Subgroups — #36524401

Order 22784.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030297	C₂	1	1	yes	maximal, characteristic
2	#26029230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019114	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019111	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019109	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019055	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019051	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019044	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019034	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018693	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018662	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018531	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₈₉	—	2	1	no	—
17	#19152130	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#19151935	C₄	1	1	yes	characteristic
20	#19151915	C₄	1	1	yes	characteristic
21	#19151901	C₄	1	1	yes	characteristic
22	#19151900	C₄	1	1	yes	characteristic
23	#19151812	C₄	1	1	yes	characteristic
24	#19151811	C₄	1	1	yes	characteristic
25	#19151750	C₄	1	1	yes	characteristic
26	#19151730	C₄	1	1	yes	characteristic
27	#19151728	C₂²	1	1	yes	characteristic, complemented
28	#19151722	C₂²	1	1	yes	characteristic, complemented
29	C₄×#13083563	C₂²	1	1	yes	characteristic
30	C₄×#13083562	C₂²	1	1	yes	characteristic
31	C₄×#13083559	C₂²	1	1	yes	characteristic
32	#19151667	—	2	1	no	—
33	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
34	D₄×#10623494	C₂²	1	1	yes	characteristic
35	D₄×#10623494	C₂²	1	1	yes	characteristic, complemented
36	#19151663	C₂²	1	1	yes	characteristic
37	C₈×C₂²⋊D₈₉	—	2	1	no	—
38	#19151661	—	2	1	no	—
39	#19151661	—	2	1	no	—
40	#19151656	—	2	1	no	—
41	#19151654	C₂²	1	1	yes	characteristic
42	#19151649	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
44	C₂²⋊C₈×D₈₉	—	2	1	no	—
45	#19151556	—	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, complemented
49	#19151350	C₂²	1	1	yes	characteristic, complemented
50	#19151348	C₂²	1	1	yes	characteristic, complemented
51	#19151330	C₂²	1	1	yes	characteristic, complemented
52	#19151328	C₂²	1	1	yes	characteristic, complemented
53	#19151327	C₂²	1	1	yes	characteristic
54	D₄⋊#10623494	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
56	#19151325	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic, complemented
58	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
59	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
61	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₈₉	—	2	1	no	—
69	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083557	—	2	1	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₂²×#10623494	—	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	—	4	4	no	—
79	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
