Subgroups — #36524580

Order 22784.

586 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030289	C₂	1	1	yes	maximal, characteristic
2	#26029348	C₂	1	1	yes	maximal, characteristic
3	#26029331	C₂	1	1	yes	maximal, characteristic
4	#26019123	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019121	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019068	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019068	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019058	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019031	C₂	1	1	yes	maximal, characteristic
12	#26018697	C₂	1	1	yes	maximal, characteristic
13	#26018671	C₂	1	1	yes	maximal, characteristic
14	#26018548	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	#19151935	C₄	1	1	yes	characteristic
19	#19151932	C₄	1	1	yes	characteristic
20	#19151892	C₄	1	1	yes	characteristic
21	#19151891	C₄	1	1	yes	characteristic
22	#19151807	C₄	1	1	yes	characteristic
23	#19151806	C₄	1	1	yes	characteristic
24	#19151755	C₄	1	1	yes	characteristic
25	#19151752	C₄	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151726	—	2	1	no	—
28	#19151725	—	2	1	no	—
29	Q₈×#10623494	C₂²	1	1	yes	characteristic
30	Q₈×#10623494	C₂²	1	1	yes	characteristic
31	C₈×Dic₁₇₈	—	2	1	no	—
32	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
33	#19151722	—	2	1	no	—
34	#19151722	C₂²	1	1	yes	characteristic
35	#19151722	C₂²	1	1	yes	characteristic
36	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
37	C₄×#13083564	C₂²	1	1	yes	characteristic
38	C₄×#13083564	C₂²	1	1	yes	characteristic
39	#19151660	—	2	1	no	—
40	#19151658	—	2	1	no	—
41	#19151654	C₂²	1	1	yes	characteristic
42	#19151650	—	2	1	no	—
43	#19151650	C₂²	1	1	yes	characteristic
44	#19151649	—	2	1	no	—
45	#19151649	C₂²	1	1	yes	characteristic
46	#19151649	C₂²	1	1	yes	characteristic
47	C₄×#13083557	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151348	C₂²	1	1	yes	characteristic
50	#19151348	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
54	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	#19151328	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	#19151320	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	—	2	1	no	—
72	#15668011	C₂×C₄	1	1	yes	characteristic
73	#15668010	C₂×C₄	1	1	yes	characteristic
74	#15668002	—	2	1	no	—
75	#15667992	C₂×C₄	1	1	yes	characteristic
76	#15667990	—	2	1	no	—
77	#15667988	C₂×C₄	1	1	yes	characteristic
78	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₇₈	—	2	1	no	—
80	C₄×Dic₁₇₈	—	2	1	no	—
81	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
82	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
83	#15667977	—	2	1	no	—
84	#15667977	C₂×C₄	1	1	yes	characteristic
85	#15667969	—	2	1	no	—
86	C₄⋊C₄×D₈₉	—	2	1	no	—
87	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₈₉	—	2	1	no	—
89	C₄²×D₈₉	C₂³	1	1	yes	characteristic
90	#15667946	C₂×C₄	1	1	yes	characteristic
91	#15667945	C₂×C₄	1	1	yes	characteristic
