Subgroups — #36525322

Order 22784.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030256	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₃₅₆	C₂	1	1	yes	maximal, characteristic
3	#26019142	C₂	1	2	yes	maximal, complemented
4	#26019095	C₂	1	2	yes	maximal, complemented
5	#26019086	C₂	1	2	yes	maximal, complemented
6	C₈×#13083561	C₂	1	2	yes	maximal, complemented
7	#26019022	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018707	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151325	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₈₉	—	2	1	no	—
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19151926	C₄	1	2	yes	—
15	#19151885	C₄	1	1	yes	characteristic
16	#19151885	C₄	1	1	yes	characteristic
17	#19151800	C₄	1	1	yes	characteristic
18	#19151800	C₄	1	1	yes	characteristic
19	#19151748	C₄	1	2	yes	—
20	C₄×#13083561	C₂²	1	2	yes	—
21	C₄×#13083561	C₂²	1	2	yes	—
22	#19151677	C₂²	1	2	yes	—
23	#19151671	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151622	C₂²	1	1	yes	characteristic
27	#19151561	—	2	1	no	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151348	C₂²	1	2	yes	complemented
30	#19151348	C₂²	1	2	yes	complemented
31	Q₈⋊#10623494	C₂²	1	2	yes	complemented
32	Q₈⋊#10623494	C₂²	1	2	yes	complemented
33	#19151325	C₂²	1	1	yes	characteristic
34	#19151325	C₂²	1	1	yes	characteristic
35	#19151325	C₂²	1	1	yes	characteristic
36	#19151325	C₂²	1	1	yes	characteristic
37	#19151319	C₂²	1	2	yes	complemented
38	C₈×#10623494	C₂²	1	2	yes	complemented
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	—	2	2	no	—
41	#446×C₈₉	C₂²	1	2	yes	complemented
42	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
43	#424×C₈₉	—	2	1	no	—
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#405×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	—	2	1	no	—
49	C₂×#13083561	C₂×C₄	1	2	yes	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083557	—	2	2	no	—
53	M₁₆×D₈₉	—	4	4	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	C₄×D₃₅₆	—	2	1	no	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
59	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
60	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
61	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×#13083551	—	2	1	no	—
64	#15667943	C₂×C₄	1	2	yes	—
65	#15667943	C₂×C₄	1	2	yes	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667936	C₂×C₄	1	2	yes	—
71	#15667936	C₂×C₄	1	2	yes	—
72	#15667932	C₂×C₄	1	2	yes	—
73	#15667932	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	C₄×#10623494	—	2	1	no	—
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₄×#10623494	C₂³	1	2	yes	—
81	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	—	2	1	no	—
84	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	#125×C₈₉	—	2	1	no	—
87	C₂²⋊Q₈×C₈₉	—	2	1	no	—
88	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₈₉	—	2	1	no	—
90	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
91	#117×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	—	2	2	no	—
94	C₄⋊C₈×C₈₉	—	2	2	no	—
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#97×C₈₉	—	2	2	no	—
99	#97×C₈₉	D₄	1	2	yes	—
100	C₄×C₈×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	C₂³×D₈₉	—	2	1	no	—
103	C₂×D₃₅₆	—	2	2	no	—
104	C₂×D₃₅₆	—	2	1	no	—
105	C₂×D₃₅₆	—	4	1	no	—
106	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	2	1	no	—
110	C₂×C₄×D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	C₂×C₄×D₈₉	—	2	1	no	—
113	C₂×C₄×D₈₉	—	4	2	no	—
114	C₂×C₄×D₈₉	—	4	2	no	—
115	#13083561	—	2	4	no	—
116	#13083561	—	4	2	no	—
117	#13083558	—	4	2	no	—
118	#13083557	—	4	4	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	4	2	no	—
123	C₂×#10623494	C₂²×C₄	1	2	yes	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₈×D₈₉	—	4	4	no	—
126	C₄⋊Dic₈₉	—	2	1	no	—
127	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	#13083551	—	2	1	no	—
130	#13083551	—	2	1	no	—
131	#13083551	—	2	1	no	—
132	#13083551	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
138	M₁₆×C₈₉	—	2	2	no	—
139	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	4	2	no	—
143	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	2	no	—