80	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
81	#15668005	—	2	1	no	—
82	#15668003	C₂×C₄	1	1	yes	characteristic
83	#15667999	C₂×C₄	1	1	yes	characteristic
84	#15667994	—	2	1	no	—
85	#15667992	C₂×C₄	1	1	yes	characteristic
86	#15667983	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
89	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
90	#15667974	C₂×C₄	1	1	yes	characteristic
91	C₄×C₂²⋊D₈₉	—	2	1	no	—
92	C₄×C₂²⋊D₈₉	—	2	1	no	—
93	#15667972	—	2	1	no	—
94	#15667971	—	2	1	no	—
95	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊C₄×D₈₉	—	2	1	no	—
97	C₄²×D₈₉	C₂³	1	1	yes	characteristic
98	#15667945	C₂×C₄	1	1	yes	characteristic
99	#15667944	C₂×C₄	1	1	yes	characteristic
100	#15667943	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
107	#15667941	C₂×C₄	1	1	yes	characteristic
108	#15667937	C₂×C₄	1	1	yes	characteristic
109	#15667935	C₂×C₄	1	1	yes	characteristic
110	#15667934	C₂×C₄	1	1	yes	characteristic
111	#15667933	C₂×C₄	1	1	yes	characteristic
112	#15667933	C₂×C₄	1	1	yes	characteristic
113	#15667932	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#10623494	—	2	1	no	—
115	C₂²⋊#10623494	—	2	1	no	—
116	#15667924	—	2	1	no	—
117	#15667924	—	2	1	no	—
118	#15667924	—	2	1	no	—
119	#15667924	C₂×C₄	1	1	yes	characteristic
120	#15667924	C₂×C₄	1	1	yes	characteristic
121	#15667922	—	2	1	no	—
122	#15667922	—	2	1	no	—
123	#15667922	—	2	1	no	—
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	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	D₄	1	1	yes	characteristic
129	C₈×Dic₈₉	D₄	1	1	yes	characteristic
130	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₈₉	—	2	1	no	—
132	C₂²×C₈×C₈₉	—	2	1	no	—
133	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₉	—	2	1	no	—
141	C₂²⋊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	C₂³×D₈₉	—	2	1	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₉	—	2	1	no	—
149	C₂×C₂²⋊D₈₉	—	2	1	no	—
150	D₄×D₈₉	—	2	2	no	—
151	D₄×D₈₉	—	2	2	no	—
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	—	4	2	no	—
157	C₂×C₄×D₈₉	—	4	2	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	#13083563	—	2	2	no	—
162	#13083562	—	2	2	no	—
163	#13083559	—	2	2	no	—
164	#13083557	—	2	4	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	—	4	2	no	—
169	C₂×#10623494	—	4	2	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	C₈×D₈₉	—	4	2	no	—
177	C₈×D₈₉	—	4	2	no	—
178	C₈×D₈₉	—	4	2	no	—
179	C₄⋊Dic₈₉	—	2	1	no	—
180	C₄⋊Dic₈₉	—	2	1	no	—
181	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
183	#13083553	—	2	1	no	—
184	#13083553	—	2	1	no	—
185	#13083553	—	2	1	no	—
186	C₂²⋊Dic₈₉	—	2	1	no	—
187	C₂²⋊Dic₈₉	—	2	1	no	—
188	C₂²⋊Dic₈₉	—	2	1	no	—
189	C₂²⋊Dic₈₉	—	2	1	no	—
190	#13083551	—	2	1	no	—
191	#13083551	—	2	1	no	—
192	#13083551	—	2	1	no	—
193	C₄×Dic₈₉	—	2	1	no	—
194	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
196	C₄×Dic₈₉	#41	1	1	yes	characteristic
