Subgroups — #36523459

Order 22784.

712 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028882	C₂	1	1	yes	maximal, characteristic
2	#432×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#13083557	C₂	1	1	yes	maximal, characteristic
4	#26019018	C₂	1	2	yes	maximal, complemented
5	#26019016	C₂	1	2	yes	maximal, complemented
6	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019013	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019013	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019003	C₂	1	2	yes	maximal, complemented
10	#26019001	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13083557	C₄	1	1	yes	characteristic
13	C₂²×#13083557	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
15	#19151655	C₂²	1	1	yes	characteristic
16	#19151655	C₂²	1	1	yes	characteristic
17	#19151654	C₂²	1	2	yes	—
18	#19151653	—	2	1	no	—
19	#19151653	—	2	1	no	—
20	#19151652	—	2	1	no	—
21	#19151650	C₂²	1	2	yes	—
22	#19151648	—	2	1	no	—
23	#19151620	C₂²	1	2	yes	—
24	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
25	#19151560	—	2	1	no	—
26	C₂²⋊C₈×D₈₉	—	2	1	no	—
27	#19151550	—	2	1	no	—
28	C₄×#13083557	C₄	1	1	yes	characteristic
29	C₄×#13083557	C₄	1	1	yes	characteristic
30	C₄×#13083557	C₄	1	1	yes	characteristic
31	C₄×#13083557	C₄	1	1	yes	characteristic
32	C₄×#13083557	C₂²	1	1	yes	characteristic
33	C₄×#13083557	C₂²	1	1	yes	characteristic
34	C₄×#13083557	C₂²	1	1	yes	characteristic
35	C₄×#13083557	C₂²	1	1	yes	characteristic
36	C₂×#15667922	C₄	1	1	yes	characteristic
37	C₂×#15667922	C₄	1	1	yes	characteristic
38	#97×D₈₉	—	2	1	no	—
39	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
40	#19151351	C₂²	1	2	yes	complemented
41	#19151350	C₂²	1	2	yes	complemented
42	#19151350	C₂²	1	2	yes	complemented
43	#19151349	C₂²	1	2	yes	complemented
44	#19151348	C₂²	1	2	yes	complemented
45	#19151348	C₂²	1	2	yes	complemented
46	#432×C₈₉	C₂²	1	1	yes	characteristic
47	#432×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	#335×C₈₉	C₂²	1	2	yes	complemented
50	#334×C₈₉	C₂²	1	2	yes	complemented
51	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
53	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
54	C₂×#13083557	—	2	4	no	—
55	C₂×#13083557	—	2	4	no	—
56	C₂×#13083557	—	2	2	no	—
57	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
58	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
59	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
60	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
61	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
62	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
63	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
64	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
65	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
66	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₈₉	—	2	2	no	—
68	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
70	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
