Subgroups — #36572039

Order 22784.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028910	C₂	1	2	yes	maximal
2	#26021006	C₂	1	1	yes	maximal, characteristic, complemented
3	#26021001	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020853	C₂	1	2	yes	maximal, complemented
5	#26020853	C₂	1	2	yes	maximal, complemented
6	#26020351	C₂	1	2	yes	maximal
7	#26020294	C₂	1	1	yes	maximal, characteristic
8	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020033	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2911	C₂	1	1	yes	maximal, characteristic
12	#19151659	—	2	2	no	—
13	#19151659	—	2	2	no	—
14	#19151655	—	2	2	no	—
15	#19151651	—	2	2	no	—
16	C₂×#15667948	C₂²	1	1	yes	characteristic
17	C₂×#15667948	C₂²	1	1	yes	characteristic
18	#19151625	C₂²	1	2	yes	—
19	#19151625	C₂²	1	2	yes	—
20	#19151562	C₂²	1	2	yes	—
21	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
22	#19151554	C₂²	1	2	yes	—
23	#19151554	C₂²	1	2	yes	—
24	C₂×#15667922	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
27	#19151363	C₂²	1	2	yes	—
28	#19151357	C₂²	1	2	yes	—
29	#19151357	C₂²	1	2	yes	—
30	#19151357	C₂²	1	2	yes	—
31	#19151357	C₂²	1	2	yes	—
32	#19151352	C₂²	1	1	yes	characteristic
33	#19151352	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	#428×C₈₉	C₄	1	2	yes	complemented
37	#428×C₈₉	C₄	1	2	yes	complemented
38	#428×C₈₉	C₄	1	2	yes	complemented
39	#428×C₈₉	C₄	1	2	yes	complemented
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#427×C₈₉	C₂²	1	2	yes	—
43	C₂×#13083558	C₂³	1	2	yes	—
44	C₂×#13083558	C₂³	1	2	yes	—
45	C₂²×#10623494	C₂³	1	1	yes	characteristic
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
50	#15667948	—	2	2	no	—
51	#15667948	—	2	2	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	2	no	—
54	C₄⋊#10623494	—	2	2	no	—
55	C₄⋊#10623494	—	2	2	no	—
56	C₂²⋊#10623494	—	2	2	no	—
57	C₂²⋊#10623494	—	2	2	no	—
58	C₂²⋊#10623494	D₄	1	2	yes	—
59	C₂²⋊#10623494	D₄	1	2	yes	—
60	#15667923	—	2	2	no	—
61	#15667923	—	2	2	no	—
62	#15667922	—	2	2	no	—
63	C₄×#10623494	—	2	2	no	—
64	C₄×#10623494	—	2	2	no	—
65	C₈×Dic₈₉	—	2	2	no	—
66	#15667919	—	2	1	no	—
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₈₉	—	2	2	no	—
69	C₂×M₁₆×C₈₉	—	2	2	no	—
70	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	#117×C₈₉	—	2	2	no	—
75	#117×C₈₉	—	2	2	no	—
76	#117×C₈₉	C₂×C₄	1	2	yes	—
77	#117×C₈₉	C₂×C₄	1	2	yes	—
78	#117×C₈₉	C₂³	1	2	yes	—
79	#117×C₈₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
83	C₂×C₄²×C₈₉	—	2	2	no	—
84	#107×C₈₉	C₂×C₄	1	2	yes	—
85	#107×C₈₉	C₂×C₄	1	2	yes	—
86	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
87	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
88	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
90	#106×C₈₉	C₂×C₄	1	2	yes	—
91	#106×C₈₉	C₂×C₄	1	2	yes	—
92	#106×C₈₉	C₂×C₄	1	2	yes	—
93	#106×C₈₉	C₂×C₄	1	2	yes	—
94	C₂²×Dic₈₉	—	2	1	no	—
95	C₂²×Dic₈₉	—	2	1	no	—
96	#13083558	—	2	2	no	—
97	#13083558	—	2	2	no	—
98	#13083558	—	2	2	no	—
99	#13083558	—	2	2	no	—
100	C₂×#10623494	—	2	1	no	—
101	C₂×#10623494	—	2	1	no	—
102	C₂×#10623494	—	2	1	no	—
103	C₂×#10623494	—	2	1	no	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
107	C₂×#10623494	C₂×D₄	1	2	yes	—
108	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
109	C₂²⋊Dic₈₉	—	4	2	no	—
110	C₄×Dic₈₉	—	2	1	no	—
111	C₄×Dic₈₉	—	2	1	no	—
112	C₄×Dic₈₉	—	2	1	no	—
113	C₄×Dic₈₉	—	2	1	no	—
114	C₂⁴×C₈₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	—	2	1	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	—	2	2	no	—
121	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₈₉	—	2	4	no	—
126	M₁₆×C₈₉	—	2	4	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₈₉	#41	1	2	yes	—
