Subgroups — #36525826

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	#26030292	C₂	1	1	yes	maximal, characteristic
2	#26029353	C₂	1	1	yes	maximal, characteristic
3	#26029339	C₂	1	1	yes	maximal, characteristic
4	#26019162	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019150	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019125	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019125	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019032	C₂	1	1	yes	maximal, characteristic
13	#26018726	C₂	1	1	yes	maximal, characteristic
14	#26018648	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1454	C₂	1	1	yes	maximal, characteristic
16	#19152155	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
18	#19151934	C₄	1	1	yes	characteristic
19	#19151934	C₄	1	1	yes	characteristic
20	#19151894	C₄	1	1	yes	characteristic
21	#19151894	C₄	1	1	yes	characteristic
22	#19151809	C₄	1	1	yes	characteristic
23	#19151809	C₄	1	1	yes	characteristic
24	#19151756	C₄	1	1	yes	characteristic
25	#19151756	C₄	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151728	C₂²	1	1	yes	characteristic
28	#19151728	C₂²	1	1	yes	characteristic
29	#19151728	C₂²	1	1	yes	characteristic
30	#19151727	—	2	1	no	—
31	#19151727	—	2	1	no	—
32	#19151725	—	2	1	no	—
33	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
35	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
37	#19151722	—	2	1	no	—
38	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
39	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
40	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
41	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
42	#19151656	—	2	1	no	—
43	#19151656	—	2	1	no	—
44	#19151655	C₂²	1	1	yes	characteristic
45	#19151652	—	2	1	no	—
46	#19151651	C₂²	1	1	yes	characteristic
47	#19151648	—	2	1	no	—
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151351	C₂²	1	1	yes	characteristic
50	#19151349	C₂²	1	1	yes	characteristic
51	#19151349	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	#19151330	C₂²	1	1	yes	characteristic
54	#19151330	C₂²	1	1	yes	characteristic
55	#19151330	C₂²	1	1	yes	characteristic
56	#19151330	C₂²	1	1	yes	characteristic
57	#19151330	C₂²	1	1	yes	characteristic
58	#19151330	C₂²	1	1	yes	characteristic
59	#19151330	C₂²	1	1	yes	characteristic
60	#431×C₈₉	C₂²	1	1	yes	characteristic
61	#431×C₈₉	C₂²	1	1	yes	characteristic
62	#431×C₈₉	C₂²	1	1	yes	characteristic
63	#322×C₈₉	C₂²	1	1	yes	characteristic
64	#322×C₈₉	C₂²	1	1	yes	characteristic
65	#322×C₈₉	C₂²	1	1	yes	characteristic
66	C₈²×C₈₉	C₂²	1	1	yes	characteristic
67	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
80	C₄×Dic₁₇₈	—	2	1	no	—
81	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
84	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
87	#15667971	—	2	1	no	—
88	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×#13083553	—	2	1	no	—
90	C₂×C₄×Dic₈₉	—	2	1	no	—
91	#15667946	C₂×C₄	1	1	yes	characteristic
92	#15667946	C₂×C₄	1	1	yes	characteristic
93	#15667946	C₂×C₄	1	1	yes	characteristic
94	#15667946	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#10623494	C₂³	1	1	yes	characteristic
96	C₄⋊#10623494	C₂³	1	1	yes	characteristic
97	C₄⋊#10623494	C₂³	1	1	yes	characteristic
98	C₄⋊#10623494	C₂³	1	1	yes	characteristic
99	#15667941	—	2	1	no	—
100	#15667941	—	2	1	no	—
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667937	C₂×C₄	1	1	yes	characteristic
108	#15667937	C₂×C₄	1	1	yes	characteristic
109	#15667937	C₂×C₄	1	1	yes	characteristic
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667937	C₂×C₄	1	1	yes	characteristic
112	#15667937	C₂×C₄	1	1	yes	characteristic
113	#15667937	C₂×C₄	1	1	yes	characteristic
114	#15667937	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#10623494	—	2	1	no	—
116	C₂²⋊#10623494	—	2	1	no	—
117	#15667923	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	#15667922	—	2	1	no	—
121	#15667922	—	2	1	no	—
122	C₄×#10623494	—	2	1	no	—
