Subgroups — #36525481

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029266	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028996	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019155	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019143	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019117	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019110	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019089	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019082	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019076	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019037	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018721	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018639	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018547	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic
16	C₂×#15668019	—	2	1	no	—
17	#19151729	C₂²	1	1	yes	characteristic
18	#19151729	C₂²	1	1	yes	characteristic
19	#19151676	C₂²	1	1	yes	characteristic
20	#19151676	C₂²	1	1	yes	characteristic
21	#19151670	—	2	1	no	—
22	#19151670	—	2	1	no	—
23	#19151670	—	2	1	no	—
24	#19151670	—	2	1	no	—
25	D₄×#10623494	C₂²	1	1	yes	characteristic
26	D₄×#10623494	C₂²	1	1	yes	characteristic
27	D₄×#10623494	C₂²	1	1	yes	characteristic
28	D₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151655	—	2	1	no	—
30	#19151655	C₂²	1	1	yes	characteristic
31	#19151651	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
33	#19151565	—	2	1	no	—
34	C₄×#13083558	C₂²	1	1	yes	characteristic
35	C₂×#15667923	—	2	1	no	—
36	#19151351	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151349	C₂²	1	1	yes	characteristic
39	#19151349	C₂²	1	1	yes	characteristic
40	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
41	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
42	D₄⋊#10623494	C₂²	1	1	yes	characteristic
43	D₄⋊#10623494	C₂²	1	1	yes	characteristic
44	D₄⋊#10623494	C₂²	1	1	yes	characteristic
45	D₄⋊#10623494	C₂²	1	1	yes	characteristic
46	D₄⋊#10623494	C₂²	1	1	yes	characteristic
47	D₄⋊#10623494	C₂²	1	1	yes	characteristic
48	#19151320	C₂²	1	1	yes	characteristic
49	#19151320	C₂²	1	1	yes	characteristic
50	#19151319	C₂²	1	1	yes	characteristic
51	C₈×#10623494	C₂²	1	1	yes	characteristic
52	#532×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	#482×C₈₉	C₄	1	1	yes	characteristic
55	#482×C₈₉	C₄	1	1	yes	characteristic
56	#477×C₈₉	C₄	1	1	yes	characteristic
57	#476×C₈₉	C₄	1	1	yes	characteristic
58	#460×C₈₉	C₄	1	1	yes	characteristic
59	#459×C₈₉	C₄	1	1	yes	characteristic
60	#449×C₈₉	C₄	1	1	yes	characteristic
61	#449×C₈₉	C₄	1	1	yes	characteristic
62	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
66	#431×C₈₉	C₂²	1	1	yes	characteristic
67	#15668019	—	4	4	no	—
68	C₂×#13083558	—	2	1	no	—
69	C₂×#13083558	—	2	1	no	—
70	C₂×#13083558	D₄	1	1	yes	characteristic
71	C₂×#13083558	D₄	1	1	yes	characteristic
72	C₂²×#10623494	—	2	1	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₂²×#10623494	—	2	1	no	—
75	C₂²×#10623494	—	2	1	no	—
76	C₂²×#10623494	—	2	1	no	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	—	2	1	no	—
80	C₄⋊#10623494	—	2	1	no	—
81	C₄⋊#10623494	C₂³	1	1	yes	characteristic
82	C₄⋊#10623494	C₂³	1	1	yes	characteristic
