Subgroups — #36707981

Order 22784.

518 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029229	C₂	1	1	yes	maximal, characteristic
2	#26022161	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022079	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022079	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022076	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022071	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022058	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022058	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022050	C₂	1	1	yes	maximal, characteristic, complemented
12	#26021850	C₂	1	1	yes	maximal, characteristic, complemented
13	#26021847	C₂	1	1	yes	maximal, characteristic, complemented
14	#346×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152135	C₄	1	1	yes	characteristic
17	C₂×#15667951	C₂²	1	1	yes	characteristic
18	C₂×#15667951	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
23	#19151729	C₄	1	1	yes	characteristic
24	#19151675	C₄	1	1	yes	characteristic
25	#19151668	C₄	1	1	yes	characteristic
26	#19151668	C₄	1	1	yes	characteristic
27	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
28	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
29	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
30	#19151658	C₄	1	1	yes	characteristic
31	#19151658	C₄	1	1	yes	characteristic
32	#19151654	C₄	1	1	yes	characteristic
33	#19151552	C₂²	1	1	yes	characteristic
34	#19151552	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
36	C₄⋊#13083549	C₂²	1	1	yes	characteristic
37	C₄⋊#13083549	C₂²	1	1	yes	characteristic
38	C₄⋊#13083549	C₂²	1	1	yes	characteristic
39	#19151377	C₂²	1	1	yes	characteristic
40	#19151377	C₂²	1	1	yes	characteristic
41	#19151377	C₂²	1	1	yes	characteristic
42	#19151377	C₂²	1	1	yes	characteristic
43	#19151377	C₂²	1	1	yes	characteristic
44	#19151377	C₂²	1	1	yes	characteristic
45	#19151374	C₂²	1	1	yes	characteristic
46	#19151374	C₂²	1	1	yes	characteristic
47	#19151373	C₂²	1	1	yes	characteristic
48	#19151373	C₂²	1	1	yes	characteristic
49	C₄×#13083549	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
52	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	#346×C₈₉	C₂²	1	1	yes	characteristic
57	#346×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
60	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
65	#15668007	C₈	1	1	yes	characteristic
66	#15668007	C₈	1	1	yes	characteristic
67	#15668003	C₈	1	1	yes	characteristic
68	#15668001	C₈	1	1	yes	characteristic
69	#15667997	C₈	1	1	yes	characteristic
70	#15667997	C₈	1	1	yes	characteristic
71	#15667988	C₈	1	1	yes	characteristic
72	#15667987	C₈	1	1	yes	characteristic
73	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
74	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
75	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
76	#15667969	C₂×C₄	1	1	yes	characteristic
77	#15667969	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
79	#15667951	—	2	2	no	—
80	#15667951	—	2	2	no	—
81	C₂×#13083549	C₂³	1	1	yes	characteristic
82	C₂×#13083549	C₂³	1	1	yes	characteristic
83	C₂×#13083549	C₂³	1	1	yes	characteristic
84	C₂×#13083549	C₂³	1	1	yes	characteristic
85	C₁₆×D₈₉	—	2	2	no	—
86	C₁₆×D₈₉	—	2	2	no	—
87	C₁₆×D₈₉	—	2	2	no	—
88	C₁₆×D₈₉	—	2	2	no	—
89	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
90	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
91	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
92	#15667924	C₂×C₄	1	1	yes	characteristic
93	#15667924	C₂×C₄	1	1	yes	characteristic
94	#15667924	C₂×C₄	1	1	yes	characteristic
