Subgroups — #36562272

Order 22784.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 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	#26029187	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668020	C₂	1	1	yes	maximal, characteristic
4	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020854	C₂	1	2	yes	maximal, complemented
6	#26020528	C₂	1	2	yes	maximal
7	#26020273	C₂	1	1	yes	maximal, characteristic
8	#26020135	C₂	1	2	yes	maximal, complemented
9	#26020121	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020093	C₂	1	2	yes	maximal
11	C₈₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	1	yes	characteristic
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19151902	C₄	1	2	yes	complemented
16	#19151895	C₄	1	2	yes	complemented
17	#19151890	C₄	1	1	yes	characteristic, complemented
18	#19151885	C₄	1	1	yes	characteristic, complemented
19	#19151880	C₄	1	1	yes	characteristic, complemented
20	#19151875	C₄	1	1	yes	characteristic, complemented
21	#19151729	—	2	1	no	—
22	#19151729	—	2	1	no	—
23	Q₈×#10623494	—	2	1	no	—
24	Q₈×#10623494	—	2	1	no	—
25	C₂×#15667947	C₂²	1	2	yes	—
26	#19151634	C₂²	1	2	yes	—
27	#19151625	C₂²	1	2	yes	—
28	#19151622	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	C₂×#15667940	C₂²	1	2	yes	—
31	#19151592	C₂²	1	2	yes	—
32	#19151556	C₂²	1	1	yes	characteristic
33	#19151556	C₂²	1	1	yes	characteristic
34	#19151555	—	2	1	no	—
35	#19151555	—	2	1	no	—
36	#19151554	C₂²	1	2	yes	—
37	C₄×#13083557	—	2	1	no	—
38	C₂×#15667923	C₂²	1	2	yes	—
39	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₈₉	—	2	1	no	—
41	#19151362	C₂²	1	2	yes	—
42	#19151358	C₂²	1	2	yes	—
43	#19151353	C₂²	1	2	yes	—
44	#533×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
47	#339×C₈₉	C₂²	1	2	yes	—
48	#339×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083574	C₂³	1	1	yes	characteristic
50	#15668020	—	2	2	no	—
51	#15668020	—	2	2	no	—
52	#15668020	—	2	2	no	—
53	#15668020	Q₈	1	4	yes	complemented
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂×#13083557	—	2	1	no	—
56	C₂×#13083557	—	2	1	no	—
57	C₂²×#10623494	C₂³	1	2	yes	—
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₈₉	—	2	1	no	—
61	C₂×C₈×D₈₉	—	2	1	no	—
62	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	#15667971	C₂³	1	1	yes	characteristic
69	#15667969	—	2	1	no	—
70	C₄²×D₈₉	—	2	1	no	—
71	#15667947	—	2	4	no	—
72	#15667945	C₂×C₄	1	2	yes	—
73	#15667945	C₂×C₄	1	2	yes	—
74	#15667943	C₂×C₄	1	2	yes	—
75	#15667943	C₂×C₄	1	2	yes	—
76	C₄⋊#10623494	—	2	2	no	—
77	C₄⋊#10623494	—	2	2	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	—	2	1	no	—
80	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
81	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#10623494	C₂×C₄	1	2	yes	—
83	#15667940	—	2	4	no	—
84	#15667935	C₂×C₄	1	2	yes	—
85	#15667935	C₂×C₄	1	2	yes	—
86	#15667932	C₂×C₄	1	2	yes	—
87	#15667932	C₂×C₄	1	2	yes	—
88	#15667923	—	2	2	no	—
89	#15667923	—	2	4	no	—
90	#15667922	—	2	1	no	—
91	#15667922	—	2	1	no	—
92	C₄×#10623494	—	2	2	no	—
93	C₄×#10623494	D₄	1	1	yes	characteristic
94	C₄×#10623494	D₄	1	1	yes	characteristic
95	C₄×#10623494	D₄	1	1	yes	characteristic
96	C₄×#10623494	D₄	1	1	yes	characteristic
97	C₈×Dic₈₉	—	2	1	no	—
98	C₈×Dic₈₉	—	2	1	no	—
99	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
103	#125×C₈₉	C₂×C₄	1	2	yes	—
104	C₂²⋊Q₈×C₈₉	—	2	1	no	—
105	C₂²⋊Q₈×C₈₉	—	2	1	no	—
106	C₄×Q₈×C₈₉	—	2	1	no	—
107	C₄×Q₈×C₈₉	—	2	1	no	—