71	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₈₉	D₄	1	1	yes	characteristic
74	C₄²×D₈₉	D₄	1	1	yes	characteristic
75	C₄²×D₈₉	Q₈	1	1	yes	characteristic
76	C₄²×D₈₉	Q₈	1	1	yes	characteristic
77	C₄²×D₈₉	C₂³	1	1	yes	characteristic
78	C₄²×D₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊#10623494	C₂³	1	2	yes	—
80	C₄⋊#10623494	C₂³	1	2	yes	—
81	#15667941	—	2	2	no	—
82	#15667941	—	2	2	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	C₂²⋊#10623494	—	2	1	no	—
85	#15667924	—	2	2	no	—
86	#15667924	—	2	2	no	—
87	#15667923	—	2	1	no	—
88	#15667923	—	2	1	no	—
89	#15667922	—	2	2	no	—
90	#15667922	C₂×C₄	1	1	yes	characteristic
91	#15667922	C₂×C₄	1	1	yes	characteristic
92	#15667922	C₂×C₄	1	1	yes	characteristic
93	#15667922	C₂×C₄	1	1	yes	characteristic
94	#15667922	C₂×C₄	1	1	yes	characteristic
95	#15667922	C₂×C₄	1	1	yes	characteristic
96	#15667922	C₂×C₄	1	1	yes	characteristic
97	#15667922	C₂×C₄	1	1	yes	characteristic
98	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
99	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
100	C₄×#10623494	C₂³	1	1	yes	characteristic
101	C₄×#10623494	C₂³	1	1	yes	characteristic
102	C₈×Dic₈₉	—	2	2	no	—
103	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
107	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
108	C₂²⋊C₈×C₈₉	—	2	1	no	—
109	C₂²⋊C₈×C₈₉	—	2	1	no	—
110	#97×C₈₉	—	2	1	no	—
111	#97×C₈₉	—	2	1	no	—
112	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₈₉	—	2	2	no	—
121	C₂×C₄×D₈₉	—	2	2	no	—
122	C₂×C₄×D₈₉	—	4	2	no	—
123	C₂×C₄×D₈₉	—	4	2	no	—
124	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
135	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
136	#13083557	—	2	2	no	—
137	#13083557	—	2	2	no	—
138	#13083557	—	2	2	no	—
139	#13083557	—	2	2	no	—
140	#13083557	—	2	2	no	—
141	#13083557	—	2	2	no	—
142	#13083557	—	4	4	no	—
143	#13083557	M₁₆	1	4	yes	complemented
144	#13083557	M₁₆	1	4	yes	complemented
145	C₂×#10623494	—	2	2	no	—
146	C₂×#10623494	—	2	2	no	—
147	C₂×#10623494	—	2	2	no	—
148	C₂×#10623494	—	2	2	no	—
149	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
150	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
151	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
152	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
153	C₈×D₈₉	—	4	4	no	—
154	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
159	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
165	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
169	C₂×C₈×C₈₉	—	2	2	no	—
170	C₂×C₈×C₈₉	—	2	2	no	—
171	C₂×C₈×C₈₉	—	2	2	no	—
172	C₂×C₈×C₈₉	—	2	2	no	—
173	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
180	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×D₈₉	—	2	2	no	—
183	C₂²×D₈₉	—	2	2	no	—
184	C₂²×D₈₉	—	4	1	no	—
185	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
197	C₂×Dic₈₉	—	2	2	no	—
198	C₂×Dic₈₉	—	2	2	no	—
199	C₂×Dic₈₉	—	4	1	no	—
200	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₄×D₈₉	—	2	2	no	—
207	C₄×D₈₉	—	2	1	no	—
208	C₄×D₈₉	—	2	1	no	—
209	C₄×D₈₉	—	2	2	no	—
