Subgroups — #36526147

Order 22784.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029381	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029373	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668034	C₂	1	1	yes	maximal, characteristic
4	#26019156	C₂	1	2	yes	maximal, complemented
5	#26019104	C₂	1	2	yes	maximal, complemented
6	#26019083	C₂	1	2	yes	maximal, complemented
7	#26019066	C₂	1	2	yes	maximal, complemented
8	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018692	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018692	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19151728	C₂²	1	2	yes	—
16	C₈×Dic₁₇₈	C₂²	1	2	yes	—
17	C₄×Dic₃₅₆	C₄	1	1	yes	characteristic
18	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
19	C₄×#13083563	C₄	1	1	yes	characteristic
20	C₄×#13083563	C₄	1	1	yes	characteristic
21	C₄×#13083563	C₂²	1	1	yes	characteristic
22	C₄×#13083563	C₂²	1	1	yes	characteristic
23	C₄×D₇₁₂	C₄	1	1	yes	characteristic
24	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
25	#19151677	C₂²	1	2	yes	—
26	#19151673	—	2	2	no	—
27	#19151672	—	2	2	no	—
28	C₈×D₃₅₆	C₂²	1	2	yes	—
29	#19151654	—	2	1	no	—
30	#19151650	—	2	1	no	—
31	#19151636	C₄	1	1	yes	characteristic
32	#19151622	C₂²	1	1	yes	characteristic
33	#19151622	C₂²	1	1	yes	characteristic
34	#19151620	—	2	1	no	—
35	C₄⋊C₈×D₈₉	—	2	1	no	—
36	#19151595	C₄	1	1	yes	characteristic
37	#19151595	C₄	1	1	yes	characteristic
38	#19151351	C₂²	1	2	yes	—
39	#19151351	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151330	C₂²	1	2	yes	—
42	#19151327	C₂²	1	2	yes	—
43	#19151327	C₂²	1	2	yes	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#322×C₈₉	C₂²	1	2	yes	—
48	#322×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
51	#15668034	—	2	4	no	—
52	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
55	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083558	—	2	1	no	—
57	C₂×#13083558	—	2	1	no	—
58	C₂×#13083557	—	2	2	no	—
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₈₉	—	2	1	no	—
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	C₄×C₂²⋊D₈₉	—	2	1	no	—
71	C₄×C₂²⋊D₈₉	—	2	1	no	—
72	#15667971	C₂×C₄	1	1	yes	characteristic
73	#15667971	C₂×C₄	1	1	yes	characteristic
74	#15667969	—	2	1	no	—
75	#15667969	—	2	1	no	—
76	C₄²×D₈₉	—	2	1	no	—
77	C₄²×D₈₉	—	2	1	no	—
78	#15667946	C₂×C₄	1	1	yes	characteristic
79	#15667946	C₂×C₄	1	1	yes	characteristic
80	#15667944	C₂×C₄	1	1	yes	characteristic
81	#15667944	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#10623494	—	2	1	no	—
83	C₄⋊#10623494	—	2	1	no	—
84	C₄⋊#10623494	C₂³	1	2	yes	—
85	C₄⋊#10623494	C₂³	1	2	yes	—
86	#15667941	—	2	2	no	—
87	#15667941	—	2	2	no	—
88	#15667937	C₂×C₄	1	1	yes	characteristic
89	#15667937	C₂×C₄	1	1	yes	characteristic
90	#15667937	C₂×C₄	1	1	yes	characteristic
