Subgroups — #36525327

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	#26029201	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#13083558	C₂	1	1	yes	maximal, characteristic
3	#26019143	C₂	1	2	yes	maximal, complemented
4	#26019096	C₂	1	2	yes	maximal, complemented
5	#26019089	C₂	1	2	yes	maximal, complemented
6	SD₁₆×#10623494	C₂	1	2	yes	maximal, complemented
7	#26019023	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018707	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
10	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3101	C₂	1	1	yes	maximal, characteristic
12	C₂²×#13083558	—	2	1	no	—
13	#19151729	—	2	2	no	—
14	#19151729	C₂²	1	2	yes	complemented
15	Q₈×#10623494	C₂²	1	2	yes	complemented
16	#19151676	C₂²	1	2	yes	—
17	#19151670	—	2	2	no	—
18	D₄×#10623494	C₂²	1	2	yes	—
19	#19151625	—	2	1	no	—
20	#19151622	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
22	#19151562	—	2	1	no	—
23	#19151554	—	2	1	no	—
24	C₄×#13083558	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151349	C₂²	1	2	yes	complemented
27	#19151349	C₂²	1	2	yes	complemented
28	Q₈⋊#10623494	C₂²	1	2	yes	complemented
29	Q₈⋊#10623494	C₂²	1	2	yes	complemented
30	D₄⋊#10623494	C₂²	1	1	yes	characteristic
31	D₄⋊#10623494	C₂²	1	1	yes	characteristic
32	D₄⋊#10623494	C₂²	1	1	yes	characteristic
33	D₄⋊#10623494	C₂²	1	1	yes	characteristic
34	#19151320	C₂²	1	2	yes	complemented
35	C₈×#10623494	C₂²	1	2	yes	complemented
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
38	#483×C₈₉	C₄	1	2	yes	—
39	#476×C₈₉	C₄	1	1	yes	characteristic
40	#476×C₈₉	C₄	1	1	yes	characteristic
41	#461×C₈₉	C₄	1	1	yes	characteristic
42	#461×C₈₉	C₄	1	1	yes	characteristic
43	#450×C₈₉	C₄	1	2	yes	—
44	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083558	—	2	2	no	—
48	C₂×#13083558	—	2	1	no	—
49	C₂×#13083558	—	4	4	no	—
50	C₂×#13083558	D₄	1	1	yes	characteristic
51	C₂×#13083558	D₄	1	1	yes	characteristic
52	C₂²×#10623494	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂²×#10623494	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
60	C₄⋊#10623494	C₂³	1	1	yes	characteristic
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₂²⋊#10623494	—	2	2	no	—
63	C₂²⋊#10623494	—	2	2	no	—
64	#15667923	—	2	2	no	—
65	#15667923	D₄	1	2	yes	—
66	C₄×#10623494	—	2	2	no	—
67	C₄×#10623494	—	2	1	no	—
68	C₄×#10623494	C₂³	1	1	yes	characteristic
69	C₄×#10623494	C₂³	1	1	yes	characteristic
70	C₄×#10623494	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₈₉	—	2	1	no	—
73	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
74	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
75	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
77	#125×C₈₉	—	2	1	no	—
78	C₂²⋊Q₈×C₈₉	—	2	1	no	—
79	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₈₉	—	2	1	no	—
81	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	#117×C₈₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	#106×C₈₉	C₂×C₄	1	2	yes	—
93	#106×C₈₉	C₂×C₄	1	2	yes	—
94	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	#103×C₈₉	C₂×C₄	1	2	yes	—
97	#103×C₈₉	C₂×C₄	1	2	yes	—
98	#102×C₈₉	C₂×C₄	1	2	yes	—
99	#102×C₈₉	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083558	—	2	2	no	—
103	#13083558	—	4	2	no	—
104	#13083558	—	4	4	no	—
105	#13083558	SD₁₆	1	4	yes	complemented
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	—	2	1	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	—	4	2	no	—
112	C₂×#10623494	—	4	2	no	—
113	C₂×#10623494	—	4	4	no	—
114	C₂×#10623494	C₂×D₄	1	2	yes	—
115	C₂×#10623494	C₂×D₄	1	2	yes	—
116	C₂⁴×C₈₉	—	2	1	no	—
117	C₂×Q₈×C₈₉	—	2	1	no	—
118	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	—	4	1	no	—
