Subgroups — #36523881

Order 22784.

782 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029273	C₂	1	2	yes	maximal, complemented
2	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019074	C₂	1	2	yes	maximal, complemented
4	#26019073	C₂	1	2	yes	maximal, complemented
5	C₈×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019046	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018999	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018641	C₂	1	2	yes	maximal, complemented
10	#26018534	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	C₄	1	1	yes	characteristic
13	C₄×D₄×D₈₉	C₂²	1	2	yes	—
14	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
15	D₈×Dic₈₉	C₄	1	1	yes	characteristic
16	#19151680	C₄	1	1	yes	characteristic
17	C₄×#13083559	C₂²	1	2	yes	—
18	#19151678	C₄	1	2	yes	—
19	C₈×D₃₅₆	C₂²	1	2	yes	complemented
20	D₄×#10623494	C₂²	1	2	yes	complemented
21	#19151663	C₂²	1	2	yes	complemented
22	C₈×C₂²⋊D₈₉	—	2	2	no	—
23	#19151661	—	2	2	no	—
24	#19151650	C₂²	1	2	yes	—
25	#19151649	C₂²	1	1	yes	characteristic
26	#19151649	C₂²	1	1	yes	characteristic
27	#107×D₈₉	C₄	1	1	yes	characteristic
28	#102×D₈₉	C₄	1	2	yes	—
29	C₂×#15667924	—	2	2	no	—
30	C₂²⋊C₈×D₈₉	—	2	2	no	—
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic, complemented
33	#19151348	C₂²	1	2	yes	complemented
34	#19151327	C₂²	1	2	yes	complemented
35	D₄⋊#10623494	C₂²	1	2	yes	complemented
36	#19151325	C₂²	1	2	yes	complemented
37	#19151320	C₂²	1	1	yes	characteristic, complemented
38	#19151320	C₂²	1	1	yes	characteristic, complemented
39	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
42	#335×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₈₉	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₈₉	—	2	2	no	—
47	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083559	C₂×C₄	1	2	yes	—
49	D₈×D₈₉	C₈	1	8	yes	complemented
50	C₂²×#10623494	—	2	2	no	—
51	C₂×C₈×D₈₉	—	2	2	no	—
52	C₂×C₈×D₈₉	—	2	2	no	—
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
55	C₄×D₃₅₆	C₂³	1	2	yes	—
56	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
57	#15667974	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₈₉	—	2	2	no	—
59	#15667972	—	2	2	no	—
60	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
61	C₂²⋊C₄×D₈₉	—	2	2	no	—
62	C₄²×D₈₉	C₂³	1	1	yes	characteristic
63	#15667946	C₂×C₄	1	1	yes	characteristic
64	#15667945	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	#15667941	—	2	1	no	—
67	#15667941	D₄	1	1	yes	characteristic
68	#15667941	D₄	1	1	yes	characteristic
69	#15667934	C₂×C₄	1	2	yes	—
70	#15667933	C₂×C₄	1	2	yes	—
71	#15667932	C₂×C₄	1	2	yes	—
72	C₂²⋊#10623494	—	2	2	no	—
73	#15667924	—	2	2	no	—
74	#15667924	—	2	1	no	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667924	D₄	1	1	yes	characteristic
78	#15667924	D₄	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₄×#10623494	C₂³	1	1	yes	characteristic
81	C₄×#10623494	C₂³	1	1	yes	characteristic
82	C₈×Dic₈₉	—	2	2	no	—
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	—	2	2	no	—
87	C₄×D₄×C₈₉	C₂³	1	2	yes	—
88	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	#102×C₈₉	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₈₉	—	2	2	no	—
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×D₈₉	—	2	2	no	—
96	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
97	C₂×C₂²⋊D₈₉	—	2	2	no	—
