Subgroups — #36572945

Order 22784.

812 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	#26029169	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151715	C₂	1	1	yes	maximal, characteristic
3	#26028861	C₂	1	2	yes	maximal, complemented
4	#26021042	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021040	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020492	C₂	1	2	yes	maximal, complemented
7	#26020490	C₂	1	2	yes	maximal, complemented
8	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020304	C₂	1	2	yes	maximal, complemented
10	#26020132	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2957	C₂	1	1	yes	maximal, characteristic
12	#19152365	C₂²	1	2	yes	—
13	C₂×#15668019	C₂²	1	2	yes	—
14	#19151720	—	2	2	no	—
15	#19151715	—	2	2	no	—
16	#19151715	C₄	1	2	yes	complemented
17	#19151715	C₄	1	2	yes	complemented
18	#19151715	C₄	1	2	yes	complemented
19	#19151715	C₄	1	2	yes	complemented
20	#19151646	—	2	4	no	—
21	#19151646	C₂²	1	2	yes	—
22	#19151646	C₂²	1	2	yes	—
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667948	C₂²	1	1	yes	characteristic
25	C₂×#15667947	—	2	4	no	—
26	C₂×#15667947	C₂²	1	2	yes	—
27	C₂×#15667947	C₂²	1	1	yes	characteristic
28	#19151634	C₂²	1	1	yes	characteristic
29	#19151621	C₂²	1	2	yes	—
30	#19151615	C₂²	1	2	yes	—
31	C₂×#15667939	C₂²	1	2	yes	—
32	#19151553	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	#19151369	C₂²	1	2	yes	—
35	#19151368	C₂²	1	2	yes	—
36	#19151359	C₂²	1	1	yes	characteristic
37	#19151357	C₂²	1	1	yes	characteristic
38	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
39	#568×C₈₉	C₂²	1	2	yes	—
40	#444×C₈₉	—	2	2	no	—
41	#443×C₈₉	—	2	2	no	—
42	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
43	#421×C₈₉	C₂²	1	2	yes	—
44	#405×C₈₉	C₂²	1	1	yes	characteristic
45	#15668019	—	2	2	no	—
46	#15668019	—	2	2	no	—
47	#15668019	—	2	4	no	—
48	#15668019	—	4	2	no	—
49	#15668019	C₂×C₄	1	4	yes	—
50	#15668019	C₂×C₄	1	4	yes	—
51	C₂×#13083558	—	2	2	no	—
52	C₂×#13083558	—	2	4	no	—
53	C₂×#13083558	C₂³	1	2	yes	—
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂×#13083558	C₂³	1	1	yes	characteristic
56	C₂²×#10623494	—	2	2	no	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	#15667971	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
60	#15667948	—	2	1	no	—
61	#15667948	—	2	1	no	—
62	#15667948	C₂×C₄	1	2	yes	—
63	#15667948	C₂×C₄	1	2	yes	—
64	#15667947	—	2	4	no	—
65	#15667947	—	2	2	no	—
66	#15667947	—	2	2	no	—
67	#15667947	—	2	4	no	—
68	#15667947	D₄	1	2	yes	—
69	#15667947	D₄	1	2	yes	—
70	#15667945	—	2	1	no	—
71	#15667943	—	2	1	no	—
72	#15667941	—	4	2	no	—
73	#15667939	—	2	4	no	—
74	#15667939	C₂×C₄	1	4	yes	—
75	#15667939	C₂×C₄	1	4	yes	—
76	#15667922	—	2	1	no	—
77	C₈×Dic₈₉	—	2	1	no	—
78	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₂×#41×C₈₉	C₂³	1	2	yes	—
83	#135×C₈₉	C₂×C₄	1	2	yes	—
84	#135×C₈₉	C₂×C₄	1	2	yes	—
85	#135×C₈₉	D₄	1	2	yes	—
86	#135×C₈₉	D₄	1	2	yes	—
87	C₂×Q₁₆×C₈₉	Q₈	1	1	yes	characteristic
88	C₂×SD₁₆×C₈₉	Q₈	1	2	yes	—
89	C₂×D₈×C₈₉	Q₈	1	1	yes	characteristic
90	#131×C₈₉	—	2	4	no	—
91	#131×C₈₉	—	4	2	no	—
92	C₂×M₁₆×C₈₉	—	2	4	no	—