91	#15667937	C₂×C₄	1	1	yes	characteristic
92	#15667934	C₂×C₄	1	1	yes	characteristic
93	#15667934	C₂×C₄	1	1	yes	characteristic
94	#15667934	C₂×C₄	1	1	yes	characteristic
95	#15667934	C₂×C₄	1	1	yes	characteristic
96	#15667924	—	2	2	no	—
97	#15667924	—	2	2	no	—
98	#15667922	—	2	2	no	—
99	C₈×Dic₈₉	—	2	2	no	—
100	C₂×M₁₆×C₈₉	—	2	1	no	—
101	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
107	#97×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₈₉	C₂³	1	2	yes	—
111	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₈₉	C₂³	1	2	yes	—
114	#13083574	—	2	2	no	—
115	#13083574	—	2	2	no	—
116	#13083574	—	4	1	no	—
117	#13083574	—	4	1	no	—
118	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₈₉	—	2	1	no	—
123	C₂×C₂²⋊D₈₉	—	2	1	no	—
124	C₂×C₄×D₈₉	—	2	1	no	—
125	C₂×C₄×D₈₉	—	2	1	no	—
126	C₂×C₄×D₈₉	—	2	1	no	—
127	C₂×C₄×D₈₉	—	2	1	no	—
128	C₂×C₄×D₈₉	—	2	1	no	—
129	C₂×C₄×D₈₉	—	2	1	no	—
130	Dic₃₅₆	—	2	2	no	—
131	#13083563	—	2	2	no	—
132	#13083563	M₁₆	1	4	yes	complemented
133	D₇₁₂	—	2	2	no	—
134	#13083558	—	8	1	no	—
135	#13083558	—	8	1	no	—
136	#13083557	—	8	2	no	—
137	C₂×#10623494	—	2	2	no	—
138	C₂×#10623494	—	2	2	no	—
139	C₈×D₈₉	—	8	2	no	—
140	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
144	#13083553	—	2	1	no	—
145	#13083553	—	2	1	no	—
146	#13083553	—	2	1	no	—
147	#13083553	—	2	1	no	—
148	C₂²⋊Dic₈₉	—	2	1	no	—
149	C₂²⋊Dic₈₉	—	2	1	no	—
150	#13083551	—	2	1	no	—
151	#13083551	—	2	1	no	—
152	#13083551	—	2	1	no	—
153	#13083551	—	2	1	no	—
154	C₄×Dic₈₉	—	2	1	no	—
155	C₄×Dic₈₉	—	2	1	no	—
156	C₄×Dic₈₉	—	2	1	no	—
157	C₄×Dic₈₉	—	2	1	no	—
158	C₄×Dic₈₉	—	2	1	no	—
159	C₄×Dic₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
163	M₁₆×C₈₉	—	4	2	no	—
164	C₂×C₈×C₈₉	—	2	2	no	—
165	C₂×C₈×C₈₉	—	2	2	no	—
166	C₂×C₈×C₈₉	—	4	1	no	—
167	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
173	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₈₉	#41	1	1	yes	characteristic
176	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₈₉	—	2	1	no	—
179	C₂²×D₈₉	—	2	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	—	2	2	no	—
185	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₂²⋊D₈₉	—	4	2	no	—
192	C₂²⋊D₈₉	—	4	2	no	—
193	C₂×Dic₈₉	—	2	1	no	—
194	C₂×Dic₈₉	—	2	1	no	—
195	C₂×Dic₈₉	—	2	1	no	—
196	C₂×Dic₈₉	—	2	1	no	—
197	C₂×Dic₈₉	—	2	1	no	—
198	C₂×Dic₈₉	—	2	1	no	—
199	D₃₅₆	—	2	1	no	—
200	D₃₅₆	—	2	1	no	—
201	D₃₅₆	—	2	1	no	—
202	D₃₅₆	C₂×M₁₆	1	2	yes	—
203	C₄×D₈₉	—	4	2	no	—
204	C₄×D₈₉	—	4	2	no	—
205	C₄×D₈₉	—	4	1	no	—
206	C₄×D₈₉	—	4	1	no	—
207	C₄×D₈₉	—	4	1	no	—
208	C₄×D₈₉	—	4	1	no	—
209	C₄×D₈₉	—	4	2	no	—
210	C₄×D₈₉	—	4	2	no	—
211	Dic₁₇₈	—	2	1	no	—
212	Dic₁₇₈	—	2	1	no	—
213	Dic₁₇₈	—	2	1	no	—
214	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
215	C₈×C₈₉	—	2	1	no	—
216	C₈×C₈₉	—	2	1	no	—
217	C₈×C₈₉	—	2	1	no	—