210	C₄×D₈₉	—	2	2	no	—
211	C₄×D₈₉	—	2	2	no	—
212	C₄×D₈₉	—	4	1	no	—
213	C₄×D₈₉	—	4	1	no	—
214	C₄×D₈₉	—	4	1	no	—
215	C₄×D₈₉	—	4	1	no	—
216	C₄×D₈₉	—	4	1	no	—
217	C₄×D₈₉	—	4	1	no	—
218	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
219	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
220	C₈×C₈₉	—	2	1	no	—
221	C₈×C₈₉	—	2	1	no	—
222	C₈×C₈₉	—	4	2	no	—
223	C₈×C₈₉	—	4	2	no	—
224	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
225	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
226	#10623494	—	2	1	no	—
227	#10623494	—	2	1	no	—
228	#10623494	—	4	2	no	—
229	#10623494	—	4	2	no	—
230	#10623494	C₂×M₁₆	1	2	yes	—
231	#10623494	C₂×M₁₆	1	2	yes	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	#430	1	2	yes	—
235	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₈₉	—	2	1	no	—
237	C₂×D₈₉	—	2	1	no	—
238	C₂×D₈₉	—	2	1	no	—
239	C₂×D₈₉	—	2	1	no	—
240	C₂×D₈₉	—	2	1	no	—
241	C₂×D₈₉	—	4	4	no	—
242	C₂×D₈₉	#423	1	2	yes	—
243	C₄×C₈₉	—	2	1	no	—
244	C₄×C₈₉	—	2	1	no	—
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
248	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
249	C₄×C₈₉	#575	1	2	yes	—
250	Dic₈₉	—	2	1	no	—
251	Dic₈₉	—	2	1	no	—
252	Dic₈₉	—	2	1	no	—
253	Dic₈₉	—	2	1	no	—
254	Dic₈₉	—	2	1	no	—
255	Dic₈₉	#423	1	2	yes	—
256	#17797	—	89	1	no	maximal, Sylow
257	C₂×C₈₉	—	2	2	no	—
258	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
259	C₂×C₈₉	#2911	1	1	yes	characteristic
260	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
261	D₈₉	—	2	2	no	—
262	D₈₉	—	4	1	no	—
263	#2920	—	89	1	no	—
264	C₂×#432	—	89	1	no	—
265	C₂×C₄×M₁₆	—	89	1	no	—
266	#1569	—	89	2	no	—
267	#1569	—	89	2	no	—
268	#1568	—	89	1	no	—
269	#1568	—	89	1	no	—
270	#1568	—	89	1	no	—
271	#1568	D₈₉	1	1	yes	characteristic, complemented
272	#1565	—	89	2	no	—
273	#1565	—	89	2	no	—
274	C₈₉	#17797	1	1	yes	characteristic, complemented, Sylow
275	C₂²×M₁₆	—	89	1	no	—
276	C₂²×M₁₆	—	89	1	no	—
277	C₂²×C₄²	—	89	1	no	—
278	#432	—	89	1	no	—
279	#432	—	89	1	no	—
280	#432	—	89	2	no	—
281	#432	—	178	1	no	—
282	#432	—	178	1	no	—
283	#432	—	178	1	no	—
284	#432	C₂×D₈₉	1	1	yes	characteristic
285	#432	C₂×D₈₉	1	1	yes	characteristic
286	#431	—	89	2	no	—
287	#431	—	178	1	no	—
288	#423	—	89	2	no	—
289	C₂×C₄⋊C₈	—	89	2	no	—
290	#407	—	178	1	no	—
291	C₂×C₂²⋊C₈	—	178	1	no	—
292	C₄×M₁₆	—	89	1	no	—
293	C₄×M₁₆	—	89	1	no	—
294	C₄×M₁₆	—	89	1	no	—
295	C₄×M₁₆	—	89	1	no	—
296	C₄×M₁₆	—	89	1	no	—
297	C₄×M₁₆	—	89	1	no	—
298	C₄×M₁₆	—	89	1	no	—
299	C₄×M₁₆	—	89	1	no	—
300	C₄×M₁₆	—	178	1	no	—
301	C₂×#97	—	89	1	no	—
302	C₂×#97	—	89	1	no	—
303	C₂×#97	—	178	1	no	—
304	C₂×C₄×C₈	—	89	1	no	—
305	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
306	#335	—	89	2	no	—
307	#335	—	89	2	no	—
308	#335	—	89	2	no	—
309	#335	C₂×D₈₉	1	2	yes	complemented
310	#334	—	89	2	no	—
311	#334	—	89	2	no	—
312	#334	—	89	2	no	—
313	#334	C₂×D₈₉	1	2	yes	complemented
314	C₂³×C₄	—	89	1	no	—
315	C₂³×C₄	—	89	1	no	—
316	C₂³×C₄	—	89	1	no	—
317	C₂×M₁₆	—	89	1	no	—
318	C₂×M₁₆	—	89	1	no	—
