Subgroups — #36525881

Order 22784.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029270	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029267	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668034	C₂	1	1	yes	maximal, characteristic
4	#26019144	C₂	1	2	yes	maximal, complemented
5	#26019104	C₂	1	2	yes	maximal, complemented
6	#26019083	C₂	1	2	yes	maximal, complemented
7	C₈×#13083563	C₂	1	2	yes	maximal, complemented
8	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018687	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018687	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₈₉	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	#19151674	—	2	2	no	—
27	#19151667	—	2	2	no	—
28	C₈×D₃₅₆	C₂²	1	2	yes	—
29	#19151655	C₂²	1	1	yes	characteristic
30	#19151655	C₂²	1	1	yes	characteristic
31	#19151653	—	2	1	no	—
32	#19151653	—	2	1	no	—
33	#19151636	C₄	1	1	yes	characteristic
34	#19151595	C₄	1	1	yes	characteristic
35	#19151595	C₄	1	1	yes	characteristic
36	#19151550	—	2	1	no	—
37	#97×D₈₉	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	—
39	#19151349	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	C₈²×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×#13083557	—	2	2	no	—
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
61	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
62	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	C₄×C₂²⋊D₈₉	—	2	1	no	—
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	#15667971	C₂×C₄	1	1	yes	characteristic
71	#15667971	C₂×C₄	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	#15667969	—	2	1	no	—
74	C₄²×D₈₉	—	2	1	no	—
75	C₄²×D₈₉	—	2	1	no	—
76	#15667946	C₂×C₄	1	1	yes	characteristic
77	#15667946	C₂×C₄	1	1	yes	characteristic
78	#15667944	C₂×C₄	1	1	yes	characteristic
79	#15667944	C₂×C₄	1	1	yes	characteristic
80	C₄⋊#10623494	C₂³	1	2	yes	—
81	C₄⋊#10623494	C₂³	1	2	yes	—
82	#15667941	—	2	2	no	—
83	#15667941	—	2	2	no	—
84	#15667937	C₂×C₄	1	1	yes	characteristic
85	#15667937	C₂×C₄	1	1	yes	characteristic
86	#15667937	C₂×C₄	1	1	yes	characteristic
87	#15667937	C₂×C₄	1	1	yes	characteristic
88	#15667934	C₂×C₄	1	1	yes	characteristic
89	#15667934	C₂×C₄	1	1	yes	characteristic
90	#15667934	C₂×C₄	1	1	yes	characteristic
91	#15667934	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊#10623494	—	2	1	no	—
93	C₂²⋊#10623494	—	2	1	no	—
94	#15667924	—	2	2	no	—
95	#15667924	—	2	2	no	—
96	#15667923	—	2	1	no	—
97	#15667923	—	2	1	no	—
98	#15667922	—	2	2	no	—
99	C₈×Dic₈₉	—	2	2	no	—
100	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
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	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	D₄	1	1	yes	characteristic
107	#97×C₈₉	D₄	1	1	yes	characteristic
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	#13083557	—	4	4	no	—
135	C₂×#10623494	—	2	2	no	—
136	C₂×#10623494	—	2	2	no	—
