Subgroups — #36523440

Order 22784.

762 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028884	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019014	C₂	1	4	yes	maximal, complemented
4	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019007	C₂	1	2	yes	maximal, complemented
6	#26018999	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₈₉	C₄	1	2	yes	—
9	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
10	#19151654	—	2	2	no	—
11	#19151654	C₂²	1	4	yes	—
12	#19151650	—	2	2	no	—
13	#19151650	C₂²	1	4	yes	—
14	#19151622	C₂²	1	2	yes	—
15	#19151561	—	2	2	no	—
16	M₁₆×Dic₈₉	—	2	2	no	—
17	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₈₉	C₄	1	2	yes	—
19	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
20	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
21	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
22	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
23	C₄×C₈×D₈₉	C₂²	1	2	yes	—
24	C₄×C₈×D₈₉	C₂²	1	2	yes	—
25	#19151351	C₂²	1	4	yes	complemented
26	#19151348	C₂²	1	8	yes	complemented
27	#423×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
29	#335×C₈₉	C₂²	1	4	yes	complemented
30	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
33	C₂×#13083558	—	2	2	no	—
34	C₂²×#10623494	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₈₉	—	2	8	no	—
36	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
40	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
42	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
43	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
44	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₈₉	D₄	1	1	yes	characteristic
46	C₄²×D₈₉	D₄	1	1	yes	characteristic
47	C₄²×D₈₉	Q₈	1	1	yes	characteristic
48	C₄²×D₈₉	Q₈	1	1	yes	characteristic
49	C₄²×D₈₉	C₂³	1	1	yes	characteristic
50	C₄²×D₈₉	C₂³	1	1	yes	characteristic
51	C₄⋊#10623494	—	2	2	no	—
52	C₄⋊#10623494	C₂³	1	4	yes	—
53	#15667924	—	2	4	no	—
54	#15667924	—	2	4	no	—
55	#15667922	—	2	4	no	—
56	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
57	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
58	C₄×#10623494	C₂³	1	2	yes	—
59	C₈×Dic₈₉	—	2	4	no	—
60	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
61	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
62	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
63	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₈₉	—	2	2	no	—
65	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₈₉	—	2	2	no	—
68	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
69	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₈₉	C₂³	1	2	yes	—
72	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄×D₈₉	—	2	2	no	—
77	C₂×C₄×D₈₉	—	2	2	no	—
78	C₂×C₄×D₈₉	—	2	4	no	—
79	C₂×C₄×D₈₉	—	2	4	no	—
80	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
92	#13083558	—	4	4	no	—
93	C₂×#10623494	—	2	4	no	—
94	C₂×#10623494	—	2	4	no	—
95	C₂×#10623494	C₂²×C₄	1	2	yes	—
96	C₂×#10623494	C₂²×C₄	1	2	yes	—
97	C₈×D₈₉	—	2	4	no	—
98	C₈×D₈₉	—	2	4	no	—
99	C₈×D₈₉	—	2	4	no	—
100	C₈×D₈₉	M₁₆	1	8	yes	complemented
101	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
110	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
111	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
116	M₁₆×C₈₉	—	4	4	no	—
117	C₂×C₈×C₈₉	—	2	4	no	—
118	C₂×C₈×C₈₉	—	2	4	no	—
119	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
124	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
125	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂²×D₈₉	—	2	2	no	—
127	C₂²×D₈₉	—	2	2	no	—
128	C₂²×D₈₉	—	2	2	no	—
129	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₈₉	#135	1	2	yes	—
137	C₂×C₄×C₈₉	#135	1	2	yes	—
138	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
141	C₂×Dic₈₉	—	2	2	no	—