122	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	4	2	no	—
130	C₂²×C₄×C₈₉	—	4	2	no	—
131	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	SD₁₆×C₈₉	—	2	4	no	—
135	SD₁₆×C₈₉	—	4	2	no	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
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	2	no	—
143	C₄⋊C₄×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₂²⋊C₄×C₈₉	—	2	1	no	—
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	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	—	2	1	no	—
158	C₂³×C₈₉	—	2	1	no	—
159	C₂³×C₈₉	—	4	2	no	—
160	C₂³×C₈₉	—	4	2	no	—
161	C₂³×C₈₉	—	8	1	no	—
162	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
163	Q₈×C₈₉	—	2	2	no	—
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	8	1	no	—
166	D₄×C₈₉	—	2	1	no	—
167	D₄×C₈₉	—	2	1	no	—
168	D₄×C₈₉	—	2	1	no	—
169	D₄×C₈₉	—	4	2	no	—
170	D₄×C₈₉	#131	1	2	yes	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	4	1	no	—
181	C₂×C₄×C₈₉	—	4	1	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	2	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	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₈₉	#135	1	2	yes	—
190	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	2	2	no	—
195	#10623494	—	2	2	no	—
196	#10623494	—	2	2	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	2	no	—
199	#10623494	—	4	1	no	—
200	#10623494	—	4	1	no	—
201	#10623494	C₂×SD₁₆	1	4	yes	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	4	1	no	—
206	C₂²×C₈₉	—	4	1	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	8	4	no	—
211	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
212	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
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	1	no	—
218	C₄×C₈₉	—	4	1	no	—
219	C₄×C₈₉	—	4	2	no	—
220	C₄×C₈₉	C₄×SD₁₆	1	2	yes	—
221	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
222	C₄×C₈₉	#568	1	1	yes	characteristic
223	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
224	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
225	#17995	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	2	2	no	—
227	C₂×C₈₉	—	4	2	no	—
228	C₂×C₈₉	—	8	1	no	—
229	C₂×C₈₉	#2933	1	1	yes	characteristic
230	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
231	C₂×C₈₉	#2956	1	1	yes	characteristic
232	#3101	D₈₉	1	1	yes	characteristic
233	#2962	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
247	#483	Dic₈₉	1	2	yes	—
248	#476	Dic₈₉	1	1	yes	characteristic
249	#476	Dic₈₉	1	1	yes	characteristic
250	#461	Dic₈₉	1	1	yes	characteristic
251	#461	Dic₈₉	1	1	yes	characteristic
252	#450	Dic₈₉	1	2	yes	—
253	#446	—	89	2	no	—
254	#446	—	178	2	no	—
255	C₈×Q₈	—	89	2	no	—
256	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
257	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
258	#436	—	89	2	no	—
259	#435	—	178	2	no	—
260	C₈×D₄	—	89	2	no	—
261	#431	C₂×D₈₉	1	1	yes	characteristic
262	#424	—	178	1	no	—
263	#423	—	89	1	no	—
264	C₂×C₄⋊C₈	—	89	1	no	—
265	#407	—	178	1	no	—
266	#405	—	178	1	no	—
267	C₄×M₁₆	—	89	1	no	—
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	C₂×Dic₈₉	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
282	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
283	C₂×M₁₆	—	89	1	no	—
284	C₂×M₁₆	—	89	1	no	—
285	C₂×M₁₆	—	356	4	no	—
286	C₂×M₁₆	—	178	2	no	—
287	C₂×M₁₆	—	178	1	no	—
288	C₂²×C₈	—	178	2	no	—
289	C₂²×C₈	—	178	1	no	—
290	C₂²×C₈	—	178	1	no	—
291	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
292	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
301	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
302	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
308	#106	C₂×Dic₈₉	1	2	yes	—
