Subgroups — #36536907

Order 22784.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030317	C₂	1	2	yes	maximal
2	C₈×#13083574	C₂	1	1	yes	maximal, characteristic
3	#26019679	C₂	1	2	yes	maximal, complemented
4	#26019672	C₂	1	2	yes	maximal, complemented
5	#26019643	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019638	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019619	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019614	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018917	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#13083574	C₂²	1	1	yes	characteristic
13	#19151936	—	2	2	no	—
14	#19151880	C₂²	1	2	yes	—
15	#19151875	C₂²	1	2	yes	—
16	#19151805	C₂²	1	2	yes	—
17	#19151800	C₂²	1	2	yes	—
18	#19151758	—	2	2	no	—
19	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
21	C₄×#13083564	—	2	2	no	—
22	C₄×#13083561	—	2	2	no	—
23	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
24	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₈₉	—	2	1	no	—
26	C₈×C₂²⋊D₈₉	—	2	1	no	—
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151651	C₂²	1	2	yes	—
29	#19151649	—	2	1	no	—
30	C₄×C₈×D₈₉	—	2	1	no	—
31	#19151351	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic
33	#19151349	C₂²	1	2	yes	—
34	#19151344	C₂²	1	2	yes	—
35	#19151344	C₂²	1	2	yes	—
36	#19151344	C₂²	1	2	yes	—
37	#19151344	C₂²	1	2	yes	—
38	#533×C₈₉	C₂²	1	2	yes	—
39	#500×C₈₉	C₂²	1	1	yes	characteristic
40	#494×C₈₉	C₂²	1	1	yes	characteristic
41	#487×C₈₉	C₂²	1	2	yes	—
42	#467×C₈₉	—	2	1	no	—
43	#467×C₈₉	—	2	1	no	—
44	C₄×Q₁₆×C₈₉	—	2	1	no	—
45	C₄×Q₁₆×C₈₉	—	2	1	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	D₄	1	1	yes	characteristic
48	C₂×#13083564	—	2	2	no	—
49	C₂×#13083561	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	1	no	—
51	C₂×C₈×D₈₉	—	2	1	no	—
52	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
53	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
54	C₄×D₃₅₆	D₄	1	1	yes	characteristic
55	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₈₉	—	2	1	no	—
57	C₄×C₂²⋊D₈₉	—	2	1	no	—
58	#15667971	D₄	1	1	yes	characteristic
59	#15667969	—	2	1	no	—
60	C₄²×D₈₉	—	2	1	no	—
61	#15667945	—	2	2	no	—
62	#15667943	—	2	2	no	—
63	C₄⋊#10623494	C₂³	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	2	yes	—
65	C₄⋊#10623494	C₂³	1	1	yes	characteristic
66	C₄⋊#10623494	C₂³	1	1	yes	characteristic
67	#15667941	—	2	1	no	—
68	#15667941	—	2	1	no	—
69	#15667936	—	2	2	no	—
70	#15667936	—	2	2	no	—
71	#15667935	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	C₂²⋊#10623494	—	2	1	no	—
74	C₂²⋊#10623494	—	2	2	no	—
75	#15667924	—	2	1	no	—
76	#15667924	—	2	1	no	—
77	C₄×#10623494	—	2	1	no	—
78	C₄×#10623494	—	2	2	no	—
79	C₈×Dic₈₉	—	2	1	no	—
80	C₈×Dic₈₉	—	2	1	no	—
81	C₂×Q₁₆×C₈₉	—	2	1	no	—
82	C₂×Q₁₆×C₈₉	—	2	1	no	—
83	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
87	#125×C₈₉	—	2	2	no	—
88	C₂²⋊Q₈×C₈₉	—	2	2	no	—
89	C₂²⋊Q₈×C₈₉	—	2	2	no	—
90	C₄×Q₈×C₈₉	—	2	2	no	—
91	C₄×Q₈×C₈₉	—	2	2	no	—
92	#117×C₈₉	—	2	2	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	#107×C₈₉	—	2	1	no	—
95	#107×C₈₉	—	2	1	no	—
96	#103×C₈₉	—	2	2	no	—
97	#103×C₈₉	—	2	2	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	#13083574	—	2	2	no	—
103	#13083574	—	2	2	no	—
104	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₈₉	—	2	1	no	—
107	C₂×C₄×D₈₉	—	2	1	no	—
108	C₂×C₄×D₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	2	1	no	—
110	#13083564	—	4	4	no	—
111	#13083561	—	4	4	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₈×D₈₉	—	4	2	no	—
117	C₈×D₈₉	—	4	2	no	—
118	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
120	#13083553	—	2	1	no	—
121	#13083553	—	2	1	no	—
122	C₂²⋊Dic₈₉	—	2	1	no	—
123	#13083551	—	2	1	no	—
124	#13083551	—	2	1	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	1	no	—
