Subgroups — #36557654

Order 22784.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028896	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668019	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020902	C₂	1	2	yes	maximal, complemented
4	#26020853	C₂	1	2	yes	maximal, complemented
5	#26020581	C₂	1	2	yes	maximal
6	#26020529	C₂	1	2	yes	maximal, complemented
7	C₄×#15667948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#15667939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#15667939	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019997	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	#19151659	—	2	2	no	—
14	#19151651	—	2	1	no	—
15	#19151651	—	2	1	no	—
16	C₂×#15667948	C₂²	1	2	yes	—
17	#19151625	C₂²	1	2	yes	—
18	C₂×#15667939	C₂²	1	2	yes	—
19	C₂×#15667939	C₂²	1	2	yes	—
20	#19151565	C₂²	1	2	yes	—
21	#19151554	—	2	2	no	—
22	#19151554	C₂²	1	2	yes	—
23	C₄×#13083558	—	2	1	no	—
24	C₄×#13083558	C₂²	1	1	yes	characteristic
25	C₄×#13083558	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10623494	—	2	1	no	—
27	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
28	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
29	#19151363	C₂²	1	2	yes	—
30	#19151357	C₂²	1	2	yes	—
31	#19151357	C₂²	1	2	yes	—
32	#19151352	C₂²	1	2	yes	—
33	#19151352	C₂²	1	2	yes	—
34	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
38	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
40	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
41	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
42	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
43	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
44	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
45	#427×C₈₉	C₂²	1	1	yes	characteristic
46	#416×C₈₉	C₂²	1	1	yes	characteristic
47	#416×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	#15668019	—	2	4	no	—
50	#15668019	—	2	4	no	—
51	C₂×#13083558	—	2	2	no	—
52	C₂×#13083558	C₂³	1	2	yes	—
53	C₂×#13083558	C₂³	1	2	yes	—
54	C₂²×#10623494	—	2	2	no	—
55	C₂²×#10623494	C₂³	1	2	yes	—
56	C₂×C₄×Dic₈₉	—	2	1	no	—
57	C₂×C₄×Dic₈₉	—	2	1	no	—
58	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
59	#15667948	—	2	4	no	—
60	C₄⋊#10623494	—	2	2	no	—
61	C₄⋊#10623494	—	2	2	no	—
62	#15667939	—	2	4	no	—
63	#15667939	—	2	4	no	—
64	C₂²⋊#10623494	—	2	2	no	—
65	C₂²⋊#10623494	—	2	2	no	—
66	#15667923	—	2	2	no	—
67	#15667923	—	2	1	no	—
68	#15667923	—	2	1	no	—
69	C₄×#10623494	—	2	2	no	—
70	C₄×#10623494	—	2	1	no	—
71	C₄×#10623494	—	2	1	no	—
72	C₄×#10623494	D₄	1	1	yes	characteristic
73	C₄×#10623494	D₄	1	1	yes	characteristic
74	C₄×#10623494	D₄	1	2	yes	—
75	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
77	#135×C₈₉	—	2	4	no	—
78	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	—	2	1	no	—
92	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
96	#117×C₈₉	—	2	1	no	—
97	#117×C₈₉	—	2	1	no	—
98	#117×C₈₉	C₂³	1	1	yes	characteristic
99	#117×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	—	2	1	no	—
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
104	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
105	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
107	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
108	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
109	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
110	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
111	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
112	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
113	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
114	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₂²×Dic₈₉	—	2	2	no	—
