Subgroups — #36707544

Order 22784.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15668018	C₂	1	1	yes	maximal, characteristic
2	#26022060	C₂	1	2	yes	maximal, complemented
3	#26022056	C₂	1	2	yes	maximal, complemented
4	#26022054	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022051	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022050	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022006	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021864	C₂	1	2	yes	maximal
10	#26021850	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₄	1	1	yes	characteristic
13	C₂×#15668018	C₂²	1	1	yes	characteristic
14	C₄×#13083574	C₄	1	1	yes	characteristic
15	C₂×#15667951	C₂²	1	2	yes	—
16	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
17	#19151553	C₄	1	1	yes	characteristic
18	#19151553	C₂²	1	1	yes	characteristic
19	#19151552	C₄	1	1	yes	characteristic
20	#19151552	C₄	1	1	yes	characteristic
21	#19151552	C₂²	1	1	yes	characteristic
22	#19151552	C₂²	1	1	yes	characteristic
23	C₄×#13083558	C₄	1	1	yes	characteristic
24	C₄×#13083557	C₄	1	1	yes	characteristic
25	C₄×#13083557	C₄	1	1	yes	characteristic
26	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₄⋊#13083549	C₂²	1	1	yes	characteristic
29	C₄⋊#13083549	C₂²	1	1	yes	characteristic
30	#19151416	C₂²	1	2	yes	—
31	#19151416	C₂²	1	2	yes	—
32	C₂²⋊#13083549	C₂²	1	2	yes	—
33	#19151377	C₂²	1	2	yes	—
34	#19151377	C₂²	1	2	yes	—
35	#19151373	C₂²	1	2	yes	—
36	C₄×#13083549	C₂²	1	2	yes	—
37	C₁₆×Dic₈₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
42	#346×C₈₉	C₂²	1	2	yes	—
43	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
44	#15668018	—	2	4	no	—
45	#15668018	—	2	2	no	—
46	#15668018	—	2	2	no	—
47	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
57	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
58	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
59	C₄×D₃₅₆	C₈	1	1	yes	characteristic
60	C₄×D₃₅₆	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
62	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
63	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
64	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
65	#15667971	C₂×C₄	1	1	yes	characteristic
66	#15667969	C₂×C₄	1	1	yes	characteristic
67	#15667969	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
70	#15667951	—	2	4	no	—
71	C₂×#13083549	C₂³	1	2	yes	—
72	C₂×#13083549	C₂³	1	2	yes	—
73	C₁₆×D₈₉	—	2	4	no	—
74	#15667923	C₂×C₄	1	1	yes	characteristic
75	#15667923	C₂×C₄	1	1	yes	characteristic
76	#15667922	C₂×C₄	1	1	yes	characteristic
77	#15667922	C₂×C₄	1	1	yes	characteristic
78	#15667922	C₂×C₄	1	1	yes	characteristic
79	#15667922	C₂×C₄	1	1	yes	characteristic
80	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
81	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
85	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
90	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
91	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	#13083574	—	2	2	no	—
96	#13083574	—	2	2	no	—
97	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
98	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
107	#13083558	—	2	2	no	—
108	#13083558	—	2	2	no	—
109	#13083557	—	2	2	no	—
110	#13083557	—	2	2	no	—
111	#13083557	—	2	2	no	—
112	#13083557	M₁₆	1	4	yes	—
113	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
114	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
115	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
117	C₈×D₈₉	—	2	2	no	—
118	C₈×D₈₉	—	2	1	no	—
119	C₈×D₈₉	—	2	1	no	—
120	C₈×D₈₉	—	2	2	no	—
121	C₈×D₈₉	#41	1	2	yes	—
122	C₈×D₈₉	#41	1	2	yes	—
123	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
125	#13083553	C₂×C₈	1	1	yes	characteristic
126	#13083553	C₂×C₈	1	1	yes	characteristic
127	#13083553	C₂×C₈	1	1	yes	characteristic
128	#13083553	C₂×C₈	1	1	yes	characteristic
129	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
