Subgroups — #36444191

Order 22784.

610 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151655	C₂	1	1	yes	maximal, characteristic
2	#26022659	C₂	1	1	yes	maximal, characteristic
3	#26018107	C₂	1	4	yes	maximal, complemented
4	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667971	C₄	1	2	yes	—
6	#19151655	—	2	1	no	—
7	#19151655	—	2	1	no	—
8	#19151655	C₄	1	2	yes	complemented
9	#19151655	C₂²	1	2	yes	—
10	C₂×C₄⋊#10623494	C₄	1	2	yes	complemented
11	C₂×C₂²⋊#10623494	—	2	1	no	—
12	C₂×#15667923	—	2	1	no	—
13	#19151468	—	2	1	no	—
14	#19151464	—	2	1	no	—
15	#19151458	—	2	1	no	—
16	#19151458	—	2	1	no	—
17	C₄×C₄⋊Dic₈₉	C₄	1	2	yes	—
18	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
20	#432×C₈₉	—	2	1	no	—
21	#432×C₈₉	—	2	1	no	—
22	#432×C₈₉	C₄	1	2	yes	complemented
23	#432×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
26	C₂×#97×C₈₉	C₄	1	2	yes	complemented
27	C₂²×#10623494	—	2	2	no	—
28	#15667971	—	4	4	no	—
29	C₂×C₄⋊Dic₈₉	—	2	2	no	—
30	C₂×C₄⋊Dic₈₉	—	2	2	no	—
31	C₂×C₄⋊Dic₈₉	—	2	2	no	—
32	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
33	C₂×C₄×Dic₈₉	C₂×C₄	1	4	yes	—
34	C₄⋊#10623494	—	2	2	no	—
35	C₄⋊#10623494	C₂×C₄	1	4	yes	—
36	C₂²⋊#10623494	—	2	2	no	—
37	C₂²⋊#10623494	—	2	2	no	—
38	#15667923	—	2	2	no	—
39	#15667923	—	2	2	no	—
40	#15667919	—	2	2	no	—
41	#15667919	—	2	2	no	—
42	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	—	2	2	no	—
46	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₈₉	—	2	2	no	—
59	C₄⋊C₈×C₈₉	—	2	2	no	—
60	C₂²⋊C₈×C₈₉	—	2	2	no	—
61	C₂²⋊C₈×C₈₉	—	2	2	no	—
62	#97×C₈₉	—	2	2	no	—
63	#97×C₈₉	C₂×C₄	1	4	yes	—
64	C₂²×Dic₈₉	—	2	4	no	—
65	C₂×#10623494	—	2	4	no	—
66	C₂×#10623494	—	4	4	no	—
67	C₄⋊Dic₈₉	—	4	4	no	—
68	C₄⋊Dic₈₉	—	4	4	no	—
69	C₄⋊Dic₈₉	—	4	4	no	—
70	C₂²⋊Dic₈₉	—	4	4	no	—
71	C₄×Dic₈₉	—	4	4	no	—
72	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₈₉	—	2	2	no	—
74	C₂²×C₄×C₈₉	—	2	2	no	—
75	C₂²×C₄×C₈₉	—	4	2	no	—
76	C₂²×C₄×C₈₉	—	4	2	no	—
77	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₈₉	—	2	4	no	—
96	C₂×C₈×C₈₉	—	4	4	no	—
97	C₄²×C₈₉	C₄²	1	1	yes	characteristic
98	C₄²×C₈₉	C₄²	1	1	yes	characteristic
99	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
113	C₂³×C₈₉	—	4	1	no	—
114	C₂³×C₈₉	—	4	1	no	—
115	C₂³×C₈₉	#95	1	1	yes	characteristic
116	C₂³×C₈₉	#95	1	1	yes	characteristic
117	C₂³×C₈₉	#100	1	2	yes	—
118	C₂³×C₈₉	#101	1	2	yes	—
119	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₈₉	—	2	2	no	—
121	C₂×C₄×C₈₉	—	2	2	no	—
122	C₂×C₄×C₈₉	—	2	2	no	—
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	2	2	no	—
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	4	1	no	—
135	C₂×C₄×C₈₉	—	4	1	no	—
136	C₂×C₄×C₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	1	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₈₉	—	4	4	no	—
153	C₂×Dic₈₉	—	4	4	no	—
154	C₂×Dic₈₉	—	4	4	no	—
155	C₈×C₈₉	—	4	4	no	—
156	#10623494	—	4	4	no	—
157	C₂²×C₈₉	—	2	1	no	—
158	C₂²×C₈₉	—	2	1	no	—
159	C₂²×C₈₉	—	2	1	no	—
160	C₂²×C₈₉	—	2	1	no	—
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	4	2	no	—
164	C₂²×C₈₉	—	4	2	no	—
165	C₂²×C₈₉	#343	1	2	yes	—
166	C₂²×C₈₉	#343	1	2	yes	—
167	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
168	C₂²×C₈₉	C₂×#100	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×#101	1	1	yes	characteristic
170	C₄×C₈₉	—	2	1	no	—
171	C₄×C₈₉	—	2	1	no	—
172	C₄×C₈₉	—	2	1	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	H(3,ℤ/4)	1	2	yes	—
181	C₄×C₈₉	#421	1	2	yes	—
182	Dic₈₉	—	8	4	no	—
183	#7952	—	89	1	no	maximal, Sylow
184	C₂×C₈₉	—	2	1	no	—
185	C₂×C₈₉	—	2	2	no	—
186	C₂×C₈₉	—	2	2	no	—
187	C₂×C₈₉	—	2	1	no	—
188	C₂×C₈₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
189	C₂×C₈₉	#1733	1	1	yes	characteristic
190	C₂×C₈₉	C₂×#343	1	1	yes	characteristic
191	C₂×#432	—	89	1	no	—
192	C₂×#432	D₈₉	1	1	yes	characteristic
193	#2285	—	89	1	no	—
194	#1285	—	89	4	no	—
195	C₈₉	#7952	1	1	yes	characteristic, complemented, Sylow
196	C₂×#117	—	89	2	no	—
197	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
198	#432	—	2	1	no	—
199	#432	—	2	1	no	—
200	#432	—	89	2	no	—
201	#432	—	89	2	no	—
202	#432	—	178	1	no	—
203	#432	—	178	1	no	—
204	#432	Dic₈₉	1	2	yes	complemented
205	#432	C₂×D₈₉	1	2	yes	—
206	C₂×C₄⋊C₈	—	2	1	no	—
207	C₂×C₄⋊C₈	—	89	2	no	—
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	C₂×C₂²⋊C₈	—	178	1	no	—
