Subgroups — #36523906

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029362	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029359	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668033	C₂	1	1	yes	maximal, characteristic
4	#26019066	C₂	1	1	yes	maximal, characteristic, complemented
5	SD₁₆⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019044	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018638	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018636	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018537	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668033	C₄	1	1	yes	characteristic
17	C₄×#13083575	C₂²	1	1	yes	characteristic
18	C₄×#13083573	C₂²	1	1	yes	characteristic
19	Q₈×#10623494	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
21	#19151722	C₂²	1	1	yes	characteristic
22	C₄×#13083564	C₂²	1	1	yes	characteristic
23	#19151690	C₄	1	1	yes	characteristic
24	C₄×#13083563	C₂²	1	1	yes	characteristic
25	SD₁₆×Dic₈₉	C₄	1	1	yes	characteristic
26	#19151685	C₄	1	1	yes	characteristic
27	C₄×#13083559	C₂²	1	1	yes	characteristic
28	#19151678	C₄	1	1	yes	characteristic
29	C₈×D₃₅₆	—	2	1	no	—
30	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
31	D₄×#10623494	C₂²	1	1	yes	characteristic
32	#19151663	—	2	1	no	—
33	#19151663	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₈₉	—	2	1	no	—
35	#19151661	—	2	1	no	—
36	#19151649	—	2	1	no	—
37	#19151649	C₂²	1	1	yes	characteristic
38	#19151649	C₂²	1	1	yes	characteristic
39	#19151648	—	2	1	no	—
40	#19151633	C₄	1	1	yes	characteristic
41	C₂×#15667941	—	2	1	no	—
42	C₄⋊C₈×D₈₉	—	2	1	no	—
43	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
44	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
45	#19151593	C₄	1	1	yes	characteristic
46	#19151591	C₄	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	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
53	#19151328	C₂²	1	1	yes	characteristic
54	#19151327	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic
56	#19151325	C₂²	1	1	yes	characteristic
57	#19151319	C₂²	1	1	yes	characteristic
58	C₈×#10623494	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083575	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083573	C₂×C₄	1	1	yes	characteristic
69	#15668033	C₈	1	8	yes	complemented
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
73	C₂²×#10623494	—	2	1	no	—
74	C₂×C₈×D₈₉	—	2	1	no	—
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	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
82	#15667977	C₂×C₄	1	1	yes	characteristic
83	C₄×D₃₅₆	—	2	1	no	—
84	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
85	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
86	#15667974	—	2	1	no	—
87	#15667974	C₂×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₈₉	—	2	1	no	—
89	#15667972	—	2	1	no	—
90	#15667970	—	2	1	no	—
91	#15667970	C₂×C₄	1	1	yes	characteristic
92	#15667970	C₂×C₄	1	1	yes	characteristic
93	#15667968	—	2	1	no	—
94	C₂×C₄×Dic₈₉	—	2	1	no	—
95	C₄²×D₈₉	—	2	1	no	—
96	C₄²×D₈₉	C₂³	1	1	yes	characteristic
97	#15667945	C₂×C₄	1	1	yes	characteristic
98	#15667945	C₂×C₄	1	1	yes	characteristic
99	#15667944	C₂×C₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
109	#15667941	D₄	1	1	yes	characteristic