98	D₄×D₈₉	—	2	4	no	—
99	D₄×D₈₉	C₂×C₈	1	8	yes	complemented
100	C₂²×Dic₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	2	no	—
102	C₂×C₄×D₈₉	—	2	2	no	—
103	C₂×C₄×D₈₉	—	2	2	no	—
104	C₂×C₄×D₈₉	—	8	2	no	—
105	C₂×C₄×D₈₉	—	8	2	no	—
106	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
109	D₇₁₂	C₂×C₈	1	4	yes	complemented
110	#13083559	C₂×C₈	1	8	yes	complemented
111	C₂×#10623494	—	2	2	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	—	8	2	no	—
114	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
115	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
117	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
118	C₈×D₈₉	—	2	2	no	—
119	C₈×D₈₉	—	8	2	no	—
120	C₈×D₈₉	—	8	2	no	—
121	C₈×D₈₉	C₂×C₈	1	4	yes	complemented
122	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
123	#13083553	—	2	2	no	—
124	C₂²⋊Dic₈₉	—	2	2	no	—
125	#13083551	—	2	2	no	—
126	#13083551	—	2	2	no	—
127	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
129	C₄×Dic₈₉	#41	1	1	yes	characteristic
130	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₈₉	—	2	2	no	—
132	D₈×C₈₉	C₂×C₈	1	4	yes	complemented
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	8	2	no	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂²⋊C₄×C₈₉	—	2	2	no	—
142	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₈₉	—	2	2	no	—
144	C₂²×D₈₉	—	2	2	no	—
145	C₂²×D₈₉	—	2	8	no	—
146	C₂²×D₈₉	—	8	2	no	—
147	C₂²×D₈₉	—	8	2	no	—
148	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
149	D₄×C₈₉	—	2	2	no	—
150	D₄×C₈₉	C₂²×C₈	1	4	yes	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
157	C₂²⋊D₈₉	—	2	8	no	—
158	C₂×Dic₈₉	—	2	2	no	—
159	C₂×Dic₈₉	—	8	2	no	—
160	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
163	D₃₅₆	—	2	2	no	—
164	D₃₅₆	C₂²×C₈	1	4	yes	—
165	C₄×D₈₉	—	2	1	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	4	1	no	—
168	C₄×D₈₉	—	4	2	no	—
169	C₄×D₈₉	—	4	2	no	—
170	C₄×D₈₉	—	8	2	no	—
171	C₄×D₈₉	—	8	2	no	—
172	C₄×D₈₉	C₂²×C₈	1	2	yes	—
173	C₄×D₈₉	#131	1	2	yes	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	—	2	1	no	—
176	C₈×C₈₉	—	2	1	no	—
177	C₈×C₈₉	—	4	1	no	—
178	C₈×C₈₉	—	4	2	no	—
179	C₈×C₈₉	C₂²×C₈	1	2	yes	—
180	#10623494	—	2	1	no	—
181	#10623494	—	2	1	no	—
182	#10623494	—	2	1	no	—
183	#10623494	—	4	1	no	—
184	#10623494	—	4	2	no	—
185	#10623494	C₂²×C₈	1	2	yes	—
186	C₂²×C₈₉	—	2	4	no	—
187	C₂²×C₈₉	—	4	2	no	—
188	C₂²×C₈₉	—	4	2	no	—
189	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	2	4	no	—
193	C₂×D₈₉	—	4	2	no	—
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	8	8	no	—
196	C₂×D₈₉	C₈×D₄	1	2	yes	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
200	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
201	C₄×C₈₉	#576	1	1	yes	characteristic
202	C₄×C₈₉	#576	1	1	yes	characteristic
203	Dic₈₉	—	2	1	no	—
204	Dic₈₉	—	2	1	no	—
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	C₈×D₄	1	2	yes	—
207	#17854	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	4	4	no	—
209	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
210	C₂×C₈₉	#2948	1	1	yes	characteristic
211	C₂×C₈₉	#2957	1	1	yes	characteristic
212	D₈₉	—	2	2	no	—
213	D₈₉	—	4	4	no	—
214	#2972	—	89	2	no	—
215	C₂×C₄×D₈	—	89	1	no	—
216	#1580	—	89	2	no	—
217	#1580	—	89	2	no	—
218	C₈×D₈	—	89	1	no	—
219	C₈×D₈	—	89	1	no	—
220	C₈×D₈	—	89	1	no	—
221	C₈×D₈	D₈₉	1	1	yes	characteristic, complemented