133	C₂×C₈×C₈₉	#41	1	2	yes	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
137	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₈₉	—	2	2	no	—
141	C₂²⋊C₄×C₈₉	—	2	2	no	—
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₂²⋊C₄×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₂³×C₈₉	—	2	1	no	—
149	C₂³×C₈₉	—	2	1	no	—
150	C₂³×C₈₉	—	4	1	no	—
151	C₂³×C₈₉	—	4	1	no	—
152	C₂³×C₈₉	C₄×D₄	1	2	yes	—
153	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	4	4	no	—
165	C₂×C₄×C₈₉	—	8	2	no	—
166	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	—	4	1	no	—
175	C₂×Dic₈₉	—	4	1	no	—
176	C₂×Dic₈₉	—	4	1	no	—
177	C₂×Dic₈₉	—	4	1	no	—
178	C₂×Dic₈₉	—	4	1	no	—
179	C₈×C₈₉	—	2	2	no	—
180	C₈×C₈₉	#117	1	2	yes	—
181	C₈×C₈₉	#117	1	2	yes	—
182	#10623494	—	2	1	no	—
183	#10623494	—	2	1	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	4	2	no	—
186	#10623494	—	4	2	no	—
187	C₂²×C₈₉	—	2	1	no	—
188	C₂²×C₈₉	—	2	1	no	—
189	C₂²×C₈₉	—	2	2	no	—
190	C₂²×C₈₉	—	2	2	no	—
191	C₂²×C₈₉	—	2	2	no	—
192	C₂²×C₈₉	—	8	1	no	—
193	C₂²×C₈₉	—	8	1	no	—
194	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₈₉	#552	1	1	yes	characteristic
196	C₂²×C₈₉	#552	1	1	yes	characteristic
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
203	C₄×C₈₉	#519	1	1	yes	characteristic
204	C₄×C₈₉	#547	1	1	yes	characteristic
205	C₄×C₈₉	#547	1	1	yes	characteristic
206	Dic₈₉	—	4	2	no	—
207	Dic₈₉	—	8	1	no	—
208	#22608	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	—	2	1	no	—
210	C₂×C₈₉	—	2	1	no	—
211	C₂×C₈₉	—	4	2	no	—
212	C₂×C₈₉	#2344	1	1	yes	characteristic
213	C₂×C₈₉	#2955	1	1	yes	characteristic
214	C₂×C₈₉	#2956	1	1	yes	characteristic
215	#2924	—	89	2	no	—
216	#2911	D₈₉	1	1	yes	characteristic
217	#1946	—	89	1	no	—
218	#1945	—	89	1	no	—
219	#1922	—	89	2	no	—
220	#1922	—	89	2	no	—
221	#1826	—	89	2	no	—
222	#1811	—	89	1	no	—
223	#1773	—	89	1	no	—
224	#1772	—	89	1	no	—
225	#1753	—	89	1	no	—
226	C₈₉	#22608	1	1	yes	characteristic, complemented, Sylow
227	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
228	C₂×#117	C₂×D₈₉	1	2	yes	—
229	#433	—	178	2	no	—
230	#433	—	178	2	no	—
231	#432	—	178	2	no	—
232	#431	—	178	2	no	—
233	C₂×#108	—	89	1	no	—
234	C₂×#108	—	89	1	no	—
235	#428	Dic₈₉	1	2	yes	complemented
236	#428	Dic₈₉	1	2	yes	complemented
237	#428	Dic₈₉	1	2	yes	complemented
238	#428	Dic₈₉	1	2	yes	complemented
239	#427	C₂×D₈₉	1	2	yes	—
240	#427	C₂×D₈₉	1	1	yes	characteristic
241	#427	C₂×D₈₉	1	1	yes	characteristic
242	#424	—	89	2	no	—
243	#424	—	89	2	no	—
244	#407	—	89	2	no	—
245	C₂×C₂²⋊C₈	—	89	1	no	—
246	#405	—	89	2	no	—
247	#405	—	89	2	no	—
248	C₂×#97	—	89	1	no	—
249	C₂×C₄×C₈	—	89	1	no	—
250	C₄×C₂²⋊C₄	—	89	1	no	—
251	#341	—	89	2	no	—
252	#339	—	89	2	no	—
253	#339	—	89	2	no	—
254	#339	—	89	2	no	—
255	#339	—	89	2	no	—
256	#336	—	89	1	no	—
257	#336	—	89	1	no	—
258	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	89	2	no	—
262	C₂×M₁₆	—	89	2	no	—
263	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
264	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
265	C₂²×C₈	—	89	1	no	—
266	C₂²×C₈	—	89	1	no	—
267	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	C₂×Dic₈₉	1	2	yes	—
272	#117	C₂×Dic₈₉	1	2	yes	—
273	#117	C₂²×D₈₉	1	2	yes	—
274	#117	C₂²×D₈₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	178	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	89	1	no	—
281	C₂×C₄²	—	89	1	no	—
282	#108	—	178	2	no	—
283	#108	—	178	2	no	—
284	#107	C₂×Dic₈₉	1	2	yes	—
285	#107	C₂×Dic₈₉	1	2	yes	—
286	#107	C₂×Dic₈₉	1	1	yes	characteristic
287	#107	C₂×Dic₈₉	1	1	yes	characteristic
288	#107	C₂×Dic₈₉	1	1	yes	characteristic
289	#107	C₂×Dic₈₉	1	1	yes	characteristic
290	#106	C₂×Dic₈₉	1	2	yes	—
291	#106	C₂×Dic₈₉	1	2	yes	—
292	#106	C₂×Dic₈₉	1	2	yes	—
