Subgroups — #36707516

Order 22784.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 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	#26022058	C₂	1	2	yes	maximal, complemented
3	#26022056	C₂	1	2	yes	maximal, complemented
4	#26022051	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022049	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022049	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022009	C₂	1	2	yes	maximal, complemented
8	#26021864	C₂	1	2	yes	maximal
9	C₄×#15667951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2162	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	2	yes	—
29	#19151416	C₂²	1	2	yes	—
30	#19151416	C₂²	1	2	yes	—
31	C₂²⋊#13083549	C₂²	1	2	yes	—
32	#19151377	C₂²	1	2	yes	—
33	#19151377	C₂²	1	2	yes	—
34	#19151373	C₂²	1	2	yes	—
35	C₄×#13083549	C₂²	1	1	yes	characteristic
36	C₄×#13083549	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₈₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₈₉	C₂²	1	2	yes	—
40	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
41	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
44	#15668018	—	2	4	no	—
45	#15668018	—	2	4	no	—
46	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083557	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×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
56	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
57	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
58	C₄×D₃₅₆	C₈	1	1	yes	characteristic
59	C₄×D₃₅₆	C₈	1	1	yes	characteristic
60	C₄×C₂²⋊D₈₉	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	#15667971	C₂×C₄	1	1	yes	characteristic
65	#15667969	C₂×C₄	1	1	yes	characteristic
66	#15667969	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
69	#15667951	—	2	4	no	—
70	C₂×#13083549	C₂³	1	2	yes	—
71	C₂×#13083549	C₂³	1	2	yes	—
72	C₁₆×D₈₉	—	2	4	no	—
73	#15667923	C₂×C₄	1	1	yes	characteristic
74	#15667923	C₂×C₄	1	1	yes	characteristic
75	#15667922	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	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
80	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
89	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
90	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#13083574	—	2	2	no	—
95	#13083574	—	2	2	no	—
96	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
97	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×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	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
106	#13083558	—	2	2	no	—
107	#13083558	—	2	2	no	—
108	#13083557	—	2	2	no	—
109	#13083557	—	2	2	no	—
110	#13083557	—	2	2	no	—
111	#13083557	—	2	2	no	—
112	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₈₉	—	2	2	no	—
117	C₈×D₈₉	—	2	2	no	—
118	C₈×D₈₉	M₁₆	1	4	yes	—
119	C₈×D₈₉	#41	1	4	yes	—
120	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
121	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
122	#13083553	C₂×C₈	1	1	yes	characteristic
123	#13083553	C₂×C₈	1	1	yes	characteristic
124	#13083553	C₂×C₈	1	1	yes	characteristic
125	#13083553	C₂×C₈	1	1	yes	characteristic
126	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
127	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
128	#13083551	C₂×C₈	1	1	yes	characteristic
129	#13083551	C₂×C₈	1	1	yes	characteristic
130	#13083551	C₂×C₈	1	1	yes	characteristic
131	#13083551	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	#13083549	—	2	2	no	—
139	#13083549	—	2	2	no	—
140	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₂×C₈×C₈₉	—	2	2	no	—
