Subgroups — #36525879

Order 22784.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029267	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668032	C₂	1	1	yes	maximal, characteristic
3	#26019140	C₂	1	2	yes	maximal, complemented
4	#26019102	C₂	1	2	yes	maximal, complemented
5	#26019079	C₂	1	2	yes	maximal, complemented
6	C₈×#13083561	C₂	1	2	yes	maximal, complemented
7	#26019013	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018686	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018684	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	#19151728	C₂²	1	2	yes	—
15	C₄×#13083564	C₄	1	1	yes	characteristic
16	C₄×#13083564	C₂²	1	1	yes	characteristic
17	C₄×#13083561	C₄	1	1	yes	characteristic
18	C₄×#13083561	C₂²	1	1	yes	characteristic
19	C₄×#13083562	C₄	1	1	yes	characteristic
20	C₄×#13083562	C₂²	1	1	yes	characteristic
21	C₄×#13083559	C₄	1	1	yes	characteristic
22	C₄×#13083559	C₂²	1	1	yes	characteristic
23	#19151667	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151655	C₂²	1	1	yes	characteristic
26	#19151653	—	2	1	no	—
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151634	C₄	1	1	yes	characteristic
29	#19151594	C₄	1	1	yes	characteristic
30	#19151592	C₄	1	1	yes	characteristic
31	#97×D₈₉	—	2	1	no	—
32	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	—
34	#19151348	C₂²	1	2	yes	—
35	Q₈⋊#10623494	C₂²	1	2	yes	—
36	#19151328	C₂²	1	2	yes	—
37	D₄⋊#10623494	C₂²	1	2	yes	—
38	#19151325	C₂²	1	2	yes	—
39	#19151319	C₂²	1	2	yes	—
40	C₈×#10623494	C₂²	1	2	yes	—
41	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
43	#436×C₈₉	—	2	2	no	—
44	#436×C₈₉	C₂²	1	2	yes	—
45	#432×C₈₉	—	2	1	no	—
46	#432×C₈₉	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₈₉	—	2	1	no	—
48	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	#15668032	—	2	4	no	—
51	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
55	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
56	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
60	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
61	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₈₉	—	2	1	no	—
63	C₄×C₂²⋊D₈₉	—	2	1	no	—
64	#15667971	C₂×C₄	1	1	yes	characteristic
65	#15667969	—	2	1	no	—
66	C₄²×D₈₉	—	2	1	no	—
67	#15667945	C₂×C₄	1	1	yes	characteristic
68	#15667945	C₂×C₄	1	1	yes	characteristic
69	#15667943	C₂×C₄	1	1	yes	characteristic
70	#15667943	C₂×C₄	1	1	yes	characteristic
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	C₂³	1	2	yes	—
73	#15667941	—	2	2	no	—
74	#15667936	C₂×C₄	1	1	yes	characteristic
75	#15667936	C₂×C₄	1	1	yes	characteristic
76	#15667935	C₂×C₄	1	1	yes	characteristic
77	#15667935	C₂×C₄	1	1	yes	characteristic
78	#15667933	C₂×C₄	1	1	yes	characteristic
79	#15667933	C₂×C₄	1	1	yes	characteristic
80	#15667932	C₂×C₄	1	1	yes	characteristic
81	#15667932	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#10623494	—	2	1	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	#15667924	—	2	2	no	—
85	#15667923	—	2	1	no	—
86	#15667922	—	2	2	no	—
87	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
88	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
89	C₄×#10623494	C₂³	1	2	yes	—
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	—	2	2	no	—
94	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
