Subgroups — D₈×#13083557 #36525845

Order 22784.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
2	D₄×#13083557	C₂	1	2	yes	maximal, complemented
3	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019136	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019081	C₂	1	2	yes	maximal, complemented
6	#26019078	C₂	1	2	yes	maximal, complemented
7	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018675	C₂	1	2	yes	maximal, complemented
10	C₈×#13083557	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	C₂²×#13083557	—	2	2	no	—
14	C₄×D₄×D₈₉	C₂²	1	2	yes	—
15	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
16	D₈×Dic₈₉	C₄	1	1	yes	characteristic
17	#19151680	C₄	1	1	yes	characteristic
18	C₄×#13083559	C₂²	1	2	yes	—
19	#19151678	C₄	1	2	yes	—
20	#19151677	C₂²	1	2	yes	complemented
21	#19151675	C₂²	1	2	yes	complemented
22	#19151669	—	2	2	no	—
23	#19151666	—	2	2	no	—
24	D₄×#10623494	C₂²	1	2	yes	complemented
25	#19151649	C₂²	1	1	yes	characteristic
26	#107×D₈₉	C₄	1	1	yes	characteristic
27	#19151620	C₂²	1	2	yes	—
28	#102×D₈₉	C₄	1	2	yes	—
29	#19151560	—	2	2	no	—
30	C₄×#13083557	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic, complemented
33	#19151350	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	#19151319	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	—	2	4	no	—
50	C₂×#13083557	—	2	2	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂×#13083557	—	2	2	no	—
53	C₂×#13083557	—	4	8	no	—
54	C₂×#13083557	D₄	1	1	yes	characteristic
55	C₂×#13083557	D₄	1	1	yes	characteristic
56	C₂²×#10623494	—	2	2	no	—
57	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄×D₃₅₆	C₂³	1	2	yes	—
60	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
61	#15667974	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₈₉	—	2	2	no	—
63	#15667972	—	2	2	no	—
64	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₈₉	—	2	2	no	—
66	C₄²×D₈₉	C₂³	1	1	yes	characteristic
67	#15667946	C₂×C₄	1	1	yes	characteristic
68	#15667945	C₂×C₄	1	2	yes	—
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667941	—	2	2	no	—
71	#15667941	—	2	1	no	—
72	#15667934	C₂×C₄	1	2	yes	—
73	#15667933	C₂×C₄	1	2	yes	—
74	#15667932	C₂×C₄	1	2	yes	—
75	C₂²⋊#10623494	—	2	2	no	—
76	#15667924	—	2	1	no	—
77	#15667924	—	2	2	no	—
78	#15667924	—	2	2	no	—
79	#15667922	D₄	1	1	yes	characteristic
80	#15667922	D₄	1	1	yes	characteristic
81	C₄×#10623494	C₂³	1	1	yes	characteristic
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₄×#10623494	C₂³	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	—	2	2	no	—
88	C₄×D₄×C₈₉	C₂³	1	2	yes	—
89	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
91	#102×C₈₉	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₈₉	—	2	2	no	—
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×D₈₉	—	2	2	no	—
97	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₈₉	—	2	2	no	—
99	D₄×D₈₉	—	2	4	no	—
100	D₄×D₈₉	—	4	2	no	—
101	C₂²×Dic₈₉	—	2	2	no	—
102	C₂×C₄×D₈₉	—	2	2	no	—
103	C₂×C₄×D₈₉	—	2	2	no	—
104	C₂×C₄×D₈₉	—	2	2	no	—
105	C₂×C₄×D₈₉	—	4	4	no	—
106	C₂×C₄×D₈₉	—	4	4	no	—
107	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
110	D₇₁₂	—	2	2	no	—
111	#13083559	—	2	4	no	—
112	#13083557	—	2	2	no	—
113	#13083557	—	4	4	no	—
114	#13083557	—	4	4	no	—
