Subgroups — #36523465

Order 22784.

666 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029366	C₂	1	2	yes	maximal
2	C₄×#15668018	C₂	1	1	yes	maximal, characteristic
3	#26019017	C₂	1	2	yes	maximal, complemented
4	#26019016	C₂	1	2	yes	maximal, complemented
5	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019012	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019006	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019001	C₂	1	2	yes	maximal, complemented
9	#26018997	C₂	1	1	yes	maximal, characteristic, complemented
10	#334×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₄	1	1	yes	characteristic
13	C₂×#15668018	C₄	1	1	yes	characteristic
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19151727	—	2	2	no	—
16	#19151674	—	2	2	no	—
17	#19151668	—	2	2	no	—
18	#19151667	—	2	2	no	—
19	#19151655	C₂²	1	2	yes	—
20	#19151654	C₂²	1	2	yes	—
21	#19151650	C₂²	1	2	yes	—
22	#19151620	C₂²	1	2	yes	—
23	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
24	#19151553	C₄	1	1	yes	characteristic
25	#19151553	C₄	1	1	yes	characteristic
26	#19151552	C₄	1	1	yes	characteristic
27	#19151552	C₄	1	1	yes	characteristic
28	#19151552	C₄	1	1	yes	characteristic
29	#19151552	C₄	1	1	yes	characteristic
30	C₄×#13083558	C₂²	1	1	yes	characteristic
31	C₄×#13083557	C₂²	1	1	yes	characteristic
32	C₄×#13083557	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
35	#19151351	C₂²	1	2	yes	—
36	#19151350	C₂²	1	2	yes	—
37	#19151350	C₂²	1	2	yes	—
38	#19151349	C₂²	1	1	yes	characteristic
39	#19151349	C₂²	1	1	yes	characteristic
40	#19151348	C₂²	1	2	yes	—
41	#19151348	C₂²	1	2	yes	—
42	#423×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#334×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#334×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	#15668018	—	2	4	no	—
49	#15668018	—	2	4	no	—
50	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083557	—	2	2	no	—
53	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
64	C₄×D₃₅₆	D₄	1	1	yes	characteristic
65	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
70	#15667971	C₂×C₄	1	1	yes	characteristic
71	#15667969	C₂×C₄	1	1	yes	characteristic
72	#15667969	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₈₉	C₂³	1	1	yes	characteristic
74	C₄²×D₈₉	C₂³	1	1	yes	characteristic
75	C₄⋊#10623494	C₂³	1	2	yes	—
76	C₄⋊#10623494	C₂³	1	2	yes	—
77	#15667941	—	2	2	no	—
78	#15667941	—	2	2	no	—
79	C₂²⋊#10623494	—	2	2	no	—
80	#15667924	—	2	2	no	—
81	#15667924	—	2	2	no	—
82	#15667923	—	2	2	no	—
83	#15667923	C₂×C₄	1	1	yes	characteristic
84	#15667923	C₂×C₄	1	1	yes	characteristic
85	#15667922	—	2	2	no	—
86	#15667922	C₂×C₄	1	1	yes	characteristic
87	#15667922	C₂×C₄	1	1	yes	characteristic
88	#15667922	C₂×C₄	1	1	yes	characteristic
89	#15667922	C₂×C₄	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₈×Dic₈₉	—	2	2	no	—
93	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂×M₁₆×C₈₉	—	2	2	no	—
98	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	—	2	2	no	—
102	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
103	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
104	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	#13083574	—	2	2	no	—
109	#13083574	—	2	2	no	—
