Subgroups — #36707627

Order 22784.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028944	C₂	1	1	yes	maximal, characteristic
3	#26022082	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	#26022075	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
7	#26022010	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021866	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151377	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#504×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
13	#19152105	C₄	1	1	yes	characteristic
14	C₂×#15667952	C₂²	1	1	yes	characteristic
15	C₂×#15667951	C₂²	1	2	yes	—
16	M₃₂×D₈₉	—	2	4	no	—
17	C₂²×#13083549	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
19	#19151667	C₄	1	2	yes	—
20	#19151667	C₄	1	2	yes	—
21	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
23	#19151626	C₄	1	1	yes	characteristic
24	#19151565	C₄	1	1	yes	characteristic
25	#19151561	C₄	1	1	yes	characteristic
26	#19151553	C₂²	1	1	yes	characteristic
27	#19151416	C₂²	1	2	yes	complemented
28	#19151416	C₂²	1	2	yes	complemented
29	C₂²⋊#13083549	C₂²	1	2	yes	complemented
30	C₂²⋊#13083549	C₂²	1	2	yes	complemented
31	#19151377	C₂²	1	1	yes	characteristic
32	#19151377	C₂²	1	1	yes	characteristic
33	#19151377	C₂²	1	1	yes	characteristic
34	#19151377	C₂²	1	1	yes	characteristic
35	#19151373	C₂²	1	2	yes	complemented
36	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
37	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
38	#504×C₈₉	—	2	4	no	—
39	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₈₉	C₂²	1	2	yes	complemented
41	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
45	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₈₉	—	2	2	no	—
47	C₂×C₈×D₈₉	—	2	2	no	—
48	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
52	#15667993	C₈	1	2	yes	—
53	#15667988	C₈	1	1	yes	characteristic
54	#15667988	C₈	1	1	yes	characteristic
55	#15667983	C₈	1	1	yes	characteristic
56	#15667983	C₈	1	1	yes	characteristic
57	#15667980	C₈	1	2	yes	—
58	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
60	#15667971	C₂×C₄	1	1	yes	characteristic
61	#15667952	—	2	2	no	—
62	#15667951	—	2	4	no	—
63	C₂×#13083549	—	2	2	no	—
64	C₂×#13083549	C₂³	1	1	yes	characteristic
65	C₂×#13083549	C₂³	1	1	yes	characteristic
66	C₂×#13083549	C₂³	1	2	yes	—
67	C₁₆×D₈₉	—	2	4	no	—
68	#15667941	C₂×C₄	1	2	yes	—
69	#15667941	C₂×C₄	1	2	yes	—
70	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
71	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
72	#15667924	C₂×C₄	1	2	yes	—
73	#15667924	C₂×C₄	1	2	yes	—
74	#15667922	C₂×C₄	1	2	yes	—
75	C₈×Dic₈₉	C₂³	1	2	yes	—
76	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
77	#131×C₈₉	—	2	2	no	—
78	#131×C₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	M₃₂×C₈₉	—	2	4	no	—
84	M₃₂×C₈₉	D₄	1	4	yes	complemented
85	C₂×C₁₆×C₈₉	—	2	2	no	—
86	C₂×C₁₆×C₈₉	—	2	4	no	—
87	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
90	C₂³×D₈₉	C₂×C₈	1	1	yes	characteristic
91	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
92	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
93	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₈₉	—	2	2	no	—