130	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
131	#13083551	C₂×C₈	1	1	yes	characteristic
132	#13083551	C₂×C₈	1	1	yes	characteristic
133	#13083551	C₂×C₈	1	1	yes	characteristic
134	#13083551	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	#13083549	—	2	2	no	—
142	#13083549	—	2	2	no	—
143	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	2	1	no	—
149	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
155	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₁₆×C₈₉	—	2	2	no	—
158	C₁₆×C₈₉	—	2	2	no	—
159	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	2	2	no	—
173	C₂²⋊D₈₉	—	2	2	no	—
174	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
180	D₃₅₆	—	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	—	4	1	no	—
186	C₄×D₈₉	—	4	1	no	—
187	C₄×D₈₉	#117	1	2	yes	—
188	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
189	Dic₁₇₈	—	2	2	no	—
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	—	2	1	no	—
192	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
193	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
194	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
195	#10623494	—	2	1	no	—
196	#10623494	—	2	1	no	—
197	#10623494	#117	1	2	yes	—
198	#10623494	C₂×M₁₆	1	2	yes	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
203	C₂×D₈₉	—	2	1	no	—
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	#431	1	2	yes	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	#504	1	2	yes	—
214	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
215	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
216	Dic₈₉	—	2	1	no	—
217	Dic₈₉	—	2	1	no	—
218	Dic₈₉	—	2	1	no	—
219	Dic₈₉	—	2	1	no	—
220	Dic₈₉	—	2	1	no	—
221	Dic₈₉	#431	1	2	yes	—
222	#33423	—	89	1	no	maximal, Sylow
223	C₂×C₈₉	—	4	1	no	—
224	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
225	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
226	C₂×C₈₉	#3407	1	1	yes	characteristic
227	D₈₉	—	2	2	no	—
228	D₈₉	—	4	1	no	—
229	C₄×#131	—	89	1	no	—
230	#2164	—	89	2	no	—
231	#2164	—	89	2	no	—
232	#2163	—	89	1	no	—
233	#2163	D₈₉	1	1	yes	characteristic, complemented
234	#2162	—	89	1	no	—
235	#2162	—	89	1	no	—
236	#2150	—	89	1	no	—
237	C₂×C₄⋊C₁₆	—	89	1	no	—
238	#2113	—	89	2	no	—
239	#2108	—	89	2	no	—
240	C₈₉	#33423	1	1	yes	characteristic, complemented, Sylow
241	C₂×#131	—	89	1	no	—
242	C₂×#131	—	89	1	no	—
243	C₄×#41	—	89	1	no	—
244	C₂×M₃₂	—	89	2	no	—
245	C₂²×C₁₆	—	89	2	no	—
246	#405	—	89	1	no	—
247	#405	—	89	1	no	—
248	#405	—	89	1	no	—
249	#405	—	89	1	no	—
250	#405	—	89	1	no	—
251	#405	—	89	1	no	—
252	C₄×M₁₆	—	89	1	no	—
253	C₄×M₁₆	—	89	1	no	—
254	C₄×M₁₆	—	89	1	no	—
255	C₂×C₄×C₈	—	89	1	no	—
256	C₂×C₄×C₈	—	89	1	no	—
257	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
258	C₄⋊C₁₆	—	89	2	no	—
259	C₄⋊C₁₆	—	89	2	no	—
260	C₄⋊C₁₆	—	89	1	no	—
261	C₄⋊C₁₆	—	89	1	no	—
262	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
264	C₂²⋊C₁₆	—	89	2	no	—
265	C₂²⋊C₁₆	—	89	2	no	—
266	C₂²⋊C₁₆	—	89	2	no	—
267	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
268	#346	—	89	2	no	—
269	#346	C₂×D₈₉	1	2	yes	—
270	C₄×C₁₆	—	89	2	no	—
271	C₄×C₁₆	—	89	2	no	—
272	C₂×#41	—	89	1	no	—
273	#131	—	178	2	no	—
274	#131	—	178	2	no	—
275	#131	—	178	4	no	—
276	C₂×M₁₆	—	89	1	no	—
277	C₂×M₁₆	—	89	1	no	—
278	C₂×M₁₆	—	89	1	no	—
279	C₂×M₁₆	—	89	1	no	—
280	C₂×M₁₆	—	89	1	no	—
281	C₂×M₁₆	—	89	1	no	—
282	C₂²×C₈	—	89	1	no	—
283	C₂²×C₈	—	89	1	no	—
284	C₂²×C₈	—	89	1	no	—
285	C₂²×C₈	—	89	1	no	—
286	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	—	89	1	no	—
290	C₄×D₄	—	89	1	no	—
291	C₄×D₄	—	89	1	no	—
292	C₄×D₄	—	89	1	no	—
293	C₄×D₄	—	89	1	no	—
294	C₄×D₄	—	89	1	no	—
295	C₄×D₄	—	89	1	no	—
296	#117	—	89	1	no	—
297	#117	—	89	1	no	—
298	#117	—	89	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₄²	—	89	1	no	—
301	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
