Subgroups — #36707619

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152016	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19152014	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028959	C₂	1	1	yes	maximal, characteristic
4	#26022080	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022079	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022078	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022077	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022076	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022075	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022074	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022006	C₂	1	1	yes	maximal, characteristic, complemented
12	#26021864	C₂	1	1	yes	maximal, characteristic, complemented
13	#26021864	C₂	1	1	yes	maximal, characteristic, complemented
14	#346×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668018	C₂²	1	1	yes	characteristic
17	C₂×#15668018	C₂²	1	1	yes	characteristic
18	#19152145	C₄	1	1	yes	characteristic
19	#19152016	—	2	4	no	—
20	#19152014	—	2	4	no	—
21	C₂×#15667952	C₂²	1	1	yes	characteristic
22	C₂×#15667951	C₂²	1	1	yes	characteristic
23	C₂×#15667951	C₂²	1	1	yes	characteristic
24	C₂×#15667951	C₂²	1	1	yes	characteristic
25	C₂×#15667951	C₂²	1	1	yes	characteristic
26	C₂²×#13083549	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
31	#19151676	C₄	1	1	yes	characteristic
32	#19151675	C₄	1	1	yes	characteristic
33	#19151673	C₄	1	1	yes	characteristic
34	#19151673	C₄	1	1	yes	characteristic
35	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
37	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
38	#19151620	C₄	1	1	yes	characteristic
39	#19151563	C₄	1	1	yes	characteristic
40	#19151563	C₄	1	1	yes	characteristic
41	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
42	C₄⋊#13083549	C₂²	1	1	yes	characteristic
43	#19151416	C₂²	1	1	yes	characteristic
44	#19151416	C₂²	1	1	yes	characteristic
45	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
46	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
47	#19151377	C₂²	1	1	yes	characteristic
48	#19151377	C₂²	1	1	yes	characteristic
49	#19151377	C₂²	1	1	yes	characteristic
50	#19151377	C₂²	1	1	yes	characteristic
51	#19151374	C₂²	1	1	yes	characteristic
52	#19151373	C₂²	1	1	yes	characteristic
53	#19151373	C₂²	1	1	yes	characteristic
54	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
55	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
57	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
58	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
60	#346×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
62	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
63	#15668018	—	2	2	no	—
64	#15668018	—	2	2	no	—
65	#15668018	—	2	2	no	—
66	#15668018	—	2	2	no	—
67	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
77	#15668011	C₈	1	1	yes	characteristic
78	#15668008	C₈	1	1	yes	characteristic
79	#15667998	C₈	1	1	yes	characteristic
80	#15667998	C₈	1	1	yes	characteristic
81	#15667987	C₈	1	1	yes	characteristic
82	#15667985	C₈	1	1	yes	characteristic
83	#15667985	C₈	1	1	yes	characteristic
84	#15667983	C₈	1	1	yes	characteristic
85	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
89	#15667952	—	2	2	no	—
