Subgroups — #36714519

Order 22784.

3578 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152073	C₂	1	2	yes	maximal
2	#26023162	C₂	1	8	yes	maximal, complemented
3	D₄×C₄⋊Dic₈₉	C₂	1	8	yes	maximal, complemented
4	#26022870	C₂	1	2	yes	maximal, complemented
5	#26022866	C₂	1	4	yes	maximal, complemented
6	#26022659	C₂	1	2	yes	maximal, complemented
7	C₂×#19151458	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic
9	#19152073	—	2	16	no	—
10	C₂×D₄×Dic₈₉	C₂²	1	16	yes	—
11	C₂×#15667971	C₂²	1	4	yes	—
12	C₂²×C₄⋊Dic₈₉	C₂²	1	8	yes	complemented
13	C₂²×C₂²⋊Dic₈₉	C₂²	1	8	yes	—
14	#19151497	C₂²	1	16	yes	complemented
15	#19151473	C₂²	1	32	yes	complemented
16	#19151468	C₂²	1	4	yes	complemented
17	#19151464	C₂²	1	4	yes	complemented
18	#19151458	C₂²	1	4	yes	—
19	#19151458	C₂²	1	4	yes	—
20	#19151458	C₂²	1	8	yes	—
21	#19151458	C₂²	1	8	yes	complemented
22	#19151458	C₂²	1	8	yes	complemented
23	C₄×C₄⋊Dic₈₉	C₂²	1	4	yes	complemented
24	C₄×C₄⋊Dic₈₉	C₂²	1	4	yes	complemented
25	C₂×#15667919	C₂²	1	8	yes	complemented
26	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₄	1	16	yes	complemented
29	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	C₂³×Dic₈₉	C₂³	1	16	yes	—
35	D₄×Dic₈₉	—	2	64	no	—
36	#15667971	—	2	16	no	—
37	C₂×C₄⋊Dic₈₉	—	4	16	no	—
38	C₂×C₄⋊Dic₈₉	C₂³	1	8	yes	—
39	C₂×C₄⋊Dic₈₉	C₂³	1	8	yes	—
40	C₂×C₄⋊Dic₈₉	C₂³	1	8	yes	—
41	C₂×C₄⋊Dic₈₉	C₂³	1	16	yes	—
42	C₂×C₂²⋊Dic₈₉	—	2	32	no	—
43	C₂×C₂²⋊Dic₈₉	C₂³	1	8	yes	—
44	C₂×C₂²⋊Dic₈₉	C₂³	1	16	yes	—
45	C₂×C₄×Dic₈₉	C₂³	1	8	yes	—
46	#15667919	C₂³	1	8	yes	—
47	#15667919	C₂³	1	16	yes	—
48	#15667919	C₂³	1	8	yes	—
49	C₂⁵×C₈₉	C₂³	1	2	yes	—
50	C₂²×D₄×C₈₉	C₂×C₄	1	8	yes	—
51	C₂²×D₄×C₈₉	D₄	1	8	yes	—
52	C₂²×D₄×C₈₉	Q₈	1	8	yes	—
53	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
54	C₂³×C₄×C₈₉	—	4	8	no	—
55	C₂³×C₄×C₈₉	C₂×C₄	1	16	yes	complemented
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₈₉	C₂×C₄	1	32	yes	complemented
63	C₄×D₄×C₈₉	C₂×C₄	1	32	yes	complemented
64	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	8	yes	complemented
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	16	yes	complemented
67	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
68	C₂×C₄²×C₈₉	C₂×C₄	1	8	yes	complemented
69	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
71	C₂²×Dic₈₉	—	2	32	no	—
72	C₂²×Dic₈₉	—	4	16	no	—
73	C₂²×Dic₈₉	—	4	16	no	—
74	C₂²×Dic₈₉	C₂⁴	1	16	yes	—
75	C₄⋊Dic₈₉	—	2	16	no	—
76	C₄⋊Dic₈₉	—	2	16	no	—
77	C₄⋊Dic₈₉	—	4	16	no	—
78	C₄⋊Dic₈₉	—	4	8	no	—
79	C₂²⋊Dic₈₉	—	2	16	no	—
80	C₂²⋊Dic₈₉	—	2	32	no	—
81	C₄×Dic₈₉	—	2	16	no	—