95	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₈₉	—	2	1	no	—
98	C₄×D₄×C₈₉	—	2	1	no	—
99	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
101	#117×C₈₉	—	2	1	no	—
102	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	—	2	1	no	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	—	2	2	no	—
106	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₈₉	—	2	1	no	—
108	C₂²⋊C₈×C₈₉	—	2	2	no	—
109	#97×C₈₉	—	2	1	no	—
110	#97×C₈₉	D₄	1	1	yes	characteristic
111	#97×C₈₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₈₉	—	2	2	no	—
113	C₄×C₈×C₈₉	C₂³	1	2	yes	—
114	#13083574	—	2	2	no	—
115	#13083574	—	4	1	no	—
116	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₉	—	2	1	no	—
119	C₂×C₄×D₈₉	—	2	1	no	—
120	C₂×C₄×D₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	#13083564	—	2	2	no	—
123	#13083562	—	2	2	no	—
124	#13083561	M₁₆	1	4	yes	complemented
125	#13083559	—	2	2	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	4	1	no	—
130	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
133	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₈₉	—	4	4	no	—
135	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	#13083553	—	2	1	no	—
138	#13083553	—	2	1	no	—
139	C₂²⋊Dic₈₉	—	2	1	no	—
140	#13083551	—	2	1	no	—
141	#13083551	—	2	1	no	—
142	C₄×Dic₈₉	—	2	1	no	—
143	C₄×Dic₈₉	—	2	1	no	—
144	C₄×Dic₈₉	—	2	1	no	—
145	#41×C₈₉	—	2	2	no	—
146	#41×C₈₉	—	4	1	no	—
147	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₈₉	—	2	1	no	—
149	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
156	M₁₆×C₈₉	—	2	4	no	—
157	M₁₆×C₈₉	—	4	4	no	—
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²⋊C₄×C₈₉	—	2	1	no	—
166	C₂²⋊C₄×C₈₉	—	2	1	no	—
167	C₂²⋊C₄×C₈₉	—	2	1	no	—
168	C₄²×C₈₉	—	2	1	no	—
169	C₄²×C₈₉	—	2	1	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₈₉	#41	1	1	yes	characteristic
174	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂³×C₈₉	—	2	1	no	—
176	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₈₉	—	2	1	no	—
178	Q₈×C₈₉	—	2	1	no	—
179	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
180	D₄×C₈₉	—	2	1	no	—
181	D₄×C₈₉	—	2	1	no	—
182	D₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	—	8	1	no	—
193	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₈₉	—	4	2	no	—
200	C₂×Dic₈₉	—	2	1	no	—
201	C₂×Dic₈₉	—	2	1	no	—
202	C₂×Dic₈₉	—	2	1	no	—
203	D₃₅₆	—	2	1	no	—
204	D₃₅₆	C₂×M₁₆	1	2	yes	—
205	C₄×D₈₉	—	4	2	no	—
206	C₄×D₈₉	—	4	2	no	—
207	C₄×D₈₉	—	8	1	no	—
208	Dic₁₇₈	—	2	1	no	—
209	Dic₁₇₈	—	2	1	no	—
210	C₈×C₈₉	—	2	2	no	—
211	C₈×C₈₉	—	4	2	no	—
212	C₈×C₈₉	#135	1	4	yes	complemented
213	#10623494	—	2	1	no	—
214	#10623494	—	2	1	no	—
215	#10623494	—	2	1	no	—
216	#10623494	—	4	2	no	—
217	#10623494	—	4	2	no	—
218	#10623494	C₂×M₁₆	1	2	yes	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	1	no	—
222	C₂²×C₈₉	—	4	1	no	—
223	C₂²×C₈₉	—	4	1	no	—
224	C₂²×C₈₉	—	4	1	no	—
225	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂×D₈₉	—	2	2	no	—
227	C₂×D₈₉	—	4	1	no	—
228	C₂×D₈₉	—	4	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	2	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	2	1	no	—
234	C₄×C₈₉	—	4	1	no	—
235	C₄×C₈₉	—	4	1	no	—
236	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
237	C₄×C₈₉	#568	1	1	yes	characteristic
238	C₄×C₈₉	C₂×#135	1	2	yes	—
239	Dic₈₉	—	4	1	no	—
240	Dic₈₉	—	4	1	no	—
