Subgroups — #36524434

Order 22784.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#10623494	C₂	1	1	yes	maximal, characteristic
2	#26029187	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019124	C₂	1	2	yes	maximal, complemented
4	#26019110	C₂	1	2	yes	maximal, complemented
5	Q₁₆×#10623494	C₂	1	2	yes	maximal, complemented
6	SD₁₆×#10623494	C₂	1	2	yes	maximal, complemented
7	#26019041	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018691	C₂	1	1	yes	maximal, characteristic
9	#26018673	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	1	no	—
13	#19151729	C₂²	1	2	yes	—
14	Q₈×#10623494	—	2	1	no	—
15	Q₈×#10623494	C₂²	1	1	yes	characteristic
16	Q₈×#10623494	C₂²	1	2	yes	—
17	Q₈×#10623494	C₂²	1	1	yes	characteristic
18	D₄×#10623494	—	2	1	no	—
19	D₄×#10623494	—	2	1	no	—
20	D₄×#10623494	C₂²	1	1	yes	characteristic
21	D₄×#10623494	C₂²	1	1	yes	characteristic
22	#19151651	—	2	1	no	—
23	#19151651	C₂²	1	1	yes	characteristic
24	#19151625	—	2	1	no	—
25	#19151622	C₂²	1	1	yes	characteristic
26	#19151554	—	2	1	no	—
27	C₄×#13083558	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	—	2	1	no	—
29	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	2	yes	—
31	#19151349	C₂²	1	2	yes	—
32	Q₈⋊#10623494	C₂²	1	2	yes	—
33	Q₈⋊#10623494	C₂²	1	2	yes	—
34	Q₈⋊#10623494	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	—
36	#19151320	C₂²	1	2	yes	—
37	C₈×#10623494	C₂²	1	2	yes	—
38	#533×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	#485×C₈₉	C₄	1	2	yes	—
41	#475×C₈₉	C₄	1	1	yes	characteristic
42	#474×C₈₉	C₄	1	1	yes	characteristic
43	#462×C₈₉	C₄	1	1	yes	characteristic
44	#461×C₈₉	C₄	1	1	yes	characteristic
45	#452×C₈₉	C₄	1	2	yes	—
46	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
47	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
48	#431×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	D₄	1	1	yes	characteristic
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₄⋊#10623494	—	2	2	no	—
56	C₄⋊#10623494	—	2	2	no	—
57	C₄⋊#10623494	—	2	1	no	—
58	C₄⋊#10623494	—	2	1	no	—
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	C₂³	1	2	yes	—
61	C₄⋊#10623494	C₂³	1	1	yes	characteristic
62	C₄⋊#10623494	C₂³	1	1	yes	characteristic
63	C₂²⋊#10623494	—	2	1	no	—
64	C₂²⋊#10623494	—	2	1	no	—
65	C₂²⋊#10623494	—	2	1	no	—
66	#15667923	—	2	2	no	—
67	#15667923	—	2	1	no	—
68	C₄×#10623494	—	2	1	no	—
69	C₄×#10623494	—	2	1	no	—
70	C₄×#10623494	—	2	2	no	—
71	C₄×#10623494	—	2	1	no	—
72	C₄×#10623494	D₄	1	1	yes	characteristic
73	C₄×#10623494	D₄	1	1	yes	characteristic
74	C₄×#10623494	C₂³	1	2	yes	—
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₄×#10623494	C₂³	1	1	yes	characteristic
77	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
79	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
80	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
82	#125×C₈₉	—	2	1	no	—
83	C₂²⋊Q₈×C₈₉	—	2	1	no	—
84	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
88	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
93	#117×C₈₉	—	2	1	no	—
94	#117×C₈₉	—	2	1	no	—
95	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	#107×C₈₉	C₂×C₄	1	2	yes	—
99	#106×C₈₉	C₂×C₄	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	#103×C₈₉	C₂×C₄	1	2	yes	—
103	#103×C₈₉	C₂×C₄	1	2	yes	—
104	#103×C₈₉	C₂×C₄	1	2	yes	—
105	#102×C₈₉	C₂×C₄	1	2	yes	—
106	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	#13083558	—	2	4	no	—
109	#13083558	—	4	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	2	2	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	4	1	no	—
116	C₂×#10623494	—	4	2	no	—
117	C₂×#10623494	—	4	2	no	—