120	#13083558	—	2	8	no	—
121	#13083558	—	2	2	no	—
122	#13083558	—	2	2	no	—
123	#13083558	—	2	2	no	—
124	#13083558	#41	1	4	yes	—
125	C₂×#10623494	—	2	8	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₂×#10623494	C₂×D₄	1	2	yes	—
131	C₂×#10623494	C₂×D₄	1	2	yes	—
132	C₄×Dic₈₉	—	2	4	no	—
133	C₄×Dic₈₉	—	2	2	no	—
134	C₄×Dic₈₉	—	2	2	no	—
135	C₄×Dic₈₉	—	4	2	no	—
136	#41×C₈₉	—	2	2	no	—
137	#41×C₈₉	—	2	2	no	—
138	#41×C₈₉	—	2	2	no	—
139	#41×C₈₉	#41	1	4	yes	—
140	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×D₄×C₈₉	—	2	1	no	—
143	C₂×D₄×C₈₉	—	2	1	no	—
144	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₈₉	—	2	2	no	—
156	SD₁₆×C₈₉	—	2	2	no	—
157	SD₁₆×C₈₉	—	2	2	no	—
158	D₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	—	2	1	no	—
167	C₄⋊C₄×C₈₉	—	2	1	no	—
168	C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₈₉	—	2	1	no	—
174	C₂²⋊C₄×C₈₉	—	2	1	no	—
175	C₂²⋊C₄×C₈₉	—	2	1	no	—
176	C₂²⋊C₄×C₈₉	—	2	1	no	—
177	C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₂²⋊C₄×C₈₉	—	2	1	no	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₄²×C₈₉	—	2	1	no	—
181	C₄²×C₈₉	—	2	1	no	—
182	C₄²×C₈₉	—	2	1	no	—
183	C₄²×C₈₉	—	2	1	no	—
184	C₄²×C₈₉	—	2	1	no	—
185	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₈₉	—	2	1	no	—
190	C₂³×C₈₉	—	2	1	no	—
191	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
192	Q₈×C₈₉	—	2	1	no	—
193	Q₈×C₈₉	—	2	1	no	—
194	Q₈×C₈₉	—	2	1	no	—
195	Q₈×C₈₉	#117	1	2	yes	—
196	D₄×C₈₉	—	2	4	no	—
197	D₄×C₈₉	—	2	1	no	—
198	D₄×C₈₉	—	2	1	no	—
199	D₄×C₈₉	—	2	1	no	—
200	D₄×C₈₉	—	4	2	no	—
201	D₄×C₈₉	#117	1	2	yes	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	4	no	—
204	C₂×C₄×C₈₉	—	2	2	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	4	2	no	—
212	C₂×C₄×C₈₉	—	4	2	no	—
213	C₂×C₄×C₈₉	—	4	2	no	—
214	C₂×C₄×C₈₉	—	4	2	no	—
215	C₂×C₄×C₈₉	—	4	2	no	—
216	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
223	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
224	C₂×Dic₈₉	—	2	4	no	—
225	C₂×Dic₈₉	—	4	2	no	—
226	C₂×Dic₈₉	—	4	2	no	—
227	C₈×C₈₉	—	2	1	no	—
228	C₈×C₈₉	—	2	1	no	—
229	C₈×C₈₉	—	2	1	no	—
230	C₈×C₈₉	—	2	1	no	—
231	#10623494	—	2	2	no	—
232	#10623494	—	2	4	no	—
233	#10623494	—	2	2	no	—
234	#10623494	—	4	2	no	—
235	C₂²×C₈₉	—	2	1	no	—
236	C₂²×C₈₉	—	2	1	no	—
237	C₂²×C₈₉	—	2	2	no	—
238	C₂²×C₈₉	—	4	1	no	—
239	C₂²×C₈₉	—	4	1	no	—
240	C₂²×C₈₉	—	4	1	no	—
241	C₂²×C₈₉	—	4	1	no	—
242	C₂²×C₈₉	—	4	1	no	—
243	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₈₉	#529	1	2	yes	—
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	2	2	no	—
248	C₄×C₈₉	—	4	1	no	—
249	C₄×C₈₉	—	4	1	no	—
250	C₄×C₈₉	—	4	1	no	—
251	C₄×C₈₉	—	4	1	no	—
252	C₄×C₈₉	—	4	1	no	—
253	C₄×C₈₉	#443	1	2	yes	—
254	C₄×C₈₉	#444	1	2	yes	—
255	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
256	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
257	C₄×C₈₉	#525	1	2	yes	—
258	Dic₈₉	—	4	4	no	—
259	#21137	—	89	1	no	maximal, Sylow
260	C₂×C₈₉	—	2	2	no	—
261	C₂×C₈₉	—	4	2	no	—
262	C₂×C₈₉	—	8	1	no	—
263	C₂×C₈₉	#2290	1	1	yes	characteristic
264	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
265	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
266	C₄×#135	D₈₉	1	1	yes	characteristic
267	#2922	—	89	1	no	—
268	C₄×#131	—	89	1	no	—
269	#1929	—	89	2	no	—
270	#1922	—	89	2	no	—
271	#1876	—	89	2	no	—
272	#1866	—	89	2	no	—
273	C₄×#108	—	89	1	no	—
274	C₄×#104	—	89	1	no	—
275	C₄×#104	—	89	1	no	—
276	#1744	—	89	1	no	—
277	C₈₉	#21137	1	1	yes	characteristic, complemented, Sylow
278	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
279	C₂×#131	—	89	2	no	—
280	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
281	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
