Subgroups — #36708159

Order 22784.

484 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	#26029220	C₂	1	1	yes	maximal, characteristic
2	#26022158	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022157	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022084	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022081	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022080	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022077	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022075	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022060	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022056	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022052	C₂	1	1	yes	maximal, characteristic, complemented
12	#26022010	C₂	1	1	yes	maximal, characteristic, complemented
13	#26022009	C₂	1	1	yes	maximal, characteristic, complemented
14	#26022007	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152128	C₄	1	1	yes	characteristic
17	C₂×#15667952	C₂²	1	1	yes	characteristic
18	C₂×#15667952	C₂²	1	1	yes	characteristic
19	C₂×#15667951	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
21	#19151727	C₄	1	1	yes	characteristic
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
23	#19151673	C₄	1	1	yes	characteristic
24	#19151670	C₄	1	1	yes	characteristic
25	#19151666	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
28	#19151658	C₄	1	1	yes	characteristic
29	#19151656	C₄	1	1	yes	characteristic
30	#19151652	C₄	1	1	yes	characteristic
31	#19151553	C₂²	1	1	yes	characteristic
32	#19151552	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₄⋊#13083549	C₂²	1	1	yes	characteristic
35	#19151416	C₂²	1	1	yes	characteristic
36	#19151416	C₂²	1	1	yes	characteristic
37	#19151416	C₂²	1	1	yes	characteristic
38	#19151416	C₂²	1	1	yes	characteristic
39	#19151416	C₂²	1	1	yes	characteristic
40	#19151416	C₂²	1	1	yes	characteristic
41	#19151416	C₂²	1	1	yes	characteristic
42	#19151416	C₂²	1	1	yes	characteristic
43	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
44	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
45	#19151377	C₂²	1	1	yes	characteristic
46	#19151377	C₂²	1	1	yes	characteristic
47	#19151373	C₂²	1	1	yes	characteristic
48	#19151373	C₂²	1	1	yes	characteristic
49	#19151373	C₂²	1	1	yes	characteristic
50	C₄×#13083549	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
52	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
58	#346×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
60	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
61	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
63	#15668007	C₈	1	1	yes	characteristic
64	#15668005	C₈	1	1	yes	characteristic
65	#15668002	C₈	1	1	yes	characteristic
66	#15667998	C₈	1	1	yes	characteristic
67	#15667996	C₈	1	1	yes	characteristic
68	#15667993	C₈	1	1	yes	characteristic
69	#15667989	C₈	1	1	yes	characteristic
70	#15667984	C₈	1	1	yes	characteristic
71	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
74	#15667971	C₂×C₄	1	1	yes	characteristic
75	#15667969	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
77	#15667952	—	4	1	no	—
78	#15667952	—	4	1	no	—
79	#15667951	—	4	1	no	—
80	C₂×#13083549	C₂³	1	1	yes	characteristic
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	C₁₆×D₈₉	—	4	1	no	—
85	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
86	#15667941	C₂×C₄	1	1	yes	characteristic
87	#15667941	C₂×C₄	1	1	yes	characteristic
88	#15667941	C₂×C₄	1	1	yes	characteristic
89	#15667941	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
92	#15667924	C₂×C₄	1	1	yes	characteristic
93	#15667924	C₂×C₄	1	1	yes	characteristic
94	#15667923	C₂×C₄	1	1	yes	characteristic
95	#15667922	C₂×C₄	1	1	yes	characteristic
