Subgroups — #36523675

Order 22784.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029214	C₂	1	1	yes	maximal, characteristic
2	#26028913	C₂	1	1	yes	maximal, characteristic
3	#26028817	C₂	1	1	yes	maximal, characteristic
4	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019039	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019036	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019035	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019025	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019021	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019018	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019001	C₂	1	1	yes	maximal, characteristic, complemented
14	#334×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668018	—	2	1	no	—
17	C₄×#13083574	C₂²	1	1	yes	characteristic
18	#19151726	C₄	1	1	yes	characteristic
19	#19151726	C₄	1	1	yes	characteristic
20	#19151674	C₄	1	1	yes	characteristic
21	#19151674	C₄	1	1	yes	characteristic
22	#19151671	C₄	1	1	yes	characteristic
23	#19151671	C₄	1	1	yes	characteristic
24	#19151667	C₄	1	1	yes	characteristic
25	#19151667	C₄	1	1	yes	characteristic
26	#19151657	—	2	1	no	—
27	#19151656	—	2	1	no	—
28	#19151655	C₂²	1	1	yes	characteristic
29	#19151654	C₂²	1	1	yes	characteristic
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151650	C₂²	1	1	yes	characteristic
32	#19151649	C₂²	1	1	yes	characteristic
33	#19151649	C₂²	1	1	yes	characteristic
34	#19151624	—	2	1	no	—
35	#19151623	—	2	1	no	—
36	#19151623	—	2	1	no	—
37	#19151622	C₂²	1	1	yes	characteristic
38	#19151620	C₂²	1	1	yes	characteristic
39	#19151620	C₂²	1	1	yes	characteristic
40	#19151620	C₂²	1	1	yes	characteristic
41	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
44	#19151563	—	2	1	no	—
45	#19151552	—	2	1	no	—
46	C₄×#13083557	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151351	C₂²	1	1	yes	characteristic
50	#19151350	C₂²	1	1	yes	characteristic
51	#19151350	C₂²	1	1	yes	characteristic
52	#19151350	C₂²	1	1	yes	characteristic
53	#19151350	C₂²	1	1	yes	characteristic
54	#19151349	C₂²	1	1	yes	characteristic
55	#19151349	C₂²	1	1	yes	characteristic
56	#19151348	C₂²	1	1	yes	characteristic
57	#19151348	C₂²	1	1	yes	characteristic
58	#19151348	C₂²	1	1	yes	characteristic
59	#19151348	C₂²	1	1	yes	characteristic
60	#431×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	#335×C₈₉	C₂²	1	1	yes	characteristic
65	#334×C₈₉	C₂²	1	1	yes	characteristic
66	#334×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	D₄	1	1	yes	characteristic
68	#15668018	—	4	4	no	—
69	C₂×#13083558	—	2	1	no	—
70	C₂×#13083557	—	2	1	no	—
71	C₂×#13083557	—	2	1	no	—
72	C₂×#13083557	—	2	1	no	—
73	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₈₉	—	2	1	no	—
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	2	1	no	—
78	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
82	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
83	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
84	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
87	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
88	#15667971	D₄	1	1	yes	characteristic
89	#15667969	D₄	1	1	yes	characteristic
90	#15667969	D₄	1	1	yes	characteristic
91	C₄²×D₈₉	C₂³	1	1	yes	characteristic
92	C₄²×D₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊#10623494	—	2	1	no	—
94	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#10623494	C₂³	1	1	yes	characteristic
97	C₄⋊#10623494	C₂³	1	1	yes	characteristic
98	C₄⋊#10623494	C₂³	1	1	yes	characteristic
99	C₄⋊#10623494	C₂³	1	1	yes	characteristic
100	#15667941	—	2	1	no	—
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	C₂×C₄	1	1	yes	characteristic
107	#15667941	C₂×C₄	1	1	yes	characteristic
108	#15667941	C₂×C₄	1	1	yes	characteristic