92	#15667945	C₂×C₄	1	1	yes	characteristic
93	C₄⋊#10623494	—	2	1	no	—
94	C₄⋊#10623494	—	2	1	no	—
95	C₄⋊#10623494	C₂³	1	1	yes	characteristic
96	C₄⋊#10623494	C₂³	1	1	yes	characteristic
97	#15667941	—	2	1	no	—
98	#15667941	—	2	1	no	—
99	#15667941	—	2	1	no	—
100	#15667941	—	2	1	no	—
101	#15667941	C₂×C₄	1	1	yes	characteristic
102	#15667941	C₂×C₄	1	1	yes	characteristic
103	#15667941	D₄	1	1	yes	characteristic
104	#15667941	D₄	1	1	yes	characteristic
105	#15667937	C₂×C₄	1	1	yes	characteristic
106	#15667937	C₂×C₄	1	1	yes	characteristic
107	#15667936	C₂×C₄	1	1	yes	characteristic
108	#15667936	C₂×C₄	1	1	yes	characteristic
109	#15667935	C₂×C₄	1	1	yes	characteristic
110	#15667935	C₂×C₄	1	1	yes	characteristic
111	#15667924	—	2	1	no	—
112	#15667924	—	2	1	no	—
113	#15667924	C₂×C₄	1	1	yes	characteristic
114	#15667924	C₂×C₄	1	1	yes	characteristic
115	#15667924	D₄	1	1	yes	characteristic
116	#15667924	D₄	1	1	yes	characteristic
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	C₄×#10623494	—	2	1	no	—
121	C₄×#10623494	—	2	1	no	—
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	—	2	1	no	—
129	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₈	—	2	1	no	—
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	Q₈×D₈₉	—	2	2	no	—
149	Q₈×D₈₉	—	2	2	no	—
150	C₂×C₄×D₈₉	—	2	1	no	—
151	C₂×C₄×D₈₉	—	2	1	no	—
152	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
155	Dic₃₅₆	—	2	2	no	—
156	#13083564	—	2	2	no	—
157	#13083564	—	2	2	no	—
158	#13083557	—	4	2	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
164	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
165	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
166	C₄⋊Dic₈₉	—	2	1	no	—
167	C₄⋊Dic₈₉	—	2	1	no	—
168	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
170	#13083553	—	2	1	no	—
171	#13083553	—	2	1	no	—
172	#13083553	—	2	1	no	—
173	#13083553	—	2	1	no	—
174	#13083553	—	2	1	no	—
175	#13083553	—	2	1	no	—
176	#13083553	—	2	1	no	—
177	#13083553	—	2	1	no	—
178	#13083551	—	2	1	no	—
179	#13083551	—	2	1	no	—
180	C₄×Dic₈₉	—	2	1	no	—
181	C₄×Dic₈₉	—	2	1	no	—
182	C₄×Dic₈₉	—	2	1	no	—
183	C₄×Dic₈₉	—	2	1	no	—
184	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
186	C₄×Dic₈₉	#41	1	1	yes	characteristic
187	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	Q₁₆×C₈₉	—	2	2	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
204	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
205	Q₈×C₈₉	—	2	1	no	—
206	Q₈×C₈₉	—	2	1	no	—
207	Q₈×C₈₉	—	2	1	no	—
208	Q₈×C₈₉	#131	1	2	yes	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
216	C₂×Dic₈₉	—	2	1	no	—
217	C₂×Dic₈₉	—	2	1	no	—
218	C₂×Dic₈₉	—	2	1	no	—
219	C₂×Dic₈₉	—	2	1	no	—
220	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
221	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
222	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
223	C₄×D₈₉	—	2	4	no	—
224	C₄×D₈₉	—	2	1	no	—
225	C₄×D₈₉	—	2	1	no	—
226	C₄×D₈₉	—	2	1	no	—
227	C₄×D₈₉	—	2	1	no	—
228	C₄×D₈₉	—	4	1	no	—
