Subgroups — #36524079

Order 22784.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029363	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029293	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019131	C₂	1	2	yes	maximal, complemented
4	#26019117	C₂	1	2	yes	maximal, complemented
5	#26019096	C₂	1	2	yes	maximal, complemented
6	#26019082	C₂	1	2	yes	maximal, complemented
7	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018634	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic
12	Q₈×#10623494	C₂²	1	2	yes	complemented
13	#19151676	—	2	1	no	—
14	#19151676	—	2	1	no	—
15	#19151676	C₂²	1	2	yes	—
16	#19151676	C₂²	1	2	yes	—
17	D₄×#10623494	—	2	2	no	—
18	D₄×#10623494	C₂²	1	2	yes	complemented
19	#19151651	—	2	1	no	—
20	#19151651	C₂²	1	1	yes	characteristic
21	#19151651	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#10623494	—	2	1	no	—
23	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
24	#19151562	—	2	2	no	—
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151351	C₂²	1	2	yes	complemented
27	#19151349	C₂²	1	2	yes	complemented
28	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
29	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
30	D₄⋊#10623494	C₂²	1	2	yes	—
31	D₄⋊#10623494	C₂²	1	2	yes	—
32	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
33	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
34	#19151320	C₂²	1	2	yes	complemented
35	#19151320	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₈₉	C₄	1	1	yes	characteristic
37	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
39	#442×C₈₉	C₄	1	2	yes	—
40	#440×C₈₉	C₄	1	2	yes	—
41	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
42	C₄×D₈×C₈₉	C₂²	1	2	yes	—
43	#428×C₈₉	C₄	1	1	yes	characteristic
44	#418×C₈₉	C₄	1	1	yes	characteristic
45	#417×C₈₉	C₄	1	1	yes	characteristic
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083558	—	2	2	no	—
48	C₂×#13083558	—	2	2	no	—
49	C₂²×#10623494	—	2	2	no	—
50	C₂²×#10623494	—	2	1	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	D₄	1	1	yes	characteristic
55	C₄⋊#10623494	D₄	1	1	yes	characteristic
56	C₄⋊#10623494	C₂³	1	2	yes	—
57	C₄⋊#10623494	C₂³	1	1	yes	characteristic
58	C₄⋊#10623494	C₂³	1	1	yes	characteristic
59	C₂²⋊#10623494	—	2	2	no	—
60	C₂²⋊#10623494	—	2	2	no	—
61	C₂²⋊#10623494	—	2	2	no	—
62	C₂²⋊#10623494	—	2	1	no	—
63	C₂²⋊#10623494	D₄	1	2	yes	—
64	C₄×#10623494	—	2	2	no	—
65	C₄×#10623494	—	2	1	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₄×#10623494	C₂³	1	1	yes	characteristic
68	C₄×#10623494	C₂³	1	1	yes	characteristic
69	C₄×#10623494	C₂³	1	2	yes	—
70	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₈₉	—	2	1	no	—
73	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
74	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
76	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
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	2	yes	—
88	#117×C₈₉	—	2	1	no	—
89	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	#107×C₈₉	C₂×C₄	1	2	yes	—
95	#106×C₈₉	C₂×C₄	1	2	yes	—
96	#103×C₈₉	C₂×C₄	1	2	yes	—
97	#102×C₈₉	C₂×C₄	1	2	yes	—
98	#102×C₈₉	C₂×C₄	1	2	yes	—
99	#102×C₈₉	C₂×C₄	1	2	yes	—
100	#97×C₈₉	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083558	—	8	2	no	—
103	#13083558	—	8	2	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	1	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	—	4	2	no	—
110	C₂×#10623494	—	8	2	no	—
111	C₂×#10623494	—	8	1	no	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₂×#10623494	C₂×D₄	1	2	yes	—
114	C₂⁴×C₈₉	—	2	1	no	—
115	#41×C₈₉	—	2	2	no	—
116	#41×C₈₉	M₁₆	1	4	yes	complemented
117	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₈₉	—	2	1	no	—
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	—	2	2	no	—
121	C₂×D₄×C₈₉	—	2	2	no	—
122	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