110	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
120	#13083558	—	2	2	no	—
121	#13083558	—	2	2	no	—
122	#13083557	—	2	2	no	—
123	#13083557	—	2	2	no	—
124	#13083557	—	2	2	no	—
125	#13083557	—	8	2	no	—
126	#13083557	M₁₆	1	4	yes	complemented
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
130	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₈₉	—	2	2	no	—
134	C₈×D₈₉	—	2	2	no	—
135	C₈×D₈₉	—	2	2	no	—
136	C₈×D₈₉	—	8	2	no	—
137	C₈×D₈₉	M₁₆	1	4	yes	complemented
138	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
139	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
140	#13083553	C₄⋊C₄	1	1	yes	characteristic
141	#13083553	C₄⋊C₄	1	1	yes	characteristic
142	#13083553	C₄⋊C₄	1	1	yes	characteristic
143	#13083553	C₄⋊C₄	1	1	yes	characteristic
144	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
145	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
146	#13083551	C₄⋊C₄	1	1	yes	characteristic
147	#13083551	C₄⋊C₄	1	1	yes	characteristic
148	#13083551	C₄⋊C₄	1	1	yes	characteristic
149	#13083551	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
159	M₁₆×C₈₉	—	8	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	2	no	—
162	C₂×C₈×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
171	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂²⋊D₈₉	—	2	2	no	—
186	C₂²⋊D₈₉	—	2	2	no	—
187	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
193	D₃₅₆	—	2	2	no	—
194	C₄×D₈₉	—	2	1	no	—
195	C₄×D₈₉	—	2	1	no	—
196	C₄×D₈₉	—	2	2	no	—
197	C₄×D₈₉	—	2	2	no	—
198	C₄×D₈₉	—	4	1	no	—
199	C₄×D₈₉	—	4	1	no	—
200	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
201	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
202	Dic₁₇₈	—	2	2	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	4	2	no	—
206	C₈×C₈₉	—	4	2	no	—
207	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
208	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
209	#10623494	—	2	1	no	—
210	#10623494	—	2	1	no	—
211	#10623494	—	4	2	no	—
212	#10623494	—	4	2	no	—
213	#10623494	C₂×M₁₆	1	2	yes	—
214	#10623494	C₂×M₁₆	1	2	yes	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	C₂×D₈₉	—	2	1	no	—
220	C₂×D₈₉	—	2	1	no	—
221	C₂×D₈₉	—	2	1	no	—
222	C₂×D₈₉	—	2	1	no	—
223	C₂×D₈₉	—	2	1	no	—
224	C₂×D₈₉	#423	1	2	yes	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	2	1	no	—
227	C₄×C₈₉	—	2	1	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
230	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
231	C₄×C₈₉	#577	1	2	yes	—
232	Dic₈₉	—	2	1	no	—
233	Dic₈₉	—	2	1	no	—
234	Dic₈₉	—	2	1	no	—
235	Dic₈₉	—	2	1	no	—
236	Dic₈₉	—	2	1	no	—
237	Dic₈₉	#423	1	2	yes	—
238	#17798	—	89	1	no	maximal, Sylow
239	C₂×C₈₉	—	4	1	no	—
240	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
241	C₂×C₈₉	#2912	1	1	yes	characteristic
242	C₂×C₈₉	#2916	1	1	yes	characteristic
243	D₈₉	—	2	2	no	—
244	D₈₉	—	4	1	no	—
245	#2989	—	89	2	no	—
246	C₄×#131	—	89	1	no	—
247	#1569	—	89	2	no	—
248	#1569	—	89	2	no	—
249	#1568	—	89	1	no	—
250	#1568	—	89	1	no	—
251	#1566	—	89	1	no	—
252	#1566	D₈₉	1	1	yes	characteristic, complemented
253	#1565	—	89	2	no	—
254	#1564	—	89	1	no	—
255	C₂×#334	—	89	1	no	—
256	C₈₉	#17798	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	89	1	no	—
258	C₂×#131	—	89	1	no	—
259	C₄×#41	—	89	1	no	—
