Subgroups — #36525984

Order 22784.

718 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029272	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668037	C₂	1	1	yes	maximal, characteristic
3	#26028987	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019163	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019134	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019127	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019119	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019092	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019084	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019067	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019049	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019017	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018696	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018555	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668037	C₄	1	1	yes	characteristic
17	C₂×M₁₆×D₈₉	—	2	1	no	—
18	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
19	Q₈×#10623494	C₂²	1	1	yes	characteristic, complemented
20	Q₈×#10623494	C₂²	1	1	yes	characteristic, complemented
21	#19151708	C₄	1	1	yes	characteristic
22	#19151708	C₄	1	1	yes	characteristic
23	#19151696	C₄	1	1	yes	characteristic
24	#19151696	C₄	1	1	yes	characteristic
25	C₄×#13083561	C₂²	1	1	yes	characteristic
26	C₄×#13083561	C₂²	1	1	yes	characteristic
27	C₄×#13083559	C₂²	1	1	yes	characteristic
28	C₄×#13083559	C₂²	1	1	yes	characteristic
29	#19151676	—	2	1	no	—
30	#19151676	—	2	1	no	—
31	#19151676	C₂²	1	1	yes	characteristic, complemented
32	#19151676	C₂²	1	1	yes	characteristic, complemented
33	#19151675	C₂²	1	1	yes	characteristic
34	#19151675	C₂²	1	1	yes	characteristic
35	#19151668	—	2	1	no	—
36	#19151668	—	2	1	no	—
37	#19151663	C₂²	1	1	yes	characteristic
38	#19151663	C₂²	1	1	yes	characteristic
39	#19151655	—	2	1	no	—
40	#19151655	C₂²	1	1	yes	characteristic
41	#19151641	C₄	1	1	yes	characteristic
42	#19151602	C₄	1	1	yes	characteristic
43	#19151599	C₄	1	1	yes	characteristic
44	#19151561	—	2	1	no	—
45	C₄×#13083558	—	2	1	no	—
46	C₄×#13083558	C₂²	1	1	yes	characteristic
47	C₄×#13083558	C₂²	1	1	yes	characteristic
48	#19151350	C₂²	1	1	yes	characteristic, complemented
49	#19151350	C₂²	1	1	yes	characteristic, complemented
50	#19151348	C₂²	1	1	yes	characteristic, complemented
51	#19151348	C₂²	1	1	yes	characteristic, complemented
52	#19151327	C₂²	1	1	yes	characteristic
53	#19151327	C₂²	1	1	yes	characteristic
54	#19151327	C₂²	1	1	yes	characteristic
55	#19151327	C₂²	1	1	yes	characteristic
56	#19151320	C₂²	1	1	yes	characteristic, complemented
57	#19151320	C₂²	1	1	yes	characteristic, complemented
58	#19151319	C₂²	1	1	yes	characteristic, complemented
59	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
61	#423×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₈₉	—	2	1	no	—
69	#15668037	—	2	4	no	—
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083558	—	2	1	no	—
75	C₂×#13083558	—	2	1	no	—
76	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
77	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
78	C₂×#13083558	D₄	1	1	yes	characteristic