108	#117×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	#97×C₈₉	—	2	1	no	—
113	C₄×C₈×C₈₉	—	2	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	#13083574	—	2	1	no	—
116	#13083574	—	2	1	no	—
117	#13083574	C₂×Q₈	1	2	yes	—
118	#13083574	#41	1	2	yes	—
119	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	2	1	no	—
124	C₂×C₄×D₈₉	—	2	1	no	—
125	#13083558	—	2	2	no	—
126	#13083558	—	2	2	no	—
127	#13083557	—	2	4	no	—
128	#13083557	—	2	4	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	2	2	no	—
132	C₂×#10623494	—	2	2	no	—
133	C₂×#10623494	—	2	2	no	—
134	C₂×#10623494	C₂²×C₄	1	2	yes	—
135	C₂×#10623494	C₂²×C₄	1	2	yes	—
136	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
137	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
138	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
139	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
140	C₂×#10623494	C₂×Q₈	1	2	yes	—
141	C₂×#10623494	#41	1	2	yes	—
142	C₈×D₈₉	—	2	4	no	—
143	C₈×D₈₉	—	2	4	no	—
144	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
146	#13083553	—	2	1	no	—
147	#13083553	—	2	1	no	—
148	C₂²⋊Dic₈₉	—	2	1	no	—
149	#13083551	—	2	1	no	—
150	#13083551	—	2	1	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₄×Dic₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	—	2	2	no	—
157	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	M₁₆×C₈₉	—	2	1	no	—
161	M₁₆×C₈₉	—	2	1	no	—
162	M₁₆×C₈₉	C₂×Q₈	1	2	yes	—
163	M₁₆×C₈₉	#41	1	2	yes	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	—	2	2	no	—
167	C₄⋊C₄×C₈₉	—	2	2	no	—
168	C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₄⋊C₄×C₈₉	—	2	1	no	—
170	C₄⋊C₄×C₈₉	—	4	2	no	—
171	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
172	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
173	C₂²⋊C₄×C₈₉	—	2	2	no	—
174	C₄²×C₈₉	—	2	2	no	—
175	C₄²×C₈₉	—	2	2	no	—
176	C₄²×C₈₉	—	2	2	no	—
177	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
182	C₂²×D₈₉	—	2	1	no	—
183	Q₈×C₈₉	—	4	2	no	—
184	Q₈×C₈₉	—	4	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₈₉	—	2	2	no	—
203	C₂²⋊D₈₉	—	2	2	no	—
204	C₂×Dic₈₉	—	2	1	no	—
205	C₂×Dic₈₉	—	2	1	no	—
206	C₂×Dic₈₉	—	2	1	no	—
207	D₃₅₆	—	2	1	no	—
208	D₃₅₆	C₄×Q₈	1	2	yes	—
209	C₄×D₈₉	—	2	2	no	—
210	C₄×D₈₉	—	2	2	no	—
211	C₄×D₈₉	—	4	2	no	—
212	C₄×D₈₉	—	4	2	no	—
213	Dic₁₇₈	—	2	1	no	—
214	Dic₁₇₈	C₄×Q₈	1	2	yes	—
215	C₈×C₈₉	—	2	2	no	—
216	C₈×C₈₉	—	2	2	no	—
217	#10623494	—	2	2	no	—
218	#10623494	—	2	2	no	—
219	#10623494	—	2	1	no	—
220	#10623494	—	2	1	no	—
221	#10623494	—	4	2	no	—
222	#10623494	C₂²⋊Q₈	1	2	yes	—
223	#10623494	C₂²⋊Q₈	1	2	yes	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₈₉	#529	1	1	yes	characteristic
228	C₂²×C₈₉	#533	1	1	yes	characteristic
229	C₂×D₈₉	—	2	2	no	—
230	C₂×D₈₉	—	4	1	no	—
231	C₂×D₈₉	—	4	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	2	1	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	4	2	no	—
236	C₄×C₈₉	—	4	2	no	—
237	C₄×C₈₉	—	8	2	no	—
238	C₄×C₈₉	#444	1	2	yes	—
239	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
240	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
241	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₈₉	#525	1	1	yes	characteristic
243	Dic₈₉	—	2	2	no	—
244	Dic₈₉	—	4	1	no	—
245	Dic₈₉	—	4	1	no	—
246	#21628	—	89	1	no	maximal, Sylow
247	C₂×C₈₉	—	2	1	no	—
248	C₂×C₈₉	—	2	1	no	—
249	C₂×C₈₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
251	C₂×C₈₉	#2955	1	1	yes	characteristic
252	D₈₉	—	4	2	no	—
253	#3076	—	89	1	no	—
254	#2960	—	89	1	no	—