83	C₄⋊#10623494	C₂³	1	1	yes	characteristic
84	C₄⋊#10623494	C₂³	1	1	yes	characteristic
85	C₂²⋊#10623494	—	2	1	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	C₂²⋊#10623494	—	2	1	no	—
88	C₂²⋊#10623494	—	2	1	no	—
89	C₂²⋊#10623494	—	2	1	no	—
90	C₂²⋊#10623494	—	2	1	no	—
91	C₂²⋊#10623494	—	2	1	no	—
92	C₂²⋊#10623494	—	2	1	no	—
93	#15667923	—	2	1	no	—
94	#15667923	—	2	1	no	—
95	#15667923	—	2	1	no	—
96	#15667923	D₄	1	1	yes	characteristic
97	#15667923	D₄	1	1	yes	characteristic
98	C₄×#10623494	C₂³	1	1	yes	characteristic
99	C₄×#10623494	C₂³	1	1	yes	characteristic
100	C₄×#10623494	C₂³	1	1	yes	characteristic
101	C₄×#10623494	C₂³	1	1	yes	characteristic
102	C₂×#41×C₈₉	—	2	1	no	—
103	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
109	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
110	#124×C₈₉	—	2	1	no	—
111	#121×C₈₉	—	2	1	no	—
112	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
113	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄×D₄×C₈₉	—	2	1	no	—
117	C₄×D₄×C₈₉	—	2	1	no	—
118	C₄×D₄×C₈₉	—	2	1	no	—
119	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
123	#117×C₈₉	—	2	1	no	—
124	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	—	2	1	no	—
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
128	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
129	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
130	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
132	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
135	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
142	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	#13083558	—	2	2	no	—
146	#13083558	—	4	1	no	—
147	#13083558	—	4	2	no	—
148	#13083558	—	4	2	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	4	2	no	—
156	C₂×#10623494	—	4	2	no	—
157	C₂×#10623494	—	4	2	no	—
158	C₂×#10623494	—	4	2	no	—
159	C₂×#10623494	—	4	2	no	—
160	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
161	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
162	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
163	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
164	#41×C₈₉	—	2	2	no	—
165	#41×C₈₉	—	4	1	no	—
166	#41×C₈₉	—	4	2	no	—
167	#41×C₈₉	—	4	2	no	—
168	C₂×Q₈×C₈₉	—	2	1	no	—
169	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	1	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
186	SD₁₆×C₈₉	—	4	1	no	—
187	SD₁₆×C₈₉	—	4	1	no	—
188	D₈×C₈₉	—	2	2	no	—
189	D₈×C₈₉	—	2	2	no	—
190	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₂²⋊C₄×C₈₉	—	2	1	no	—
203	C₂²⋊C₄×C₈₉	—	2	1	no	—
204	C₂²⋊C₄×C₈₉	—	2	1	no	—
205	C₂²⋊C₄×C₈₉	—	2	1	no	—
206	C₂²⋊C₄×C₈₉	—	2	1	no	—
207	C₂²⋊C₄×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	2	1	no	—
209	C₄²×C₈₉	—	2	1	no	—
210	C₄²×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₈₉	#41	1	1	yes	characteristic
214	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂³×C₈₉	—	2	1	no	—
216	C₂³×C₈₉	—	2	1	no	—
217	C₂³×C₈₉	—	2	1	no	—
218	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
219	Q₈×C₈₉	—	2	1	no	—
220	Q₈×C₈₉	—	2	1	no	—
221	Q₈×C₈₉	—	4	2	no	—
222	D₄×C₈₉	—	2	1	no	—
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	2	1	no	—
225	D₄×C₈₉	—	2	1	no	—
226	D₄×C₈₉	—	2	1	no	—
