Subgroups — #36536870

Order 22784.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030034	C₂	1	2	yes	maximal
2	C₈×#13083574	C₂	1	1	yes	maximal, characteristic
3	#26019707	C₂	1	2	yes	maximal, complemented
4	#26019700	C₂	1	2	yes	maximal, complemented
5	#26019653	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019648	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	C₂×#19151351	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018909	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	#19151902	—	2	2	no	—
14	#19151895	—	2	2	no	—
15	#19151890	C₂²	1	2	yes	—
16	#19151885	C₂²	1	2	yes	—
17	#19151880	C₂²	1	2	yes	—
18	#19151875	C₂²	1	2	yes	—
19	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
21	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
22	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₈₉	—	2	1	no	—
24	C₈×C₂²⋊D₈₉	—	2	1	no	—
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151649	—	2	1	no	—
27	#19151634	—	2	2	no	—
28	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
29	#19151592	—	2	2	no	—
30	C₄×C₈×D₈₉	—	2	1	no	—
31	#19151351	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic
33	#19151351	C₂²	1	2	yes	—
34	#19151347	C₂²	1	2	yes	—
35	#19151347	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	C₂²×#10623494	—	2	2	no	—
49	C₂×C₈×D₈₉	—	2	1	no	—
50	C₂×C₈×D₈₉	—	2	1	no	—
51	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
52	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
53	C₄×D₃₅₆	D₄	1	1	yes	characteristic
54	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₈₉	—	2	1	no	—
56	C₄×C₂²⋊D₈₉	—	2	1	no	—
57	#15667971	D₄	1	1	yes	characteristic
58	#15667969	—	2	1	no	—
59	C₄²×D₈₉	—	2	1	no	—
60	#15667945	—	2	2	no	—
61	#15667945	—	2	2	no	—
62	#15667943	—	2	2	no	—
63	#15667943	—	2	2	no	—
64	C₄⋊#10623494	—	2	2	no	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	#15667941	—	2	1	no	—
70	#15667941	—	2	1	no	—
71	#15667935	—	2	2	no	—
72	#15667935	—	2	2	no	—
73	#15667932	—	2	2	no	—
74	#15667932	—	2	2	no	—
75	C₂²⋊#10623494	—	2	1	no	—
76	#15667924	—	2	1	no	—
77	#15667924	—	2	1	no	—
78	C₄×#10623494	—	2	1	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	Q₁₆	1	4	yes	complemented
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	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	—	2	1	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	4	4	no	—
115	C₈×D₈₉	—	4	2	no	—
116	C₈×D₈₉	—	4	2	no	—
117	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
118	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
119	#13083553	—	2	1	no	—
120	#13083553	—	2	1	no	—
121	C₂²⋊Dic₈₉	—	2	1	no	—
122	#13083551	—	2	1	no	—
123	#13083551	—	2	1	no	—
124	C₄×Dic₈₉	—	2	1	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	2	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
132	Q₁₆×C₈₉	—	4	2	no	—
133	Q₁₆×C₈₉	—	4	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	4	1	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₈₉	—	2	2	no	—
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	—	4	2	no	—
145	C₄⋊C₄×C₈₉	—	4	2	no	—
146	C₂²⋊C₄×C₈₉	—	4	2	no	—
147	C₄²×C₈₉	—	4	2	no	—
148	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	#41	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	#121	1	1	yes	characteristic
153	C₂²×D₈₉	—	2	1	no	—
154	Q₈×C₈₉	—	4	2	no	—
155	Q₈×C₈₉	—	4	2	no	—
156	Q₈×C₈₉	—	8	2	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
