Subgroups — #36538373

Order 22784.

608 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	#26030766	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030414	C₂	1	2	yes	maximal
3	#26019656	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019651	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019646	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019641	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019634	C₂	1	2	yes	maximal, complemented
8	#26019627	C₂	1	2	yes	maximal, complemented
9	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018960	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
12	#19152155	C₂²	1	2	yes	—
13	#19152003	C₂²	1	1	yes	characteristic
14	#19152003	C₂²	1	1	yes	characteristic
15	#19152000	—	2	1	no	—
16	#19152000	—	2	1	no	—
17	#19151996	C₂²	1	2	yes	—
18	#19151939	—	2	2	no	—
19	#19151893	C₂²	1	2	yes	—
20	#19151888	C₂²	1	2	yes	—
21	#19151808	C₂²	1	2	yes	—
22	#19151803	C₂²	1	2	yes	—
23	#19151760	—	2	2	no	—
24	#19151703	—	2	2	no	—
25	#19151698	—	2	2	no	—
26	#19151655	C₂²	1	2	yes	—
27	#19151636	—	2	1	no	—
28	#19151636	—	2	1	no	—
29	#19151351	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	1	yes	characteristic
31	#19151349	C₂²	1	2	yes	—
32	#19151346	C₂²	1	2	yes	—
33	#19151346	C₂²	1	2	yes	—
34	#19151343	C₂²	1	2	yes	—
35	#19151343	C₂²	1	2	yes	—
36	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₈₉	—	2	1	no	—
40	C₈×D₄×C₈₉	—	2	1	no	—
41	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₈₉	—	2	1	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083564	—	2	2	no	—
48	C₂×#13083562	—	2	2	no	—
49	#15668012	C₂³	1	2	yes	—
50	#15668012	C₂³	1	2	yes	—
51	#15668004	—	2	2	no	—
52	#15667991	—	2	2	no	—
53	#15667991	—	2	2	no	—
54	C₄×Dic₁₇₈	—	2	2	no	—
55	C₄×Dic₁₇₈	—	2	2	no	—
56	#15667971	—	2	2	no	—
57	#15667946	—	2	1	no	—
58	#15667946	—	2	1	no	—
59	#15667946	—	2	1	no	—
60	#15667946	—	2	1	no	—
61	#15667945	—	2	2	no	—
62	#15667944	—	2	2	no	—
63	#15667944	—	2	2	no	—
64	#15667943	—	2	2	no	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	#15667936	—	2	2	no	—
68	#15667935	—	2	2	no	—
69	#15667935	—	2	2	no	—
70	#15667933	—	2	2	no	—
71	C₂²⋊#10623494	—	2	2	no	—
72	#15667923	—	2	2	no	—
73	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	—	2	1	no	—
76	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	#117×C₈₉	—	2	1	no	—
85	#117×C₈₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₈₉	—	2	1	no	—
93	C₂²⋊C₈×C₈₉	—	2	1	no	—
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	C₄×C₈×C₈₉	—	2	1	no	—
96	C₄×C₈×C₈₉	—	2	1	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₇₈	—	2	2	no	—
103	C₂×Dic₁₇₈	—	2	2	no	—
104	#13083564	—	4	4	no	—
105	#13083562	—	4	4	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₄⋊Dic₈₉	—	2	2	no	—
109	C₄⋊Dic₈₉	—	2	2	no	—
110	C₄⋊Dic₈₉	—	2	2	no	—
111	C₄⋊Dic₈₉	—	2	2	no	—
112	#13083553	—	4	2	no	—
113	#13083553	—	4	2	no	—
114	C₂²⋊Dic₈₉	—	4	2	no	—
115	C₄×Dic₈₉	—	4	2	no	—
116	#41×C₈₉	—	2	2	no	—
117	#41×C₈₉	—	2	2	no	—
118	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	4	2	no	—
132	C₂×C₈×C₈₉	—	4	2	no	—
133	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₈₉	#41	1	1	yes	characteristic
150	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂³×C₈₉	—	2	1	no	—
152	C₂³×C₈₉	#121	1	1	yes	characteristic
153	Q₈×C₈₉	—	2	1	no	—
154	Q₈×C₈₉	#135	1	2	yes	—
155	D₄×C₈₉	—	2	4	no	—
156	D₄×C₈₉	—	2	1	no	—
157	D₄×C₈₉	#135	1	2	yes	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	4	2	no	—
178	Dic₁₇₈	—	4	2	no	—
179	Dic₁₇₈	—	4	2	no	—
180	Dic₁₇₈	—	8	2	no	—
181	C₈×C₈₉	—	2	1	no	—
182	C₈×C₈₉	—	2	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	—	4	1	no	—
185	C₈×C₈₉	#137	1	2	yes	—
186	C₈×C₈₉	#137	1	2	yes	—
187	#10623494	—	4	2	no	—
188	#10623494	—	4	2	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	2	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	1	no	—
195	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	2	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	4	1	no	—
202	C₄×C₈₉	—	4	1	no	—
203	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
205	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
206	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
207	Dic₈₉	—	8	2	no	—
208	Dic₈₉	—	8	2	no	—
209	#19273	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	4	1	no	—
211	C₂×C₈₉	—	4	2	no	—
212	C₂×C₈₉	#3039	1	1	yes	characteristic
213	C₂×C₈₉	#3050	1	1	yes	characteristic
214	C₂×C₈₉	#3067	1	1	yes	characteristic
215	#3160	—	89	1	no	—
216	#3116	—	89	2	no	—
217	C₈×#41	D₈₉	1	1	yes	characteristic
218	#1676	—	89	1	no	—
219	#1675	—	89	1	no	—
220	#1674	—	89	1	no	—
221	#1673	—	89	1	no	—
222	#1672	—	89	2	no	—
