Subgroups — #36520012

Order 22784.

914 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151651	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#13083558	C₂	1	1	yes	maximal, characteristic
3	#26018536	C₂	1	4	yes	maximal, complemented
4	#26018533	C₂	1	4	yes	maximal, complemented
5	C₈×#13083558	C₂	1	4	yes	maximal, complemented
6	C₂×#431×C₈₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×#13083558	C₄	1	2	yes	—
8	#19151651	C₄	1	2	yes	—
9	#19151651	C₄	1	2	yes	—
10	#19151651	C₂²	1	2	yes	—
11	#19151651	C₂²	1	2	yes	—
12	C₂×C₄⋊#10623494	C₄	1	2	yes	—
13	C₂×C₂²⋊#10623494	C₄	1	2	yes	—
14	C₄×#13083558	C₄	1	2	yes	—
15	C₄×#13083558	C₄	1	2	yes	—
16	C₄×#13083558	C₂²	1	2	yes	—
17	C₄×#13083558	C₂²	1	2	yes	—
18	C₂×#15667923	C₄	1	2	yes	—
19	C₂×C₄×#10623494	C₂²	1	2	yes	—
20	C₂×C₄×#10623494	C₂²	1	2	yes	—
21	#19151320	C₂²	1	8	yes	complemented
22	C₈×#10623494	C₂²	1	8	yes	complemented
23	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
24	#431×C₈₉	C₄	1	2	yes	—
25	#431×C₈₉	C₄	1	2	yes	—
26	#431×C₈₉	C₂²	1	2	yes	—
27	#431×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₈₉	C₄	1	2	yes	—
29	C₂×C₂²⋊C₈×C₈₉	C₄	1	2	yes	—
30	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
31	C₂×#13083558	C₈	1	16	yes	complemented
32	C₂×#13083558	C₂×C₄	1	4	yes	—
33	C₂×#13083558	C₂×C₄	1	4	yes	—
34	C₂²×#10623494	C₂×C₄	1	4	yes	—
35	C₂²×#10623494	C₂×C₄	1	4	yes	—
36	C₄⋊#10623494	C₂×C₄	1	4	yes	—
37	C₄⋊#10623494	C₂×C₄	1	4	yes	—
38	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
39	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
40	#15667923	C₂×C₄	1	4	yes	—
41	#15667923	C₂×C₄	1	4	yes	—
42	C₄×#10623494	C₂×C₄	1	4	yes	—
43	C₄×#10623494	C₂×C₄	1	4	yes	—
44	C₄×#10623494	C₂³	1	4	yes	—
45	C₄×#10623494	C₂³	1	4	yes	—
46	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
63	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
64	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
65	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
66	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₈₉	C₂³	1	4	yes	—
68	#13083558	C₂×C₈	1	16	yes	complemented
69	#13083558	C₂×C₈	1	16	yes	complemented
70	C₂×#10623494	—	4	4	no	—
71	C₂×#10623494	C₂×C₈	1	16	yes	complemented
72	C₂×#10623494	C₂²×C₄	1	8	yes	—
73	C₂×#10623494	C₂²×C₄	1	8	yes	—
74	C₂⁴×C₈₉	C₄²	1	1	yes	characteristic
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	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₂×C₈	1	8	yes	—
87	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₈₉	—	4	4	no	—
97	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
98	C₄²×C₈₉	C₄²	1	1	yes	characteristic
99	C₄²×C₈₉	C₄²	1	1	yes	characteristic
100	C₄²×C₈₉	C₄²	1	1	yes	characteristic
101	C₄²×C₈₉	C₄²	1	1	yes	characteristic
102	C₄²×C₈₉	C₄²	1	1	yes	characteristic
103	C₄²×C₈₉	C₄²	1	1	yes	characteristic
104	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₈₉	C₂²×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	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
114	C₂³×C₈₉	—	4	1	no	—
115	C₂³×C₈₉	—	4	1	no	—
116	C₂³×C₈₉	C₄×C₈	1	4	yes	—
117	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
118	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
119	C₂³×C₈₉	C₂×C₄²	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	2	no	—
125	C₂×C₄×C₈₉	—	2	2	no	—