222	#1564	—	89	1	no	—
223	#1478	—	89	2	no	—
224	#1450	—	89	1	no	—
225	C₈₉	#17854	1	1	yes	characteristic, complemented, Sylow
226	C₂²×D₈	—	89	1	no	—
227	C₂×C₄×D₄	—	89	2	no	—
228	C₄×D₈	—	89	1	no	—
229	C₄×D₈	—	89	2	no	—
230	C₄×D₈	—	89	1	no	—
231	C₄×D₈	—	89	2	no	—
232	C₄×D₈	—	89	1	no	—
233	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
234	C₈×D₄	—	89	2	no	—
235	C₈×D₄	—	89	2	no	—
236	C₈×D₄	—	89	2	no	—
237	C₈×D₄	—	178	2	no	—
238	C₈×D₄	—	178	2	no	—
239	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
240	#431	—	89	1	no	—
241	#431	—	89	1	no	—
242	#431	—	89	2	no	—
243	C₂×#107	—	89	1	no	—
244	C₂×#102	—	89	2	no	—
245	C₂×C₂²⋊C₈	—	178	2	no	—
246	C₂×C₂²⋊C₈	—	178	2	no	—
247	C₂×C₄×C₈	—	89	1	no	—
248	#335	—	89	1	no	—
249	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
250	#334	—	89	2	no	—
251	D₄⋊C₈	—	89	2	no	—
252	D₄⋊C₈	—	89	2	no	—
253	D₄⋊C₈	—	89	2	no	—
254	D₄⋊C₈	C₂×D₈₉	1	2	yes	complemented
255	#322	—	89	1	no	—
256	#322	—	89	1	no	—
257	C₈²	—	89	1	no	—
258	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
259	C₂²×D₄	—	89	2	no	—
260	C₂³×C₄	—	178	2	no	—
261	C₂×D₈	—	89	2	no	—
262	C₂×D₈	—	89	8	no	—
263	C₂×D₈	—	89	1	no	—
264	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	89	1	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	178	2	no	—
269	C₂²×C₈	—	178	2	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₄×D₄	—	89	2	no	—
272	C₄×D₄	—	89	2	no	—
273	C₄×D₄	—	89	2	no	—
274	C₄×D₄	—	178	2	no	—
275	C₄×D₄	—	178	2	no	—
276	C₄×D₄	C₂²×D₈₉	1	2	yes	—
277	C₂×C₄⋊C₄	—	89	2	no	—
278	C₂×C₂²⋊C₄	—	178	2	no	—
279	C₂×C₄²	—	89	1	no	—
280	#107	—	89	1	no	—
281	#107	—	89	2	no	—
282	#107	C₄×D₈₉	1	1	yes	characteristic
283	C₄⋊C₈	—	89	1	no	—
284	C₄⋊C₈	—	89	1	no	—
285	C₄⋊C₈	—	89	2	no	—
286	C₄⋊C₈	—	178	1	no	—
287	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
288	#102	—	89	2	no	—
289	#102	—	89	2	no	—
290	#102	—	89	2	no	—
291	#102	C₄×D₈₉	1	2	yes	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	89	1	no	—
294	C₂²⋊C₈	—	89	1	no	—
295	C₂²⋊C₈	—	178	2	no	—
296	C₂²⋊C₈	—	178	2	no	—
297	C₂²⋊C₈	—	178	1	no	—
298	C₂²⋊C₈	—	178	2	no	—
299	C₂²⋊C₈	—	178	2	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	—	89	1	no	—
302	C₄×C₈	—	89	1	no	—
303	C₄×C₈	—	89	1	no	—
304	C₄×C₈	—	89	1	no	—
305	C₄×C₈	—	178	2	no	—
306	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₂⁴	—	178	2	no	—
310	C₂×D₄	—	89	8	no	—
311	C₂×D₄	—	89	2	no	—
312	C₂×D₄	—	178	4	no	—
313	C₂×D₄	—	178	2	no	—
314	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	89	1	no	—
317	C₂²×C₄	—	89	1	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	178	2	no	—
320	C₂²×C₄	—	178	2	no	—
321	C₂²×C₄	—	178	2	no	—
322	C₂²×C₄	—	178	2	no	—
323	C₂²×C₄	—	712	2	no	—
324	C₂²×C₄	—	712	2	no	—
325	D₈	—	89	8	no	—
326	D₈	—	89	4	no	—
327	D₈	C₈×D₈₉	1	4	yes	complemented
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	8	2	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	89	4	no	—
333	C₂×C₈	—	89	1	no	—
334	C₂×C₈	—	89	1	no	—
335	C₂×C₈	—	89	1	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	—	712	2	no	—
340	C₂×C₈	—	712	2	no	—
341	C₂×C₈	—	712	2	no	—
342	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
344	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
345	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
346	C₄⋊C₄	—	89	2	no	—
347	C₄⋊C₄	—	178	2	no	—
