Subgroups — #36520034

Order 22784.

834 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151649	C₂	1	1	yes	maximal, characteristic
2	#431×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26018543	C₂	1	2	yes	maximal, complemented
5	#26018543	C₂	1	2	yes	maximal, complemented
6	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018540	C₂	1	2	yes	maximal, complemented
9	#26018539	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018538	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₈₉	C₄	1	2	yes	—
13	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
14	#19151651	C₂²	1	1	yes	characteristic
15	#19151650	C₄	1	2	yes	—
16	#19151649	C₄	1	2	yes	—
17	#19151649	C₄	1	2	yes	—
18	#19151649	C₂²	1	2	yes	—
19	#19151649	C₂²	1	1	yes	characteristic
20	#19151649	C₂²	1	1	yes	characteristic
21	#19151649	C₂²	1	1	yes	characteristic
22	#19151649	C₂²	1	1	yes	characteristic
23	#19151648	C₄	1	2	yes	—
24	C₂×#15667941	C₄	1	2	yes	—
25	C₄⋊C₈×D₈₉	C₄	1	2	yes	—
26	C₂×#15667924	C₄	1	2	yes	—
27	C₂²⋊C₈×D₈₉	C₄	1	2	yes	—
28	C₄×#13083558	C₂²	1	1	yes	characteristic
29	#19151550	C₄	1	2	yes	—
30	M₁₆×Dic₈₉	C₄	1	2	yes	—
31	C₄×#13083557	C₂²	1	2	yes	—
32	#97×D₈₉	C₄	1	2	yes	—
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	C₂²	1	2	yes	—
35	C₄×C₈×D₈₉	C₂²	1	2	yes	—
36	#19151320	C₂²	1	2	yes	complemented
37	#19151320	C₂²	1	2	yes	complemented
38	#19151320	C₂²	1	2	yes	complemented
39	#19151320	C₂²	1	2	yes	complemented
40	#19151319	C₂²	1	2	yes	complemented
41	#19151319	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	M₁₆×D₈₉	—	2	8	no	—
53	C₂²×#10623494	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
55	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
56	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	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	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₈₉	C₂³	1	1	yes	characteristic
66	C₄²×D₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊#10623494	C₂×C₄	1	2	yes	—
68	#15667941	C₂×C₄	1	4	yes	—
69	#15667941	C₂×C₄	1	2	yes	—
70	#15667941	C₂×C₄	1	2	yes	—
71	#15667941	C₂×C₄	1	2	yes	—
72	#15667941	C₂×C₄	1	2	yes	—
73	C₂²⋊#10623494	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	2	yes	—
78	#15667924	C₂×C₄	1	4	yes	—
79	#15667923	C₂×C₄	1	2	yes	—
80	#15667922	C₂×C₄	1	4	yes	—
81	C₄×#10623494	C₂×C₄	1	2	yes	—
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₄×#10623494	C₂³	1	1	yes	characteristic
84	C₄×#10623494	C₂³	1	2	yes	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
87	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
88	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
89	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
93	#97×C₈₉	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₈₉	C₂³	1	2	yes	—
98	C₄×C₈×C₈₉	C₂³	1	2	yes	—
99	C₂³×D₈₉	C₄²	1	1	yes	characteristic
100	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
101	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
102	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
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	M₁₆	1	8	yes	—
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	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
118	#13083558	—	2	4	no	—
119	#13083557	—	2	8	no	—
120	C₂×#10623494	—	4	2	no	—
121	C₂×#10623494	C₂²×C₄	1	4	yes	—
122	C₂×#10623494	C₂²×C₄	1	4	yes	—
123	C₂×#10623494	C₂²×C₄	1	2	yes	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₈×D₈₉	—	2	8	no	—
126	C₈×D₈₉	—	4	4	no	—
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	C₄²	1	1	yes	characteristic
131	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
132	C₄×Dic₈₉	C₄²	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	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	M₁₆×C₈₉	—	2	4	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