126	C₂×C₄×C₈₉	—	4	1	no	—
127	C₂×C₄×C₈₉	—	4	1	no	—
128	C₂×C₄×C₈₉	—	4	1	no	—
129	C₂×C₄×C₈₉	—	4	1	no	—
130	C₂×C₄×C₈₉	—	4	1	no	—
131	C₂×C₄×C₈₉	—	4	1	no	—
132	C₂×C₄×C₈₉	C₄×C₈	1	4	yes	—
133	C₂×C₄×C₈₉	C₄×C₈	1	4	yes	—
134	C₂×C₄×C₈₉	C₄×C₈	1	4	yes	—
135	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
145	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
147	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
150	C₈×C₈₉	—	2	8	no	—
151	#10623494	—	2	8	no	—
152	#10623494	C₂²×C₈	1	16	yes	—
153	C₂²×C₈₉	—	2	1	no	—
154	C₂²×C₈₉	—	2	1	no	—
155	C₂²×C₈₉	—	2	1	no	—
156	C₂²×C₈₉	—	2	1	no	—
157	C₂²×C₈₉	—	2	1	no	—
158	C₂²×C₈₉	—	2	1	no	—
159	C₂²×C₈₉	—	4	4	no	—
160	C₂²×C₈₉	C₂×C₄×C₈	1	2	yes	—
161	C₂²×C₈₉	C₂×C₄×C₈	1	2	yes	—
162	C₂²×C₈₉	C₂×C₄×C₈	1	2	yes	—
163	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
164	C₄×C₈₉	—	2	1	no	—
165	C₄×C₈₉	—	2	1	no	—
166	C₄×C₈₉	—	2	1	no	—
167	C₄×C₈₉	—	2	1	no	—
168	C₄×C₈₉	—	2	1	no	—
169	C₄×C₈₉	—	2	1	no	—
170	C₄×C₈₉	C₂×C₄×C₈	1	2	yes	—
171	C₄×C₈₉	C₂×C₄×C₈	1	2	yes	—
172	C₄×C₈₉	C₂×C₄×C₈	1	2	yes	—
173	C₄×C₈₉	C₂³×C₈	1	2	yes	—
174	C₄×C₈₉	#568	1	2	yes	—
175	C₄×C₈₉	#568	1	2	yes	—
176	#17314	—	89	1	no	maximal, Sylow
177	C₂×C₈₉	—	2	2	no	—
178	C₂×C₈₉	—	2	2	no	—
179	C₂×C₈₉	—	2	2	no	—
180	C₂×C₈₉	C₂²×C₄×C₈	1	1	yes	characteristic
181	C₂×C₈₉	#2873	1	1	yes	characteristic
182	C₂×C₈₉	#2873	1	1	yes	characteristic
183	C₂×#431	—	89	1	no	—
184	C₂×#431	D₈₉	1	1	yes	characteristic
185	C₂×C₄×M₁₆	—	89	1	no	—
186	#1450	—	89	4	no	—
187	C₈×M₁₆	—	89	4	no	—
188	C₈×M₁₆	—	89	4	no	—
189	C₈₉	#17314	1	1	yes	characteristic, complemented, Sylow
190	C₂²×M₁₆	—	89	2	no	—
191	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
192	#431	—	89	2	no	—
193	#431	—	89	2	no	—
194	#431	—	89	2	no	—
195	#431	—	89	2	no	—
196	#431	Dic₈₉	1	2	yes	—
197	#431	Dic₈₉	1	2	yes	—
198	#431	C₂×D₈₉	1	2	yes	—
199	#431	C₂×D₈₉	1	2	yes	—
200	C₂×C₄⋊C₈	—	89	2	no	—
201	C₂×C₄⋊C₈	Dic₈₉	1	2	yes	—
202	C₂×C₂²⋊C₈	—	89	2	no	—
203	C₂×C₂²⋊C₈	Dic₈₉	1	2	yes	—
204	C₄×M₁₆	—	89	2	no	—
205	C₄×M₁₆	—	89	2	no	—
206	C₄×M₁₆	—	89	2	no	—
207	C₄×M₁₆	—	89	2	no	—
208	C₂×#97	—	89	2	no	—
209	C₂×C₄×C₈	—	89	2	no	—
210	C₂×C₄×C₈	—	89	2	no	—
211	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
212	#322	—	89	8	no	—
213	C₈²	—	89	8	no	—
214	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
215	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
217	C₂×M₁₆	—	89	16	no	—
218	C₂×M₁₆	—	89	4	no	—
219	C₂×M₁₆	—	89	4	no	—
220	C₂²×C₈	—	89	4	no	—
221	C₂²×C₈	—	89	4	no	—
222	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
223	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
235	C₄⋊C₈	—	89	4	no	—
236	C₄⋊C₈	—	89	4	no	—
237	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
238	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
239	C₂²⋊C₈	—	89	4	no	—
240	C₂²⋊C₈	—	89	4	no	—
241	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
242	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
243	#97	—	89	4	no	—
244	#97	—	89	4	no	—
245	C₄×C₈	—	89	4	no	—
246	C₄×C₈	—	89	4	no	—
247	C₄×C₈	—	89	4	no	—
248	C₄×C₈	—	89	4	no	—
249	C₄×C₈	C₂×Dic₈₉	1	4	yes	—
250	C₄×C₈	C₂²×D₈₉	1	4	yes	—
251	C₂⁴	C₄×Dic₈₉	1	1	yes	characteristic
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
256	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
259	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