227	D₄×C₈₉	—	4	2	no	—
228	D₄×C₈₉	—	4	2	no	—
229	D₄×C₈₉	—	4	2	no	—
230	D₄×C₈₉	—	4	2	no	—
231	D₄×C₈₉	—	8	1	no	—
232	D₄×C₈₉	#131	1	2	yes	complemented
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	1	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	1	no	—
242	C₂×C₄×C₈₉	—	4	1	no	—
243	C₂×C₄×C₈₉	—	4	2	no	—
244	C₂×C₄×C₈₉	—	4	1	no	—
245	C₂×C₄×C₈₉	—	4	1	no	—
246	C₂×C₄×C₈₉	—	4	1	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	—	4	1	no	—
250	C₂×C₄×C₈₉	—	8	1	no	—
251	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
257	C₈×C₈₉	—	2	1	no	—
258	C₈×C₈₉	—	2	1	no	—
259	C₈×C₈₉	—	2	1	no	—
260	C₈×C₈₉	—	2	1	no	—
261	#10623494	—	2	1	no	—
262	#10623494	—	2	1	no	—
263	#10623494	—	2	1	no	—
264	#10623494	—	4	1	no	—
265	#10623494	—	4	1	no	—
266	#10623494	—	4	1	no	—
267	#10623494	—	4	1	no	—
268	#10623494	—	4	1	no	—
269	#10623494	—	4	1	no	—
270	#10623494	AGL(1,ℤ/8)	1	2	yes	—
271	C₂²×C₈₉	—	2	1	no	—
272	C₂²×C₈₉	—	2	2	no	—
273	C₂²×C₈₉	—	2	1	no	—
274	C₂²×C₈₉	—	2	1	no	—
275	C₂²×C₈₉	—	4	1	no	—
276	C₂²×C₈₉	—	4	1	no	—
277	C₂²×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	—	4	1	no	—
279	C₂²×C₈₉	—	4	1	no	—
280	C₂²×C₈₉	—	4	1	no	—
281	C₂²×C₈₉	—	4	1	no	—
282	C₂²×C₈₉	—	4	1	no	—
283	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₈₉	—	2	1	no	—
285	C₄×C₈₉	—	2	1	no	—
286	C₄×C₈₉	—	2	1	no	—
287	C₄×C₈₉	—	2	1	no	—
288	C₄×C₈₉	—	4	1	no	—
289	C₄×C₈₉	—	4	1	no	—
290	C₄×C₈₉	—	4	1	no	—
291	C₄×C₈₉	—	4	1	no	—
292	C₄×C₈₉	—	4	1	no	—
293	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
294	C₄×C₈₉	#568	1	1	yes	characteristic
295	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₄×C₈₉	#575	1	1	yes	characteristic
297	#18007	—	89	1	no	maximal, Sylow
298	C₂×C₈₉	—	4	1	no	—
299	C₂×C₈₉	—	4	2	no	—
300	C₂×C₈₉	—	8	1	no	—
301	C₂×C₈₉	—	8	1	no	—
302	C₂×C₈₉	#2933	1	1	yes	characteristic
303	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂×C₈₉	#2957	1	1	yes	characteristic
305	#3106	D₈₉	1	1	yes	characteristic
306	#2970	—	89	1	no	—
307	#2935	—	89	1	no	—
308	#1592	—	89	1	no	—
309	#1590	—	89	1	no	—
310	#1586	—	89	1	no	—
311	#1585	—	89	1	no	—
312	#1582	—	89	1	no	—
313	#1581	—	89	1	no	—
314	#1580	—	89	1	no	—
315	C₈×D₈	—	89	1	no	—
316	#1573	—	89	1	no	—
317	#1496	—	89	1	no	—
318	#1477	—	89	1	no	—
319	#1453	—	89	1	no	—
320	C₈₉	#18007	1	1	yes	characteristic, complemented, Sylow
321	C₂×#131	—	178	1	no	—
322	#532	C₂×D₈₉	1	1	yes	characteristic
323	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
324	#482	Dic₈₉	1	1	yes	characteristic
325	#482	Dic₈₉	1	1	yes	characteristic
326	#477	Dic₈₉	1	1	yes	characteristic
327	#476	Dic₈₉	1	1	yes	characteristic
328	#460	Dic₈₉	1	1	yes	characteristic
329	#459	Dic₈₉	1	1	yes	characteristic
330	#449	Dic₈₉	1	1	yes	characteristic
331	#449	Dic₈₉	1	1	yes	characteristic
332	#446	—	89	1	no	—
333	#446	—	89	1	no	—
334	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
335	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
336	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
337	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
338	#436	—	89	1	no	—
339	#436	—	89	1	no	—
340	#435	—	178	1	no	—
341	#435	—	178	1	no	—
342	#435	—	178	1	no	—
343	#435	—	178	1	no	—
344	C₈×D₄	—	89	1	no	—
345	C₈×D₄	—	89	1	no	—