218	C₈×C₈₉	—	2	2	no	—
219	C₈×C₈₉	—	2	2	no	—
220	C₈×C₈₉	—	4	2	no	—
221	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
222	#10623494	—	4	2	no	—
223	#10623494	—	4	2	no	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂×D₈₉	—	2	2	no	—
229	C₂×D₈₉	—	4	1	no	—
230	C₂×D₈₉	—	4	1	no	—
231	C₂×D₈₉	—	4	1	no	—
232	C₂×D₈₉	—	4	1	no	—
233	C₂×D₈₉	—	4	1	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	#444	1	2	yes	—
238	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
239	C₄×C₈₉	#568	1	1	yes	characteristic
240	C₄×C₈₉	#576	1	1	yes	characteristic
241	C₄×C₈₉	#578	1	1	yes	characteristic
242	Dic₈₉	—	2	2	no	—
243	Dic₈₉	—	4	1	no	—
244	Dic₈₉	—	4	1	no	—
245	Dic₈₉	—	4	1	no	—
246	Dic₈₉	—	4	1	no	—
247	Dic₈₉	—	4	1	no	—
248	#18061	—	89	1	no	maximal, Sylow
249	C₂×C₈₉	—	4	1	no	—
250	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
251	C₂×C₈₉	#2951	1	1	yes	characteristic
252	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
253	D₈₉	—	4	2	no	—
254	D₈₉	—	8	1	no	—
255	#2991	—	89	1	no	—
256	#2990	—	89	1	no	—
257	C₄×#135	—	89	1	no	—
258	#1592	—	89	2	no	—
259	#1584	—	89	2	no	—
260	#1581	—	89	2	no	—
261	SD₁₆⋊C₈	—	89	2	no	—
262	#1567	—	89	1	no	—
263	#1489	—	89	1	no	—
264	#1489	—	89	1	no	—
265	#1451	D₈₉	1	1	yes	characteristic, complemented
266	C₈₉	#18061	1	1	yes	characteristic, complemented, Sylow
267	C₂×#135	—	89	1	no	—
268	C₄×#41	—	89	1	no	—
269	C₄×#41	—	89	1	no	—
270	#446	—	89	2	no	—
271	C₈×Q₈	—	89	2	no	—
272	C₄×Q₁₆	—	89	1	no	—
273	C₄×Q₁₆	—	89	1	no	—
274	C₄×SD₁₆	—	89	1	no	—
275	C₄×SD₁₆	—	89	1	no	—
276	C₄×SD₁₆	—	89	1	no	—
277	C₄×SD₁₆	—	89	1	no	—
278	C₄×D₈	—	89	1	no	—
279	C₄×D₈	—	89	1	no	—
280	#436	—	89	2	no	—
281	#436	—	178	2	no	—
282	#435	—	178	2	no	—
283	C₈×D₄	—	89	2	no	—
284	#432	—	178	1	no	—
285	#431	—	178	1	no	—
286	#431	C₂×D₈₉	1	1	yes	characteristic
287	#427	—	89	1	no	—
288	#423	—	89	1	no	—
289	#423	—	89	1	no	—
290	#423	—	178	1	no	—
291	C₂×C₄⋊C₈	—	178	1	no	—
292	#416	—	89	1	no	—
293	#416	—	89	1	no	—
294	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
296	#335	—	89	2	no	—
297	#335	—	89	2	no	—
298	Q₈⋊C₈	—	89	2	no	—
299	Q₈⋊C₈	—	89	2	no	—
300	D₄⋊C₈	—	89	2	no	—
301	D₄⋊C₈	—	89	2	no	—
302	#322	C₂×D₈₉	1	2	yes	—
303	#322	C₂×D₈₉	1	2	yes	—
304	C₂×#41	—	89	1	no	—
305	C₂×#41	—	89	1	no	—
306	#135	—	178	4	no	—
307	C₂×Q₁₆	—	89	1	no	—
308	C₂×SD₁₆	—	89	1	no	—
309	C₂×SD₁₆	—	89	1	no	—
310	C₂×D₈	—	89	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	178	1	no	—
313	C₂×M₁₆	—	178	1	no	—
314	C₂×M₁₆	—	178	2	no	—
315	C₂²×C₈	—	178	2	no	—
316	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
317	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
318	C₄×Q₈	—	89	1	no	—
319	C₄×Q₈	—	89	1	no	—
320	C₄×Q₈	—	89	1	no	—
321	C₄×Q₈	—	89	1	no	—
322	C₄×D₄	—	89	1	no	—
323	C₄×D₄	—	89	1	no	—
324	C₄×D₄	—	89	1	no	—
