Subgroups — #36525822

Order 22784.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030291	C₂	1	1	yes	maximal, characteristic
2	#26029353	C₂	1	1	yes	maximal, characteristic
3	#26019159	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019123	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	#26019100	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	#26019033	C₂	1	1	yes	maximal, characteristic
12	#26018724	C₂	1	1	yes	maximal, characteristic
13	#26018647	C₂	1	1	yes	maximal, characteristic
14	#26018552	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2984	C₂	1	1	yes	maximal, characteristic
16	#19152155	C₂²	1	1	yes	characteristic
17	#19151933	C₄	1	1	yes	characteristic
18	#19151933	C₄	1	1	yes	characteristic
19	#19151893	C₄	1	1	yes	characteristic
20	#19151893	C₄	1	1	yes	characteristic
21	#19151808	C₄	1	1	yes	characteristic
22	#19151808	C₄	1	1	yes	characteristic
23	#19151754	C₄	1	1	yes	characteristic
24	#19151754	C₄	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151725	—	2	1	no	—
28	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
29	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
30	#19151722	—	2	1	no	—
31	C₄×#13083564	C₂²	1	1	yes	characteristic
32	C₄×#13083564	C₂²	1	1	yes	characteristic
33	C₄×#13083564	C₂²	1	1	yes	characteristic
34	C₄×#13083564	C₂²	1	1	yes	characteristic
35	#19151656	—	2	1	no	—
36	#19151656	—	2	1	no	—
37	#19151651	C₂²	1	1	yes	characteristic
38	#19151651	C₂²	1	1	yes	characteristic
39	#19151651	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	#19151328	C₂²	1	1	yes	characteristic
51	#19151328	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	C₂×C₄×Q₈×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	#432×C₈₉	—	2	1	no	—
64	#432×C₈₉	C₂²	1	1	yes	characteristic
65	#431×C₈₉	—	2	1	no	—
66	#431×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×#13083564	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	#15668012	C₂×C₄	1	1	yes	characteristic
72	#15668012	C₂×C₄	1	1	yes	characteristic
73	#15668004	—	2	1	no	—
74	#15667991	—	2	1	no	—
75	#15667991	C₂×C₄	1	1	yes	characteristic
76	#15667991	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₇₈	—	2	1	no	—
78	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	#15667971	—	2	1	no	—
81	#15667945	C₂×C₄	1	1	yes	characteristic
82	#15667945	C₂×C₄	1	1	yes	characteristic
83	#15667945	C₂×C₄	1	1	yes	characteristic
84	#15667945	C₂×C₄	1	1	yes	characteristic
85	C₄⋊#10623494	—	2	1	no	—
86	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
87	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
88	C₄⋊#10623494	C₂³	1	1	yes	characteristic
89	C₄⋊#10623494	C₂³	1	1	yes	characteristic
90	#15667941	—	2	1	no	—
91	#15667941	—	2	1	no	—
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	#15667935	C₂×C₄	1	1	yes	characteristic
101	#15667935	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊#10623494	—	2	1	no	—
103	C₂²⋊#10623494	—	2	1	no	—
104	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
106	#15667922	—	2	1	no	—
107	#15667922	—	2	1	no	—
108	C₄×#10623494	—	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	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₈₉	—	2	1	no	—
117	C₄×Q₈×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	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	—	2	1	no	—
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₈₉	—	2	1	no	—
127	C₄⋊C₈×C₈₉	—	2	1	no	—
128	C₄⋊C₈×C₈₉	—	2	1	no	—
129	C₄⋊C₈×C₈₉	—	2	1	no	—
130	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
137	#97×C₈₉	—	2	1	no	—
138	#97×C₈₉	—	2	1	no	—
139	#97×C₈₉	—	2	1	no	—
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	#13083564	—	4	1	no	—
150	#13083564	—	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	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊Dic₈₉	—	2	1	no	—
160	C₄⋊Dic₈₉	—	2	1	no	—
161	C₄⋊Dic₈₉	—	2	1	no	—
162	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	#13083553	—	2	1	no	—
165	#13083553	—	2	1	no	—
166	#13083553	—	2	1	no	—
167	#13083553	—	2	1	no	—
168	C₂²⋊Dic₈₉	—	2	1	no	—
169	C₂²⋊Dic₈₉	—	2	1	no	—
170	C₄×Dic₈₉	—	2	1	no	—
171	C₄×Dic₈₉	—	2	1	no	—
172	C₂×Q₈×C₈₉	—	2	1	no	—
173	C₂×Q₈×C₈₉	—	2	2	no	—
174	C₂×Q₈×C₈₉	—	4	1	no	—
