Subgroups — #36576502

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030034	C₂	1	1	yes	maximal, characteristic
2	#26028817	C₂	1	1	yes	maximal, characteristic
3	#26021230	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021002	C₂	1	2	yes	maximal, complemented
6	#26020851	C₂	1	2	yes	maximal, complemented
7	#26020526	C₂	1	2	yes	maximal
8	#26020107	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020098	C₂	1	2	yes	maximal
10	C₄×#15667938	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	2	yes	—
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	#19151902	C₄	1	2	yes	complemented
15	#19151895	C₄	1	2	yes	complemented
16	#19151890	C₄	1	1	yes	characteristic, complemented
17	#19151885	C₄	1	1	yes	characteristic, complemented
18	#19151880	C₄	1	1	yes	characteristic, complemented
19	#19151875	C₄	1	1	yes	characteristic, complemented
20	C₂×#15667947	C₂²	1	2	yes	—
21	#19151634	C₂²	1	2	yes	—
22	#19151624	C₂²	1	2	yes	—
23	#19151623	—	2	2	no	—
24	#19151622	C₂²	1	1	yes	characteristic
25	#19151620	—	2	1	no	—
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	C₄⋊C₈×D₈₉	—	2	1	no	—
28	C₂×#15667938	C₂²	1	1	yes	characteristic
29	C₂×#15667938	C₂²	1	1	yes	characteristic
30	#19151592	C₂²	1	2	yes	—
31	C₂×#15667922	C₂²	1	2	yes	—
32	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
33	#19151362	C₂²	1	2	yes	—
34	#19151359	C₂²	1	1	yes	characteristic
35	#19151359	C₂²	1	1	yes	characteristic
36	#19151357	C₂²	1	2	yes	—
37	#19151357	C₂²	1	2	yes	—
38	#19151352	C₂²	1	2	yes	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	—	2	2	no	—
41	#446×C₈₉	—	2	1	no	—
42	C₈×Q₈×C₈₉	—	2	1	no	—
43	#424×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#405×C₈₉	C₂²	1	2	yes	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	C₂³	1	1	yes	characteristic
48	#15668018	—	2	4	no	—
49	#15668018	—	4	2	no	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083557	—	2	2	no	—
52	C₂²×#10623494	C₂³	1	2	yes	—
53	C₂×C₈×D₈₉	—	2	2	no	—
54	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
56	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
57	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₈₉	—	2	1	no	—
59	C₄×C₂²⋊D₈₉	—	2	1	no	—
60	#15667971	C₂³	1	1	yes	characteristic
61	#15667969	—	2	1	no	—
62	C₂×C₄×Dic₈₉	—	2	1	no	—
63	C₂×C₄×Dic₈₉	—	2	1	no	—
64	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
66	C₄²×D₈₉	—	2	1	no	—
67	#15667947	—	4	2	no	—
68	#15667945	C₂×C₄	1	2	yes	—
69	#15667945	C₂×C₄	1	2	yes	—
70	#15667943	C₂×C₄	1	2	yes	—
71	#15667943	C₂×C₄	1	2	yes	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	—	2	1	no	—
74	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
75	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
76	C₄⋊#10623494	C₂×C₄	1	2	yes	—
77	#15667941	—	2	2	no	—
78	#15667941	—	2	2	no	—
79	#15667938	—	2	2	no	—
80	#15667938	Q₈	1	4	yes	complemented
81	#15667935	C₂×C₄	1	2	yes	—
82	#15667935	C₂×C₄	1	2	yes	—
83	#15667932	C₂×C₄	1	2	yes	—
84	#15667932	C₂×C₄	1	2	yes	—
85	#15667922	—	4	2	no	—
86	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	#125×C₈₉	C₂×C₄	1	2	yes	—
92	C₂²⋊Q₈×C₈₉	—	2	1	no	—
93	C₂²⋊Q₈×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	#117×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	—	2	2	no	—
99	C₄⋊C₈×C₈₉	—	2	2	no	—