115	#13083557	—	4	4	no	—
116	#13083557	D₈	1	4	yes	direct product factor
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	4	4	no	—
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₈×D₈₉	—	2	2	no	—
125	C₈×D₈₉	—	4	1	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	#13083553	—	2	2	no	—
128	C₂²⋊Dic₈₉	—	2	2	no	—
129	#13083551	—	2	2	no	—
130	#13083551	—	2	2	no	—
131	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₈₉	#41	1	1	yes	characteristic
134	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₈₉	—	2	2	no	—
136	D₈×C₈₉	M₁₆	1	4	yes	complemented
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	4	4	no	—
140	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
145	C₂²⋊C₄×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₈₉	—	2	2	no	—
148	C₂²×D₈₉	—	2	2	no	—
149	C₂²×D₈₉	—	4	4	no	—
150	C₂²×D₈₉	—	4	4	no	—
151	C₂²×D₈₉	—	8	2	no	—
152	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
153	D₄×C₈₉	—	2	2	no	—
154	D₄×C₈₉	C₂×M₁₆	1	4	yes	complemented
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₈₉	—	4	4	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	—	4	4	no	—
164	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
165	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
167	D₃₅₆	—	2	2	no	—
168	D₃₅₆	—	2	2	no	—
169	C₄×D₈₉	—	2	1	no	—
170	C₄×D₈₉	—	2	1	no	—
171	C₄×D₈₉	—	4	1	no	—
172	C₄×D₈₉	—	4	4	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	4	no	—
176	C₄×D₈₉	C₂×D₈	1	2	yes	—
177	C₄×D₈₉	#135	1	2	yes	—
178	C₈×C₈₉	—	2	1	no	—
179	C₈×C₈₉	—	2	1	no	—
180	C₈×C₈₉	—	4	1	no	—
181	C₈×C₈₉	—	4	2	no	—
182	C₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
183	C₈×C₈₉	C₂×D₈	1	2	yes	complemented
184	#10623494	—	2	1	no	—
185	#10623494	—	2	1	no	—
186	#10623494	—	2	1	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	2	no	—
189	#10623494	C₂×D₈	1	2	yes	complemented
190	C₂²×C₈₉	—	2	4	no	—
191	C₂²×C₈₉	—	4	2	no	—
192	C₂²×C₈₉	—	4	2	no	—
193	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₈₉	—	2	1	no	—
195	C₂×D₈₉	—	2	1	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	4	2	no	—
198	C₂×D₈₉	—	4	2	no	—
199	C₂×D₈₉	—	8	8	no	—
200	C₂×D₈₉	C₄×D₈	1	2	yes	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
204	C₄×C₈₉	#568	1	1	yes	characteristic
205	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
206	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
207	Dic₈₉	—	2	1	no	—
208	Dic₈₉	—	2	1	no	—
209	Dic₈₉	—	4	2	no	—
210	Dic₈₉	C₄×D₈	1	2	yes	—
211	M₁₆×D₈	—	89	1	no	maximal, Sylow
212	C₂×C₈₉	—	4	4	no	—
213	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
214	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
215	C₂×C₈₉	#2957	1	1	yes	characteristic
216	D₈₉	—	2	2	no	—
217	D₈₉	—	8	2	no	—
218	C₂×C₄×D₈	—	89	1	no	—
219	D₄×M₁₆	—	89	2	no	—
220	#1589	—	89	1	no	—
221	#1589	—	89	1	no	—
222	#1581	—	89	2	no	—
223	#1581	—	89	2	no	—
224	C₈×D₈	—	89	1	no	—
225	C₈×D₈	D₈₉	1	1	yes	characteristic, complemented
226	#1567	—	89	1	no	—
227	#1486	—	89	2	no	—
228	C₈×M₁₆	—	89	1	no	—
229	C₈₉	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
230	C₂²×D₈	—	89	1	no	—
231	C₂²×M₁₆	—	178	2	no	—
232	C₂×C₄×D₄	—	89	2	no	—
233	C₄×D₈	—	89	1	no	—
234	C₄×D₈	—	89	2	no	—
235	C₄×D₈	—	89	1	no	—
236	C₄×D₈	—	89	2	no	—