109	#15667941	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊#10623494	—	2	1	no	—
111	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
113	#15667924	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	C₂×C₄	1	1	yes	characteristic
116	#15667924	C₂×C₄	1	1	yes	characteristic
117	#15667924	C₂×C₄	1	1	yes	characteristic
118	#15667924	C₂×C₄	1	1	yes	characteristic
119	#15667923	—	2	1	no	—
120	#15667922	—	2	1	no	—
121	#15667922	C₂×C₄	1	1	yes	characteristic
122	#15667922	C₂×C₄	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
129	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂²×C₈×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₄⋊C₈×C₈₉	—	2	1	no	—
133	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²⋊C₈×C₈₉	—	2	1	no	—
138	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	#13083574	—	2	2	no	—
144	#13083574	—	2	2	no	—
145	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
146	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
155	#13083558	—	4	2	no	—
156	#13083557	—	2	2	no	—
157	#13083557	—	4	1	no	—
158	#13083557	—	4	2	no	—
159	#13083557	—	4	2	no	—
160	#13083557	—	4	2	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	—	2	1	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
166	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
167	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
168	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₈₉	—	2	2	no	—
170	C₈×D₈₉	—	4	1	no	—
171	C₈×D₈₉	—	4	2	no	—
172	C₈×D₈₉	—	4	2	no	—
173	C₈×D₈₉	—	4	2	no	—
174	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
175	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
176	#13083553	C₄⋊C₄	1	1	yes	characteristic
177	#13083553	C₄⋊C₄	1	1	yes	characteristic
178	#13083553	C₄⋊C₄	1	1	yes	characteristic
179	#13083553	C₄⋊C₄	1	1	yes	characteristic
180	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
181	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
182	#13083551	C₄⋊C₄	1	1	yes	characteristic
183	#13083551	C₄⋊C₄	1	1	yes	characteristic
184	#13083551	C₄⋊C₄	1	1	yes	characteristic
185	#13083551	C₄⋊C₄	1	1	yes	characteristic
186	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
189	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
191	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
195	M₁₆×C₈₉	—	2	2	no	—
196	M₁₆×C₈₉	—	4	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	4	2	no	—
202	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
209	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	4	1	no	—
218	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
224	C₂²⋊D₈₉	—	2	2	no	—
225	C₂²⋊D₈₉	—	2	2	no	—
226	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
232	D₃₅₆	—	2	2	no	—
233	C₄×D₈₉	—	2	1	no	—
234	C₄×D₈₉	—	2	1	no	—
235	C₄×D₈₉	—	2	1	no	—
236	C₄×D₈₉	—	2	1	no	—
237	C₄×D₈₉	—	2	1	no	—
238	C₄×D₈₉	—	2	1	no	—
239	C₄×D₈₉	—	4	1	no	—
240	C₄×D₈₉	—	4	1	no	—
241	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
242	C₄×D₈₉	#137	1	2	yes	—
243	Dic₁₇₈	—	2	2	no	—
244	C₈×C₈₉	—	2	1	no	—
245	C₈×C₈₉	—	2	1	no	—
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₈×C₈₉	#131	1	2	yes	complemented
252	#10623494	—	2	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	2	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	C₂²×C₈₉	—	2	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	2	1	no	—
263	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₂×D₈₉	—	2	1	no	—
265	C₂×D₈₉	—	2	1	no	—
266	C₂×D₈₉	—	2	1	no	—
267	C₂×D₈₉	—	2	1	no	—
268	C₂×D₈₉	—	2	1	no	—
269	C₂×D₈₉	#428	1	2	yes	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
275	C₄×C₈₉	#568	1	1	yes	characteristic
276	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
278	Dic₈₉	—	2	1	no	—
279	Dic₈₉	—	2	1	no	—
280	Dic₈₉	—	2	1	no	—
281	Dic₈₉	—	2	1	no	—
282	Dic₈₉	—	2	1	no	—
283	Dic₈₉	#428	1	2	yes	—