146	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
148	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
153	C₂²×D₈₉	—	4	1	no	—
154	C₂²×D₈₉	—	4	1	no	—
155	C₂²×D₈₉	#97	1	4	yes	—
156	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
164	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	#97	1	4	yes	—
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	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
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	—	4	1	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	C₄×D₈₉	—	4	1	no	—
184	C₄×D₈₉	#97	1	4	yes	—
185	C₄×D₈₉	#97	1	4	yes	—
186	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
187	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
188	C₈×C₈₉	—	2	4	no	—
189	C₈×C₈₉	—	2	2	no	—
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	2	4	no	—
192	#10623494	—	2	4	no	—
193	#10623494	—	2	4	no	—
194	#10623494	—	2	2	no	—
195	#10623494	—	2	2	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	C₂×#97	1	2	yes	—
199	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
200	C₂×D₈₉	—	2	1	no	—
201	C₂×D₈₉	—	2	1	no	—
202	C₂×D₈₉	—	2	1	no	—
203	C₂×D₈₉	—	2	1	no	—
204	C₂×D₈₉	—	4	4	no	—
205	C₂×D₈₉	C₂×#97	1	2	yes	—
206	C₂×D₈₉	C₂×#97	1	2	yes	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	C₂×#97	1	2	yes	—
210	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
211	C₄×C₈₉	#568	1	2	yes	—
212	C₄×C₈₉	#568	1	2	yes	—
213	Dic₈₉	—	2	1	no	—
214	Dic₈₉	—	2	1	no	—
215	Dic₈₉	—	2	1	no	—
216	Dic₈₉	—	2	1	no	—
217	Dic₈₉	C₂×#97	1	2	yes	—
218	Dic₈₉	C₂×#97	1	2	yes	—
219	#17319	—	89	1	no	maximal, Sylow
220	C₂×C₈₉	—	2	2	no	—
221	C₂×C₈₉	C₂²×#97	1	1	yes	characteristic
222	C₂×C₈₉	#2873	1	1	yes	characteristic
223	C₂×C₈₉	#2873	1	1	yes	characteristic
224	D₈₉	—	2	2	no	—
225	D₈₉	—	2	2	no	—
226	C₂×#431	—	89	1	no	—
227	C₂×#431	—	89	1	no	—
228	C₂×C₄×M₁₆	—	89	1	no	—
229	#1452	—	89	2	no	—
230	#1452	—	89	2	no	—
231	#1451	—	89	1	no	—
232	#1451	—	89	1	no	—
233	#1451	—	89	1	no	—
234	#1451	—	89	2	no	—
235	#1451	—	89	2	no	—
236	#1451	D₈₉	1	1	yes	characteristic, complemented
237	C₈₉	#17319	1	1	yes	characteristic, complemented, Sylow
238	C₂²×M₁₆	—	89	2	no	—
239	C₂²×C₄²	—	89	1	no	—
240	#431	—	89	1	no	—
241	#431	—	89	2	no	—
242	#431	—	89	2	no	—
243	#431	—	89	2	no	—
244	#431	—	89	2	no	—
245	#431	—	89	1	no	—
246	#431	—	89	1	no	—
247	#431	—	89	2	no	—
248	#431	—	89	1	no	—
249	#431	—	89	1	no	—
250	#431	C₂×D₈₉	1	1	yes	characteristic
251	C₂×C₄⋊C₈	—	89	2	no	—
252	C₂×C₄⋊C₈	—	89	2	no	—
253	C₂×C₂²⋊C₈	—	89	2	no	—
254	C₂×C₂²⋊C₈	—	89	2	no	—
255	C₄×M₁₆	—	89	2	no	—
256	C₄×M₁₆	—	89	1	no	—
257	C₄×M₁₆	—	89	2	no	—
258	C₄×M₁₆	—	89	2	no	—
259	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
260	C₂×#97	—	89	2	no	—
261	C₂×C₄×C₈	—	89	1	no	—
262	C₂×C₄×C₈	—	89	2	no	—
263	C₂×C₄×C₈	—	89	2	no	—
264	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
265	#322	—	89	2	no	—
266	#322	—	89	2	no	—
267	#322	—	89	2	no	—
268	#322	—	89	2	no	—
269	#322	—	89	2	no	—
270	#322	—	89	2	no	—
271	#322	C₂×D₈₉	1	2	yes	complemented
272	#322	C₂×D₈₉	1	2	yes	complemented
273	C₂³×C₄	—	89	1	no	—
274	C₂³×C₄	—	89	1	no	—
275	C₂³×C₄	—	89	1	no	—
276	C₂×M₁₆	—	89	2	no	—
277	C₂×M₁₆	—	89	4	no	—
278	C₂×M₁₆	—	178	8	no	—
279	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
280	C₂²×C₈	—	89	2	no	—
281	C₂²×C₈	—	89	4	no	—
282	C₂²×C₈	—	89	4	no	—
283	C₂²×C₈	C₄×D₈₉	1	2	yes	—
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	—	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	C₂²×D₈₉	1	1	yes	characteristic
296	C₄⋊C₈	—	89	4	no	—
297	C₄⋊C₈	—	89	2	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	89	2	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	89	2	no	—
302	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
303	C₂²⋊C₈	—	89	2	no	—
304	C₂²⋊C₈	—	89	4	no	—