302	M₃₂	—	178	4	no	—
303	C₂×C₁₆	—	89	2	no	—
304	C₂×C₁₆	—	89	2	no	—
305	C₂×C₁₆	—	178	4	no	—
306	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
307	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
308	#97	—	89	1	no	—
309	#97	—	89	1	no	—
310	#97	—	89	1	no	—
311	#97	—	89	1	no	—
312	#97	—	89	1	no	—
313	#97	—	89	1	no	—
314	C₄×C₈	—	89	1	no	—
315	C₄×C₈	—	89	1	no	—
316	C₄×C₈	—	89	1	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
321	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	#41	—	178	2	no	—
325	#41	—	178	2	no	—
326	C₂×Q₈	—	89	1	no	—
327	C₂×D₄	—	89	1	no	—
328	C₂×D₄	—	89	1	no	—
329	C₂×D₄	—	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	C₈×D₈₉	1	1	yes	characteristic
337	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
339	M₁₆	—	89	4	no	—
340	M₁₆	—	178	2	no	—
341	M₁₆	—	178	2	no	—
342	M₁₆	—	178	2	no	—
343	M₁₆	—	178	2	no	—
344	M₁₆	—	178	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	89	2	no	—
351	C₂×C₈	—	89	2	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	178	2	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	—	178	1	no	—
357	C₂×C₈	—	178	1	no	—
358	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
361	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
362	C₄⋊C₄	—	89	1	no	—
363	C₄⋊C₄	—	89	1	no	—
364	C₄⋊C₄	—	89	1	no	—
365	C₄⋊C₄	—	89	1	no	—
366	C₄⋊C₄	—	89	1	no	—
367	C₄⋊C₄	—	89	1	no	—
368	C₂²⋊C₄	—	89	1	no	—
369	C₂²⋊C₄	—	89	1	no	—
370	C₂²⋊C₄	—	89	1	no	—
371	C₂²⋊C₄	—	89	1	no	—
372	C₂²⋊C₄	—	89	1	no	—
373	C₂²⋊C₄	—	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	C₈×D₈₉	1	1	yes	characteristic
381	C₄²	C₈×D₈₉	1	1	yes	characteristic
382	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
383	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
384	C₁₆	—	2	2	no	—
385	C₁₆	—	2	2	no	—
386	C₁₆	—	178	2	no	—
387	C₁₆	—	178	2	no	—
388	C₂³	—	89	1	no	—
389	C₂³	—	89	1	no	—
390	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
391	Q₈	—	178	2	no	—
392	D₄	—	178	2	no	—
393	D₄	—	178	2	no	—
394	D₄	—	178	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	89	1	no	—
400	C₂×C₄	—	89	2	no	—
401	C₂×C₄	—	89	2	no	—
402	C₂×C₄	—	89	1	no	—
403	C₂×C₄	—	89	1	no	—
404	C₂×C₄	—	89	1	no	—
405	C₂×C₄	—	89	1	no	—
406	C₂×C₄	—	89	1	no	—
407	C₂×C₄	—	356	1	no	—
408	C₂×C₄	—	356	1	no	—
409	C₂×C₄	—	178	2	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	—	178	1	no	—
412	C₂×C₄	—	178	1	no	—
413	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	89	2	no	—
422	C₈	—	89	2	no	—
423	C₈	—	178	1	no	—
424	C₈	—	178	1	no	—
425	C₈	M₁₆×D₈₉	1	2	yes	—
426	C₈	#41×D₈₉	1	1	yes	characteristic
427	C₈	#41×D₈₉	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	89	2	no	—
432	C₂²	—	178	1	no	—
433	C₂²	—	178	1	no	—
434	C₂²	—	178	1	no	—
435	C₂²	—	178	1	no	—
436	C₂²	—	178	1	no	—
437	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	89	2	no	—
443	C₄	—	178	1	no	—
444	C₄	—	178	1	no	—
445	C₄	—	178	1	no	—
446	C₄	—	178	1	no	—
447	C₄	—	178	1	no	—
448	C₄	#19152016	1	2	yes	—
449	C₄	#117×D₈₉	1	1	yes	characteristic
450	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	356	1	no	—
453	C₂	—	178	2	no	—
454	C₂	#431×D₈₉	1	1	yes	characteristic
455	C₂	C₂×#19152016	1	1	yes	characteristic
456	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2163	C₂
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2163	D₈₉
hypocenter	C₈₉	#33423
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #26022060	C₂	semidirect
3. #26022056	C₂	semidirect
4. #26022054	C₂	semidirect
5. #26022051	C₂	semidirect
6. #26022050	C₂	semidirect
7. #26022006	C₂	semidirect
8. C₄⋊C₁₆×D₈₉	C₂	semidirect
10. #26021850	C₂	semidirect
11. C₈₉×#2163	C₂	semidirect
233. #2163	D₈₉	semidirect
240. C₈₉	#33423	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668018	2
#26022060	2
#26022056	2
#26022054	2
#26022051	2
#26022050	2
#26022006	2
C₄⋊C₁₆×D₈₉	2
#26021864	2
#26021850	2
C₈₉×#2163	2
#33423	89