Subgroups — #36526130

Order 22784.

668 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029286	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#13083561	C₂	1	1	yes	maximal, characteristic
3	#26019152	C₂	1	2	yes	maximal, complemented
4	#26019095	C₂	1	2	yes	maximal, complemented
5	#26019086	C₂	1	2	yes	maximal, complemented
6	#26019062	C₂	1	2	yes	maximal, complemented
7	#26019013	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018699	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018694	C₂	1	1	yes	maximal, characteristic
10	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13083561	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	C₄×#13083561	C₄	1	1	yes	characteristic
15	C₄×#13083561	C₄	1	1	yes	characteristic
16	C₄×#13083561	C₄	1	1	yes	characteristic
17	C₄×#13083561	C₄	1	1	yes	characteristic
18	C₄×#13083561	C₂²	1	1	yes	characteristic
19	C₄×#13083561	C₂²	1	1	yes	characteristic
20	C₄×#13083561	C₂²	1	1	yes	characteristic
21	C₄×#13083561	C₂²	1	1	yes	characteristic
22	#19151677	C₂²	1	2	yes	—
23	#19151668	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151655	C₂²	1	1	yes	characteristic
26	C₂×#15667943	C₄	1	1	yes	characteristic
27	C₂×#15667936	C₄	1	1	yes	characteristic
28	C₂×#15667932	C₄	1	1	yes	characteristic
29	#19151560	—	2	1	no	—
30	C₂²⋊C₈×D₈₉	—	2	1	no	—
31	C₄×#13083558	C₂²	1	1	yes	characteristic
32	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	complemented
34	#19151348	C₂²	1	2	yes	complemented
35	Q₈⋊#10623494	C₂²	1	2	yes	complemented
36	Q₈⋊#10623494	C₂²	1	2	yes	complemented
37	#19151325	C₂²	1	2	yes	—
38	#19151325	C₂²	1	2	yes	—
39	#19151320	C₂²	1	2	yes	complemented
40	#19151319	C₂²	1	2	yes	complemented
41	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	#446×C₈₉	—	2	2	no	—
43	#446×C₈₉	C₂²	1	2	yes	complemented
44	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
45	#432×C₈₉	—	2	1	no	—
46	#432×C₈₉	C₂²	1	1	yes	characteristic
47	#431×C₈₉	—	2	1	no	—
48	#431×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	C₂×#13083561	—	2	4	no	—
52	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083558	—	2	1	no	—
57	C₂×#13083557	—	2	2	no	—
58	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
59	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₈₉	—	2	2	no	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₄×D₃₅₆	—	2	1	no	—
63	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083551	—	2	1	no	—
69	#15667943	C₂×C₄	1	1	yes	characteristic
70	#15667943	C₂×C₄	1	1	yes	characteristic
71	#15667943	C₂×C₄	1	1	yes	characteristic
72	#15667943	C₂×C₄	1	1	yes	characteristic
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667936	C₂×C₄	1	1	yes	characteristic
75	#15667936	C₂×C₄	1	1	yes	characteristic
76	#15667936	C₂×C₄	1	1	yes	characteristic
77	#15667936	C₂×C₄	1	1	yes	characteristic
78	#15667932	C₂×C₄	1	1	yes	characteristic
79	#15667932	C₂×C₄	1	1	yes	characteristic
80	#15667932	C₂×C₄	1	1	yes	characteristic
81	#15667932	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#10623494	—	2	1	no	—
83	#15667924	—	2	2	no	—
84	#15667924	—	2	2	no	—
85	#15667923	—	2	1	no	—
86	#15667923	—	2	1	no	—
87	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
88	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
89	C₄×#10623494	C₂³	1	2	yes	—
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	—	2	1	no	—
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₈₉	—	2	2	no	—
104	C₄⋊C₈×C₈₉	—	2	2	no	—