197	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	D₈×C₈₉	—	2	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	—	4	2	no	—
207	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₈₉	—	2	1	no	—
214	C₂²⋊C₄×C₈₉	—	2	1	no	—
215	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
216	C₂³×C₈₉	—	2	1	no	—
217	C₂³×C₈₉	—	2	1	no	—
218	C₂²×D₈₉	—	2	4	no	—
219	C₂²×D₈₉	—	2	1	no	—
220	C₂²×D₈₉	—	4	2	no	—
221	C₂²×D₈₉	—	4	2	no	—
222	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	2	1	no	—
225	D₄×C₈₉	—	2	1	no	—
226	D₄×C₈₉	#131	1	2	yes	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	4	1	no	—
232	C₂×C₄×C₈₉	—	4	1	no	—
233	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
236	C₂²⋊D₈₉	—	2	4	no	—
237	C₂²⋊D₈₉	—	4	2	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	4	2	no	—
242	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
243	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
245	D₃₅₆	—	2	1	no	—
246	D₃₅₆	#131	1	2	yes	—
247	C₄×D₈₉	—	2	2	no	—
248	C₄×D₈₉	—	2	1	no	—
249	C₄×D₈₉	—	2	1	no	—
250	C₄×D₈₉	—	2	1	no	—
251	C₄×D₈₉	—	2	1	no	—
252	C₄×D₈₉	—	4	2	no	—
253	C₄×D₈₉	—	4	2	no	—
254	C₄×D₈₉	—	4	1	no	—
255	C₄×D₈₉	—	4	1	no	—
256	Dic₁₇₈	—	2	1	no	—
257	Dic₁₇₈	—	2	1	no	—
258	C₈×C₈₉	—	2	2	no	—
259	C₈×C₈₉	—	2	1	no	—
260	C₈×C₈₉	—	2	1	no	—
261	C₈×C₈₉	—	2	1	no	—
262	C₈×C₈₉	—	2	1	no	—
263	C₈×C₈₉	—	4	1	no	—
264	C₈×C₈₉	—	4	1	no	—
265	#10623494	—	2	2	no	—
266	#10623494	—	2	1	no	—
267	#10623494	—	2	1	no	—
268	#10623494	—	2	1	no	—
269	#10623494	—	4	1	no	—
270	#10623494	—	4	1	no	—
271	#10623494	AGL(1,ℤ/8)	1	2	yes	—
272	C₂²×C₈₉	—	2	2	no	—
273	C₂²×C₈₉	—	4	1	no	—
274	C₂²×C₈₉	—	4	1	no	—
275	C₂²×C₈₉	—	4	1	no	—
276	C₂²×C₈₉	—	4	1	no	—
277	C₂²×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂×D₈₉	—	2	1	no	—
280	C₂×D₈₉	—	2	1	no	—
281	C₂×D₈₉	—	2	2	no	—
282	C₂×D₈₉	—	4	8	no	—
283	C₂×D₈₉	—	4	1	no	—
284	C₂×D₈₉	—	4	1	no	—
285	C₂×D₈₉	#443	1	2	yes	—
286	C₄×C₈₉	—	2	1	no	—
287	C₄×C₈₉	—	4	1	no	—
288	C₄×C₈₉	—	4	1	no	—
289	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
290	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
291	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₄×C₈₉	#575	1	1	yes	characteristic
293	Dic₈₉	—	2	1	no	—
294	Dic₈₉	—	2	1	no	—
295	Dic₈₉	—	2	1	no	—
296	Dic₈₉	—	4	1	no	—
297	Dic₈₉	—	4	1	no	—
298	Dic₈₉	—	4	1	no	—
299	#17910	—	89	1	no	maximal, Sylow
300	C₂×C₈₉	—	4	2	no	—
301	C₂×C₈₉	—	8	1	no	—
302	C₂×C₈₉	#2929	1	1	yes	characteristic
303	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
305	D₈₉	—	2	2	no	—
306	D₈₉	—	4	2	no	—
307	#3105	—	89	1	no	—
308	#2966	—	89	1	no	—
309	C₂×C₈×D₄	—	89	1	no	—
310	#1586	—	89	1	no	—
311	#1586	D₈₉	1	1	yes	characteristic, complemented
312	#1585	—	89	1	no	—
313	#1585	—	89	1	no	—
314	C₈×SD₁₆	—	89	1	no	—
315	C₈×SD₁₆	—	89	1	no	—
316	C₈×D₈	—	89	1	no	—
317	C₈×D₈	—	89	1	no	—
318	#1573	—	89	1	no	—
319	#1490	—	89	1	no	—
320	#1483	—	89	1	no	—