223	#1671	—	89	2	no	—
224	#1568	—	89	1	no	—
225	#1554	—	89	2	no	—
226	C₈₉	#19273	1	1	yes	characteristic, complemented, Sylow
227	#533	—	89	2	no	—
228	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
229	#500	—	89	1	no	—
230	#500	—	89	1	no	—
231	#499	—	178	1	no	—
232	#499	—	178	1	no	—
233	#498	—	89	2	no	—
234	#485	—	178	2	no	—
235	#477	—	89	2	no	—
236	#476	—	89	2	no	—
237	#462	—	89	2	no	—
238	#461	—	89	2	no	—
239	#452	—	178	2	no	—
240	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
241	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
242	#441	—	178	2	no	—
243	#440	—	178	2	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
247	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
248	#432	—	89	2	no	—
249	#431	—	2	1	no	—
250	#431	C₂×D₈₉	1	1	yes	characteristic
251	#427	—	178	1	no	—
252	#427	—	178	1	no	—
253	C₂×C₄×C₈	—	2	1	no	—
254	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
255	#335	—	89	1	no	—
256	#335	—	89	1	no	—
257	#334	—	89	2	no	—
258	#333	—	89	2	no	—
259	#333	—	89	2	no	—
260	#332	—	89	2	no	—
261	#332	—	89	2	no	—
262	C₂×#41	D₃₅₆	1	1	yes	characteristic
263	C₂×Q₁₆	—	178	2	no	—
264	C₂×SD₁₆	—	178	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
269	C₄⋊Q₈	—	89	2	no	—
270	C₄⋊Q₈	—	89	2	no	—
271	#125	—	178	2	no	—
272	C₂²⋊Q₈	—	178	2	no	—
273	C₂²⋊Q₈	—	178	2	no	—
274	C₄×Q₈	—	178	2	no	—
275	C₄×Q₈	—	178	2	no	—
276	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₃₅₆	1	1	yes	characteristic
281	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	178	2	no	—
284	#117	D₃₅₆	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
287	#107	—	178	1	no	—
288	#107	—	178	1	no	—
289	#107	—	178	1	no	—
290	#107	—	178	1	no	—
291	#107	—	178	2	no	—
292	#106	—	178	2	no	—
293	#106	—	178	2	no	—
294	#106	—	178	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	89	2	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
301	#103	—	178	2	no	—
302	#103	—	178	2	no	—
303	#103	—	178	2	no	—
304	#102	—	178	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	178	2	no	—
309	#97	—	178	2	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
314	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	—	178	2	no	—
320	C₂×Q₈	—	178	2	no	—
321	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
329	C₂²×C₄	#13083574	1	1	yes	characteristic
330	Q₁₆	—	356	4	no	—
331	SD₁₆	—	356	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	—	178	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	356	2	no	—
347	C₄⋊C₄	—	356	2	no	—
348	C₄⋊C₄	—	178	2	no	—
349	C₄⋊C₄	—	178	2	no	—
350	C₄⋊C₄	—	178	2	no	—
351	C₄⋊C₄	—	178	2	no	—
352	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	356	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	356	2	no	—
362	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
364	C₄²	#13083574	1	1	yes	characteristic
365	C₄²	C₂³×D₈₉	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	#15667986	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	356	2	no	—
370	Q₈	—	356	2	no	—
371	Q₈	—	712	2	no	—
372	Q₈	#15668034	1	2	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	#15668034	1	2	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	356	2	no	—
389	C₂×C₄	—	356	2	no	—
390	C₂×C₄	#15667986	1	1	yes	characteristic
391	C₂×C₄	#15667986	1	1	yes	characteristic
392	C₂×C₄	#15667986	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
395	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	356	2	no	—
401	C₈	—	356	2	no	—
402	C₈	#15668042	1	2	yes	—
403	C₈	#15668042	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#15667986	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	712	2	no	—
419	C₄	—	712	2	no	—
420	C₄	C₂×#15668034	1	1	yes	characteristic
421	C₄	C₂×#15668034	1	1	yes	characteristic
422	C₄	C₂×#15668042	1	1	yes	characteristic
423	C₄	C₂×#15668042	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#26029739	1	1	yes	characteristic
427	C₂	#26029833	1	1	yes	characteristic
428	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#41×C₈₉	D₄
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#19273
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #26030766	C₂	semidirect
3. #26019656	C₂	semidirect
4. #26019651	C₂	semidirect
5. #26019646	C₂	semidirect
6. #26019641	C₂	semidirect
7. #26019634	C₂	semidirect
8. #26019627	C₂	semidirect
9. #26019015	C₂	semidirect
10. #26018960	C₂	semidirect
226. C₈₉	#19273	semidirect

Maximal subgroups

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

subgroup	index
#26030766	2
#26030414	2
#26019656	2
#26019651	2
#26019646	2
#26019641	2
#26019634	2
#26019627	2
#26019015	2
#26018960	2
C₈×#41×C₈₉	2
#19273	89