Subgroups — #36520064

Order 22784.

742 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028883	C₂	1	1	yes	maximal, characteristic
2	#26028880	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151649	C₂	1	1	yes	maximal, characteristic
4	#26018553	C₂	1	2	yes	maximal, complemented
5	#26018553	C₂	1	2	yes	maximal, complemented
6	#26018550	C₂	1	2	yes	maximal, complemented
7	#26018548	C₂	1	2	yes	maximal, complemented
8	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
13	#19151654	C₄	1	2	yes	—
14	#19151653	C₄	1	2	yes	—
15	#19151653	C₄	1	2	yes	—
16	#19151652	C₄	1	2	yes	—
17	#19151651	C₂²	1	1	yes	characteristic
18	#19151649	C₄	1	2	yes	—
19	#19151649	C₄	1	2	yes	—
20	#19151649	C₂²	1	1	yes	characteristic
21	#19151649	C₂²	1	1	yes	characteristic
22	#19151649	C₂²	1	1	yes	characteristic
23	#19151649	C₂²	1	1	yes	characteristic
24	#19151649	C₂²	1	2	yes	—
25	#19151649	C₂²	1	2	yes	—
26	#19151649	C₂²	1	2	yes	—
27	#19151621	C₄	1	2	yes	—
28	#19151620	C₄	1	2	yes	—
29	C₂×#15667941	C₄	1	2	yes	—
30	#19151561	C₄	1	2	yes	—
31	#19151560	C₄	1	2	yes	—
32	C₂×#15667924	C₄	1	2	yes	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₄×#13083557	C₂²	1	2	yes	—
35	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
36	#19151320	C₂²	1	2	yes	complemented
37	#19151320	C₂²	1	2	yes	complemented
38	#19151319	C₂²	1	2	yes	complemented
39	#19151319	C₂²	1	2	yes	complemented
40	C₈×#10623494	C₂²	1	2	yes	complemented
41	C₈×#10623494	C₂²	1	2	yes	complemented
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#322×C₈₉	C₂²	1	2	yes	complemented
46	#322×C₈₉	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083558	C₂×C₄	1	2	yes	—
51	C₂×#13083557	C₂×C₄	1	4	yes	—
52	C₂²×#10623494	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₈₉	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₈₉	C₂³	1	1	yes	characteristic
63	C₄²×D₈₉	C₂³	1	1	yes	characteristic
64	C₄⋊#10623494	C₂×C₄	1	2	yes	—
65	#15667941	C₂×C₄	1	2	yes	—
66	#15667941	C₂×C₄	1	2	yes	—
67	#15667941	C₂×C₄	1	2	yes	—
68	#15667941	C₂×C₄	1	2	yes	—
69	#15667941	C₂×C₄	1	4	yes	—
70	#15667941	C₂×C₄	1	4	yes	—
71	#15667941	C₂×C₄	1	4	yes	—
72	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
73	#15667924	C₂×C₄	1	2	yes	—
74	#15667924	C₂×C₄	1	2	yes	—
75	#15667924	C₂×C₄	1	2	yes	—
76	#15667924	C₂×C₄	1	2	yes	—
77	#15667924	C₂×C₄	1	4	yes	—
78	#15667924	C₂×C₄	1	4	yes	—
79	#15667924	C₂×C₄	1	4	yes	—
80	#15667923	C₂×C₄	1	2	yes	—
81	#15667922	C₂×C₄	1	4	yes	—
82	C₄×#10623494	C₂×C₄	1	2	yes	—
83	C₄×#10623494	C₂³	1	1	yes	characteristic
84	C₄×#10623494	C₂³	1	1	yes	characteristic
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₄×#10623494	C₂³	1	2	yes	—
87	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
92	#97×C₈₉	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	2	yes	—
97	C₄×C₈×C₈₉	C₂³	1	2	yes	—
98	C₂³×D₈₉	C₄²	1	1	yes	characteristic
99	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
100	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
101	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₈₉	—	2	4	no	—
103	C₂×C₄×D₈₉	—	4	2	no	—