137	C₈×D₈₉	—	4	4	no	—
138	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
142	#13083553	—	2	1	no	—
143	#13083553	—	2	1	no	—
144	#13083553	—	2	1	no	—
145	#13083553	—	2	1	no	—
146	C₂²⋊Dic₈₉	—	2	1	no	—
147	C₂²⋊Dic₈₉	—	2	1	no	—
148	#13083551	—	2	1	no	—
149	#13083551	—	2	1	no	—
150	#13083551	—	2	1	no	—
151	#13083551	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₄×Dic₈₉	—	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	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
161	M₁₆×C₈₉	—	2	4	no	—
162	C₂×C₈×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	—	4	1	no	—
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
170	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
171	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₈₉	#41	1	1	yes	characteristic
174	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂²×D₈₉	—	2	1	no	—
177	C₂²×D₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	4	1	no	—
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂²⋊D₈₉	—	4	2	no	—
189	C₂²⋊D₈₉	—	4	2	no	—
190	C₂×Dic₈₉	—	2	1	no	—
191	C₂×Dic₈₉	—	2	1	no	—
192	C₂×Dic₈₉	—	2	1	no	—
193	C₂×Dic₈₉	—	2	1	no	—
194	C₂×Dic₈₉	—	2	1	no	—
195	C₂×Dic₈₉	—	2	1	no	—
196	D₃₅₆	—	2	1	no	—
197	D₃₅₆	—	2	1	no	—
198	D₃₅₆	—	2	1	no	—
199	D₃₅₆	C₂×M₁₆	1	2	yes	—
200	C₄×D₈₉	—	4	2	no	—
201	C₄×D₈₉	—	4	2	no	—
202	C₄×D₈₉	—	4	2	no	—
203	C₄×D₈₉	—	4	2	no	—
204	C₄×D₈₉	—	8	1	no	—
205	C₄×D₈₉	—	8	1	no	—
206	Dic₁₇₈	—	2	1	no	—
207	Dic₁₇₈	—	2	1	no	—
208	Dic₁₇₈	—	2	1	no	—
209	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
210	C₈×C₈₉	—	2	1	no	—
211	C₈×C₈₉	—	2	1	no	—
212	C₈×C₈₉	—	2	1	no	—
213	C₈×C₈₉	—	2	2	no	—
214	C₈×C₈₉	—	4	2	no	—
215	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
216	C₈×C₈₉	#135	1	4	yes	complemented
217	#10623494	—	4	2	no	—
218	#10623494	—	4	2	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	1	no	—
222	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂×D₈₉	—	2	2	no	—
224	C₂×D₈₉	—	4	1	no	—
225	C₂×D₈₉	—	4	1	no	—
226	C₂×D₈₉	—	4	1	no	—
227	C₂×D₈₉	—	4	1	no	—
228	C₂×D₈₉	—	4	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₈₉	#568	1	1	yes	characteristic
235	C₄×C₈₉	C₂×#135	1	2	yes	—
236	Dic₈₉	—	2	2	no	—
237	Dic₈₉	—	4	1	no	—
238	Dic₈₉	—	4	1	no	—
239	Dic₈₉	—	4	1	no	—
240	Dic₈₉	—	4	1	no	—
241	Dic₈₉	—	4	1	no	—
242	#18037	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	4	1	no	—
244	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
245	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
246	C₂×C₈₉	#2957	1	1	yes	characteristic
247	D₈₉	—	4	2	no	—
248	D₈₉	—	8	1	no	—
249	#2971	—	89	1	no	—
250	#2970	—	89	1	no	—
251	C₄×#135	—	89	1	no	—
252	#1590	—	89	2	no	—
253	#1584	—	89	2	no	—
254	#1581	—	89	2	no	—
255	C₈×SD₁₆	—	89	2	no	—
256	#1568	—	89	1	no	—
257	#1488	—	89	1	no	—
258	#1488	—	89	1	no	—
259	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
260	C₈₉	#18037	1	1	yes	characteristic, complemented, Sylow