95	#15667924	C₂×C₄	1	1	yes	characteristic
96	#15667924	C₂×C₄	1	1	yes	characteristic
97	#15667924	C₂×C₄	1	1	yes	characteristic
98	#15667923	C₂×C₄	1	1	yes	characteristic
99	#15667923	C₂×C₄	1	1	yes	characteristic
100	#15667922	C₂×C₄	1	1	yes	characteristic
101	#15667922	C₂×C₄	1	1	yes	characteristic
102	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
105	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
117	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
118	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
124	#13083557	—	2	2	no	—
125	#13083557	—	2	2	no	—
126	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
127	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
128	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
129	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₈₉	—	2	1	no	—
131	C₈×D₈₉	—	2	1	no	—
132	C₈×D₈₉	—	2	1	no	—
133	C₈×D₈₉	—	2	1	no	—
134	C₈×D₈₉	—	2	1	no	—
135	C₈×D₈₉	—	2	1	no	—
136	C₈×D₈₉	—	2	2	no	—
137	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
138	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
139	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
140	#13083553	C₂×C₈	1	1	yes	characteristic
141	#13083553	C₂×C₈	1	1	yes	characteristic
142	#13083553	C₂×C₈	1	1	yes	characteristic
143	#13083553	C₂×C₈	1	1	yes	characteristic
144	#13083551	C₂×C₈	1	1	yes	characteristic
145	#13083551	C₂×C₈	1	1	yes	characteristic
146	#13083551	C₂×C₈	1	1	yes	characteristic
147	#13083551	C₂×C₈	1	1	yes	characteristic
148	#13083551	C₂×C₈	1	1	yes	characteristic
149	#13083551	C₂×C₈	1	1	yes	characteristic
150	#13083551	C₂×C₈	1	1	yes	characteristic
151	#13083551	C₂×C₈	1	1	yes	characteristic
152	#13083551	C₂×C₈	1	1	yes	characteristic
153	#13083551	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
157	#13083549	—	2	1	no	—
158	#13083549	—	2	1	no	—
159	#13083549	—	2	1	no	—
160	#13083549	#41	1	2	yes	—
161	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
167	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
168	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
169	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₁₆×C₈₉	—	2	1	no	—
173	C₁₆×C₈₉	—	2	1	no	—
174	C₁₆×C₈₉	—	2	1	no	—
175	C₁₆×C₈₉	#41	1	2	yes	—
176	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
177	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
179	Q₈×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
187	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
191	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
192	D₃₅₆	—	2	2	no	—
193	D₃₅₆	—	2	2	no	—
194	D₃₅₆	—	4	1	no	—
195	C₄×D₈₉	—	2	2	no	—
196	C₄×D₈₉	—	2	1	no	—
197	C₄×D₈₉	—	2	1	no	—
198	C₄×D₈₉	—	2	1	no	—
199	C₄×D₈₉	—	2	1	no	—
200	C₄×D₈₉	—	2	1	no	—
201	C₄×D₈₉	—	2	1	no	—
202	C₄×D₈₉	—	4	1	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
208	#10623494	—	2	1	no	—
209	#10623494	—	2	1	no	—
210	#10623494	—	2	1	no	—
211	#10623494	#131	1	2	yes	—
212	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
213	C₂×D₈₉	—	2	1	no	—
214	C₂×D₈₉	—	2	1	no	—
215	C₂×D₈₉	—	2	1	no	—
216	C₂×D₈₉	—	2	1	no	—
217	C₂×D₈₉	—	2	1	no	—
218	C₂×D₈₉	—	2	1	no	—
219	C₂×D₈₉	—	2	1	no	—
220	C₂×D₈₉	—	2	1	no	—
221	C₂×D₈₉	#504	1	2	yes	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	2	1	no	—
227	C₄×C₈₉	—	2	1	no	—
228	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
229	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
230	Dic₈₉	—	2	1	no	—
231	Dic₈₉	—	2	1	no	—
232	Dic₈₉	—	2	1	no	—
233	Dic₈₉	—	2	1	no	—
234	Dic₈₉	—	2	1	no	—
235	#33482	—	89	1	no	maximal, Sylow
236	C₂×C₈₉	C₈×#41	1	1	yes	characteristic
