Subgroups — #36526297

Order 22784.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030852	C₂	1	1	yes	maximal, characteristic
2	#26029256	C₂	1	1	yes	maximal, characteristic
3	#26019152	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019130	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019121	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019102	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019086	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019069	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018673	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018663	C₂	1	1	yes	maximal, characteristic
14	#26018555	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152132	C₂²	1	1	yes	characteristic
17	#19152004	C₄	1	1	yes	characteristic
18	#19151990	C₄	1	1	yes	characteristic
19	#19151966	C₄	1	1	yes	characteristic
20	#19151960	C₄	1	1	yes	characteristic
21	#19151854	C₄	1	1	yes	characteristic
22	#19151854	C₄	1	1	yes	characteristic
23	#19151846	C₄	1	1	yes	characteristic
24	#19151846	C₄	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	C₄×#13083564	C₂²	1	1	yes	characteristic
28	C₄×#13083564	C₂²	1	1	yes	characteristic
29	C₄×#13083561	C₂²	1	1	yes	characteristic
30	C₄×#13083561	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	1	yes	characteristic
32	#19151674	—	2	1	no	—
33	#19151667	—	2	1	no	—
34	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
35	#19151660	—	2	1	no	—
36	#19151651	C₂²	1	1	yes	characteristic
37	#19151555	—	2	1	no	—
38	C₄×#13083558	C₂²	1	1	yes	characteristic
39	C₄×#13083558	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	1	yes	characteristic
41	#19151350	C₂²	1	1	yes	characteristic
42	#19151348	C₂²	1	1	yes	characteristic
43	#19151348	C₂²	1	1	yes	characteristic
44	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
45	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
46	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
47	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
48	#19151328	C₂²	1	1	yes	characteristic
49	#19151328	C₂²	1	1	yes	characteristic
50	#19151325	C₂²	1	1	yes	characteristic
51	#19151325	C₂²	1	1	yes	characteristic
52	#19151320	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	#19151319	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	#533×C₈₉	C₂²	1	1	yes	characteristic
57	#446×C₈₉	—	2	1	no	—
58	#446×C₈₉	—	2	1	no	—
59	#446×C₈₉	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
63	#424×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	#405×C₈₉	—	2	1	no	—
66	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083558	—	2	1	no	—
72	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083557	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	#15668006	—	2	1	no	—
77	#15668004	C₂×C₄	1	1	yes	characteristic
78	#15668000	C₂×C₄	1	1	yes	characteristic
79	#15667995	—	2	1	no	—
80	#15667991	C₂×C₄	1	1	yes	characteristic
81	#15667986	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
83	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
84	C₄×C₂²⋊D₈₉	—	2	1	no	—
85	#15667969	—	2	1	no	—
86	#15667945	C₂×C₄	1	1	yes	characteristic
87	#15667945	C₂×C₄	1	1	yes	characteristic
88	#15667943	C₂×C₄	1	1	yes	characteristic
89	#15667943	C₂×C₄	1	1	yes	characteristic
90	C₄⋊#10623494	C₂³	1	1	yes	characteristic
91	C₄⋊#10623494	C₂³	1	1	yes	characteristic
92	#15667941	—	2	1	no	—
93	#15667941	—	2	1	no	—
94	#15667936	C₂×C₄	1	1	yes	characteristic
95	#15667936	C₂×C₄	1	1	yes	characteristic
96	#15667936	C₂×C₄	1	1	yes	characteristic
97	#15667936	C₂×C₄	1	1	yes	characteristic
98	#15667935	C₂×C₄	1	1	yes	characteristic
99	#15667935	C₂×C₄	1	1	yes	characteristic
