²×#10623494	C₂³	1	1	yes	characteristic
54	C₂²×#10623494	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	—	2	2	no	—
56	C₂×C₄×Dic₈₉	—	2	2	no	—
57	C₂×C₄×Dic₈₉	—	2	1	no	—
58	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
60	#15667948	—	2	2	no	—
61	#15667948	—	2	2	no	—
62	C₄⋊#10623494	—	2	4	no	—
63	#15667939	—	2	4	no	—
64	#15667939	—	2	4	no	—
65	C₂²⋊#10623494	—	2	4	no	—
66	C₂²⋊#10623494	—	2	4	no	—
67	#15667923	—	2	2	no	—
68	#15667922	—	2	2	no	—
69	#15667922	—	2	2	no	—
70	C₄×#10623494	—	2	2	no	—
71	C₈×Dic₈₉	—	2	2	no	—
72	C₈×Dic₈₉	D₄	1	4	yes	complemented
73	C₂×#41×C₈₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	#135×C₈₉	—	2	2	no	—
76	#135×C₈₉	—	2	2	no	—
77	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
79	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂×M₁₆×C₈₉	—	2	2	no	—
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	#123×C₈₉	—	2	2	no	—
87	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
88	#121×C₈₉	C₂×C₄	1	4	yes	—
89	#120×C₈₉	—	2	2	no	—
90	C₄×D₄×C₈₉	—	2	4	no	—
91	#117×C₈₉	C₂³	1	2	yes	—
92	#107×C₈₉	C₂×C₄	1	2	yes	complemented
93	#106×C₈₉	C₂×C₄	1	2	yes	complemented
94	#103×C₈₉	C₂×C₄	1	4	yes	complemented
95	#102×C₈₉	C₂×C₄	1	4	yes	complemented
96	C₂²×Dic₈₉	—	2	1	no	—
97	C₂²×Dic₈₉	—	2	4	no	—
98	C₂²×Dic₈₉	—	2	1	no	—
99	C₂²×Dic₈₉	—	4	4	no	—
100	#13083558	—	2	4	no	—
101	#13083558	—	2	4	no	—
102	#13083558	—	2	2	no	—
103	#13083558	—	2	2	no	—
104	#13083558	—	2	2	no	—
105	#13083558	—	2	2	no	—
106	#13083558	—	4	4	no	—
107	C₂×#10623494	—	2	1	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	4	4	no	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
114	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
115	C₂×#10623494	C₂×D₄	1	2	yes	—
116	C₂×#10623494	#41	1	2	yes	—
117	C₄×Dic₈₉	—	2	4	no	—
118	C₄×Dic₈₉	—	2	1	no	—
119	C₄×Dic₈₉	—	2	1	no	—
120	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
121	C₄×Dic₈₉	#41	1	2	yes	—
122	C₂⁴×C₈₉	#41	1	1	yes	characteristic
123	#41×C₈₉	—	2	2	no	—
124	#41×C₈₉	—	2	2	no	—
125	#41×C₈₉	—	2	2	no	—
126	#41×C₈₉	—	2	2	no	—
127	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₈₉	—	2	2	no	—
129	C₂×D₄×C₈₉	—	2	4	no	—
130	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	—	2	2	no	—
136	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₈₉	—	2	2	no	—
141	SD₁₆×C₈₉	—	2	4	no	—
142	D₈×C₈₉	—	2	2	no	—
143	M₁₆×C₈₉	—	2	4	no	—
144	M₁₆×C₈₉	—	2	4	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₈₉	#41	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	4	no	—
153	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
154	C₂²⋊C₄×C₈₉	—	2	4	no	—
155	C₂²⋊C₄×C₈₉	—	2	2	no	—
156	C₂²⋊C₄×C₈₉	—	2	4	no	—
157	C₄²×C₈₉	—	2	2	no	—
158	C₂³×C₈₉	—	2	1	no	—
159	C₂³×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	—	2	2	no	—
161	C₂³×C₈₉	—	4	2	no	—
162	C₂³×C₈₉	C₄×D₄	1	2	yes	—
163	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	2	2	no	—
166	D₄×C₈₉	—	2	2	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	4	2	no	—
169	D₄×C₈₉	—	4	2	no	—
170	D₄×C₈₉	—	8	4	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₈₉	—	2	4	no	—
189	C₂×Dic₈₉	—	2	2	no	—
190	C₂×Dic₈₉	—	2	2	no	—
191	C₂×Dic₈₉	—	4	8	no	—
192	C₂×Dic₈₉	—	4	2	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	C₄×D₄	1	2	yes	—
195	C₈×C₈₉	C₄×D₄	1	2	yes	—
196	#10623494	—	2	2	no	—
197	#10623494	—	4	2	no	—
198	#10623494	—	4	2	no	—
199	#10623494	#121	1	2	yes	—
200	#10623494	#121	1	2	yes	—
201	C₂²×C₈₉	—	2	2	no	—
202	C₂²×C₈₉	—	2	4	no	—