175	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄²×C₈₉	—	2	1	no	—
196	C₄²×C₈₉	—	2	1	no	—
197	C₄²×C₈₉	—	2	1	no	—
198	C₄²×C₈₉	—	2	1	no	—
199	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₈₉	#41	1	1	yes	characteristic
202	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
204	Q₈×C₈₉	—	2	1	no	—
205	Q₈×C₈₉	—	2	1	no	—
206	Q₈×C₈₉	—	2	1	no	—
207	Q₈×C₈₉	—	4	2	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	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	4	1	no	—
218	C₂×C₄×C₈₉	—	4	2	no	—
219	C₂×C₄×C₈₉	—	4	2	no	—
220	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	—	2	1	no	—
230	Dic₁₇₈	—	2	1	no	—
231	Dic₁₇₈	—	2	1	no	—
232	Dic₁₇₈	—	2	1	no	—
233	Dic₁₇₈	—	2	1	no	—
234	Dic₁₇₈	—	4	2	no	—
235	C₈×C₈₉	—	2	1	no	—
236	C₈×C₈₉	—	2	1	no	—
237	C₈×C₈₉	—	2	1	no	—
238	C₈×C₈₉	—	2	1	no	—
239	C₈×C₈₉	—	4	1	no	—
240	C₈×C₈₉	—	4	1	no	—
241	#10623494	—	2	1	no	—
242	#10623494	—	2	1	no	—
243	#10623494	—	2	1	no	—
244	#10623494	—	2	1	no	—
245	#10623494	—	4	1	no	—
246	#10623494	—	4	1	no	—
247	#10623494	—	4	1	no	—
248	#10623494	—	4	1	no	—
249	C₂²×C₈₉	—	2	1	no	—
250	C₂²×C₈₉	—	2	1	no	—
251	C₂²×C₈₉	—	2	1	no	—
252	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₈₉	—	2	1	no	—
254	C₄×C₈₉	—	2	2	no	—
255	C₄×C₈₉	—	2	1	no	—
256	C₄×C₈₉	—	2	1	no	—
257	C₄×C₈₉	—	2	1	no	—
258	C₄×C₈₉	—	4	1	no	—
259	C₄×C₈₉	—	4	1	no	—
260	C₄×C₈₉	—	4	1	no	—
261	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
262	C₄×C₈₉	#568	1	1	yes	characteristic
263	C₄×C₈₉	#578	1	1	yes	characteristic
264	C₄×C₈₉	#578	1	1	yes	characteristic
265	Dic₈₉	—	4	1	no	—
266	Dic₈₉	—	4	1	no	—
267	Dic₈₉	—	4	1	no	—
268	Dic₈₉	—	4	1	no	—
269	#18032	—	89	1	no	maximal, Sylow
270	C₂×C₈₉	—	4	1	no	—
271	C₂×C₈₉	#2933	1	1	yes	characteristic
272	C₂×C₈₉	#2950	1	1	yes	characteristic
273	C₂×C₈₉	#2955	1	1	yes	characteristic
274	#3104	—	89	1	no	—
275	#2986	—	89	1	no	—
276	#2984	D₈₉	1	1	yes	characteristic
277	#1593	—	89	1	no	—
278	#1591	—	89	1	no	—
279	#1587	—	89	1	no	—
280	#1587	—	89	1	no	—
281	#1584	—	89	1	no	—
282	#1584	—	89	1	no	—
283	#1579	—	89	1	no	—
284	C₈×Q₁₆	—	89	1	no	—
285	#1572	—	89	1	no	—
286	#1497	—	89	1	no	—
287	#1479	—	89	1	no	—
288	#1454	—	89	1	no	—
289	C₈₉	#18032	1	1	yes	characteristic, complemented, Sylow
290	#533	—	89	1	no	—
291	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
292	#484	—	89	1	no	—
293	#484	—	89	1	no	—
294	#477	—	89	1	no	—
295	#477	—	89	1	no	—
296	#462	—	89	1	no	—
297	#462	—	89	1	no	—
298	#451	—	89	1	no	—
299	#451	—	89	1	no	—
300	#446	—	2	1	no	—
301	#446	—	2	1	no	—
302	#446	—	89	1	no	—
303	#446	—	89	1	no	—
304	#446	—	178	1	no	—
305	#446	C₂×D₈₉	1	1	yes	characteristic
306	#446	C₂×D₈₉	1	1	yes	characteristic
307	C₈×Q₈	—	89	1	no	—
308	C₈×Q₈	—	89	1	no	—
309	C₈×Q₈	—	178	1	no	—
310	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
311	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
312	C₄×Q₁₆	—	89	1	no	—
313	C₄×Q₁₆	—	89	1	no	—
314	C₄×Q₁₆	—	89	1	no	—
315	C₄×Q₁₆	—	89	1	no	—
316	#433	—	178	1	no	—
317	#433	—	178	1	no	—
318	#432	—	2	1	no	—
319	#432	C₂×D₈₉	1	1	yes	characteristic
320	#431	—	2	1	no	—
321	#431	—	89	1	no	—
322	#431	—	89	1	no	—
323	#431	—	89	1	no	—
324	#431	C₂×D₈₉	1	1	yes	characteristic
325	#335	—	89	1	no	—
326	#335	—	89	1	no	—
327	#334	—	89	1	no	—
328	#334	—	89	1	no	—
329	Q₈⋊C₈	—	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	—	89	1	no	—
337	#322	—	89	1	no	—
338	#322	—	89	1	no	—
339	#322	—	89	1	no	—
340	C₈²	—	89	1	no	—
341	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
342	C₂×Q₁₆	—	89	1	no	—
343	C₂×Q₁₆	—	89	1	no	—
344	C₂×Q₁₆	—	89	1	no	—
345	C₂×Q₁₆	—	89	1	no	—
346	C₄⋊Q₈	—	89	1	no	—
347	C₄⋊Q₈	—	89	1	no	—
348	#125	—	178	1	no	—
349	C₂²⋊Q₈	—	89	1	no	—
350	C₂²⋊Q₈	—	89	1	no	—
351	C₂²⋊Q₈	—	178	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	89	1	no	—
355	C₄×Q₈	—	89	1	no	—
356	C₄×Q₈	—	178	1	no	—
357	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
358	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
359	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
360	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
361	#117	—	178	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
366	#107	—	89	1	no	—
367	#107	—	89	1	no	—
368	#107	—	89	1	no	—