348	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	178	2	no	—
351	C₂²⋊C₄	—	178	2	no	—
352	C₂²⋊C₄	—	178	2	no	—
353	C₄²	—	89	1	no	—
354	C₄²	—	89	1	no	—
355	C₄²	—	89	1	no	—
356	C₄²	C₂³×D₈₉	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	89	1	no	—
359	C₂³	—	178	8	no	—
360	C₂³	—	178	2	no	—
361	C₂³	—	712	2	no	—
362	C₂³	—	712	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	89	4	no	—
365	D₄	—	178	8	no	—
366	D₄	—	178	2	no	—
367	D₄	C₂×C₈×D₈₉	1	4	yes	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	89	1	no	—
372	C₂×C₄	—	89	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	89	1	no	—
375	C₂×C₄	—	89	1	no	—
376	C₂×C₄	—	356	1	no	—
377	C₂×C₄	—	356	2	no	—
378	C₂×C₄	—	356	2	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	1	no	—
381	C₂×C₄	—	178	1	no	—
382	C₂×C₄	—	712	2	no	—
383	C₂×C₄	—	712	2	no	—
384	C₂×C₄	—	712	2	no	—
385	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
387	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	2	no	—
393	C₈	—	89	2	no	—
394	C₈	—	356	1	no	—
395	C₈	—	356	2	no	—
396	C₈	—	178	1	no	—
397	C₈	—	178	1	no	—
398	C₈	—	178	1	no	—
399	C₈	C₂×C₈×D₈₉	1	2	yes	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	89	2	no	—
404	C₂²	—	356	2	no	—
405	C₂²	—	356	2	no	—
406	C₂²	—	178	4	no	—
407	C₂²	—	178	1	no	—
408	C₂²	—	178	1	no	—
409	C₂²	—	712	8	no	—
410	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	89	2	no	—
414	C₄	—	356	2	no	—
415	C₄	—	178	1	no	—
416	C₄	—	178	1	no	—
417	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
418	C₄	#131×D₈₉	1	1	yes	characteristic
419	C₄	#19152399	1	1	yes	characteristic
420	C₄	#19152400	1	1	yes	characteristic
421	C₂	—	4	4	no	—
422	C₂	—	356	4	no	—
423	C₂	—	178	2	no	—
424	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
425	C₂	#26029099	1	1	yes	characteristic
426	C₂	#26029164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×D₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×D₈×D₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×D₈	D₈₉
hypocenter	C₈₉	#17854
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #26029273	C₂	semidirect
3. #26019074	C₂	semidirect
4. #26019073	C₂	semidirect
5. C₈×D₇₁₂	C₂	semidirect
6. D₈×#10623494	C₂	semidirect
7. #26019046	C₂	semidirect
8. #26018999	C₂	semidirect
9. #26018641	C₂	semidirect
10. #26018534	C₂	semidirect
11. C₈×D₈×C₈₉	C₂	semidirect
19. C₈×D₃₅₆	C₂²	semidirect
20. D₄×#10623494	C₂²	semidirect
21. #19151663	C₂²	semidirect
32. #19151351	C₂²	semidirect
33. #19151348	C₂²	semidirect
34. #19151327	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151325	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. C₈×#10623494	C₂²	semidirect
41. C₈×D₄×C₈₉	C₂²	semidirect
42. #335×C₈₉	C₂²	semidirect
43. D₄⋊C₈×C₈₉	C₂²	semidirect
44. C₈²×C₈₉	C₂²	semidirect
49. D₈×D₈₉	C₈	semidirect
99. D₄×D₈₉	C₂×C₈	semidirect
109. D₇₁₂	C₂×C₈	semidirect
110. #13083559	C₂×C₈	semidirect
121. C₈×D₈₉	C₂×C₈	semidirect
132. D₈×C₈₉	C₂×C₈	semidirect
221. C₈×D₈	D₈₉	semidirect
225. C₈₉	#17854	semidirect
239. C₈×D₄	C₂×D₈₉	semidirect
249. #335	C₂×D₈₉	semidirect
254. D₄⋊C₈	C₂×D₈₉	semidirect
258. C₈²	C₂×D₈₉	semidirect
327. D₈	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029273	2
C₄×D₈×D₈₉	2
#26019074	2
#26019073	2
C₈×D₇₁₂	2
D₈×#10623494	2
#26019046	2
#26018999	2
#26018641	2
#26018534	2
C₈×D₈×C₈₉	2
#17854	89