319	C₂×M₁₆	—	89	1	no	—
320	C₂×M₁₆	—	89	1	no	—
321	C₂×M₁₆	—	89	1	no	—
322	C₂×M₁₆	—	89	1	no	—
323	C₂×M₁₆	—	89	1	no	—
324	C₂×M₁₆	—	89	1	no	—
325	C₂×M₁₆	—	178	4	no	—
326	C₂×M₁₆	—	178	4	no	—
327	C₂×M₁₆	—	178	2	no	—
328	C₂²×C₈	—	89	1	no	—
329	C₂²×C₈	—	89	1	no	—
330	C₂²×C₈	—	178	2	no	—
331	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
332	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
333	C₂×C₄²	—	89	1	no	—
334	C₂×C₄²	—	89	1	no	—
335	C₂×C₄²	—	89	1	no	—
336	C₂×C₄²	—	89	1	no	—
337	C₂×C₄²	—	89	1	no	—
338	C₂×C₄²	—	89	1	no	—
339	C₂×C₄²	—	89	1	no	—
340	C₂×C₄²	—	89	1	no	—
341	C₂×C₄²	—	89	1	no	—
342	C₂×C₄²	—	89	1	no	—
343	C₂×C₄²	—	89	1	no	—
344	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
345	C₄⋊C₈	—	89	2	no	—
346	C₄⋊C₈	—	89	2	no	—
347	C₄⋊C₈	—	178	2	no	—
348	C₄⋊C₈	—	178	2	no	—
349	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
350	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	178	2	no	—
354	C₂²⋊C₈	—	178	2	no	—
355	C₂²⋊C₈	—	178	1	no	—
356	C₂²⋊C₈	—	178	1	no	—
357	#97	—	2	1	no	—
358	#97	—	2	1	no	—
359	#97	—	89	1	no	—
360	#97	—	89	1	no	—
361	#97	—	89	1	no	—
362	#97	—	89	1	no	—
363	#97	—	89	1	no	—
364	#97	—	89	1	no	—
365	#97	—	89	1	no	—
366	#97	—	89	1	no	—
367	#97	—	178	2	no	—
368	#97	—	178	1	no	—
369	#97	—	178	1	no	—
370	C₄×C₈	—	89	1	no	—
371	C₄×C₈	—	89	1	no	—
372	C₄×C₈	—	89	1	no	—
373	C₄×C₈	—	89	1	no	—
374	C₄×C₈	—	178	2	no	—
375	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
376	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
377	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
379	C₂⁴	—	89	1	no	—
380	C₂²×C₄	—	89	1	no	—
381	C₂²×C₄	—	89	1	no	—
382	C₂²×C₄	—	89	1	no	—
383	C₂²×C₄	—	89	1	no	—
384	C₂²×C₄	—	89	1	no	—
385	C₂²×C₄	—	89	1	no	—
386	C₂²×C₄	—	89	1	no	—
387	C₂²×C₄	—	89	1	no	—
388	C₂²×C₄	—	89	1	no	—
389	C₂²×C₄	—	89	1	no	—
390	C₂²×C₄	—	89	1	no	—
391	C₂²×C₄	—	89	1	no	—
392	C₂²×C₄	—	89	1	no	—
393	C₂²×C₄	—	89	1	no	—
394	C₂²×C₄	—	89	1	no	—
395	C₂²×C₄	—	356	2	no	—
396	C₂²×C₄	—	356	2	no	—
397	C₂²×C₄	—	178	2	no	—
398	C₂²×C₄	—	178	2	no	—
399	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
400	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
401	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
402	M₁₆	—	89	4	no	—
403	M₁₆	—	89	4	no	—
404	M₁₆	—	356	4	no	—
405	M₁₆	—	178	2	no	—
406	M₁₆	—	178	2	no	—
407	M₁₆	—	178	2	no	—
408	M₁₆	—	178	2	no	—
409	M₁₆	—	178	2	no	—
410	M₁₆	—	178	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	89	1	no	—
416	C₂×C₈	—	89	1	no	—
417	C₂×C₈	—	89	1	no	—
418	C₂×C₈	—	89	1	no	—
419	C₂×C₈	—	356	4	no	—
420	C₂×C₈	—	178	2	no	—
421	C₂×C₈	—	178	2	no	—
422	C₂×C₈	—	178	2	no	—
423	C₂×C₈	—	178	2	no	—
424	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
425	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
426	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
428	C₄²	—	89	1	no	—
429	C₄²	—	89	1	no	—
430	C₄²	—	89	1	no	—
431	C₄²	—	89	1	no	—
432	C₄²	—	89	1	no	—
433	C₄²	—	89	1	no	—
434	C₄²	—	89	1	no	—
435	C₄²	—	89	1	no	—
