Subgroups — #36552980

Order 22784.

1046 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151716	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151714	C₂	1	1	yes	maximal, characteristic
3	#26029023	C₂	1	1	yes	maximal, characteristic
4	#26028674	C₂	1	2	yes	maximal, complemented
5	#108×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020091	C₂	1	2	yes	maximal, complemented
8	#26020086	C₂	1	2	yes	maximal, complemented
9	#26020056	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	2	yes	—
15	#19152066	C₂²	1	2	yes	—
16	#19151716	C₄	1	8	yes	complemented
17	#19151714	C₄	1	8	yes	complemented
18	#19151692	C₄	1	2	yes	complemented
19	#19151685	C₄	1	4	yes	complemented
20	#19151680	C₄	1	2	yes	complemented
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667940	C₂²	1	2	yes	—
23	C₂×#15667938	C₂²	1	2	yes	—
24	#19151592	C₂²	1	2	yes	—
25	#19151555	—	2	2	no	—
26	#19151554	C₂²	1	2	yes	—
27	#19151552	—	2	2	no	—
28	#19151550	—	2	2	no	—
29	M₁₆×Dic₈₉	C₂²	1	2	yes	—
30	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	—	2	2	no	—
36	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
37	#19151362	C₂²	1	2	yes	—
38	#19151357	C₂²	1	2	yes	—
39	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#405×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#339×C₈₉	C₂²	1	2	yes	—
44	C₂×#13083574	C₂³	1	2	yes	—
45	#15668034	C₂×C₄	1	4	yes	—
46	#15668034	C₂×C₄	1	4	yes	—
47	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083563	C₂×C₄	1	2	yes	—
49	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
50	#15668020	—	2	4	no	—
51	#15668020	C₂×C₄	1	8	yes	complemented
52	#15668018	—	2	4	no	—
53	#15668018	C₂×C₄	1	8	yes	complemented
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×#13083557	—	2	2	no	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₂×C₈×D₈₉	—	2	2	no	—
61	#15667977	C₂×C₄	1	4	yes	—
62	#15667974	C₂×C₄	1	4	yes	—
63	#15667972	—	2	4	no	—
64	#15667969	—	2	2	no	—
65	C₂×C₄×Dic₈₉	—	2	2	no	—
66	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
68	C₄²×D₈₉	—	2	2	no	—
69	#15667948	C₂×C₄	1	4	yes	complemented
70	#15667940	C₂×C₄	1	8	yes	complemented
71	#15667938	C₂×C₄	1	8	yes	complemented
72	#15667935	C₂×C₄	1	4	yes	—
73	#15667932	C₂×C₄	1	4	yes	—
74	#15667923	—	2	2	no	—
75	#15667922	—	2	2	no	—
76	C₄×#10623494	—	2	2	no	—
77	C₄×#10623494	—	2	2	no	—
78	C₈×Dic₈₉	—	2	2	no	—
79	C₈×Dic₈₉	—	2	2	no	—
80	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
81	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
82	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
83	C₈×Dic₈₉	D₄	1	1	yes	characteristic
84	C₈×Dic₈₉	D₄	1	1	yes	characteristic
85	C₈×Dic₈₉	D₄	1	1	yes	characteristic
86	C₈×Dic₈₉	D₄	1	1	yes	characteristic
87	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	#117×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	#108×C₈₉	C₂×C₄	1	4	yes	complemented
93	#107×C₈₉	C₂×C₄	1	2	yes	—
94	#106×C₈₉	C₂×C₄	1	2	yes	—
95	#97×C₈₉	—	2	2	no	—
96	C₄×C₈×C₈₉	—	2	2	no	—
97	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