260	#446	—	178	2	no	—
261	#436	—	178	2	no	—
262	#435	—	178	2	no	—
263	#435	—	178	2	no	—
264	#432	—	89	2	no	—
265	#432	—	89	2	no	—
266	#431	—	89	2	no	—
267	#423	—	89	2	no	—
268	#423	C₂×D₈₉	1	2	yes	—
269	C₂×C₄⋊C₈	—	89	2	no	—
270	#405	—	89	1	no	—
271	#405	—	89	1	no	—
272	#405	—	89	1	no	—
273	#405	—	89	1	no	—
274	#405	—	89	1	no	—
275	#405	—	89	1	no	—
276	C₄×M₁₆	—	89	1	no	—
277	C₄×M₁₆	—	89	1	no	—
278	C₄×M₁₆	—	89	1	no	—
279	C₂×C₄×C₈	—	89	1	no	—
280	C₂×C₄×C₈	—	89	1	no	—
281	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
282	#335	—	89	2	no	—
283	#335	—	89	2	no	—
284	#335	—	89	2	no	—
285	#334	—	89	2	no	—
286	#334	—	89	2	no	—
287	#334	—	89	1	no	—
288	#334	—	89	1	no	—
289	#334	C₂×D₈₉	1	1	yes	characteristic
290	#334	C₂×D₈₉	1	1	yes	characteristic
291	#334	C₂×D₈₉	1	2	yes	—
292	C₂×#41	—	89	1	no	—
293	#131	—	178	4	no	—
294	#131	—	178	4	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	89	1	no	—
297	C₂×M₁₆	—	89	1	no	—
298	C₂×M₁₆	—	89	1	no	—
299	C₂×M₁₆	—	89	1	no	—
300	C₂×M₁₆	—	89	1	no	—
301	C₂×M₁₆	—	89	1	no	—
302	C₂×M₁₆	—	178	2	no	—
303	C₂²×C₈	—	89	1	no	—
304	C₂²×C₈	—	89	1	no	—
305	C₂²×C₈	—	89	1	no	—
306	C₂²×C₈	—	89	1	no	—
307	C₂²×C₈	—	178	2	no	—
308	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
310	C₄×Q₈	—	89	1	no	—
311	C₄×Q₈	—	89	1	no	—
312	C₄×D₄	—	89	1	no	—
313	C₄×D₄	—	89	1	no	—
314	C₄×D₄	—	89	1	no	—
315	C₄×D₄	—	89	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	#117	—	89	1	no	—
319	#117	—	89	1	no	—
320	#117	—	89	1	no	—
321	C₂×C₄²	—	89	1	no	—
322	C₂×C₄²	—	89	1	no	—
323	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	89	2	no	—
326	C₄⋊C₈	—	89	2	no	—
327	C₄⋊C₈	—	178	2	no	—
328	C₄⋊C₈	—	178	2	no	—
329	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
330	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
331	C₂²⋊C₈	—	178	2	no	—
332	C₂²⋊C₈	—	178	2	no	—
333	C₂²⋊C₈	—	178	2	no	—
334	#97	—	89	1	no	—
335	#97	—	89	1	no	—
336	#97	—	89	1	no	—
337	#97	—	89	1	no	—
338	#97	—	89	1	no	—
339	#97	—	89	1	no	—
340	#97	—	178	2	no	—
341	#97	—	178	2	no	—
342	C₄×C₈	—	89	1	no	—
343	C₄×C₈	—	89	1	no	—
344	C₄×C₈	—	89	1	no	—
345	C₄×C₈	—	89	1	no	—
346	C₄×C₈	—	89	1	no	—
347	C₄×C₈	—	89	1	no	—
348	C₄×C₈	—	178	2	no	—
349	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
350	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
351	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
352	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
353	#41	—	178	2	no	—
354	#41	—	178	2	no	—
355	C₂×Q₈	—	89	1	no	—
356	C₂×D₄	—	89	1	no	—
357	C₂×D₄	—	89	1	no	—
358	C₂×D₄	—	89	1	no	—
359	C₂²×C₄	—	89	1	no	—
360	C₂²×C₄	—	89	1	no	—
361	C₂²×C₄	—	89	1	no	—
362	C₂²×C₄	—	89	1	no	—
363	C₂²×C₄	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
367	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
368	M₁₆	—	8	2	no	—
369	M₁₆	—	89	4	no	—
370	M₁₆	—	178	2	no	—
371	M₁₆	—	178	2	no	—
372	M₁₆	—	178	2	no	—
373	M₁₆	—	178	2	no	—
374	M₁₆	—	178	2	no	—
375	M₁₆	—	712	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	89	1	no	—
381	C₂×C₈	—	89	1	no	—
382	C₂×C₈	—	89	4	no	—
383	C₂×C₈	—	89	1	no	—
384	C₂×C₈	—	89	1	no	—
385	C₂×C₈	—	178	2	no	—
386	C₂×C₈	—	178	2	no	—
387	C₂×C₈	—	178	2	no	—
388	C₂×C₈	—	178	2	no	—
389	C₂×C₈	—	178	2	no	—