346	C₈×D₄	—	89	1	no	—
347	C₈×D₄	—	89	1	no	—
348	#432	—	89	1	no	—
349	#432	—	178	1	no	—
350	#431	—	89	1	no	—
351	#431	C₂×D₈₉	1	1	yes	characteristic
352	C₂×C₄⋊C₈	—	89	1	no	—
353	#408	—	178	1	no	—
354	C₄×M₁₆	—	89	1	no	—
355	C₂×#97	—	178	1	no	—
356	#335	—	89	1	no	—
357	#335	—	89	1	no	—
358	#334	—	89	1	no	—
359	#334	—	89	1	no	—
360	Q₈⋊C₈	—	89	1	no	—
361	Q₈⋊C₈	—	89	1	no	—
362	D₄⋊C₈	—	89	1	no	—
363	D₄⋊C₈	—	89	1	no	—
364	D₄⋊C₈	—	89	1	no	—
365	D₄⋊C₈	—	89	1	no	—
366	D₄⋊C₈	—	89	1	no	—
367	D₄⋊C₈	—	89	1	no	—
368	#322	—	89	1	no	—
369	#322	—	89	1	no	—
370	#322	—	89	1	no	—
371	C₈²	—	89	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
374	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
375	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
376	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
377	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
378	#131	—	356	4	no	—
379	C₂×M₁₆	—	89	1	no	—
380	C₂×M₁₆	—	89	1	no	—
381	C₂×M₁₆	—	178	1	no	—
382	C₂×M₁₆	—	178	1	no	—
383	C₂²×C₈	—	178	1	no	—
384	C₂²×C₈	—	178	1	no	—
385	C₂²×C₈	—	178	1	no	—
386	C₂²×C₈	—	178	1	no	—
387	C₂²×C₈	—	178	1	no	—
388	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
389	#127	C₂×Dic₈₉	1	1	yes	characteristic
390	#124	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	C₂×Dic₈₉	1	1	yes	characteristic
393	#121	C₂×Dic₈₉	1	1	yes	characteristic
394	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
395	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
400	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
401	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
402	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
403	#117	—	2	1	no	—
404	#117	C₂×Dic₈₉	1	1	yes	characteristic
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
407	#107	C₂×Dic₈₉	1	1	yes	characteristic
408	#107	C₂×Dic₈₉	1	1	yes	characteristic
409	#106	C₂×Dic₈₉	1	1	yes	characteristic
410	#106	C₂×Dic₈₉	1	1	yes	characteristic
411	C₄⋊C₈	—	89	1	no	—
412	C₄⋊C₈	—	89	1	no	—
413	C₄⋊C₈	—	89	1	no	—
414	C₄⋊C₈	—	89	1	no	—
415	C₄⋊C₈	—	178	1	no	—
416	C₄⋊C₈	—	178	1	no	—
417	C₄⋊C₈	—	178	1	no	—
418	C₄⋊C₈	—	178	1	no	—
419	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
421	#103	C₂×Dic₈₉	1	1	yes	characteristic
422	#103	C₂×Dic₈₉	1	1	yes	characteristic
423	#102	C₂×Dic₈₉	1	1	yes	characteristic
424	#102	C₂×Dic₈₉	1	1	yes	characteristic
425	#102	C₂×Dic₈₉	1	1	yes	characteristic
426	#102	C₂×Dic₈₉	1	1	yes	characteristic
427	#102	C₂×Dic₈₉	1	1	yes	characteristic
428	#102	C₂×Dic₈₉	1	1	yes	characteristic
429	C₂²⋊C₈	—	178	1	no	—
430	C₂²⋊C₈	—	178	1	no	—
431	C₂²⋊C₈	—	178	1	no	—
432	C₂²⋊C₈	—	178	1	no	—
433	C₂²⋊C₈	—	178	1	no	—
434	C₂²⋊C₈	—	178	1	no	—
435	C₂²⋊C₈	—	178	1	no	—
436	C₂²⋊C₈	—	178	1	no	—
437	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
438	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
439	#97	—	89	1	no	—
440	#97	—	89	1	no	—
441	#97	—	178	1	no	—
442	#97	—	178	1	no	—
443	#97	—	178	1	no	—
444	C₄×C₈	—	89	1	no	—
445	C₄×C₈	—	89	1	no	—
446	C₄×C₈	—	89	1	no	—
447	C₄×C₈	—	89	1	no	—
448	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
449	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
450	#41	—	2	2	no	—
451	#41	—	4	1	no	—
452	#41	—	4	2	no	—
