Subgroups — #36449005

Order 22784.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
2	#26021047	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018087	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018079	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×#10623494	—	2	1	no	—
9	D₄×#10623494	—	2	2	no	—
10	D₄×#10623494	—	2	2	no	—
11	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊#10623494	—	2	1	no	—
14	C₂×C₂²⋊#10623494	—	2	1	no	—
15	C₂×C₂²⋊#10623494	—	2	1	no	—
16	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
17	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
18	D₄⋊#10623494	—	2	2	no	—
19	D₄⋊#10623494	—	2	2	no	—
20	C₂²×D₈×C₈₉	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₈₉	—	2	2	no	—
24	C₄×D₈×C₈₉	—	2	2	no	—
25	C₂×#107×C₈₉	C₄	1	1	yes	characteristic
26	C₂×#102×C₈₉	C₄	1	1	yes	characteristic
27	C₂×#102×C₈₉	C₄	1	1	yes	characteristic
28	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×#10623494	—	2	4	no	—
30	C₂²×#10623494	—	2	1	no	—
31	C₂²×#10623494	—	2	1	no	—
32	C₂²×#10623494	—	2	1	no	—
33	C₂²×#10623494	—	4	2	no	—
34	C₂²×#10623494	—	4	2	no	—
35	C₂²×#10623494	D₄	1	1	yes	characteristic
36	C₂²×#10623494	D₄	1	1	yes	characteristic
37	C₄⋊#10623494	—	2	1	no	—
38	C₄⋊#10623494	—	2	1	no	—
39	C₄⋊#10623494	—	2	1	no	—
40	C₄⋊#10623494	D₄	1	2	yes	—
41	C₂²⋊#10623494	—	2	4	no	—
42	C₂²⋊#10623494	—	4	2	no	—
43	C₂²⋊#10623494	—	4	2	no	—
44	C₄×#10623494	—	2	1	no	—
45	C₄×#10623494	—	2	1	no	—
46	C₄×#10623494	—	2	1	no	—
47	C₄×#10623494	—	2	1	no	—
48	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	—	2	1	no	—
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	C₂×D₈×C₈₉	—	2	2	no	—
53	C₂×D₈×C₈₉	—	2	2	no	—
54	C₂×D₈×C₈₉	C₈	1	4	yes	complemented
55	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₈₉	—	2	1	no	—
58	C₄×D₄×C₈₉	—	2	1	no	—
59	C₄×D₄×C₈₉	—	2	1	no	—
60	C₄×D₄×C₈₉	—	2	1	no	—
61	C₄×D₄×C₈₉	—	2	1	no	—
62	C₄×D₄×C₈₉	—	2	1	no	—
63	C₄×D₄×C₈₉	D₄	1	2	yes	—
64	C₄×D₄×C₈₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#107×C₈₉	—	2	2	no	—
71	#102×C₈₉	—	2	2	no	—
72	#102×C₈₉	—	2	2	no	—
73	C₄×C₈×C₈₉	—	2	1	no	—
74	C₄×C₈×C₈₉	—	2	1	no	—
75	C₂×#10623494	—	2	1	no	—
76	C₂×#10623494	—	2	1	no	—
77	C₂×#10623494	—	2	2	no	—
78	C₂×#10623494	—	2	2	no	—
79	C₂×#10623494	—	2	1	no	—
80	C₂×#10623494	—	2	1	no	—
81	C₂×#10623494	—	2	1	no	—
82	C₂×#10623494	—	4	8	no	—
83	C₂×#10623494	—	4	1	no	—
84	C₂×#10623494	—	4	1	no	—
85	C₂×#10623494	—	4	1	no	—
86	C₂×#10623494	—	4	1	no	—
87	C₂×#10623494	—	4	1	no	—
88	C₂×#10623494	—	4	1	no	—
89	C₂×#10623494	—	4	1	no	—
90	C₂×#10623494	D₈	1	2	yes	complemented
91	C₂⁴×C₈₉	—	2	1	no	—
92	C₂⁴×C₈₉	—	2	1	no	—
93	C₂×D₄×C₈₉	—	2	1	no	—
94	C₂×D₄×C₈₉	—	2	1	no	—
95	C₂×D₄×C₈₉	—	2	1	no	—
96	C₂×D₄×C₈₉	—	2	1	no	—
97	C₂×D₄×C₈₉	—	2	1	no	—
98	C₂×D₄×C₈₉	—	2	1	no	—
99	C₂×D₄×C₈₉	—	2	1	no	—
100	C₂×D₄×C₈₉	—	2	1	no	—
101	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
102	C₂×D₄×C₈₉	C₂×C₈	1	2	yes	—