90	#15667951	—	2	2	no	—
91	#15667951	—	2	2	no	—
92	#15667951	—	2	2	no	—
93	#15667951	—	2	2	no	—
94	C₂×#13083549	—	2	2	no	—
95	C₂×#13083549	C₂³	1	1	yes	characteristic
96	C₂×#13083549	C₂³	1	1	yes	characteristic
97	C₂×#13083549	C₂³	1	1	yes	characteristic
98	C₂×#13083549	C₂³	1	1	yes	characteristic
99	C₁₆×D₈₉	—	2	2	no	—
100	C₁₆×D₈₉	—	2	2	no	—
101	C₁₆×D₈₉	—	2	2	no	—
102	C₁₆×D₈₉	D₄	1	4	yes	complemented
103	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
104	#15667941	C₂×C₄	1	1	yes	characteristic
105	#15667941	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
108	#15667924	C₂×C₄	1	1	yes	characteristic
109	#15667924	C₂×C₄	1	1	yes	characteristic
110	#15667924	C₂×C₄	1	1	yes	characteristic
111	#15667924	C₂×C₄	1	1	yes	characteristic
112	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
113	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
118	M₃₂×C₈₉	—	2	2	no	—
119	C₂×C₁₆×C₈₉	—	2	2	no	—
120	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
127	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
128	#13083574	—	2	2	no	—
129	#13083574	—	2	2	no	—
130	#13083574	—	2	2	no	—
131	#13083574	—	2	2	no	—
132	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
133	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
134	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
135	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
136	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
142	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
148	#13083558	—	2	2	no	—
149	#13083558	—	2	2	no	—
150	#13083557	—	2	2	no	—
151	#13083557	—	2	2	no	—
152	#13083557	—	2	2	no	—
153	#13083557	—	2	2	no	—
154	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
155	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
156	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
157	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
158	C₈×D₈₉	—	2	2	no	—
159	C₈×D₈₉	—	2	1	no	—
160	C₈×D₈₉	—	2	1	no	—
161	C₈×D₈₉	—	2	1	no	—
162	C₈×D₈₉	—	2	1	no	—
163	C₈×D₈₉	C₂×D₄	1	2	yes	—
164	C₈×D₈₉	#41	1	2	yes	—
165	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
166	#13083553	C₂×C₈	1	1	yes	characteristic
167	#13083553	C₂×C₈	1	1	yes	characteristic
168	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
170	#13083551	C₂×C₈	1	1	yes	characteristic
171	#13083551	C₂×C₈	1	1	yes	characteristic
172	#13083551	C₂×C₈	1	1	yes	characteristic
173	#13083551	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
177	#13083549	—	2	1	no	—
178	#13083549	—	2	1	no	—
179	#13083549	—	2	1	no	—
180	#13083549	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	—	2	1	no	—
188	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
193	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
194	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
195	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₁₆×C₈₉	—	2	1	no	—
197	C₁₆×C₈₉	—	2	1	no	—
198	C₁₆×C₈₉	—	2	1	no	—
199	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
200	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
201	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
202	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
204	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
205	D₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
215	C₂²⋊D₈₉	—	2	2	no	—
