Subgroups — #36525885

Order 22784.

638 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029204	C₂	1	1	yes	maximal, characteristic
2	Q₈×#13083557	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019146	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019009	C₂	1	1	yes	maximal, characteristic
12	#26018679	C₂	1	1	yes	maximal, characteristic
13	#26018679	C₂	1	1	yes	maximal, characteristic
14	#26018531	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	#19151729	C₂²	1	1	yes	characteristic
20	#19151728	—	2	1	no	—
21	#19151728	C₂²	1	1	yes	characteristic
22	#19151727	—	2	1	no	—
23	#19151726	—	2	1	no	—
24	#19151725	—	2	1	no	—
25	#19151725	C₂²	1	1	yes	characteristic
26	Q₈×#10623494	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
28	#19151722	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic
31	#19151692	C₄	1	1	yes	characteristic
32	C₄×#13083564	C₂²	1	1	yes	characteristic
33	C₄×#13083564	C₂²	1	1	yes	characteristic
34	#19151690	C₄	1	1	yes	characteristic
35	#19151690	C₄	1	1	yes	characteristic
36	#19151649	C₂²	1	1	yes	characteristic
37	#107×D₈₉	C₄	1	1	yes	characteristic
38	#19151620	—	2	1	no	—
39	#19151620	—	2	1	no	—
40	#19151620	C₂²	1	1	yes	characteristic
41	#19151620	C₂²	1	1	yes	characteristic
42	#103×D₈₉	C₄	1	1	yes	characteristic
43	#103×D₈₉	C₄	1	1	yes	characteristic
44	#19151550	—	2	1	no	—
45	C₄×#13083557	—	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	#19151350	C₂²	1	1	yes	characteristic
50	#19151350	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
54	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	#19151328	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	C₈×#10623494	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₈₉	—	2	4	no	—
73	C₂×#13083557	—	2	1	no	—
74	C₂×#13083557	—	2	1	no	—
75	C₂×#13083557	D₄	1	1	yes	characteristic
76	C₂×#13083557	D₄	1	1	yes	characteristic
77	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
79	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
80	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₇₈	—	2	1	no	—
82	C₄×Dic₁₇₈	—	2	1	no	—
83	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
84	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	#15667977	—	2	1	no	—
86	#15667977	—	2	1	no	—
87	#15667977	C₂×C₄	1	1	yes	characteristic
88	#15667977	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₈₉	—	2	1	no	—
90	C₄⋊C₄×D₈₉	—	2	1	no	—
91	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₈₉	—	2	1	no	—
94	C₄²×D₈₉	—	2	1	no	—
95	C₄²×D₈₉	C₂³	1	1	yes	characteristic
96	#15667946	C₂×C₄	1	1	yes	characteristic
97	#15667945	C₂×C₄	1	1	yes	characteristic
98	#15667945	C₂×C₄	1	1	yes	characteristic
99	C₄⋊#10623494	—	2	1	no	—
100	C₄⋊#10623494	—	2	1	no	—
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	C₄⋊#10623494	C₂³	1	1	yes	characteristic
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667941	—	2	1	no	—
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667937	C₂×C₄	1	1	yes	characteristic
112	#15667936	C₂×C₄	1	1	yes	characteristic
113	#15667936	C₂×C₄	1	1	yes	characteristic
114	#15667935	C₂×C₄	1	1	yes	characteristic
115	#15667935	C₂×C₄	1	1	yes	characteristic
116	#15667924	—	2	1	no	—
117	#15667923	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	#15667922	D₄	1	1	yes	characteristic
121	#15667922	D₄	1	1	yes	characteristic
122	C₄×#10623494	—	2	1	no	—
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₄×#10623494	C₂³	1	1	yes	characteristic