369	#107	—	89	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
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	—	178	1	no	—
379	C₄⋊C₈	—	178	1	no	—
380	C₄⋊C₈	—	178	1	no	—
381	C₄⋊C₈	—	178	1	no	—
382	C₄⋊C₈	—	178	1	no	—
383	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
384	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
385	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
387	#103	—	89	1	no	—
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	—	89	1	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	89	1	no	—
397	C₂²⋊C₈	—	89	1	no	—
398	C₂²⋊C₈	—	178	1	no	—
399	C₂²⋊C₈	—	178	1	no	—
400	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
401	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
402	#97	—	2	1	no	—
403	#97	—	2	1	no	—
404	#97	—	2	1	no	—
405	#97	—	178	1	no	—
406	#97	—	178	1	no	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	89	1	no	—
410	C₄×C₈	—	89	1	no	—
411	C₄×C₈	—	89	1	no	—
412	C₄×C₈	—	89	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	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	89	1	no	—
422	C₂×Q₈	—	89	1	no	—
423	C₂×Q₈	—	178	1	no	—
424	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
425	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
430	C₂²×C₄	#13083574	1	1	yes	characteristic
431	Q₁₆	—	356	1	no	—
432	Q₁₆	—	356	1	no	—
433	Q₁₆	—	178	2	no	—
434	Q₁₆	—	178	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	89	1	no	—
438	C₂×C₈	—	89	1	no	—
439	C₂×C₈	—	89	1	no	—
440	C₂×C₈	—	89	1	no	—
441	C₂×C₈	—	178	1	no	—
442	C₂×C₈	—	178	1	no	—
443	C₂×C₈	—	178	1	no	—
444	C₂×C₈	—	178	1	no	—
445	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
446	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
447	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	89	1	no	—
455	C₄⋊C₄	—	89	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	C₂×C₄×D₈₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
465	C₂²⋊C₄	—	178	1	no	—
466	C₂²⋊C₄	—	178	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	178	1	no	—
472	C₄²	—	178	1	no	—
473	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
475	C₄²	#13083574	1	1	yes	characteristic
476	C₄²	C₂³×D₈₉	1	1	yes	characteristic
477	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	356	2	no	—
483	Q₈	—	178	1	no	—
484	Q₈	—	178	1	no	—
485	Q₈	—	178	1	no	—
486	Q₈	—	178	1	no	—
487	Q₈	#15668020	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	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	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
504	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
505	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
507	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
508	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₈	—	356	1	no	—
516	C₈	—	356	1	no	—
517	C₈	—	356	1	no	—
518	C₈	—	356	1	no	—
519	C₈	—	178	1	no	—
520	C₈	—	178	1	no	—
521	C₈	—	178	1	no	—
522	C₈	—	178	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	356	1	no	—
536	C₄	—	356	1	no	—
537	C₄	—	356	1	no	—
538	C₄	—	356	1	no	—
539	C₄	C₂×#15668020	1	1	yes	characteristic
540	C₄	#19152364	1	1	yes	characteristic
541	C₄	#19152413	1	1	yes	characteristic
542	C₄	#19152413	1	1	yes	characteristic
543	C₂	—	4	1	no	—
544	C₂	#26028977	1	1	yes	characteristic
545	C₂	#26029118	1	1	yes	characteristic
546	C₂	#26029153	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×#2984	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂³×C₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2984	D₈₉
hypocenter	C₈₉	#18032
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2984

Complements

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

N	H ≅ G/N	type
3. #26019159	C₂	semidirect
4. #26019147	C₂	semidirect
5. #26019123	C₂	semidirect
6. #26019121	C₂	semidirect
7. #26019102	C₂	semidirect
8. #26019100	C₂	semidirect
9. #26019069	C₂	semidirect
10. C₈×#13083564	C₂	semidirect
289. C₈₉	#18032	semidirect

Maximal subgroups

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

subgroup	index
#26030291	2
#26029353	2
#26019159	2
#26019147	2
#26019123	2
#26019121	2
#26019102	2
#26019100	2
#26019069	2
C₈×#13083564	2
#26019033	2
#26018724	2
#26018647	2
#26018552	2
C₈₉×#2984	2
#18032	89