95	C₂×C₄×D₈₉	—	2	2	no	—
96	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
100	#13083558	—	2	2	no	—
101	C₂×#10623494	—	2	2	no	—
102	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
103	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
104	C₂×#10623494	C₂²×C₄	1	2	yes	—
105	C₈×D₈₉	—	2	2	no	—
106	C₈×D₈₉	—	2	2	no	—
107	C₈×D₈₉	—	2	1	no	—
108	C₈×D₈₉	—	2	1	no	—
109	C₈×D₈₉	—	2	1	no	—
110	C₈×D₈₉	—	2	1	no	—
111	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
112	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
113	#13083553	C₂×C₈	1	2	yes	—
114	#13083553	C₂×C₈	1	2	yes	—
115	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
116	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
117	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
118	#13083551	C₂×C₈	1	2	yes	—
119	#13083551	C₂×C₈	1	2	yes	—
120	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
121	#13083549	—	2	2	no	—
122	#13083549	—	2	1	no	—
123	#13083549	—	2	1	no	—
124	#41×C₈₉	—	2	2	no	—
125	#41×C₈₉	—	2	2	no	—
126	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
127	C₂×D₄×C₈₉	C₂×C₈	1	2	yes	—
128	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₈₉	—	2	2	no	—
132	M₁₆×C₈₉	—	2	4	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₈₉	#41	1	2	yes	—
139	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₁₆×C₈₉	—	2	1	no	—
141	C₁₆×C₈₉	—	2	1	no	—
142	C₁₆×C₈₉	C₂×D₄	1	4	yes	—
143	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
144	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₈₉	—	2	2	no	—
146	C₂²×D₈₉	—	2	2	no	—
147	C₂²×D₈₉	—	4	1	no	—
148	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
150	Q₈×C₈₉	—	2	2	no	—
151	D₄×C₈₉	—	2	4	no	—
152	D₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#131	1	2	yes	—
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₈₉	—	2	4	no	—
161	C₂²⋊D₈₉	—	4	2	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
164	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
165	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
167	C₄×D₈₉	—	2	1	no	—
168	C₄×D₈₉	—	2	1	no	—
169	C₄×D₈₉	—	2	1	no	—
170	C₄×D₈₉	—	2	1	no	—
171	C₄×D₈₉	—	2	2	no	—
172	C₄×D₈₉	—	2	2	no	—
173	C₈×C₈₉	—	2	2	no	—
174	C₈×C₈₉	C₄×D₄	1	2	yes	—
175	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
177	#10623494	—	2	1	no	—
178	#10623494	—	2	1	no	—
179	#10623494	—	2	2	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	2	2	no	—
184	C₂²×C₈₉	—	2	2	no	—
185	C₂²×C₈₉	C₈×D₄	1	2	yes	—
186	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
187	C₂×D₈₉	—	2	1	no	—
188	C₂×D₈₉	—	2	1	no	—
189	C₂×D₈₉	—	2	1	no	—
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	4	4	no	—
193	C₂×D₈₉	#504	1	2	yes	complemented
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	C₈×D₄	1	2	yes	—
196	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
198	Dic₈₉	—	2	2	no	—
199	Dic₈₉	—	2	2	no	—
200	Dic₈₉	—	2	1	no	—
201	Dic₈₉	—	2	1	no	—
202	#33436	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	—	2	2	no	—
204	C₂×C₈₉	—	4	2	no	—
205	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
206	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
207	C₂×C₈₉	#3407	1	1	yes	characteristic
208	D₈₉	—	2	2	no	—