325	C₄×D₄	—	89	1	no	—
326	C₄×D₄	—	178	1	no	—
327	C₄×D₄	—	178	1	no	—
328	C₄×D₄	—	178	1	no	—
329	C₄×D₄	—	178	1	no	—
330	#117	—	89	1	no	—
331	#117	—	89	1	no	—
332	#117	—	178	1	no	—
333	#117	—	178	1	no	—
334	C₂×C₄²	—	178	1	no	—
335	C₂×C₄²	—	178	1	no	—
336	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
337	#107	—	89	1	no	—
338	#107	—	89	1	no	—
339	#106	—	89	1	no	—
340	#106	—	89	1	no	—
341	C₄⋊C₈	—	89	2	no	—
342	C₄⋊C₈	—	89	2	no	—
343	C₄⋊C₈	—	178	2	no	—
344	C₄⋊C₈	—	178	2	no	—
345	C₄⋊C₈	—	178	1	no	—
346	C₄⋊C₈	—	178	1	no	—
347	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
348	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
349	#103	—	89	1	no	—
350	#103	—	89	1	no	—
351	#103	—	89	1	no	—
352	#103	—	89	1	no	—
353	#102	—	89	1	no	—
354	#102	—	89	1	no	—
355	#102	—	89	1	no	—
356	#102	—	89	1	no	—
357	C₂²⋊C₈	—	178	2	no	—
358	C₂²⋊C₈	—	178	2	no	—
359	C₂²⋊C₈	D₃₅₆	1	2	yes	—
360	#97	—	2	1	no	—
361	#97	—	178	2	no	—
362	C₄×C₈	—	178	2	no	—
363	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
364	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
365	C₄×C₈	C₂²×D₈₉	1	2	yes	—
366	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
367	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
368	C₄×C₈	C₂²×D₈₉	1	2	yes	—
369	#41	—	356	1	no	—
370	#41	—	356	1	no	—
371	#41	—	178	2	no	—
372	#41	—	178	2	no	—
373	C₂×Q₈	—	89	1	no	—
374	C₂×Q₈	—	89	1	no	—
375	C₂×D₄	—	89	1	no	—
376	C₂×D₄	—	89	1	no	—
377	C₂×D₄	—	178	1	no	—
378	C₂×D₄	—	178	1	no	—
379	C₂²×C₄	—	178	1	no	—
380	C₂²×C₄	—	178	1	no	—
381	C₂²×C₄	—	178	1	no	—
382	C₂²×C₄	—	178	1	no	—
383	C₂²×C₄	—	178	1	no	—
384	C₂²×C₄	—	178	1	no	—
385	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
387	C₂²×C₄	#13083574	1	1	yes	characteristic
388	Q₁₆	—	178	2	no	—
389	SD₁₆	—	89	4	no	—
390	SD₁₆	—	178	2	no	—
391	D₈	—	178	2	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	712	2	no	—
394	M₁₆	—	712	1	no	—
395	M₁₆	—	712	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	178	2	no	—
400	C₂×C₈	—	178	2	no	—
401	C₂×C₈	—	712	2	no	—
402	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
403	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
404	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
405	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
406	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
407	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
408	C₄⋊C₄	—	89	1	no	—
409	C₄⋊C₄	—	89	1	no	—
410	C₄⋊C₄	—	89	1	no	—
411	C₄⋊C₄	—	89	1	no	—
412	C₄⋊C₄	—	178	1	no	—
413	C₄⋊C₄	—	178	1	no	—
414	C₄⋊C₄	—	178	1	no	—
415	C₄⋊C₄	—	178	1	no	—
416	C₂²⋊C₄	—	178	1	no	—
417	C₂²⋊C₄	—	178	1	no	—
418	C₂²⋊C₄	—	178	1	no	—
419	C₂²⋊C₄	—	178	1	no	—
420	C₂²⋊C₄	—	178	1	no	—
421	C₂²⋊C₄	—	178	1	no	—
422	C₄²	—	178	1	no	—
423	C₄²	—	178	1	no	—
424	C₄²	—	178	1	no	—