293	#106	C₂×Dic₈₉	1	2	yes	—
294	C₄⋊C₈	—	178	2	no	—
295	C₄⋊C₈	—	178	2	no	—
296	C₄⋊C₈	—	178	2	no	—
297	C₄⋊C₈	—	178	2	no	—
298	C₂²⋊C₈	—	89	2	no	—
299	C₂²⋊C₈	—	89	2	no	—
300	C₂²⋊C₈	—	178	2	no	—
301	C₂²⋊C₈	—	178	2	no	—
302	#97	—	178	2	no	—
303	#97	—	178	2	no	—
304	#97	—	178	2	no	—
305	C₄×C₈	—	178	2	no	—
306	C₄×C₈	—	178	2	no	—
307	C₄×C₈	—	178	2	no	—
308	#95	—	178	1	no	—
309	C₂⁴	#13083573	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	178	1	no	—
317	C₂²×C₄	—	178	1	no	—
318	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
319	C₂²×C₄	D₄×D₈₉	1	2	yes	—
320	C₂²×C₄	#13083573	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	178	2	no	—
325	M₁₆	—	178	2	no	—
326	M₁₆	—	178	2	no	—
327	M₁₆	—	178	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	89	1	no	—
331	C₂×C₈	—	89	2	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	178	2	no	—
334	C₂×C₈	—	178	2	no	—
335	C₂×C₈	—	178	1	no	—
336	C₂×C₈	—	178	1	no	—
337	C₂×C₈	—	178	1	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
340	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
341	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
342	C₂×C₈	#13083574	1	2	yes	—
343	C₂×C₈	#13083574	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
347	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
348	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
349	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	356	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	178	1	no	—
360	C₄²	—	178	1	no	—
361	C₄²	—	178	1	no	—
362	C₄²	—	178	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	D₄×Dic₈₉	1	2	yes	—
368	C₂³	C₂×#13083573	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	356	1	no	—
382	C₂×C₄	—	356	1	no	—
383	C₂×C₄	—	356	1	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	1	no	—
386	C₂×C₄	—	178	2	no	—
387	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
388	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
391	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
392	C₂×C₄	#15668060	1	1	yes	characteristic
393	C₂×C₄	#15668060	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	356	2	no	—
396	C₈	—	356	2	no	—
397	C₈	—	178	1	no	—
398	C₈	—	178	2	no	—
399	C₈	—	178	1	no	—
400	C₈	#15667971	1	2	yes	—
401	C₈	#15667971	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
410	C₂²	#19152283	1	1	yes	characteristic
411	C₂²	#19152283	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	356	2	no	—
418	C₄	—	712	1	no	—
419	C₄	C₂×#15667971	1	1	yes	characteristic
420	C₄	#19152076	1	1	yes	characteristic
421	C₄	#19152249	1	1	yes	characteristic
422	C₄	#19152249	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#26023121	1	1	yes	characteristic
427	C₂	#26029155	1	1	yes	characteristic
428	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2911	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂⁴×C₈₉	#41
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2911	D₈₉
hypocenter	C₈₉	#22608
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2911

Complements

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

N	H ≅ G/N	type
2. #26021006	C₂	semidirect
3. #26021001	C₂	semidirect
4. #26020853	C₂	semidirect
5. #26020853	C₂	semidirect
8. #26020138	C₂	semidirect
9. #26020133	C₂	semidirect
36. #428×C₈₉	C₄	semidirect
37. #428×C₈₉	C₄	semidirect
38. #428×C₈₉	C₄	semidirect
39. #428×C₈₉	C₄	semidirect
226. C₈₉	#22608	semidirect
235. #428	Dic₈₉	semidirect
236. #428	Dic₈₉	semidirect
237. #428	Dic₈₉	semidirect
238. #428	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028910	2
#26021006	2
#26021001	2
#26020853	2
#26020351	2
#26020294	2
#26020138	2
#26020133	2
#26020033	2
C₈₉×#2911	2
#22608	89