118	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	#41×C₈₉	—	2	2	no	—
123	#41×C₈₉	—	2	2	no	—
124	C₂×Q₈×C₈₉	—	2	1	no	—
125	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₈₉	—	2	1	no	—
128	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
135	Q₁₆×C₈₉	—	2	4	no	—
136	SD₁₆×C₈₉	—	2	4	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	—	2	2	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₂²⋊C₄×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	—	2	1	no	—
156	C₄²×C₈₉	—	2	2	no	—
157	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	#41	1	1	yes	characteristic
160	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
163	Q₈×C₈₉	—	2	1	no	—
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	2	2	no	—
166	Q₈×C₈₉	—	4	2	no	—
167	Q₈×C₈₉	#131	1	2	yes	—
168	D₄×C₈₉	—	2	4	no	—
169	D₄×C₈₉	—	2	1	no	—
170	D₄×C₈₉	#131	1	2	yes	—
171	C₂×C₄×C₈₉	—	2	4	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	4	2	no	—
185	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	2	2	no	—
193	#10623494	—	2	4	no	—
194	#10623494	—	2	1	no	—
195	#10623494	—	2	1	no	—
196	#10623494	—	2	1	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	1	no	—
199	#10623494	—	4	2	no	—
200	#10623494	#137	1	2	yes	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	2	2	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	1	no	—
205	C₂²×C₈₉	—	4	1	no	—
206	C₂²×C₈₉	—	4	1	no	—
207	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	4	2	no	—
213	C₄×C₈₉	—	4	1	no	—
214	C₄×C₈₉	—	4	1	no	—
215	C₄×C₈₉	—	4	2	no	—
216	C₄×C₈₉	#443	1	2	yes	—
217	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
218	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
219	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
220	C₄×C₈₉	#575	1	1	yes	characteristic
221	#17913	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	4	1	no	—
223	C₂×C₈₉	—	4	2	no	—
224	C₂×C₈₉	#2929	1	1	yes	characteristic
225	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
226	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
227	#3107	D₈₉	1	1	yes	characteristic
228	C₈×#41	—	89	1	no	—
229	#2960	—	89	1	no	—
230	#1587	—	89	2	no	—
231	#1585	—	89	2	no	—
232	C₈×Q₁₆	—	89	2	no	—
233	C₈×SD₁₆	—	89	2	no	—
234	#1574	—	89	1	no	—
235	#1489	—	89	1	no	—
236	#1485	—	89	1	no	—
237	C₈×M₁₆	—	89	1	no	—
238	C₈₉	#17913	1	1	yes	characteristic, complemented, Sylow
239	#533	C₂×D₈₉	1	1	yes	characteristic
240	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
241	#485	Dic₈₉	1	2	yes	—
242	#475	Dic₈₉	1	1	yes	characteristic
243	#474	Dic₈₉	1	1	yes	characteristic
244	#462	Dic₈₉	1	1	yes	characteristic
245	#461	Dic₈₉	1	1	yes	characteristic
246	#452	Dic₈₉	1	2	yes	—
247	#446	—	89	2	no	—
248	#446	—	178	1	no	—
249	C₈×Q₈	—	89	2	no	—
250	C₈×Q₈	—	89	1	no	—
251	C₈×Q₈	—	89	1	no	—
252	C₈×Q₈	—	178	1	no	—
253	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
254	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
255	C₈×D₄	—	89	1	no	—
256	C₈×D₄	—	89	1	no	—
257	C₈×D₄	—	178	1	no	—
258	C₈×D₄	—	178	1	no	—
259	#431	—	89	1	no	—
260	#431	—	178	1	no	—
261	#431	C₂×D₈₉	1	1	yes	characteristic
262	#424	—	178	1	no	—
263	#423	—	89	1	no	—
264	#405	—	178	1	no	—
265	C₄×M₁₆	—	89	1	no	—
266	C₂×C₄×C₈	—	89	1	no	—
267	C₂×C₄×C₈	—	178	1	no	—
268	#335	—	89	2	no	—
269	#334	—	89	2	no	—
270	Q₈⋊C₈	—	89	2	no	—
271	Q₈⋊C₈	—	89	2	no	—
272	Q₈⋊C₈	—	89	2	no	—
273	D₄⋊C₈	—	89	2	no	—
274	#322	—	89	2	no	—
275	C₈²	—	89	2	no	—
276	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
277	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
278	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
279	C₂×M₁₆	—	178	1	no	—