79	C₂×#13083558	D₄	1	1	yes	characteristic
80	C₂×#13083557	—	2	1	no	—
81	C₂×#13083557	—	2	1	no	—
82	M₁₆×D₈₉	—	4	4	no	—
83	C₂×C₈×D₈₉	—	2	1	no	—
84	C₂×C₈×D₈₉	—	2	1	no	—
85	C₄×D₃₅₆	—	2	1	no	—
86	C₄×D₃₅₆	—	2	1	no	—
87	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
88	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
89	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
90	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂×#13083551	—	2	1	no	—
93	#15667945	C₂×C₄	1	1	yes	characteristic
94	#15667945	C₂×C₄	1	1	yes	characteristic
95	#15667943	C₂×C₄	1	1	yes	characteristic
96	#15667943	C₂×C₄	1	1	yes	characteristic
97	C₄⋊#10623494	—	2	1	no	—
98	C₄⋊#10623494	—	2	1	no	—
99	C₄⋊#10623494	C₂³	1	1	yes	characteristic
100	C₄⋊#10623494	C₂³	1	1	yes	characteristic
101	#15667936	C₂×C₄	1	1	yes	characteristic
102	#15667936	C₂×C₄	1	1	yes	characteristic
103	#15667933	C₂×C₄	1	1	yes	characteristic
104	#15667933	C₂×C₄	1	1	yes	characteristic
105	#15667932	C₂×C₄	1	1	yes	characteristic
106	#15667932	C₂×C₄	1	1	yes	characteristic
107	#15667932	C₂×C₄	1	1	yes	characteristic
108	#15667932	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊#10623494	—	2	1	no	—
110	C₂²⋊#10623494	—	2	1	no	—
111	C₂²⋊#10623494	—	2	1	no	—
112	#15667924	—	2	1	no	—
113	#15667924	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	—	2	1	no	—
116	#15667923	—	2	1	no	—
117	#15667923	C₂×C₄	1	1	yes	characteristic
118	#15667923	C₂×C₄	1	1	yes	characteristic
119	#15667923	D₄	1	1	yes	characteristic
120	#15667923	D₄	1	1	yes	characteristic
121	C₄×#10623494	—	2	1	no	—
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	C₄×#10623494	C₂³	1	1	yes	characteristic
127	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×M₁₆×C₈₉	—	2	1	no	—
129	C₂×M₁₆×C₈₉	—	2	1	no	—
130	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₈₉	—	2	1	no	—
133	C₄×D₄×C₈₉	—	2	1	no	—
134	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
135	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
136	#117×C₈₉	—	2	1	no	—
137	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₈₉	—	2	1	no	—
139	C₂×C₄²×C₈₉	C₂³	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	#97×C₈₉	—	2	1	no	—
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂³×D₈₉	—	2	1	no	—
147	C₂×D₃₅₆	—	2	2	no	—
148	C₂×D₃₅₆	—	2	1	no	—
149	C₂×D₃₅₆	—	4	1	no	—
150	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₈₉	—	2	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	—	4	2	no	—
158	C₂×C₄×D₈₉	—	4	2	no	—
159	#13083561	—	2	2	no	—
160	#13083561	M₁₆	1	4	yes	complemented
161	#13083559	—	2	2	no	—
162	#13083559	—	2	2	no	—
163	#13083558	—	2	2	no	—
164	#13083558	—	2	2	no	—
165	#13083558	—	4	1	no	—
166	#13083558	—	4	1	no	—
167	#13083558	—	4	2	no	—
168	#13083558	—	4	2	no	—
169	#13083557	—	4	2	no	—
170	#13083557	—	4	2	no	—
171	C₂×#10623494	—	2	1	no	—
172	C₂×#10623494	—	2	1	no	—
173	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
174	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
175	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
176	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
177	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