305	C₂²⋊C₈	—	89	2	no	—
306	C₂²⋊C₈	—	89	2	no	—
307	C₂²⋊C₈	—	89	2	no	—
308	C₂²⋊C₈	—	89	2	no	—
309	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
310	#97	—	89	4	no	—
311	#97	—	89	2	no	—
312	#97	C₄×D₈₉	1	2	yes	—
313	C₄×C₈	—	89	4	no	—
314	C₄×C₈	—	89	4	no	—
315	C₄×C₈	—	89	2	no	—
316	C₄×C₈	—	89	2	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	2	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	C₄×D₈₉	1	2	yes	—
321	C₄×C₈	C₂²×D₈₉	1	2	yes	—
322	C₄×C₈	C₂²×D₈₉	1	2	yes	—
323	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₂⁴	—	89	1	no	—
326	C₂²×C₄	—	89	1	no	—
327	C₂²×C₄	—	89	8	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	—	89	1	no	—
342	C₂²×C₄	—	356	2	no	—
343	C₂²×C₄	—	356	2	no	—
344	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
347	M₁₆	—	2	4	no	—
348	M₁₆	—	178	8	no	—
349	M₁₆	—	178	4	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	89	4	no	—
352	C₂×C₈	—	89	4	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	89	2	no	—
355	C₂×C₈	—	356	4	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	178	8	no	—
358	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
359	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
360	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
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	—	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	C₂×C₄×D₈₉	1	1	yes	characteristic
375	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
377	C₄²	C₂³×D₈₉	1	1	yes	characteristic
378	C₂³	—	89	4	no	—
379	C₂³	—	89	1	no	—
380	C₂³	—	89	1	no	—
381	C₂³	—	356	1	no	—
382	C₂³	—	356	1	no	—
383	C₂³	C₄²×D₈₉	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	89	1	no	—
387	C₂×C₄	—	89	1	no	—
388	C₂×C₄	—	89	4	no	—
389	C₂×C₄	—	89	4	no	—
390	C₂×C₄	—	89	4	no	—
391	C₂×C₄	—	89	4	no	—
392	C₂×C₄	—	89	4	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	356	1	no	—
398	C₂×C₄	—	356	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	1	no	—
402	C₂×C₄	—	356	1	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	178	2	no	—
405	C₂×C₄	—	178	2	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
410	C₂×C₄	M₁₆×D₈₉	1	4	yes	—
411	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	178	4	no	—
419	C₈	—	178	4	no	—
420	C₈	—	178	2	no	—
421	C₈	—	178	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	89	2	no	—
425	C₂²	—	89	2	no	—
426	C₂²	—	356	4	no	—
427	C₂²	—	178	1	no	—
428	C₂²	—	178	1	no	—
429	C₂²	—	178	1	no	—
430	C₂²	—	178	1	no	—
431	C₂²	#97×D₈₉	1	2	yes	—
432	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	89	2	no	—
436	C₄	—	89	2	no	—
437	C₄	—	178	1	no	—
438	C₄	—	178	1	no	—
439	C₄	—	178	1	no	—
440	C₄	—	178	1	no	—
441	C₄	#97×D₈₉	1	2	yes	—
442	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
443	C₄	#19152363	1	2	yes	—
444	C₄	#19152364	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	178	2	no	—
447	C₂	—	178	2	no	—
448	C₂	C₂×#97×D₈₉	1	1	yes	characteristic
449	C₂	#26028668	1	1	yes	characteristic
450	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	#17319
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. #26018543	C₂	semidirect
5. #26018543	C₂	semidirect
6. #26018542	C₂	semidirect
7. #26018541	C₂	semidirect
8. #26018540	C₂	semidirect
9. #26018539	C₂	semidirect
10. #26018538	C₂	semidirect
11. C₈₉×#1451	C₂	semidirect
36. #19151320	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. #19151320	C₂²	semidirect
40. #19151319	C₂²	semidirect
41. #19151319	C₂²	semidirect
45. #322×C₈₉	C₂²	semidirect
46. #322×C₈₉	C₂²	semidirect
236. #1451	D₈₉	semidirect
237. C₈₉	#17319	semidirect
271. #322	C₂×D₈₉	semidirect
272. #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
C₂×#19151649	2
#431×D₈₉	2
C₄×M₁₆×D₈₉	2
#26018543	2
#26018542	2
#26018541	2
#26018540	2
#26018539	2
#26018538	2
C₈₉×#1451	2
#17319	89