Subgroups — #36557665

Order 22784.

772 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	#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	#26020158	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020062	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020062	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	#19151659	—	2	1	no	—
14	#19151659	—	2	1	no	—
15	#19151651	—	2	2	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	#19151444	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	#442×C₈₉	C₄	1	2	yes	complemented
38	#441×C₈₉	C₄	1	2	yes	complemented
39	#440×C₈₉	C₄	1	2	yes	complemented
40	#440×C₈₉	C₄	1	2	yes	complemented
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#416×C₈₉	C₂²	1	1	yes	characteristic
43	#416×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
45	#15668019	—	2	4	no	—
46	#15668019	—	2	4	no	—
47	C₂×#13083558	—	2	2	no	—
48	C₂×#13083558	C₂³	1	2	yes	—
49	C₂×#13083558	C₂³	1	2	yes	—
50	C₂²×#10623494	—	2	2	no	—
51	C₂²×#10623494	C₂³	1	2	yes	—
52	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
53	#15667948	—	2	4	no	—
54	C₄⋊#10623494	—	2	2	no	—
55	C₄⋊#10623494	—	2	2	no	—
56	#15667939	—	2	4	no	—
57	#15667939	—	2	4	no	—
58	C₂²⋊#10623494	—	2	2	no	—
59	C₂²⋊#10623494	—	2	2	no	—
60	#15667923	—	2	2	no	—
61	#15667923	—	2	1	no	—
62	#15667923	—	2	1	no	—
63	C₄×#10623494	—	2	2	no	—
64	C₄×#10623494	—	2	1	no	—
65	C₄×#10623494	—	2	1	no	—
66	C₄×#10623494	D₄	1	2	yes	—
67	C₄×#10623494	D₄	1	1	yes	characteristic
68	C₄×#10623494	D₄	1	1	yes	characteristic
69	#15667919	—	2	2	no	—
70	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
71	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
72	#135×C₈₉	—	2	4	no	—
73	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
81	C₄×D₄×C₈₉	—	2	2	no	—
82	C₄×D₄×C₈₉	—	2	2	no	—
83	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
84	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
85	#117×C₈₉	—	2	1	no	—
86	#117×C₈₉	—	2	1	no	—
87	#117×C₈₉	C₂³	1	1	yes	characteristic
88	#117×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	#107×C₈₉	C₂×C₄	1	2	yes	—
93	#106×C₈₉	C₂×C₄	1	2	yes	—
94	#103×C₈₉	C₂×C₄	1	2	yes	—
95	#103×C₈₉	C₂×C₄	1	2	yes	—
96	#102×C₈₉	C₂×C₄	1	2	yes	—
97	#102×C₈₉	C₂×C₄	1	2	yes	—
98	#97×C₈₉	C₂×C₄	1	2	yes	—
99	#97×C₈₉	C₂×C₄	1	2	yes	—
100	C₂²×Dic₈₉	—	2	2	no	—
101	#13083558	—	2	8	no	—
102	#13083558	—	2	2	no	—
103	#13083558	—	2	2	no	—
104	#13083558	—	2	2	no	—
105	#13083558	#41	1	4	yes	—
106	C₂×#10623494	—	2	8	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₄×Dic₈₉	—	2	2	no	—
114	C₄×Dic₈₉	—	2	2	no	—
115	#41×C₈₉	—	2	2	no	—
116	#41×C₈₉	—	2	2	no	—
117	#41×C₈₉	—	2	2	no	—
118	#41×C₈₉	#41	1	4	yes	—
119	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	2	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	#41	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₈₉	—	2	2	no	—
132	SD₁₆×C₈₉	—	2	2	no	—
133	SD₁₆×C₈₉	—	2	2	no	—
134	D₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	—	2	1	no	—
157	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
158	Q₈×C₈₉	—	2	1	no	—
159	Q₈×C₈₉	—	2	1	no	—
160	Q₈×C₈₉	—	2	1	no	—
161	Q₈×C₈₉	#117	1	2	yes	—
162	D₄×C₈₉	—	2	4	no	—
163	D₄×C₈₉	—	2	1	no	—
164	D₄×C₈₉	—	2	1	no	—
165	D₄×C₈₉	—	2	1	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	#117	1	2	yes	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	4	no	—