93	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
94	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	#117×C₈₉	C₂³	1	1	yes	characteristic
97	#108×C₈₉	—	2	1	no	—
98	#108×C₈₉	—	2	1	no	—
99	#104×C₈₉	—	2	4	no	—
100	#97×C₈₉	—	2	1	no	—
101	C₄×C₈×C₈₉	—	2	1	no	—
102	C₂²×Dic₈₉	—	2	1	no	—
103	#13083558	—	2	2	no	—
104	#13083558	—	2	1	no	—
105	#13083558	—	2	4	no	—
106	#13083558	—	2	4	no	—
107	#13083558	—	2	2	no	—
108	#13083558	—	2	2	no	—
109	#13083558	—	4	4	no	—
110	#13083558	C₂²×C₄	1	4	yes	—
111	#13083558	C₂×D₄	1	2	yes	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	4	no	—
115	C₂×#10623494	—	2	4	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	4	4	no	—
118	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	#41	1	1	yes	characteristic
123	C₂×#10623494	#41	1	1	yes	characteristic
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₂²⋊Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	1	no	—
127	C₄×Dic₈₉	—	2	1	no	—
128	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	#41×C₈₉	—	2	2	no	—
131	#41×C₈₉	—	2	2	no	—
132	#41×C₈₉	C₂²×C₄	1	4	yes	—
133	#41×C₈₉	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
137	C₂²×C₄×C₈₉	—	2	2	no	—
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₈₉	C₄⋊C₄	1	2	yes	—
140	Q₁₆×C₈₉	C₄⋊C₄	1	2	yes	—
141	SD₁₆×C₈₉	C₄⋊C₄	1	4	yes	—
142	SD₁₆×C₈₉	C₄⋊C₄	1	4	yes	—
143	D₈×C₈₉	C₄⋊C₄	1	2	yes	—
144	D₈×C₈₉	C₄⋊C₄	1	2	yes	—
145	M₁₆×C₈₉	—	2	1	no	—
146	M₁₆×C₈₉	—	2	2	no	—
147	M₁₆×C₈₉	—	2	2	no	—
148	M₁₆×C₈₉	—	4	4	no	—
149	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₈₉	—	2	1	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	4	4	no	—
153	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₈₉	—	2	4	no	—
167	D₄×C₈₉	—	2	4	no	—
168	D₄×C₈₉	—	2	2	no	—
169	D₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	4	no	—
172	C₂×C₄×C₈₉	—	2	4	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×Dic₈₉	—	2	1	no	—
181	C₂×Dic₈₉	—	2	1	no	—
182	C₂×Dic₈₉	—	4	2	no	—
183	C₂×Dic₈₉	—	4	1	no	—
184	C₈×C₈₉	—	2	2	no	—
185	C₈×C₈₉	—	4	2	no	—
186	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	#10623494	—	2	4	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	4	2	no	—
193	#10623494	C₄×D₄	1	1	yes	characteristic
194	#10623494	C₄×D₄	1	1	yes	characteristic
195	#10623494	C₄×D₄	1	1	yes	characteristic
196	#10623494	C₄×D₄	1	1	yes	characteristic
197	C₂²×C₈₉	—	2	4	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	8	2	no	—
200	C₂²×C₈₉	#520	1	1	yes	characteristic
201	C₂²×C₈₉	#547	1	1	yes	characteristic
202	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
203	C₄×C₈₉	—	2	4	no	—
204	C₄×C₈₉	—	8	1	no	—
205	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₈₉	D₄²	1	1	yes	characteristic
208	C₄×C₈₉	#554	1	1	yes	characteristic
209	Dic₈₉	—	2	2	no	—
210	Dic₈₉	—	4	1	no	—
211	Dic₈₉	—	8	1	no	—
212	#22694	—	89	1	no	maximal, Sylow
213	C₂×C₈₉	—	2	1	no	—
214	C₂×C₈₉	—	2	1	no	—
215	C₂×C₈₉	—	2	1	no	—
216	C₂×C₈₉	—	4	4	no	—
217	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
218	#2957	—	89	1	no	—
219	#2957	D₈₉	1	1	yes	characteristic
220	C₂×#443	—	89	1	no	—
221	#2916	—	89	2	no	—