98	#13083574	—	2	2	no	—
99	#13083574	—	2	2	no	—
100	#13083574	C₂²×C₄	1	4	yes	—
101	#13083574	C₂²×C₄	1	4	yes	—
102	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
103	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
104	C₂×C₂²⋊D₈₉	—	2	2	no	—
105	C₂²×Dic₈₉	—	2	1	no	—
106	C₂²×Dic₈₉	#41	1	2	yes	—
107	C₂×C₄×D₈₉	—	2	2	no	—
108	C₂×C₄×D₈₉	—	2	4	no	—
109	Dic₃₅₆	C₄²	1	4	yes	complemented
110	#13083563	C₄²	1	8	yes	complemented
111	D₇₁₂	C₄²	1	4	yes	complemented
112	#13083558	—	2	2	no	—
113	#13083558	C₂²×C₄	1	4	yes	—
114	#13083557	—	2	8	no	—
115	#13083557	—	2	8	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	C₂²×C₄	1	2	yes	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	#41	1	2	yes	—
124	C₈×D₈₉	—	2	8	no	—
125	C₈×D₈₉	—	2	8	no	—
126	#13083553	—	2	4	no	—
127	#13083551	—	2	4	no	—
128	C₄×Dic₈₉	—	2	8	no	—
129	C₄×Dic₈₉	—	2	1	no	—
130	C₄×Dic₈₉	—	2	4	no	—
131	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
132	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
133	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	#41	1	2	yes	—
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
149	C₂²⋊C₄×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
153	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
154	C₂²×D₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₈₉	—	2	4	no	—
165	C₂²⋊D₈₉	—	2	4	no	—
166	C₂×Dic₈₉	—	2	4	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	2	no	—
169	C₂×Dic₈₉	—	2	4	no	—
170	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
171	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
172	D₃₅₆	—	2	2	no	—
173	D₃₅₆	C₂×C₄²	1	4	yes	—
174	C₄×D₈₉	—	2	4	no	—
175	C₄×D₈₉	—	2	4	no	—
176	C₄×D₈₉	—	4	8	no	—
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	C₂×C₄²	1	4	yes	—
179	C₈×C₈₉	—	2	4	no	—
180	C₈×C₈₉	C₂×C₄²	1	2	yes	—
181	C₈×C₈₉	C₂×C₄²	1	2	yes	—
182	C₈×C₈₉	C₄×D₄	1	2	yes	—
183	C₈×C₈₉	C₄×D₄	1	2	yes	—
184	#10623494	—	2	4	no	—
185	#10623494	—	2	2	no	—
186	#10623494	C₄×D₄	1	2	yes	—
187	#10623494	C₄×D₄	1	2	yes	—
188	C₂²×C₈₉	—	2	2	no	—
189	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
191	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
192	C₂×D₈₉	—	2	4	no	—
193	C₂×D₈₉	—	4	4	no	—
194	C₄×C₈₉	—	2	4	no	—
195	C₄×C₈₉	—	4	4	no	—
196	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
197	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
200	Dic₈₉	—	2	4	no	—
201	Dic₈₉	—	2	2	no	—
202	Dic₈₉	—	2	4	no	—
203	Dic₈₉	#443	1	4	yes	complemented
204	C₄×#443	—	89	1	no	maximal, Sylow
205	C₂×C₈₉	—	2	1	no	—
206	C₂×C₈₉	—	2	1	no	—
207	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
208	C₂×C₈₉	C₂×#443	1	2	yes	—
209	D₈₉	—	4	4	no	—
210	C₂×#443	—	89	1	no	—
211	C₂×#443	—	89	1	no	—
212	C₄×#135	—	89	1	no	—
213	C₄×#131	—	89	2	no	—
214	C₄×#108	—	89	1	no	—
215	#1772	—	89	1	no	—
216	#1772	D₈₉	1	1	yes	characteristic, complemented
217	#1764	—	89	2	no	—
218	#1764	—	89	2	no	—
219	C₄×#104	—	89	2	no	—
220	C₄²×C₈	—	89	1	no	—
221	C₈₉	C₄×#443	1	1	yes	characteristic, complemented, Sylow
222	C₂×#135	—	89	1	no	—