100	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
103	#97×C₈₉	—	2	2	no	—
104	#97×C₈₉	—	2	1	no	—
105	C₄×C₈×C₈₉	—	2	2	no	—
106	C₄×C₈×C₈₉	—	2	1	no	—
107	#13083574	—	2	1	no	—
108	#13083574	—	2	1	no	—
109	#13083574	C₂×Q₈	1	2	yes	—
110	#13083574	#41	1	2	yes	—
111	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	—	2	1	no	—
114	C₂²×Dic₈₉	—	2	1	no	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	C₂×C₄×D₈₉	—	2	1	no	—
119	#13083558	—	2	2	no	—
120	#13083558	—	2	2	no	—
121	#13083557	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	C₂²×C₄	1	2	yes	—
126	C₂×#10623494	C₂²×C₄	1	2	yes	—
127	C₈×D₈₉	—	4	4	no	—
128	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	#13083553	—	2	1	no	—
131	#13083553	—	2	1	no	—
132	C₂²⋊Dic₈₉	—	2	1	no	—
133	#13083551	—	2	1	no	—
134	#13083551	—	2	1	no	—
135	C₄×Dic₈₉	—	2	1	no	—
136	C₄×Dic₈₉	—	2	1	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	4	2	no	—
142	C₄×Dic₈₉	—	4	2	no	—
143	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
144	C₂×Q₈×C₈₉	—	2	1	no	—
145	C₂×Q₈×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
149	M₁₆×C₈₉	—	2	1	no	—
150	M₁₆×C₈₉	—	2	1	no	—
151	M₁₆×C₈₉	—	2	1	no	—
152	M₁₆×C₈₉	C₂×Q₈	1	2	yes	—
153	C₂×C₈×C₈₉	—	2	1	no	—
154	C₂×C₈×C₈₉	—	2	2	no	—
155	C₂×C₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	2	1	no	—
157	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₈₉	—	2	2	no	—
160	C₄⋊C₄×C₈₉	—	2	2	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
164	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
165	C₂²⋊C₄×C₈₉	—	2	2	no	—
166	C₄²×C₈₉	—	2	2	no	—
167	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂²×D₈₉	—	2	1	no	—
173	Q₈×C₈₉	—	4	2	no	—
174	Q₈×C₈₉	—	8	1	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂²⋊D₈₉	—	2	2	no	—
190	C₂²⋊D₈₉	—	2	2	no	—
191	C₂×Dic₈₉	—	2	1	no	—
192	C₂×Dic₈₉	—	2	2	no	—
193	C₂×Dic₈₉	—	2	1	no	—
194	C₂×Dic₈₉	—	2	1	no	—
195	C₂×Dic₈₉	—	2	2	no	—
196	C₂×Dic₈₉	—	4	1	no	—
197	C₂×Dic₈₉	—	4	1	no	—
198	C₂×Dic₈₉	—	4	1	no	—
199	C₂×Dic₈₉	—	4	1	no	—
200	D₃₅₆	—	2	1	no	—
201	D₃₅₆	C₄×Q₈	1	2	yes	—
202	C₄×D₈₉	—	2	2	no	—
203	C₄×D₈₉	—	2	2	no	—
204	C₄×D₈₉	—	4	2	no	—
205	C₄×D₈₉	—	8	1	no	—
206	Dic₁₇₈	—	2	1	no	—
207	Dic₁₇₈	C₄×Q₈	1	2	yes	—
208	C₈×C₈₉	—	2	2	no	—
209	C₈×C₈₉	—	2	2	no	—
210	C₈×C₈₉	—	2	2	no	—
211	C₈×C₈₉	—	4	1	no	—
212	#10623494	—	2	2	no	—
213	#10623494	—	2	2	no	—
214	#10623494	—	4	2	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₈₉	#552	1	1	yes	characteristic
219	C₂²×C₈₉	#554	1	1	yes	characteristic
220	C₂×D₈₉	—	2	2	no	—
221	C₂×D₈₉	—	4	1	no	—
222	C₂×D₈₉	—	4	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	4	2	no	—
227	C₄×C₈₉	—	4	2	no	—
228	C₄×C₈₉	#444	1	2	yes	—
229	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₄×C₈₉	#520	1	1	yes	characteristic
231	C₄×C₈₉	#546	1	1	yes	characteristic
232	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
233	Dic₈₉	—	2	2	no	—
234	Dic₈₉	—	4	2	no	—
235	Dic₈₉	—	4	2	no	—
236	Dic₈₉	—	4	1	no	—
237	Dic₈₉	—	4	1	no	—
238	#22983	—	89	1	no	maximal, Sylow
239	C₂×C₈₉	—	2	1	no	—
240	C₂×C₈₉	—	2	1	no	—
241	C₂×C₈₉	#2360	1	1	yes	characteristic
242	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
243	C₂×C₈₉	#2956	1	1	yes	characteristic
244	D₈₉	—	4	2	no	—
245	#3076	—	89	1	no	—
246	#2962	D₈₉	1	1	yes	characteristic, complemented
247	#2906	—	89	1	no	—
248	#1994	—	89	1	no	—