105	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
106	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₈₉	—	2	1	no	—
108	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
109	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
110	#97×C₈₉	—	2	2	no	—
111	#97×C₈₉	—	2	1	no	—
112	C₄×C₈×C₈₉	—	2	2	no	—
113	C₄×C₈×C₈₉	C₂³	1	2	yes	—
114	C₂³×D₈₉	—	2	1	no	—
115	C₂×D₃₅₆	—	2	2	no	—
116	C₂×D₃₅₆	—	2	1	no	—
117	C₂×D₃₅₆	—	4	1	no	—
118	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	2	1	no	—
124	C₂×C₄×D₈₉	—	2	1	no	—
125	C₂×C₄×D₈₉	—	8	2	no	—
126	#13083561	—	2	2	no	—
127	#13083561	—	2	2	no	—
128	#13083561	—	2	2	no	—
129	#13083561	M₁₆	1	4	yes	complemented
130	#13083558	—	4	2	no	—
131	#13083557	—	8	2	no	—
132	C₂×#10623494	—	2	2	no	—
133	C₂×#10623494	—	2	2	no	—
134	C₂×#10623494	—	2	2	no	—
135	C₂×#10623494	—	4	1	no	—
136	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
137	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
138	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
139	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
140	C₈×D₈₉	—	8	2	no	—
141	C₄⋊Dic₈₉	—	2	1	no	—
142	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
144	#13083551	—	2	1	no	—
145	#13083551	—	2	1	no	—
146	#13083551	—	2	1	no	—
147	#13083551	—	2	1	no	—
148	C₂×Q₈×C₈₉	—	2	1	no	—
149	C₂×Q₈×C₈₉	—	2	2	no	—
150	C₂×Q₈×C₈₉	—	4	1	no	—
151	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	1	no	—
165	C₄⋊C₄×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	—	2	1	no	—
169	C₄²×C₈₉	—	2	1	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	—	2	1	no	—
172	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₈₉	#41	1	1	yes	characteristic
175	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₈₉	—	2	1	no	—
178	C₂²×D₈₉	—	2	1	no	—
179	C₂²×D₈₉	—	4	2	no	—
180	C₂²×D₈₉	—	4	2	no	—
181	C₂²×D₈₉	—	8	1	no	—
182	Q₈×C₈₉	—	2	1	no	—
183	Q₈×C₈₉	—	2	1	no	—
184	Q₈×C₈₉	—	2	1	no	—
185	Q₈×C₈₉	—	4	2	no	—
186	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₈₉	—	2	1	no	—
204	C₂×Dic₈₉	—	2	1	no	—
205	C₂×Dic₈₉	—	8	1	no	—
206	D₃₅₆	—	2	1	no	—
207	D₃₅₆	—	2	1	no	—
208	D₃₅₆	—	2	1	no	—
209	D₃₅₆	—	4	2	no	—
210	D₃₅₆	C₂×M₁₆	1	2	yes	—
211	C₄×D₈₉	—	4	2	no	—
212	C₄×D₈₉	—	4	2	no	—
213	C₄×D₈₉	—	8	1	no	—
214	C₄×D₈₉	—	8	1	no	—
215	C₈×C₈₉	—	2	2	no	—
216	C₈×C₈₉	—	2	2	no	—
217	C₈×C₈₉	—	4	2	no	—
218	#10623494	—	2	1	no	—
219	#10623494	—	2	1	no	—
220	#10623494	—	2	1	no	—
221	#10623494	—	4	2	no	—
222	#10623494	—	4	2	no	—
223	#10623494	C₂×M₁₆	1	2	yes	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	#444	1	2	yes	—
227	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂×D₈₉	—	2	2	no	—
229	C₂×D₈₉	—	4	1	no	—
230	C₂×D₈₉	—	4	1	no	—
231	C₂×D₈₉	—	4	1	no	—
232	C₂×D₈₉	—	4	1	no	—
233	C₂×D₈₉	—	4	1	no	—
234	C₂×D₈₉	—	8	4	no	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	2	no	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	2	1	no	—
240	C₄×C₈₉	—	4	1	no	—
241	C₄×C₈₉	—	4	1	no	—
242	C₄×C₈₉	—	4	1	no	—
243	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
244	C₄×C₈₉	#568	1	1	yes	characteristic
245	C₄×C₈₉	#577	1	2	yes	—
246	Dic₈₉	—	4	1	no	—
247	Dic₈₉	—	4	1	no	—
248	#18060	—	89	1	no	maximal, Sylow
249	C₂×C₈₉	—	2	2	no	—
250	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
251	C₂×C₈₉	#2949	1	1	yes	characteristic
252	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
253	D₈₉	—	4	2	no	—
254	D₈₉	—	8	1	no	—
255	#2984	D₈₉	1	1	yes	characteristic, complemented
256	#2974	—	89	1	no	—