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
133	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	—	2	1	no	—
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#97×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₉	—	2	2	no	—
150	Q₈×D₈₉	—	2	2	no	—
151	Q₈×D₈₉	—	4	1	no	—
152	Q₈×D₈₉	—	4	1	no	—
153	C₂×C₄×D₈₉	—	2	1	no	—
154	C₂×C₄×D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
160	Dic₃₅₆	—	2	2	no	—
161	#13083564	—	2	2	no	—
162	#13083564	M₁₆	1	4	yes	complemented
163	#13083557	—	2	2	no	—
164	#13083557	—	4	2	no	—
165	#13083557	—	4	2	no	—
166	#13083557	Q₁₆	1	4	yes	complemented
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	—	2	1	no	—
169	C₂×#10623494	—	2	1	no	—
170	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
171	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
172	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
173	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
174	C₈×D₈₉	—	2	2	no	—
175	C₈×D₈₉	—	4	1	no	—
176	C₄⋊Dic₈₉	—	2	1	no	—
177	C₄⋊Dic₈₉	—	2	1	no	—
178	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
180	#13083553	—	2	1	no	—
181	#13083553	—	2	1	no	—
182	#13083553	—	2	1	no	—
183	#13083553	—	2	1	no	—
184	#13083553	—	2	1	no	—
185	#13083553	—	2	1	no	—
186	C₄×Dic₈₉	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	—	2	1	no	—
190	C₄×Dic₈₉	—	2	1	no	—
191	C₄×Dic₈₉	—	2	1	no	—
192	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₈₉	#41	1	1	yes	characteristic
195	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	Q₁₆×C₈₉	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₉	—	2	1	no	—
206	C₄⋊C₄×C₈₉	—	2	1	no	—
207	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₈₉	—	2	1	no	—
210	C₄²×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	—	2	1	no	—
216	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₈₉	—	2	1	no	—
225	C₂×Dic₈₉	—	2	1	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
231	C₄×D₈₉	—	2	1	no	—
232	C₄×D₈₉	—	2	1	no	—
233	C₄×D₈₉	—	4	1	no	—
234	C₄×D₈₉	—	4	2	no	—
235	C₄×D₈₉	—	4	2	no	—
236	C₄×D₈₉	—	8	1	no	—
237	C₄×D₈₉	—	8	1	no	—
238	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
239	C₄×D₈₉	#135	1	2	yes	—
240	Dic₁₇₈	—	2	1	no	—
241	Dic₁₇₈	—	2	1	no	—
242	Dic₁₇₈	—	2	1	no	—
243	Dic₁₇₈	—	4	2	no	—
244	Dic₁₇₈	—	4	2	no	—
245	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₈×C₈₉	—	4	1	no	—
252	C₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	4	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	C₂×M₁₆	1	2	yes	—
259	#10623494	C₂×Q₁₆	1	2	yes	complemented
260	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂×D₈₉	—	2	1	no	—
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	4	1	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
270	C₄×C₈₉	#568	1	1	yes	characteristic
271	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
272	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
273	Dic₈₉	—	2	2	no	—
274	Dic₈₉	—	2	1	no	—
275	Dic₈₉	—	2	1	no	—
276	Dic₈₉	—	4	1	no	—
277	Dic₈₉	—	4	1	no	—
278	Dic₈₉	—	4	1	no	—
279	Dic₈₉	C₄×Q₁₆	1	2	yes	—
280	M₁₆×Q₁₆	—	89	1	no	maximal, Sylow
281	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
282	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
283	C₂×C₈₉	#2957	1	1	yes	characteristic
284	D₈₉	—	2	2	no	—
285	Q₈×M₁₆	—	89	1	no	—
286	Q₈×M₁₆	—	89	1	no	—
287	C₂×C₄×Q₁₆	—	89	1	no	—
288	#1591	—	89	1	no	—
289	#1591	—	89	1	no	—
290	#1584	—	89	1	no	—
291	#1584	—	89	1	no	—
292	#1584	—	89	1	no	—