103	C₂×D₄×C₈₉	C₂×C₈	1	2	yes	complemented
104	C₂×D₄×C₈₉	M₁₆	1	2	yes	—
105	C₂²×C₄×C₈₉	—	2	1	no	—
106	C₂²×C₄×C₈₉	—	2	2	no	—
107	C₂²×C₄×C₈₉	—	2	2	no	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	4	1	no	—
110	C₂²×C₄×C₈₉	—	4	1	no	—
111	C₂²×C₄×C₈₉	—	4	1	no	—
112	C₂²×C₄×C₈₉	—	4	1	no	—
113	C₂²×C₄×C₈₉	—	4	1	no	—
114	C₂²×C₄×C₈₉	—	4	1	no	—
115	C₂²×C₄×C₈₉	—	4	1	no	—
116	C₂²×C₄×C₈₉	—	4	1	no	—
117	C₂²×C₄×C₈₉	—	4	1	no	—
118	C₂²×C₄×C₈₉	—	4	1	no	—
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
122	D₈×C₈₉	—	2	8	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	C₂×C₈	1	2	yes	complemented
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
133	C₂²⋊C₄×C₈₉	—	2	2	no	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	4	1	no	—
136	C₂²⋊C₄×C₈₉	—	4	1	no	—
137	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₈₉	#41	1	1	yes	characteristic
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	—	2	2	no	—
143	C₂³×C₈₉	—	2	2	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	—	4	1	no	—
146	C₂³×C₈₉	—	4	1	no	—
147	C₂³×C₈₉	—	4	1	no	—
148	C₂³×C₈₉	—	4	1	no	—
149	C₂³×C₈₉	—	4	1	no	—
150	C₂³×C₈₉	—	4	1	no	—
151	C₂³×C₈₉	—	4	1	no	—
152	C₂³×C₈₉	—	4	1	no	—
153	C₂³×C₈₉	—	4	1	no	—
154	C₂³×C₈₉	—	4	1	no	—
155	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	2	2	no	—
158	D₄×C₈₉	—	2	2	no	—
159	D₄×C₈₉	—	2	2	no	—
160	D₄×C₈₉	—	2	2	no	—
161	D₄×C₈₉	—	4	1	no	—
162	D₄×C₈₉	—	4	1	no	—
163	D₄×C₈₉	C₂²⋊C₈	1	4	yes	complemented
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	1	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	8	1	no	—
177	C₂×C₄×C₈₉	—	8	1	no	—
178	C₂×C₄×C₈₉	—	8	1	no	—
179	C₂×C₄×C₈₉	—	8	1	no	—
180	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
192	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₈×C₈₉	—	2	2	no	—
195	C₈×C₈₉	—	4	1	no	—
196	#10623494	—	2	2	no	—
197	#10623494	—	4	2	no	—
198	#10623494	—	4	2	no	—
199	#10623494	—	4	1	no	—
200	#10623494	—	8	1	no	—
201	C₂²×C₈₉	—	2	4	no	—
202	C₂²×C₈₉	—	4	2	no	—
203	C₂²×C₈₉	—	4	2	no	—
204	C₂²×C₈₉	—	4	2	no	—
205	C₂²×C₈₉	—	4	2	no	—
206	C₂²×C₈₉	—	4	2	no	—
207	C₂²×C₈₉	—	4	2	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	—	8	1	no	—
212	C₂²×C₈₉	—	8	1	no	—
213	C₂²×C₈₉	—	8	1	no	—
214	C₂²×C₈₉	—	8	1	no	—
215	C₂²×C₈₉	#386	1	1	yes	characteristic
216	C₂²×C₈₉	C₈×D₄	1	1	yes	characteristic
217	C₂²×C₈₉	#435	1	1	yes	characteristic
218	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
219	C₂²×C₈₉	#442	1	1	yes	characteristic
220	C₂²×C₈₉	#443	1	1	yes	characteristic
221	C₂²×C₈₉	#444	1	1	yes	characteristic
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	—	8	1	no	—
226	C₄×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
227	C₄×C₈₉	#408	1	1	yes	characteristic
228	C₄×C₈₉	C₈×D₄	1	1	yes	characteristic
229	C₄×C₈₉	#435	1	1	yes	characteristic
230	C₄×C₈₉	#447	1	1	yes	characteristic
231	C₄×C₈₉	#449	1	1	yes	characteristic
232	C₄×C₈₉	#459	1	1	yes	characteristic
233	C₄×C₈₉	#463	1	1	yes	characteristic