175	C₂×C₄×C₈₉	—	4	4	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
182	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
183	C₂×Dic₈₉	—	4	4	no	—
184	C₂×Dic₈₉	—	4	2	no	—
185	C₈×C₈₉	—	2	1	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	2	no	—
188	#10623494	—	2	2	no	—
189	#10623494	—	2	4	no	—
190	#10623494	—	2	2	no	—
191	#10623494	—	4	2	no	—
192	C₂²×C₈₉	—	2	2	no	—
193	C₂²×C₈₉	—	2	2	no	—
194	C₂²×C₈₉	—	4	2	no	—
195	C₂²×C₈₉	—	4	2	no	—
196	C₂²×C₈₉	—	4	1	no	—
197	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₈₉	#529	1	2	yes	—
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	2	2	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	—	4	2	no	—
204	C₄×C₈₉	—	4	1	no	—
205	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
206	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
207	C₄×C₈₉	#525	1	2	yes	—
208	Dic₈₉	—	8	2	no	—
209	#21138	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	2	2	no	—
211	C₂×C₈₉	—	4	2	no	—
212	C₂×C₈₉	—	8	1	no	—
213	C₂×C₈₉	#2290	1	1	yes	characteristic
214	C₂×C₈₉	#2955	1	2	yes	—
215	#2943	D₈₉	1	1	yes	characteristic
216	#2922	—	89	1	no	—
217	C₄×#131	—	89	1	no	—
218	#1929	—	89	2	no	—
219	#1922	—	89	2	no	—
220	#1876	—	89	2	no	—
221	#1866	—	89	2	no	—
222	#1778	—	89	1	no	—
223	#1759	—	89	1	no	—
224	#1759	—	89	1	no	—
225	#1746	—	89	1	no	—
226	C₈₉	#21138	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
228	C₂×#131	—	89	2	no	—
229	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
230	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
231	#442	Dic₈₉	1	2	yes	complemented
232	#441	Dic₈₉	1	2	yes	complemented
233	#440	Dic₈₉	1	2	yes	complemented
234	#440	Dic₈₉	1	2	yes	complemented
235	#433	—	178	1	no	—
236	#433	—	178	1	no	—
237	#431	—	178	2	no	—
238	C₂×#108	—	89	2	no	—
239	#427	C₂×D₈₉	1	1	yes	characteristic
240	#424	—	89	2	no	—
241	C₂×#104	—	89	2	no	—
242	C₂×#104	—	89	2	no	—
243	#416	C₂×D₈₉	1	1	yes	characteristic
244	#416	C₂×D₈₉	1	1	yes	characteristic
245	#408	—	89	2	no	—
246	#405	—	89	2	no	—
247	#405	—	178	2	no	—
248	C₄×M₁₆	—	89	1	no	—
249	C₄×M₁₆	—	89	1	no	—
250	C₄×M₁₆	—	178	1	no	—
251	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
252	C₂×C₄×C₈	—	89	1	no	—
253	C₂×C₄×C₈	—	178	1	no	—
254	#376	—	89	1	no	—
255	#341	—	89	2	no	—
256	#339	—	89	2	no	—
257	#339	—	89	2	no	—
258	#336	—	89	2	no	—
259	#336	—	89	2	no	—
260	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
261	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
262	#135	—	2	4	no	—
263	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
265	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
266	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
267	#131	—	178	4	no	—
268	#131	—	178	4	no	—
269	C₂×M₁₆	—	89	2	no	—
270	C₂×M₁₆	—	89	2	no	—
271	C₂×M₁₆	—	178	2	no	—
272	C₂²×C₈	—	89	2	no	—
273	C₂²×C₈	—	178	2	no	—
274	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
276	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
277	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
281	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	C₂²×D₈₉	1	1	yes	characteristic
285	#117	C₂²×D₈₉	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	89	2	no	—
289	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
290	#108	—	178	4	no	—
291	#107	C₂×Dic₈₉	1	2	yes	—