229	C₄×D₈₉	—	8	1	no	—
230	Dic₁₇₈	—	2	4	no	—
231	Dic₁₇₈	—	2	1	no	—
232	Dic₁₇₈	—	2	1	no	—
233	Dic₁₇₈	—	2	1	no	—
234	Dic₁₇₈	—	8	1	no	—
235	Dic₁₇₈	#131	1	2	yes	—
236	C₈×C₈₉	—	2	1	no	—
237	C₈×C₈₉	—	2	1	no	—
238	C₈×C₈₉	—	2	1	no	—
239	C₈×C₈₉	—	2	1	no	—
240	C₈×C₈₉	—	4	1	no	—
241	C₈×C₈₉	—	4	1	no	—
242	C₈×C₈₉	—	4	1	no	—
243	#10623494	—	2	2	no	—
244	#10623494	—	2	1	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	2	1	no	—
247	#10623494	—	2	1	no	—
248	#10623494	—	4	1	no	—
249	#10623494	—	4	1	no	—
250	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂×D₈₉	—	2	1	no	—
252	C₂×D₈₉	—	2	1	no	—
253	C₂×D₈₉	—	2	1	no	—
254	C₄×C₈₉	—	2	2	no	—
255	C₄×C₈₉	—	2	1	no	—
256	C₄×C₈₉	—	4	1	no	—
257	C₄×C₈₉	—	4	1	no	—
258	C₄×C₈₉	—	4	1	no	—
259	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
260	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
261	C₄×C₈₉	#578	1	1	yes	characteristic
262	C₄×C₈₉	#578	1	1	yes	characteristic
263	Dic₈₉	—	2	1	no	—
264	Dic₈₉	—	2	2	no	—
265	Dic₈₉	—	2	1	no	—
266	Dic₈₉	—	2	1	no	—
267	Dic₈₉	—	4	1	no	—
268	Dic₈₉	—	4	1	no	—
269	Dic₈₉	—	4	1	no	—
270	#17925	—	89	1	no	maximal, Sylow
271	C₂×C₈₉	#2929	1	1	yes	characteristic
272	C₂×C₈₉	#2950	1	1	yes	characteristic
273	C₂×C₈₉	#2956	1	1	yes	characteristic
274	D₈₉	—	4	1	no	—
275	#3104	—	89	1	no	—
276	#2985	—	89	1	no	—
277	#2982	—	89	1	no	—
278	#1587	—	89	1	no	—
279	#1587	—	89	1	no	—
280	#1584	—	89	1	no	—
281	#1584	D₈₉	1	1	yes	characteristic, complemented
282	#1579	—	89	1	no	—
283	#1579	—	89	1	no	—
284	C₈×Q₁₆	—	89	1	no	—
285	C₈×Q₁₆	—	89	1	no	—
286	#1572	—	89	1	no	—
287	#1491	—	89	1	no	—
288	#1485	—	89	1	no	—
289	#1453	—	89	1	no	—
290	C₈₉	#17925	1	1	yes	characteristic, complemented, Sylow
291	#533	—	89	1	no	—
292	C₂×C₄×Q₈	—	89	1	no	—
293	#484	—	89	1	no	—
294	#484	—	89	1	no	—
295	#477	—	89	1	no	—
296	#477	—	89	1	no	—
297	#462	—	89	1	no	—
298	#462	—	89	1	no	—
299	#451	—	89	1	no	—
300	#451	—	89	1	no	—
301	#446	—	89	1	no	—
302	#446	—	178	1	no	—
303	#446	—	178	1	no	—
304	#446	C₂×D₈₉	1	1	yes	characteristic
305	C₈×Q₈	—	89	1	no	—
306	C₈×Q₈	—	89	1	no	—
307	C₈×Q₈	—	89	1	no	—
308	C₈×Q₈	—	89	1	no	—
309	C₈×Q₈	—	89	1	no	—
310	C₈×Q₈	—	178	1	no	—
311	C₈×Q₈	—	178	1	no	—
312	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
313	C₄×Q₁₆	—	89	1	no	—
314	C₄×Q₁₆	—	89	1	no	—
315	C₄×Q₁₆	—	89	1	no	—
316	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
317	#433	—	178	1	no	—
318	#433	—	178	1	no	—
319	#432	—	89	1	no	—
320	#431	—	89	1	no	—
321	#431	—	89	1	no	—
322	#431	—	89	1	no	—
323	#431	—	178	1	no	—
324	#431	—	178	1	no	—
325	C₄×M₁₆	—	89	1	no	—
326	#335	—	89	1	no	—
327	#335	C₂×D₈₉	1	1	yes	characteristic
328	#334	—	89	1	no	—
329	#334	—	89	1	no	—
330	Q₈⋊C₈	—	89	1	no	—
331	Q₈⋊C₈	—	89	1	no	—
332	Q₈⋊C₈	—	89	1	no	—
333	Q₈⋊C₈	—	89	1	no	—
334	Q₈⋊C₈	—	89	1	no	—
335	Q₈⋊C₈	—	89	1	no	—
336	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
337	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
338	#322	—	89	1	no	—
339	#322	—	89	1	no	—