104	C₂×C₄×D₈₉	—	4	2	no	—
105	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₂²×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	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
117	#13083558	—	2	4	no	—
118	#13083557	—	4	4	no	—
119	C₂×#10623494	—	4	2	no	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₂×#10623494	C₂²×C₄	1	2	yes	—
122	C₂×#10623494	C₂²×C₄	1	4	yes	—
123	C₂×#10623494	C₂²×C₄	1	4	yes	—
124	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
125	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
126	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
127	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
128	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
129	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
130	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₈₉	C₂²×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	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	M₁₆×C₈₉	—	2	4	no	—
140	C₂×C₈×C₈₉	—	4	2	no	—
141	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
142	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
145	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
150	C₂²×D₈₉	—	2	2	no	—
151	C₂²×D₈₉	—	4	1	no	—
152	C₂²×D₈₉	—	4	1	no	—
153	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
154	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#131	1	4	yes	—
161	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	4	1	no	—
166	C₂×Dic₈₉	—	4	1	no	—
167	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
168	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
169	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₈₉	—	2	2	no	—
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	2	2	no	—
176	C₄×D₈₉	—	2	2	no	—
177	C₄×D₈₉	—	2	2	no	—
178	C₄×D₈₉	—	2	2	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	—	2	2	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	C₄×D₈₉	—	4	1	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₈×C₈₉	—	2	4	no	—
186	C₈×C₈₉	—	2	2	no	—
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	—	2	4	no	—
189	#10623494	—	2	4	no	—
190	#10623494	—	2	2	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	2	4	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	#405	1	2	yes	—
196	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
197	C₂×D₈₉	—	2	1	no	—
198	C₂×D₈₉	—	2	1	no	—
199	C₂×D₈₉	—	2	1	no	—
200	C₂×D₈₉	—	2	1	no	—
201	C₂×D₈₉	—	2	1	no	—
202	C₂×D₈₉	—	2	1	no	—
203	C₂×D₈₉	—	4	4	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	#405	1	2	yes	—
207	C₄×C₈₉	C₂×#131	1	2	yes	—
208	C₄×C₈₉	#568	1	2	yes	—
209	C₄×C₈₉	#568	1	2	yes	—
210	Dic₈₉	—	2	1	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	—	2	1	no	—
214	Dic₈₉	—	2	1	no	—
215	Dic₈₉	—	2	1	no	—
216	#17324	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
219	C₂×C₈₉	#2873	1	1	yes	characteristic
220	C₂×C₈₉	#2873	1	1	yes	characteristic
221	D₈₉	—	4	1	no	—
222	D₈₉	—	4	1	no	—
223	#2920	—	89	1	no	—
224	#2920	—	89	1	no	—
225	C₂×#431	—	89	1	no	—
226	#1454	—	89	2	no	—
227	#1454	—	89	2	no	—
