Subgroups — #36524477

Order 22784.

692 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030312	C₂	1	1	yes	maximal, characteristic
2	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019095	C₂	1	2	yes	maximal, complemented
4	#26019081	C₂	1	2	yes	maximal, complemented
5	#26019074	C₂	1	2	yes	maximal, complemented
6	#26019062	C₂	1	2	yes	maximal, complemented
7	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018691	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018668	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151922	C₄	1	2	yes	—
15	#19151893	C₄	1	1	yes	characteristic
16	#19151888	C₄	1	1	yes	characteristic
17	#19151798	C₄	1	1	yes	characteristic
18	#19151793	C₄	1	1	yes	characteristic
19	#19151743	C₄	1	2	yes	—
20	C₄×#13083561	C₂²	1	2	yes	—
21	C₄×#13083559	C₂²	1	2	yes	—
22	#19151677	—	2	1	no	—
23	#19151677	C₂²	1	2	yes	—
24	C₈×D₃₅₆	—	2	1	no	—
25	C₈×D₃₅₆	C₂²	1	2	yes	—
26	#19151651	C₂²	1	1	yes	characteristic
27	#19151622	C₂²	1	1	yes	characteristic
28	#19151564	—	2	1	no	—
29	C₄×#13083558	C₂²	1	1	yes	characteristic
30	#19151350	C₂²	1	2	yes	—
31	#19151348	C₂²	1	2	yes	—
32	Q₈⋊#10623494	C₂²	1	2	yes	—
33	D₄⋊#10623494	C₂²	1	2	yes	—
34	#19151325	C₂²	1	2	yes	—
35	#19151325	C₂²	1	2	yes	—
36	#19151320	C₂²	1	2	yes	—
37	#19151319	C₂²	1	2	yes	—
38	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₈₉	—	2	1	no	—
42	C₈×D₄×C₈₉	—	2	1	no	—
43	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	#431×C₈₉	—	2	1	no	—
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	—	2	1	no	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083559	C₂×C₄	1	2	yes	—
52	#15668018	—	4	4	no	—
53	C₂×#13083558	—	2	1	no	—
54	C₂×#13083558	—	2	1	no	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×C₈×D₈₉	—	2	2	no	—
57	#15668012	C₂×C₄	1	1	yes	characteristic
58	#15668009	C₂×C₄	1	1	yes	characteristic
59	#15668000	—	2	1	no	—
60	#15667986	—	2	1	no	—
61	#15667986	C₂×C₄	1	2	yes	—
62	C₄×D₃₅₆	—	2	1	no	—
63	C₄×D₃₅₆	C₂³	1	2	yes	—
64	#15667945	C₂×C₄	1	2	yes	—
65	#15667943	C₂×C₄	1	2	yes	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667936	C₂×C₄	1	2	yes	—
71	#15667933	C₂×C₄	1	2	yes	—
72	#15667932	C₂×C₄	1	2	yes	—
73	#15667932	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667923	—	2	1	no	—
78	C₄×#10623494	C₂³	1	2	yes	—
79	C₄×#10623494	C₂³	1	2	yes	—
80	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	—	2	1	no	—
82	C₂²×C₈×C₈₉	—	2	1	no	—
83	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₈₉	—	2	1	no	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
91	#117×C₈₉	—	2	1	no	—
92	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	—	2	1	no	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₈₉	—	2	1	no	—
100	C₂²⋊C₈×C₈₉	—	2	1	no	—
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	—	2	1	no	—
104	C₄×C₈×C₈₉	—	2	1	no	—
105	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	#13083574	—	4	2	no	—
110	#13083574	—	4	2	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×D₃₅₆	—	2	1	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
115	C₂×C₂²⋊D₈₉	—	2	2	no	—
116	C₂×C₄×D₈₉	—	2	2	no	—
117	#13083561	—	2	4	no	—
118	#13083559	—	2	4	no	—
119	#13083558	—	4	2	no	—
120	#13083558	—	4	2	no	—
121	#13083557	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₂×#10623494	C₂²×C₄	1	2	yes	—
126	C₈×D₈₉	—	4	4	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
129	#13083551	—	2	2	no	—
130	#13083551	—	2	2	no	—
131	#41×C₈₉	—	2	2	no	—
132	#41×C₈₉	—	2	2	no	—
133	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	4	1	no	—
146	C₂×C₈×C₈₉	—	4	2	no	—
147	C₂×C₈×C₈₉	—	4	2	no	—
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₈₉	—	2	1	no	—
157	C₂²⋊C₄×C₈₉	—	2	1	no	—
158	C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	—	2	1	no	—
160	C₄²×C₈₉	—	2	1	no	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₈₉	#41	1	1	yes	characteristic