166	C₂×C₄×C₈₉	#135	1	2	yes	—
167	C₂×C₄×C₈₉	C₂²×D₄	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	C₂²⋊D₈₉	—	2	4	no	—
171	C₂×Dic₈₉	—	2	1	no	—
172	C₂×Dic₈₉	—	2	1	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	D₃₅₆	—	2	1	no	—
175	D₃₅₆	C₂×Q₁₆	1	2	yes	—
176	C₄×D₈₉	—	2	4	no	—
177	C₄×D₈₉	—	4	2	no	—
178	C₄×D₈₉	—	4	1	no	—
179	C₄×D₈₉	—	4	1	no	—
180	Dic₁₇₈	—	2	1	no	—
181	Dic₁₇₈	C₂×Q₁₆	1	2	yes	—
182	C₈×C₈₉	—	2	1	no	—
183	C₈×C₈₉	—	2	1	no	—
184	C₈×C₈₉	—	2	1	no	—
185	C₈×C₈₉	#135	1	2	yes	—
186	#10623494	—	4	1	no	—
187	#10623494	—	4	2	no	—
188	#10623494	—	4	2	no	—
189	#10623494	—	4	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	#467	1	2	yes	—
193	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂×D₈₉	—	2	2	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	8	2	no	—
201	C₄×C₈₉	—	8	2	no	—
202	C₄×C₈₉	#467	1	2	yes	—
203	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
205	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
206	C₄×C₈₉	#575	1	1	yes	characteristic
207	Dic₈₉	—	2	2	no	—
208	Dic₈₉	—	4	1	no	—
209	Dic₈₉	—	4	1	no	—
210	#19126	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	—	2	2	no	—
212	C₂×C₈₉	#3035	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
214	C₂×C₈₉	#3067	1	1	yes	characteristic
215	D₈₉	—	4	2	no	—
216	#3170	D₈₉	1	1	yes	characteristic, complemented
217	#3076	—	89	2	no	—
218	C₈×#41	—	89	1	no	—
219	#1684	—	89	2	no	—
220	#1683	—	89	2	no	—
221	#1676	—	89	1	no	—
222	#1675	—	89	1	no	—
223	#1670	—	89	1	no	—
224	#1669	—	89	1	no	—
225	C₂×#335	—	89	1	no	—
226	#1542	—	89	2	no	—
227	C₈₉	#19126	1	1	yes	characteristic, complemented, Sylow
228	#533	C₂×D₈₉	1	2	yes	—
229	C₄×#41	—	89	1	no	—
230	#500	C₂×D₈₉	1	1	yes	characteristic
231	#494	C₂×D₈₉	1	1	yes	characteristic
232	#487	C₂×D₈₉	1	2	yes	—
233	#479	—	178	2	no	—
234	#478	—	178	2	no	—
235	#477	—	89	2	no	—
236	#476	—	89	2	no	—
237	#475	—	89	2	no	—
238	#474	—	89	2	no	—
239	#467	—	2	1	no	—
240	#467	—	2	1	no	—
241	C₈×Q₈	—	89	1	no	—
242	C₈×Q₈	—	89	1	no	—
243	C₄×Q₁₆	—	2	1	no	—
244	C₄×Q₁₆	—	2	1	no	—
245	C₈×D₄	—	89	1	no	—
246	C₈×D₄	—	89	1	no	—
247	C₈×D₄	—	178	1	no	—
248	C₈×D₄	—	178	1	no	—
249	#431	—	89	1	no	—
250	#431	—	178	1	no	—
251	#427	—	178	2	no	—
252	C₂×C₄⋊C₈	—	89	2	no	—
253	#416	—	178	2	no	—
254	C₂×C₄×C₈	—	178	1	no	—
255	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
256	#335	—	89	1	no	—
257	#335	—	89	1	no	—
258	#335	—	89	2	no	—
259	#333	—	89	2	no	—
260	#333	—	89	2	no	—
261	#332	—	89	2	no	—
262	#332	—	89	2	no	—
263	C₂×#41	—	89	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂²×C₈	—	178	2	no	—
267	C₂²×C₈	—	178	1	no	—
268	C₂²×C₈	—	178	1	no	—
269	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
271	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
272	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
273	#125	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	89	1	no	—
279	C₄×Q₈	—	89	1	no	—
280	C₄×D₄	—	89	1	no	—
281	C₄×D₄	—	89	1	no	—
282	C₄×D₄	—	178	1	no	—
283	C₄×D₄	—	178	1	no	—
284	#117	—	2	2	no	—
285	#117	—	89	1	no	—
286	#117	—	178	1	no	—
287	C₂×C₄²	—	178	1	no	—
288	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	178	2	no	—
292	#107	—	178	2	no	—
293	#106	—	178	2	no	—
294	#106	—	178	2	no	—
295	C₄⋊C₈	—	89	1	no	—
296	C₄⋊C₈	—	89	1	no	—
297	C₄⋊C₈	—	89	2	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	178	1	no	—
300	C₄⋊C₈	—	178	1	no	—
301	C₄⋊C₈	—	178	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	178	2	no	—
