Subgroups — #36525569

Order 22784.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030323	C₂	1	1	yes	maximal, characteristic
2	#26029199	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019154	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019140	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019128	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019123	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019102	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019093	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019069	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019038	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018724	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018639	C₂	1	1	yes	maximal, characteristic
14	#26018549	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic
16	#19152155	C₂²	1	1	yes	characteristic
17	#19151939	C₄	1	1	yes	characteristic
18	#19151939	C₄	1	1	yes	characteristic
19	#19151883	C₄	1	1	yes	characteristic
20	#19151878	C₄	1	1	yes	characteristic
21	#19151808	C₄	1	1	yes	characteristic
22	#19151803	C₄	1	1	yes	characteristic
23	#19151760	C₄	1	1	yes	characteristic
24	#19151760	C₄	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151726	—	2	1	no	—
28	#19151726	—	2	1	no	—
29	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
31	C₄×#13083564	C₂²	1	1	yes	characteristic
32	C₄×#13083564	C₂²	1	1	yes	characteristic
33	C₄×#13083562	C₂²	1	1	yes	characteristic
34	C₄×#13083562	C₂²	1	1	yes	characteristic
35	#19151651	C₂²	1	1	yes	characteristic
36	#19151651	C₂²	1	1	yes	characteristic
37	#19151626	—	2	1	no	—
38	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
39	#19151556	—	2	1	no	—
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	#19151328	C₂²	1	1	yes	characteristic
47	#19151328	C₂²	1	1	yes	characteristic
48	#19151328	C₂²	1	1	yes	characteristic
49	#19151328	C₂²	1	1	yes	characteristic
50	D₄⋊#10623494	C₂²	1	1	yes	characteristic
51	D₄⋊#10623494	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	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
59	#436×C₈₉	—	2	1	no	—
60	#436×C₈₉	—	2	1	no	—
61	#436×C₈₉	C₂²	1	1	yes	characteristic
62	#436×C₈₉	C₂²	1	1	yes	characteristic
63	#432×C₈₉	—	2	1	no	—
64	#432×C₈₉	C₂²	1	1	yes	characteristic
65	C₄×M₁₆×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×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
71	C₂²×#10623494	—	2	1	no	—
72	#15668012	C₂×C₄	1	1	yes	characteristic
73	#15668012	C₂×C₄	1	1	yes	characteristic
74	#15668004	—	2	1	no	—
75	#15667991	—	2	1	no	—
76	#15667991	C₂×C₄	1	1	yes	characteristic
77	#15667991	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₇₈	—	2	1	no	—
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
81	#15667971	—	2	1	no	—
82	#15667945	C₂×C₄	1	1	yes	characteristic
83	#15667945	C₂×C₄	1	1	yes	characteristic
84	#15667943	C₂×C₄	1	1	yes	characteristic
85	#15667943	C₂×C₄	1	1	yes	characteristic
86	C₄⋊#10623494	—	2	1	no	—
87	C₄⋊#10623494	—	2	1	no	—
88	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
89	C₄⋊#10623494	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	#15667941	—	2	1	no	—
95	#15667941	—	2	1	no	—
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	#15667935	C₂×C₄	1	1	yes	characteristic
101	#15667935	C₂×C₄	1	1	yes	characteristic
102	#15667933	C₂×C₄	1	1	yes	characteristic