165	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₂³×C₈₉	—	2	1	no	—
167	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₈₉	—	2	2	no	—
169	Q₈×C₈₉	—	2	1	no	—
170	Q₈×C₈₉	#131	1	2	yes	complemented
171	D₄×C₈₉	—	2	4	no	—
172	D₄×C₈₉	—	2	1	no	—
173	D₄×C₈₉	#131	1	2	yes	complemented
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	4	1	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₈₉	—	4	4	no	—
193	C₂×Dic₈₉	—	2	2	no	—
194	D₃₅₆	—	2	2	no	—
195	D₃₅₆	—	2	2	no	—
196	D₃₅₆	—	4	2	no	—
197	D₃₅₆	—	4	2	no	—
198	C₄×D₈₉	—	4	2	no	—
199	C₄×D₈₉	—	4	2	no	—
200	Dic₁₇₈	—	4	2	no	—
201	C₈×C₈₉	—	2	1	no	—
202	C₈×C₈₉	—	2	1	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	4	1	no	—
205	C₈×C₈₉	—	4	1	no	—
206	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
207	#10623494	—	2	2	no	—
208	#10623494	—	2	2	no	—
209	#10623494	—	4	2	no	—
210	#10623494	—	4	2	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	—	2	2	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	2	1	no	—
215	C₂²×C₈₉	—	4	1	no	—
216	C₂²×C₈₉	—	4	1	no	—
217	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂×D₈₉	—	4	2	no	—
219	C₂×D₈₉	—	4	2	no	—
220	C₂×D₈₉	—	4	2	no	—
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	4	1	no	—
226	C₄×C₈₉	—	4	1	no	—
227	C₄×C₈₉	#444	1	2	yes	—
228	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
229	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
230	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₈₉	#575	1	1	yes	characteristic
232	Dic₈₉	—	4	2	no	—
233	#17917	—	89	1	no	maximal, Sylow
234	C₂×C₈₉	—	4	1	no	—
235	C₂×C₈₉	—	4	2	no	—
236	C₂×C₈₉	#2929	1	1	yes	characteristic
237	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
239	D₈₉	—	8	2	no	—
240	#3106	—	89	1	no	—
241	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
242	#2931	—	89	1	no	—
243	#1583	—	89	2	no	—
244	#1581	—	89	2	no	—
245	#1580	—	89	2	no	—
246	SD₁₆⋊C₈	—	89	2	no	—
247	#1574	—	89	1	no	—
248	#1489	—	89	1	no	—
249	#1484	—	89	1	no	—
250	#1451	—	89	1	no	—
251	C₈₉	#17917	1	1	yes	characteristic, complemented, Sylow
252	C₂×#131	—	178	1	no	—
253	#532	—	89	1	no	—
254	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
255	#482	—	89	2	no	—
256	#477	—	89	1	no	—
257	#476	—	89	1	no	—
258	#460	—	89	1	no	—
259	#459	—	89	1	no	—
260	#449	—	89	2	no	—
261	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
262	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
263	C₄×SD₁₆	—	89	2	no	—
264	C₄×D₈	—	89	2	no	—
265	#436	—	89	2	no	—
266	#436	—	178	1	no	—
267	C₈×D₄	—	2	1	no	—
268	C₈×D₄	—	2	1	no	—
269	C₈×D₄	—	89	2	no	—
270	C₈×D₄	—	178	1	no	—
271	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
272	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
273	#431	—	2	1	no	—
274	#431	—	89	1	no	—
275	#431	C₂×D₈₉	1	1	yes	characteristic
276	#423	—	89	1	no	—
277	#408	—	178	1	no	—
278	C₄×M₁₆	—	89	1	no	—
279	C₂×C₄×C₈	—	2	1	no	—
280	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
281	#335	—	89	2	no	—
282	#334	—	89	2	no	—
283	Q₈⋊C₈	—	89	2	no	—
284	D₄⋊C₈	—	89	2	no	—
285	D₄⋊C₈	—	89	2	no	—
286	D₄⋊C₈	—	89	2	no	—
287	#322	—	89	2	no	—
288	#322	—	89	2	no	—
289	C₂×#41	—	178	1	no	—
290	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
291	C₂×SD₁₆	—	89	2	no	—
292	C₂×D₈	—	89	2	no	—
293	#131	—	356	4	no	—
294	C₂×M₁₆	—	178	1	no	—
295	C₂×M₁₆	—	178	1	no	—
296	C₂×M₁₆	—	178	2	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	178	2	no	—
300	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
302	C₄⋊Q₈	—	89	1	no	—
303	#127	—	89	1	no	—
304	#124	—	178	1	no	—
305	#121	—	89	2	no	—
306	#121	—	178	1	no	—
307	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
308	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	89	2	no	—
312	C₄×D₄	—	178	1	no	—
313	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