209	D₈₉	—	4	1	no	—
210	C₂×#504	D₈₉	1	1	yes	characteristic, complemented
211	C₂²×M₃₂	—	89	1	no	—
212	#2929	—	89	1	no	—
213	#2169	—	89	2	no	—
214	#2168	—	89	2	no	—
215	#2168	—	89	2	no	—
216	D₄×C₁₆	—	89	2	no	—
217	#2151	—	89	1	no	—
218	#2113	—	89	1	no	—
219	C₂×C₂²⋊C₁₆	—	89	1	no	—
220	#2108	—	89	1	no	—
221	C₈₉	#33436	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
223	C₂³×C₈	—	89	1	no	—
224	#525	—	89	1	no	—
225	#504	—	2	4	no	—
226	C₂×M₃₂	—	89	1	no	—
227	C₂×M₃₂	—	89	2	no	—
228	C₂×M₃₂	—	178	4	no	—
229	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
230	C₂×M₃₂	C₂×D₈₉	1	2	yes	complemented
231	C₂²×C₁₆	—	89	1	no	—
232	C₂²×C₁₆	—	89	2	no	—
233	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
234	C₂²×C₁₆	C₂×D₈₉	1	2	yes	complemented
235	#435	—	89	2	no	—
236	#435	—	89	2	no	—
237	C₈×D₄	—	89	2	no	—
238	C₈×D₄	—	89	2	no	—
239	#424	—	89	1	no	—
240	#408	—	89	1	no	—
241	#407	—	89	1	no	—
242	#405	—	89	1	no	—
243	C₄⋊C₁₆	—	89	2	no	—
244	C₄⋊C₁₆	—	89	2	no	—
245	C₂²⋊C₁₆	—	89	2	no	—
246	C₂²⋊C₁₆	—	89	2	no	—
247	C₂²⋊C₁₆	—	89	1	no	—
248	C₂²⋊C₁₆	—	89	1	no	—
249	C₂²⋊C₁₆	—	89	1	no	—
250	C₂²⋊C₁₆	—	89	1	no	—
251	#346	—	89	2	no	—
252	C₄×C₁₆	—	89	2	no	—
253	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
254	C₂³×C₄	—	89	1	no	—
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	C₂×M₁₆	—	89	1	no	—
258	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
259	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	—	89	1	no	—
265	C₂²×C₈	—	178	2	no	—
266	C₂²×C₈	—	178	2	no	—
267	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
268	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
269	#123	—	89	2	no	—
270	C₂²⋊Q₈	—	89	1	no	—
271	C₂²⋊Q₈	—	89	1	no	—
272	#121	—	89	1	no	—
273	#121	—	89	1	no	—
274	#120	—	89	2	no	—
275	C₄×D₄	—	89	2	no	—
276	C₄×D₄	—	89	2	no	—
277	#117	—	89	1	no	—
278	M₃₂	—	2	4	no	—
279	M₃₂	—	178	2	no	—
280	M₃₂	—	178	4	no	—
281	M₃₂	C₂²⋊D₈₉	1	4	yes	complemented
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	2	4	no	—
284	C₂×C₁₆	—	89	1	no	—
285	C₂×C₁₆	—	89	1	no	—
286	C₂×C₁₆	—	89	2	no	—
287	C₂×C₁₆	—	178	2	no	—
288	C₂×C₁₆	—	178	4	no	—
289	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
291	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
292	C₄⋊C₈	—	89	2	no	—
293	C₄⋊C₈	—	89	2	no	—
294	C₂²⋊C₈	—	89	2	no	—
295	C₂²⋊C₈	—	89	2	no	—
296	C₂²⋊C₈	—	89	2	no	—
297	C₂²⋊C₈	—	89	2	no	—
298	#97	—	89	2	no	—
299	C₄×C₈	—	89	2	no	—
300	C₂⁴	—	89	1	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	C₈×D₈₉	1	1	yes	characteristic
304	C₂×D₄	—	89	2	no	—
305	C₂×D₄	—	89	2	no	—
306	C₂×D₄	C₈×D₈₉	1	2	yes	—
307	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	89	1	no	—
311	C₂²×C₄	—	89	1	no	—
312	C₂²×C₄	—	89	1	no	—
313	C₂²×C₄	—	178	2	no	—
314	C₂²×C₄	—	178	2	no	—
315	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	178	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	1	no	—
324	C₂×C₈	—	89	1	no	—
325	C₂×C₈	—	178	2	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	—	178	2	no	—
328	C₂×C₈	—	178	1	no	—
329	C₂×C₈	—	178	1	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	1	no	—
332	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