255	C₄×#131	—	89	1	no	—
256	#1986	D₈₉	1	1	yes	characteristic, complemented
257	#1950	—	89	1	no	—
258	#1922	—	89	2	no	—
259	#1866	—	89	2	no	—
260	#1806	—	89	1	no	—
261	#1773	—	89	2	no	—
262	#1770	—	89	1	no	—
263	#1765	—	89	2	no	—
264	C₈₉	#21628	1	1	yes	characteristic, complemented, Sylow
265	C₂×#131	—	89	1	no	—
266	C₂×#131	—	89	1	no	—
267	#533	C₂×D₈₉	1	1	yes	characteristic
268	C₄×#41	—	89	1	no	—
269	#479	—	89	2	no	—
270	#478	—	89	2	no	—
271	#477	—	89	1	no	—
272	#476	—	89	1	no	—
273	#475	—	89	1	no	—
274	#474	—	89	1	no	—
275	#446	—	178	1	no	—
276	#446	—	178	1	no	—
277	C₈×Q₈	—	178	1	no	—
278	C₈×Q₈	—	178	1	no	—
279	C₂×#108	—	89	2	no	—
280	#427	—	89	2	no	—
281	#424	—	89	2	no	—
282	#423	—	89	1	no	—
283	C₂×C₄⋊C₈	—	89	1	no	—
284	C₂×#104	—	89	2	no	—
285	#416	—	89	2	no	—
286	#405	—	89	1	no	—
287	#405	—	89	1	no	—
288	#405	—	89	2	no	—
289	#405	—	178	1	no	—
290	#405	—	178	1	no	—
291	C₄×M₁₆	—	178	1	no	—
292	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
293	C₂×#97	—	89	2	no	—
294	C₂×C₄×C₈	—	89	1	no	—
295	C₂×C₄×C₈	—	178	1	no	—
296	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
297	#341	—	89	2	no	—
298	#339	—	89	2	no	—
299	#339	C₂×D₈₉	1	2	yes	—
300	#339	C₂×D₈₉	1	2	yes	—
301	#336	—	89	2	no	—
302	C₂×#41	—	89	1	no	—
303	#131	—	89	4	no	—
304	#131	—	178	2	no	—
305	#131	—	178	2	no	—
306	#131	—	178	2	no	—
307	C₂×M₁₆	—	89	2	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂×M₁₆	—	178	1	no	—
310	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
311	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
312	C₂²×C₈	—	89	1	no	—
313	C₂²×C₈	—	89	1	no	—
314	C₂²×C₈	—	89	2	no	—
315	C₂²×C₈	—	178	1	no	—
316	C₂²×C₈	—	178	1	no	—
317	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
319	#125	C₄×D₈₉	1	2	yes	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	89	1	no	—
325	C₄×Q₈	—	89	1	no	—
326	C₄×D₄	—	89	1	no	—
327	C₄×D₄	—	89	1	no	—
328	C₄×D₄	—	178	1	no	—
329	C₄×D₄	—	178	1	no	—
330	#117	—	89	1	no	—
331	#117	—	178	1	no	—
332	#117	C₂²×D₈₉	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	178	1	no	—
335	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
336	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
337	#108	—	178	4	no	—
338	#107	—	89	2	no	—
339	#107	—	89	2	no	—
340	#106	—	89	2	no	—
341	#106	—	89	2	no	—
342	C₄⋊C₈	—	89	1	no	—
343	C₄⋊C₈	—	89	1	no	—
344	C₄⋊C₈	—	89	2	no	—
345	C₄⋊C₈	—	178	2	no	—
346	C₄⋊C₈	—	178	2	no	—
347	C₄⋊C₈	—	178	1	no	—
348	C₄⋊C₈	—	178	1	no	—
349	#104	—	178	4	no	—
350	#103	—	89	2	no	—
351	#103	—	89	2	no	—
352	#102	—	89	2	no	—
353	#102	—	89	2	no	—
354	#97	—	2	1	no	—
355	#97	—	178	4	no	—
356	#97	—	178	2	no	—
357	#97	—	178	1	no	—
358	#97	—	178	1	no	—
359	C₄×C₈	—	2	1	no	—
360	C₄×C₈	—	89	1	no	—
361	C₄×C₈	—	89	1	no	—
362	C₄×C₈	—	89	1	no	—
363	C₄×C₈	—	89	1	no	—
364	C₄×C₈	—	178	2	no	—
365	C₄×C₈	—	178	1	no	—
366	C₄×C₈	—	178	1	no	—
367	#95	—	2	1	no	—
368	#41	—	89	2	no	—
369	#41	—	89	2	no	—
370	#41	—	178	1	no	—
371	#41	—	178	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	89	1	no	—
375	C₂×D₄	—	89	1	no	—
376	C₂×D₄	—	178	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	178	1	no	—
379	C₂²×C₄	—	178	1	no	—
380	C₂²×C₄	—	178	1	no	—
381	C₂²×C₄	#13083573	1	1	yes	characteristic
382	C₂²×C₄	#13083573	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	178	4	no	—
387	M₁₆	—	178	4	no	—
388	M₁₆	—	178	2	no	—
389	M₁₆	—	178	2	no	—
390	M₁₆	Q₈×D₈₉	1	2	yes	—
391	M₁₆	#13083575	1	2	yes	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	89	1	no	—