216	C₂²⋊D₈₉	—	2	2	no	—
217	C₂²⋊D₈₉	—	2	2	no	—
218	C₂²⋊D₈₉	—	2	2	no	—
219	C₂²⋊D₈₉	—	4	1	no	—
220	C₂²⋊D₈₉	—	4	1	no	—
221	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
222	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
223	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
224	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
225	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
226	D₃₅₆	—	2	2	no	—
227	D₃₅₆	—	2	2	no	—
228	D₃₅₆	—	4	1	no	—
229	C₄×D₈₉	—	2	1	no	—
230	C₄×D₈₉	—	2	1	no	—
231	C₄×D₈₉	—	2	1	no	—
232	C₄×D₈₉	—	2	1	no	—
233	C₄×D₈₉	—	4	1	no	—
234	C₄×D₈₉	—	4	1	no	—
235	C₄×D₈₉	C₄×D₄	1	2	yes	—
236	C₄×D₈₉	#131	1	2	yes	—
237	Dic₁₇₈	—	2	2	no	—
238	Dic₁₇₈	—	2	2	no	—
239	C₈×C₈₉	—	2	1	no	—
240	C₈×C₈₉	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
243	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
244	#10623494	—	2	1	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	2	1	no	—
247	#10623494	C₄×D₄	1	2	yes	—
248	C₂²×C₈₉	—	2	1	no	—
249	C₂²×C₈₉	—	2	1	no	—
250	C₂²×C₈₉	—	2	1	no	—
251	C₂²×C₈₉	—	2	1	no	—
252	C₂²×C₈₉	—	2	1	no	—
253	C₂²×C₈₉	—	2	1	no	—
254	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
255	C₂×D₈₉	—	2	1	no	—
256	C₂×D₈₉	—	2	1	no	—
257	C₂×D₈₉	—	2	1	no	—
258	C₂×D₈₉	—	2	1	no	—
259	C₂×D₈₉	—	2	1	no	—
260	C₂×D₈₉	—	2	1	no	—
261	C₂×D₈₉	—	2	1	no	—
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	C₈×D₄	1	2	yes	—
264	C₄×C₈₉	—	2	1	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	1	no	—
268	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
270	Dic₈₉	—	2	1	no	—
271	Dic₈₉	—	2	1	no	—
272	Dic₈₉	—	2	1	no	—
273	Dic₈₉	—	2	1	no	—
274	Dic₈₉	C₈×D₄	1	2	yes	—
275	#33435	—	89	1	no	maximal, Sylow
276	C₂×C₈₉	—	4	1	no	—
277	C₂×C₈₉	—	4	1	no	—
278	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
279	C₂×C₈₉	#3407	1	1	yes	characteristic
280	C₂×C₈₉	#3407	1	1	yes	characteristic
281	D₈₉	—	2	2	no	—
282	D₈₉	—	4	1	no	—
283	D₈₉	—	4	1	no	—
284	C₂×#504	—	89	1	no	—
285	C₂×#504	—	89	1	no	—
286	#2931	—	89	1	no	—
287	#2168	—	89	1	no	—
288	#2168	—	89	1	no	—
289	#2168	—	89	1	no	—
290	#2168	—	89	1	no	—
291	#2168	—	89	1	no	—
292	#2168	—	89	1	no	—
293	#2168	—	89	1	no	—
294	#2168	D₈₉	1	1	yes	characteristic, complemented
295	#2150	—	89	1	no	—
296	#2113	—	89	1	no	—
297	#2113	—	89	1	no	—
298	C₂×#346	—	89	1	no	—
299	C₈₉	#33435	1	1	yes	characteristic, complemented, Sylow
300	C₂×#131	—	89	1	no	—
301	C₂×#131	—	89	1	no	—
302	#532	—	89	1	no	—
303	#504	—	178	4	no	—
304	#504	—	178	4	no	—
305	C₂×M₃₂	—	89	1	no	—
306	C₂×M₃₂	—	89	1	no	—
307	C₂×M₃₂	—	89	1	no	—
308	C₂×M₃₂	—	89	1	no	—
309	C₂×M₃₂	—	89	1	no	—
310	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
311	C₂²×C₁₆	—	89	1	no	—
312	C₂²×C₁₆	—	89	1	no	—
313	C₂²×C₁₆	—	89	1	no	—
314	C₂²×C₁₆	—	89	1	no	—
315	C₂²×C₁₆	—	89	1	no	—
316	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
317	#436	—	89	1	no	—
318	#436	—	89	1	no	—
319	#436	—	89	1	no	—
320	#436	—	89	1	no	—
321	C₈×D₄	—	89	1	no	—
322	C₈×D₄	—	89	1	no	—
323	C₈×D₄	—	89	1	no	—
324	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
325	#423	—	89	1	no	—
326	#408	—	89	1	no	—
327	#408	—	89	1	no	—
328	C₂×C₄×C₈	—	89	1	no	—
329	C₄⋊C₁₆	—	89	1	no	—
330	C₄⋊C₁₆	—	89	1	no	—
331	C₄⋊C₁₆	—	89	1	no	—
332	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