282	C₄×Q₁₆	Dic₈₉	1	1	yes	characteristic, complemented
283	C₄×Q₁₆	Dic₈₉	1	1	yes	characteristic, complemented
284	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic, complemented
285	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic, complemented
286	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic, complemented
287	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic, complemented
288	C₄×D₈	Dic₈₉	1	1	yes	characteristic, complemented
289	C₄×D₈	Dic₈₉	1	1	yes	characteristic, complemented
290	#433	—	178	2	no	—
291	#431	—	178	1	no	—
292	#431	—	178	1	no	—
293	C₂×#108	—	89	2	no	—
294	#427	C₂×D₈₉	1	1	yes	characteristic
295	#424	—	89	2	no	—
296	C₂×#104	—	89	2	no	—
297	C₂×#104	—	89	2	no	—
298	#416	C₂×D₈₉	1	1	yes	characteristic
299	#416	C₂×D₈₉	1	1	yes	characteristic
300	#408	—	89	2	no	—
301	#405	—	89	2	no	—
302	#405	—	178	2	no	—
303	C₄×M₁₆	—	89	1	no	—
304	C₄×M₁₆	—	89	1	no	—
305	C₄×M₁₆	—	178	1	no	—
306	C₂×C₄×C₈	—	89	1	no	—
307	C₂×C₄×C₈	—	178	1	no	—
308	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
309	C₄³	—	89	1	no	—
310	#341	—	89	2	no	—
311	#339	—	89	2	no	—
312	#339	—	89	2	no	—
313	#336	—	89	2	no	—
314	#336	—	89	2	no	—
315	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
316	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
317	#135	—	2	4	no	—
318	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
319	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
320	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
321	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
322	#131	—	178	4	no	—
323	#131	—	178	4	no	—
324	C₂×M₁₆	—	89	2	no	—
325	C₂×M₁₆	—	89	2	no	—
326	C₂×M₁₆	—	178	2	no	—
327	C₂²×C₈	—	89	2	no	—
328	C₂²×C₈	—	178	2	no	—
329	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
331	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
332	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
333	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
334	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
340	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
341	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
342	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂²×D₈₉	1	1	yes	characteristic
346	#117	C₂²×D₈₉	1	1	yes	characteristic
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	89	2	no	—
350	C₂×C₄²	—	178	1	no	—
351	C₂×C₄²	—	178	1	no	—
352	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
353	#108	—	178	4	no	—
354	#107	C₂×Dic₈₉	1	1	yes	characteristic
355	#107	C₂×Dic₈₉	1	1	yes	characteristic
356	#106	C₂×Dic₈₉	1	1	yes	characteristic
357	#106	C₂×Dic₈₉	1	1	yes	characteristic
358	C₄⋊C₈	—	178	2	no	—
359	C₄⋊C₈	—	178	2	no	—
360	#104	—	178	4	no	—
361	#104	—	178	4	no	—
362	#103	C₂×Dic₈₉	1	1	yes	characteristic
363	#103	C₂×Dic₈₉	1	1	yes	characteristic
364	#103	C₂×Dic₈₉	1	1	yes	characteristic
365	#103	C₂×Dic₈₉	1	1	yes	characteristic
366	#102	C₂×Dic₈₉	1	1	yes	characteristic
367	#102	C₂×Dic₈₉	1	1	yes	characteristic
368	#102	C₂×Dic₈₉	1	1	yes	characteristic
369	#102	C₂×Dic₈₉	1	1	yes	characteristic
370	C₂²⋊C₈	—	178	2	no	—
371	C₂²⋊C₈	—	178	2	no	—
372	#97	—	178	2	no	—
373	#97	—	178	1	no	—
374	#97	—	178	1	no	—
375	C₄×C₈	—	89	2	no	—
376	C₄×C₈	—	89	1	no	—
377	C₄×C₈	—	89	1	no	—
378	C₄×C₈	—	178	2	no	—
379	C₄×C₈	—	178	1	no	—
380	C₄×C₈	—	178	1	no	—
381	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
382	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
383	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
384	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	#13083574	1	4	yes	—
389	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