203	C₂²×C₈₉	—	2	2	no	—
204	C₂²×C₈₉	—	4	2	no	—
205	C₂²×C₈₉	—	4	2	no	—
206	C₂²×C₈₉	—	4	4	no	—
207	C₂²×C₈₉	—	4	2	no	—
208	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₈₉	#525	1	1	yes	characteristic
210	C₂²×C₈₉	#529	1	1	yes	characteristic
211	C₄×C₈₉	—	2	2	no	—
212	C₄×C₈₉	—	4	4	no	—
213	C₄×C₈₉	—	4	2	no	—
214	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
216	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
217	C₄×C₈₉	#532	1	1	yes	characteristic
218	Dic₈₉	—	2	4	no	—
219	Dic₈₉	—	4	2	no	—
220	#21549	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	—	2	1	no	—
222	C₂×C₈₉	—	2	1	no	—
223	C₂×C₈₉	—	4	2	no	—
224	C₂×C₈₉	—	8	2	no	—
225	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
226	C₂×C₈₉	#2956	1	2	yes	—
227	#3054	D₈₉	1	1	yes	characteristic
228	C₂×#443	—	89	1	no	—
229	#2930	—	89	2	no	—
230	C₂×C₄×M₁₆	—	89	1	no	—
231	#1975	—	89	1	no	—
232	#1946	—	89	1	no	—
233	#1937	—	89	2	no	—
234	#1896	—	89	2	no	—
235	#1811	—	89	1	no	—
236	#1772	—	89	1	no	—
237	#1765	—	89	2	no	—
238	C₈₉	#21549	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
240	C₂×#131	—	89	2	no	—
241	C₂²×M₁₆	—	89	1	no	—
242	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
243	#525	C₂×D₈₉	1	2	yes	—
244	C₂²×C₄²	—	89	1	no	—
245	#470	Dic₈₉	1	2	yes	complemented
246	#469	Dic₈₉	1	2	yes	complemented
247	#468	Dic₈₉	1	4	yes	complemented
248	#443	—	178	4	no	—
249	#436	—	178	4	no	—
250	#435	—	178	4	no	—
251	C₂×#108	—	89	1	no	—
252	C₂×#108	—	89	1	no	—
253	#427	C₂×D₈₉	1	1	yes	characteristic
254	#424	—	89	2	no	—
255	C₂×#104	—	89	2	no	—
256	C₂×#104	—	89	2	no	—
257	#416	C₂×D₈₉	1	2	yes	—
258	#408	—	89	2	no	—
259	#407	—	89	2	no	—
260	#405	—	89	2	no	—
261	C₄×M₁₆	—	178	4	no	—
262	C₂×#97	—	89	1	no	—
263	C₂×#97	—	89	1	no	—
264	C₂×C₄×C₈	—	89	1	no	—
265	C₂×C₄×C₈	—	89	1	no	—
266	#341	—	89	2	no	—
267	#339	—	89	2	no	—
268	#339	—	89	2	no	—
269	C₂×#41	C₂²×D₈₉	1	2	yes	—
270	C₂³×C₄	—	178	1	no	—
271	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
272	#135	—	2	2	no	—
273	#135	—	2	2	no	—
274	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	complemented
276	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic, complemented
277	#131	—	178	4	no	—
278	#131	—	178	4	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	89	2	no	—
282	C₂×M₁₆	—	89	2	no	—
283	C₂×M₁₆	—	89	2	no	—
284	C₂×M₁₆	—	89	2	no	—
285	C₂×M₁₆	—	178	2	no	—
286	C₂×M₁₆	—	178	2	no	—
287	C₂×M₁₆	—	178	2	no	—
288	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
289	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
290	C₂²×C₈	—	89	1	no	—
291	C₂²×C₈	—	89	1	no	—
292	C₂²×C₈	—	178	2	no	—
293	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
295	#123	—	2	2	no	—
296	C₂²⋊Q₈	C₂×Dic₈₉	1	4	yes	—
297	#121	C₂×Dic₈₉	1	4	yes	—
298	#120	—	2	2	no	—
299	C₄×D₄	—	2	4	no	—
300	#117	C₂²×D₈₉	1	2	yes	—
301	C₂×C₄²	—	89	1	no	—
302	C₂×C₄²	—	89	1	no	—
303	C₂×C₄²	—	178	2	no	—
304	C₂×C₄²	—	178	2	no	—
305	C₂×C₄²	—	178	1	no	—
306	#108	—	178	2	no	—
307	#108	—	178	2	no	—
308	#107	C₂×Dic₈₉	1	2	yes	complemented
309	#106	C₂×Dic₈₉	1	2	yes	complemented
310	C₄⋊C₈	—	178	4	no	—
311	#104	—	178	4	no	—
312	#104	—	178	4	no	—
313	#103	C₂×Dic₈₉	1	4	yes	complemented
314	#102	C₂×Dic₈₉	1	4	yes	complemented
315	C₂²⋊C₈	—	178	4	no	—
316	C₂²⋊C₈	—	178	4	no	—
317	#97	—	178	2	no	—
318	#97	—	178	2	no	—
319	#97	—	178	2	no	—
320	C₄×C₈	—	89	4	no	—
321	C₄×C₈	—	178	2	no	—
322	C₄×C₈	—	178	2	no	—
323	C₂⁴	#13083573	1	1	yes	characteristic
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	356	4	no	—