241	Dic₈₉	—	4	1	no	—
242	#18037	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	4	1	no	—
244	C₂×C₈₉	—	8	1	no	—
245	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
246	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
247	C₂×C₈₉	#2957	1	1	yes	characteristic
248	D₈₉	—	4	2	no	—
249	#2971	D₈₉	1	1	yes	characteristic, complemented
250	#2970	—	89	1	no	—
251	C₄×#135	—	89	1	no	—
252	#1590	—	89	2	no	—
253	#1584	—	89	2	no	—
254	#1581	—	89	2	no	—
255	C₈×SD₁₆	—	89	2	no	—
256	#1568	—	89	1	no	—
257	#1488	—	89	1	no	—
258	#1488	—	89	1	no	—
259	C₈×M₁₆	—	89	1	no	—
260	C₈₉	#18037	1	1	yes	characteristic, complemented, Sylow
261	C₂×#135	—	89	1	no	—
262	C₄×#41	—	89	1	no	—
263	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
264	#446	—	89	2	no	—
265	C₈×Q₈	C₂×D₈₉	1	2	yes	—
266	C₄×Q₁₆	—	89	1	no	—
267	C₄×Q₁₆	—	89	1	no	—
268	C₄×SD₁₆	—	89	1	no	—
269	C₄×SD₁₆	—	89	1	no	—
270	C₄×SD₁₆	—	89	1	no	—
271	C₄×SD₁₆	—	89	1	no	—
272	C₄×D₈	—	89	1	no	—
273	C₄×D₈	—	89	1	no	—
274	#436	—	2	2	no	—
275	#436	C₂×D₈₉	1	2	yes	—
276	#435	—	178	2	no	—
277	C₈×D₄	—	89	2	no	—
278	#432	—	2	1	no	—
279	#432	—	89	1	no	—
280	#432	—	178	1	no	—
281	#432	C₂×D₈₉	1	1	yes	characteristic
282	#431	—	89	1	no	—
283	#427	—	89	1	no	—
284	#416	—	89	1	no	—
285	#416	—	89	1	no	—
286	C₄×M₁₆	—	2	1	no	—
287	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
288	C₂×#97	—	178	1	no	—
289	C₂×C₄×C₈	—	89	1	no	—
290	#335	—	89	2	no	—
291	#334	—	89	2	no	—
292	Q₈⋊C₈	—	89	2	no	—
293	Q₈⋊C₈	—	89	2	no	—
294	D₄⋊C₈	—	89	2	no	—
295	D₄⋊C₈	—	89	2	no	—
296	#322	—	89	2	no	—
297	C₈²	—	89	2	no	—
298	C₂×#41	—	89	1	no	—
299	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
300	#135	—	178	4	no	—
301	C₂×Q₁₆	—	89	1	no	—
302	C₂×SD₁₆	—	89	1	no	—
303	C₂×SD₁₆	—	89	1	no	—
304	C₂×D₈	—	89	1	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	C₂²⋊D₈₉	1	2	yes	—
307	C₂²×C₈	—	89	1	no	—
308	C₂²×C₈	—	89	1	no	—
309	C₂²×C₈	—	178	2	no	—
310	C₄×Q₈	—	89	1	no	—
311	C₄×Q₈	—	89	1	no	—
312	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	—	89	1	no	—
324	#117	—	178	1	no	—
325	#117	C₄×D₈₉	1	1	yes	characteristic
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	178	1	no	—
328	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
329	#107	—	89	1	no	—
330	#107	—	89	1	no	—
331	#106	—	89	1	no	—
332	#106	—	89	1	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	89	2	no	—
335	C₄⋊C₈	—	178	2	no	—
336	C₄⋊C₈	—	178	1	no	—
337	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
338	#103	—	89	1	no	—
339	#103	—	89	1	no	—
340	#103	—	89	1	no	—
341	#103	—	89	1	no	—
342	#102	—	89	1	no	—
343	#102	—	89	1	no	—
344	#102	—	89	1	no	—
345	#102	—	89	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	178	1	no	—
349	C₂²⋊C₈	—	178	1	no	—
350	C₂²⋊C₈	—	178	2	no	—
351	#97	—	2	1	no	—
352	#97	—	178	2	no	—
353	#97	—	178	1	no	—
354	#97	C₂²⋊D₈₉	1	1	yes	characteristic
355	#97	C₂²⋊D₈₉	1	1	yes	characteristic
356	C₄×C₈	—	2	2	no	—
357	C₄×C₈	—	89	1	no	—
358	C₄×C₈	—	89	1	no	—
359	C₄×C₈	—	89	1	no	—
360	C₄×C₈	—	89	1	no	—
361	C₄×C₈	—	89	2	no	—
362	C₄×C₈	C₂²×D₈₉	1	2	yes	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	#41	—	356	1	no	—
366	#41	—	178	2	no	—
367	C₂×Q₈	—	89	1	no	—
368	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	89	1	no	—
371	C₂×D₄	—	178	1	no	—
372	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	178	1	no	—