178	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
179	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
180	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
181	C₈×D₈₉	—	4	2	no	—
182	C₈×D₈₉	—	4	2	no	—
183	C₄⋊Dic₈₉	—	2	1	no	—
184	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
186	#13083551	—	2	1	no	—
187	#13083551	—	2	1	no	—
188	#13083551	—	2	1	no	—
189	#13083551	—	2	1	no	—
190	#41×C₈₉	—	2	2	no	—
191	#41×C₈₉	—	4	1	no	—
192	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
201	M₁₆×C₈₉	—	4	2	no	—
202	M₁₆×C₈₉	—	4	2	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	2	1	no	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₄⋊C₄×C₈₉	—	2	1	no	—
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
213	C₂²⋊C₄×C₈₉	—	2	1	no	—
214	C₄²×C₈₉	—	2	1	no	—
215	C₄²×C₈₉	—	2	1	no	—
216	C₄²×C₈₉	—	2	1	no	—
217	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₈₉	#41	1	1	yes	characteristic
220	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂³×C₈₉	—	2	1	no	—
222	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
223	C₂²×D₈₉	—	2	1	no	—
224	C₂²×D₈₉	—	2	1	no	—
225	C₂²×D₈₉	—	4	2	no	—
226	C₂²×D₈₉	—	4	2	no	—
227	C₂²×D₈₉	—	8	1	no	—
228	Q₈×C₈₉	—	2	1	no	—
229	Q₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
230	D₄×C₈₉	—	2	1	no	—
231	D₄×C₈₉	—	2	1	no	—
232	D₄×C₈₉	—	4	2	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	1	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	4	1	no	—
241	C₂×C₄×C₈₉	—	4	2	no	—
242	C₂×C₄×C₈₉	—	4	1	no	—
243	C₂×C₄×C₈₉	—	4	1	no	—
244	C₂×C₄×C₈₉	—	8	1	no	—
245	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
251	C₂×Dic₈₉	—	2	1	no	—
252	C₂×Dic₈₉	—	2	1	no	—
253	C₂×Dic₈₉	—	4	2	no	—
254	D₃₅₆	—	2	1	no	—
255	D₃₅₆	—	2	1	no	—
256	D₃₅₆	—	2	1	no	—
257	D₃₅₆	—	4	2	no	—
258	D₃₅₆	C₂×M₁₆	1	2	yes	—
259	C₄×D₈₉	—	4	2	no	—
260	C₄×D₈₉	—	4	2	no	—
261	C₄×D₈₉	—	4	1	no	—
262	C₄×D₈₉	—	4	1	no	—
263	C₄×D₈₉	—	4	1	no	—
264	C₄×D₈₉	—	4	1	no	—
265	C₈×C₈₉	—	2	2	no	—
266	C₈×C₈₉	—	4	1	no	—
267	C₈×C₈₉	—	4	1	no	—
268	C₈×C₈₉	—	4	1	no	—
269	#10623494	—	2	1	no	—
270	#10623494	—	2	1	no	—
271	#10623494	—	2	1	no	—
272	#10623494	—	2	1	no	—
273	#10623494	—	2	1	no	—
274	#10623494	—	2	1	no	—
275	#10623494	—	4	1	no	—
276	#10623494	—	4	1	no	—
277	#10623494	C₂×M₁₆	1	2	yes	complemented
278	#10623494	AGL(1,ℤ/8)	1	2	yes	complemented
279	C₂²×C₈₉	—	2	1	no	—
280	C₂²×C₈₉	—	2	1	no	—
281	C₂²×C₈₉	—	2	1	no	—
282	C₂²×C₈₉	—	4	1	no	—
283	C₂²×C₈₉	—	4	1	no	—
284	C₂²×C₈₉	—	4	1	no	—
285	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂×D₈₉	—	2	2	no	—
287	C₂×D₈₉	—	4	1	no	—
288	C₂×D₈₉	—	4	1	no	—
289	C₂×D₈₉	—	4	1	no	—
290	C₂×D₈₉	—	4	1	no	—
291	C₂×D₈₉	—	4	1	no	—
292	C₂×D₈₉	—	8	4	no	—
293	C₄×C₈₉	—	2	1	no	—
294	C₄×C₈₉	—	2	2	no	—
295	C₄×C₈₉	—	2	1	no	—
296	C₄×C₈₉	—	2	1	no	—
297	C₄×C₈₉	—	2	1	no	—
298	C₄×C₈₉	—	4	1	no	—
299	C₄×C₈₉	—	4	1	no	—
300	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
301	C₄×C₈₉	#568	1	1	yes	characteristic
302	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₄×C₈₉	#575	1	1	yes	characteristic
304	Dic₈₉	—	4	1	no	—
305	Dic₈₉	—	4	1	no	—
306	#18048	—	89	1	no	maximal, Sylow
307	C₂×C₈₉	—	4	1	no	—
308	C₂×C₈₉	—	8	1	no	—