338	C₂²×C₄	—	178	4	no	—
339	C₂²×C₄	—	178	1	no	—
340	C₂²×C₄	—	178	1	no	—
341	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
342	C₂²×C₄	D₄×D₈₉	1	2	yes	—
343	C₂²×C₄	#13083573	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	SD₁₆	—	2	4	no	—
347	D₈	—	2	2	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	356	4	no	—
351	M₁₆	—	178	4	no	—
352	M₁₆	—	178	4	no	—
353	M₁₆	—	178	2	no	—
354	M₁₆	—	178	2	no	—
355	M₁₆	—	178	2	no	—
356	M₁₆	—	178	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	89	2	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	—	89	2	no	—
363	C₂×C₈	—	89	2	no	—
364	C₂×C₈	—	356	4	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
370	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
371	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
372	C₂×C₈	D₄×D₈₉	1	2	yes	—
373	C₂×C₈	#13083573	1	2	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	89	2	no	—
381	C₄²	—	89	2	no	—
382	C₄²	—	178	4	no	—
383	C₄²	—	178	1	no	—
384	C₄²	—	178	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	D₄×Dic₈₉	1	2	yes	—
390	C₂³	C₂×#13083573	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	8	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	—	178	4	no	—
412	C₂×C₄	—	178	2	no	—
413	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
414	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
417	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
418	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	89	2	no	—
422	C₈	—	89	2	no	—
423	C₈	—	356	2	no	—
424	C₈	—	356	2	no	—
425	C₈	—	178	2	no	—
426	C₈	D₄×Dic₈₉	1	2	yes	—
427	C₈	D₄×Dic₈₉	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
436	C₂²	#19152108	1	1	yes	characteristic
437	C₂²	#19152129	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	356	2	no	—
442	C₄	—	178	4	no	—
443	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
444	C₄	#41×Dic₈₉	1	1	yes	characteristic
445	C₄	#121×D₈₉	1	1	yes	characteristic
446	C₄	#19152143	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	#121×Dic₈₉	1	1	yes	characteristic
452	C₂	#26029162	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3054	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3054	D₈₉
hypocenter	C₈₉	#21549
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. C₂×#19151715	C₂	semidirect
2. #26028956	C₂	semidirect
3. C₂×M₁₆×Dic₈₉	C₂	semidirect
4. #26021146	C₂	semidirect
5. #26021006	C₂	semidirect
6. #26020958	C₂	semidirect
7. #26020696	C₂	semidirect
8. #26020294	C₂	semidirect
9. #26020133	C₂	semidirect
10. #26020099	C₂	semidirect
37. #470×C₈₉	C₄	semidirect
38. #469×C₈₉	C₄	semidirect
39. #468×C₈₉	C₄	semidirect
72. C₈×Dic₈₉	D₄	semidirect
77. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
78. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
79. C₂×D₈×C₈₉	C₂×C₄	semidirect
92. #107×C₈₉	C₂×C₄	semidirect
93. #106×C₈₉	C₂×C₄	semidirect
94. #103×C₈₉	C₂×C₄	semidirect
95. #102×C₈₉	C₂×C₄	semidirect
238. C₈₉	#21549	semidirect
245. #470	Dic₈₉	semidirect
246. #469	Dic₈₉	semidirect
247. #468	Dic₈₉	semidirect
274. C₂×Q₁₆	C₂×Dic₈₉	semidirect
275. C₂×SD₁₆	C₂×Dic₈₉	semidirect
276. C₂×D₈	C₂×Dic₈₉	semidirect
308. #107	C₂×Dic₈₉	semidirect
309. #106	C₂×Dic₈₉	semidirect
313. #103	C₂×Dic₈₉	semidirect
314. #102	C₂×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151715	2
#26028956	2
C₂×M₁₆×Dic₈₉	2
#26021146	2
#26021006	2
#26020958	2
#26020696	2
#26020294	2
#26020133	2
#26020099	2
C₈₉×#3054	2
#21549	89