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	2	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	2	2	no	—
130	C₂²×C₄×C₈₉	—	8	1	no	—
131	C₂²×C₄×C₈₉	—	8	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	SD₁₆×C₈₉	—	2	4	no	—
136	D₈×C₈₉	—	2	4	no	—
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₂²⋊C₄×C₈₉	—	2	2	no	—
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	2	2	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	#41	1	1	yes	characteristic
158	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	—	2	2	no	—
161	C₂³×C₈₉	—	4	2	no	—
162	C₂³×C₈₉	—	8	1	no	—
163	C₂³×C₈₉	—	8	1	no	—
164	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₈₉	—	2	1	no	—
166	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
167	D₄×C₈₉	—	2	4	no	—
168	D₄×C₈₉	—	2	2	no	—
169	D₄×C₈₉	—	2	1	no	—
170	D₄×C₈₉	—	2	2	no	—
171	D₄×C₈₉	—	4	2	no	—
172	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
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	4	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	4	1	no	—
181	C₂×C₄×C₈₉	—	4	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	—	8	1	no	—
186	C₂×C₄×C₈₉	—	8	2	no	—
187	C₂×C₄×C₈₉	—	8	1	no	—
188	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₈₉	#131	1	2	yes	—
193	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
196	C₈×C₈₉	—	2	2	no	—
197	C₈×C₈₉	—	2	2	no	—
198	#10623494	—	2	2	no	—
199	#10623494	—	2	2	no	—
200	#10623494	—	2	2	no	—
201	#10623494	—	4	1	no	—
202	#10623494	—	4	2	no	—
203	#10623494	—	4	1	no	—
204	#10623494	—	4	1	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	—	4	2	no	—
212	C₂²×C₈₉	—	4	2	no	—
213	C₂²×C₈₉	—	8	4	no	—
214	C₂²×C₈₉	#435	1	2	yes	—
215	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₈₉	—	2	2	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	4	1	no	—
221	C₄×C₈₉	—	4	2	no	—
222	C₄×C₈₉	—	4	1	no	—
223	C₄×C₈₉	#435	1	2	yes	—
224	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
225	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
226	C₄×C₈₉	#576	1	1	yes	characteristic
227	C₄×C₈₉	#577	1	1	yes	characteristic
228	#17875	—	89	1	no	maximal, Sylow
229	C₂×C₈₉	—	2	2	no	—
230	C₂×C₈₉	—	4	2	no	—
231	C₂×C₈₉	—	8	2	no	—
232	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
233	C₂×C₈₉	#2946	1	1	yes	characteristic
234	C₂×C₈₉	#2956	1	1	yes	characteristic
235	#2988	—	89	1	no	—
236	#2975	—	89	1	no	—
237	C₄×AGL(1,ℤ/8)	D₈₉	1	1	yes	characteristic
238	#1588	—	89	2	no	—
239	#1586	—	89	2	no	—
240	#1583	—	89	2	no	—
241	#1581	—	89	2	no	—
242	#1565	—	89	1	no	—
243	#1476	—	89	1	no	—
244	C₂×D₄⋊C₈	—	89	1	no	—
245	#1451	—	89	1	no	—
246	C₈₉	#17875	1	1	yes	characteristic, complemented, Sylow
247	C₂×AGL(1,ℤ/8)	Dic₈₉	1	1	yes	characteristic
248	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
250	C₈×Q₈	—	89	2	no	—
251	#442	Dic₈₉	1	2	yes	—
252	#440	Dic₈₉	1	2	yes	—
253	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
254	C₄×D₈	C₂×D₈₉	1	2	yes	—
255	#436	—	89	2	no	—
256	#436	—	89	2	no	—
257	#436	—	178	1	no	—
258	#436	—	178	1	no	—
259	C₈×D₄	—	89	2	no	—
260	C₈×D₄	—	178	2	no	—
261	#431	—	89	1	no	—
262	#431	—	89	1	no	—
263	#431	—	178	1	no	—
264	#428	Dic₈₉	1	1	yes	characteristic
265	C₂×C₄⋊C₈	—	89	1	no	—
266	C₂×C₄⋊C₈	—	178	1	no	—
267	#418	Dic₈₉	1	1	yes	characteristic
268	#417	Dic₈₉	1	1	yes	characteristic
269	#407	—	178	2	no	—
270	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
271	C₂×C₄×C₈	—	89	1	no	—
272	#335	—	89	2	no	—
273	#334	—	89	2	no	—
274	Q₈⋊C₈	—	89	1	no	—
275	Q₈⋊C₈	—	89	1	no	—
276	D₄⋊C₈	—	89	1	no	—
277	D₄⋊C₈	—	89	2	no	—
278	D₄⋊C₈	—	89	1	no	—
279	D₄⋊C₈	—	89	2	no	—
280	#322	—	89	2	no	—
281	#322	—	89	2	no	—
282	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
283	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	—	2	4	no	—
286	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
287	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
288	C₂×M₁₆	—	178	2	no	—
