Subgroups — #36525421

Order 22784.

594 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030291	C₂	1	1	yes	maximal, characteristic
2	Q₈×#13083558	C₂	1	1	yes	maximal, characteristic
3	#26029195	C₂	1	1	yes	maximal, characteristic
4	#26019158	C₂	1	2	yes	maximal, complemented
5	#26019126	C₂	1	2	yes	maximal, complemented
6	#26019120	C₂	1	2	yes	maximal, complemented
7	#26019068	C₂	1	2	yes	maximal, complemented
8	#26019022	C₂	1	1	yes	maximal, characteristic
9	#26018708	C₂	1	1	yes	maximal, characteristic
10	#26018541	C₂	1	1	yes	maximal, characteristic
11	C₂×Q₈⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	#19152155	C₂²	1	1	yes	characteristic
13	#19151933	C₄	1	2	yes	—
14	#19151893	C₄	1	1	yes	characteristic
15	#19151893	C₄	1	1	yes	characteristic
16	#19151808	C₄	1	1	yes	characteristic
17	#19151808	C₄	1	1	yes	characteristic
18	#19151754	C₄	1	2	yes	—
19	#19151729	—	2	2	no	—
20	#19151729	C₂²	1	2	yes	—
21	#19151727	—	2	2	no	—
22	#19151725	C₂²	1	2	yes	—
23	Q₈×#10623494	C₂²	1	2	yes	—
24	#19151722	C₂²	1	2	yes	—
25	C₄×#13083564	C₂²	1	2	yes	—
26	C₄×#13083564	C₂²	1	2	yes	—
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151624	—	2	1	no	—
29	#19151622	—	2	1	no	—
30	#19151622	C₂²	1	1	yes	characteristic
31	#19151553	—	2	1	no	—
32	C₄×#13083558	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151348	C₂²	1	2	yes	—
35	#19151348	C₂²	1	2	yes	—
36	#19151330	C₂²	1	2	yes	—
37	#19151330	C₂²	1	2	yes	—
38	#19151320	C₂²	1	2	yes	—
39	#19151319	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083564	C₂×C₄	1	2	yes	—
48	C₂×#13083564	C₂×C₄	1	2	yes	—
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	D₄	1	1	yes	characteristic
51	C₂×#13083558	D₄	1	1	yes	characteristic
52	#15668012	C₂×C₄	1	1	yes	characteristic
53	#15668012	C₂×C₄	1	1	yes	characteristic
54	#15668004	—	2	1	no	—
55	#15667991	—	2	1	no	—
56	#15667991	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₇₈	—	2	1	no	—
58	C₄×Dic₁₇₈	C₂³	1	2	yes	—
59	#15667971	—	2	1	no	—
60	#15667945	C₂×C₄	1	2	yes	—
61	#15667945	C₂×C₄	1	2	yes	—
62	C₄⋊#10623494	—	2	2	no	—
63	C₄⋊#10623494	—	2	2	no	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	#15667941	—	2	2	no	—
69	#15667941	—	2	2	no	—
70	#15667936	C₂×C₄	1	2	yes	—
71	#15667936	C₂×C₄	1	2	yes	—
72	#15667935	C₂×C₄	1	2	yes	—
73	#15667935	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
75	#15667923	—	2	2	no	—
76	#15667923	D₄	1	2	yes	—
77	#15667922	—	2	2	no	—
78	C₄×#10623494	—	2	2	no	—
79	C₄×#10623494	C₂³	1	2	yes	—
80	C₄×#10623494	C₂³	1	2	yes	—
81	C₈×Dic₈₉	—	2	2	no	—
82	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	—	2	1	no	—
84	C₂²×C₈×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	—	2	1	no	—
87	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	—	2	1	no	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₈₉	—	2	1	no	—
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×Dic₁₇₈	—	2	1	no	—
102	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
103	#13083564	—	2	4	no	—
104	#13083564	—	4	2	no	—
105	#13083558	—	2	2	no	—
106	#13083558	—	2	2	no	—
107	#13083558	—	4	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	C₂²×C₄	1	2	yes	—
110	C₂×#10623494	C₂²×C₄	1	2	yes	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₄⋊Dic₈₉	—	2	1	no	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₄⋊Dic₈₉	—	2	1	no	—
116	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
117	#13083553	—	2	2	no	—
118	#13083553	—	2	2	no	—
119	C₂²⋊Dic₈₉	—	2	2	no	—
120	C₄×Dic₈₉	—	2	2	no	—
121	C₂×Q₈×C₈₉	—	2	1	no	—