100	#15667932	C₂×C₄	1	1	yes	characteristic
101	#15667932	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊#10623494	—	2	1	no	—
103	#15667924	—	2	1	no	—
104	#15667924	—	2	1	no	—
105	#15667923	—	2	1	no	—
106	#15667923	C₂×C₄	1	1	yes	characteristic
107	#15667923	C₂×C₄	1	1	yes	characteristic
108	#15667922	—	2	1	no	—
109	C₄×#10623494	—	2	1	no	—
110	C₄×#10623494	C₂³	1	1	yes	characteristic
111	C₄×#10623494	C₂³	1	1	yes	characteristic
112	C₄×#10623494	C₂³	1	1	yes	characteristic
113	C₄×#10623494	C₂³	1	1	yes	characteristic
114	C₈×Dic₈₉	—	2	1	no	—
115	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
116	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
117	C₂²×C₈×C₈₉	—	2	1	no	—
118	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
120	#125×C₈₉	—	2	1	no	—
121	C₂²⋊Q₈×C₈₉	—	2	1	no	—
122	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₄×Q₈×C₈₉	—	2	1	no	—
125	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	#117×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₈₉	—	2	1	no	—
130	C₄⋊C₈×C₈₉	—	2	1	no	—
131	C₄⋊C₈×C₈₉	—	2	1	no	—
132	C₄⋊C₈×C₈₉	—	2	1	no	—
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	#97×C₈₉	—	2	1	no	—
137	#97×C₈₉	—	2	1	no	—
138	#97×C₈₉	D₄	1	1	yes	characteristic
139	#97×C₈₉	D₄	1	1	yes	characteristic
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₈₉	—	2	1	no	—
147	C₂×C₄×D₈₉	—	2	1	no	—
148	#13083564	—	2	2	no	—
149	#13083564	—	4	1	no	—
150	#13083561	—	2	2	no	—
151	#13083561	—	4	1	no	—
152	#13083558	—	2	2	no	—
153	#13083558	—	4	1	no	—
154	#13083558	—	4	2	no	—
155	#13083557	—	4	2	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₈₉	—	4	2	no	—
165	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
167	#13083553	—	2	1	no	—
168	#13083553	—	2	1	no	—
169	#13083553	—	2	1	no	—
170	#13083553	—	2	1	no	—
171	C₂²⋊Dic₈₉	—	2	1	no	—
172	#13083551	—	2	1	no	—
173	#13083551	—	2	1	no	—
174	#13083551	—	2	1	no	—
175	#13083551	—	2	1	no	—
176	C₄×Dic₈₉	—	2	1	no	—
177	C₂×Q₈×C₈₉	—	2	1	no	—
178	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
183	M₁₆×C₈₉	—	2	2	no	—
184	M₁₆×C₈₉	—	4	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	—	4	2	no	—
188	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₂²⋊C₄×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₈₉	#41	1	1	yes	characteristic
208	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
210	C₂²×D₈₉	—	2	1	no	—
211	Q₈×C₈₉	—	2	1	no	—
212	Q₈×C₈₉	—	2	1	no	—
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	—	8	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
231	C₂²⋊D₈₉	—	8	1	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	D₃₅₆	—	2	1	no	—
236	D₃₅₆	—	2	1	no	—
237	C₄×D₈₉	—	4	1	no	—
238	C₄×D₈₉	—	4	1	no	—
239	Dic₁₇₈	—	2	1	no	—
240	Dic₁₇₈	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	—	4	1	no	—
245	C₈×C₈₉	—	4	1	no	—
246	C₈×C₈₉	#137	1	2	yes	—
247	#10623494	—	2	2	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	2	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	#131	1	2	yes	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	1	no	—
257	C₂²×C₈₉	—	2	1	no	—
258	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₈₉	—	4	1	no	—
260	C₂×D₈₉	—	4	1	no	—
261	C₂×D₈₉	—	4	1	no	—
262	C₄×C₈₉	—	2	1	no	—
263	C₄×C₈₉	—	2	1	no	—
264	C₄×C₈₉	—	2	1	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	4	1	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
271	C₄×C₈₉	#568	1	1	yes	characteristic
272	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
273	C₄×C₈₉	#575	1	1	yes	characteristic
274	Dic₈₉	—	4	1	no	—
275	Dic₈₉	—	4	1	no	—
276	Dic₈₉	—	4	1	no	—
277	#18077	—	89	1	no	maximal, Sylow
278	C₂×C₈₉	—	4	1	no	—