123	C₈×Dic₈₉	—	2	1	no	—
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₈₉	—	2	1	no	—
129	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
132	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₈₉	—	2	1	no	—
134	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
135	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
137	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
138	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
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	2	no	—
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	—	4	1	no	—
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₈₉	—	2	1	no	—
153	C₂²×Dic₈₉	—	2	1	no	—
154	Dic₃₅₆	—	2	2	no	—
155	Dic₃₅₆	—	2	2	no	—
156	Dic₃₅₆	—	4	1	no	—
157	Dic₃₅₆	—	4	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₄⋊Dic₈₉	—	2	1	no	—
163	C₄⋊Dic₈₉	—	2	1	no	—
164	C₄⋊Dic₈₉	—	2	1	no	—
165	C₄⋊Dic₈₉	—	2	1	no	—
166	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊Dic₈₉	—	2	1	no	—
179	C₂²⋊Dic₈₉	—	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	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂×Dic₈₉	—	2	1	no	—
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	—	2	1	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	2	1	no	—
223	C₂×Dic₈₉	—	4	2	no	—
224	C₂×Dic₈₉	—	4	2	no	—
225	Dic₁₇₈	—	2	1	no	—
226	Dic₁₇₈	—	2	1	no	—
227	Dic₁₇₈	—	2	1	no	—
228	Dic₁₇₈	—	2	1	no	—
229	Dic₁₇₈	—	2	1	no	—
230	Dic₁₇₈	—	2	1	no	—
231	Dic₁₇₈	—	2	1	no	—
232	Dic₁₇₈	—	4	2	no	—
233	Dic₁₇₈	—	4	2	no	—
234	Dic₁₇₈	#131	1	2	yes	—
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	—	2	1	no	—
240	C₈×C₈₉	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	4	1	no	—
244	C₈×C₈₉	—	4	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	1	no	—
255	C₄×C₈₉	—	2	1	no	—
256	C₄×C₈₉	—	2	1	no	—
257	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
258	C₄×C₈₉	#568	1	1	yes	characteristic
259	C₄×C₈₉	#578	1	1	yes	characteristic
260	C₄×C₈₉	#578	1	1	yes	characteristic
261	Dic₈₉	—	2	2	no	—
262	Dic₈₉	—	4	1	no	—
263	Dic₈₉	—	4	1	no	—
264	Dic₈₉	—	4	1	no	—
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	—	89	1	no	—
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	D₈₉	1	1	yes	characteristic
289	C₈₉	#18032	1	1	yes	characteristic, complemented, Sylow
290	#533	—	89	1	no	—
291	C₂×C₄×Q₈	—	89	1	no	—
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	—	89	1	no	—
301	#446	—	89	1	no	—
302	#446	—	89	1	no	—
303	#446	—	89	1	no	—
304	#446	—	178	1	no	—
305	#446	—	178	1	no	—
306	#446	—	178	1	no	—
307	C₈×Q₈	—	89	1	no	—
308	C₈×Q₈	—	89	1	no	—
309	C₈×Q₈	—	89	1	no	—
310	C₈×Q₈	—	89	1	no	—
311	C₈×Q₈	—	178	1	no	—
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	—	89	1	no	—
319	#432	—	178	1	no	—
320	#431	—	89	1	no	—
321	#431	—	178	1	no	—
322	#431	C₂×D₈₉	1	1	yes	characteristic
323	#431	C₂×D₈₉	1	1	yes	characteristic
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	C₂×D₈₉	1	1	yes	characteristic
338	#322	C₂×D₈₉	1	1	yes	characteristic
339	#322	C₂×D₈₉	1	1	yes	characteristic
340	C₈²	C₂×D₈₉	1	1	yes	characteristic
341	C₂²×Q₈	—	89	1	no	—
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	—	89	1	no	—
353	C₄×Q₈	—	89	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	#117	—	178	1	no	—
362	C₂×C₄⋊C₄	—	89	1	no	—
363	C₂×C₄⋊C₄	—	178	1	no	—
364	C₂×C₄²	—	178	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	—	89	1	no	—
372	C₄⋊C₈	—	89	1	no	—
373	C₄⋊C₈	—	89	1	no	—
374	C₄⋊C₈	—	89	1	no	—
375	C₄⋊C₈	—	178	1	no	—
376	C₄⋊C₈	—	178	1	no	—
377	C₄⋊C₈	—	178	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	C₄×D₈₉	1	1	yes	characteristic
384	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
385	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
386	C₄⋊C₈	D₃₅₆	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	—	178	1	no	—
397	C₂²⋊C₈	—	178	1	no	—
398	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
399	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
400	C₂²⋊C₈	D₃₅₆	1	1	yes	characteristic