122	C₂×Q₈×C₈₉	—	2	2	no	—
123	C₂×Q₈×C₈₉	—	4	1	no	—
124	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	4	2	no	—
136	C₂×C₈×C₈₉	—	4	2	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	C₂²×C₄	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	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₈₉	—	2	1	no	—
154	Q₈×C₈₉	—	2	1	no	—
155	Q₈×C₈₉	—	2	1	no	—
156	Q₈×C₈₉	—	4	2	no	—
157	Q₈×C₈₉	#131	1	2	yes	—
158	C₂×C₄×C₈₉	—	2	1	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	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	8	1	no	—
167	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#137	1	2	yes	—
171	C₂×C₄×C₈₉	#137	1	2	yes	—
172	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	—	2	2	no	—
179	Dic₁₇₈	—	8	1	no	—
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	4	1	no	—
182	C₈×C₈₉	—	4	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	2	2	no	—
186	#10623494	—	2	2	no	—
187	#10623494	—	2	2	no	—
188	#10623494	—	4	2	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	#441	1	2	yes	—
192	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	#441	1	2	yes	—
201	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
202	C₄×C₈₉	#568	1	1	yes	characteristic
203	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	4	2	no	—
207	#18003	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	2	2	no	—
209	C₂×C₈₉	#2933	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#441	1	1	yes	characteristic
211	C₂×C₈₉	#2956	1	1	yes	characteristic
212	#3104	—	89	1	no	—
213	Q₈×M₁₆	—	89	1	no	—
214	#2962	—	89	1	no	—
215	#1593	—	89	2	no	—
216	#1587	—	89	2	no	—
217	#1587	—	89	2	no	—
218	#1579	—	89	2	no	—
219	#1570	—	89	1	no	—
220	#1493	—	89	1	no	—
221	C₂×Q₈⋊C₈	D₈₉	1	1	yes	characteristic
222	#1451	—	89	1	no	—
223	C₈₉	#18003	1	1	yes	characteristic, complemented, Sylow
224	#533	—	89	1	no	—
225	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
226	#484	—	89	2	no	—
227	#477	—	89	1	no	—
228	#477	—	89	1	no	—
229	#462	—	89	1	no	—
230	#462	—	89	1	no	—
231	#451	—	89	2	no	—
232	#446	—	89	2	no	—
233	#446	—	89	2	no	—
234	#446	—	178	2	no	—
235	#446	—	178	2	no	—
236	C₈×Q₈	—	89	2	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₄×Q₁₆	—	89	2	no	—
239	C₄×Q₁₆	—	89	2	no	—
240	#431	—	89	1	no	—
241	#424	—	178	1	no	—
242	#423	—	89	1	no	—
243	#423	—	178	1	no	—
244	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
245	#405	—	178	1	no	—
246	C₄×M₁₆	—	89	1	no	—
247	C₄×M₁₆	—	178	1	no	—
248	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
249	#334	—	89	2	no	—
250	#334	—	89	2	no	—
251	Q₈⋊C₈	—	89	2	no	—
252	Q₈⋊C₈	—	89	2	no	—
253	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
254	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
255	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
256	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
257	#322	—	89	2	no	—
258	#322	—	89	2	no	—
259	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
260	C₂×Q₁₆	—	89	2	no	—
261	C₂×Q₁₆	—	89	2	no	—
262	C₂×M₁₆	—	89	1	no	—
263	C₂×M₁₆	—	89	1	no	—
264	C₂×M₁₆	—	178	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₄⋊Q₈	—	89	1	no	—
268	C₄⋊Q₈	—	89	1	no	—
269	#125	—	178	1	no	—
270	C₂²⋊Q₈	—	89	2	no	—
271	C₂²⋊Q₈	—	178	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	89	2	no	—
275	C₄×Q₈	—	178	1	no	—
276	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
277	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
278	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
279	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