293	#1584	D₈₉	1	1	yes	characteristic, complemented
294	C₈×Q₁₆	—	89	1	no	—
295	C₈×Q₁₆	—	89	1	no	—
296	#1567	—	89	1	no	—
297	#1487	—	89	1	no	—
298	#1487	—	89	1	no	—
299	C₈×M₁₆	—	89	1	no	—
300	C₈₉	M₁₆×Q₁₆	1	1	yes	characteristic, complemented, Sylow
301	C₂²×Q₁₆	—	89	1	no	—
302	C₂×C₄×Q₈	—	89	1	no	—
303	C₂×C₄×Q₈	—	89	1	no	—
304	#446	—	89	1	no	—
305	#446	—	89	1	no	—
306	#446	—	89	1	no	—
307	#446	—	178	1	no	—
308	#446	—	178	1	no	—
309	#446	—	178	1	no	—
310	#446	—	178	1	no	—
311	#446	C₂×D₈₉	1	1	yes	characteristic
312	C₈×Q₈	—	89	1	no	—
313	C₈×Q₈	—	89	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
316	C₄×Q₁₆	—	89	1	no	—
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×Q₁₆	—	89	1	no	—
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×Q₁₆	—	89	1	no	—
322	C₄×Q₁₆	—	89	1	no	—
323	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
324	#431	—	89	1	no	—
325	C₂×#107	—	89	1	no	—
326	#423	—	89	1	no	—
327	#423	—	89	1	no	—
328	#423	—	178	1	no	—
329	#423	—	178	1	no	—
330	C₂×#103	—	89	1	no	—
331	C₂×#103	—	89	1	no	—
332	C₄×M₁₆	—	89	1	no	—
333	C₄×M₁₆	—	178	1	no	—
334	C₄×M₁₆	—	178	1	no	—
335	C₂×C₄×C₈	—	89	1	no	—
336	#335	—	89	1	no	—
337	#335	—	89	1	no	—
338	#335	—	89	1	no	—
339	#335	C₂×D₈₉	1	1	yes	characteristic
340	Q₈⋊C₈	—	89	1	no	—
341	Q₈⋊C₈	—	89	1	no	—
342	Q₈⋊C₈	—	89	1	no	—
343	Q₈⋊C₈	—	89	1	no	—
344	Q₈⋊C₈	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
347	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
348	#322	—	89	1	no	—
349	#322	C₂×D₈₉	1	1	yes	characteristic
350	C₈²	—	89	1	no	—
351	C₈²	—	89	1	no	—
352	C₂²×Q₈	—	89	1	no	—
353	C₂²×Q₈	—	89	1	no	—
354	C₂×Q₁₆	—	89	1	no	—
355	C₂×Q₁₆	—	89	1	no	—
356	C₂×Q₁₆	—	89	1	no	—
357	C₂×Q₁₆	—	178	4	no	—
358	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
359	C₂×M₁₆	—	89	1	no	—
360	C₂×M₁₆	—	89	1	no	—
361	C₂×M₁₆	—	178	1	no	—
362	C₂×M₁₆	—	178	1	no	—
363	C₂²×C₈	—	89	1	no	—
364	C₂²×C₈	—	89	1	no	—
365	C₄×Q₈	—	89	1	no	—
366	C₄×Q₈	—	89	1	no	—
367	C₄×Q₈	—	89	1	no	—
368	C₄×Q₈	—	89	1	no	—
369	C₄×Q₈	—	89	1	no	—
370	C₄×Q₈	—	89	1	no	—
371	C₄×Q₈	—	178	1	no	—
372	C₄×Q₈	—	178	1	no	—
373	C₄×Q₈	—	178	1	no	—
374	C₄×Q₈	—	178	1	no	—
375	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	89	1	no	—
378	C₂×C₄⋊C₄	—	89	1	no	—
379	C₂×C₄⋊C₄	—	178	1	no	—
380	C₂×C₄⋊C₄	—	178	1	no	—
381	C₂×C₄²	—	89	1	no	—
382	C₂×C₄²	—	178	1	no	—
383	C₂×C₄²	—	178	1	no	—
384	#107	—	89	1	no	—
385	#107	—	89	1	no	—
386	#107	—	89	1	no	—
387	#107	C₄×D₈₉	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	89	1	no	—
391	C₄⋊C₈	—	89	1	no	—
392	C₄⋊C₈	—	178	1	no	—
393	C₄⋊C₈	—	178	1	no	—
394	C₄⋊C₈	—	178	1	no	—
395	C₄⋊C₈	—	178	1	no	—
396	C₄⋊C₈	—	178	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
403	#103	—	89	1	no	—
404	#103	—	89	1	no	—
405	#103	—	89	1	no	—
406	#103	—	89	1	no	—
407	#103	—	89	1	no	—
408	#103	—	89	1	no	—
409	#103	C₄×D₈₉	1	1	yes	characteristic
410	#103	C₄×D₈₉	1	1	yes	characteristic
411	C₂²⋊C₈	—	178	1	no	—
412	#97	—	2	1	no	—
413	#97	—	89	1	no	—
414	#97	—	89	1	no	—
415	#97	—	178	1	no	—
416	#97	—	178	1	no	—
417	#97	—	178	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	89	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	178	1	no	—
425	C₄×C₈	—	178	1	no	—
426	C₄×C₈	—	178	1	no	—
427	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
430	C₂×Q₈	—	89	1	no	—
431	C₂×Q₈	—	89	1	no	—
432	C₂×Q₈	—	356	1	no	—
433	C₂×Q₈	—	356	1	no	—
434	C₂×Q₈	—	178	1	no	—
435	C₂×Q₈	—	178	1	no	—
436	C₂×Q₈	—	178	2	no	—