314	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₄×D₈₉	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	#107	—	89	2	no	—
320	#106	—	89	2	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	89	1	no	—
324	C₄⋊C₈	—	89	1	no	—
325	C₄⋊C₈	—	89	2	no	—
326	C₄⋊C₈	—	178	1	no	—
327	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
328	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
329	#103	—	89	2	no	—
330	#102	—	89	2	no	—
331	#102	—	89	2	no	—
332	#102	—	89	2	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	89	2	no	—
337	C₂²⋊C₈	—	178	2	no	—
338	C₂²⋊C₈	—	178	2	no	—
339	#97	—	178	1	no	—
340	C₄×C₈	—	2	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	89	2	no	—
344	C₄×C₈	—	89	2	no	—
345	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
346	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	—	356	2	no	—
352	#41	—	356	2	no	—
353	C₂×Q₈	—	178	1	no	—
354	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	89	2	no	—
357	C₂×D₄	—	178	2	no	—
358	C₂×D₄	—	178	1	no	—
359	C₂×D₄	—	178	1	no	—
360	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	178	2	no	—
365	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
367	C₂²×C₄	#13083574	1	1	yes	characteristic
368	SD₁₆	—	178	4	no	—
369	D₈	—	178	4	no	—
370	M₁₆	—	356	2	no	—
371	M₁₆	—	356	2	no	—
372	M₁₆	—	356	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	89	2	no	—
380	C₂×C₈	—	89	2	no	—
381	C₂×C₈	—	356	4	no	—
382	C₂×C₈	—	178	2	no	—
383	C₂×C₈	—	178	2	no	—
384	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	89	2	no	—
391	C₄⋊C₄	—	178	1	no	—
392	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
393	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	178	2	no	—
398	C₂²⋊C₄	—	178	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
403	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
404	C₄²	#13083574	1	1	yes	characteristic
405	C₄²	C₂³×D₈₉	1	1	yes	characteristic
406	C₂³	—	2	1	no	—
407	C₂³	—	178	2	no	—
408	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	356	2	no	—
411	Q₈	#15668018	1	2	yes	complemented
412	D₄	—	2	4	no	—
413	D₄	—	2	1	no	—
414	D₄	—	356	2	no	—
415	D₄	—	356	4	no	—
416	D₄	—	356	2	no	—
417	D₄	—	178	2	no	—
418	D₄	—	178	2	no	—
419	D₄	#15668018	1	2	yes	complemented
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	356	2	no	—
433	C₂×C₄	—	356	2	no	—
434	C₂×C₄	—	178	2	no	—
435	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
437	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	356	2	no	—
447	C₈	—	356	2	no	—
448	C₈	—	178	2	no	—
449	C₈	—	178	2	no	—
450	C₈	#15668037	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	356	2	no	—
458	C₂²	—	356	2	no	—
459	C₂²	—	356	2	no	—
460	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	356	2	no	—
468	C₄	#19151718	1	2	yes	—
469	C₄	C₂×#15668018	1	1	yes	characteristic
470	C₄	C₂×#15668018	1	1	yes	characteristic
471	C₄	C₂×#15668037	1	1	yes	characteristic
472	C₄	#19152396	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	712	2	no	—
476	C₂	#26028946	1	1	yes	characteristic
477	C₂	C₄×#15668037	1	1	yes	characteristic
478	C₂	C₂×#19151718	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030312	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#17917
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #26028965	C₂	semidirect
3. #26019095	C₂	semidirect
4. #26019081	C₂	semidirect
5. #26019074	C₂	semidirect
6. #26019062	C₂	semidirect
7. #26019040	C₂	semidirect
8. #26018691	C₂	semidirect
9. #26018668	C₂	semidirect
10. #26018541	C₂	semidirect
11. C₈×#41×C₈₉	C₂	semidirect
170. Q₈×C₈₉	#131	semidirect
173. D₄×C₈₉	#131	semidirect
241. C₈×#41	D₈₉	semidirect
251. C₈₉	#17917	semidirect
411. Q₈	#15668018	semidirect
419. D₄	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26030312	2
#26028965	2
#26019095	2
#26019081	2
#26019074	2
#26019062	2
#26019040	2
#26018691	2
#26018668	2
#26018541	2
C₈×#41×C₈₉	2
#17917	89