223	C₂×#131	—	89	2	no	—
224	C₂×#131	—	89	2	no	—
225	C₄×#41	—	89	2	no	—
226	#443	—	89	8	no	—
227	#443	—	89	8	no	—
228	C₄×Q₁₆	—	89	2	no	—
229	C₄×SD₁₆	—	89	4	no	—
230	C₄×D₈	—	89	2	no	—
231	C₂×#108	—	89	1	no	—
232	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
233	#427	C₂×D₈₉	1	1	yes	characteristic
234	C₂×#104	—	89	2	no	—
235	C₂×#104	—	89	2	no	—
236	#416	—	89	2	no	—
237	#405	—	89	2	no	—
238	#405	—	178	2	no	—
239	#405	—	178	2	no	—
240	#405	C₂×D₈₉	1	2	yes	—
241	C₄×M₁₆	—	89	2	no	—
242	C₄×M₁₆	—	178	2	no	—
243	C₂×C₄×C₈	—	89	1	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	C₂×C₄×C₈	—	89	1	no	—
246	C₂×C₄×C₈	—	89	1	no	—
247	C₂×C₄×C₈	—	89	1	no	—
248	C₂×C₄×C₈	—	178	2	no	—
249	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
250	C₄³	—	89	1	no	—
251	#341	—	89	2	no	—
252	#339	—	89	2	no	—
253	#339	C₂×D₈₉	1	2	yes	—
254	C₂×#41	—	89	2	no	—
255	#135	—	89	4	no	—
256	#135	—	89	4	no	—
257	C₂×Q₁₆	—	89	1	no	—
258	C₂×SD₁₆	—	89	2	no	—
259	C₂×D₈	—	89	1	no	—
260	#131	—	89	8	no	—
261	#131	—	89	8	no	—
262	#131	—	178	4	no	—
263	#131	—	178	4	no	—
264	C₂×M₁₆	—	89	2	no	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂×M₁₆	—	178	2	no	—
267	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	89	1	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₂²×C₈	—	178	2	no	—
272	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
274	C₄×Q₈	—	89	4	no	—
275	C₄×D₄	—	89	4	no	—
276	C₄×D₄	—	178	4	no	—
277	#117	—	178	2	no	—
278	#117	C₂²×D₈₉	1	2	yes	—
279	C₂×C₄²	—	89	1	no	—
280	C₂×C₄²	—	89	1	no	—
281	C₂×C₄²	—	178	2	no	—
282	C₂×C₄²	—	178	2	no	—
283	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
284	#108	—	89	4	no	—
285	#108	C₄×D₈₉	1	4	yes	complemented
286	#107	C₄×D₈₉	1	2	yes	—
287	#106	C₄×D₈₉	1	2	yes	—
288	#104	—	89	8	no	—
289	#104	—	89	8	no	—
290	#103	—	89	4	no	—
291	#102	—	89	4	no	—
292	#97	—	2	2	no	—
293	#97	—	178	2	no	—
294	#97	—	178	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	89	2	no	—
297	C₄×C₈	—	89	2	no	—
298	C₄×C₈	—	89	4	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	—	89	1	no	—
302	C₄×C₈	—	89	1	no	—
303	C₄×C₈	—	178	2	no	—
304	C₄×C₈	—	178	2	no	—
305	C₄×C₈	—	178	2	no	—
306	C₄×C₈	—	178	2	no	—
307	C₄×C₈	C₄×D₈₉	1	4	yes	complemented
308	#41	—	89	4	no	—
309	#41	—	89	4	no	—
310	#41	—	178	2	no	—
311	#41	—	178	2	no	—
312	C₂×Q₈	—	89	2	no	—
313	C₂×D₄	—	89	2	no	—
314	C₂×D₄	—	178	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	89	2	no	—
317	C₂²×C₄	—	178	4	no	—
318	C₂²×C₄	—	178	1	no	—
319	C₂²×C₄	—	178	2	no	—
320	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
321	Q₁₆	—	89	4	no	—
322	SD₁₆	—	89	8	no	—
323	D₈	—	89	4	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	89	4	no	—
326	M₁₆	—	178	8	no	—
327	M₁₆	—	178	2	no	—
328	M₁₆	—	178	8	no	—
329	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	89	2	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	89	1	no	—
334	C₂×C₈	—	89	2	no	—
335	C₂×C₈	—	89	2	no	—
336	C₂×C₈	—	178	8	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	—	178	1	no	—
340	C₂×C₈	—	178	8	no	—