249	#1950	—	89	1	no	—
250	#1946	—	89	2	no	—
251	#1922	—	89	2	no	—
252	#1866	—	89	2	no	—
253	#1767	—	89	1	no	—
254	#1765	—	89	2	no	—
255	C₄×#104	—	89	1	no	—
256	C₈₉	#22983	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	89	2	no	—
258	#533	C₂×D₈₉	1	1	yes	characteristic
259	C₄×#41	—	89	1	no	—
260	#479	—	89	2	no	—
261	#478	—	89	2	no	—
262	#477	—	89	1	no	—
263	#476	—	89	1	no	—
264	#475	—	89	1	no	—
265	#474	—	89	1	no	—
266	#446	—	2	2	no	—
267	#446	—	2	1	no	—
268	C₈×Q₈	—	2	1	no	—
269	C₂×#108	—	89	2	no	—
270	#427	—	89	2	no	—
271	#424	—	89	2	no	—
272	#424	—	178	2	no	—
273	#424	C₂×D₈₉	1	2	yes	—
274	#423	—	89	1	no	—
275	#423	—	178	1	no	—
276	C₂×C₄⋊C₈	—	89	1	no	—
277	C₂×C₄⋊C₈	—	178	1	no	—
278	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
279	C₂×#104	—	89	1	no	—
280	C₂×#104	—	89	1	no	—
281	#416	—	89	2	no	—
282	#405	C₂×D₈₉	1	2	yes	—
283	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
284	C₂×#97	—	89	2	no	—
285	C₄³	—	89	1	no	—
286	#341	—	89	2	no	—
287	#339	—	89	1	no	—
288	#339	—	89	1	no	—
289	#339	—	89	2	no	—
290	#339	—	89	2	no	—
291	#336	—	89	2	no	—
292	C₂×#41	—	89	1	no	—
293	#131	—	356	2	no	—
294	#131	—	178	4	no	—
295	C₂×M₁₆	—	89	2	no	—
296	C₂×M₁₆	—	178	2	no	—
297	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
298	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
299	C₂²×C₈	—	89	2	no	—
300	C₂²×C₈	—	178	2	no	—
301	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
302	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
304	#125	C₄×D₈₉	1	2	yes	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	89	1	no	—
310	C₄×Q₈	—	89	1	no	—
311	C₄×D₄	—	89	1	no	—
312	C₄×D₄	—	89	1	no	—
313	C₄×D₄	—	178	1	no	—
314	C₄×D₄	—	178	1	no	—
315	#117	—	89	1	no	—
316	#117	—	178	1	no	—
317	#117	C₂²×D₈₉	1	2	yes	—
318	C₂×C₄²	—	89	1	no	—
319	C₂×C₄²	—	89	1	no	—
320	C₂×C₄²	—	178	1	no	—
321	C₂×C₄²	—	178	1	no	—
322	C₂×C₄²	—	178	1	no	—
323	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
324	#108	—	356	2	no	—
325	#107	—	89	2	no	—
326	#107	—	89	2	no	—
327	#106	—	89	2	no	—
328	#106	—	89	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	89	1	no	—
332	C₄⋊C₈	—	89	1	no	—
333	C₄⋊C₈	—	89	2	no	—
334	C₄⋊C₈	—	178	2	no	—
335	C₄⋊C₈	—	178	2	no	—
336	C₄⋊C₈	—	178	1	no	—
337	C₄⋊C₈	—	178	1	no	—
338	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
339	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
340	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
341	#104	—	89	4	no	—
342	#104	—	178	2	no	—
343	#103	—	89	2	no	—
344	#103	—	89	2	no	—
345	#102	—	89	2	no	—
346	#102	—	89	2	no	—
347	#97	—	2	2	no	—
348	#97	—	2	1	no	—
349	#97	—	356	2	no	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	—	2	1	no	—
352	#41	—	89	2	no	—
353	#41	—	89	2	no	—
354	#41	—	178	1	no	—
355	#41	—	178	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	89	1	no	—
359	C₂×D₄	—	89	1	no	—
360	C₂×D₄	—	178	1	no	—
361	C₂²×C₄	—	178	1	no	—
362	C₂²×C₄	—	178	1	no	—
363	C₂²×C₄	—	178	1	no	—
364	C₂²×C₄	—	178	1	no	—
365	C₂²×C₄	—	178	1	no	—
366	C₂²×C₄	#13083574	1	1	yes	characteristic
367	C₂²×C₄	#13083574	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	356	4	no	—
373	M₁₆	—	178	2	no	—
374	M₁₆	—	178	2	no	—
375	M₁₆	Q₈×D₈₉	1	2	yes	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	89	2	no	—
381	C₂×C₈	—	89	2	no	—