309	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
310	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₂×C₈₉	#2956	1	1	yes	characteristic
312	D₈₉	—	4	2	no	—
313	D₈₉	—	8	1	no	—
314	#2971	—	89	1	no	—
315	C₄×AGL(1,ℤ/8)	—	89	1	no	—
316	D₄×M₁₆	—	89	1	no	—
317	#1594	—	89	1	no	—
318	#1589	—	89	1	no	—
319	#1588	—	89	1	no	—
320	#1586	—	89	1	no	—
321	#1583	—	89	1	no	—
322	#1581	—	89	1	no	—
323	SD₁₆⋊C₈	—	89	1	no	—
324	C₈×SD₁₆	—	89	1	no	—
325	#1569	—	89	1	no	—
326	#1490	—	89	1	no	—
327	#1489	D₈₉	1	1	yes	characteristic, complemented
328	#1455	—	89	1	no	—
329	C₈₉	#18048	1	1	yes	characteristic, complemented, Sylow
330	C₂×AGL(1,ℤ/8)	—	89	1	no	—
331	C₂²×M₁₆	—	178	1	no	—
332	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
333	C₂×C₄×D₄	—	89	1	no	—
334	C₈×Q₈	—	89	1	no	—
335	C₈×Q₈	—	89	1	no	—
336	#442	—	89	1	no	—
337	#442	—	89	1	no	—
338	#440	—	89	1	no	—
339	#440	—	89	1	no	—
340	C₄×SD₁₆	—	89	1	no	—
341	C₄×SD₁₆	—	89	1	no	—
342	C₄×D₈	—	89	1	no	—
343	C₄×D₈	—	89	1	no	—
344	#436	—	89	1	no	—
345	#436	—	89	1	no	—
346	#436	—	89	1	no	—
347	#436	—	89	1	no	—
348	#436	—	178	1	no	—
349	#436	—	178	1	no	—
350	#435	—	178	1	no	—
351	#435	—	178	1	no	—
352	C₈×D₄	—	89	1	no	—
353	C₈×D₄	—	89	1	no	—
354	#432	—	89	1	no	—
355	#432	—	178	1	no	—
356	#428	—	89	1	no	—
357	#423	C₂×D₈₉	1	1	yes	characteristic
358	#418	—	89	1	no	—
359	#417	—	89	1	no	—
360	#407	—	178	1	no	—
361	C₄×M₁₆	—	89	1	no	—
362	C₄×M₁₆	—	89	1	no	—
363	C₄×M₁₆	—	178	1	no	—
364	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
365	#335	—	89	1	no	—
366	#335	—	89	1	no	—
367	#334	—	89	1	no	—
368	#334	—	89	1	no	—
369	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
370	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
371	D₄⋊C₈	—	89	1	no	—
372	D₄⋊C₈	—	89	1	no	—
373	D₄⋊C₈	—	89	1	no	—
374	D₄⋊C₈	—	89	1	no	—
375	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
376	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
377	#322	—	89	1	no	—
378	#322	—	89	1	no	—
379	#322	—	89	1	no	—
380	C₈²	—	89	1	no	—
381	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
382	C₂²×D₄	—	89	1	no	—
383	C₂³×C₄	—	178	1	no	—
384	AGL(1,ℤ/8)	—	178	4	no	—
385	C₂×SD₁₆	—	89	1	no	—
386	C₂×SD₁₆	—	89	1	no	—
387	C₂×D₈	—	89	1	no	—
388	C₂×D₈	—	89	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	89	1	no	—
392	C₂×M₁₆	—	89	1	no	—
393	C₂×M₁₆	—	89	1	no	—
394	C₂×M₁₆	—	89	1	no	—
395	C₂×M₁₆	—	356	4	no	—
396	C₂×M₁₆	—	178	1	no	—
397	C₂×M₁₆	—	178	1	no	—
398	C₂×M₁₆	—	178	1	no	—
399	C₂×M₁₆	—	178	1	no	—
400	C₂²×C₈	—	178	1	no	—
401	C₂²×C₈	—	178	1	no	—
402	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
403	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	89	1	no	—
407	C₄×D₄	—	89	1	no	—
408	C₄×D₄	—	89	1	no	—
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	178	1	no	—
411	C₄×D₄	—	178	1	no	—
412	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
413	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
414	#117	—	2	1	no	—
415	#117	C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	89	1	no	—
417	C₂×C₂²⋊C₄	—	178	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
420	#107	—	89	1	no	—
421	#107	—	89	1	no	—
422	#106	—	89	1	no	—