335	C₂×C₈	#13083574	1	2	yes	—
336	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
337	C₄⋊C₄	—	89	1	no	—
338	C₄⋊C₄	—	89	1	no	—
339	C₄⋊C₄	—	89	2	no	—
340	C₄⋊C₄	—	89	2	no	—
341	C₂²⋊C₄	—	89	2	no	—
342	C₂²⋊C₄	—	89	2	no	—
343	C₂²⋊C₄	—	89	2	no	—
344	C₂²⋊C₄	—	89	2	no	—
345	C₂²⋊C₄	—	89	2	no	—
346	C₄²	—	89	2	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	178	2	no	—
350	C₁₆	—	178	1	no	—
351	C₁₆	—	178	1	no	—
352	C₁₆	C₂×C₂²⋊D₈₉	1	4	yes	—
353	C₂³	—	89	1	no	—
354	C₂³	—	89	1	no	—
355	C₂³	—	356	1	no	—
356	C₂³	—	178	2	no	—
357	C₂³	—	178	2	no	—
358	C₂³	C₂×C₈×D₈₉	1	2	yes	—
359	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	356	2	no	—
364	D₄	—	178	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	89	2	no	—
368	C₂×C₄	—	89	2	no	—
369	C₂×C₄	—	89	1	no	—
370	C₂×C₄	—	89	1	no	—
371	C₂×C₄	—	178	2	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	178	1	no	—
375	C₂×C₄	—	178	1	no	—
376	C₂×C₄	—	178	1	no	—
377	C₂×C₄	—	178	1	no	—
378	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
379	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
380	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
381	C₂×C₄	#15668018	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	178	1	no	—
385	C₈	—	178	1	no	—
386	C₈	—	178	2	no	—
387	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
388	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
389	C₈	C₂×#13083574	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	89	2	no	—
396	C₂²	—	356	4	no	—
397	C₂²	—	178	1	no	—
398	C₂²	—	178	1	no	—
399	C₂²	—	178	1	no	—
400	C₂²	—	178	1	no	—
401	C₂²	—	178	1	no	—
402	C₂²	C₈×C₂²⋊D₈₉	1	2	yes	—
403	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	178	1	no	—
406	C₄	—	178	1	no	—
407	C₄	—	178	2	no	—
408	C₄	—	178	2	no	—
409	C₄	C₈×C₂²⋊D₈₉	1	2	yes	—
410	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
411	C₄	C₂×#15668018	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	—	356	1	no	—
415	C₂	—	178	2	no	—
416	C₂	C₂×C₈×C₂²⋊D₈₉	1	1	yes	characteristic
417	C₂	#504×D₈₉	1	1	yes	characteristic
418	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₂×#504×C₈₉	C₂
prime radical	#19152105	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#504	D₈₉
hypocenter	C₈₉	#33436
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₈₉	C₂	semidirect
3. #26022082	C₂	semidirect
4. #26022077	C₂	semidirect
5. #26022075	C₂	semidirect
6. C₁₆×C₂²⋊D₈₉	C₂	semidirect
7. #26022010	C₂	semidirect
8. #26021866	C₂	semidirect
9. C₂×#19151377	C₂	semidirect
10. #26021851	C₂	semidirect
11. C₂×#504×C₈₉	C₂	semidirect
27. #19151416	C₂²	semidirect
28. #19151416	C₂²	semidirect
29. C₂²⋊#13083549	C₂²	semidirect
30. C₂²⋊#13083549	C₂²	semidirect
35. #19151373	C₂²	semidirect
36. C₁₆×Dic₈₉	C₂²	semidirect
40. C₂×M₃₂×C₈₉	C₂²	semidirect
42. C₂²×C₁₆×C₈₉	C₂²	semidirect
84. M₃₂×C₈₉	D₄	semidirect
193. C₂×D₈₉	#504	semidirect
210. C₂×#504	D₈₉	semidirect
221. C₈₉	#33436	semidirect
230. C₂×M₃₂	C₂×D₈₉	semidirect
234. C₂²×C₁₆	C₂×D₈₉	semidirect
281. M₃₂	C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₈₉	2
#26028944	2
#26022082	2
#26022077	2
#26022075	2
C₁₆×C₂²⋊D₈₉	2
#26022010	2
#26021866	2
C₂×#19151377	2
#26021851	2
C₂×#504×C₈₉	2
#33436	89