96	#15667922	C₂×C₄	1	1	yes	characteristic
97	#15667922	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
101	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
102	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
106	M₃₂×C₈₉	—	4	1	no	—
107	C₂×C₁₆×C₈₉	—	4	1	no	—
108	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
119	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
122	#13083558	—	4	1	no	—
123	#13083557	—	4	1	no	—
124	C₂×#10623494	—	4	1	no	—
125	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₈₉	—	2	1	no	—
130	C₈×D₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
132	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
134	#13083553	C₂×C₈	1	1	yes	characteristic
135	#13083553	C₂×C₈	1	1	yes	characteristic
136	#13083553	C₂×C₈	1	1	yes	characteristic
137	#13083553	C₂×C₈	1	1	yes	characteristic
138	#13083553	C₂×C₈	1	1	yes	characteristic
139	#13083553	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
141	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
142	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₈₉	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	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
153	#13083549	—	2	1	no	—
154	#13083549	—	2	1	no	—
155	#13083549	—	2	1	no	—
156	#13083549	—	2	1	no	—
157	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₈₉	C₂×C₈	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	—	2	1	no	—
176	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
179	D₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₈₉	—	4	1	no	—
190	C₂²⋊D₈₉	—	4	1	no	—
191	C₂×Dic₈₉	—	4	1	no	—
192	C₂×Dic₈₉	—	4	1	no	—
193	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
200	C₄×D₈₉	—	2	1	no	—
201	C₄×D₈₉	—	2	1	no	—
202	Dic₁₇₈	—	4	1	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
207	C₈×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
208	#10623494	—	2	1	no	—
209	#10623494	—	2	1	no	—
210	#10623494	—	2	1	no	—
211	#10623494	—	2	1	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	2	1	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
219	C₂×D₈₉	—	2	1	no	—
220	C₂×D₈₉	—	2	1	no	—
221	C₂×D₈₉	—	2	1	no	—
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	#520	1	1	yes	characteristic
227	C₄×C₈₉	#568	1	1	yes	characteristic
228	Dic₈₉	—	2	1	no	—
229	Dic₈₉	—	2	1	no	—
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	#33509	—	89	1	no	maximal, Sylow
236	C₂×C₈₉	—	4	1	no	—
237	C₂×C₈₉	—	4	1	no	—
238	C₂×C₈₉	#2988	1	1	yes	characteristic
239	C₂×C₈₉	#3407	1	1	yes	characteristic
240	C₂×C₈₉	#3407	1	1	yes	characteristic
241	D₈₉	—	4	1	no	—
242	#2966	—	89	1	no	—
243	#2183	—	89	1	no	—
244	#2183	—	89	1	no	—
245	#2169	—	89	1	no	—
246	#2169	—	89	1	no	—
247	#2168	—	89	1	no	—
248	#2168	—	89	1	no	—
249	#2168	—	89	1	no	—
250	#2168	D₈₉	1	1	yes	characteristic, complemented
251	#2164	—	89	1	no	—
252	#2164	—	89	1	no	—
253	#2163	—	89	1	no	—
254	#2151	—	89	1	no	—
255	#2151	—	89	1	no	—
256	#2150	—	89	1	no	—
257	C₈₉	#33509	1	1	yes	characteristic, complemented, Sylow
258	#529	—	89	1	no	—
259	C₂×M₃₂	—	89	1	no	—
260	C₂×M₃₂	—	89	1	no	—
261	C₂×M₃₂	—	89	1	no	—
262	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
263	C₂²×C₁₆	—	89	1	no	—
264	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
265	#446	—	89	1	no	—
266	C₈×Q₈	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
283	C₄⋊C₁₆	—	89	1	no	—
284	C₄⋊C₁₆	—	89	1	no	—
285	C₄⋊C₁₆	—	89	1	no	—
286	C₄⋊C₁₆	—	89	1	no	—
287	C₄⋊C₁₆	—	89	1	no	—
288	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
289	C₂²⋊C₁₆	—	89	1	no	—
290	C₂²⋊C₁₆	—	89	1	no	—
291	C₂²⋊C₁₆	—	89	1	no	—
292	C₂²⋊C₁₆	—	89	1	no	—
293	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
294	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
295	#346	—	89	1	no	—