423	#106	—	89	1	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	—	89	1	no	—
426	C₄⋊C₈	—	89	1	no	—
427	C₄⋊C₈	—	178	1	no	—
428	C₄⋊C₈	—	178	1	no	—
429	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
430	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
431	#103	—	89	1	no	—
432	#103	—	89	1	no	—
433	#102	—	89	1	no	—
434	#102	—	89	1	no	—
435	#102	—	89	1	no	—
436	#102	—	89	1	no	—
437	#102	—	89	1	no	—
438	#102	—	89	1	no	—
439	C₂²⋊C₈	—	178	1	no	—
440	C₂²⋊C₈	—	178	1	no	—
441	C₂²⋊C₈	—	178	1	no	—
442	C₂²⋊C₈	—	178	1	no	—
443	C₂²⋊C₈	—	178	1	no	—
444	C₂²⋊C₈	—	178	1	no	—
445	C₂²⋊C₈	—	178	1	no	—
446	#97	—	2	1	no	—
447	#97	—	89	1	no	—
448	#97	—	89	1	no	—
449	#97	—	89	1	no	—
450	#97	—	89	1	no	—
451	#97	—	178	1	no	—
452	C₄×C₈	—	89	1	no	—
453	C₄×C₈	—	89	1	no	—
454	C₄×C₈	—	89	1	no	—
455	C₄×C₈	—	89	1	no	—
456	C₄×C₈	—	178	1	no	—
457	C₄×C₈	—	178	1	no	—
458	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
459	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
460	C₂⁴	—	178	1	no	—
461	#41	—	2	2	no	—
462	#41	—	4	1	no	—
463	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	89	1	no	—
466	C₂×D₄	—	89	1	no	—
467	C₂×D₄	—	356	1	no	—
468	C₂×D₄	—	178	2	no	—
469	C₂×D₄	—	178	1	no	—
470	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	356	2	no	—
475	C₂²×C₄	—	356	2	no	—
476	C₂²×C₄	—	178	1	no	—
477	C₂²×C₄	—	178	1	no	—
478	C₂²×C₄	—	178	1	no	—
479	C₂²×C₄	—	178	1	no	—
480	C₂²×C₄	—	178	1	no	—
481	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
482	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
483	C₂²×C₄	#13083573	1	1	yes	characteristic
484	SD₁₆	—	89	4	no	—
485	SD₁₆	—	178	2	no	—
486	D₈	—	178	2	no	—
487	D₈	—	178	2	no	—
488	M₁₆	—	4	2	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	356	2	no	—
491	M₁₆	—	356	2	no	—
492	M₁₆	—	356	2	no	—
493	M₁₆	—	356	2	no	—
494	M₁₆	—	356	1	no	—
495	M₁₆	—	356	1	no	—
496	M₁₆	—	178	2	no	—
497	M₁₆	—	178	2	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	89	1	no	—
503	C₂×C₈	—	89	1	no	—
504	C₂×C₈	—	89	1	no	—
505	C₂×C₈	—	89	1	no	—
506	C₂×C₈	—	89	1	no	—
507	C₂×C₈	—	89	1	no	—
508	C₂×C₈	—	89	1	no	—
509	C₂×C₈	—	89	1	no	—
510	C₂×C₈	—	356	2	no	—
511	C₂×C₈	—	356	2	no	—
512	C₂×C₈	—	178	1	no	—
513	C₂×C₈	—	178	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	89	1	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	178	1	no	—
519	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	178	1	no	—
525	C₂²⋊C₄	—	178	1	no	—
526	C₂²⋊C₄	—	178	1	no	—
527	C₂²⋊C₄	—	178	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
532	C₄²	D₄×D₈₉	1	1	yes	characteristic
533	C₄²	#13083573	1	1	yes	characteristic
534	C₄²	C₂³×D₈₉	1	1	yes	characteristic
535	C₂³	—	2	1	no	—
536	C₂³	—	356	2	no	—
537	C₂³	—	356	2	no	—
538	C₂³	—	178	1	no	—
539	C₂³	—	178	1	no	—
540	C₂³	—	712	1	no	—
541	C₂³	#15667972	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	M₁₆×D₈₉	1	2	yes	complemented
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	89	2	no	—
548	D₄	—	356	2	no	—
549	D₄	—	178	1	no	—
550	D₄	—	178	1	no	—
551	D₄	—	178	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	—	356	2	no	—
565	C₂×C₄	—	356	2	no	—
566	C₂×C₄	—	356	2	no	—
567	C₂×C₄	—	356	1	no	—