222	#1953	—	89	1	no	—
223	#1953	—	89	1	no	—
224	#1861	—	89	2	no	—
225	#1861	—	89	2	no	—
226	#1848	—	89	1	no	—
227	#1814	—	89	2	no	—
228	#1772	—	89	1	no	—
229	C₈₉	#22694	1	1	yes	characteristic, complemented, Sylow
230	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
231	#568	—	89	2	no	—
232	#568	C₂×D₈₉	1	2	yes	—
233	C₂×#131	—	89	2	no	—
234	#444	—	2	2	no	—
235	#444	—	178	2	no	—
236	#443	—	2	2	no	—
237	#443	—	89	2	no	—
238	#443	—	89	2	no	—
239	#443	—	89	2	no	—
240	#443	—	89	2	no	—
241	#443	—	178	2	no	—
242	#430	—	89	2	no	—
243	#430	—	89	2	no	—
244	#430	—	178	4	no	—
245	C₂×#108	—	89	1	no	—
246	C₂×#108	—	89	1	no	—
247	C₂×#108	—	89	2	no	—
248	C₂×#108	—	89	1	no	—
249	C₂×#108	—	178	4	no	—
250	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
251	#427	—	89	1	no	—
252	#423	—	89	2	no	—
253	#421	—	89	2	no	—
254	#421	C₂×D₈₉	1	2	yes	—
255	C₂×#104	—	89	2	no	—
256	#405	—	89	1	no	—
257	#405	C₂×D₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	—	89	1	no	—
259	#344	—	89	2	no	—
260	#344	—	89	2	no	—
261	#339	—	89	1	no	—
262	#339	—	89	1	no	—
263	C₂×#41	C₂²×D₈₉	1	2	yes	—
264	#135	C₄×D₈₉	1	2	yes	—
265	#135	C₄×D₈₉	1	2	yes	—
266	#135	C₂²⋊D₈₉	1	2	yes	—
267	#135	C₂²⋊D₈₉	1	2	yes	—
268	C₂×Q₁₆	Dic₁₇₈	1	1	yes	characteristic
269	C₂×SD₁₆	Dic₁₇₈	1	2	yes	—
270	C₂×D₈	Dic₁₇₈	1	1	yes	characteristic
271	#131	—	2	4	no	—
272	#131	—	4	2	no	—
273	#131	—	89	4	no	—
274	#131	—	89	4	no	—
275	#131	—	356	2	no	—
276	#131	—	178	2	no	—
277	#131	—	178	2	no	—
278	#131	—	178	4	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	89	2	no	—
281	C₂×M₁₆	—	89	1	no	—
282	C₂×M₁₆	—	89	2	no	—
283	C₂×M₁₆	—	178	2	no	—
284	C₂×M₁₆	—	178	4	no	—
285	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
286	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	178	2	no	—
289	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	#117	—	89	1	no	—
291	#117	C₂²×D₈₉	1	1	yes	characteristic
292	C₂×C₄²	—	89	1	no	—
293	#108	—	2	1	no	—
294	#108	—	2	1	no	—
295	#108	—	89	2	no	—
296	#108	—	89	2	no	—
297	#108	—	89	2	no	—
298	#108	—	89	2	no	—
299	#108	—	178	2	no	—
300	#108	—	178	2	no	—
301	#108	—	178	4	no	—
302	#108	—	178	4	no	—
303	#108	—	178	1	no	—
304	#108	—	178	1	no	—
305	#107	—	178	1	no	—
306	#106	—	178	1	no	—
307	C₄⋊C₈	—	356	2	no	—
308	#104	—	2	4	no	—
309	#104	—	89	4	no	—
310	#104	—	89	4	no	—
311	#104	—	178	4	no	—
312	#97	—	2	1	no	—
313	#97	—	178	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	89	1	no	—
316	C₄×C₈	—	89	1	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	178	1	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	C₂×C₄×D₈₉	1	4	yes	—
323	#41	C₂×C₂²⋊D₈₉	1	4	yes	—
324	C₂×Q₈	C₂×Dic₁₇₈	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	C₂×Dic₁₇₈	1	2	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	178	1	no	—
329	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
330	Q₁₆	#13083553	1	2	yes	—
331	Q₁₆	#13083553	1	2	yes	—
332	SD₁₆	#13083553	1	4	yes	—
333	SD₁₆	#13083553	1	4	yes	—
334	D₈	#13083553	1	2	yes	—
335	D₈	#13083553	1	2	yes	—
336	M₁₆	—	2	1	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	4	4	no	—
340	M₁₆	—	89	4	no	—