333	C₂²⋊C₁₆	—	89	1	no	—
334	C₂²⋊C₁₆	—	89	1	no	—
335	C₂²⋊C₁₆	—	89	1	no	—
336	C₂²⋊C₁₆	—	89	1	no	—
337	C₂²⋊C₁₆	—	89	1	no	—
338	C₂²⋊C₁₆	—	89	1	no	—
339	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
340	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
341	#346	—	89	1	no	—
342	#346	—	89	1	no	—
343	#346	—	89	1	no	—
344	#346	C₂×D₈₉	1	1	yes	characteristic
345	C₂×#41	—	89	1	no	—
346	C₂×#41	—	89	1	no	—
347	#131	—	178	2	no	—
348	#131	—	178	2	no	—
349	#131	—	178	2	no	—
350	#131	—	178	2	no	—
351	C₂×M₁₆	—	89	1	no	—
352	C₂×M₁₆	—	89	1	no	—
353	C₂×M₁₆	—	89	1	no	—
354	C₂×M₁₆	—	89	1	no	—
355	C₂×M₁₆	—	89	1	no	—
356	C₂×M₁₆	—	89	1	no	—
357	C₂²×C₈	—	89	1	no	—
358	C₂²×C₈	—	89	1	no	—
359	C₂²×C₈	—	89	1	no	—
360	C₂²×C₈	—	89	1	no	—
361	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
362	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
363	C₄⋊Q₈	—	89	1	no	—
364	#127	—	89	1	no	—
365	#124	—	89	1	no	—
366	#124	—	89	1	no	—
367	#121	—	89	1	no	—
368	#121	—	89	1	no	—
369	#121	—	89	1	no	—
370	#121	—	89	1	no	—
371	C₄×D₄	—	89	1	no	—
372	C₄×D₄	—	89	1	no	—
373	C₄×D₄	—	89	1	no	—
374	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
375	C₂×C₄²	—	89	1	no	—
376	M₃₂	—	2	2	no	—
377	M₃₂	—	178	2	no	—
378	M₃₂	—	178	2	no	—
379	M₃₂	—	178	2	no	—
380	M₃₂	—	178	2	no	—
381	M₃₂	—	178	2	no	—
382	C₂×C₁₆	—	2	2	no	—
383	C₂×C₁₆	—	89	1	no	—
384	C₂×C₁₆	—	89	4	no	—
385	C₂×C₁₆	—	89	1	no	—
386	C₂×C₁₆	—	89	1	no	—
387	C₂×C₁₆	—	89	1	no	—
388	C₂×C₁₆	—	178	2	no	—
389	C₂×C₁₆	—	178	2	no	—
390	C₂×C₁₆	—	178	2	no	—
391	C₂×C₁₆	—	178	2	no	—
392	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
393	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
394	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
395	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	89	1	no	—
398	C₄⋊C₈	—	89	1	no	—
399	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
400	C₂²⋊C₈	—	89	1	no	—
401	C₂²⋊C₈	—	89	1	no	—
402	C₂²⋊C₈	—	89	1	no	—
403	C₂²⋊C₈	—	89	1	no	—
404	C₂²⋊C₈	—	89	1	no	—
405	C₂²⋊C₈	—	89	1	no	—
406	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
407	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
408	C₄×C₈	—	89	1	no	—
409	C₄×C₈	—	89	1	no	—
410	C₄×C₈	—	89	1	no	—
411	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
412	#41	—	178	2	no	—
413	#41	—	178	2	no	—
414	#41	—	178	2	no	—
415	#41	—	178	2	no	—
416	C₂×Q₈	—	89	1	no	—
417	C₂×Q₈	—	89	1	no	—
418	C₂×D₄	—	89	1	no	—
419	C₂×D₄	—	89	1	no	—
420	C₂×D₄	—	89	1	no	—
421	C₂×D₄	—	89	1	no	—
422	C₂×D₄	—	89	1	no	—
423	C₂×D₄	—	89	1	no	—
424	C₂×D₄	—	89	1	no	—
425	C₂×D₄	—	89	1	no	—
426	C₂×D₄	—	89	1	no	—
427	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
428	C₂²×C₄	—	89	1	no	—
429	C₂²×C₄	—	89	1	no	—
430	C₂²×C₄	—	89	1	no	—
431	C₂²×C₄	—	89	1	no	—
432	C₂²×C₄	—	89	1	no	—
433	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	M₁₆	—	178	2	no	—
436	M₁₆	—	178	2	no	—
437	M₁₆	—	178	2	no	—
438	M₁₆	—	178	2	no	—
439	M₁₆	—	178	2	no	—
440	M₁₆	—	178	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	89	1	no	—
446	C₂×C₈	—	89	2	no	—
447	C₂×C₈	—	89	2	no	—
448	C₂×C₈	—	89	1	no	—
449	C₂×C₈	—	89	1	no	—
450	C₂×C₈	—	89	1	no	—
451	C₂×C₈	—	178	2	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	178	1	no	—
455	C₂×C₈	—	178	1	no	—
456	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