280	C₂×M₁₆	—	178	1	no	—
281	C₂²×C₈	—	89	1	no	—
282	C₂²×C₈	—	89	1	no	—
283	C₂²×C₈	—	178	1	no	—
284	C₂²×C₈	—	178	1	no	—
285	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
292	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	C₂×Dic₈₉	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
303	#107	C₂×Dic₈₉	1	2	yes	—
304	#106	C₂×Dic₈₉	1	2	yes	—
305	C₄⋊C₈	—	89	2	no	—
306	C₄⋊C₈	—	89	1	no	—
307	C₄⋊C₈	—	89	1	no	—
308	C₄⋊C₈	—	178	2	no	—
309	C₄⋊C₈	—	178	2	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	—	178	1	no	—
312	C₄⋊C₈	—	178	1	no	—
313	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
315	#103	C₂×Dic₈₉	1	2	yes	—
316	#103	C₂×Dic₈₉	1	2	yes	—
317	#103	C₂×Dic₈₉	1	2	yes	—
318	#102	C₂×Dic₈₉	1	2	yes	—
319	C₂²⋊C₈	—	178	1	no	—
320	C₂²⋊C₈	—	178	1	no	—
321	C₂²⋊C₈	—	178	1	no	—
322	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
323	#97	—	178	2	no	—
324	#97	—	178	1	no	—
325	C₄×C₈	—	89	1	no	—
326	C₄×C₈	—	89	1	no	—
327	C₄×C₈	—	89	1	no	—
328	C₄×C₈	—	89	1	no	—
329	C₄×C₈	—	89	2	no	—
330	C₄×C₈	—	178	1	no	—
331	C₄×C₈	—	178	1	no	—
332	C₄×C₈	—	178	2	no	—
333	C₄×C₈	—	178	1	no	—
334	C₄×C₈	C₂²×D₈₉	1	2	yes	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
339	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	#13083573	1	1	yes	characteristic
348	Q₁₆	—	2	4	no	—
349	SD₁₆	—	2	4	no	—
350	M₁₆	—	356	2	no	—
351	M₁₆	—	178	4	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	89	1	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	356	2	no	—
358	C₂×C₈	—	356	1	no	—
359	C₂×C₈	—	178	2	no	—
360	C₂×C₈	—	178	1	no	—
361	C₂×C₈	—	178	1	no	—
362	C₂×C₈	—	178	2	no	—
363	C₂×C₈	—	178	2	no	—
364	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
365	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
374	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
375	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
385	C₄²	D₄×D₈₉	1	1	yes	characteristic
386	C₄²	#13083573	1	1	yes	characteristic
387	C₄²	C₂³×D₈₉	1	1	yes	characteristic
388	C₂³	—	2	1	no	—
389	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
390	Q₈	—	2	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	#15668019	1	2	yes	—
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	#15668019	1	2	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
413	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
414	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	89	2	no	—
421	C₈	—	356	1	no	—
422	C₈	—	356	1	no	—
423	C₈	—	356	2	no	—
424	C₈	—	178	4	no	—
425	C₈	—	178	1	no	—
426	C₈	—	178	1	no	—
427	C₈	—	178	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	#19151715	1	2	yes	—
444	C₄	C₂×#15668019	1	1	yes	characteristic
445	C₄	C₂×#15668019	1	1	yes	characteristic
446	C₄	#137×D₈₉	1	1	yes	characteristic
447	C₄	#19152397	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	#26028947	1	1	yes	characteristic
451	C₂	#137×Dic₈₉	1	1	yes	characteristic
452	C₂	C₂×#19151715	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3107	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3107	D₈₉
hypocenter	C₈₉	#17913
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #26029187	C₂	semidirect
3. #26019124	C₂	semidirect
4. #26019110	C₂	semidirect
5. Q₁₆×#10623494	C₂	semidirect
6. SD₁₆×#10623494	C₂	semidirect
7. #26019041	C₂	semidirect
9. #26018673	C₂	semidirect
10. #26018533	C₂	semidirect
238. C₈₉	#17913	semidirect

Maximal subgroups

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

subgroup	index
#41×#10623494	2
#26029187	2
#26019124	2
#26019110	2
Q₁₆×#10623494	2
SD₁₆×#10623494	2
#26019041	2
#26018691	2
#26018673	2
#26018533	2
C₈₉×#3107	2
#17913	89