237	C₄×D₈	—	89	1	no	—
238	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
239	#436	—	89	2	no	—
240	#436	—	89	2	no	—
241	#435	—	178	2	no	—
242	#435	—	178	2	no	—
243	C₈×D₄	—	89	2	no	—
244	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
245	#431	—	89	1	no	—
246	C₂×#107	—	89	1	no	—
247	#423	—	89	2	no	—
248	C₂×#102	—	89	2	no	—
249	#407	—	178	2	no	—
250	C₄×M₁₆	—	89	1	no	—
251	C₂×C₄×C₈	—	89	1	no	—
252	#335	—	89	2	no	—
253	#335	—	89	1	no	—
254	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
255	D₄⋊C₈	—	89	2	no	—
256	D₄⋊C₈	—	89	2	no	—
257	D₄⋊C₈	—	89	2	no	—
258	D₄⋊C₈	C₂×D₈₉	1	2	yes	complemented
259	#322	—	89	1	no	—
260	#322	—	89	1	no	—
261	C₈²	—	89	1	no	—
262	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
263	C₂²×D₄	—	89	2	no	—
264	C₂³×C₄	—	178	2	no	—
265	C₂×D₈	—	89	2	no	—
266	C₂×D₈	—	89	1	no	—
267	C₂×D₈	—	178	4	no	—
268	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
269	C₂×M₁₆	—	89	1	no	—
270	C₂×M₁₆	—	89	1	no	—
271	C₂×M₁₆	—	356	8	no	—
272	C₂×M₁₆	—	178	2	no	—
273	C₂×M₁₆	—	178	2	no	—
274	C₂×M₁₆	—	178	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	89	1	no	—
277	C₂²×C₈	—	89	1	no	—
278	C₂²×C₈	—	178	2	no	—
279	C₄×D₄	—	89	2	no	—
280	C₄×D₄	—	89	2	no	—
281	C₄×D₄	—	89	2	no	—
282	C₄×D₄	—	178	2	no	—
283	C₄×D₄	—	178	2	no	—
284	C₄×D₄	C₂²×D₈₉	1	2	yes	—
285	C₂×C₄⋊C₄	—	89	2	no	—
286	C₂×C₂²⋊C₄	—	178	2	no	—
287	C₂×C₄²	—	89	1	no	—
288	#107	—	89	1	no	—
289	#107	—	89	2	no	—
290	#107	C₄×D₈₉	1	1	yes	characteristic
291	C₄⋊C₈	—	89	2	no	—
292	C₄⋊C₈	—	178	2	no	—
293	C₄⋊C₈	—	178	1	no	—
294	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
295	#102	—	89	2	no	—
296	#102	—	89	2	no	—
297	#102	—	89	2	no	—
298	#102	C₄×D₈₉	1	2	yes	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	178	2	no	—
301	C₂²⋊C₈	—	178	1	no	—
302	C₂²⋊C₈	—	178	2	no	—
303	C₂²⋊C₈	—	178	2	no	—
304	#97	—	89	1	no	—
305	#97	—	89	1	no	—
306	C₄×C₈	—	89	1	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	—	89	1	no	—
309	C₄×C₈	—	89	1	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₂⁴	—	178	2	no	—
315	C₂×D₄	—	89	2	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂×D₄	—	178	4	no	—
319	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	89	1	no	—
322	C₂²×C₄	—	89	1	no	—
323	C₂²×C₄	—	89	1	no	—
324	C₂²×C₄	—	356	4	no	—
325	C₂²×C₄	—	356	4	no	—
326	C₂²×C₄	—	178	2	no	—
327	C₂²×C₄	—	178	2	no	—
328	C₂²×C₄	—	178	2	no	—
329	C₂²×C₄	—	178	2	no	—
330	D₈	—	178	4	no	—
331	D₈	—	178	2	no	—
332	D₈	#13083557	1	4	yes	direct product factor
333	M₁₆	—	89	4	no	—
334	M₁₆	—	356	4	no	—
335	M₁₆	—	356	4	no	—
336	M₁₆	—	356	4	no	—
337	M₁₆	—	178	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	—	89	1	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	89	1	no	—
344	C₂×C₈	—	89	1	no	—
345	C₂×C₈	—	356	1	no	—
346	C₂×C₈	—	356	4	no	—
347	C₂×C₈	—	178	2	no	—
348	C₂×C₈	—	178	1	no	—
349	C₂×C₈	—	178	2	no	—
350	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
352	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
353	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
354	C₄⋊C₄	—	89	2	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	178	2	no	—
359	C₂²⋊C₄	—	178	2	no	—
360	C₂²⋊C₄	—	178	2	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	89	1	no	—