142	C₂×Dic₈₉	—	2	2	no	—
143	C₂×Dic₈₉	—	2	2	no	—
144	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₄×D₈₉	—	2	2	no	—
151	C₄×D₈₉	—	2	2	no	—
152	C₄×D₈₉	—	2	2	no	—
153	C₄×D₈₉	—	2	1	no	—
154	C₄×D₈₉	—	2	1	no	—
155	C₄×D₈₉	—	2	1	no	—
156	C₄×D₈₉	—	2	1	no	—
157	C₄×D₈₉	—	2	2	no	—
158	C₄×D₈₉	—	2	2	no	—
159	C₄×D₈₉	—	2	2	no	—
160	C₄×D₈₉	—	2	2	no	—
161	C₄×D₈₉	—	2	2	no	—
162	C₄×D₈₉	#108	1	4	yes	—
163	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
164	C₈×C₈₉	—	2	2	no	—
165	C₈×C₈₉	—	4	4	no	—
166	C₈×C₈₉	C₂×M₁₆	1	4	yes	—
167	#10623494	—	2	2	no	—
168	#10623494	—	4	4	no	—
169	#10623494	C₂×M₁₆	1	4	yes	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	#427	1	2	yes	—
173	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂×D₈₉	—	2	8	no	—
175	C₂×D₈₉	—	2	1	no	—
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	2	1	no	—
178	C₂×D₈₉	—	2	1	no	—
179	C₂×D₈₉	#423	1	2	yes	—
180	C₂×D₈₉	C₂×#108	1	2	yes	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	#427	1	2	yes	—
184	C₄×C₈₉	C₂×#108	1	2	yes	—
185	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
186	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
187	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
188	Dic₈₉	—	2	1	no	—
189	Dic₈₉	—	2	1	no	—
190	Dic₈₉	—	2	1	no	—
191	Dic₈₉	—	2	1	no	—
192	Dic₈₉	#423	1	2	yes	—
193	Dic₈₉	C₂×#108	1	2	yes	—
194	#17793	—	89	1	no	maximal, Sylow
195	C₂×C₈₉	—	2	2	no	—
196	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
197	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
198	C₂×C₈₉	C₂²×#108	1	1	yes	characteristic
199	D₈₉	—	2	2	no	—
200	D₈₉	—	2	2	no	—
201	#2920	—	89	2	no	—
202	C₂²×C₄×C₈	—	89	1	no	—
203	#1568	—	89	4	no	—
204	#1567	—	89	1	no	—
205	#1567	D₈₉	1	1	yes	characteristic, complemented
206	#1566	—	89	2	no	—
207	#1564	—	89	4	no	—
208	C₈₉	#17793	1	1	yes	characteristic, complemented, Sylow
209	C₂³×C₈	—	89	2	no	—
210	C₂²×C₄²	—	89	1	no	—
211	#432	—	89	4	no	—
212	#432	—	178	2	no	—
213	#431	—	89	4	no	—
214	#431	—	178	2	no	—
215	#423	—	89	2	no	—
216	#423	C₂×D₈₉	1	2	yes	—
217	#407	—	178	2	no	—
218	C₄×M₁₆	—	178	2	no	—
219	C₂×C₄×C₈	—	89	2	no	—
220	C₂×C₄×C₈	—	89	1	no	—
221	C₂×C₄×C₈	—	89	1	no	—
222	C₂×C₄×C₈	—	89	1	no	—
223	C₂×C₄×C₈	—	89	1	no	—
224	C₂×C₄×C₈	—	89	1	no	—
225	C₂×C₄×C₈	—	89	2	no	—
226	C₂×C₄×C₈	—	89	2	no	—
227	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
228	#335	—	89	4	no	—
229	#335	C₂×D₈₉	1	4	yes	complemented
230	#334	—	89	8	no	—
231	C₂³×C₄	—	89	1	no	—
232	C₂³×C₄	—	89	1	no	—
233	C₂³×C₄	—	89	1	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	178	2	no	—
236	C₂²×C₈	—	89	2	no	—
237	C₂²×C₈	—	89	2	no	—
238	C₂²×C₈	—	89	2	no	—
239	C₂²×C₈	—	89	2	no	—
240	C₂²×C₈	—	89	2	no	—
241	C₂²×C₈	—	178	8	no	—
242	C₂²×C₈	C₄×D₈₉	1	2	yes	—
243	C₂×C₄²	—	89	1	no	—
244	C₂×C₄²	—	89	1	no	—
245	C₂×C₄²	—	89	1	no	—
246	C₂×C₄²	—	89	1	no	—
247	C₂×C₄²	—	89	1	no	—
248	C₂×C₄²	—	89	1	no	—
249	C₂×C₄²	—	89	1	no	—
250	C₂×C₄²	—	89	1	no	—
251	C₂×C₄²	—	89	1	no	—
252	C₂×C₄²	—	89	1	no	—
253	C₂×C₄²	—	89	1	no	—
254	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	89	4	no	—
257	C₄⋊C₈	—	178	2	no	—
258	C₄⋊C₈	C₂²×D₈₉	1	4	yes	—
259	C₂²⋊C₈	—	178	4	no	—
260	C₂²⋊C₈	—	178	4	no	—
261	#97	—	178	4	no	—
262	C₄×C₈	—	89	2	no	—
263	C₄×C₈	—	89	2	no	—
264	C₄×C₈	—	89	2	no	—
265	C₄×C₈	—	89	2	no	—
266	C₄×C₈	—	89	1	no	—
267	C₄×C₈	—	89	1	no	—
268	C₄×C₈	—	89	2	no	—
269	C₄×C₈	—	178	4	no	—
270	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
271	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
272	C₄×C₈	C₂²×D₈₉	1	2	yes	—
273	C₂⁴	—	89	1	no	—
274	C₂²×C₄	—	89	1	no	—
275	C₂²×C₄	—	89	1	no	—
276	C₂²×C₄	—	89	1	no	—
277	C₂²×C₄	—	89	1	no	—
278	C₂²×C₄	—	89	1	no	—
279	C₂²×C₄	—	89	1	no	—
280	C₂²×C₄	—	89	1	no	—
281	C₂²×C₄	—	89	1	no	—
282	C₂²×C₄	—	89	1	no	—