305	#103	—	178	2	no	—
306	#102	—	178	2	no	—
307	#102	—	178	2	no	—
308	C₂²⋊C₈	—	178	1	no	—
309	C₂²⋊C₈	—	178	1	no	—
310	C₂²⋊C₈	—	178	1	no	—
311	C₄×C₈	—	178	1	no	—
312	C₄×C₈	—	178	1	no	—
313	C₄×C₈	—	178	1	no	—
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	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
318	#41	—	89	4	no	—
319	#41	—	178	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	89	1	no	—
323	C₂×D₄	—	89	1	no	—
324	C₂×D₄	—	178	1	no	—
325	C₂²×C₄	—	178	1	no	—
326	C₂²×C₄	—	178	1	no	—
327	C₂²×C₄	—	178	1	no	—
328	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
330	C₂²×C₄	#13083573	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	356	2	no	—
336	C₂×C₈	—	356	4	no	—
337	C₂×C₈	—	356	2	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	—	178	2	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	—	178	1	no	—
342	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	89	1	no	—
353	C₄⋊C₄	—	89	1	no	—
354	C₄⋊C₄	—	178	1	no	—
355	C₄⋊C₄	—	178	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	178	1	no	—
358	C₂²⋊C₄	—	178	1	no	—
359	C₂²⋊C₄	—	178	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	—	178	1	no	—
362	C₄²	—	178	1	no	—
363	C₄²	—	178	1	no	—
364	C₄²	D₄×D₈₉	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
366	C₄²	#13083573	1	1	yes	characteristic
367	C₄²	C₂³×D₈₉	1	1	yes	characteristic
368	C₂³	—	178	1	no	—
369	C₂³	#15667983	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	2	no	—
373	Q₈	—	89	2	no	—
374	Q₈	—	178	1	no	—
375	D₄	—	89	2	no	—
376	D₄	—	178	4	no	—
377	D₄	—	178	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	1	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	—	178	4	no	—
390	C₂×C₄	#15667983	1	1	yes	characteristic
391	C₂×C₄	#15667983	1	1	yes	characteristic
392	C₂×C₄	#15667983	1	1	yes	characteristic
393	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
394	C₂×C₄	#15668035	1	2	yes	—
395	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	356	1	no	—
402	C₈	—	356	1	no	—
403	C₈	—	356	2	no	—
404	C₈	—	356	2	no	—
405	C₈	#15668032	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	356	1	no	—
409	C₂²	—	356	1	no	—
410	C₂²	—	178	2	no	—
411	C₂²	#19151836	1	2	yes	—
412	C₂²	C₂×#15667983	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	356	1	no	—
419	C₄	—	356	1	no	—
420	C₄	—	178	2	no	—
421	C₄	#19151836	1	2	yes	—
422	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
423	C₄	C₂×#15668032	1	1	yes	characteristic
424	C₄	C₂×#15668035	1	1	yes	characteristic
425	C₄	#19152396	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	356	2	no	—
428	C₂	#26029701	1	1	yes	characteristic
429	C₂	C₂×#19151836	1	1	yes	characteristic
430	C₂	#26029968	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	#19126
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. #26019707	C₂	semidirect
4. #26019700	C₂	semidirect
5. #26019653	C₂	semidirect
6. #26019648	C₂	semidirect
7. #26019619	C₂	semidirect
8. #26019614	C₂	semidirect
9. C₂×#19151351	C₂	semidirect
10. #26018909	C₂	semidirect
11. C₈₉×#3170	C₂	semidirect
103. #13083574	Q₁₆	semidirect
216. #3170	D₈₉	semidirect
227. C₈₉	#19126	semidirect

Maximal subgroups

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

subgroup	index
#26030034	2
C₈×#13083574	2
#26019707	2
#26019700	2
#26019653	2
#26019648	2
#26019619	2
#26019614	2
C₂×#19151351	2
#26018909	2
C₈₉×#3170	2
#19126	89