395	C₂×C₈	—	89	1	no	—
396	C₂×C₈	—	89	2	no	—
397	C₂×C₈	—	89	2	no	—
398	C₂×C₈	—	89	2	no	—
399	C₂×C₈	—	89	2	no	—
400	C₂×C₈	—	89	1	no	—
401	C₂×C₈	—	89	1	no	—
402	C₂×C₈	—	178	4	no	—
403	C₂×C₈	—	178	4	no	—
404	C₂×C₈	—	178	2	no	—
405	C₂×C₈	—	178	2	no	—
406	C₂×C₈	—	178	1	no	—
407	C₂×C₈	—	178	2	no	—
408	C₂×C₈	—	178	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	89	1	no	—
415	C₄⋊C₄	—	89	1	no	—
416	C₄⋊C₄	—	178	1	no	—
417	C₄⋊C₄	—	178	1	no	—
418	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
419	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	178	1	no	—
422	C₂²⋊C₄	—	178	1	no	—
423	C₂²⋊C₄	—	178	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	178	1	no	—
428	C₄²	—	178	1	no	—
429	C₄²	—	178	1	no	—
430	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
432	C₄²	D₄×D₈₉	1	1	yes	characteristic
433	C₄²	D₄×D₈₉	1	1	yes	characteristic
434	C₂³	—	178	1	no	—
435	C₂³	C₂×#13083573	1	1	yes	characteristic
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	89	2	no	—
439	Q₈	—	178	1	no	—
440	D₄	—	89	2	no	—
441	D₄	—	178	2	no	—
442	D₄	—	178	2	no	—
443	D₄	—	178	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	356	2	no	—
452	C₂×C₄	—	356	2	no	—
453	C₂×C₄	—	178	1	no	—
454	C₂×C₄	—	178	1	no	—
455	C₂×C₄	—	178	1	no	—
456	C₂×C₄	—	178	2	no	—
457	C₂×C₄	—	178	2	no	—
458	C₂×C₄	#15667972	1	1	yes	characteristic
459	C₂×C₄	#15667972	1	1	yes	characteristic
460	C₂×C₄	#15667972	1	1	yes	characteristic
461	C₂×C₄	#15667972	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
465	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
466	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	89	2	no	—
471	C₈	—	89	2	no	—
472	C₈	—	356	2	no	—
473	C₈	—	178	2	no	—
474	C₈	—	178	2	no	—
475	C₈	—	178	1	no	—
476	C₈	—	178	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	356	1	no	—
480	C₂²	—	356	1	no	—
481	C₂²	—	178	2	no	—
482	C₂²	C₂×#15667972	1	1	yes	characteristic
483	C₂²	#19152127	1	1	yes	characteristic
484	C₂²	#19152153	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	2	no	—
491	C₄	—	356	1	no	—
492	C₄	—	356	1	no	—
493	C₄	—	178	2	no	—
494	C₄	#19151717	1	2	yes	—
495	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
496	C₄	C₄×#13083575	1	1	yes	characteristic
497	C₄	C₂²⋊Q₈×D₈₉	1	1	yes	characteristic
498	C₄	#19152111	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	356	2	no	—
502	C₂	#26022790	1	1	yes	characteristic
503	C₂	C₂×#19151717	1	1	yes	characteristic
504	C₂	#26029151	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1986	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂³
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1986	D₈₉
hypocenter	C₈₉	#21628
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1986

Complements

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

N	H ≅ G/N	type
2. #26029187	C₂	semidirect
4. #26021027	C₂	semidirect
5. #26020854	C₂	semidirect
8. #26020135	C₂	semidirect
9. #26020121	C₂	semidirect
11. C₈₉×#1986	C₂	semidirect
15. #19151902	C₄	semidirect
16. #19151895	C₄	semidirect
17. #19151890	C₄	semidirect
18. #19151885	C₄	semidirect
19. #19151880	C₄	semidirect
20. #19151875	C₄	semidirect
53. #15668020	Q₈	semidirect
256. #1986	D₈₉	semidirect
264. C₈₉	#21628	semidirect

Maximal subgroups

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

subgroup	index
#26030034	2
#26029187	2
C₄×#15668020	2
#26021027	2
#26020854	2
#26020528	2
#26020273	2
#26020135	2
#26020121	2
#26020093	2
C₈₉×#1986	2
#21628	89