283	C₂²×C₄	—	89	1	no	—
284	C₂²×C₄	—	89	1	no	—
285	C₂²×C₄	—	89	1	no	—
286	C₂²×C₄	—	89	1	no	—
287	C₂²×C₄	—	89	1	no	—
288	C₂²×C₄	—	89	1	no	—
289	C₂²×C₄	—	178	4	no	—
290	C₂²×C₄	—	178	4	no	—
291	C₂²×C₄	—	178	2	no	—
292	C₂²×C₄	—	178	2	no	—
293	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
295	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
296	M₁₆	—	4	4	no	—
297	M₁₆	—	356	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	89	2	no	—
301	C₂×C₈	—	89	8	no	—
302	C₂×C₈	—	89	2	no	—
303	C₂×C₈	—	178	4	no	—
304	C₂×C₈	—	178	4	no	—
305	C₂×C₈	—	178	4	no	—
306	C₂×C₈	—	178	4	no	—
307	C₂×C₈	—	178	4	no	—
308	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
309	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
310	C₄²	—	89	1	no	—
311	C₄²	—	89	1	no	—
312	C₄²	—	89	1	no	—
313	C₄²	—	89	1	no	—
314	C₄²	—	89	1	no	—
315	C₄²	—	89	1	no	—
316	C₄²	—	89	1	no	—
317	C₄²	—	89	1	no	—
318	C₄²	—	89	1	no	—
319	C₄²	—	89	1	no	—
320	C₄²	—	89	1	no	—
321	C₄²	—	89	1	no	—
322	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
323	C₄²	D₄×D₈₉	1	1	yes	characteristic
324	C₄²	Q₈×D₈₉	1	1	yes	characteristic
325	C₄²	C₂³×D₈₉	1	1	yes	characteristic
326	C₂³	—	89	1	no	—
327	C₂³	—	89	1	no	—
328	C₂³	—	178	2	no	—
329	C₂³	—	178	2	no	—
330	C₂³	—	178	2	no	—
331	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	89	1	no	—
335	C₂×C₄	—	89	1	no	—
336	C₂×C₄	—	89	4	no	—
337	C₂×C₄	—	89	4	no	—
338	C₂×C₄	—	89	1	no	—
339	C₂×C₄	—	89	1	no	—
340	C₂×C₄	—	89	1	no	—
341	C₂×C₄	—	89	1	no	—
342	C₂×C₄	—	178	2	no	—
343	C₂×C₄	—	178	2	no	—
344	C₂×C₄	—	178	2	no	—
345	C₂×C₄	—	178	2	no	—
346	C₂×C₄	—	178	2	no	—
347	C₂×C₄	—	178	2	no	—
348	C₂×C₄	—	178	2	no	—
349	C₂×C₄	—	178	2	no	—
350	C₂×C₄	—	178	2	no	—
351	C₂×C₄	—	178	2	no	—
352	C₂×C₄	—	178	2	no	—
353	C₂×C₄	—	178	1	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	—	178	1	no	—
356	C₂×C₄	—	178	1	no	—
357	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
359	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
360	C₂×C₄	#15668031	1	2	yes	—
361	C₂×C₄	#15668035	1	2	yes	—
362	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
363	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
364	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	4	4	no	—
367	C₈	—	89	4	no	—
368	C₈	—	356	4	no	—
369	C₈	—	178	2	no	—
370	C₈	M₁₆×D₈₉	1	4	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	89	2	no	—
374	C₂²	—	89	2	no	—
375	C₂²	—	178	8	no	—
376	C₂²	—	178	1	no	—
377	C₂²	—	178	1	no	—
378	C₂²	—	178	1	no	—
379	C₂²	—	178	1	no	—
380	C₂²	#19151635	1	2	yes	—
381	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	89	2	no	—
385	C₄	—	89	2	no	—
386	C₄	—	178	1	no	—
387	C₄	—	178	1	no	—
388	C₄	—	178	1	no	—
389	C₄	—	178	1	no	—
390	C₄	#19151635	1	2	yes	—
391	C₄	#108×D₈₉	1	2	yes	—
392	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
393	C₄	C₂×#15668031	1	1	yes	characteristic
394	C₄	C₂×#15668035	1	1	yes	characteristic
395	C₂	—	2	2	no	—
396	C₂	—	178	2	no	—
397	C₂	—	178	2	no	—
398	C₂	#423×D₈₉	1	1	yes	characteristic
399	C₂	C₂×#19151635	1	1	yes	characteristic
400	C₂	C₂×#108×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1567	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1567	D₈₉
hypocenter	C₈₉	#17793
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
3. #26019014	C₂	semidirect
4. #26019011	C₂	semidirect
5. #26019007	C₂	semidirect
6. #26018999	C₂	semidirect
7. C₈₉×#1567	C₂	semidirect
25. #19151351	C₂²	semidirect
26. #19151348	C₂²	semidirect
29. #335×C₈₉	C₂²	semidirect
100. C₈×D₈₉	M₁₆	semidirect
205. #1567	D₈₉	semidirect
208. C₈₉	#17793	semidirect
229. #335	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028884	2
C₂×C₄×C₈×D₈₉	2
#26019014	2
#26019011	2
#26019007	2
#26018999	2
C₈₉×#1567	2
#17793	89