145	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
150	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
151	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₈₉	—	2	2	no	—
154	C₁₆×C₈₉	—	2	2	no	—
155	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
156	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂²⋊D₈₉	—	2	2	no	—
169	C₂²⋊D₈₉	—	2	2	no	—
170	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
176	D₃₅₆	—	2	2	no	—
177	C₄×D₈₉	—	2	1	no	—
178	C₄×D₈₉	—	2	1	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	—	2	2	no	—
181	C₄×D₈₉	—	2	2	no	—
182	C₄×D₈₉	—	2	2	no	—
183	C₄×D₈₉	#117	1	2	yes	—
184	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
185	Dic₁₇₈	—	2	2	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
189	C₈×C₈₉	C₂×#41	1	2	yes	—
190	#10623494	—	2	1	no	—
191	#10623494	—	2	1	no	—
192	#10623494	#117	1	2	yes	—
193	#10623494	C₂×M₁₆	1	2	yes	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
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	#431	1	2	yes	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	#504	1	2	yes	—
208	C₄×C₈₉	#504	1	2	yes	—
209	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
210	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
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	Dic₈₉	#431	1	2	yes	—
217	#33420	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	—	4	1	no	—
219	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
221	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
222	D₈₉	—	2	2	no	—
223	D₈₉	—	4	1	no	—
224	C₄×#131	—	89	1	no	—
225	#2164	—	89	2	no	—
226	#2164	—	89	2	no	—
227	#2162	—	89	1	no	—
228	#2162	—	89	1	no	—
229	#2162	—	89	1	no	—
230	#2162	D₈₉	1	1	yes	characteristic, complemented
231	#2151	—	89	2	no	—
232	#2113	—	89	2	no	—
233	C₄×M₃₂	—	89	1	no	—
234	C₂×C₄×C₁₆	—	89	1	no	—
235	C₈₉	#33420	1	1	yes	characteristic, complemented, Sylow
236	C₂×#131	—	89	1	no	—
237	C₂×#131	—	89	1	no	—
238	C₄×#41	—	89	1	no	—
239	C₂×M₃₂	—	89	2	no	—
240	C₂²×C₁₆	—	89	2	no	—
241	#405	—	89	1	no	—
242	#405	—	89	1	no	—
243	#405	—	89	1	no	—
244	#405	—	89	1	no	—
245	#405	—	89	1	no	—
246	#405	—	89	1	no	—
247	C₄×M₁₆	—	89	1	no	—
248	C₄×M₁₆	—	89	1	no	—
249	C₄×M₁₆	—	89	1	no	—
250	C₂×C₄×C₈	—	89	1	no	—
251	C₂×C₄×C₈	—	89	1	no	—
252	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
253	C₄⋊C₁₆	—	89	2	no	—
254	C₄⋊C₁₆	—	89	2	no	—
255	C₄⋊C₁₆	—	89	2	no	—
256	C₄⋊C₁₆	C₂×D₈₉	1	2	yes	—
257	C₂²⋊C₁₆	—	89	2	no	—
258	C₂²⋊C₁₆	—	89	2	no	—
259	C₂²⋊C₁₆	—	89	2	no	—
260	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
261	#346	—	89	2	no	—
262	C₄×C₁₆	—	89	2	no	—
263	C₄×C₁₆	—	89	1	no	—
264	C₄×C₁₆	—	89	1	no	—
265	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
266	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
267	C₂×#41	—	89	1	no	—
268	#131	—	178	4	no	—
269	#131	—	178	4	no	—
270	C₂×M₁₆	—	89	1	no	—
271	C₂×M₁₆	—	89	1	no	—
272	C₂×M₁₆	—	89	1	no	—
273	C₂×M₁₆	—	89	1	no	—
274	C₂×M₁₆	—	89	1	no	—
275	C₂×M₁₆	—	89	1	no	—
276	C₂²×C₈	—	89	1	no	—
277	C₂²×C₈	—	89	1	no	—
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	—	89	1	no	—
280	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₄×Q₈	—	89	1	no	—
283	C₄×Q₈	—	89	1	no	—
284	C₄×D₄	—	89	1	no	—
285	C₄×D₄	—	89	1	no	—
286	C₄×D₄	—	89	1	no	—
287	C₄×D₄	—	89	1	no	—
288	C₄×D₄	—	89	1	no	—
289	C₄×D₄	—	89	1	no	—
290	#117	—	89	1	no	—
291	#117	—	89	1	no	—
292	#117	—	89	1	no	—
293	C₂×C₄²	—	89	1	no	—
294	C₂×C₄²	—	89	1	no	—
295	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
296	M₃₂	—	178	4	no	—
297	C₂×C₁₆	—	89	2	no	—