82	C₂⁴×C₈₉	—	4	4	no	—
83	C₂⁴×C₈₉	—	4	4	no	—
84	C₂⁴×C₈₉	C₂²×C₄	1	8	yes	—
85	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
86	C₂⁴×C₈₉	C₂×Q₈	1	8	yes	—
87	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
88	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
89	C₂×D₄×C₈₉	C₄⋊C₄	1	64	yes	complemented
90	C₂×D₄×C₈₉	C₂²×C₄	1	16	yes	—
91	C₂×D₄×C₈₉	C₂×D₄	1	16	yes	—
92	C₂×D₄×C₈₉	C₂×Q₈	1	16	yes	—
93	C₂²×C₄×C₈₉	—	2	4	no	—
94	C₂²×C₄×C₈₉	—	2	16	no	—
95	C₂²×C₄×C₈₉	—	4	32	no	—
96	C₂²×C₄×C₈₉	—	4	8	no	—
97	C₂²×C₄×C₈₉	—	4	4	no	—
98	C₂²×C₄×C₈₉	—	4	2	no	—
99	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₈₉	C₂²×C₄	1	16	yes	—
101	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₈₉	C₂²×C₄	1	16	yes	—
104	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₈₉	C₂²×C₄	1	16	yes	—
113	C₂²⋊C₄×C₈₉	C₂²×C₄	1	32	yes	—
114	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
115	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
116	C₂³×C₈₉	—	2	2	no	—
117	C₂³×C₈₉	—	2	8	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	—	2	8	no	—
120	C₂³×C₈₉	—	4	8	no	—
121	C₂³×C₈₉	—	4	8	no	—
122	C₂³×C₈₉	—	4	16	no	—
123	C₂³×C₈₉	—	4	16	no	—
124	C₂³×C₈₉	C₂×C₄⋊C₄	1	32	yes	complemented
125	C₂³×C₈₉	C₂³×C₄	1	8	yes	—
126	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
127	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
128	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
129	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
130	C₂³×C₈₉	C₂²×Q₈	1	8	yes	—
131	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
132	D₄×C₈₉	C₂×C₄⋊C₄	1	64	yes	complemented
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	8	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	8	no	—
137	C₂×C₄×C₈₉	—	2	32	no	—
138	C₂×C₄×C₈₉	—	4	16	no	—
139	C₂×C₄×C₈₉	—	4	8	no	—
140	C₂×C₄×C₈₉	—	4	4	no	—
141	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	16	yes	complemented
142	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
144	C₂×C₄×C₈₉	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
147	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
149	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
150	C₂×Dic₈₉	—	2	16	no	—
151	C₂×Dic₈₉	—	2	16	no	—
152	C₂×Dic₈₉	—	2	16	no	—
153	C₂×Dic₈₉	—	8	32	no	—
154	C₂²×C₈₉	—	2	2	no	—
155	C₂²×C₈₉	—	2	8	no	—
156	C₂²×C₈₉	—	2	2	no	—
157	C₂²×C₈₉	—	2	8	no	—
158	C₂²×C₈₉	—	2	16	no	—
159	C₂²×C₈₉	—	2	4	no	—
160	C₂²×C₈₉	—	2	4	no	—
161	C₂²×C₈₉	—	2	16	no	—
162	C₂²×C₈₉	—	4	32	no	—
163	C₂²×C₈₉	C₂²×C₄⋊C₄	1	4	yes	—
164	C₂²×C₈₉	C₂²×C₄⋊C₄	1	16	yes	—