437	C₂×Q₈	—	178	2	no	—
438	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
439	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
440	C₂²×C₄	—	89	1	no	—
441	C₂²×C₄	—	89	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	178	1	no	—
444	C₂²×C₄	—	178	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	—	178	1	no	—
447	Q₁₆	—	2	2	no	—
448	Q₁₆	—	89	4	no	—
449	Q₁₆	—	178	2	no	—
450	Q₁₆	—	178	2	no	—
451	M₁₆	—	89	4	no	—
452	M₁₆	—	356	2	no	—
453	M₁₆	—	356	2	no	—
454	M₁₆	—	178	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	89	1	no	—
462	C₂×C₈	—	356	1	no	—
463	C₂×C₈	—	178	2	no	—
464	C₂×C₈	—	178	1	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
470	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	89	1	no	—
474	C₄⋊C₄	—	89	1	no	—
475	C₄⋊C₄	—	178	1	no	—
476	C₄⋊C₄	—	178	1	no	—
477	C₄⋊C₄	—	178	1	no	—
478	C₄⋊C₄	—	178	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	89	1	no	—
488	C₄²	—	89	1	no	—
489	C₄²	—	89	1	no	—
490	C₄²	—	178	1	no	—
491	C₄²	—	178	1	no	—
492	C₄²	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	—	178	1	no	—
496	C₄²	C₂³×D₈₉	1	1	yes	characteristic
497	C₂³	—	89	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	89	2	no	—
502	Q₈	—	356	2	no	—
503	Q₈	—	356	2	no	—
504	Q₈	—	178	1	no	—
505	Q₈	—	178	1	no	—
506	Q₈	—	178	1	no	—
507	Q₈	M₁₆×D₈₉	1	2	yes	—
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	—	89	1	no	—
513	C₂×C₄	—	89	2	no	—
514	C₂×C₄	—	89	2	no	—
515	C₂×C₄	—	89	1	no	—
516	C₂×C₄	—	89	1	no	—
517	C₂×C₄	—	356	2	no	—
518	C₂×C₄	—	356	1	no	—
519	C₂×C₄	—	356	2	no	—
520	C₂×C₄	—	178	1	no	—
521	C₂×C₄	—	178	1	no	—
522	C₂×C₄	—	178	1	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	712	1	no	—
527	C₂×C₄	—	712	1	no	—
528	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
530	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	89	2	no	—
538	C₈	—	89	2	no	—
539	C₈	—	356	1	no	—
540	C₈	—	356	1	no	—
541	C₈	—	356	1	no	—
542	C₈	—	178	1	no	—
543	C₈	—	178	1	no	—
544	C₈	Q₁₆×D₈₉	1	2	yes	complemented
545	C₂²	—	89	2	no	—
546	C₂²	—	178	1	no	—
547	C₂²	—	178	1	no	—
548	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	89	2	no	—
555	C₄	—	356	1	no	—
556	C₄	—	356	1	no	—
557	C₄	—	356	1	no	—
558	C₄	—	178	1	no	—
559	C₄	—	178	1	no	—
560	C₄	—	178	2	no	—
561	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
562	C₄	#19152363	1	1	yes	characteristic
563	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
564	C₄	#135×D₈₉	1	1	yes	characteristic
565	C₂	—	178	2	no	—
566	C₂	#26028985	1	1	yes	characteristic
567	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
568	C₂	#26029166	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×#1584	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1584	D₈₉
hypocenter	C₈₉	M₁₆×Q₁₆
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #26019147	C₂	semidirect
5. #26019146	C₂	semidirect
6. #26019104	C₂	semidirect
7. #26019103	C₂	semidirect
8. #26019101	C₂	semidirect
9. C₈×#13083564	C₂	semidirect
10. #26019056	C₂	semidirect
15. C₈₉×#1584	C₂	semidirect
162. #13083564	M₁₆	semidirect
166. #13083557	Q₁₆	semidirect
252. C₈×C₈₉	C₂×Q₁₆	semidirect
259. #10623494	C₂×Q₁₆	semidirect
293. #1584	D₈₉	semidirect
300. C₈₉	M₁₆×Q₁₆	semidirect
544. C₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029204	2
Q₈×#13083557	2
C₄×Q₁₆×D₈₉	2
#26019147	2
#26019146	2
#26019104	2
#26019103	2
#26019101	2
C₈×#13083564	2
#26019056	2
#26019009	2
#26018679	2
#26018531	2
C₈₉×#1584	2
M₁₆×Q₁₆	89