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667936	C₂×C₄	1	1	yes	characteristic
112	#15667935	C₂×C₄	1	1	yes	characteristic
113	#15667934	C₂×C₄	1	1	yes	characteristic
114	#15667933	C₂×C₄	1	1	yes	characteristic
115	#15667932	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#10623494	—	2	1	no	—
117	#15667924	—	2	1	no	—
118	#15667924	—	2	1	no	—
119	#15667924	—	2	1	no	—
120	#15667924	D₄	1	1	yes	characteristic
121	#15667924	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×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₈₉	—	2	1	no	—
132	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
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	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×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	#13083575	—	2	2	no	—
146	#13083575	C₂×C₈	1	4	yes	complemented
147	#13083573	—	2	2	no	—
148	#13083573	C₂×C₈	1	4	yes	complemented
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₅₆	—	2	1	no	—
151	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	C₂²×Dic₈₉	—	2	1	no	—
154	C₂²×Dic₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	—	2	1	no	—
158	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
161	#13083564	C₂×C₈	1	4	yes	complemented
162	#13083563	C₂×C₈	1	4	yes	complemented
163	#13083559	C₂×C₈	1	4	yes	complemented
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	8	1	no	—
168	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
169	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
170	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
171	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
172	C₈×D₈₉	—	2	2	no	—
173	C₈×D₈₉	—	8	1	no	—
174	C₈×D₈₉	—	8	1	no	—
175	C₈×D₈₉	—	8	1	no	—
176	C₈×D₈₉	—	8	1	no	—
177	C₈×D₈₉	C₂×C₈	1	4	yes	complemented
178	C₄⋊Dic₈₉	—	2	1	no	—
179	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
181	#13083553	—	2	1	no	—
182	#13083553	—	2	1	no	—
183	C₂²⋊Dic₈₉	—	2	1	no	—
184	#13083551	—	2	1	no	—
185	#13083551	—	2	1	no	—
186	#13083551	—	2	1	no	—
187	#13083551	—	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	—	2	1	no	—
193	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₈₉	#41	1	1	yes	characteristic
196	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	SD₁₆×C₈₉	C₂×C₈	1	4	yes	complemented
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	8	1	no	—
204	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	—	2	1	no	—
209	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₈₉	—	2	1	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂³×C₈₉	—	2	1	no	—
215	C₂²×D₈₉	—	2	1	no	—
216	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
217	Q₈×C₈₉	—	2	1	no	—
218	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
219	D₄×C₈₉	—	2	1	no	—
220	D₄×C₈₉	C₂²×C₈	1	2	yes	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
229	C₂²⋊D₈₉	—	2	4	no	—
230	C₂×Dic₈₉	—	2	1	no	—
231	C₂×Dic₈₉	—	2	4	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	8	1	no	—
235	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
238	D₃₅₆	—	2	4	no	—
239	D₃₅₆	—	2	1	no	—
240	D₃₅₆	C₂²×C₈	1	2	yes	—
241	C₄×D₈₉	—	2	1	no	—
242	C₄×D₈₉	—	2	1	no	—
243	C₄×D₈₉	—	2	4	no	—
244	C₄×D₈₉	—	4	1	no	—
245	C₄×D₈₉	—	4	1	no	—
246	C₄×D₈₉	—	4	1	no	—
247	C₄×D₈₉	—	8	1	no	—
248	C₄×D₈₉	C₂²×C₈	1	2	yes	—
249	C₄×D₈₉	#131	1	2	yes	—
250	Dic₁₇₈	—	2	1	no	—