234	#8947	—	89	1	no	maximal, Sylow
235	C₂×C₈₉	—	4	4	no	—
236	C₂×C₈₉	—	8	2	no	—
237	C₂×C₈₉	C₈×D₈	1	1	yes	characteristic
238	C₂×C₈₉	#1580	1	1	yes	characteristic
239	C₂×C₈₉	#1581	1	1	yes	characteristic
240	C₂×C₈₉	#1586	1	1	yes	characteristic
241	C₂×C₈₉	#1869	1	1	yes	characteristic
242	C₂×C₈₉	#1876	1	1	yes	characteristic
243	C₂×C₈₉	#1879	1	1	yes	characteristic
244	C₂×C₄×D₈	D₈₉	1	1	yes	characteristic
245	C₂×C₈×D₄	—	89	1	no	—
246	#1954	—	89	1	no	—
247	C₂×D₄⋊C₈	—	89	1	no	—
248	C₂×D₄⋊C₈	—	89	1	no	—
249	#1277	—	89	1	no	—
250	#1273	—	89	1	no	—
251	C₈₉	#8947	1	1	yes	characteristic, complemented, Sylow
252	C₂²×D₈	Dic₈₉	1	1	yes	characteristic
253	C₂³×C₈	—	178	1	no	—
254	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
256	C₄×D₈	—	2	2	no	—
257	C₄×D₈	—	2	2	no	—
258	C₈×D₄	—	178	2	no	—
259	C₈×D₄	—	178	2	no	—
260	C₂×#107	Dic₈₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	89	1	no	—
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×#102	Dic₈₉	1	1	yes	characteristic
264	C₂×#102	Dic₈₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	—	178	1	no	—
266	C₂×C₂²⋊C₈	—	178	1	no	—
267	C₂×C₂²⋊C₈	—	178	1	no	—
268	C₂×C₄×C₈	—	89	1	no	—
269	C₂×C₄×C₈	—	89	1	no	—
270	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
271	D₄⋊C₈	—	178	2	no	—
272	D₄⋊C₈	—	178	2	no	—
273	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
274	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	#10623494	1	4	yes	complemented
280	C₂²×C₈	—	89	1	no	—
281	C₂²×C₈	—	89	1	no	—
282	C₂²×C₈	—	356	2	no	—
283	C₂²×C₈	—	356	2	no	—
284	C₂²×C₈	—	178	1	no	—
285	C₂²×C₈	—	178	4	no	—
286	C₂²×C₈	—	178	1	no	—
287	C₂²×C₈	—	178	1	no	—
288	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
289	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²⋊D₈₉	1	2	yes	—
297	C₄×D₄	C₂²⋊D₈₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	C₄⋊C₈	—	89	2	no	—
305	C₄⋊C₈	—	178	1	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	—	178	1	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	C₂²⋊C₈	—	356	2	no	—
311	C₂²⋊C₈	—	356	2	no	—
312	C₂²⋊C₈	—	178	4	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	178	1	no	—
316	C₄×C₈	—	178	1	no	—
317	C₄×C₈	—	178	1	no	—
318	C₄×C₈	—	178	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂²⋊Dic₈₉	1	2	yes	—
330	C₂×D₄	C₂×#10623494	1	2	yes	—
331	C₂×D₄	C₂×#10623494	1	2	yes	complemented
332	C₂×D₄	#13083558	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
349	C₂²×C₄	#13083573	1	1	yes	characteristic
350	D₈	—	2	8	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	89	2	no	—
357	C₂×C₈	—	356	1	no	—
358	C₂×C₈	—	356	1	no	—
359	C₂×C₈	—	356	1	no	—
360	C₂×C₈	—	356	1	no	—
361	C₂×C₈	—	356	8	no	—
362	C₂×C₈	—	356	1	no	—
363	C₂×C₈	—	356	1	no	—
364	C₂×C₈	—	356	1	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	1	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	—	178	1	no	—
370	C₂×C₈	—	178	1	no	—
371	C₂×C₈	—	178	1	no	—
372	C₂×C₈	C₂×#10623494	1	2	yes	complemented