257	C₂×C₄×SD₁₆	—	89	1	no	—
258	#1592	—	89	2	no	—
259	#1583	—	89	2	no	—
260	#1582	—	89	2	no	—
261	SD₁₆⋊C₈	—	89	2	no	—
262	#1568	—	89	1	no	—
263	#1491	—	89	1	no	—
264	#1490	—	89	1	no	—
265	#1451	—	89	1	no	—
266	C₈₉	#18060	1	1	yes	characteristic, complemented, Sylow
267	C₂²×SD₁₆	—	89	1	no	—
268	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
269	C₂×C₄×D₄	—	89	1	no	—
270	#446	—	2	2	no	—
271	#446	C₂×D₈₉	1	2	yes	complemented
272	C₈×Q₈	C₂×D₈₉	1	2	yes	complemented
273	C₄×SD₁₆	—	89	1	no	—
274	C₄×SD₁₆	—	89	1	no	—
275	C₄×SD₁₆	—	89	1	no	—
276	C₄×SD₁₆	—	89	1	no	—
277	C₄×SD₁₆	—	89	1	no	—
278	C₄×SD₁₆	—	89	1	no	—
279	C₄×SD₁₆	—	89	1	no	—
280	C₄×SD₁₆	—	89	1	no	—
281	#436	—	89	2	no	—
282	#435	—	178	2	no	—
283	C₈×D₄	—	89	2	no	—
284	#432	—	2	1	no	—
285	#432	—	89	1	no	—
286	#432	C₂×D₈₉	1	1	yes	characteristic
287	#431	—	2	1	no	—
288	#431	C₂×D₈₉	1	1	yes	characteristic
289	C₂×#106	—	89	1	no	—
290	C₂×#103	—	89	1	no	—
291	C₂×#102	—	89	1	no	—
292	#407	—	178	1	no	—
293	C₂×C₂²⋊C₈	—	178	1	no	—
294	C₄×M₁₆	—	89	1	no	—
295	C₂×C₄×C₈	—	89	1	no	—
296	#335	—	89	2	no	—
297	#334	—	89	2	no	—
298	Q₈⋊C₈	—	89	2	no	—
299	Q₈⋊C₈	—	89	2	no	—
300	D₄⋊C₈	—	89	2	no	—
301	D₄⋊C₈	—	89	2	no	—
302	#322	—	89	2	no	—
303	#322	—	89	2	no	—
304	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
305	C₂²×D₄	—	89	1	no	—
306	C₂³×C₄	—	178	1	no	—
307	C₂×SD₁₆	—	89	1	no	—
308	C₂×SD₁₆	—	89	1	no	—
309	C₂×SD₁₆	—	89	1	no	—
310	C₂×SD₁₆	—	89	1	no	—
311	C₂×SD₁₆	—	178	4	no	—
312	C₂×M₁₆	—	178	1	no	—
313	C₂×M₁₆	—	178	2	no	—
314	C₂²×C₈	—	89	1	no	—
315	C₂²×C₈	—	89	1	no	—
316	C₂²×C₈	—	178	2	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
320	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
321	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
322	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₄×D₄	—	89	1	no	—
324	C₄×D₄	—	89	1	no	—
325	C₄×D₄	—	89	1	no	—
326	C₄×D₄	—	89	1	no	—
327	C₄×D₄	—	178	1	no	—
328	C₄×D₄	—	178	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	89	1	no	—
331	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	178	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
335	#106	—	89	1	no	—
336	#106	—	89	1	no	—
337	#106	—	89	1	no	—
338	#106	—	89	1	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	—	89	2	no	—
342	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
343	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
344	#103	—	89	1	no	—
345	#103	—	89	1	no	—
346	#103	—	89	1	no	—
347	#103	—	89	1	no	—
348	#102	—	89	1	no	—
349	#102	—	89	1	no	—
350	#102	—	89	1	no	—
351	#102	—	89	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	178	1	no	—
354	C₂²⋊C₈	—	178	2	no	—
355	C₂²⋊C₈	—	178	2	no	—
356	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
357	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
358	#97	—	2	2	no	—
359	#97	—	2	1	no	—
360	#97	—	178	1	no	—
361	#97	—	178	1	no	—
362	C₄×C₈	—	2	2	no	—
363	C₄×C₈	—	89	1	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	89	1	no	—
366	C₄×C₈	—	89	1	no	—
367	C₄×C₈	—	89	2	no	—
368	C₄×C₈	C₂²×D₈₉	1	2	yes	—
369	C₂⁴	—	178	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
375	C₂×D₄	—	89	1	no	—
376	C₂×D₄	—	89	1	no	—
377	C₂×D₄	—	356	1	no	—
378	C₂×D₄	—	178	2	no	—
379	C₂×D₄	—	178	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	178	1	no	—
383	C₂²×C₄	—	178	1	no	—
384	C₂²×C₄	—	178	1	no	—
385	C₂²×C₄	—	178	1	no	—
386	C₂²×C₄	—	178	1	no	—
387	C₂²×C₄	—	712	2	no	—
388	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