251	Dic₁₇₈	C₂²×C₈	1	2	yes	—
252	C₈×C₈₉	—	2	1	no	—
253	C₈×C₈₉	—	2	1	no	—
254	C₈×C₈₉	—	2	1	no	—
255	C₈×C₈₉	—	4	1	no	—
256	C₈×C₈₉	—	4	1	no	—
257	C₈×C₈₉	—	4	1	no	—
258	C₈×C₈₉	C₂²×C₈	1	2	yes	—
259	#10623494	—	2	1	no	—
260	#10623494	—	2	1	no	—
261	#10623494	—	2	1	no	—
262	#10623494	—	4	1	no	—
263	#10623494	—	4	1	no	—
264	#10623494	—	4	1	no	—
265	#10623494	C₂²×C₈	1	2	yes	—
266	C₂²×C₈₉	—	2	2	no	—
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	4	1	no	—
269	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂×D₈₉	—	2	1	no	—
271	C₂×D₈₉	—	2	1	no	—
272	C₂×D₈₉	—	2	2	no	—
273	C₂×D₈₉	—	4	1	no	—
274	C₂×D₈₉	—	4	1	no	—
275	C₂×D₈₉	C₈×D₄	1	2	yes	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	2	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
281	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
282	C₄×C₈₉	#576	1	1	yes	characteristic
283	C₄×C₈₉	#578	1	1	yes	characteristic
284	Dic₈₉	—	2	2	no	—
285	Dic₈₉	—	2	1	no	—
286	Dic₈₉	—	2	1	no	—
287	Dic₈₉	—	4	1	no	—
288	Dic₈₉	—	4	1	no	—
289	Dic₈₉	C₈×D₄	1	2	yes	—
290	#17857	—	89	1	no	maximal, Sylow
291	C₂×C₈₉	—	4	2	no	—
292	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
293	C₂×C₈₉	#2951	1	1	yes	characteristic
294	C₂×C₈₉	#2957	1	1	yes	characteristic
295	D₈₉	—	2	2	no	—
296	D₈₉	—	4	2	no	—
297	#2988	—	89	1	no	—
298	#2988	—	89	1	no	—
299	C₄×#135	—	89	1	no	—
300	SD₁₆⋊C₈	—	89	1	no	—
301	SD₁₆⋊C₈	—	89	1	no	—
302	SD₁₆⋊C₈	—	89	1	no	—
303	SD₁₆⋊C₈	D₈₉	1	1	yes	characteristic, complemented
304	C₈×Q₁₆	—	89	1	no	—
305	C₈×Q₁₆	—	89	1	no	—
306	C₈×D₈	—	89	1	no	—
307	C₈×D₈	—	89	1	no	—
308	C₂×#335	—	89	1	no	—
309	#1477	—	89	1	no	—
310	#1477	—	89	1	no	—
311	#1450	—	89	1	no	—
312	C₈₉	#17857	1	1	yes	characteristic, complemented, Sylow
313	C₂×#135	—	89	1	no	—
314	C₄×#41	—	89	1	no	—
315	C₄×#41	—	89	1	no	—
316	C₈×Q₈	—	89	1	no	—
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	—	89	1	no	—
319	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×Q₁₆	—	89	1	no	—
322	C₄×SD₁₆	—	89	1	no	—
323	C₄×SD₁₆	—	89	1	no	—
324	C₄×SD₁₆	—	89	1	no	—
325	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
326	C₄×D₈	—	89	1	no	—
327	C₄×D₈	—	89	1	no	—
328	C₈×D₄	—	89	1	no	—
329	C₈×D₄	—	89	1	no	—
330	C₈×D₄	—	89	1	no	—
331	C₈×D₄	—	178	1	no	—
332	C₈×D₄	—	178	1	no	—
333	C₈×D₄	—	178	1	no	—
334	C₈×D₄	—	178	1	no	—
335	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
336	#431	—	89	1	no	—
337	#431	—	89	1	no	—
338	#431	—	178	1	no	—
339	#431	—	178	1	no	—
340	#427	—	89	1	no	—
341	C₂×C₄⋊C₈	—	89	1	no	—
342	C₂×C₄⋊C₈	—	89	1	no	—
343	C₂×C₄⋊C₈	—	178	1	no	—
344	C₂×C₄⋊C₈	—	178	1	no	—
345	#416	—	89	1	no	—
346	#416	—	89	1	no	—
347	C₂×C₄×C₈	—	89	1	no	—
348	#335	—	89	1	no	—
349	#335	—	89	1	no	—
350	#335	—	89	1	no	—
351	#335	C₂×D₈₉	1	1	yes	characteristic
352	Q₈⋊C₈	—	89	1	no	—
353	Q₈⋊C₈	—	89	1	no	—
354	Q₈⋊C₈	—	89	1	no	—
355	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
356	D₄⋊C₈	—	89	1	no	—
357	D₄⋊C₈	—	89	1	no	—
358	D₄⋊C₈	—	89	1	no	—
359	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
360	#322	—	89	1	no	—
361	#322	C₂×D₈₉	1	1	yes	characteristic
362	C₈²	—	89	1	no	—
363	C₈²	—	89	1	no	—
364	C₂×#41	—	89	1	no	—
365	C₂×#41	—	89	1	no	—
366	#135	—	89	8	no	—
367	C₂×Q₁₆	—	89	1	no	—
368	C₂×SD₁₆	—	89	1	no	—
369	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