321	C₈×M₁₆	—	89	1	no	—
322	C₈₉	#17910	1	1	yes	characteristic, complemented, Sylow
323	C₂³×C₈	—	178	1	no	—
324	#529	—	89	1	no	—
325	C₂×C₄×D₄	—	89	1	no	—
326	#484	—	89	1	no	—
327	#481	—	89	1	no	—
328	#478	—	89	1	no	—
329	#478	—	89	1	no	—
330	#463	—	89	1	no	—
331	#463	—	89	1	no	—
332	#450	—	89	1	no	—
333	#447	—	89	1	no	—
334	#446	—	89	1	no	—
335	C₈×Q₈	—	89	1	no	—
336	C₄×SD₁₆	—	89	1	no	—
337	C₄×SD₁₆	—	89	1	no	—
338	C₄×D₈	—	89	1	no	—
339	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
340	#436	C₂×D₈₉	1	1	yes	characteristic, complemented
341	#435	—	178	1	no	—
342	C₈×D₄	—	89	1	no	—
343	C₈×D₄	—	89	1	no	—
344	C₈×D₄	—	89	1	no	—
345	C₈×D₄	—	89	1	no	—
346	C₈×D₄	—	178	1	no	—
347	C₈×D₄	—	178	1	no	—
348	C₈×D₄	—	178	1	no	—
349	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
350	#433	—	178	1	no	—
351	#432	—	89	1	no	—
352	#431	—	89	1	no	—
353	C₂×C₄⋊C₈	—	89	1	no	—
354	C₂×C₂²⋊C₈	—	178	1	no	—
355	#405	—	178	1	no	—
356	C₄×M₁₆	—	89	1	no	—
357	C₂×C₄×C₈	—	89	1	no	—
358	#335	—	89	1	no	—
359	#335	—	89	1	no	—
360	#334	—	89	1	no	—
361	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
362	Q₈⋊C₈	—	89	1	no	—
363	Q₈⋊C₈	—	89	1	no	—
364	D₄⋊C₈	—	89	1	no	—
365	D₄⋊C₈	—	89	1	no	—
366	D₄⋊C₈	—	89	1	no	—
367	D₄⋊C₈	—	89	1	no	—
368	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
369	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
370	#322	—	89	1	no	—
371	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
372	C₈²	—	89	1	no	—
373	C₈²	—	89	1	no	—
374	C₂²×D₄	—	89	1	no	—
375	C₂³×C₄	—	178	1	no	—
376	C₂×SD₁₆	—	89	1	no	—
377	C₂×SD₁₆	—	89	1	no	—
378	C₂×D₈	—	89	1	no	—
379	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	178	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	89	1	no	—
384	C₂²×C₈	—	89	1	no	—
385	C₂²×C₈	—	356	4	no	—
386	C₂²×C₈	—	178	1	no	—
387	C₂²×C₈	—	178	1	no	—
388	C₂²×C₈	—	178	1	no	—
389	C₂²×C₈	—	178	1	no	—
390	C₂²×C₈	—	178	1	no	—
391	#126	—	178	1	no	—
392	#125	—	89	1	no	—
393	#124	—	89	1	no	—
394	#123	—	178	1	no	—
395	C₂²⋊Q₈	—	89	1	no	—
396	#121	—	89	1	no	—
397	C₄×Q₈	—	89	1	no	—
398	C₄×D₄	—	89	1	no	—
399	C₄×D₄	—	89	1	no	—
400	C₄×D₄	—	89	1	no	—
401	C₄×D₄	—	178	1	no	—
402	C₄×D₄	—	178	1	no	—
403	C₄×D₄	—	178	1	no	—
404	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
405	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
406	#117	—	178	1	no	—
407	C₂×C₄⋊C₄	—	89	1	no	—
408	C₂×C₂²⋊C₄	—	178	1	no	—
409	C₂×C₄²	—	89	1	no	—
410	#107	—	89	1	no	—
411	#107	C₄×D₈₉	1	1	yes	characteristic
412	#106	—	89	1	no	—
413	#106	—	89	1	no	—
414	C₄⋊C₈	—	89	1	no	—
415	C₄⋊C₈	—	89	1	no	—
416	C₄⋊C₈	—	89	1	no	—
417	C₄⋊C₈	—	89	1	no	—
418	C₄⋊C₈	—	178	1	no	—
419	C₄⋊C₈	—	178	1	no	—
420	C₄⋊C₈	—	178	1	no	—
421	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
422	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
423	#103	—	89	1	no	—
424	#103	—	89	1	no	—
425	#102	—	89	1	no	—
426	#102	—	89	1	no	—