425	C₄²	—	178	1	no	—
426	C₄²	—	178	1	no	—
427	C₄²	—	178	1	no	—
428	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
430	C₄²	#13083574	1	1	yes	characteristic
431	C₄²	C₂³×D₈₉	1	1	yes	characteristic
432	C₂³	—	178	1	no	—
433	C₂³	—	178	1	no	—
434	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
435	Q₈	—	89	2	no	—
436	Q₈	—	178	1	no	—
437	Q₈	—	178	1	no	—
438	Q₈	—	178	1	no	—
439	D₄	—	89	2	no	—
440	D₄	—	356	2	no	—
441	D₄	—	356	2	no	—
442	D₄	—	178	1	no	—
443	D₄	—	178	1	no	—
444	D₄	—	178	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	356	2	no	—
451	C₂×C₄	—	356	2	no	—
452	C₂×C₄	—	356	1	no	—
453	C₂×C₄	—	356	1	no	—
454	C₂×C₄	—	356	1	no	—
455	C₂×C₄	—	356	1	no	—
456	C₂×C₄	—	356	2	no	—
457	C₂×C₄	—	356	2	no	—
458	C₂×C₄	—	178	1	no	—
459	C₂×C₄	—	178	1	no	—
460	C₂×C₄	—	178	1	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	178	1	no	—
464	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
465	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
466	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
469	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	1	no	—
474	C₈	—	2	1	no	—
475	C₈	—	4	2	no	—
476	C₈	—	356	2	no	—
477	C₈	—	356	2	no	—
478	C₈	M₁₆×D₈₉	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	356	1	no	—
483	C₂²	—	356	1	no	—
484	C₂²	—	356	1	no	—
485	C₂²	—	356	1	no	—
486	C₂²	—	356	1	no	—
487	C₂²	—	178	2	no	—
488	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	356	1	no	—
493	C₄	—	356	1	no	—
494	C₄	—	356	1	no	—
495	C₄	—	356	1	no	—
496	C₄	—	356	1	no	—
497	C₄	—	178	2	no	—
498	C₄	#19151721	1	2	yes	—
499	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
500	C₄	#19152364	1	1	yes	characteristic
501	C₄	#19152403	1	1	yes	characteristic
502	C₄	#19152415	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	356	2	no	—
505	C₂	—	712	1	no	—
506	C₂	M₁₆×D₃₅₆	1	1	yes	characteristic
507	C₂	#26029129	1	1	yes	characteristic
508	C₂	C₂×#19151721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1451	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1451	D₈₉
hypocenter	C₈₉	#18061
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1451

Complements

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

N	H ≅ G/N	type
1. #26029381	C₂	semidirect
2. #26029373	C₂	semidirect
4. #26019156	C₂	semidirect
5. #26019104	C₂	semidirect
6. #26019083	C₂	semidirect
7. #26019066	C₂	semidirect
8. #26019011	C₂	semidirect
9. #26018692	C₂	semidirect
10. #26018692	C₂	semidirect
11. C₈₉×#1451	C₂	semidirect
132. #13083563	M₁₆	semidirect
265. #1451	D₈₉	semidirect
266. C₈₉	#18061	semidirect

Maximal subgroups

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

subgroup	index
#26029381	2
#26029373	2
C₄×#15668034	2
#26019156	2
#26019104	2
#26019083	2
#26019066	2
#26019011	2
#26018692	2
C₈₉×#1451	2
#18061	89