280	#117	—	178	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	#107	—	89	2	no	—
286	#107	—	89	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	89	1	no	—
289	C₄⋊C₈	—	89	1	no	—
290	C₄⋊C₈	—	89	2	no	—
291	C₄⋊C₈	—	178	2	no	—
292	C₄⋊C₈	—	178	2	no	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	2	no	—
295	C₄⋊C₈	—	178	1	no	—
296	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
298	#103	—	89	2	no	—
299	#103	—	89	2	no	—
300	#103	—	89	2	no	—
301	#103	—	89	2	no	—
302	C₂²⋊C₈	—	89	2	no	—
303	#97	—	89	2	no	—
304	#97	—	178	2	no	—
305	#97	—	178	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	89	2	no	—
308	C₄×C₈	—	89	2	no	—
309	C₄×C₈	—	178	2	no	—
310	C₄×C₈	—	178	2	no	—
311	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×Q₈	—	89	2	no	—
317	C₂×Q₈	—	178	1	no	—
318	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
319	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
324	C₂²×C₄	#13083573	1	1	yes	characteristic
325	Q₁₆	—	356	2	no	—
326	Q₁₆	—	178	4	no	—
327	M₁₆	—	356	2	no	—
328	M₁₆	—	178	2	no	—
329	M₁₆	—	178	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	89	2	no	—
337	C₂×C₈	—	89	2	no	—
338	C₂×C₈	—	89	2	no	—
339	C₂×C₈	—	89	2	no	—
340	C₂×C₈	—	178	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	89	2	no	—
347	C₄⋊C₄	—	178	1	no	—
348	C₄⋊C₄	—	178	1	no	—
349	C₄⋊C₄	—	178	2	no	—
350	C₄⋊C₄	—	178	1	no	—
351	C₄⋊C₄	—	178	2	no	—
352	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
353	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
354	C₂²⋊C₄	—	178	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	178	2	no	—
360	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
361	C₄²	D₄×D₈₉	1	1	yes	characteristic
362	C₄²	#13083573	1	1	yes	characteristic
363	C₄²	C₂³×D₈₉	1	1	yes	characteristic
364	C₂³	#15667972	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	178	2	no	—
370	Q₈	—	178	2	no	—
371	Q₈	—	712	1	no	—
372	Q₈	#15668018	1	2	yes	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	178	2	no	—
383	C₂×C₄	—	178	2	no	—
384	C₂×C₄	#15667972	1	1	yes	characteristic
385	C₂×C₄	#15667972	1	1	yes	characteristic
386	C₂×C₄	#15667972	1	1	yes	characteristic
387	C₂×C₄	#15668041	1	2	yes	—
388	C₂×C₄	#15668044	1	2	yes	—
389	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	356	2	no	—
397	C₈	—	178	2	no	—
398	C₈	—	178	2	no	—
399	C₈	—	178	2	no	—
400	C₈	—	178	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	#19151702	1	2	yes	—
404	C₂²	C₂×#15667972	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	356	2	no	—
413	C₄	—	356	2	no	—
414	C₄	#19151702	1	2	yes	—
415	C₄	C₂×#15668018	1	1	yes	characteristic
416	C₄	#19152364	1	1	yes	characteristic
417	C₄	C₂×#15668041	1	1	yes	characteristic
418	C₄	C₂×#15668044	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	#26028973	1	1	yes	characteristic
421	C₂	C₂×#19151702	1	1	yes	characteristic
422	C₂	#26029158	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×Q₈⋊C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂³×C₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₈₉
hypocenter	C₈₉	#18003
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. #26019158	C₂	semidirect
5. #26019126	C₂	semidirect
6. #26019120	C₂	semidirect
7. #26019068	C₂	semidirect
223. C₈₉	#18003	semidirect

Maximal subgroups

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

subgroup	index
#26030291	2
Q₈×#13083558	2
#26029195	2
#26019158	2
#26019126	2
#26019120	2
#26019068	2
#26019022	2
#26018708	2
#26018541	2
C₂×Q₈⋊C₈×C₈₉	2
#18003	89