370	C₂×D₈	—	89	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	89	1	no	—
373	C₂²×C₈	—	89	1	no	—
374	C₂²×C₈	—	178	1	no	—
375	C₂²×C₈	—	178	1	no	—
376	C₂²×C₈	—	178	1	no	—
377	C₂²×C₈	—	178	1	no	—
378	C₂²×C₈	—	178	1	no	—
379	C₄×Q₈	—	89	1	no	—
380	C₄×Q₈	—	89	1	no	—
381	C₄×Q₈	—	89	1	no	—
382	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
383	C₄×D₄	—	89	1	no	—
384	C₄×D₄	—	89	1	no	—
385	C₄×D₄	—	89	1	no	—
386	C₄×D₄	—	178	1	no	—
387	C₄×D₄	—	178	1	no	—
388	C₄×D₄	—	178	1	no	—
389	C₄×D₄	—	178	1	no	—
390	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
391	#117	—	89	1	no	—
392	#117	—	89	1	no	—
393	#117	—	178	1	no	—
394	#117	—	178	1	no	—
395	C₂×C₄²	—	89	1	no	—
396	C₂×C₄²	—	178	1	no	—
397	C₂×C₄²	—	178	1	no	—
398	#107	—	89	1	no	—
399	#107	—	89	1	no	—
400	#106	—	89	1	no	—
401	#106	C₄×D₈₉	1	1	yes	characteristic
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	89	1	no	—
404	C₄⋊C₈	—	89	1	no	—
405	C₄⋊C₈	—	89	1	no	—
406	C₄⋊C₈	—	89	1	no	—
407	C₄⋊C₈	—	178	1	no	—
408	C₄⋊C₈	—	178	1	no	—
409	C₄⋊C₈	—	178	1	no	—
410	C₄⋊C₈	—	178	1	no	—
411	C₄⋊C₈	—	178	1	no	—
412	C₄⋊C₈	—	178	1	no	—
413	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
415	#103	—	89	1	no	—
416	#103	—	89	1	no	—
417	#103	—	89	1	no	—
418	#103	C₄×D₈₉	1	1	yes	characteristic
419	#102	—	89	1	no	—
420	#102	—	89	1	no	—
421	#102	—	89	1	no	—
422	#102	C₄×D₈₉	1	1	yes	characteristic
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	89	1	no	—
425	C₂²⋊C₈	—	89	1	no	—
426	C₂²⋊C₈	—	178	1	no	—
427	C₂²⋊C₈	—	178	1	no	—
428	C₂²⋊C₈	—	178	1	no	—
429	C₂²⋊C₈	—	178	1	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	—	89	1	no	—
432	C₄×C₈	—	89	1	no	—
433	C₄×C₈	—	89	1	no	—
434	C₄×C₈	—	89	1	no	—
435	C₄×C₈	—	89	1	no	—
436	C₄×C₈	—	178	1	no	—
437	C₄×C₈	—	178	1	no	—
438	C₄×C₈	—	178	1	no	—
439	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
440	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
442	#41	—	89	4	no	—
443	#41	—	89	4	no	—
444	#41	—	178	2	no	—
445	#41	—	178	2	no	—
446	C₂×Q₈	—	89	1	no	—
447	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
448	C₂×D₄	—	89	1	no	—
449	C₂×D₄	—	178	1	no	—
450	C₂×D₄	—	178	1	no	—
451	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	89	1	no	—
454	C₂²×C₄	—	89	1	no	—
455	C₂²×C₄	—	89	1	no	—
456	C₂²×C₄	—	178	1	no	—
457	C₂²×C₄	—	178	1	no	—
458	C₂²×C₄	—	178	1	no	—
459	C₂²×C₄	—	178	1	no	—
460	C₂²×C₄	—	178	1	no	—
461	Q₁₆	—	89	4	no	—
462	SD₁₆	—	89	4	no	—
463	SD₁₆	C₈×D₈₉	1	4	yes	complemented
464	D₈	—	89	4	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	8	1	no	—
469	C₂×C₈	—	89	1	no	—
470	C₂×C₈	—	89	4	no	—
471	C₂×C₈	—	89	1	no	—
472	C₂×C₈	—	89	1	no	—
473	C₂×C₈	—	89	1	no	—
474	C₂×C₈	—	178	2	no	—
475	C₂×C₈	—	178	1	no	—
476	C₂×C₈	—	178	1	no	—
477	C₂×C₈	—	178	1	no	—
478	C₂×C₈	—	712	1	no	—
479	C₂×C₈	—	712	1	no	—
480	C₂×C₈	—	712	1	no	—
481	C₂×C₈	—	712	1	no	—
482	C₂×C₈	—	712	1	no	—
483	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
484	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
485	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
486	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	—	89	1	no	—
490	C₄⋊C₄	—	178	1	no	—
491	C₄⋊C₄	—	178	1	no	—
492	C₄⋊C₄	—	178	1	no	—
493	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	178	1	no	—
497	C₂²⋊C₄	—	178	1	no	—
498	C₂²⋊C₄	—	178	1	no	—
499	C₂²⋊C₄	—	178	1	no	—