340	#322	C₂×D₈₉	1	1	yes	characteristic
341	C₈²	—	89	1	no	—
342	C₂²×Q₈	—	89	1	no	—
343	C₂×Q₁₆	—	89	1	no	—
344	C₂×Q₁₆	—	89	1	no	—
345	C₂×Q₁₆	—	89	1	no	—
346	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
347	C₂×M₁₆	—	178	1	no	—
348	C₄⋊Q₈	—	89	1	no	—
349	C₄⋊Q₈	—	89	1	no	—
350	#125	—	178	1	no	—
351	C₂²⋊Q₈	—	89	1	no	—
352	C₂²⋊Q₈	—	89	1	no	—
353	C₂²⋊Q₈	—	178	1	no	—
354	C₄×Q₈	—	89	1	no	—
355	C₄×Q₈	—	89	1	no	—
356	C₄×Q₈	—	89	1	no	—
357	C₄×Q₈	—	89	1	no	—
358	C₄×Q₈	—	178	1	no	—
359	C₄×Q₈	—	178	1	no	—
360	C₄×Q₈	—	178	1	no	—
361	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
362	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
363	#117	—	178	1	no	—
364	C₂×C₄⋊C₄	—	89	1	no	—
365	C₂×C₄⋊C₄	—	178	1	no	—
366	C₂×C₄²	—	89	1	no	—
367	C₂×C₄²	—	178	1	no	—
368	#107	—	89	1	no	—
369	#107	—	89	1	no	—
370	#107	—	89	1	no	—
371	#107	C₄×D₈₉	1	1	yes	characteristic
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	89	1	no	—
375	C₄⋊C₈	—	89	1	no	—
376	C₄⋊C₈	—	89	1	no	—
377	C₄⋊C₈	—	89	1	no	—
378	C₄⋊C₈	—	89	1	no	—
379	C₄⋊C₈	—	89	1	no	—
380	C₄⋊C₈	—	178	1	no	—
381	C₄⋊C₈	—	178	1	no	—
382	C₄⋊C₈	—	178	1	no	—
383	C₄⋊C₈	—	178	1	no	—
384	C₄⋊C₈	—	178	1	no	—
385	C₄⋊C₈	—	178	1	no	—
386	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
387	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
388	#103	—	89	1	no	—
389	#103	—	89	1	no	—
390	#103	—	89	1	no	—
391	#103	—	89	1	no	—
392	#103	—	89	1	no	—
393	#103	—	89	1	no	—
394	#103	C₄×D₈₉	1	1	yes	characteristic
395	#103	C₄×D₈₉	1	1	yes	characteristic
396	C₂²⋊C₈	—	89	1	no	—
397	C₂²⋊C₈	—	89	1	no	—
398	C₂²⋊C₈	—	89	1	no	—
399	C₂²⋊C₈	—	89	1	no	—
400	C₂²⋊C₈	—	178	1	no	—
401	C₂²⋊C₈	—	178	1	no	—
402	#97	—	2	1	no	—
403	#97	—	178	1	no	—
404	#97	—	178	1	no	—
405	#97	—	178	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	89	1	no	—
408	C₄×C₈	—	89	1	no	—
409	C₄×C₈	—	89	1	no	—
410	C₄×C₈	—	178	1	no	—
411	C₄×C₈	—	178	1	no	—
412	C₄×C₈	—	178	1	no	—
413	C₄×C₈	—	178	1	no	—
414	C₄×C₈	—	178	1	no	—
415	C₄×C₈	—	178	1	no	—
416	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
417	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
418	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
419	C₂×Q₈	—	89	1	no	—
420	C₂×Q₈	—	89	1	no	—
421	C₂×Q₈	—	178	1	no	—
422	C₂×Q₈	—	178	1	no	—
423	C₂×Q₈	—	178	2	no	—
424	C₂×Q₈	—	178	2	no	—
425	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
426	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₂²×C₄	—	89	1	no	—
428	C₂²×C₄	—	89	1	no	—
429	C₂²×C₄	—	89	1	no	—
430	C₂²×C₄	—	178	1	no	—
431	C₂²×C₄	—	178	1	no	—
432	Q₁₆	—	2	2	no	—
433	Q₁₆	—	178	2	no	—
434	Q₁₆	—	178	2	no	—
435	Q₁₆	—	178	2	no	—
436	M₁₆	—	356	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	89	1	no	—
441	C₂×C₈	—	89	1	no	—
442	C₂×C₈	—	89	1	no	—
443	C₂×C₈	—	89	1	no	—
444	C₂×C₈	—	178	1	no	—
445	C₂×C₈	—	178	1	no	—
446	C₂×C₈	—	178	1	no	—
447	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
448	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