364	C₄²	C₂³×D₈₉	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	89	1	no	—
367	C₂³	—	356	4	no	—
368	C₂³	—	356	4	no	—
369	C₂³	—	178	2	no	—
370	C₂³	—	712	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	356	4	no	—
373	D₄	—	178	2	no	—
374	D₄	—	178	2	no	—
375	D₄	C₂×#13083557	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	89	1	no	—
380	C₂×C₄	—	89	2	no	—
381	C₂×C₄	—	89	2	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	89	1	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	4	no	—
386	C₂×C₄	—	356	4	no	—
387	C₂×C₄	—	356	4	no	—
388	C₂×C₄	—	356	2	no	—
389	C₂×C₄	—	356	2	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	—	178	1	no	—
392	C₂×C₄	—	178	1	no	—
393	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	89	2	no	—
401	C₈	—	356	1	no	—
402	C₈	—	356	2	no	—
403	C₈	—	178	1	no	—
404	C₈	—	178	1	no	—
405	C₈	—	178	1	no	—
406	C₈	C₂×#13083557	1	2	yes	complemented
407	C₈	D₈×D₈₉	1	2	yes	complemented
408	C₂²	—	2	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	89	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	356	2	no	—
414	C₂²	—	356	2	no	—
415	C₂²	—	178	1	no	—
416	C₂²	—	178	1	no	—
417	C₂²	—	712	8	no	—
418	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	89	2	no	—
422	C₄	—	356	2	no	—
423	C₄	—	178	1	no	—
424	C₄	—	178	1	no	—
425	C₄	C₂²×#13083557	1	1	yes	characteristic
426	C₄	#19152363	1	1	yes	characteristic
427	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
428	C₄	#135×D₈₉	1	1	yes	characteristic
429	C₂	—	4	4	no	—
430	C₂	—	178	2	no	—
431	C₂	—	712	2	no	—
432	C₂	D₄×#13083557	1	1	yes	characteristic
433	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
434	C₂	#26029164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
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	M₁₆×D₈
LCS	G ▷ C₂×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
2. D₄×#13083557	C₂	semidirect
3. #26019138	C₂	semidirect
4. #26019136	C₂	semidirect
5. #26019081	C₂	semidirect
6. #26019078	C₂	semidirect
7. D₈×#10623494	C₂	semidirect
8. #26019009	C₂	semidirect
9. #26018675	C₂	semidirect
10. C₈×#13083557	C₂	semidirect
11. C₈×D₈×C₈₉	C₂	semidirect
20. #19151677	C₂²	semidirect
21. #19151675	C₂²	semidirect
24. D₄×#10623494	C₂²	semidirect
32. #19151351	C₂²	semidirect
33. #19151350	C₂²	semidirect
34. #19151327	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151325	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151319	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
116. #13083557	D₈	direct (N × H)
136. D₈×C₈₉	M₁₆	semidirect
154. D₄×C₈₉	C₂×M₁₆	semidirect
182. C₈×C₈₉	C₂×M₁₆	semidirect
183. C₈×C₈₉	C₂×D₈	semidirect
189. #10623494	C₂×D₈	semidirect
225. C₈×D₈	D₈₉	semidirect
229. C₈₉	M₁₆×D₈	semidirect
244. C₈×D₄	C₂×D₈₉	semidirect
254. #335	C₂×D₈₉	semidirect
258. D₄⋊C₈	C₂×D₈₉	semidirect
262. C₈²	C₂×D₈₉	semidirect
332. D₈	#13083557	direct (N × H)
375. D₄	C₂×#13083557	semidirect
406. C₈	C₂×#13083557	semidirect
407. C₈	D₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₈₉	2
D₄×#13083557	2
#26019138	2
#26019136	2
#26019081	2
#26019078	2
D₈×#10623494	2
#26019009	2
#26018675	2
C₈×#13083557	2
C₈×D₈×C₈₉	2
M₁₆×D₈	89

Subgroups — D8×#13083557 #36525845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#13083557 #36525845