103	#15667933	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊#10623494	—	2	1	no	—
105	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
107	#15667922	—	2	1	no	—
108	#15667922	—	2	1	no	—
109	C₄×#10623494	C₂³	1	1	yes	characteristic
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	C₈×Dic₈₉	—	2	1	no	—
114	C₈×Dic₈₉	—	2	1	no	—
115	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₂×M₁₆×C₈₉	—	2	1	no	—
117	C₂×M₁₆×C₈₉	—	2	1	no	—
118	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
119	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₈₉	—	2	1	no	—
123	C₄×D₄×C₈₉	—	2	1	no	—
124	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	#117×C₈₉	—	2	1	no	—
127	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₈₉	—	2	1	no	—
131	C₄⋊C₈×C₈₉	—	2	1	no	—
132	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²⋊C₈×C₈₉	—	2	1	no	—
135	C₂²⋊C₈×C₈₉	—	2	1	no	—
136	C₂²⋊C₈×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	—	2	1	no	—
145	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	#13083564	—	2	2	no	—
148	#13083564	—	2	2	no	—
149	#13083562	—	4	1	no	—
150	#13083562	—	4	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	4	2	no	—
156	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
157	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
158	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
159	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₈₉	—	2	1	no	—
161	C₄⋊Dic₈₉	—	2	1	no	—
162	C₄⋊Dic₈₉	—	2	1	no	—
163	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
165	#13083553	—	2	1	no	—
166	#13083553	—	2	1	no	—
167	#13083553	—	2	1	no	—
168	#13083553	—	2	1	no	—
169	C₂²⋊Dic₈₉	—	2	1	no	—
170	C₂²⋊Dic₈₉	—	2	1	no	—
171	C₄×Dic₈₉	—	2	1	no	—
172	C₄×Dic₈₉	—	2	1	no	—
173	#41×C₈₉	—	2	2	no	—
174	#41×C₈₉	—	4	1	no	—
175	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	1	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
184	M₁₆×C₈₉	—	2	2	no	—
185	M₁₆×C₈₉	—	4	1	no	—
186	M₁₆×C₈₉	—	4	2	no	—
187	M₁₆×C₈₉	—	4	2	no	—
188	C₂×C₈×C₈₉	—	2	1	no	—
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₈₉	—	2	1	no	—
199	C₂²⋊C₄×C₈₉	—	2	1	no	—
200	C₂²⋊C₄×C₈₉	—	2	1	no	—
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₈₉	#41	1	1	yes	characteristic
207	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₂³×C₈₉	—	2	1	no	—
209	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₈₉	—	2	1	no	—
211	Q₈×C₈₉	#131	1	2	yes	—
212	D₄×C₈₉	—	2	1	no	—
213	D₄×C₈₉	—	2	1	no	—
214	D₄×C₈₉	—	4	2	no	—
215	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	2	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	8	1	no	—
227	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	Dic₁₇₈	—	2	1	no	—
238	Dic₁₇₈	—	2	1	no	—
239	Dic₁₇₈	—	2	1	no	—
240	Dic₁₇₈	—	2	1	no	—
241	Dic₁₇₈	—	8	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	—	2	1	no	—
245	C₈×C₈₉	—	4	1	no	—
246	C₈×C₈₉	—	4	1	no	—
247	C₈×C₈₉	#137	1	2	yes	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	2	1	no	—
251	#10623494	—	2	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	#10623494	—	4	1	no	—
256	C₂²×C₈₉	—	2	1	no	—
257	C₂²×C₈₉	—	2	1	no	—
258	C₂²×C₈₉	—	2	1	no	—
259	C₂²×C₈₉	—	4	1	no	—
260	C₂²×C₈₉	—	4	1	no	—
261	C₂²×C₈₉	—	4	1	no	—
262	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₈₉	—	2	1	no	—
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	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	Dic₈₉	—	4	1	no	—