309	#106	C₂×Dic₈₉	1	2	yes	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	2	no	—
313	C₄⋊C₈	—	178	2	no	—
314	C₄⋊C₈	—	178	2	no	—
315	C₄⋊C₈	—	178	1	no	—
316	C₄⋊C₈	—	178	1	no	—
317	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
319	#103	C₂×Dic₈₉	1	2	yes	—
320	#103	C₂×Dic₈₉	1	2	yes	—
321	#102	C₂×Dic₈₉	1	2	yes	—
322	#102	C₂×Dic₈₉	1	2	yes	—
323	C₂²⋊C₈	—	178	2	no	—
324	C₂²⋊C₈	—	178	2	no	—
325	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
326	#97	—	89	2	no	—
327	#97	—	178	2	no	—
328	C₄×C₈	—	89	2	no	—
329	C₄×C₈	—	89	1	no	—
330	C₄×C₈	—	89	1	no	—
331	C₄×C₈	—	178	2	no	—
332	C₄×C₈	—	178	1	no	—
333	C₄×C₈	C₂²×D₈₉	1	2	yes	—
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
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	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	#13083573	1	1	yes	characteristic
352	SD₁₆	—	2	4	no	—
353	SD₁₆	—	4	2	no	—
354	M₁₆	—	89	4	no	—
355	M₁₆	—	356	4	no	—
356	M₁₆	—	356	2	no	—
357	M₁₆	—	178	2	no	—
358	C₂×C₈	—	89	2	no	—
359	C₂×C₈	—	89	2	no	—
360	C₂×C₈	—	356	4	no	—
361	C₂×C₈	—	356	2	no	—
362	C₂×C₈	—	356	2	no	—
363	C₂×C₈	—	178	1	no	—
364	C₂×C₈	—	178	1	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	1	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
369	C₂×C₈	C₂²×Dic₈₉	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	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
377	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
386	C₄²	D₄×D₈₉	1	1	yes	characteristic
387	C₄²	#13083573	1	1	yes	characteristic
388	C₄²	C₂³×D₈₉	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	2	1	no	—
401	D₄	—	4	2	no	—
402	D₄	#15668019	1	2	yes	—
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	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
418	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
419	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
420	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
421	C₂×C₄	#15668033	1	2	yes	—
422	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	89	4	no	—
428	C₈	—	356	1	no	—
429	C₈	—	356	2	no	—
430	C₈	—	356	1	no	—
431	C₈	—	356	1	no	—
432	C₈	—	178	2	no	—
433	C₈	—	178	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	8	4	no	—
443	C₂²	SD₁₆×Dic₈₉	1	2	yes	—
444	C₂²	C₂×D₄×Dic₈₉	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	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	SD₁₆×Dic₈₉	1	2	yes	—
453	C₄	C₂×#15668019	1	1	yes	characteristic
454	C₄	#19152365	1	1	yes	characteristic
455	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
456	C₄	C₂×#15668033	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#26028979	1	1	yes	characteristic
461	C₂	C₂×SD₁₆×Dic₈₉	1	1	yes	characteristic
462	C₂	#26029162	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×#3101	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3101	D₈₉
hypocenter	C₈₉	#17995
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #26029201	C₂	semidirect
3. #26019143	C₂	semidirect
4. #26019096	C₂	semidirect
5. #26019089	C₂	semidirect
6. SD₁₆×#10623494	C₂	semidirect
7. #26019023	C₂	semidirect
8. #26018707	C₂	semidirect
10. #26018533	C₂	semidirect
14. #19151729	C₂²	semidirect
15. Q₈×#10623494	C₂²	semidirect
26. #19151349	C₂²	semidirect
27. #19151349	C₂²	semidirect
28. Q₈⋊#10623494	C₂²	semidirect
29. Q₈⋊#10623494	C₂²	semidirect
34. #19151320	C₂²	semidirect
35. C₈×#10623494	C₂²	semidirect
105. #13083558	SD₁₆	semidirect
243. C₈₉	#17995	semidirect

Maximal subgroups

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

subgroup	index
#26029201	2
D₄×#13083558	2
#26019143	2
#26019096	2
#26019089	2
SD₁₆×#10623494	2
#26019023	2
#26018707	2
C₂×D₄⋊#10623494	2
#26018533	2
C₈₉×#3101	2
#17995	89