260	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
261	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
263	C₂²×C₄	C₈×D₈₉	1	8	yes	—
264	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
273	M₁₆	—	89	16	no	—
274	M₁₆	—	89	16	no	—
275	C₂×C₈	—	4	4	no	—
276	C₂×C₈	—	89	16	no	—
277	C₂×C₈	—	89	8	no	—
278	C₂×C₈	—	89	8	no	—
279	C₂×C₈	—	356	4	no	—
280	C₂×C₈	C₂²×Dic₈₉	1	8	yes	—
281	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
282	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
283	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
284	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
285	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
286	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
287	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
288	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
289	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
290	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
291	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
293	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
294	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
295	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
296	C₄²	C₂³×D₈₉	1	1	yes	characteristic
297	C₂³	—	4	1	no	—
298	C₂³	—	4	1	no	—
299	C₂³	C₈×Dic₈₉	1	4	yes	—
300	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
301	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
302	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	C₈×Dic₈₉	1	4	yes	—
316	C₂×C₄	C₈×Dic₈₉	1	4	yes	—
317	C₂×C₄	C₈×Dic₈₉	1	4	yes	—
318	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
323	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
324	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
327	C₂×C₄	C₂×C₈×D₈₉	1	4	yes	—
328	C₂×C₄	C₂×C₈×D₈₉	1	4	yes	—
329	C₂×C₄	C₂×C₈×D₈₉	1	4	yes	—
330	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
333	C₈	—	2	8	no	—
334	C₈	—	89	16	no	—
335	C₈	—	178	8	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	4	4	no	—
343	C₂²	C₂×C₈×Dic₈₉	1	2	yes	—
344	C₂²	C₂×C₈×Dic₈₉	1	2	yes	—
345	C₂²	C₂×C₈×Dic₈₉	1	2	yes	—
346	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	C₂×C₈×Dic₈₉	1	2	yes	—
354	C₄	C₂×C₈×Dic₈₉	1	2	yes	—
355	C₄	C₂×C₈×Dic₈₉	1	2	yes	—
356	C₄	C₂²×C₈×D₈₉	1	2	yes	—
357	C₄	#19152364	1	2	yes	—
358	C₄	#19152365	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	2	2	no	—
362	C₂	C₂²×C₈×Dic₈₉	1	1	yes	characteristic
363	C₂	#26028670	1	1	yes	characteristic
364	C₂	#26028671	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₈₉
commutator	C₂×C₈₉	C₂²×C₄×C₈
Fitting	C₂×#431×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₄²
prime radical	C₂⁴×C₈₉	C₄²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#431	D₈₉
hypocenter	C₈₉	#17314
LCS	G ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #26018536	C₂	semidirect
4. #26018533	C₂	semidirect
5. C₈×#13083558	C₂	semidirect
21. #19151320	C₂²	semidirect
22. C₈×#10623494	C₂²	semidirect
31. C₂×#13083558	C₈	semidirect
68. #13083558	C₂×C₈	semidirect
69. #13083558	C₂×C₈	semidirect
71. C₂×#10623494	C₂×C₈	semidirect
189. C₈₉	#17314	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151651	2
C₂×C₄×#13083558	2
#26018536	2
#26018533	2
C₈×#13083558	2
C₂×#431×C₈₉	2
#17314	89