237	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
238	C₂×C₈₉	#3407	1	1	yes	characteristic
239	D₈₉	—	2	2	no	—
240	D₈₉	—	4	1	no	—
241	D₈₉	—	4	1	no	—
242	#2966	—	89	1	no	—
243	#2183	—	89	1	no	—
244	#2183	D₈₉	1	1	yes	characteristic, complemented
245	#2168	—	89	1	no	—
246	#2168	—	89	1	no	—
247	#2168	—	89	1	no	—
248	#2168	—	89	1	no	—
249	D₄×C₁₆	—	89	1	no	—
250	D₄×C₁₆	—	89	1	no	—
251	#2164	—	89	1	no	—
252	#2164	—	89	1	no	—
253	#2162	—	89	1	no	—
254	#2108	—	89	1	no	—
255	#2108	—	89	1	no	—
256	C₂×#346	—	89	1	no	—
257	C₈₉	#33482	1	1	yes	characteristic, complemented, Sylow
258	#529	—	89	1	no	—
259	C₂×M₃₂	—	89	1	no	—
260	C₂×M₃₂	—	89	1	no	—
261	C₂²×C₁₆	—	89	1	no	—
262	C₂²×C₁₆	—	89	1	no	—
263	C₂²×C₁₆	—	89	1	no	—
264	C₂²×C₁₆	—	89	1	no	—
265	#446	—	89	1	no	—
266	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
267	#436	—	89	1	no	—
268	#435	—	89	1	no	—
269	#435	—	89	1	no	—
270	C₈×D₄	—	89	1	no	—
271	C₈×D₄	—	89	1	no	—
272	C₈×D₄	—	89	1	no	—
273	#433	—	89	1	no	—
274	#433	—	89	1	no	—
275	#432	—	89	1	no	—
276	#405	—	89	1	no	—
277	#405	—	89	1	no	—
278	C₂×C₄×C₈	—	89	1	no	—
279	C₄⋊C₁₆	—	89	1	no	—
280	C₄⋊C₁₆	—	89	1	no	—
281	C₄⋊C₁₆	—	89	1	no	—
282	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
283	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
284	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
285	C₂²⋊C₁₆	—	89	1	no	—
286	C₂²⋊C₁₆	—	89	1	no	—
287	C₂²⋊C₁₆	—	89	1	no	—
288	C₂²⋊C₁₆	—	89	1	no	—
289	C₂²⋊C₁₆	—	89	1	no	—
290	C₂²⋊C₁₆	—	89	1	no	—
291	#346	—	89	1	no	—
292	#346	—	89	1	no	—
293	#346	—	89	1	no	—
294	#346	—	89	1	no	—
295	#346	C₂×D₈₉	1	1	yes	characteristic
296	#346	C₂×D₈₉	1	1	yes	characteristic
297	C₄×C₁₆	—	89	1	no	—
298	C₄×C₁₆	—	89	1	no	—
299	C₄×C₁₆	—	89	1	no	—
300	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
301	C₂×M₁₆	—	89	1	no	—
302	C₂×M₁₆	—	89	1	no	—
303	C₂²×C₈	—	89	1	no	—
304	C₂²×C₈	—	89	1	no	—
305	C₂²×C₈	—	89	1	no	—
306	C₂²×C₈	—	89	1	no	—
307	#126	—	89	1	no	—
308	#126	—	89	1	no	—
309	#125	—	89	1	no	—
310	#124	—	89	1	no	—
311	#123	—	89	1	no	—
312	#123	—	89	1	no	—
313	C₂²⋊Q₈	—	89	1	no	—
314	#121	—	89	1	no	—
315	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	89	1	no	—
319	#117	—	89	1	no	—
320	#117	—	89	1	no	—
321	C₂×C₄²	—	89	1	no	—
322	M₃₂	—	178	2	no	—
323	M₃₂	—	178	2	no	—
324	C₂×C₁₆	—	89	1	no	—
325	C₂×C₁₆	—	89	1	no	—
326	C₂×C₁₆	—	89	1	no	—
327	C₂×C₁₆	—	89	1	no	—
328	C₂×C₁₆	—	178	2	no	—
329	C₂×C₁₆	—	178	2	no	—
330	C₂×C₁₆	—	178	2	no	—
331	C₂×C₁₆	—	178	2	no	—
332	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
333	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
334	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
335	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
336	C₄⋊C₈	—	89	1	no	—
337	C₄⋊C₈	—	89	1	no	—
338	C₄⋊C₈	—	89	1	no	—
339	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
340	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
341	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
342	C₂²⋊C₈	—	89	1	no	—
343	C₂²⋊C₈	—	89	1	no	—
344	C₂²⋊C₈	—	89	1	no	—
345	C₂²⋊C₈	—	89	1	no	—
346	C₂²⋊C₈	—	89	1	no	—
347	C₂²⋊C₈	—	89	1	no	—
348	#97	—	89	1	no	—
349	#97	—	89	1	no	—
350	#97	—	89	1	no	—
351	#97	—	89	1	no	—
352	C₄×C₈	—	89	1	no	—
353	C₄×C₈	—	89	1	no	—
354	C₄×C₈	—	89	1	no	—
355	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
358	C₂×Q₈	C₈×D₈₉	1	1	yes	characteristic
359	C₂×D₄	—	89	1	no	—
360	C₂×D₄	—	89	1	no	—
361	C₂×D₄	—	89	1	no	—
362	C₂²×C₄	—	89	1	no	—
363	C₂²×C₄	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	—	89	1	no	—
366	C₂²×C₄	—	89	1	no	—
367	M₁₆	—	178	2	no	—
368	M₁₆	—	178	2	no	—