278	#18013	—	89	1	no	maximal, Sylow
279	C₂×C₈₉	—	4	1	no	—
280	C₂×C₈₉	—	8	1	no	—
281	C₂×C₈₉	#2933	1	1	yes	characteristic
282	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
283	C₂×C₈₉	#2957	1	1	yes	characteristic
284	#3107	—	89	1	no	—
285	#2971	D₈₉	1	1	yes	characteristic
286	#2962	—	89	1	no	—
287	#1592	—	89	1	no	—
288	#1590	—	89	1	no	—
289	#1588	—	89	1	no	—
290	#1587	—	89	1	no	—
291	#1584	—	89	1	no	—
292	#1583	—	89	1	no	—
293	#1579	—	89	1	no	—
294	C₈×Q₁₆	—	89	1	no	—
295	#1573	—	89	1	no	—
296	#1497	—	89	1	no	—
297	#1477	—	89	1	no	—
298	#1453	—	89	1	no	—
299	C₈₉	#18013	1	1	yes	characteristic, complemented, Sylow
300	#533	—	89	1	no	—
301	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
302	#485	—	89	1	no	—
303	#485	—	89	1	no	—
304	#475	—	89	1	no	—
305	#474	—	89	1	no	—
306	#462	—	89	1	no	—
307	#461	—	89	1	no	—
308	#452	—	89	1	no	—
309	#452	—	89	1	no	—
310	#446	—	89	1	no	—
311	#446	—	89	1	no	—
312	#446	—	178	1	no	—
313	#446	—	178	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
317	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×Q₁₆	—	89	1	no	—
320	C₄×SD₁₆	—	89	1	no	—
321	C₄×SD₁₆	—	89	1	no	—
322	#436	—	2	1	no	—
323	#436	—	2	1	no	—
324	#436	C₂×D₈₉	1	1	yes	characteristic
325	#436	C₂×D₈₉	1	1	yes	characteristic
326	#432	—	2	1	no	—
327	#432	C₂×D₈₉	1	1	yes	characteristic
328	#431	—	89	1	no	—
329	#431	—	89	1	no	—
330	#424	—	178	1	no	—
331	C₂×C₄⋊C₈	—	89	1	no	—
332	#405	—	178	1	no	—
333	C₄×M₁₆	—	2	1	no	—
334	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
335	#335	—	89	1	no	—
336	#335	—	89	1	no	—
337	#334	—	89	1	no	—
338	#334	—	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	Q₈⋊C₈	—	89	1	no	—
345	D₄⋊C₈	—	89	1	no	—
346	D₄⋊C₈	—	89	1	no	—
347	#322	—	89	1	no	—
348	#322	—	89	1	no	—
349	#322	—	89	1	no	—
350	C₈²	—	89	1	no	—
351	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
352	C₂×Q₁₆	—	89	1	no	—
353	C₂×Q₁₆	—	89	1	no	—
354	C₂×SD₁₆	—	89	1	no	—
355	C₂×SD₁₆	—	89	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
359	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
360	C₂²×C₈	—	178	1	no	—
361	C₄⋊Q₈	—	89	1	no	—
362	C₄⋊Q₈	—	89	1	no	—
363	#125	—	178	1	no	—
364	C₂²⋊Q₈	—	89	1	no	—
365	C₂²⋊Q₈	—	89	1	no	—
366	C₂²⋊Q₈	—	178	1	no	—
367	C₄×Q₈	—	89	1	no	—
368	C₄×Q₈	—	89	1	no	—
369	C₄×Q₈	—	178	1	no	—
370	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
371	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
375	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
376	#117	—	2	1	no	—
377	#117	—	178	1	no	—
378	#117	C₄×D₈₉	1	1	yes	characteristic
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
381	#107	—	89	1	no	—
382	#107	—	89	1	no	—
383	#106	—	89	1	no	—
384	#106	—	89	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	89	1	no	—
388	C₄⋊C₈	—	89	1	no	—
389	C₄⋊C₈	—	89	1	no	—
390	C₄⋊C₈	—	89	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	—	178	1	no	—
393	C₄⋊C₈	—	178	1	no	—
394	C₄⋊C₈	—	178	1	no	—
395	C₄⋊C₈	—	178	1	no	—
396	C₄⋊C₈	—	178	1	no	—
397	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
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	#103	—	89	1	no	—
405	#102	—	89	1	no	—
406	#102	—	89	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	89	1	no	—
411	C₂²⋊C₈	—	89	1	no	—
412	C₂²⋊C₈	—	178	1	no	—
413	#97	—	2	1	no	—
414	#97	—	178	1	no	—
415	#97	—	178	1	no	—