228	#1453	—	89	2	no	—
229	#1453	—	89	2	no	—
230	#1451	—	89	1	no	—
231	#1451	D₈₉	1	1	yes	characteristic, complemented
232	C₈×M₁₆	—	89	1	no	—
233	C₈×M₁₆	—	89	1	no	—
234	C₈₉	#17324	1	1	yes	characteristic, complemented, Sylow
235	C₂²×C₄²	—	89	1	no	—
236	#432	—	89	2	no	—
237	#432	—	89	2	no	—
238	#432	—	89	2	no	—
239	#432	—	89	2	no	—
240	#431	—	89	1	no	—
241	#431	—	89	2	no	—
242	#431	—	89	2	no	—
243	#431	—	89	1	no	—
244	#431	—	89	1	no	—
245	#431	—	89	1	no	—
246	#431	—	89	1	no	—
247	#431	—	89	2	no	—
248	#431	—	89	2	no	—
249	#431	—	89	2	no	—
250	#431	C₂×D₈₉	1	1	yes	characteristic
251	#423	—	89	2	no	—
252	#423	—	89	2	no	—
253	C₂×C₄⋊C₈	—	89	2	no	—
254	#407	—	89	2	no	—
255	#407	—	89	2	no	—
256	C₂×C₂²⋊C₈	—	89	2	no	—
257	C₄×M₁₆	—	89	1	no	—
258	C₄×M₁₆	—	89	2	no	—
259	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
260	C₂×C₄×C₈	—	89	1	no	—
261	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
262	#322	—	89	2	no	—
263	#322	—	89	2	no	—
264	#322	—	89	2	no	—
265	#322	—	89	2	no	—
266	#322	C₂×D₈₉	1	2	yes	complemented
267	#322	C₂×D₈₉	1	2	yes	complemented
268	C₈²	—	89	2	no	—
269	C₈²	—	89	2	no	—
270	C₂³×C₄	—	89	1	no	—
271	C₂³×C₄	—	89	1	no	—
272	C₂³×C₄	—	89	1	no	—
273	C₂×M₁₆	—	89	2	no	—
274	C₂×M₁₆	—	89	4	no	—
275	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
276	C₂²×C₈	—	89	2	no	—
277	C₂²×C₈	C₄×D₈₉	1	2	yes	—
278	C₂×C₄²	—	89	1	no	—
279	C₂×C₄²	—	89	1	no	—
280	C₂×C₄²	—	89	1	no	—
281	C₂×C₄²	—	89	1	no	—
282	C₂×C₄²	—	89	1	no	—
283	C₂×C₄²	—	89	1	no	—
284	C₂×C₄²	—	89	1	no	—
285	C₂×C₄²	—	89	1	no	—
286	C₂×C₄²	—	89	1	no	—
287	C₂×C₄²	—	89	1	no	—
288	C₂×C₄²	—	89	1	no	—
289	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
290	C₄⋊C₈	—	89	2	no	—
291	C₄⋊C₈	—	89	2	no	—
292	C₄⋊C₈	—	89	2	no	—
293	C₄⋊C₈	—	89	2	no	—
294	C₄⋊C₈	—	89	4	no	—
295	C₄⋊C₈	—	89	4	no	—
296	C₄⋊C₈	—	89	4	no	—
297	C₄⋊C₈	—	89	2	no	—
298	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
299	C₂²⋊C₈	—	89	2	no	—
300	C₂²⋊C₈	—	89	2	no	—
301	C₂²⋊C₈	—	89	2	no	—
302	C₂²⋊C₈	—	89	2	no	—
303	C₂²⋊C₈	—	89	2	no	—
304	C₂²⋊C₈	—	89	4	no	—
305	C₂²⋊C₈	—	89	4	no	—
306	C₂²⋊C₈	—	89	4	no	—
307	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
308	#97	—	89	4	no	—
309	#97	—	89	2	no	—
310	#97	C₄×D₈₉	1	2	yes	—
311	C₄×C₈	—	89	2	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	2	no	—
315	C₄×C₈	—	89	2	no	—
316	C₄×C₈	C₄×D₈₉	1	2	yes	—
317	C₄×C₈	C₂²×D₈₉	1	2	yes	—
318	C₄×C₈	C₂²×D₈₉	1	2	yes	—
319	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₂⁴	—	89	1	no	—
322	C₂²×C₄	—	89	1	no	—
323	C₂²×C₄	—	89	1	no	—
324	C₂²×C₄	—	89	1	no	—
325	C₂²×C₄	—	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	—	356	2	no	—
338	C₂²×C₄	—	356	2	no	—
339	C₂²×C₄	—	178	4	no	—
340	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
343	M₁₆	—	2	4	no	—
344	M₁₆	—	356	4	no	—
345	M₁₆	—	178	4	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	89	2	no	—
348	C₂×C₈	—	89	2	no	—
349	C₂×C₈	—	89	4	no	—
350	C₂×C₈	—	89	4	no	—
351	C₂×C₈	—	356	2	no	—
352	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
354	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