150	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂²⋊C₄×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	1	no	—
159	C₂²×D₈₉	—	2	1	no	—
160	C₂²×D₈₉	—	4	2	no	—
161	C₂²×D₈₉	—	4	2	no	—
162	C₂²×D₈₉	—	8	1	no	—
163	Q₈×C₈₉	—	2	2	no	—
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	8	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₈₉	#135	1	2	yes	—
176	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₈₉	—	2	1	no	—
180	C₂×Dic₈₉	—	2	1	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	D₃₅₆	—	2	1	no	—
183	D₃₅₆	—	2	1	no	—
184	D₃₅₆	—	2	1	no	—
185	D₃₅₆	—	4	2	no	—
186	D₃₅₆	#131	1	2	yes	—
187	C₄×D₈₉	—	4	1	no	—
188	C₄×D₈₉	—	4	1	no	—
189	C₄×D₈₉	—	4	1	no	—
190	C₄×D₈₉	—	4	1	no	—
191	C₄×D₈₉	—	4	2	no	—
192	C₄×D₈₉	—	4	2	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
197	#10623494	—	2	2	no	—
198	#10623494	—	2	2	no	—
199	#10623494	—	2	2	no	—
200	#10623494	—	4	1	no	—
201	#10623494	—	4	2	no	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
205	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×D₈₉	—	2	2	no	—
207	C₂×D₈₉	—	4	1	no	—
208	C₂×D₈₉	—	4	1	no	—
209	C₂×D₈₉	—	4	1	no	—
210	C₂×D₈₉	—	4	1	no	—
211	C₂×D₈₉	—	4	1	no	—
212	C₂×D₈₉	—	8	4	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	4	2	no	—
217	C₄×C₈₉	—	4	2	no	—
218	C₄×C₈₉	C₄×SD₁₆	1	2	yes	—
219	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
220	C₄×C₈₉	#568	1	1	yes	characteristic
221	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
222	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
223	Dic₈₉	—	4	1	no	—
224	Dic₈₉	—	4	1	no	—
225	#17995	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	2	2	no	—
227	C₂×C₈₉	#2933	1	1	yes	characteristic
228	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
229	C₂×C₈₉	#2956	1	1	yes	characteristic
230	D₈₉	—	4	2	no	—
231	D₈₉	—	8	1	no	—
232	#3101	—	89	1	no	—
233	#2962	D₈₉	1	1	yes	characteristic, complemented
234	D₄×M₁₆	—	89	1	no	—
235	#1590	—	89	2	no	—
236	#1583	—	89	2	no	—
237	#1582	—	89	2	no	—
238	C₈×SD₁₆	—	89	2	no	—
239	#1570	—	89	1	no	—
240	#1493	—	89	1	no	—
241	C₂×D₄⋊C₈	—	89	1	no	—
242	C₈×M₁₆	—	89	1	no	—
243	C₈₉	#17995	1	1	yes	characteristic, complemented, Sylow
244	C₂²×M₁₆	—	178	1	no	—
245	#533	C₂×D₈₉	1	1	yes	characteristic
246	C₂×C₄×D₄	—	89	1	no	—
247	#483	—	89	2	no	—
248	#476	—	89	1	no	—
249	#476	—	89	1	no	—
250	#461	—	89	1	no	—
251	#461	—	89	1	no	—
252	#450	—	89	2	no	—
253	#446	—	2	2	no	—
254	#446	C₂×D₈₉	1	2	yes	complemented
255	C₈×Q₈	C₂×D₈₉	1	2	yes	complemented
256	C₄×SD₁₆	—	89	2	no	—
257	C₄×SD₁₆	—	89	2	no	—
258	#436	—	89	2	no	—
259	#435	—	178	2	no	—
260	C₈×D₄	—	89	2	no	—
261	#431	—	89	1	no	—
262	#424	—	2	1	no	—
263	#423	—	89	1	no	—
264	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
265	#407	—	178	1	no	—
266	#405	—	2	1	no	—
267	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
268	C₂×C₄×C₈	—	89	1	no	—
269	#334	—	89	2	no	—
270	#334	—	89	2	no	—
271	Q₈⋊C₈	—	89	2	no	—
272	Q₈⋊C₈	—	89	2	no	—
273	D₄⋊C₈	—	89	1	no	—
274	D₄⋊C₈	—	89	1	no	—
275	D₄⋊C₈	—	89	1	no	—
276	D₄⋊C₈	—	89	1	no	—
277	#322	—	89	2	no	—
278	C₈²	—	89	2	no	—
279	C₂²×D₄	—	89	1	no	—
280	C₂³×C₄	—	178	1	no	—
281	C₂×SD₁₆	—	89	2	no	—
282	C₂×SD₁₆	—	89	2	no	—
283	C₂×M₁₆	—	356	4	no	—
284	C₂×M₁₆	—	178	1	no	—
285	C₂×M₁₆	—	178	2	no	—
286	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
287	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	178	1	no	—
290	C₂²×C₈	—	178	2	no	—
291	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
292	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₈₉	1	2	yes	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
298	C₄×D₄	—	89	1	no	—
299	C₄×D₄	—	89	1	no	—
300	C₄×D₄	—	89	1	no	—
301	C₄×D₄	—	89	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	—	178	1	no	—
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	89	1	no	—
306	C₂×C₂²⋊C₄	—	178	1	no	—
307	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
308	#106	—	89	2	no	—
309	#106	—	89	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	—	89	1	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	89	2	no	—
316	C₄⋊C₈	—	178	1	no	—