377	C₂²×C₄	—	178	1	no	—
378	C₂²×C₄	—	178	1	no	—
379	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂²×C₄	#13083574	1	1	yes	characteristic
382	Q₁₆	—	178	2	no	—
383	SD₁₆	—	89	4	no	—
384	SD₁₆	—	178	2	no	—
385	D₈	—	178	2	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	89	1	no	—
390	C₂×C₈	—	89	1	no	—
391	C₂×C₈	—	89	1	no	—
392	C₂×C₈	—	89	1	no	—
393	C₂×C₈	—	356	4	no	—
394	C₂×C₈	—	356	1	no	—
395	C₂×C₈	—	178	2	no	—
396	C₂×C₈	—	178	2	no	—
397	C₂×C₈	—	178	2	no	—
398	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
399	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	89	1	no	—
403	C₄⋊C₄	—	89	1	no	—
404	C₄⋊C₄	—	178	1	no	—
405	C₄⋊C₄	—	178	1	no	—
406	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
407	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	178	1	no	—
412	C₂²⋊C₄	—	178	1	no	—
413	C₂²⋊C₄	—	178	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	178	1	no	—
418	C₄²	—	178	1	no	—
419	C₄²	—	178	1	no	—
420	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
421	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
422	C₄²	#13083574	1	1	yes	characteristic
423	C₄²	C₂³×D₈₉	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	178	1	no	—
426	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	178	1	no	—
429	Q₈	—	178	1	no	—
430	Q₈	M₁₆×D₈₉	1	2	yes	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	89	2	no	—
435	D₄	—	356	2	no	—
436	D₄	—	178	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	356	2	no	—
448	C₂×C₄	—	356	2	no	—
449	C₂×C₄	—	178	1	no	—
450	C₂×C₄	—	178	1	no	—
451	C₂×C₄	—	178	1	no	—
452	C₂×C₄	—	712	1	no	—
453	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	89	2	no	—
462	C₈	—	356	2	no	—
463	C₈	—	356	2	no	—
464	C₈	—	178	1	no	—
465	C₈	—	178	1	no	—
466	C₈	—	178	1	no	—
467	C₈	#15668032	1	4	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	356	1	no	—
475	C₂²	—	356	1	no	—
476	C₂²	—	178	2	no	—
477	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	356	1	no	—
486	C₄	—	356	1	no	—
487	C₄	—	356	1	no	—
488	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
489	C₄	#19152364	1	1	yes	characteristic
490	C₄	C₂×#15668032	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	8	1	no	—
493	C₂	—	356	2	no	—
494	C₂	M₁₆×C₂²⋊D₈₉	1	1	yes	characteristic
495	C₂	C₄×#15668032	1	1	yes	characteristic
496	C₂	#26029167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2971	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2971	D₈₉
hypocenter	C₈₉	#18037
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2971

Complements

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

N	H ≅ G/N	type
1. #26029267	C₂	semidirect
3. #26019140	C₂	semidirect
4. #26019102	C₂	semidirect
5. #26019079	C₂	semidirect
6. C₈×#13083561	C₂	semidirect
7. #26019013	C₂	semidirect
8. #26018686	C₂	semidirect
9. #26018684	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#2971	C₂	semidirect
124. #13083561	M₁₆	semidirect
212. C₈×C₈₉	#135	semidirect
249. #2971	D₈₉	semidirect
260. C₈₉	#18037	semidirect
467. C₈	#15668032	semidirect

Maximal subgroups

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

subgroup	index
#26029267	2
C₄×#15668032	2
#26019140	2
#26019102	2
#26019079	2
C₈×#13083561	2
#26019013	2
#26018686	2
#26018684	2
M₁₆×#10623494	2
C₈₉×#2971	2
#18037	89