355	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
356	C₄²	—	89	1	no	—
357	C₄²	—	89	1	no	—
358	C₄²	—	89	1	no	—
359	C₄²	—	89	1	no	—
360	C₄²	—	89	1	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	89	1	no	—
364	C₄²	—	89	1	no	—
365	C₄²	—	89	1	no	—
366	C₄²	—	89	1	no	—
367	C₄²	—	89	1	no	—
368	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
369	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
370	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
371	C₄²	C₂³×D₈₉	1	1	yes	characteristic
372	C₂³	—	89	1	no	—
373	C₂³	—	89	1	no	—
374	C₂³	—	356	1	no	—
375	C₂³	—	356	1	no	—
376	C₂³	—	178	2	no	—
377	C₂³	C₄²×D₈₉	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	89	1	no	—
384	C₂×C₄	—	89	1	no	—
385	C₂×C₄	—	89	1	no	—
386	C₂×C₄	—	356	1	no	—
387	C₂×C₄	—	356	1	no	—
388	C₂×C₄	—	356	1	no	—
389	C₂×C₄	—	356	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	356	1	no	—
392	C₂×C₄	—	178	2	no	—
393	C₂×C₄	—	178	2	no	—
394	C₂×C₄	—	178	2	no	—
395	C₂×C₄	—	178	2	no	—
396	C₂×C₄	—	178	2	no	—
397	C₂×C₄	—	178	2	no	—
398	C₂×C₄	—	178	2	no	—
399	C₂×C₄	—	178	2	no	—
400	C₂×C₄	—	178	2	no	—
401	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
403	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
404	C₂×C₄	#15668020	1	4	yes	—
405	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	178	4	no	—
413	C₈	—	178	4	no	—
414	C₈	—	178	2	no	—
415	C₈	—	178	2	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	356	4	no	—
419	C₂²	—	178	1	no	—
420	C₂²	—	178	1	no	—
421	C₂²	—	178	1	no	—
422	C₂²	—	178	1	no	—
423	C₂²	—	178	1	no	—
424	C₂²	—	178	1	no	—
425	C₂²	#19151555	1	2	yes	—
426	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	178	1	no	—
430	C₄	—	178	1	no	—
431	C₄	—	178	1	no	—
432	C₄	—	178	1	no	—
433	C₄	—	178	1	no	—
434	C₄	—	178	1	no	—
435	C₄	#19151555	1	2	yes	—
436	C₄	C₂×#15668020	1	2	yes	—
437	C₄	#19152363	1	2	yes	—
438	C₄	#19152364	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	356	1	no	—
441	C₂	—	356	1	no	—
442	C₂	C₂×#19151555	1	1	yes	characteristic
443	C₂	#26028668	1	1	yes	characteristic
444	C₂	#26028669	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#1451	C₂
prime radical	C₂³×D₈₉	C₄²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1451	D₈₉
hypocenter	C₈₉	#17324
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #26018553	C₂	semidirect
5. #26018553	C₂	semidirect
6. #26018550	C₂	semidirect
7. #26018548	C₂	semidirect
8. #26018541	C₂	semidirect
9. #26018533	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#1451	C₂	semidirect
36. #19151320	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151319	C₂²	semidirect
39. #19151319	C₂²	semidirect
40. C₈×#10623494	C₂²	semidirect
41. C₈×#10623494	C₂²	semidirect
45. #322×C₈₉	C₂²	semidirect
46. #322×C₈₉	C₂²	semidirect
231. #1451	D₈₉	semidirect
234. C₈₉	#17324	semidirect
266. #322	C₂×D₈₉	semidirect
267. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028883	2
#26028880	2
C₂×#19151649	2
#26018553	2
#26018550	2
#26018548	2
#26018541	2
#26018533	2
M₁₆×#10623494	2
C₈₉×#1451	2
#17324	89