292	#106	C₂×Dic₈₉	1	2	yes	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	2	no	—
295	#104	—	178	4	no	—
296	#104	—	178	4	no	—
297	#103	C₂×Dic₈₉	1	2	yes	—
298	#103	C₂×Dic₈₉	1	2	yes	—
299	#102	C₂×Dic₈₉	1	2	yes	—
300	#102	C₂×Dic₈₉	1	2	yes	—
301	C₂²⋊C₈	—	178	2	no	—
302	C₂²⋊C₈	—	178	2	no	—
303	#97	—	178	2	no	—
304	#97	—	178	1	no	—
305	#97	—	178	1	no	—
306	#97	C₂×Dic₈₉	1	2	yes	—
307	#97	C₂×Dic₈₉	1	2	yes	—
308	C₄×C₈	—	89	1	no	—
309	C₄×C₈	—	89	1	no	—
310	C₄×C₈	—	89	2	no	—
311	C₄×C₈	—	178	2	no	—
312	C₄×C₈	—	178	1	no	—
313	C₄×C₈	—	178	1	no	—
314	#95	—	178	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	#13083574	1	4	yes	—
319	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
320	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
324	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	178	2	no	—
330	C₂²×C₄	#13083573	1	2	yes	—
331	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
332	Q₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	2	no	—
335	D₈	—	2	2	no	—
336	M₁₆	—	89	4	no	—
337	M₁₆	—	178	2	no	—
338	M₁₆	—	178	2	no	—
339	M₁₆	—	178	8	no	—
340	M₁₆	—	178	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	89	2	no	—
344	C₂×C₈	—	89	2	no	—
345	C₂×C₈	—	178	2	no	—
346	C₂×C₈	—	178	8	no	—
347	C₂×C₈	—	178	2	no	—
348	C₂×C₈	—	178	2	no	—
349	C₂×C₈	—	178	2	no	—
350	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
351	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
352	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	178	2	no	—
366	C₄²	—	178	2	no	—
367	C₄²	C₂²×Dic₈₉	1	2	yes	—
368	C₄²	D₄×D₈₉	1	1	yes	characteristic
369	C₄²	D₄×D₈₉	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	C₂×#13083573	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	#15667971	1	2	yes	—
377	D₄	—	2	4	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	#15667971	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	356	4	no	—
393	C₂×C₄	—	356	2	no	—
394	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
395	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
396	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
398	C₂×C₄	#41×D₈₉	1	2	yes	—
399	C₂×C₄	C₂×#13083574	1	2	yes	—
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	2	no	—
403	C₈	—	356	2	no	—
404	C₈	—	178	2	no	—
405	C₈	—	178	2	no	—
406	C₈	—	178	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
413	C₂²	#19152128	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	712	2	no	—
421	C₄	C₂×#15667971	1	1	yes	characteristic
422	C₄	#41×Dic₈₉	1	1	yes	characteristic
423	C₄	#19152107	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	#26022697	1	1	yes	characteristic
428	C₂	#26029155	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2943	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2943	D₈₉
hypocenter	C₈₉	#21138
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

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. #26020158	C₂	semidirect
8. #26020062	C₂	semidirect
9. #26020062	C₂	semidirect
10. #26020005	C₂	semidirect
37. #442×C₈₉	C₄	semidirect
38. #441×C₈₉	C₄	semidirect
39. #440×C₈₉	C₄	semidirect
40. #440×C₈₉	C₄	semidirect
226. C₈₉	#21138	semidirect
231. #442	Dic₈₉	semidirect
232. #441	Dic₈₉	semidirect
233. #440	Dic₈₉	semidirect
234. #440	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
#26020158	2
#26020062	2
#26020005	2
C₈₉×#2943	2
#21138	89