317	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
319	#103	—	89	2	no	—
320	#103	—	89	2	no	—
321	#102	—	89	2	no	—
322	#102	—	89	2	no	—
323	C₂²⋊C₈	—	89	2	no	—
324	C₂²⋊C₈	—	178	2	no	—
325	C₂²⋊C₈	—	178	2	no	—
326	#97	—	2	2	no	—
327	#97	C₂²⋊D₈₉	1	2	yes	—
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	—	89	2	no	—
330	C₄×C₈	—	89	1	no	—
331	C₄×C₈	—	89	1	no	—
332	C₄×C₈	—	178	1	no	—
333	C₄×C₈	C₂²×D₈₉	1	2	yes	—
334	C₂⁴	—	178	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
337	C₂×D₄	—	89	1	no	—
338	C₂×D₄	—	89	1	no	—
339	C₂×D₄	—	356	1	no	—
340	C₂×D₄	—	178	2	no	—
341	C₂×D₄	—	178	1	no	—
342	C₂²×C₄	—	356	2	no	—
343	C₂²×C₄	—	356	2	no	—
344	C₂²×C₄	—	178	1	no	—
345	C₂²×C₄	—	178	1	no	—
346	C₂²×C₄	—	178	1	no	—
347	C₂²×C₄	—	178	1	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
351	C₂²×C₄	#13083574	1	1	yes	characteristic
352	SD₁₆	—	356	2	no	—
353	SD₁₆	—	178	4	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	356	2	no	—
356	M₁₆	—	356	4	no	—
357	M₁₆	#13083561	1	4	yes	complemented
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	89	2	no	—
362	C₂×C₈	—	89	2	no	—
363	C₂×C₈	—	356	2	no	—
364	C₂×C₈	—	356	4	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	1	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	89	1	no	—
376	C₄⋊C₄	—	89	1	no	—
377	C₄⋊C₄	—	178	1	no	—
378	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	178	1	no	—
381	C₂²⋊C₄	—	178	1	no	—
382	C₂²⋊C₄	—	178	1	no	—
383	C₂²⋊C₄	—	178	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
386	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₄²	#13083574	1	1	yes	characteristic
388	C₄²	C₂³×D₈₉	1	1	yes	characteristic
389	C₂³	—	356	2	no	—
390	C₂³	—	356	2	no	—
391	C₂³	—	178	1	no	—
392	C₂³	—	178	1	no	—
393	C₂³	—	712	1	no	—
394	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	89	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	178	1	no	—
401	D₄	—	178	1	no	—
402	D₄	—	178	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	356	1	no	—
412	C₂×C₄	—	356	1	no	—
413	C₂×C₄	—	356	1	no	—
414	C₂×C₄	—	356	1	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
418	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#13083561	1	2	yes	—
421	C₂×C₄	#15668032	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	356	1	no	—
429	C₈	—	356	2	no	—
430	C₈	—	178	2	no	—
431	C₈	—	178	2	no	—
432	C₈	—	178	2	no	—
433	C₈	C₂×#13083561	1	4	yes	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	356	1	no	—
437	C₂²	—	356	1	no	—
438	C₂²	—	356	1	no	—
439	C₂²	—	356	1	no	—
440	C₂²	—	356	1	no	—
441	C₂²	—	178	2	no	—
442	C₂²	—	712	4	no	—
443	C₂²	C₄×#13083561	1	2	yes	—
444	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	356	1	no	—
451	C₄	—	356	1	no	—
452	C₄	C₄×#13083561	1	2	yes	—
453	C₄	#131×D₈₉	1	1	yes	characteristic
454	C₄	#19152363	1	1	yes	characteristic
455	C₄	C₂²×#13083561	1	1	yes	characteristic
456	C₄	C₂×#15668032	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	356	2	no	—
459	C₂	—	712	1	no	—
460	C₂	#26028974	1	1	yes	characteristic
461	C₂	C₂×C₄×#13083561	1	1	yes	characteristic
462	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	C₂²×D₃₅₆	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2962	D₈₉
hypocenter	C₈₉	#17995
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. #26019142	C₂	semidirect
4. #26019095	C₂	semidirect
5. #26019086	C₂	semidirect
6. C₈×#13083561	C₂	semidirect
7. #26019022	C₂	semidirect
8. #26018707	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#2962	C₂	semidirect
29. #19151348	C₂²	semidirect
30. #19151348	C₂²	semidirect
31. Q₈⋊#10623494	C₂²	semidirect
32. Q₈⋊#10623494	C₂²	semidirect
37. #19151319	C₂²	semidirect
38. C₈×#10623494	C₂²	semidirect
41. #446×C₈₉	C₂²	semidirect
42. C₈×Q₈×C₈₉	C₂²	semidirect
139. M₁₆×C₈₉	SD₁₆	semidirect
233. #2962	D₈₉	semidirect
243. C₈₉	#17995	semidirect
254. #446	C₂×D₈₉	semidirect
255. C₈×Q₈	C₂×D₈₉	semidirect
357. M₁₆	#13083561	semidirect

Maximal subgroups

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

subgroup	index
#26030256	2
M₁₆×D₃₅₆	2
#26019142	2
#26019095	2
#26019086	2
C₈×#13083561	2
#26019022	2
#26018707	2
C₂×#19151325	2
M₁₆×#10623494	2
C₈₉×#2962	2
#17995	89