369	C₂×C₈	—	89	1	no	—
370	C₂×C₈	—	89	1	no	—
371	C₂×C₈	—	89	1	no	—
372	C₂×C₈	—	89	1	no	—
373	C₂×C₈	—	178	2	no	—
374	C₂×C₈	—	178	1	no	—
375	C₂×C₈	—	178	1	no	—
376	C₂×C₈	—	178	1	no	—
377	C₂×C₈	—	178	1	no	—
378	C₂×C₈	—	178	1	no	—
379	C₂×C₈	—	178	1	no	—
380	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
383	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
384	C₄⋊C₄	—	89	1	no	—
385	C₄⋊C₄	—	89	1	no	—
386	C₄⋊C₄	—	89	1	no	—
387	C₄⋊C₄	—	89	1	no	—
388	C₄⋊C₄	—	89	1	no	—
389	C₄⋊C₄	—	89	1	no	—
390	C₄⋊C₄	—	89	1	no	—
391	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
392	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
393	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
394	C₂²⋊C₄	—	89	1	no	—
395	C₂²⋊C₄	—	89	1	no	—
396	C₂²⋊C₄	—	89	1	no	—
397	C₂²⋊C₄	—	89	1	no	—
398	C₂²⋊C₄	—	89	1	no	—
399	C₂²⋊C₄	—	89	1	no	—
400	C₂²⋊C₄	—	89	1	no	—
401	C₂²⋊C₄	—	89	1	no	—
402	C₂²⋊C₄	—	89	1	no	—
403	C₂²⋊C₄	—	89	1	no	—
404	C₄²	—	89	1	no	—
405	C₄²	—	89	1	no	—
406	C₄²	—	89	1	no	—
407	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
408	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
409	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	2	1	no	—
413	C₁₆	—	89	2	no	—
414	C₁₆	—	178	1	no	—
415	C₁₆	—	178	1	no	—
416	C₁₆	—	178	1	no	—
417	C₁₆	#13083575	1	2	yes	—
418	C₂³	—	89	1	no	—
419	C₂³	—	89	1	no	—
420	C₂³	—	89	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	356	1	no	—
423	D₄	—	178	2	no	—
424	D₄	—	178	2	no	—
425	C₂×C₄	—	89	1	no	—
426	C₂×C₄	—	89	1	no	—
427	C₂×C₄	—	89	1	no	—
428	C₂×C₄	—	89	1	no	—
429	C₂×C₄	—	89	1	no	—
430	C₂×C₄	—	356	1	no	—
431	C₂×C₄	—	178	2	no	—
432	C₂×C₄	—	178	1	no	—
433	C₂×C₄	—	178	1	no	—
434	C₂×C₄	—	178	1	no	—
435	C₂×C₄	—	178	1	no	—
436	C₂×C₄	—	178	1	no	—
437	C₂×C₄	—	178	1	no	—
438	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
439	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
443	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	89	2	no	—
449	C₈	—	178	1	no	—
450	C₈	—	178	1	no	—
451	C₈	—	178	1	no	—
452	C₈	#41×D₈₉	1	1	yes	characteristic
453	C₈	C₂×#13083575	1	1	yes	characteristic
454	C₂²	—	89	2	no	—
455	C₂²	—	178	1	no	—
456	C₂²	—	178	1	no	—
457	C₂²	—	178	1	no	—
458	C₂²	—	178	1	no	—
459	C₂²	—	178	1	no	—
460	C₂²	—	178	1	no	—
461	C₂²	—	178	1	no	—
462	C₂²	—	178	1	no	—
463	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	178	1	no	—
471	C₄	—	178	1	no	—
472	C₄	—	178	1	no	—
473	C₄	—	178	1	no	—
474	C₄	—	178	1	no	—
475	C₄	C₄×#13083575	1	1	yes	characteristic
476	C₄	#131×D₈₉	1	1	yes	characteristic
477	C₂	—	356	1	no	—
478	C₂	—	356	1	no	—
479	C₂	—	178	2	no	—
480	C₂	C₈×#13083575	1	1	yes	characteristic
481	C₂	#504×D₈₉	1	1	yes	characteristic
482	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2183	C₂
prime radical	#15667987	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2183	D₈₉
hypocenter	C₈₉	#33482
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #26022161	C₂	semidirect
3. #26022079	C₂	semidirect
4. #26022079	C₂	semidirect
5. #26022076	C₂	semidirect
6. #26022076	C₂	semidirect
7. C₁₆×D₃₅₆	C₂	semidirect
8. #26022071	C₂	semidirect
9. #26022058	C₂	semidirect
10. #26022058	C₂	semidirect
11. #26022050	C₂	semidirect
12. #26021850	C₂	semidirect
13. #26021847	C₂	semidirect
14. #346×D₈₉	C₂	semidirect
15. C₈₉×#2183	C₂	semidirect
244. #2183	D₈₉	semidirect
257. C₈₉	#33482	semidirect

Maximal subgroups

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

subgroup	index
#26029229	2
#26022161	2
#26022079	2
#26022076	2
C₁₆×D₃₅₆	2
#26022071	2
#26022058	2
#26022050	2
#26021850	2
#26021847	2
#346×D₈₉	2
C₈₉×#2183	2
#33482	89