165	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
166	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
167	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
168	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₈₉	#585	1	2	yes	—
170	C₄×C₈₉	—	2	2	no	—
171	C₄×C₈₉	—	2	8	no	—
172	C₄×C₈₉	—	2	4	no	—
173	C₄×C₈₉	C₂²×C₄⋊C₄	1	8	yes	—
174	C₄×C₈₉	#518	1	4	yes	complemented
175	Dic₈₉	—	4	16	no	—
176	#34181	—	89	1	no	maximal, Sylow
177	C₂×C₈₉	—	2	4	no	—
178	C₂×C₈₉	—	2	16	no	—
179	C₂×C₈₉	C₂³×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
181	C₂×C₈₉	#3428	1	1	yes	characteristic
182	C₂×C₈₉	#3496	1	2	yes	—
183	C₂×C₈₉	#3501	1	2	yes	—
184	C₂×#518	—	89	2	no	—
185	C₂²×C₄×D₄	D₈₉	1	1	yes	characteristic
186	#2349	—	89	8	no	—
187	D₄×C₄⋊C₄	—	89	8	no	—
188	#2316	—	89	2	no	—
189	#2315	—	89	4	no	—
190	#2285	—	89	2	no	—
191	C₂×#380	—	89	4	no	—
192	C₈₉	#34181	1	1	yes	characteristic, complemented, Sylow
193	C₂³×D₄	C₂×D₈₉	1	1	yes	characteristic
194	C₂⁴×C₄	C₂×D₈₉	1	2	yes	—
195	#518	—	178	16	no	—
196	C₂×C₄×D₄	—	89	16	no	—
197	C₂×C₄×D₄	Dic₈₉	1	16	yes	complemented
198	C₂×C₄×D₄	C₂×D₈₉	1	4	yes	—
199	C₂×C₄×D₄	C₂×D₈₉	1	4	yes	—
200	C₂×#117	—	89	4	no	—
201	C₂²×C₄⋊C₄	—	89	8	no	—
202	C₂²×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
203	C₂²×C₂²⋊C₄	—	89	8	no	—
204	C₂²×C₂²⋊C₄	C₂×D₈₉	1	2	yes	—
205	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
206	#389	—	89	16	no	—
207	#385	—	89	32	no	—
208	#384	—	89	4	no	—
209	#382	—	89	4	no	—
210	#380	—	89	4	no	—
211	#380	—	89	8	no	—
212	#380	—	89	8	no	—
213	#380	—	89	8	no	—
214	#380	—	89	4	no	—
215	C₄×C₄⋊C₄	—	89	4	no	—
216	C₄×C₄⋊C₄	—	89	4	no	—
217	C₂×#95	—	89	8	no	—
218	C₂⁵	C₂²×D₈₉	1	2	yes	—
219	C₂²×D₄	Dic₁₇₈	1	8	yes	—
220	C₂²×D₄	D₃₅₆	1	8	yes	—
221	C₂²×D₄	C₂×Dic₈₉	1	8	yes	—
222	C₂²×D₄	C₂²×D₈₉	1	4	yes	—
223	C₂³×C₄	—	4	8	no	—
224	C₂³×C₄	—	89	16	no	—
225	C₂³×C₄	C₂×Dic₈₉	1	16	yes	complemented
226	C₂³×C₄	C₂²×D₈₉	1	4	yes	—
227	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₈₉	1	2	yes	—
230	C₂³×C₄	C₂²×D₈₉	1	4	yes	—
231	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
232	C₄×D₄	—	178	64	no	—
233	C₄×D₄	C₂×Dic₈₉	1	32	yes	complemented
234	C₄×D₄	C₂×Dic₈₉	1	32	yes	complemented
235	#117	—	178	16	no	—
236	C₂×C₄⋊C₄	—	89	16	no	—
237	C₂×C₄⋊C₄	—	89	8	no	—
238	C₂×C₄⋊C₄	—	89	8	no	—
239	C₂×C₄⋊C₄	—	89	8	no	—
240	C₂×C₄⋊C₄	—	356	16	no	—
241	C₂×C₄⋊C₄	C₂×Dic₈₉	1	8	yes	complemented
242	C₂×C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
243	C₂×C₂²⋊C₄	—	89	8	no	—
244	C₂×C₂²⋊C₄	—	89	16	no	—
245	C₂×C₂²⋊C₄	—	178	32	no	—
246	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	16	yes	complemented