453	#41	—	4	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
462	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
463	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
471	C₂²×C₄	#13083573	1	1	yes	characteristic
472	SD₁₆	—	4	1	no	—
473	SD₁₆	—	4	1	no	—
474	D₈	—	2	2	no	—
475	D₈	—	2	2	no	—
476	M₁₆	—	356	2	no	—
477	M₁₆	—	356	2	no	—
478	M₁₆	—	356	1	no	—
479	M₁₆	—	178	2	no	—
480	C₂×C₈	—	89	1	no	—
481	C₂×C₈	—	89	1	no	—
482	C₂×C₈	—	89	1	no	—
483	C₂×C₈	—	89	1	no	—
484	C₂×C₈	—	356	2	no	—
485	C₂×C₈	—	356	2	no	—
486	C₂×C₈	—	356	2	no	—
487	C₂×C₈	—	356	2	no	—
488	C₂×C₈	—	356	2	no	—
489	C₂×C₈	—	178	1	no	—
490	C₂×C₈	—	178	1	no	—
491	C₂×C₈	—	178	1	no	—
492	C₂×C₈	—	178	1	no	—
493	C₂×C₈	—	178	1	no	—
494	C₂×C₈	—	178	1	no	—
495	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
496	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
497	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
498	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
517	C₄²	D₄×D₈₉	1	1	yes	characteristic
518	C₄²	#13083573	1	1	yes	characteristic
519	C₄²	C₂³×D₈₉	1	1	yes	characteristic
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
524	Q₈	—	2	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	4	2	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	D₄	#15668019	1	2	yes	complemented
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	8	1	no	—
556	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
557	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
558	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
559	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
560	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
561	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	89	2	no	—
567	C₈	—	356	1	no	—
568	C₈	—	356	1	no	—
569	C₈	—	356	1	no	—
570	C₈	—	356	1	no	—
571	C₈	—	356	1	no	—
572	C₈	—	356	1	no	—
573	C₈	—	178	1	no	—
574	C₈	—	178	1	no	—
575	C₈	—	178	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	C₂×#15668019	1	1	yes	characteristic
599	C₄	#19152365	1	1	yes	characteristic
600	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
601	C₄	#19152394	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	1	no	—
606	C₂	#26028979	1	1	yes	characteristic
607	C₂	AGL(1,ℤ/8)×Dic₈₉	1	1	yes	characteristic
608	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3106	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3106	D₈₉
hypocenter	C₈₉	#18007
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
1. #26029266	C₂	semidirect
2. #26028996	C₂	semidirect
3. #26019155	C₂	semidirect
4. #26019143	C₂	semidirect
5. #26019117	C₂	semidirect
6. #26019110	C₂	semidirect
7. #26019089	C₂	semidirect
8. #26019082	C₂	semidirect
9. #26019076	C₂	semidirect
10. D₈×#10623494	C₂	semidirect
11. #26019037	C₂	semidirect
12. #26018721	C₂	semidirect
13. #26018639	C₂	semidirect
14. #26018547	C₂	semidirect
232. D₄×C₈₉	#131	semidirect
320. C₈₉	#18007	semidirect
537. D₄	#15668019	semidirect

Maximal subgroups

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

subgroup	index
#26029266	2
#26028996	2
#26019155	2
#26019143	2
#26019117	2
#26019110	2
#26019089	2
#26019082	2
#26019076	2
D₈×#10623494	2
#26019037	2
#26018721	2
#26018639	2
#26018547	2
C₈₉×#3106	2
#18007	89