500	C₂²⋊C₄	—	178	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	89	1	no	—
503	C₄²	—	89	1	no	—
504	C₄²	—	89	1	no	—
505	C₄²	—	178	1	no	—
506	C₄²	—	178	1	no	—
507	C₄²	—	178	1	no	—
508	C₄²	—	178	1	no	—
509	C₄²	—	178	1	no	—
510	C₄²	C₂³×D₈₉	1	1	yes	characteristic
511	C₂³	—	2	1	no	—
512	C₂³	—	89	1	no	—
513	C₂³	—	178	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	89	2	no	—
516	Q₈	—	178	1	no	—
517	Q₈	C₂×C₈×D₈₉	1	2	yes	—
518	D₄	—	2	1	no	—
519	D₄	—	89	2	no	—
520	D₄	—	178	4	no	—
521	D₄	—	178	4	no	—
522	D₄	—	178	1	no	—
523	D₄	C₂×C₈×D₈₉	1	2	yes	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	89	1	no	—
530	C₂×C₄	—	89	2	no	—
531	C₂×C₄	—	89	2	no	—
532	C₂×C₄	—	89	1	no	—
533	C₂×C₄	—	89	1	no	—
534	C₂×C₄	—	356	1	no	—
535	C₂×C₄	—	356	1	no	—
536	C₂×C₄	—	356	1	no	—
537	C₂×C₄	—	178	4	no	—
538	C₂×C₄	—	178	4	no	—
539	C₂×C₄	—	178	1	no	—
540	C₂×C₄	—	178	1	no	—
541	C₂×C₄	—	178	1	no	—
542	C₂×C₄	—	178	1	no	—
543	C₂×C₄	—	178	1	no	—
544	C₂×C₄	—	712	1	no	—
545	C₂×C₄	—	712	1	no	—
546	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
547	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
548	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	89	2	no	—
556	C₈	—	356	1	no	—
557	C₈	—	356	1	no	—
558	C₈	—	356	1	no	—
559	C₈	—	178	1	no	—
560	C₈	—	178	1	no	—
561	C₈	—	178	1	no	—
562	C₈	C₂×C₈×D₈₉	1	2	yes	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	89	2	no	—
567	C₂²	—	356	1	no	—
568	C₂²	—	356	1	no	—
569	C₂²	—	178	2	no	—
570	C₂²	—	178	1	no	—
571	C₂²	—	178	1	no	—
572	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	89	2	no	—
578	C₄	—	356	1	no	—
579	C₄	—	356	1	no	—
580	C₄	—	178	1	no	—
581	C₄	—	178	1	no	—
582	C₄	—	178	2	no	—
583	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
584	C₄	#131×D₈₉	1	1	yes	characteristic
585	C₄	#19152402	1	1	yes	characteristic
586	C₄	#19152414	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	—	356	2	no	—
589	C₂	—	178	2	no	—
590	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
591	C₂	#26029124	1	1	yes	characteristic
592	C₂	#26029166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×SD₁₆⋊C₈	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668033	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₈₉
hypocenter	C₈₉	#17857
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
1. #26029362	C₂	semidirect
2. #26029359	C₂	semidirect
4. #26019066	C₂	semidirect
5. SD₁₆⋊#10623494	C₂	semidirect
6. #26019063	C₂	semidirect
7. C₈×#13083564	C₂	semidirect
8. #26019056	C₂	semidirect
9. C₈×#13083559	C₂	semidirect
10. #26019044	C₂	semidirect
11. #335×D₈₉	C₂	semidirect
12. #26018638	C₂	semidirect
13. #26018636	C₂	semidirect
14. #26018537	C₂	semidirect
15. C₈₉×SD₁₆⋊C₈	C₂	semidirect
69. #15668033	C₈	semidirect
146. #13083575	C₂×C₈	semidirect
148. #13083573	C₂×C₈	semidirect
161. #13083564	C₂×C₈	semidirect
162. #13083563	C₂×C₈	semidirect
163. #13083559	C₂×C₈	semidirect
177. C₈×D₈₉	C₂×C₈	semidirect
199. SD₁₆×C₈₉	C₂×C₈	semidirect
303. SD₁₆⋊C₈	D₈₉	semidirect
312. C₈₉	#17857	semidirect
463. SD₁₆	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029362	2
#26029359	2
C₄×#15668033	2
#26019066	2
SD₁₆⋊#10623494	2
#26019063	2
C₈×#13083564	2
#26019056	2
C₈×#13083559	2
#26019044	2
#335×D₈₉	2
#26018638	2
#26018636	2
#26018537	2
C₈₉×SD₁₆⋊C₈	2
#17857	89