459	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
460	C₄⋊C₄	—	89	1	no	—
461	C₄⋊C₄	—	89	1	no	—
462	C₄⋊C₄	—	89	1	no	—
463	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
464	C₂²⋊C₄	—	89	1	no	—
465	C₂²⋊C₄	—	89	1	no	—
466	C₂²⋊C₄	—	89	1	no	—
467	C₂²⋊C₄	—	89	1	no	—
468	C₂²⋊C₄	—	89	1	no	—
469	C₂²⋊C₄	—	89	1	no	—
470	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
471	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
472	C₄²	—	89	1	no	—
473	C₄²	—	89	1	no	—
474	C₄²	—	89	1	no	—
475	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
476	C₁₆	—	2	1	no	—
477	C₁₆	—	2	1	no	—
478	C₁₆	—	2	1	no	—
479	C₁₆	—	89	2	no	—
480	C₁₆	—	178	1	no	—
481	C₁₆	—	178	1	no	—
482	C₁₆	—	178	1	no	—
483	C₁₆	D₄×D₈₉	1	2	yes	—
484	C₂³	—	89	1	no	—
485	C₂³	—	89	1	no	—
486	C₂³	—	89	1	no	—
487	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
488	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
489	Q₈	—	178	2	no	—
490	Q₈	—	178	2	no	—
491	D₄	—	4	1	no	—
492	D₄	—	356	1	no	—
493	D₄	—	356	1	no	—
494	D₄	—	356	1	no	—
495	D₄	—	178	2	no	—
496	D₄	—	178	2	no	—
497	D₄	—	178	2	no	—
498	D₄	—	178	2	no	—
499	D₄	—	178	2	no	—
500	D₄	—	178	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	89	1	no	—
506	C₂×C₄	—	89	2	no	—
507	C₂×C₄	—	89	2	no	—
508	C₂×C₄	—	89	1	no	—
509	C₂×C₄	—	89	1	no	—
510	C₂×C₄	—	89	1	no	—
511	C₂×C₄	—	89	1	no	—
512	C₂×C₄	—	356	1	no	—
513	C₂×C₄	—	356	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
519	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	89	2	no	—
527	C₈	—	178	1	no	—
528	C₈	—	178	1	no	—
529	C₈	—	178	1	no	—
530	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
531	C₈	#41×D₈₉	1	1	yes	characteristic
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	89	2	no	—
539	C₂²	—	178	1	no	—
540	C₂²	—	178	1	no	—
541	C₂²	—	178	1	no	—
542	C₂²	—	178	1	no	—
543	C₂²	—	178	1	no	—
544	C₂²	—	178	1	no	—
545	C₂²	—	178	1	no	—
546	C₂²	—	178	1	no	—
547	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	89	2	no	—
553	C₄	—	178	1	no	—
554	C₄	—	178	1	no	—
555	C₄	—	178	1	no	—
556	C₄	—	178	1	no	—
557	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
558	C₄	#131×D₈₉	1	1	yes	characteristic
559	C₂	—	4	1	no	—
560	C₂	—	4	1	no	—
561	C₂	—	356	1	no	—
562	C₂	—	356	1	no	—
563	C₂	—	178	2	no	—
564	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
565	C₂	#26033353	1	1	yes	characteristic
566	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2168	C₂
prime radical	#19152145	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2168	D₈₉
hypocenter	C₈₉	#33435
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×#19152016	C₂	semidirect
2. C₂×#19152014	C₂	semidirect
4. #26022080	C₂	semidirect
5. #26022079	C₂	semidirect
6. #26022078	C₂	semidirect
7. #26022077	C₂	semidirect
8. #26022076	C₂	semidirect
9. #26022075	C₂	semidirect
10. #26022074	C₂	semidirect
11. #26022006	C₂	semidirect
12. #26021864	C₂	semidirect
13. #26021864	C₂	semidirect
14. #346×D₈₉	C₂	semidirect
15. C₈₉×#2168	C₂	semidirect
102. C₁₆×D₈₉	D₄	semidirect
294. #2168	D₈₉	semidirect
299. C₈₉	#33435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152016	2
C₂×#19152014	2
#26028959	2
#26022080	2
#26022079	2
#26022078	2
#26022077	2
#26022076	2
#26022075	2
#26022074	2
#26022006	2
#26021864	2
#346×D₈₉	2
C₈₉×#2168	2
#33435	89