390	C₂×C₈	—	712	2	no	—
391	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
392	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
393	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
394	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
395	C₄⋊C₄	—	89	1	no	—
396	C₄⋊C₄	—	89	1	no	—
397	C₄⋊C₄	—	89	1	no	—
398	C₄⋊C₄	—	89	1	no	—
399	C₄⋊C₄	—	89	1	no	—
400	C₄⋊C₄	—	89	1	no	—
401	C₂²⋊C₄	—	89	1	no	—
402	C₂²⋊C₄	—	89	1	no	—
403	C₂²⋊C₄	—	89	1	no	—
404	C₂²⋊C₄	—	89	1	no	—
405	C₂²⋊C₄	—	89	1	no	—
406	C₂²⋊C₄	—	89	1	no	—
407	C₄²	—	89	1	no	—
408	C₄²	—	89	1	no	—
409	C₄²	—	89	1	no	—
410	C₄²	—	89	1	no	—
411	C₄²	—	89	1	no	—
412	C₄²	—	89	1	no	—
413	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄²	D₄×D₈₉	1	1	yes	characteristic
415	C₄²	Q₈×D₈₉	1	1	yes	characteristic
416	C₄²	C₂³×D₈₉	1	1	yes	characteristic
417	C₂³	—	89	1	no	—
418	C₂³	—	89	1	no	—
419	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
420	Q₈	—	178	2	no	—
421	D₄	—	178	2	no	—
422	D₄	—	178	2	no	—
423	D₄	—	178	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	89	1	no	—
429	C₂×C₄	—	89	2	no	—
430	C₂×C₄	—	89	2	no	—
431	C₂×C₄	—	89	1	no	—
432	C₂×C₄	—	89	1	no	—
433	C₂×C₄	—	89	1	no	—
434	C₂×C₄	—	89	1	no	—
435	C₂×C₄	—	89	1	no	—
436	C₂×C₄	—	356	1	no	—
437	C₂×C₄	—	356	1	no	—
438	C₂×C₄	—	178	2	no	—
439	C₂×C₄	—	178	2	no	—
440	C₂×C₄	—	178	1	no	—
441	C₂×C₄	—	178	1	no	—
442	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
443	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
447	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₈	—	89	2	no	—
453	C₈	—	89	2	no	—
454	C₈	—	356	2	no	—
455	C₈	—	356	2	no	—
456	C₈	—	178	1	no	—
457	C₈	—	178	1	no	—
458	C₈	M₁₆×D₈₉	1	2	yes	—
459	C₈	M₁₆×D₈₉	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	89	2	no	—
464	C₂²	—	178	1	no	—
465	C₂²	—	178	1	no	—
466	C₂²	—	178	1	no	—
467	C₂²	—	178	1	no	—
468	C₂²	—	178	1	no	—
469	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	89	2	no	—
475	C₄	—	178	1	no	—
476	C₄	—	178	1	no	—
477	C₄	—	178	1	no	—
478	C₄	—	178	1	no	—
479	C₄	—	178	1	no	—
480	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
481	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
482	C₄	#19152404	1	2	yes	—
483	C₂	—	4	1	no	—
484	C₂	—	356	1	no	—
485	C₂	—	178	2	no	—
486	C₂	#423×D₈₉	1	1	yes	characteristic
487	C₂	#26028843	1	1	yes	characteristic
488	C₂	#26028860	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×#1566	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1566	D₈₉
hypocenter	C₈₉	#17798
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

Complements

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

N	H ≅ G/N	type
3. #26019017	C₂	semidirect
4. #26019016	C₂	semidirect
5. #26019015	C₂	semidirect
6. #26019012	C₂	semidirect
7. #26019006	C₂	semidirect
8. #26019001	C₂	semidirect
9. #26018997	C₂	semidirect
10. #334×D₈₉	C₂	semidirect
11. C₈₉×#1566	C₂	semidirect
126. #13083557	M₁₆	semidirect
137. C₈×D₈₉	M₁₆	semidirect
252. #1566	D₈₉	semidirect
256. C₈₉	#17798	semidirect

Maximal subgroups

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

subgroup	index
#26029366	2
C₄×#15668018	2
#26019017	2
#26019016	2
#26019015	2
#26019012	2
#26019006	2
#26019001	2
#26018997	2
#334×D₈₉	2
C₈₉×#1566	2
#17798	89