568	C₂×C₄	—	356	1	no	—
569	C₂×C₄	—	356	1	no	—
570	C₂×C₄	—	356	1	no	—
571	C₂×C₄	—	178	1	no	—
572	C₂×C₄	—	178	1	no	—
573	C₂×C₄	#15667972	1	1	yes	characteristic
574	C₂×C₄	#15667972	1	1	yes	characteristic
575	C₂×C₄	#15667972	1	1	yes	characteristic
576	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
577	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
578	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
579	C₈	—	2	2	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	89	2	no	—
584	C₈	—	89	2	no	—
585	C₈	—	356	1	no	—
586	C₈	—	356	1	no	—
587	C₈	—	178	1	no	—
588	C₈	—	178	1	no	—
589	C₈	—	178	1	no	—
590	C₈	—	178	1	no	—
591	C₈	—	178	1	no	—
592	C₈	—	178	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	356	1	no	—
600	C₂²	—	356	1	no	—
601	C₂²	—	356	1	no	—
602	C₂²	—	356	1	no	—
603	C₂²	—	356	1	no	—
604	C₂²	—	178	2	no	—
605	C₂²	—	712	4	no	—
606	C₂²	C₂×#15667972	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	356	1	no	—
615	C₄	—	356	1	no	—
616	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
617	C₄	#19152364	1	1	yes	characteristic
618	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
619	C₄	#19152397	1	1	yes	characteristic
620	C₂	—	4	1	no	—
621	C₂	—	8	1	no	—
622	C₂	—	356	2	no	—
623	C₂	—	712	1	no	—
624	C₂	#26028984	1	1	yes	characteristic
625	C₂	#26029065	1	1	yes	characteristic
626	C₂	#26029158	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×#1489	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668037	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1489	D₈₉
hypocenter	C₈₉	#18048
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1489

Complements

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

N	H ≅ G/N	type
1. #26029272	C₂	semidirect
3. #26028987	C₂	semidirect
4. #26019163	C₂	semidirect
5. #26019134	C₂	semidirect
6. #26019127	C₂	semidirect
7. #26019119	C₂	semidirect
8. #26019092	C₂	semidirect
9. #26019084	C₂	semidirect
10. #26019067	C₂	semidirect
11. #26019049	C₂	semidirect
12. #26019017	C₂	semidirect
13. #26018696	C₂	semidirect
14. #26018555	C₂	semidirect
15. C₈₉×#1489	C₂	semidirect
19. Q₈×#10623494	C₂²	semidirect
20. Q₈×#10623494	C₂²	semidirect
31. #19151676	C₂²	semidirect
32. #19151676	C₂²	semidirect
48. #19151350	C₂²	semidirect
49. #19151350	C₂²	semidirect
50. #19151348	C₂²	semidirect
51. #19151348	C₂²	semidirect
56. #19151320	C₂²	semidirect
57. #19151320	C₂²	semidirect
58. #19151319	C₂²	semidirect
59. C₈×#10623494	C₂²	semidirect
63. Q₈⋊C₈×C₈₉	C₂²	semidirect
64. Q₈⋊C₈×C₈₉	C₂²	semidirect
65. D₄⋊C₈×C₈₉	C₂²	semidirect
66. D₄⋊C₈×C₈₉	C₂²	semidirect
160. #13083561	M₁₆	semidirect
229. Q₈×C₈₉	C₂×M₁₆	semidirect
277. #10623494	C₂×M₁₆	semidirect
278. #10623494	AGL(1,ℤ/8)	semidirect
327. #1489	D₈₉	semidirect
329. C₈₉	#18048	semidirect
369. Q₈⋊C₈	C₂×D₈₉	semidirect
370. Q₈⋊C₈	C₂×D₈₉	semidirect
375. D₄⋊C₈	C₂×D₈₉	semidirect
376. D₄⋊C₈	C₂×D₈₉	semidirect
543. Q₈	M₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029272	2
C₄×#15668037	2
#26028987	2
#26019163	2
#26019134	2
#26019127	2
#26019119	2
#26019092	2
#26019084	2
#26019067	2
#26019049	2
#26019017	2
#26018696	2
#26018555	2
C₈₉×#1489	2
#18048	89