284	#17830	—	89	1	no	maximal, Sylow
285	C₂×C₈₉	—	4	1	no	—
286	C₂×C₈₉	#2906	1	1	yes	characteristic
287	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
288	C₂×C₈₉	#2916	1	1	yes	characteristic
289	D₈₉	—	2	2	no	—
290	D₈₉	—	4	1	no	—
291	#2965	—	89	1	no	—
292	#2925	—	89	1	no	—
293	#2906	—	89	1	no	—
294	#1574	—	89	1	no	—
295	#1574	—	89	1	no	—
296	#1573	—	89	1	no	—
297	#1573	—	89	1	no	—
298	#1571	—	89	1	no	—
299	#1570	—	89	1	no	—
300	#1569	—	89	1	no	—
301	#1569	—	89	1	no	—
302	#1567	—	89	1	no	—
303	#1565	—	89	1	no	—
304	#1565	D₈₉	1	1	yes	characteristic, complemented
305	C₂×#334	—	89	1	no	—
306	C₈₉	#17830	1	1	yes	characteristic, complemented, Sylow
307	C₂×#131	—	178	1	no	—
308	C₄×#41	—	89	1	no	—
309	#446	—	89	1	no	—
310	#446	—	89	1	no	—
311	#436	—	89	1	no	—
312	#436	—	89	1	no	—
313	#435	—	89	1	no	—
314	#435	—	89	1	no	—
315	#435	—	89	1	no	—
316	#435	—	89	1	no	—
317	#433	—	178	1	no	—
318	#433	—	178	1	no	—
319	#432	—	89	1	no	—
320	#432	—	89	1	no	—
321	#431	—	89	1	no	—
322	#431	—	89	1	no	—
323	#431	—	89	1	no	—
324	#431	—	89	1	no	—
325	#431	C₂×D₈₉	1	1	yes	characteristic
326	#424	—	178	1	no	—
327	#424	—	178	1	no	—
328	#424	—	178	1	no	—
329	#423	—	89	1	no	—
330	#423	—	89	1	no	—
331	#423	—	89	1	no	—
332	#423	—	89	1	no	—
333	C₂×C₄⋊C₈	—	89	1	no	—
334	C₂×C₄⋊C₈	—	89	1	no	—
335	C₂×C₄⋊C₈	—	89	1	no	—
336	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
337	#408	—	178	1	no	—
338	#405	—	178	1	no	—
339	C₄×M₁₆	—	89	1	no	—
340	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
341	C₂×C₄×C₈	—	89	1	no	—
342	#335	—	89	1	no	—
343	#335	—	89	1	no	—
344	#335	—	89	1	no	—
345	#335	—	89	1	no	—
346	#335	—	89	1	no	—
347	#335	—	89	1	no	—
348	#335	C₂×D₈₉	1	1	yes	characteristic
349	#335	C₂×D₈₉	1	1	yes	characteristic
350	#334	—	89	1	no	—
351	#334	—	89	1	no	—
352	#334	—	89	1	no	—
353	#334	—	89	1	no	—
354	#334	—	89	1	no	—
355	#334	—	89	1	no	—
356	#334	C₂×D₈₉	1	1	yes	characteristic
357	#334	C₂×D₈₉	1	1	yes	characteristic
358	C₂×#41	—	89	1	no	—
359	#131	—	356	4	no	—
360	C₂×M₁₆	—	89	1	no	—
361	C₂×M₁₆	—	89	1	no	—
362	C₂×M₁₆	—	178	1	no	—
363	C₂×M₁₆	—	178	1	no	—
364	C₂×M₁₆	—	178	1	no	—
365	C₂×M₁₆	—	178	1	no	—
366	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
367	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	89	1	no	—
370	C₂²×C₈	—	89	1	no	—
371	C₂²×C₈	—	178	1	no	—
372	C₂²×C₈	—	178	1	no	—
373	C₂²×C₈	—	178	1	no	—
374	C₄×Q₈	—	89	1	no	—
375	C₄×Q₈	—	89	1	no	—
376	C₄×D₄	—	89	1	no	—
377	C₄×D₄	—	89	1	no	—
378	C₄×D₄	—	89	1	no	—
379	C₄×D₄	—	89	1	no	—
380	C₄×D₄	—	89	1	no	—
381	C₄×D₄	—	89	1	no	—
382	#117	—	89	1	no	—
383	#117	—	89	1	no	—
384	#117	—	89	1	no	—
385	C₂×C₄²	—	89	1	no	—
386	C₂×C₄²	—	89	1	no	—
387	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	89	1	no	—
390	C₄⋊C₈	—	89	1	no	—
391	C₄⋊C₈	—	89	1	no	—
392	C₄⋊C₈	—	89	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	89	1	no	—
398	C₄⋊C₈	—	89	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	—	178	1	no	—
403	C₄⋊C₈	—	178	1	no	—
404	C₄⋊C₈	—	178	1	no	—
405	C₄⋊C₈	—	178	1	no	—
406	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	89	1	no	—
412	C₂²⋊C₈	—	89	1	no	—
413	C₂²⋊C₈	—	89	1	no	—
414	C₂²⋊C₈	—	89	1	no	—
415	C₂²⋊C₈	—	89	1	no	—
416	C₂²⋊C₈	—	89	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	—	178	1	no	—
419	C₂²⋊C₈	—	178	1	no	—
420	#97	—	89	1	no	—
421	#97	—	89	1	no	—
422	#97	—	178	1	no	—
423	#97	—	178	1	no	—
424	#97	C₄×D₈₉	1	1	yes	characteristic
425	#97	C₄×D₈₉	1	1	yes	characteristic
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	89	1	no	—
428	C₄×C₈	—	89	1	no	—
429	C₄×C₈	—	89	1	no	—
430	C₄×C₈	—	89	1	no	—
431	C₄×C₈	—	178	1	no	—
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	#41	—	178	2	no	—
435	#41	—	178	2	no	—
436	C₂×Q₈	—	89	1	no	—
437	C₂×D₄	—	89	1	no	—
438	C₂×D₄	—	89	1	no	—
439	C₂×D₄	—	89	1	no	—