382	C₂×C₈	—	356	4	no	—
383	C₂×C₈	—	178	2	no	—
384	C₂×C₈	—	178	2	no	—
385	C₂×C₈	—	178	2	no	—
386	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	89	1	no	—
393	C₄⋊C₄	—	89	1	no	—
394	C₄⋊C₄	—	178	1	no	—
395	C₄⋊C₄	—	178	1	no	—
396	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
397	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	178	1	no	—
400	C₂²⋊C₄	—	178	1	no	—
401	C₂²⋊C₄	—	178	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	89	2	no	—
404	C₄²	—	356	2	no	—
405	C₄²	—	356	2	no	—
406	C₄²	—	178	1	no	—
407	C₄²	—	178	1	no	—
408	C₄²	—	178	1	no	—
409	C₄²	—	178	1	no	—
410	C₄²	—	178	1	no	—
411	C₄²	—	178	1	no	—
412	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
413	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
416	C₂³	—	178	1	no	—
417	C₂³	C₂×#13083574	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	8	1	no	—
420	Q₈	—	89	2	no	—
421	Q₈	—	178	1	no	—
422	D₄	—	89	2	no	—
423	D₄	—	178	2	no	—
424	D₄	—	178	2	no	—
425	D₄	—	178	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	356	1	no	—
431	C₂×C₄	—	356	1	no	—
432	C₂×C₄	—	356	1	no	—
433	C₂×C₄	—	356	1	no	—
434	C₂×C₄	—	356	2	no	—
435	C₂×C₄	—	178	2	no	—
436	C₂×C₄	—	178	2	no	—
437	C₂×C₄	—	178	1	no	—
438	C₂×C₄	—	178	1	no	—
439	C₂×C₄	—	178	1	no	—
440	C₂×C₄	—	178	2	no	—
441	C₂×C₄	—	178	2	no	—
442	C₂×C₄	—	712	1	no	—
443	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
446	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
450	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
451	C₂×C₄	#15668058	1	1	yes	characteristic
452	C₂×C₄	#15668060	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	356	2	no	—
458	C₈	—	178	2	no	—
459	C₈	—	178	2	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	356	1	no	—
463	C₂²	—	356	1	no	—
464	C₂²	—	178	2	no	—
465	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
466	C₂²	#19152289	1	1	yes	characteristic
467	C₂²	#19152308	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	356	2	no	—
474	C₄	—	356	2	no	—
475	C₄	—	356	1	no	—
476	C₄	—	356	1	no	—
477	C₄	—	178	2	no	—
478	C₄	#19151718	1	2	yes	—
479	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
480	C₄	#19152080	1	1	yes	characteristic
481	C₄	#19152236	1	1	yes	characteristic
482	C₄	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	356	2	no	—
486	C₂	#26023253	1	1	yes	characteristic
487	C₂	C₂×#19151718	1	1	yes	characteristic
488	C₂	#26029159	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2962	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂³
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2962	D₈₉
hypocenter	C₈₉	#22983
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #26021230	C₂	semidirect
4. #26021027	C₂	semidirect
5. #26021002	C₂	semidirect
6. #26020851	C₂	semidirect
8. #26020107	C₂	semidirect
11. C₈₉×#2962	C₂	semidirect
14. #19151902	C₄	semidirect
15. #19151895	C₄	semidirect
16. #19151890	C₄	semidirect
17. #19151885	C₄	semidirect
18. #19151880	C₄	semidirect
19. #19151875	C₄	semidirect
80. #15667938	Q₈	semidirect
246. #2962	D₈₉	semidirect
256. C₈₉	#22983	semidirect

Maximal subgroups

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

subgroup	index
#26030034	2
#26028817	2
#26021230	2
#26021027	2
#26021002	2
#26020851	2
#26020526	2
#26020107	2
#26020098	2
C₄×#15667938	2
C₈₉×#2962	2
#22983	89