296	#346	—	89	1	no	—
297	#346	—	89	1	no	—
298	#346	C₂×D₈₉	1	1	yes	characteristic
299	C₄×C₁₆	—	89	1	no	—
300	C₄×C₁₆	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
319	#117	—	89	1	no	—
320	#117	—	89	1	no	—
321	C₂×C₄²	—	89	1	no	—
322	M₃₂	—	4	1	no	—
323	M₃₂	—	356	1	no	—
324	M₃₂	—	356	1	no	—
325	M₃₂	—	356	1	no	—
326	C₂×C₁₆	—	4	1	no	—
327	C₂×C₁₆	—	89	1	no	—
328	C₂×C₁₆	—	89	1	no	—
329	C₂×C₁₆	—	89	1	no	—
330	C₂×C₁₆	—	89	1	no	—
331	C₂×C₁₆	—	356	1	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	—	89	1	no	—
340	C₄⋊C₈	—	89	1	no	—
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	C₄×D₈₉	1	1	yes	characteristic
347	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
356	C₄×C₈	—	89	1	no	—
357	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
358	C₂×Q₈	—	89	1	no	—
359	C₂×D₄	—	89	1	no	—
360	C₂×D₄	—	89	1	no	—
361	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
362	C₂²×C₄	—	89	1	no	—
363	C₂²×C₄	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
367	M₁₆	—	356	1	no	—
368	M₁₆	—	356	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	89	1	no	—
374	C₂×C₈	—	89	1	no	—
375	C₂×C₈	—	89	1	no	—
376	C₂×C₈	—	89	1	no	—
377	C₂×C₈	—	356	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	—	89	1	no	—
392	C₄⋊C₄	—	89	1	no	—
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	C₈×D₈₉	1	1	yes	characteristic
403	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
404	C₄²	—	89	1	no	—
405	C₄²	—	89	1	no	—
406	C₄²	—	89	1	no	—
407	C₄²	—	89	1	no	—
408	C₄²	—	89	1	no	—
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	—	2	1	no	—
414	C₁₆	—	178	1	no	—
415	C₁₆	—	178	1	no	—
416	C₁₆	—	178	1	no	—
417	C₁₆	—	178	1	no	—
418	C₂³	—	89	1	no	—
419	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
420	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
421	Q₈	—	356	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	356	1	no	—
424	D₄	—	356	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	89	1	no	—
430	C₂×C₄	—	89	1	no	—
431	C₂×C₄	—	89	1	no	—
432	C₂×C₄	—	89	1	no	—
433	C₂×C₄	—	89	1	no	—
434	C₂×C₄	—	89	1	no	—
435	C₂×C₄	—	89	1	no	—
436	C₂×C₄	—	356	1	no	—
437	C₂×C₄	—	356	1	no	—
438	C₂×C₄	—	178	1	no	—
439	C₂×C₄	—	178	1	no	—
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	—	178	1	no	—
449	C₈	—	178	1	no	—
450	C₈	—	178	1	no	—
451	C₈	—	178	1	no	—
452	C₈	#15668057	1	1	yes	characteristic
453	C₈	#15668059	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	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	—	178	1	no	—
469	C₄	—	178	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	#19152077	1	1	yes	characteristic
476	C₄	#19152363	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	4	1	no	—
479	C₂	—	356	1	no	—
480	C₂	#26029359	1	1	yes	characteristic
481	C₂	#26033353	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×#2168	C₂
prime radical	#15667984	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2168	D₈₉
hypocenter	C₈₉	#33509
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
2. #26022158	C₂	semidirect
3. #26022157	C₂	semidirect
4. #26022084	C₂	semidirect
5. #26022081	C₂	semidirect
6. #26022080	C₂	semidirect
7. #26022077	C₂	semidirect
8. #26022075	C₂	semidirect
9. #26022060	C₂	semidirect
10. #26022056	C₂	semidirect
11. #26022052	C₂	semidirect
12. #26022010	C₂	semidirect
13. #26022009	C₂	semidirect
14. #26022007	C₂	semidirect
15. C₈₉×#2168	C₂	semidirect
250. #2168	D₈₉	semidirect
257. C₈₉	#33509	semidirect

Maximal subgroups

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

subgroup	index
#26029220	2
#26022158	2
#26022157	2
#26022084	2
#26022081	2
#26022080	2
#26022077	2
#26022075	2
#26022060	2
#26022056	2
#26022052	2
#26022010	2
#26022009	2
#26022007	2
C₈₉×#2168	2
#33509	89