390	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
394	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	178	2	no	—
402	C₂²×C₄	#13083573	1	1	yes	characteristic
403	C₂²×C₄	#13083573	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
405	Q₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	SD₁₆	—	2	2	no	—
408	D₈	—	2	2	no	—
409	M₁₆	—	89	4	no	—
410	M₁₆	—	178	2	no	—
411	M₁₆	—	178	2	no	—
412	M₁₆	—	178	8	no	—
413	M₁₆	—	178	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	89	2	no	—
417	C₂×C₈	—	89	2	no	—
418	C₂×C₈	—	178	2	no	—
419	C₂×C₈	—	178	8	no	—
420	C₂×C₈	—	178	2	no	—
421	C₂×C₈	—	178	2	no	—
422	C₂×C₈	—	178	2	no	—
423	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
424	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
425	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
426	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
433	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
434	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	356	2	no	—
448	C₄²	—	178	4	no	—
449	C₄²	—	178	2	no	—
450	C₄²	—	178	2	no	—
451	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
452	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
453	C₄²	D₄×D₈₉	1	1	yes	characteristic
454	C₄²	D₄×D₈₉	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	C₂×#13083573	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	#15667971	1	2	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	4	2	no	—
467	D₄	#15667971	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	356	2	no	—
483	C₂×C₄	—	356	2	no	—
484	C₂×C₄	—	178	4	no	—
485	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
486	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
487	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
488	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
489	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
491	C₂×C₄	#41×D₈₉	1	2	yes	—
492	C₂×C₄	C₂×#13083574	1	2	yes	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	356	2	no	—
498	C₈	—	178	2	no	—
499	C₈	—	178	2	no	—
500	C₈	—	178	4	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
510	C₂²	#19152128	1	2	yes	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	356	4	no	—
520	C₄	#19151715	1	2	yes	—
521	C₄	#19151720	1	2	yes	—
522	C₄	C₂×#15667971	1	1	yes	characteristic
523	C₄	#41×Dic₈₉	1	1	yes	characteristic
524	C₄	#19152107	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	1	no	—
528	C₂	#26022697	1	1	yes	characteristic
529	C₂	C₂×#19151715	1	1	yes	characteristic
530	C₂	C₂×#19151720	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#135×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#135	D₈₉
hypocenter	C₈₉	#21137
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #26028896	C₂	semidirect
2. C₄×#15668019	C₂	semidirect
3. #26020902	C₂	semidirect
4. #26020853	C₂	semidirect
6. #26020529	C₂	semidirect
7. C₄×#15667948	C₂	semidirect
8. C₄×#15667939	C₂	semidirect
9. C₄×#15667939	C₂	semidirect
10. #26019997	C₂	semidirect
37. C₄×Q₁₆×C₈₉	C₄	semidirect
38. C₄×Q₁₆×C₈₉	C₄	semidirect
39. C₄×SD₁₆×C₈₉	C₄	semidirect
40. C₄×SD₁₆×C₈₉	C₄	semidirect
41. C₄×SD₁₆×C₈₉	C₄	semidirect
42. C₄×SD₁₆×C₈₉	C₄	semidirect
43. C₄×D₈×C₈₉	C₄	semidirect
44. C₄×D₈×C₈₉	C₄	semidirect
277. C₈₉	#21137	semidirect
282. C₄×Q₁₆	Dic₈₉	semidirect
283. C₄×Q₁₆	Dic₈₉	semidirect
284. C₄×SD₁₆	Dic₈₉	semidirect
285. C₄×SD₁₆	Dic₈₉	semidirect
286. C₄×SD₁₆	Dic₈₉	semidirect
287. C₄×SD₁₆	Dic₈₉	semidirect
288. C₄×D₈	Dic₈₉	semidirect
289. C₄×D₈	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028896	2
C₄×#15668019	2
#26020902	2
#26020853	2
#26020581	2
#26020529	2
C₄×#15667948	2
C₄×#15667939	2
#26019997	2
C₄×#135×C₈₉	2
#21137	89