279	C₂×C₈₉	#2935	1	1	yes	characteristic
280	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
281	C₂×C₈₉	#2956	1	1	yes	characteristic
282	D₈₉	—	8	1	no	—
283	#3172	—	89	1	no	—
284	#2969	—	89	1	no	—
285	#2962	D₈₉	1	1	yes	characteristic, complemented
286	#1592	—	89	1	no	—
287	#1591	—	89	1	no	—
288	#1588	—	89	1	no	—
289	#1587	—	89	1	no	—
290	#1584	—	89	1	no	—
291	#1582	—	89	1	no	—
292	#1579	—	89	1	no	—
293	C₈×SD₁₆	—	89	1	no	—
294	#1565	—	89	1	no	—
295	#1485	—	89	1	no	—
296	#1483	—	89	1	no	—
297	#1455	—	89	1	no	—
298	C₈₉	#18077	1	1	yes	characteristic, complemented, Sylow
299	#533	C₂×D₈₉	1	1	yes	characteristic
300	#529	—	89	1	no	—
301	#501	—	89	1	no	—
302	#497	—	89	1	no	—
303	#491	—	89	1	no	—
304	#489	—	89	1	no	—
305	#470	—	89	1	no	—
306	#470	—	89	1	no	—
307	#468	—	89	1	no	—
308	#468	—	89	1	no	—
309	#446	—	2	1	no	—
310	#446	—	2	1	no	—
311	#446	—	89	1	no	—
312	#446	C₂×D₈₉	1	1	yes	characteristic
313	#446	C₂×D₈₉	1	1	yes	characteristic
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
316	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×SD₁₆	—	89	1	no	—
320	C₄×SD₁₆	—	89	1	no	—
321	#436	—	89	1	no	—
322	#436	—	178	1	no	—
323	#435	—	178	1	no	—
324	C₈×D₄	—	89	1	no	—
325	#433	—	178	1	no	—
326	#431	—	89	1	no	—
327	#424	—	2	1	no	—
328	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
329	#405	—	2	1	no	—
330	#405	—	178	1	no	—
331	C₄×M₁₆	—	89	1	no	—
332	C₄×M₁₆	—	89	1	no	—
333	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
334	#335	—	89	1	no	—
335	#335	—	89	1	no	—
336	#334	—	89	1	no	—
337	#334	—	89	1	no	—
338	Q₈⋊C₈	—	89	1	no	—
339	Q₈⋊C₈	—	89	1	no	—
340	Q₈⋊C₈	—	89	1	no	—
341	Q₈⋊C₈	—	89	1	no	—
342	Q₈⋊C₈	—	89	1	no	—
343	Q₈⋊C₈	—	89	1	no	—
344	D₄⋊C₈	—	89	1	no	—
345	D₄⋊C₈	—	89	1	no	—
346	#322	—	89	1	no	—
347	#322	—	89	1	no	—
348	#322	—	89	1	no	—
349	C₈²	—	89	1	no	—
350	C₂×Q₁₆	—	89	1	no	—
351	C₂×Q₁₆	—	89	1	no	—
352	C₂×SD₁₆	—	89	1	no	—
353	C₂×SD₁₆	—	89	1	no	—
354	C₂×M₁₆	—	89	1	no	—
355	C₂×M₁₆	—	89	1	no	—
356	C₂×M₁₆	—	178	1	no	—
357	C₂×M₁₆	—	178	1	no	—
358	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
359	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	178	1	no	—
362	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
363	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
364	#126	—	178	1	no	—
365	#125	—	2	1	no	—
366	#125	—	89	1	no	—
367	#124	—	89	1	no	—
368	#123	—	178	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	89	1	no	—
371	C₂²⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
372	C₂²⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
373	#121	—	89	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	89	1	no	—
376	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄×D₄	—	89	1	no	—
379	C₄×D₄	—	178	1	no	—
380	#117	—	2	1	no	—
381	#117	—	178	1	no	—
382	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
383	#107	—	89	1	no	—
384	#107	—	89	1	no	—
385	#106	—	89	1	no	—
386	#106	—	89	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	89	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	178	1	no	—
395	C₄⋊C₈	—	178	1	no	—
396	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
398	#103	—	89	1	no	—
399	#103	—	89	1	no	—
400	#103	—	89	1	no	—
401	#103	—	89	1	no	—
402	#103	—	89	1	no	—
403	#103	—	89	1	no	—
404	#102	—	89	1	no	—
405	#102	—	89	1	no	—
406	C₂²⋊C₈	—	178	1	no	—
407	C₂²⋊C₈	—	178	1	no	—
408	C₂²⋊C₈	—	178	1	no	—
409	#97	—	2	1	no	—
410	#97	—	2	1	no	—
411	#97	—	89	1	no	—
412	#97	—	89	1	no	—
413	#97	—	178	1	no	—
414	#97	—	178	1	no	—
415	#97	C₂²⋊D₈₉	1	1	yes	characteristic
416	#97	C₂²⋊D₈₉	1	1	yes	characteristic
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	89	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	178	1	no	—