247	C₂×C₂²⋊C₄	C₂²×D₈₉	1	8	yes	—
248	C₂×C₄²	—	89	8	no	—
249	C₂×C₄²	C₂×Dic₈₉	1	8	yes	complemented
250	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
251	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
252	#95	—	89	8	no	—
253	#95	—	89	16	no	—
254	#95	—	89	8	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	C₂²×Dic₈₉	1	8	yes	—
258	C₂⁴	C₂×D₃₅₆	1	8	yes	—
259	C₂⁴	C₂×Dic₁₇₈	1	8	yes	—
260	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
261	C₂⁴	C₂³×D₈₉	1	4	yes	—
262	C₂×D₄	C₄⋊Dic₈₉	1	64	yes	complemented
263	C₂×D₄	C₂²×Dic₈₉	1	16	yes	—
264	C₂×D₄	C₂×D₃₅₆	1	16	yes	—
265	C₂×D₄	C₂×Dic₁₇₈	1	16	yes	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	4	32	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	8	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	89	16	no	—
273	C₂²×C₄	—	356	16	no	—
274	C₂²×C₄	—	356	16	no	—
275	C₂²×C₄	—	178	32	no	—
276	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
277	C₂²×C₄	C₂²×Dic₈₉	1	16	yes	—
278	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
279	C₂²×C₄	C₂²×Dic₈₉	1	8	yes	—
280	C₂²×C₄	C₂²×Dic₈₉	1	16	yes	—
281	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
282	C₂²×C₄	C₂×D₃₅₆	1	4	yes	—
283	C₂²×C₄	C₂×Dic₁₇₈	1	4	yes	—
284	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₈₉	1	2	yes	—
286	C₂²×C₄	C₂³×D₈₉	1	4	yes	—
287	C₂²×C₄	C₂³×D₈₉	1	2	yes	—
288	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
289	C₄⋊C₄	—	356	16	no	—
290	C₄⋊C₄	—	356	8	no	—
291	C₄⋊C₄	—	178	16	no	—
292	C₄⋊C₄	—	178	16	no	—
293	C₄⋊C₄	C₂²×Dic₈₉	1	16	yes	—
294	C₂²⋊C₄	—	178	16	no	—
295	C₂²⋊C₄	—	178	32	no	—
296	C₂²⋊C₄	C₂²×Dic₈₉	1	32	yes	—
297	C₄²	—	178	16	no	—
298	C₄²	C₂²×Dic₈₉	1	8	yes	—
299	C₄²	C₂²×Dic₈₉	1	8	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	4	8	no	—
305	C₂³	—	4	8	no	—
306	C₂³	—	4	16	no	—
307	C₂³	—	4	16	no	—
308	C₂³	C₂×C₄⋊Dic₈₉	1	32	yes	complemented
309	C₂³	C₂³×Dic₈₉	1	8	yes	—
310	C₂³	C₂³×Dic₈₉	1	2	yes	—
311	C₂³	C₂²×D₃₅₆	1	2	yes	—
312	C₂³	C₂²×D₃₅₆	1	8	yes	—
313	C₂³	C₂²×Dic₁₇₈	1	2	yes	—
314	C₂³	C₂²×Dic₁₇₈	1	8	yes	—
315	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
316	D₄	C₂×C₄⋊Dic₈₉	1	64	yes	complemented
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	32	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	178	16	no	—
326	C₂×C₄	—	178	16	no	—
327	C₂×C₄	—	178	16	no	—
328	C₂×C₄	—	712	32	no	—
329	C₂×C₄	C₂×C₄⋊Dic₈₉	1	16	yes	complemented
330	C₂×C₄	C₂³×Dic₈₉	1	4	yes	—
331	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
332	C₂×C₄	C₂³×Dic₈₉	1	8	yes	—
333	C₂×C₄	C₂³×Dic₈₉	1	4	yes	—