289	C₂×M₁₆	—	178	2	no	—
290	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
292	C₂²×C₈	—	178	2	no	—
293	C₂²×C₈	—	178	1	no	—
294	C₂²×C₈	—	178	1	no	—
295	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
302	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₈₉	1	2	yes	—
304	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₂×Dic₈₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
311	#107	C₂×Dic₈₉	1	2	yes	—
312	#106	C₂×Dic₈₉	1	2	yes	—
313	C₄⋊C₈	—	89	1	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	89	2	no	—
316	C₄⋊C₈	—	89	1	no	—
317	C₄⋊C₈	—	89	1	no	—
318	C₄⋊C₈	—	178	2	no	—
319	C₄⋊C₈	—	178	1	no	—
320	#103	C₂×Dic₈₉	1	2	yes	—
321	#102	C₂×Dic₈₉	1	2	yes	—
322	#102	C₂×Dic₈₉	1	2	yes	—
323	#102	C₂×Dic₈₉	1	2	yes	—
324	C₂²⋊C₈	—	89	2	no	—
325	C₂²⋊C₈	—	178	2	no	—
326	C₂²⋊C₈	—	178	2	no	—
327	C₂²⋊C₈	—	178	2	no	—
328	C₂²⋊C₈	—	178	1	no	—
329	#97	C₂×Dic₈₉	1	2	yes	—
330	C₄×C₈	—	89	2	no	—
331	C₄×C₈	—	89	1	no	—
332	C₄×C₈	—	89	1	no	—
333	C₄×C₈	—	178	2	no	—
334	C₄×C₈	—	178	1	no	—
335	C₄×C₈	—	178	1	no	—
336	C₄×C₈	C₂²×D₈₉	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	2	2	no	—
339	#41	#13083558	1	4	yes	complemented
340	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
346	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
357	C₂²×C₄	#13083573	1	1	yes	characteristic
358	SD₁₆	—	2	4	no	—
359	D₈	—	2	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	712	2	no	—
363	M₁₆	—	712	2	no	—
364	C₂×C₈	—	89	2	no	—
365	C₂×C₈	—	89	2	no	—
366	C₂×C₈	—	356	2	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	—	178	1	no	—
371	C₂×C₈	—	178	1	no	—
372	C₂×C₈	—	712	1	no	—
373	C₂×C₈	—	712	2	no	—
374	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
375	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
391	C₄²	D₄×D₈₉	1	1	yes	characteristic
392	C₄²	#13083573	1	1	yes	characteristic
393	C₄²	C₂³×D₈₉	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×#13083558	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	C₂×#13083558	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
424	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#13083558	1	2	yes	—
427	C₂×C₄	#15668019	1	2	yes	—
428	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	356	1	no	—
434	C₈	—	356	2	no	—
435	C₈	—	356	1	no	—
436	C₈	—	356	1	no	—
437	C₈	—	178	2	no	—
438	C₈	—	178	2	no	—
439	C₈	—	178	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	#19151670	1	2	yes	—
450	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	#19151670	1	2	yes	—
459	C₄	C₂²×#13083558	1	1	yes	characteristic
460	C₄	C₂×#15668019	1	1	yes	characteristic
461	C₄	#19152402	1	1	yes	characteristic
462	C₄	#19152408	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₂×#19151670	1	1	yes	characteristic
467	C₂	#26029085	1	1	yes	characteristic
468	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	C₄×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#17875
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #26029363	C₂	semidirect
2. #26029293	C₂	semidirect
3. #26019131	C₂	semidirect
4. #26019117	C₂	semidirect
5. #26019096	C₂	semidirect
6. #26019082	C₂	semidirect
7. #26019004	C₂	semidirect
8. #26018634	C₂	semidirect
9. C₂×D₄⋊#10623494	C₂	semidirect
10. #26018539	C₂	semidirect
12. Q₈×#10623494	C₂²	semidirect
18. D₄×#10623494	C₂²	semidirect
26. #19151351	C₂²	semidirect
27. #19151349	C₂²	semidirect
28. Q₈⋊#10623494	C₂²	semidirect
29. Q₈⋊#10623494	C₂²	semidirect
32. D₄⋊#10623494	C₂²	semidirect
33. D₄⋊#10623494	C₂²	semidirect
34. #19151320	C₂²	semidirect
35. #19151320	C₂²	semidirect
116. #41×C₈₉	M₁₆	semidirect
246. C₈₉	#17875	semidirect
339. #41	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26029363	2
#26029293	2
#26019131	2
#26019117	2
#26019096	2
#26019082	2
#26019004	2
#26018634	2
C₂×D₄⋊#10623494	2
#26018539	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#17875	89