449	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
450	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	89	1	no	—
454	C₄⋊C₄	—	89	1	no	—
455	C₄⋊C₄	—	178	1	no	—
456	C₄⋊C₄	—	178	1	no	—
457	C₄⋊C₄	—	178	1	no	—
458	C₄⋊C₄	—	178	1	no	—
459	C₄⋊C₄	—	178	1	no	—
460	C₄⋊C₄	—	178	1	no	—
461	C₄⋊C₄	—	178	1	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
466	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
467	C₂²⋊C₄	—	178	1	no	—
468	C₂²⋊C₄	—	178	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	89	1	no	—
472	C₄²	—	89	1	no	—
473	C₄²	—	89	1	no	—
474	C₄²	—	178	1	no	—
475	C₄²	—	178	1	no	—
476	C₄²	—	178	1	no	—
477	C₄²	—	178	1	no	—
478	C₄²	C₂³×D₈₉	1	1	yes	characteristic
479	C₂³	—	89	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	89	2	no	—
484	Q₈	—	178	4	no	—
485	Q₈	—	178	1	no	—
486	Q₈	—	178	1	no	—
487	Q₈	—	178	1	no	—
488	Q₈	—	712	1	no	—
489	Q₈	#15668020	1	2	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	89	1	no	—
495	C₂×C₄	—	89	1	no	—
496	C₂×C₄	—	89	1	no	—
497	C₂×C₄	—	356	1	no	—
498	C₂×C₄	—	178	4	no	—
499	C₂×C₄	—	178	1	no	—
500	C₂×C₄	—	178	1	no	—
501	C₂×C₄	—	178	1	no	—
502	C₂×C₄	—	178	1	no	—
503	C₂×C₄	—	178	1	no	—
504	C₂×C₄	—	178	1	no	—
505	C₂×C₄	—	178	1	no	—
506	C₂×C₄	—	178	1	no	—
507	C₂×C₄	—	712	1	no	—
508	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
509	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
510	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	356	1	no	—
519	C₈	—	356	1	no	—
520	C₈	—	178	2	no	—
521	C₈	—	178	1	no	—
522	C₈	—	178	1	no	—
523	C₈	—	178	1	no	—
524	C₈	—	178	1	no	—
525	C₂²	—	178	1	no	—
526	C₂²	—	178	1	no	—
527	C₂²	—	178	1	no	—
528	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
529	C₄	—	2	1	no	—
530	C₄	—	2	2	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	356	1	no	—
535	C₄	—	356	1	no	—
536	C₄	—	356	1	no	—
537	C₄	—	178	1	no	—
538	C₄	—	178	1	no	—
539	C₄	—	178	1	no	—
540	C₄	—	178	2	no	—
541	C₄	#131×D₈₉	1	1	yes	characteristic
542	C₄	C₂×#15668020	1	1	yes	characteristic
543	C₄	#19152411	1	1	yes	characteristic
544	C₄	#19152412	1	1	yes	characteristic
545	C₂	—	356	1	no	—
546	C₂	#26028943	1	1	yes	characteristic
547	C₂	#26029115	1	1	yes	characteristic
548	C₂	#26029160	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1584	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1584	D₈₉
hypocenter	C₈₉	#17925
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #26019123	C₂	semidirect
5. #26019121	C₂	semidirect
6. #26019104	C₂	semidirect
7. #26019068	C₂	semidirect
8. #26019068	C₂	semidirect
9. Q₁₆×#10623494	C₂	semidirect
10. #26019058	C₂	semidirect
15. C₈₉×#1584	C₂	semidirect
281. #1584	D₈₉	semidirect
290. C₈₉	#17925	semidirect

Maximal subgroups

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

subgroup	index
#26030289	2
#26029348	2
#26029331	2
#26019123	2
#26019121	2
#26019104	2
#26019068	2
Q₁₆×#10623494	2
#26019058	2
#26019031	2
#26018697	2
#26018671	2
#26018548	2
C₈₉×#1584	2
#17925	89