427	#102	—	89	1	no	—
428	#102	—	89	1	no	—
429	#102	C₄×D₈₉	1	1	yes	characteristic
430	#102	C₄×D₈₉	1	1	yes	characteristic
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	89	1	no	—
434	C₂²⋊C₈	—	89	1	no	—
435	C₂²⋊C₈	—	178	1	no	—
436	C₂²⋊C₈	—	178	1	no	—
437	C₂²⋊C₈	—	178	1	no	—
438	C₂²⋊C₈	—	178	1	no	—
439	C₂²⋊C₈	—	178	1	no	—
440	#97	—	178	1	no	—
441	#97	—	178	1	no	—
442	#97	—	178	1	no	—
443	C₄×C₈	—	89	1	no	—
444	C₄×C₈	—	89	1	no	—
445	C₄×C₈	—	89	1	no	—
446	C₄×C₈	—	89	1	no	—
447	C₄×C₈	—	89	1	no	—
448	C₄×C₈	—	178	1	no	—
449	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
450	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
451	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
452	C₂⁴	—	178	1	no	—
453	C₂×Q₈	—	89	1	no	—
454	C₂×D₄	—	89	1	no	—
455	C₂×D₄	—	178	1	no	—
456	C₂×D₄	—	178	2	no	—
457	C₂×D₄	—	178	1	no	—
458	C₂×D₄	—	178	2	no	—
459	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
460	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	89	1	no	—
464	C₂²×C₄	—	89	1	no	—
465	C₂²×C₄	—	89	1	no	—
466	C₂²×C₄	—	356	2	no	—
467	C₂²×C₄	—	356	2	no	—
468	C₂²×C₄	—	178	1	no	—
469	C₂²×C₄	—	178	1	no	—
470	C₂²×C₄	—	178	1	no	—
471	C₂²×C₄	—	178	1	no	—
472	SD₁₆	—	178	2	no	—
473	SD₁₆	—	178	2	no	—
474	D₈	—	2	2	no	—
475	D₈	—	178	2	no	—
476	M₁₆	—	4	2	no	—
477	M₁₆	—	178	4	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	—	89	1	no	—
483	C₂×C₈	—	89	1	no	—
484	C₂×C₈	—	89	1	no	—
485	C₂×C₈	—	89	1	no	—
486	C₂×C₈	—	356	2	no	—
487	C₂×C₈	—	356	1	no	—
488	C₂×C₈	—	356	2	no	—
489	C₂×C₈	—	356	2	no	—
490	C₂×C₈	—	356	2	no	—
491	C₂×C₈	—	356	2	no	—
492	C₂×C₈	—	178	2	no	—
493	C₂×C₈	—	178	1	no	—
494	C₂×C₈	—	178	1	no	—
495	C₂×C₈	—	178	1	no	—
496	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
497	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
498	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
499	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
500	C₄⋊C₄	—	89	1	no	—
501	C₄⋊C₄	—	89	1	no	—
502	C₄⋊C₄	—	178	1	no	—
503	C₄⋊C₄	—	178	1	no	—
504	C₄⋊C₄	—	178	1	no	—
505	C₄⋊C₄	—	178	1	no	—
506	C₄⋊C₄	—	178	1	no	—
507	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	178	1	no	—
512	C₂²⋊C₄	—	178	1	no	—
513	C₂²⋊C₄	—	178	1	no	—
514	C₂²⋊C₄	—	178	1	no	—
515	C₂²⋊C₄	—	178	1	no	—
516	C₂²⋊C₄	—	178	1	no	—
517	C₂²⋊C₄	—	178	1	no	—
518	C₄²	—	89	1	no	—
519	C₄²	—	89	1	no	—
520	C₄²	—	89	1	no	—
521	C₄²	—	178	1	no	—
522	C₄²	C₂³×D₈₉	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	89	1	no	—
526	C₂³	—	356	2	no	—
527	C₂³	—	356	2	no	—
528	C₂³	—	178	4	no	—
529	C₂³	—	178	1	no	—
530	Q₈	—	178	1	no	—
531	Q₈	—	178	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	89	2	no	—
536	D₄	—	356	2	no	—
537	D₄	—	178	4	no	—
538	D₄	—	178	1	no	—
539	D₄	#15668020	1	2	yes	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	89	1	no	—
547	C₂×C₄	—	89	1	no	—
548	C₂×C₄	—	89	1	no	—
549	C₂×C₄	—	356	2	no	—