416	#97	C₂²⋊D₈₉	1	1	yes	characteristic
417	#97	C₂²⋊D₈₉	1	1	yes	characteristic
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	178	1	no	—
425	C₄×C₈	—	178	1	no	—
426	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
428	#41	—	2	2	no	—
429	#41	—	4	1	no	—
430	C₂×Q₈	—	89	1	no	—
431	C₂×Q₈	—	89	1	no	—
432	C₂×Q₈	—	178	1	no	—
433	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
441	C₂²×C₄	#13083574	1	1	yes	characteristic
442	Q₁₆	—	178	2	no	—
443	Q₁₆	—	178	2	no	—
444	SD₁₆	—	356	1	no	—
445	SD₁₆	—	356	1	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	4	2	no	—
449	M₁₆	—	4	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	89	1	no	—
453	C₂×C₈	—	89	1	no	—
454	C₂×C₈	—	89	1	no	—
455	C₂×C₈	—	89	1	no	—
456	C₂×C₈	—	356	2	no	—
457	C₂×C₈	—	178	1	no	—
458	C₂×C₈	—	178	1	no	—
459	C₂×C₈	—	178	1	no	—
460	C₂×C₈	—	178	1	no	—
461	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
462	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
463	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
464	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	89	1	no	—
468	C₄⋊C₄	—	89	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	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	—	2	1	no	—
481	C₂²⋊C₄	—	178	1	no	—
482	C₂²⋊C₄	—	178	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	178	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	—	2	1	no	—
493	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	178	1	no	—
496	Q₈	—	178	1	no	—
497	Q₈	—	178	1	no	—
498	Q₈	—	178	1	no	—
499	Q₈	—	712	1	no	—
500	Q₈	#15668020	1	2	yes	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	4	2	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	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	—	178	1	no	—
519	C₂×C₄	—	178	1	no	—
520	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
522	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	356	1	no	—
532	C₈	—	356	1	no	—
533	C₈	—	356	1	no	—
534	C₈	—	356	1	no	—
535	C₈	—	178	1	no	—
536	C₈	—	178	1	no	—
537	C₈	—	178	1	no	—
538	C₈	—	178	1	no	—
539	C₈	#15668042	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	356	1	no	—
555	C₄	—	356	1	no	—
556	C₄	—	356	1	no	—
557	C₄	—	356	1	no	—
558	C₄	C₂×#15668020	1	1	yes	characteristic
559	C₄	#19152364	1	1	yes	characteristic
560	C₄	C₂×#15668042	1	1	yes	characteristic
561	C₄	#19152396	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	8	1	no	—
564	C₂	#26028977	1	1	yes	characteristic
565	C₂	C₄×#15668042	1	1	yes	characteristic
566	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×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2971	D₈₉
hypocenter	C₈₉	#18013
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
2. #26029199	C₂	semidirect
3. #26019154	C₂	semidirect
4. #26019140	C₂	semidirect
5. #26019128	C₂	semidirect
6. #26019123	C₂	semidirect
7. #26019102	C₂	semidirect
8. #26019093	C₂	semidirect
9. #26019069	C₂	semidirect
10. C₈×#13083564	C₂	semidirect
11. #26019038	C₂	semidirect
12. #26018724	C₂	semidirect
14. #26018549	C₂	semidirect
299. C₈₉	#18013	semidirect

Maximal subgroups

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

subgroup	index
#26030323	2
#26029199	2
#26019154	2
#26019140	2
#26019128	2
#26019123	2
#26019102	2
#26019093	2
#26019069	2
C₈×#13083564	2
#26019038	2
#26018724	2
#26018639	2
#26018549	2
C₈₉×#2971	2
#18013	89