127	C₄×Dic₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂×Q₈×C₈₉	—	2	2	no	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	Q₁₆×C₈₉	—	4	2	no	—
134	Q₁₆×C₈₉	—	4	2	no	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	4	1	no	—
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	—	2	2	no	—
143	C₄⋊C₄×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	—	4	2	no	—
146	C₄⋊C₄×C₈₉	—	4	2	no	—
147	C₂²⋊C₄×C₈₉	—	4	2	no	—
148	C₄²×C₈₉	—	4	2	no	—
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₈₉	#41	1	1	yes	characteristic
152	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂³×C₈₉	#121	1	1	yes	characteristic
154	C₂²×D₈₉	—	2	1	no	—
155	Q₈×C₈₉	—	4	2	no	—
156	Q₈×C₈₉	—	4	2	no	—
157	Q₈×C₈₉	—	4	2	no	—
158	Q₈×C₈₉	—	4	2	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	2	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	2	4	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	—	2	1	no	—
175	C₂×Dic₈₉	—	2	1	no	—
176	D₃₅₆	—	2	1	no	—
177	D₃₅₆	#135	1	2	yes	—
178	C₄×D₈₉	—	2	4	no	—
179	C₄×D₈₉	—	4	1	no	—
180	C₄×D₈₉	—	4	1	no	—
181	C₄×D₈₉	—	4	2	no	—
182	Dic₁₇₈	—	2	1	no	—
183	Dic₁₇₈	#135	1	2	yes	—
184	C₈×C₈₉	—	2	1	no	—
185	C₈×C₈₉	—	2	1	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	#135	1	2	yes	—
188	#10623494	—	4	1	no	—
189	#10623494	—	4	2	no	—
190	#10623494	—	4	2	no	—
191	#10623494	—	4	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
196	C₂×D₈₉	—	2	2	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	4	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	8	2	no	—
203	C₄×C₈₉	—	8	2	no	—
204	C₄×C₈₉	#473	1	2	yes	—
205	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
206	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
207	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
208	C₄×C₈₉	#575	1	1	yes	characteristic
209	Dic₈₉	—	2	2	no	—
210	Dic₈₉	—	4	1	no	—
211	Dic₈₉	—	4	1	no	—
212	#19129	—	89	1	no	maximal, Sylow
213	C₂×C₈₉	—	4	1	no	—
214	C₂×C₈₉	#3035	1	1	yes	characteristic
215	C₂×C₈₉	#3050	1	1	yes	characteristic
216	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
217	D₈₉	—	4	2	no	—
218	#3170	D₈₉	1	1	yes	characteristic, complemented
219	#3107	—	89	2	no	—
220	C₈×#41	—	89	1	no	—
221	#1680	—	89	2	no	—
222	#1679	—	89	2	no	—
223	#1674	—	89	1	no	—
224	#1673	—	89	1	no	—
225	#1670	—	89	1	no	—
226	#1669	—	89	1	no	—
227	#1564	—	89	1	no	—
228	#1544	—	89	2	no	—
229	C₈₉	#19129	1	1	yes	characteristic, complemented, Sylow
230	#533	C₂×D₈₉	1	2	yes	—
231	C₄×#41	—	89	1	no	—
232	#500	C₂×D₈₉	1	1	yes	characteristic
233	#494	C₂×D₈₉	1	1	yes	characteristic
234	#487	C₂×D₈₉	1	2	yes	—
235	#485	—	178	2	no	—
236	#475	—	89	2	no	—
237	#474	—	89	2	no	—
238	#467	—	2	1	no	—
239	#467	—	2	1	no	—
240	#462	—	89	2	no	—
241	#461	—	89	2	no	—
242	#452	—	178	2	no	—
243	C₈×Q₈	—	89	1	no	—
244	C₈×Q₈	—	89	1	no	—
245	C₄×Q₁₆	—	2	1	no	—
246	C₄×Q₁₆	—	2	1	no	—
247	C₄×Q₁₆	—	178	2	no	—
248	C₄×SD₁₆	—	178	2	no	—
249	C₈×D₄	—	89	1	no	—
250	C₈×D₄	—	89	1	no	—
251	C₈×D₄	—	178	1	no	—
252	C₈×D₄	—	178	1	no	—
253	#431	—	89	1	no	—
254	#431	—	89	2	no	—
255	#431	—	178	1	no	—
256	C₂×C₄×C₈	—	178	1	no	—
257	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
258	#335	—	89	1	no	—
259	#335	—	89	1	no	—
260	#334	—	89	2	no	—
261	#332	—	89	2	no	—
262	#332	—	89	2	no	—
263	#332	—	89	2	no	—
264	#332	—	89	2	no	—
265	C₂×#41	—	89	1	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	2	1	no	—
268	C₂×Q₁₆	—	178	2	no	—
269	C₂×SD₁₆	—	178	2	no	—
270	C₂²×C₈	—	178	1	no	—
271	C₂²×C₈	—	178	1	no	—
272	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
274	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
275	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
276	#125	—	2	2	no	—
277	C₂²⋊Q₈	—	2	2	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	89	1	no	—
282	C₄×Q₈	—	89	1	no	—
283	C₄×D₄	—	89	1	no	—
284	C₄×D₄	—	89	1	no	—
285	C₄×D₄	—	178	1	no	—
286	C₄×D₄	—	178	1	no	—
287	#117	—	2	2	no	—
288	#117	—	89	1	no	—
289	#117	—	178	1	no	—