334	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
335	C₂×C₄	C₂²×D₃₅₆	1	4	yes	—
336	C₂×C₄	C₂²×Dic₁₇₈	1	4	yes	—
337	C₂×C₄	#15668057	1	4	yes	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	16	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	4	32	no	—
347	C₂²	C₂²×C₄⋊Dic₈₉	1	4	yes	—
348	C₂²	C₂²×C₄⋊Dic₈₉	1	16	yes	—
349	C₂²	C₂⁴×Dic₈₉	1	1	yes	characteristic
350	C₂²	C₂³×D₃₅₆	1	1	yes	characteristic
351	C₂²	C₂³×Dic₁₇₈	1	1	yes	characteristic
352	C₂²	C₂×#15668057	1	2	yes	—
353	C₂²	#19152434	1	2	yes	—
354	C₄	—	2	2	no	—
355	C₄	—	2	8	no	—
356	C₄	—	2	4	no	—
357	C₄	—	356	16	no	—
358	C₄	C₂²×C₄⋊Dic₈₉	1	8	yes	—
359	C₄	#19152073	1	4	yes	complemented
360	C₂	—	2	4	no	—
361	C₂	—	2	16	no	—
362	C₂	C₂³×C₄⋊Dic₈₉	1	1	yes	characteristic
363	C₂	C₂×#19152073	1	1	yes	characteristic
364	C₂	#26033455	1	1	yes	characteristic
365	C₂	#26034016	1	2	yes	—
366	C₂	#26034055	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₂²×C₄×D₄×C₈₉	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂³×D₄×C₈₉	C₂²
hypercenter	C₂²×C₄×D₄	D₈₉
hypocenter	C₈₉	#34181
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #26023162	C₂	semidirect
3. D₄×C₄⋊Dic₈₉	C₂	semidirect
4. #26022870	C₂	semidirect
5. #26022866	C₂	semidirect
6. #26022659	C₂	semidirect
7. C₂×#19151458	C₂	semidirect
12. C₂²×C₄⋊Dic₈₉	C₂²	semidirect
14. #19151497	C₂²	semidirect
15. #19151473	C₂²	semidirect
16. #19151468	C₂²	semidirect
17. #19151464	C₂²	semidirect
21. #19151458	C₂²	semidirect
22. #19151458	C₂²	semidirect
23. C₄×C₄⋊Dic₈₉	C₂²	semidirect
24. C₄×C₄⋊Dic₈₉	C₂²	semidirect
25. C₂×#15667919	C₂²	semidirect
28. C₂×C₄×D₄×C₈₉	C₄	semidirect
55. C₂³×C₄×C₈₉	C₂×C₄	semidirect
62. C₄×D₄×C₈₉	C₂×C₄	semidirect
63. C₄×D₄×C₈₉	C₂×C₄	semidirect
64. C₂×C₄⋊C₄×C₈₉	C₂×C₄	semidirect
66. C₂×C₂²⋊C₄×C₈₉	C₂×C₄	semidirect
68. C₂×C₄²×C₈₉	C₂×C₄	semidirect
89. C₂×D₄×C₈₉	C₄⋊C₄	semidirect
124. C₂³×C₈₉	C₂×C₄⋊C₄	semidirect
132. D₄×C₈₉	C₂×C₄⋊C₄	semidirect
141. C₂×C₄×C₈₉	C₂×C₄⋊C₄	semidirect
174. C₄×C₈₉	#518	semidirect
192. C₈₉	#34181	semidirect
197. C₂×C₄×D₄	Dic₈₉	semidirect
225. C₂³×C₄	C₂×Dic₈₉	semidirect
233. C₄×D₄	C₂×Dic₈₉	semidirect
234. C₄×D₄	C₂×Dic₈₉	semidirect
241. C₂×C₄⋊C₄	C₂×Dic₈₉	semidirect
246. C₂×C₂²⋊C₄	C₂×Dic₈₉	semidirect
249. C₂×C₄²	C₂×Dic₈₉	semidirect
262. C₂×D₄	C₄⋊Dic₈₉	semidirect
308. C₂³	C₂×C₄⋊Dic₈₉	semidirect
316. D₄	C₂×C₄⋊Dic₈₉	semidirect
329. C₂×C₄	C₂×C₄⋊Dic₈₉	semidirect
359. C₄	#19152073	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152073	2
#26023162	2
D₄×C₄⋊Dic₈₉	2
#26022870	2
#26022866	2
#26022659	2
C₂×#19151458	2
C₂²×C₄×D₄×C₈₉	2
#34181	89