341	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
346	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
348	C₂×C₈	#13083575	1	2	yes	—
349	C₄⋊C₄	—	178	4	no	—
350	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	178	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	89	2	no	—
356	C₄²	—	89	1	no	—
357	C₄²	—	89	1	no	—
358	C₄²	—	89	2	no	—
359	C₄²	—	178	4	no	—
360	C₄²	—	178	8	no	—
361	C₄²	—	178	1	no	—
362	C₄²	C₂×C₄×D₈₉	1	2	yes	—
363	C₂³	—	178	2	no	—
364	C₂³	#41×D₈₉	1	1	yes	characteristic
365	Q₈	—	89	4	no	—
366	Q₈	—	178	2	no	—
367	D₄	—	89	4	no	—
368	D₄	—	178	4	no	—
369	D₄	—	178	4	no	—
370	D₄	—	178	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	89	2	no	—
375	C₂×C₄	—	89	2	no	—
376	C₂×C₄	—	356	8	no	—
377	C₂×C₄	—	178	4	no	—
378	C₂×C₄	—	178	4	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	2	no	—
381	C₂×C₄	—	178	4	no	—
382	C₂×C₄	—	178	4	no	—
383	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
387	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	—	89	2	no	—
391	C₈	—	89	2	no	—
392	C₈	—	178	4	no	—
393	C₈	—	178	2	no	—
394	C₈	C₄²×D₈₉	1	2	yes	—
395	C₈	C₄²×D₈₉	1	2	yes	—
396	C₈	#15667974	1	2	yes	—
397	C₈	#15667974	1	2	yes	—
398	C₂²	—	2	2	no	—
399	C₂²	—	356	4	no	—
400	C₂²	—	178	4	no	—
401	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
402	C₂²	#19152066	1	1	yes	characteristic
403	C₂²	C₄×#13083575	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	89	4	no	—
407	C₄	—	178	4	no	—
408	C₄	—	178	2	no	—
409	C₄	—	178	4	no	—
410	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
411	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
412	C₄	C₂×#15667974	1	1	yes	characteristic
413	C₄	C₄×#13083575	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	356	4	no	—
417	C₂	C₄×#15667974	1	1	yes	characteristic
418	C₂	#443×D₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1772	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1772	D₈₉
hypocenter	C₈₉	C₄×#443
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. #26028674	C₂	semidirect
5. #108×Dic₈₉	C₂	semidirect
6. #26020133	C₂	semidirect
7. #26020091	C₂	semidirect
8. #26020086	C₂	semidirect
9. #26020056	C₂	semidirect
10. C₄×C₈×Dic₈₉	C₂	semidirect
11. C₈₉×#1772	C₂	semidirect
16. #19151716	C₄	semidirect
17. #19151714	C₄	semidirect
18. #19151692	C₄	semidirect
19. #19151685	C₄	semidirect
20. #19151680	C₄	semidirect
51. #15668020	C₂×C₄	semidirect
53. #15668018	C₂×C₄	semidirect
69. #15667948	C₂×C₄	semidirect
70. #15667940	C₂×C₄	semidirect
71. #15667938	C₂×C₄	semidirect
82. C₈×Dic₈₉	C₂×C₄	semidirect
92. #108×C₈₉	C₂×C₄	semidirect
97. C₄×C₈×C₈₉	C₂×C₄	semidirect
109. Dic₃₅₆	C₄²	semidirect
110. #13083563	C₄²	semidirect
111. D₇₁₂	C₄²	semidirect
203. Dic₈₉	#443	semidirect
216. #1772	D₈₉	semidirect
221. C₈₉	C₄×#443	semidirect
285. #108	C₄×D₈₉	semidirect
307. C₄×C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151716	2
C₂×#19151714	2
#26029023	2
#26028674	2
#108×Dic₈₉	2
#26020133	2
#26020091	2
#26020086	2
#26020056	2
C₄×C₈×Dic₈₉	2
C₈₉×#1772	2
C₄×#443	89