290	C₂×C₄²	—	178	1	no	—
291	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
292	#107	—	2	1	no	—
293	#107	—	2	1	no	—
294	#107	—	178	2	no	—
295	#106	—	178	2	no	—
296	C₄⋊C₈	—	89	1	no	—
297	C₄⋊C₈	—	89	1	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	89	2	no	—
300	C₄⋊C₈	—	178	1	no	—
301	C₄⋊C₈	—	178	1	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	178	2	no	—
305	#103	—	178	2	no	—
306	#103	—	178	2	no	—
307	#102	—	178	2	no	—
308	C₂²⋊C₈	—	178	2	no	—
309	C₂²⋊C₈	—	178	1	no	—
310	C₂²⋊C₈	—	178	1	no	—
311	C₂²⋊C₈	—	178	1	no	—
312	C₄×C₈	—	178	1	no	—
313	C₄×C₈	—	178	1	no	—
314	C₄×C₈	—	178	2	no	—
315	C₄×C₈	—	178	1	no	—
316	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
317	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
320	#41	—	178	2	no	—
321	#41	—	178	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	89	1	no	—
325	C₂×D₄	—	89	1	no	—
326	C₂×D₄	—	178	1	no	—
327	C₂²×C₄	—	178	1	no	—
328	C₂²×C₄	—	178	1	no	—
329	C₂²×C₄	—	178	1	no	—
330	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
332	C₂²×C₄	#13083573	1	1	yes	characteristic
333	Q₁₆	—	4	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	—	356	4	no	—
336	SD₁₆	—	356	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	356	2	no	—
340	C₂×C₈	—	356	2	no	—
341	C₂×C₈	—	178	2	no	—
342	C₂×C₈	—	178	2	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	—	178	1	no	—
345	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	89	1	no	—
356	C₄⋊C₄	—	89	1	no	—
357	C₄⋊C₄	—	178	1	no	—
358	C₄⋊C₄	—	178	1	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	178	1	no	—
361	C₂²⋊C₄	—	178	1	no	—
362	C₂²⋊C₄	—	178	1	no	—
363	C₄²	—	4	2	no	—
364	C₄²	—	178	1	no	—
365	C₄²	—	178	1	no	—
366	C₄²	—	178	1	no	—
367	C₄²	D₄×D₈₉	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₄²	#13083573	1	1	yes	characteristic
370	C₄²	C₂³×D₈₉	1	1	yes	characteristic
371	C₂³	—	178	1	no	—
372	C₂³	#15667983	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	89	2	no	—
378	Q₈	—	178	1	no	—
379	D₄	—	89	2	no	—
380	D₄	—	178	4	no	—
381	D₄	—	178	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	356	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	356	2	no	—
392	C₂×C₄	—	178	4	no	—
393	C₂×C₄	—	178	1	no	—
394	C₂×C₄	—	178	1	no	—
395	C₂×C₄	—	178	1	no	—
396	C₂×C₄	#15667983	1	1	yes	characteristic
397	C₂×C₄	#15667983	1	1	yes	characteristic
398	C₂×C₄	#15667983	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	356	1	no	—
406	C₈	—	356	2	no	—
407	C₈	—	356	2	no	—
408	C₈	—	356	1	no	—
409	C₈	#15668032	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	356	1	no	—
414	C₂²	—	356	1	no	—
415	C₂²	—	178	2	no	—
416	C₂²	C₂×#15667983	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	356	1	no	—
423	C₄	—	356	1	no	—
424	C₄	—	178	2	no	—
425	C₄	#19151870	1	2	yes	—
426	C₄	#135×D₈₉	1	1	yes	characteristic
427	C₄	#135×D₈₉	1	1	yes	characteristic
428	C₄	C₂×#15668032	1	1	yes	characteristic
429	C₄	#19152396	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	356	2	no	—
432	C₂	#26029701	1	1	yes	characteristic
433	C₂	#26029829	1	1	yes	characteristic
434	C₂	C₂×#19151870	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3170	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#13083574	D₄
hypercenter	#3170	D₈₉
hypocenter	C₈₉	#19129
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
3. #26019679	C₂	semidirect
4. #26019672	C₂	semidirect
5. #26019643	C₂	semidirect
6. #26019638	C₂	semidirect
7. #26019619	C₂	semidirect
8. #26019614	C₂	semidirect
9. #26019000	C₂	semidirect
10. #26018917	C₂	semidirect
11. C₈₉×#3170	C₂	semidirect
218. #3170	D₈₉	semidirect
229. C₈₉	#19129	semidirect

Maximal subgroups

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

subgroup	index
#26030317	2
C₈×#13083574	2
#26019679	2
#26019672	2
#26019643	2
#26019638	2
#26019619	2
#26019614	2
#26019000	2
#26018917	2
C₈₉×#3170	2
#19129	89