436	C₄²	—	89	1	no	—
437	C₄²	—	89	1	no	—
438	C₄²	—	89	1	no	—
439	C₄²	—	89	1	no	—
440	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
441	C₄²	D₄×D₈₉	1	1	yes	characteristic
442	C₄²	Q₈×D₈₉	1	1	yes	characteristic
443	C₄²	C₂³×D₈₉	1	1	yes	characteristic
444	C₂³	—	89	1	no	—
445	C₂³	—	89	1	no	—
446	C₂³	—	356	1	no	—
447	C₂³	—	178	2	no	—
448	C₂³	—	178	2	no	—
449	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	89	1	no	—
455	C₂×C₄	—	89	2	no	—
456	C₂×C₄	—	89	2	no	—
457	C₂×C₄	—	89	1	no	—
458	C₂×C₄	—	89	1	no	—
459	C₂×C₄	—	89	1	no	—
460	C₂×C₄	—	89	1	no	—
461	C₂×C₄	—	89	1	no	—
462	C₂×C₄	—	356	1	no	—
463	C₂×C₄	—	356	1	no	—
464	C₂×C₄	—	356	1	no	—
465	C₂×C₄	—	356	1	no	—
466	C₂×C₄	—	356	1	no	—
467	C₂×C₄	—	356	1	no	—
468	C₂×C₄	—	356	1	no	—
469	C₂×C₄	—	178	2	no	—
470	C₂×C₄	—	178	2	no	—
471	C₂×C₄	—	178	2	no	—
472	C₂×C₄	—	178	2	no	—
473	C₂×C₄	—	178	2	no	—
474	C₂×C₄	—	178	2	no	—
475	C₂×C₄	—	178	1	no	—
476	C₂×C₄	—	178	1	no	—
477	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
478	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
479	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₈	—	89	2	no	—
488	C₈	—	89	2	no	—
489	C₈	—	356	2	no	—
490	C₈	—	356	2	no	—
491	C₈	—	178	1	no	—
492	C₈	—	178	1	no	—
493	C₈	M₁₆×D₈₉	1	2	yes	—
494	C₈	M₁₆×D₈₉	1	2	yes	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	89	2	no	—
498	C₂²	—	356	4	no	—
499	C₂²	—	178	1	no	—
500	C₂²	—	178	1	no	—
501	C₂²	—	178	1	no	—
502	C₂²	—	178	1	no	—
503	C₂²	—	178	1	no	—
504	C₂²	#19151645	1	2	yes	—
505	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	89	2	no	—
511	C₄	—	178	1	no	—
512	C₄	—	178	1	no	—
513	C₄	—	178	1	no	—
514	C₄	—	178	1	no	—
515	C₄	—	178	1	no	—
516	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
517	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
518	C₄	#19152395	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	356	1	no	—
521	C₂	—	178	2	no	—
522	C₂	#423×D₈₉	1	1	yes	characteristic
523	C₂	#26028840	1	1	yes	characteristic
524	C₂	C₂×#19151645	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×#1568	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1568	D₈₉
hypocenter	C₈₉	#17797
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
4. #26019018	C₂	semidirect
5. #26019016	C₂	semidirect
6. #26019015	C₂	semidirect
7. #26019013	C₂	semidirect
8. #26019013	C₂	semidirect
9. #26019003	C₂	semidirect
10. #26019001	C₂	semidirect
11. C₈₉×#1568	C₂	semidirect
40. #19151351	C₂²	semidirect
41. #19151350	C₂²	semidirect
42. #19151350	C₂²	semidirect
43. #19151349	C₂²	semidirect
44. #19151348	C₂²	semidirect
45. #19151348	C₂²	semidirect
49. #335×C₈₉	C₂²	semidirect
50. #334×C₈₉	C₂²	semidirect
143. #13083557	M₁₆	semidirect
144. #13083557	M₁₆	semidirect
271. #1568	D₈₉	semidirect
274. C₈₉	#17797	semidirect
309. #335	C₂×D₈₉	semidirect
313. #334	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028882	2
#432×D₈₉	2
C₂×C₄×#13083557	2
#26019018	2
#26019016	2
#26019015	2
#26019013	2
#26019003	2
#26019001	2
C₈₉×#1568	2
#17797	89