440	C₂²×C₄	—	89	1	no	—
441	C₂²×C₄	—	89	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	89	1	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
448	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
449	M₁₆	—	2	2	no	—
450	M₁₆	—	4	1	no	—
451	M₁₆	—	356	1	no	—
452	M₁₆	—	356	2	no	—
453	M₁₆	—	356	2	no	—
454	M₁₆	—	356	2	no	—
455	M₁₆	—	356	2	no	—
456	M₁₆	—	178	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	89	1	no	—
463	C₂×C₈	—	89	1	no	—
464	C₂×C₈	—	89	1	no	—
465	C₂×C₈	—	89	1	no	—
466	C₂×C₈	—	356	1	no	—
467	C₂×C₈	—	356	2	no	—
468	C₂×C₈	—	356	2	no	—
469	C₂×C₈	—	356	2	no	—
470	C₂×C₈	—	178	1	no	—
471	C₂×C₈	—	178	1	no	—
472	C₂×C₈	—	178	1	no	—
473	C₂×C₈	—	178	1	no	—
474	C₂×C₈	—	178	2	no	—
475	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
477	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
478	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
479	C₄⋊C₄	—	89	1	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	1	no	—
482	C₄⋊C₄	—	89	1	no	—
483	C₄⋊C₄	—	89	1	no	—
484	C₄⋊C₄	—	89	1	no	—
485	C₂²⋊C₄	—	89	1	no	—
486	C₂²⋊C₄	—	89	1	no	—
487	C₂²⋊C₄	—	89	1	no	—
488	C₂²⋊C₄	—	89	1	no	—
489	C₂²⋊C₄	—	89	1	no	—
490	C₂²⋊C₄	—	89	1	no	—
491	C₄²	—	89	1	no	—
492	C₄²	—	89	1	no	—
493	C₄²	—	89	1	no	—
494	C₄²	—	89	1	no	—
495	C₄²	—	89	1	no	—
496	C₄²	—	89	1	no	—
497	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
498	C₄²	D₄×D₈₉	1	1	yes	characteristic
499	C₄²	Q₈×D₈₉	1	1	yes	characteristic
500	C₄²	C₂³×D₈₉	1	1	yes	characteristic
501	C₂³	—	89	1	no	—
502	C₂³	—	89	1	no	—
503	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
504	Q₈	—	178	2	no	—
505	D₄	—	178	2	no	—
506	D₄	—	178	2	no	—
507	D₄	—	178	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	89	1	no	—
514	C₂×C₄	—	89	2	no	—
515	C₂×C₄	—	89	2	no	—
516	C₂×C₄	—	89	1	no	—
517	C₂×C₄	—	89	1	no	—
518	C₂×C₄	—	89	1	no	—
519	C₂×C₄	—	89	1	no	—
520	C₂×C₄	—	89	1	no	—
521	C₂×C₄	—	356	1	no	—
522	C₂×C₄	—	356	1	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
530	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	356	1	no	—
543	C₈	—	356	1	no	—
544	C₈	—	356	1	no	—
545	C₈	—	356	1	no	—
546	C₈	—	178	1	no	—
547	C₈	—	178	1	no	—
548	C₈	—	178	1	no	—
549	C₈	—	178	1	no	—
550	C₈	#15668018	1	2	yes	complemented
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	89	2	no	—
555	C₂²	—	178	1	no	—
556	C₂²	—	178	1	no	—
557	C₂²	—	178	1	no	—
558	C₂²	—	178	1	no	—
559	C₂²	—	178	1	no	—
560	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	89	2	no	—
566	C₄	—	178	1	no	—
567	C₄	—	178	1	no	—
568	C₄	—	178	1	no	—
569	C₄	—	178	1	no	—
570	C₄	—	178	1	no	—
571	C₄	C₂×#15668018	1	1	yes	characteristic
572	C₄	#19152364	1	1	yes	characteristic
573	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
574	C₄	#137×D₈₉	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	356	1	no	—
577	C₂	—	178	2	no	—
578	C₂	#26028817	1	1	yes	characteristic
579	C₂	#428×D₈₉	1	1	yes	characteristic
580	C₂	#26028862	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×#1565	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1565	D₈₉
hypocenter	C₈₉	#17830
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #26019040	C₂	semidirect
5. #26019039	C₂	semidirect
6. #26019036	C₂	semidirect
7. #26019035	C₂	semidirect
8. #26019025	C₂	semidirect
9. #26019021	C₂	semidirect
10. #26019019	C₂	semidirect
11. #26019018	C₂	semidirect
12. #26019009	C₂	semidirect
13. #26019001	C₂	semidirect
14. #334×D₈₉	C₂	semidirect
15. C₈₉×#1565	C₂	semidirect
251. C₈×C₈₉	#131	semidirect
304. #1565	D₈₉	semidirect
306. C₈₉	#17830	semidirect
550. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26029214	2
#26028913	2
#26028817	2
#26019040	2
#26019039	2
#26019036	2
#26019035	2
#26019025	2
#26019021	2
#26019019	2
#26019018	2
#26019009	2
#26019001	2
#334×D₈₉	2
C₈₉×#1565	2
#17830	89