210	C₂×#97	—	178	1	no	—
211	C₂×#97	Dic₈₉	1	2	yes	complemented
212	#384	—	178	1	no	—
213	#382	—	178	1	no	—
214	#380	—	178	1	no	—
215	#380	—	178	1	no	—
216	C₄×C₄⋊C₄	—	89	2	no	—
217	C₄×C₄⋊C₄	—	89	2	no	—
218	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
219	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	178	2	no	—
223	#117	—	356	4	no	—
224	C₂×C₄⋊C₄	—	178	2	no	—
225	C₂×C₄⋊C₄	—	178	2	no	—
226	C₂×C₄⋊C₄	—	178	2	no	—
227	C₂×C₂²⋊C₄	—	178	2	no	—
228	C₂×C₄²	—	89	4	no	—
229	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
230	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
234	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	89	4	no	—
244	C₄⋊C₈	—	178	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	178	2	no	—
248	C₂²⋊C₈	—	178	2	no	—
249	#97	—	2	2	no	—
250	#97	—	178	2	no	—
251	#97	—	178	2	no	—
252	#97	C₂×Dic₈₉	1	4	yes	—
253	#95	—	178	2	no	—
254	#95	—	178	2	no	—
255	C₂⁴	#13083551	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	178	4	no	—
261	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
263	C₂²×C₄	#13083551	1	1	yes	characteristic
264	C₂²×C₄	#13083551	1	1	yes	characteristic
265	C₂²×C₄	#13083551	1	1	yes	characteristic
266	C₂²×C₄	#13083551	1	1	yes	characteristic
267	C₂²×C₄	#13083551	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
270	C₂²×C₄	#13083553	1	1	yes	characteristic
271	C₂²×C₄	#13083553	1	1	yes	characteristic
272	C₂²×C₄	#13083553	1	1	yes	characteristic
273	C₂²×C₄	#13083553	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₂×C₈	—	356	4	no	—
282	C₂×C₈	—	178	4	no	—
283	C₄⋊C₄	—	356	4	no	—
284	C₄⋊C₄	—	356	4	no	—
285	C₄⋊C₄	—	356	4	no	—
286	C₂²⋊C₄	—	356	4	no	—
287	C₄²	—	356	4	no	—
288	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
289	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
290	C₄²	#13083551	1	1	yes	characteristic
291	C₄²	#13083551	1	1	yes	characteristic
292	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
293	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
294	C₄²	#13083553	1	1	yes	characteristic
295	C₄²	#13083553	1	1	yes	characteristic
296	C₄²	#13083553	1	1	yes	characteristic
297	C₄²	#13083553	1	1	yes	characteristic
298	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
299	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
301	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
303	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	#15667919	1	1	yes	characteristic
307	C₂³	#15667919	1	1	yes	characteristic
308	C₂³	#15667928	1	2	yes	—
309	C₂³	#15667930	1	2	yes	—
310	C₂³	C₂×#13083551	1	1	yes	characteristic
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	356	4	no	—
332	C₂×C₄	—	356	4	no	—
333	C₂×C₄	—	356	4	no	—
334	C₂×C₄	#15667919	1	1	yes	characteristic
335	C₂×C₄	#15667919	1	1	yes	characteristic
336	C₂×C₄	#15667919	1	1	yes	characteristic
337	C₂×C₄	#15667919	1	1	yes	characteristic
338	C₂×C₄	#15667919	1	1	yes	characteristic
339	C₂×C₄	#15667919	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
341	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
343	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
344	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	356	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	#19151366	1	2	yes	—
357	C₂²	#19151366	1	2	yes	—
358	C₂²	C₂×#15667919	1	1	yes	characteristic
359	C₂²	C₂×#15667928	1	1	yes	characteristic
360	C₂²	C₂×#15667930	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	712	4	no	—
372	C₄	#19151354	1	2	yes	—
373	C₄	#19151614	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	1	no	—
378	C₂	C₂×#19151354	1	1	yes	characteristic
379	C₂	#26019963	1	1	yes	characteristic
380	C₂	C₂×#19151366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667919
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×#432×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#95
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×#432	D₈₉
hypocenter	C₈₉	#7952
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #26018107	C₂	semidirect
8. #19151655	C₄	semidirect
10. C₂×C₄⋊#10623494	C₄	semidirect
22. #432×C₈₉	C₄	semidirect
26. C₂×#97×C₈₉	C₄	semidirect
195. C₈₉	#7952	semidirect
204. #432	Dic₈₉	semidirect
211. C₂×#97	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151655	2
#26022659	2
#26018107	2
C₂×#432×C₈₉	2
#7952	89