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	C₂²⋊Dic₈₉	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	D₄×D₈₉	1	1	yes	characteristic
382	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₄²	#13083573	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	C₂²⋊#10623494	1	4	yes	complemented
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
426	C₂×C₄	#15667980	1	1	yes	characteristic
427	C₂×C₄	#15667984	1	1	yes	characteristic
428	C₂×C₄	#15667984	1	1	yes	characteristic
429	C₂×C₄	#15667993	1	1	yes	characteristic
430	C₂×C₄	C₂²×#10623494	1	1	yes	characteristic
431	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
432	C₂×C₄	#15668019	1	1	yes	characteristic
433	C₂×C₄	#15668019	1	1	yes	characteristic
434	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
435	C₂×C₄	#15668031	1	1	yes	characteristic
436	C₂×C₄	#15668036	1	1	yes	characteristic
437	C₂×C₄	#15668036	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	356	2	no	—
441	C₈	—	356	2	no	—
442	C₈	—	356	1	no	—
443	C₈	—	178	2	no	—
444	C₈	—	712	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	#19151478	1	1	yes	characteristic
460	C₂²	D₄×#10623494	1	1	yes	characteristic
461	C₂²	#19151670	1	1	yes	characteristic
462	C₂²	D₈×Dic₈₉	1	1	yes	characteristic
463	C₂²	#19151710	1	1	yes	characteristic
464	C₂²	#19151715	1	1	yes	characteristic
465	C₂²	#19151720	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₂²⋊#10623494	1	1	yes	characteristic
471	C₄	#19151565	1	1	yes	characteristic
472	C₄	D₄×#10623494	1	1	yes	characteristic
473	C₄	#19151670	1	1	yes	characteristic
474	C₄	#19151730	1	1	yes	characteristic
475	C₄	#19151740	1	1	yes	characteristic
476	C₄	#19151791	1	1	yes	characteristic
477	C₄	#19151811	1	1	yes	characteristic
478	C₂	—	4	4	no	—
479	C₂	—	8	2	no	—
480	C₂	D₈×#10623494	1	1	yes	characteristic
481	C₂	#26019076	1	1	yes	characteristic
482	C₂	#26019082	1	1	yes	characteristic
483	C₂	#26019117	1	1	yes	characteristic
484	C₂	#26020545	1	1	yes	characteristic
485	C₂	#26020581	1	1	yes	characteristic
486	C₂	#26020602	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×C₄×D₈×C₈₉	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂²×D₈×C₈₉	C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×C₄×D₈	D₈₉
hypocenter	C₈₉	#8947
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×#10623494	C₂	semidirect
2. #26021047	C₂	semidirect
3. C₂×D₄⋊#10623494	C₂	semidirect
4. C₂×D₄⋊#10623494	C₂	semidirect
5. #26018087	C₂	semidirect
6. #26018079	C₂	semidirect
54. C₂×D₈×C₈₉	C₈	semidirect
90. C₂×#10623494	D₈	semidirect
103. C₂×D₄×C₈₉	C₂×C₈	semidirect
128. C₂×C₈×C₈₉	C₂×C₈	semidirect
163. D₄×C₈₉	C₂²⋊C₈	semidirect
251. C₈₉	#8947	semidirect
279. C₂×D₈	#10623494	semidirect
331. C₂×D₄	C₂×#10623494	semidirect
372. C₂×C₈	C₂×#10623494	semidirect
407. D₄	C₂²⋊#10623494	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×#10623494	2
#26021047	2
C₂×D₄⋊#10623494	2
#26018087	2
#26018079	2
C₂×C₄×D₈×C₈₉	2
#8947	89