424	C₄×C₈	—	178	1	no	—
425	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	89	1	no	—
429	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
430	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₂×D₄	—	89	1	no	—
432	C₂×D₄	—	178	1	no	—
433	C₂²×C₄	—	178	1	no	—
434	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
436	C₂²×C₄	#13083574	1	1	yes	characteristic
437	Q₁₆	—	356	1	no	—
438	Q₁₆	—	178	2	no	—
439	SD₁₆	—	356	1	no	—
440	SD₁₆	—	178	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	356	2	no	—
444	M₁₆	—	356	2	no	—
445	M₁₆	—	356	1	no	—
446	M₁₆	—	178	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	4	2	no	—
450	C₂×C₈	—	89	1	no	—
451	C₂×C₈	—	89	1	no	—
452	C₂×C₈	—	89	1	no	—
453	C₂×C₈	—	89	1	no	—
454	C₂×C₈	—	356	2	no	—
455	C₂×C₈	—	178	1	no	—
456	C₂×C₈	—	178	1	no	—
457	C₂×C₈	—	178	1	no	—
458	C₂×C₈	—	178	1	no	—
459	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
461	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
462	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	89	1	no	—
471	C₄⋊C₄	—	89	1	no	—
472	C₄⋊C₄	—	178	1	no	—
473	C₄⋊C₄	—	178	1	no	—
474	C₄⋊C₄	—	178	1	no	—
475	C₄⋊C₄	—	178	1	no	—
476	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	178	1	no	—
481	C₂²⋊C₄	—	178	1	no	—
482	C₂²⋊C₄	—	178	1	no	—
483	C₂²⋊C₄	—	178	1	no	—
484	C₂²⋊C₄	—	178	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	178	1	no	—
488	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
489	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
490	C₄²	#13083574	1	1	yes	characteristic
491	C₄²	C₂³×D₈₉	1	1	yes	characteristic
492	C₂³	—	178	1	no	—
493	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	8	1	no	—
499	Q₈	—	178	1	no	—
500	Q₈	—	178	1	no	—
501	D₄	—	178	1	no	—
502	D₄	—	178	1	no	—
503	D₄	—	712	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	356	1	no	—
514	C₂×C₄	—	356	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
519	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
523	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	89	2	no	—
530	C₈	—	356	1	no	—
531	C₈	—	356	1	no	—
532	C₈	—	356	1	no	—
533	C₈	—	178	2	no	—
534	C₈	—	178	1	no	—
535	C₈	—	178	1	no	—
536	C₈	—	178	1	no	—
537	C₈	#15668043	1	2	yes	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	356	1	no	—
542	C₂²	—	356	1	no	—
543	C₂²	—	356	1	no	—
544	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	356	1	no	—
554	C₄	—	356	1	no	—
555	C₄	—	356	1	no	—
556	C₄	#131×D₈₉	1	1	yes	characteristic
557	C₄	#19152363	1	1	yes	characteristic
558	C₄	C₂×#15668043	1	1	yes	characteristic
559	C₄	#19152396	1	1	yes	characteristic
560	C₂	—	4	1	no	—
561	C₂	—	712	1	no	—
562	C₂	#26028994	1	1	yes	characteristic
563	C₂	C₄×#15668043	1	1	yes	characteristic
564	C₂	#26029159	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×#2962	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2962	D₈₉
hypocenter	C₈₉	#18077
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #26019152	C₂	semidirect
4. #26019147	C₂	semidirect
5. #26019130	C₂	semidirect
6. #26019121	C₂	semidirect
7. #26019102	C₂	semidirect
8. #26019086	C₂	semidirect
9. #26019069	C₂	semidirect
10. C₈×#13083561	C₂	semidirect
11. #26019002	C₂	semidirect
12. #26018673	C₂	semidirect
14. #26018555	C₂	semidirect
15. C₈₉×#2962	C₂	semidirect
285. #2962	D₈₉	semidirect
298. C₈₉	#18077	semidirect

Maximal subgroups

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

subgroup	index
#26030852	2
#26029256	2
#26019152	2
#26019147	2
#26019130	2
#26019121	2
#26019102	2
#26019086	2
#26019069	2
C₈×#13083561	2
#26019002	2
#26018673	2
#26018663	2
#26018555	2
C₈₉×#2962	2
#18077	89