390	C₂²×C₄	#13083574	1	1	yes	characteristic
391	SD₁₆	—	89	4	no	—
392	SD₁₆	—	178	2	no	—
393	SD₁₆	—	178	2	no	—
394	SD₁₆	—	178	2	no	—
395	M₁₆	—	356	2	no	—
396	M₁₆	—	712	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	89	1	no	—
399	C₂×C₈	—	89	1	no	—
400	C₂×C₈	—	89	1	no	—
401	C₂×C₈	—	89	1	no	—
402	C₂×C₈	—	356	1	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	2	no	—
405	C₂×C₈	—	178	2	no	—
406	C₂×C₈	—	712	2	no	—
407	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
408	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	89	1	no	—
415	C₄⋊C₄	—	89	1	no	—
416	C₄⋊C₄	—	178	1	no	—
417	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
418	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
419	C₂²⋊C₄	—	178	1	no	—
420	C₂²⋊C₄	—	178	1	no	—
421	C₂²⋊C₄	—	178	1	no	—
422	C₂²⋊C₄	—	178	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
428	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
429	C₄²	#13083574	1	1	yes	characteristic
430	C₄²	C₂³×D₈₉	1	1	yes	characteristic
431	C₂³	—	356	2	no	—
432	C₂³	—	356	2	no	—
433	C₂³	—	178	1	no	—
434	C₂³	—	178	1	no	—
435	C₂³	—	712	1	no	—
436	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
437	Q₈	—	2	1	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	4	2	no	—
441	Q₈	M₁₆×D₈₉	1	2	yes	—
442	D₄	—	89	2	no	—
443	D₄	—	356	2	no	—
444	D₄	—	178	1	no	—
445	D₄	—	178	1	no	—
446	D₄	—	178	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	356	2	no	—
458	C₂×C₄	—	356	2	no	—
459	C₂×C₄	—	178	1	no	—
460	C₂×C₄	—	178	1	no	—
461	C₂×C₄	—	712	1	no	—
462	C₂×C₄	—	712	1	no	—
463	C₂×C₄	—	712	1	no	—
464	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
465	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	89	2	no	—
474	C₈	—	356	2	no	—
475	C₈	—	356	2	no	—
476	C₈	—	178	1	no	—
477	C₈	—	178	1	no	—
478	C₈	—	178	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	356	1	no	—
482	C₂²	—	356	1	no	—
483	C₂²	—	356	1	no	—
484	C₂²	—	356	1	no	—
485	C₂²	—	356	1	no	—
486	C₂²	—	178	2	no	—
487	C₂²	—	712	4	no	—
488	C₂²	#19151718	1	2	yes	—
489	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	356	1	no	—
499	C₄	—	356	1	no	—
500	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
501	C₄	#19152364	1	1	yes	characteristic
502	C₄	#19152406	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	356	2	no	—
505	C₂	—	712	1	no	—
506	C₂	M₁₆×C₂²⋊D₈₉	1	1	yes	characteristic
507	C₂	#26029111	1	1	yes	characteristic
508	C₂	C₂×#19151718	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	C₂²×D₃₅₆	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2984	D₈₉
hypocenter	C₈₉	#18060
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. #26019152	C₂	semidirect
4. #26019095	C₂	semidirect
5. #26019086	C₂	semidirect
6. #26019062	C₂	semidirect
7. #26019013	C₂	semidirect
8. #26018699	C₂	semidirect
10. #26018542	C₂	semidirect
11. C₈₉×#2984	C₂	semidirect
33. #19151350	C₂²	semidirect
34. #19151348	C₂²	semidirect
35. Q₈⋊#10623494	C₂²	semidirect
36. Q₈⋊#10623494	C₂²	semidirect
39. #19151320	C₂²	semidirect
40. #19151319	C₂²	semidirect
43. #446×C₈₉	C₂²	semidirect
44. C₈×Q₈×C₈₉	C₂²	semidirect
129. #13083561	M₁₆	semidirect
255. #2984	D₈₉	semidirect
266. C₈₉	#18060	semidirect
271. #446	C₂×D₈₉	semidirect
272. C₈×Q₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029286	2
C₂×C₄×#13083561	2
#26019152	2
#26019095	2
#26019086	2
#26019062	2
#26019013	2
#26018699	2
#26018694	2
#26018542	2
C₈₉×#2984	2
#18060	89