401	C₂²⋊C₈	D₃₅₆	1	1	yes	characteristic
402	#97	—	178	1	no	—
403	#97	—	178	1	no	—
404	#97	—	178	1	no	—
405	#97	—	178	1	no	—
406	#97	—	178	1	no	—
407	C₄×C₈	—	178	1	no	—
408	C₄×C₈	—	178	1	no	—
409	C₄×C₈	—	178	1	no	—
410	C₄×C₈	—	178	1	no	—
411	C₄×C₈	—	178	1	no	—
412	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
416	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
417	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
418	C₂×Q₈	—	89	1	no	—
419	C₂×Q₈	—	89	1	no	—
420	C₂×Q₈	—	89	1	no	—
421	C₂×Q₈	—	89	1	no	—
422	C₂×Q₈	—	356	1	no	—
423	C₂×Q₈	—	178	2	no	—
424	C₂×Q₈	—	178	1	no	—
425	C₂×Q₈	—	178	1	no	—
426	C₂²×C₄	—	178	1	no	—
427	C₂²×C₄	—	178	1	no	—
428	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₃₅₆	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	—	178	1	no	—
438	C₂×C₈	—	178	1	no	—
439	C₂×C₈	—	178	1	no	—
440	C₂×C₈	—	178	1	no	—
441	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
442	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
443	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
445	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
446	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
447	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
448	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
449	C₄⋊C₄	—	89	1	no	—
450	C₄⋊C₄	—	89	1	no	—
451	C₄⋊C₄	—	89	1	no	—
452	C₄⋊C₄	—	89	1	no	—
453	C₄⋊C₄	—	178	1	no	—
454	C₄⋊C₄	—	178	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	C₂²⋊C₄	—	178	1	no	—
466	C₂²⋊C₄	—	178	1	no	—
467	C₄²	—	178	1	no	—
468	C₄²	—	178	1	no	—
469	C₄²	—	178	1	no	—
470	C₄²	—	178	1	no	—
471	C₄²	—	178	1	no	—
472	C₄²	—	178	1	no	—
473	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
475	C₄²	#13083574	1	1	yes	characteristic
476	C₄²	C₂³×D₈₉	1	1	yes	characteristic
477	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
478	Q₈	—	89	2	no	—
479	Q₈	—	356	2	no	—
480	Q₈	—	356	2	no	—
481	Q₈	—	178	1	no	—
482	Q₈	—	178	1	no	—
483	Q₈	—	178	1	no	—
484	Q₈	—	178	1	no	—
485	Q₈	—	178	1	no	—
486	Q₈	—	178	1	no	—
487	Q₈	—	178	1	no	—
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	—	4	1	no	—
493	C₂×C₄	—	356	2	no	—
494	C₂×C₄	—	356	2	no	—
495	C₂×C₄	—	178	1	no	—
496	C₂×C₄	—	178	1	no	—
497	C₂×C₄	—	178	1	no	—
498	C₂×C₄	—	178	1	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×D₃₅₆	1	1	yes	characteristic
504	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
505	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₃₅₆	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	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	356	1	no	—
520	C₈	—	356	1	no	—
521	C₈	—	356	1	no	—
522	C₈	—	356	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	C₂×C₄×D₃₅₆	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	—	356	1	no	—
532	C₄	—	356	1	no	—
533	C₄	—	356	1	no	—
534	C₄	—	356	1	no	—
535	C₄	—	356	1	no	—
536	C₄	—	356	1	no	—
537	C₄	—	356	1	no	—
538	C₄	—	178	2	no	—
539	C₄	#131×D₈₉	1	1	yes	characteristic
540	C₄	#19152363	1	1	yes	characteristic
541	C₄	#19152415	1	1	yes	characteristic
542	C₄	#19152415	1	1	yes	characteristic
543	C₂	—	4	1	no	—
544	C₂	#26028980	1	1	yes	characteristic
545	C₂	#26029121	1	1	yes	characteristic
546	C₂	#26029156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1454	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂³×C₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1454	D₈₉
hypocenter	C₈₉	#18032
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1454

Complements

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

N	H ≅ G/N	type
4. #26019162	C₂	semidirect
5. #26019150	C₂	semidirect
6. #26019125	C₂	semidirect
7. #26019125	C₂	semidirect
8. #26019104	C₂	semidirect
9. #26019104	C₂	semidirect
10. #26019072	C₂	semidirect
11. C₈×Dic₃₅₆	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
#26030292	2
#26029353	2
#26029339	2
#26019162	2
#26019150	2
#26019125	2
#26019104	2
#26019072	2
C₈×Dic₃₅₆	2
#26019032	2
#26018726	2
#26018648	2
C₈₉×#1454	2
#18032	89