550	C₂×C₄	—	356	2	no	—
551	C₂×C₄	—	356	2	no	—
552	C₂×C₄	—	356	1	no	—
553	C₂×C₄	—	356	1	no	—
554	C₂×C₄	—	178	2	no	—
555	C₂×C₄	—	178	1	no	—
556	C₂×C₄	—	178	1	no	—
557	C₂×C₄	—	178	1	no	—
558	C₂×C₄	—	178	1	no	—
559	C₂×C₄	—	178	1	no	—
560	C₂×C₄	—	178	1	no	—
561	C₂×C₄	—	178	1	no	—
562	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
564	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	89	2	no	—
573	C₈	—	356	1	no	—
574	C₈	—	356	1	no	—
575	C₈	—	178	2	no	—
576	C₈	—	178	1	no	—
577	C₈	—	178	1	no	—
578	C₈	—	178	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	89	2	no	—
586	C₂²	—	356	8	no	—
587	C₂²	—	356	1	no	—
588	C₂²	—	356	1	no	—
589	C₂²	—	178	2	no	—
590	C₂²	—	178	1	no	—
591	C₂²	—	178	1	no	—
592	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	356	1	no	—
597	C₄	—	356	1	no	—
598	C₄	—	356	1	no	—
599	C₄	—	178	1	no	—
600	C₄	—	178	1	no	—
601	C₄	—	178	1	no	—
602	C₄	#131×D₈₉	1	1	yes	characteristic
603	C₄	C₂×#15668020	1	1	yes	characteristic
604	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
605	C₄	#19152394	1	1	yes	characteristic
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	—	356	2	no	—
609	C₂	—	178	2	no	—
610	C₂	#26028943	1	1	yes	characteristic
611	C₂	#26029063	1	1	yes	characteristic
612	C₂	#443×D₈₉	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×#1586	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151730	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1586	D₈₉
hypocenter	C₈₉	#17910
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1586

Complements

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

N	H ≅ G/N	type
2. #26029230	C₂	semidirect
3. C₈×D₄×D₈₉	C₂	semidirect
4. #26019114	C₂	semidirect
5. #26019111	C₂	semidirect
6. #26019109	C₂	semidirect
7. #26019055	C₂	semidirect
8. #26019051	C₂	semidirect
9. D₈×#10623494	C₂	semidirect
10. #26019044	C₂	semidirect
11. #26019034	C₂	semidirect
12. #26018693	C₂	semidirect
13. #26018662	C₂	semidirect
14. #26018531	C₂	semidirect
15. C₈₉×#1586	C₂	semidirect
27. #19151728	C₂²	semidirect
28. #19151722	C₂²	semidirect
35. D₄×#10623494	C₂²	semidirect
48. #19151351	C₂²	semidirect
49. #19151350	C₂²	semidirect
50. #19151348	C₂²	semidirect
51. #19151330	C₂²	semidirect
52. #19151328	C₂²	semidirect
55. D₄⋊#10623494	C₂²	semidirect
57. #19151320	C₂²	semidirect
58. C₈×#10623494	C₂²	semidirect
59. C₈×#10623494	C₂²	semidirect
61. #436×C₈₉	C₂²	semidirect
63. #334×C₈₉	C₂²	semidirect
65. D₄⋊C₈×C₈₉	C₂²	semidirect
66. #322×C₈₉	C₂²	semidirect
311. #1586	D₈₉	semidirect
322. C₈₉	#17910	semidirect
340. #436	C₂×D₈₉	semidirect
361. #334	C₂×D₈₉	semidirect
369. D₄⋊C₈	C₂×D₈₉	semidirect
371. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030297	2
#26029230	2
C₈×D₄×D₈₉	2
#26019114	2
#26019111	2
#26019109	2
#26019055	2
#26019051	2
D₈×#10623494	2
#26019044	2
#26019034	2
#26018693	2
#26018662	2
#26018531	2
C₈₉×#1586	2
#17910	89