298	C₂×C₁₆	—	89	2	no	—
299	C₂×C₁₆	—	178	4	no	—
300	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
301	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
302	#97	—	89	1	no	—
303	#97	—	89	1	no	—
304	#97	—	89	1	no	—
305	#97	—	89	1	no	—
306	#97	—	89	1	no	—
307	#97	—	89	1	no	—
308	C₄×C₈	—	89	1	no	—
309	C₄×C₈	—	89	1	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
315	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
318	#41	—	178	2	no	—
319	#41	—	178	2	no	—
320	C₂×Q₈	—	89	1	no	—
321	C₂×D₄	—	89	1	no	—
322	C₂×D₄	—	89	1	no	—
323	C₂×D₄	—	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	C₈×D₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
333	M₁₆	—	178	2	no	—
334	M₁₆	—	178	2	no	—
335	M₁₆	—	178	2	no	—
336	M₁₆	—	178	2	no	—
337	M₁₆	—	178	2	no	—
338	M₁₆	—	178	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	89	1	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	89	4	no	—
344	C₂×C₈	—	89	4	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	1	no	—
347	C₂×C₈	—	178	2	no	—
348	C₂×C₈	—	178	2	no	—
349	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
353	C₄⋊C₄	—	89	1	no	—
354	C₄⋊C₄	—	89	1	no	—
355	C₄⋊C₄	—	89	1	no	—
356	C₄⋊C₄	—	89	1	no	—
357	C₄⋊C₄	—	89	1	no	—
358	C₄⋊C₄	—	89	1	no	—
359	C₂²⋊C₄	—	89	1	no	—
360	C₂²⋊C₄	—	89	1	no	—
361	C₂²⋊C₄	—	89	1	no	—
362	C₂²⋊C₄	—	89	1	no	—
363	C₂²⋊C₄	—	89	1	no	—
364	C₂²⋊C₄	—	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	C₈×D₈₉	1	1	yes	characteristic
372	C₄²	C₈×D₈₉	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₁₆	—	178	2	no	—
378	C₁₆	—	178	2	no	—
379	C₂³	—	89	1	no	—
380	C₂³	—	89	1	no	—
381	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
382	Q₈	—	178	2	no	—
383	D₄	—	178	2	no	—
384	D₄	—	178	2	no	—
385	D₄	—	178	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	89	1	no	—
391	C₂×C₄	—	89	2	no	—
392	C₂×C₄	—	89	2	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	—	89	1	no	—
398	C₂×C₄	—	178	2	no	—
399	C₂×C₄	—	178	2	no	—
400	C₂×C₄	—	178	2	no	—
401	C₂×C₄	—	178	2	no	—
402	C₂×C₄	—	178	1	no	—
403	C₂×C₄	—	178	1	no	—
404	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	89	2	no	—
413	C₈	—	89	2	no	—
414	C₈	—	178	1	no	—
415	C₈	—	178	1	no	—
416	C₈	M₁₆×D₈₉	1	2	yes	—
417	C₈	#41×D₈₉	1	2	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	89	2	no	—
422	C₂²	—	178	1	no	—
423	C₂²	—	178	1	no	—
424	C₂²	—	178	1	no	—
425	C₂²	—	178	1	no	—
426	C₂²	—	178	1	no	—
427	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	89	2	no	—
432	C₄	—	178	1	no	—
433	C₄	—	178	1	no	—
434	C₄	—	178	1	no	—
435	C₄	—	178	1	no	—
436	C₄	—	178	1	no	—
437	C₄	#19152014	1	2	yes	—
438	C₄	#19152016	1	2	yes	—
439	C₄	#117×D₈₉	1	1	yes	characteristic
440	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	356	1	no	—
443	C₂	—	178	2	no	—
444	C₂	#431×D₈₉	1	1	yes	characteristic
445	C₂	C₂×#19152014	1	1	yes	characteristic
446	C₂	C₂×#19152016	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2162	C₂
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2162	D₈₉
hypocenter	C₈₉	#33420
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #26022058	C₂	semidirect
3. #26022056	C₂	semidirect
4. #26022051	C₂	semidirect
5. #26022049	C₂	semidirect
6. #26022049	C₂	semidirect
7. #26022009	C₂	semidirect
9. C₄×#15667951	C₂	semidirect
10. C₄×C₁₆×D₈₉	C₂	semidirect
11. C₈₉×#2162	C₂	semidirect
230. #2162	D₈₉	semidirect
235. C₈₉	#33420	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
#26022058	2
#26022056	2
#26022051	2
#26022049	2
#26022009	2
#26021864	2
C₄×#15667951	2
C₄×C₁₆×D₈₉	2
C₈₉×#2162	2
#33420	89