341	M₁₆	—	89	2	no	—
342	M₁₆	—	356	4	no	—
343	M₁₆	—	178	4	no	—
344	M₁₆	—	178	4	no	—
345	M₁₆	—	178	2	no	—
346	M₁₆	—	178	2	no	—
347	M₁₆	—	178	2	no	—
348	M₁₆	—	178	1	no	—
349	M₁₆	D₄×D₈₉	1	2	yes	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	89	1	no	—
356	C₂×C₈	—	89	1	no	—
357	C₂×C₈	—	89	1	no	—
358	C₂×C₈	—	89	1	no	—
359	C₂×C₈	—	356	4	no	—
360	C₂×C₈	—	178	4	no	—
361	C₂×C₈	—	178	4	no	—
362	C₂×C₈	—	178	2	no	—
363	C₂×C₈	—	178	2	no	—
364	C₂×C₈	—	178	1	no	—
365	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
367	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
368	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₂×C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
370	C₂×C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	178	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	178	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	89	1	no	—
377	C₄²	—	89	1	no	—
378	C₄²	—	178	1	no	—
379	C₄²	—	178	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	#15668059	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	C₂×#13083553	1	4	yes	—
384	D₄	—	2	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	C₂×#13083553	1	4	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	356	1	no	—
394	C₂×C₄	—	178	1	no	—
395	C₂×C₄	—	178	1	no	—
396	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
400	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
401	C₂×C₄	#15668057	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	89	1	no	—
405	C₈	—	89	1	no	—
406	C₈	—	89	1	no	—
407	C₈	—	89	1	no	—
408	C₈	—	356	2	no	—
409	C₈	—	178	2	no	—
410	C₈	—	178	4	no	—
411	C₈	C₂×#13083553	1	1	yes	characteristic
412	C₈	C₂×#13083553	1	1	yes	characteristic
413	C₈	C₂×#13083553	1	1	yes	characteristic
414	C₈	C₂×#13083553	1	1	yes	characteristic
415	C₂²	—	2	4	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	#19152077	1	1	yes	characteristic
419	C₂²	#19152247	1	1	yes	characteristic
420	C₂²	D₄×Dic₁₇₈	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	8	1	no	—
423	C₄	—	356	1	no	—
424	C₄	—	178	2	no	—
425	C₄	—	712	1	no	—
426	C₄	C₂²×#13083553	1	1	yes	characteristic
427	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
428	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
429	C₄	#19152307	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	4	4	no	—
434	C₂	D₄×#13083553	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2957	C₂
socle	C₂×C₈₉	D₄×C₄⋊C₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2957	D₈₉
hypocenter	C₈₉	#22694
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
3. #26028861	C₂	semidirect
4. #26021042	C₂	semidirect
5. #26021040	C₂	semidirect
6. #26020492	C₂	semidirect
7. #26020490	C₂	semidirect
8. #26020422	C₂	semidirect
9. #26020304	C₂	semidirect
10. #26020132	C₂	semidirect
16. #19151715	C₄	semidirect
17. #19151715	C₄	semidirect
18. #19151715	C₄	semidirect
19. #19151715	C₄	semidirect
229. C₈₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#26029169	2
C₂×#19151715	2
#26028861	2
#26021042	2
#26021040	2
#26020492	2
#26020490	2
#26020422	2
#26020304	2
#26020132	2
C₈₉×#2957	2
#22694	89