261	C₂×#135	—	89	1	no	—
262	C₄×#41	—	89	1	no	—
263	C₄×#41	—	89	1	no	—
264	#446	—	89	2	no	—
265	C₈×Q₈	—	89	2	no	—
266	C₄×Q₁₆	—	89	1	no	—
267	C₄×Q₁₆	—	89	1	no	—
268	C₄×SD₁₆	—	89	1	no	—
269	C₄×SD₁₆	—	89	1	no	—
270	C₄×SD₁₆	—	89	1	no	—
271	C₄×SD₁₆	—	89	1	no	—
272	C₄×D₈	—	89	1	no	—
273	C₄×D₈	—	89	1	no	—
274	#436	—	89	2	no	—
275	#436	—	178	2	no	—
276	#435	—	178	2	no	—
277	C₈×D₄	—	89	2	no	—
278	#432	—	89	1	no	—
279	#432	—	89	1	no	—
280	#432	—	178	1	no	—
281	#432	—	178	1	no	—
282	#431	C₂×D₈₉	1	1	yes	characteristic
283	#427	—	89	1	no	—
284	#416	—	89	1	no	—
285	#416	—	89	1	no	—
286	C₄×M₁₆	—	178	1	no	—
287	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
288	C₂×#97	—	178	1	no	—
289	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
290	#335	—	89	2	no	—
291	#334	—	89	2	no	—
292	Q₈⋊C₈	—	89	2	no	—
293	Q₈⋊C₈	—	89	2	no	—
294	D₄⋊C₈	—	89	2	no	—
295	D₄⋊C₈	—	89	2	no	—
296	#322	C₂×D₈₉	1	2	yes	—
297	C₈²	C₂×D₈₉	1	2	yes	—
298	C₂×#41	—	89	1	no	—
299	C₂×#41	—	89	1	no	—
300	#135	—	178	4	no	—
301	C₂×Q₁₆	—	89	1	no	—
302	C₂×SD₁₆	—	89	1	no	—
303	C₂×SD₁₆	—	89	1	no	—
304	C₂×D₈	—	89	1	no	—
305	C₂×M₁₆	—	178	2	no	—
306	C₂×M₁₆	D₃₅₆	1	2	yes	—
307	C₂²×C₈	—	178	2	no	—
308	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
310	C₄×Q₈	—	89	1	no	—
311	C₄×Q₈	—	89	1	no	—
312	C₄×Q₈	—	89	1	no	—
313	C₄×Q₈	—	89	1	no	—
314	C₄×D₄	—	89	1	no	—
315	C₄×D₄	—	89	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	C₄×D₄	—	178	1	no	—
321	C₄×D₄	—	178	1	no	—
322	#117	—	89	1	no	—
323	#117	—	89	1	no	—
324	#117	—	178	1	no	—
325	#117	—	178	1	no	—
326	C₂×C₄²	—	178	1	no	—
327	C₂×C₄²	—	178	1	no	—
328	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
329	#107	—	89	1	no	—
330	#107	—	89	1	no	—
331	#106	—	89	1	no	—
332	#106	—	89	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	—	89	2	no	—
335	C₄⋊C₈	—	89	2	no	—
336	C₄⋊C₈	—	178	2	no	—
337	C₄⋊C₈	—	178	2	no	—
338	#103	—	89	1	no	—
339	#103	—	89	1	no	—
340	#103	—	89	1	no	—
341	#103	—	89	1	no	—
342	#102	—	89	1	no	—
343	#102	—	89	1	no	—
344	#102	—	89	1	no	—
345	#102	—	89	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	178	1	no	—
348	C₂²⋊C₈	—	178	1	no	—
349	C₂²⋊C₈	—	178	2	no	—
350	C₂²⋊C₈	—	178	2	no	—
351	#97	—	178	2	no	—
352	#97	—	178	1	no	—
353	#97	—	178	1	no	—
354	#97	D₃₅₆	1	1	yes	characteristic
355	#97	D₃₅₆	1	1	yes	characteristic
356	C₄×C₈	—	178	2	no	—
357	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
358	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₈₉	1	2	yes	—
360	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
361	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
362	C₄×C₈	C₂²×D₈₉	1	2	yes	—
363	#41	—	356	1	no	—
364	#41	—	356	1	no	—
365	#41	—	178	2	no	—
366	#41	—	178	2	no	—
367	C₂×Q₈	—	89	1	no	—
368	C₂×Q₈	—	89	1	no	—
369	C₂×D₄	—	89	1	no	—
370	C₂×D₄	—	89	1	no	—
371	C₂×D₄	—	178	1	no	—
372	C₂×D₄	—	178	1	no	—
373	C₂²×C₄	—	178	1	no	—
374	C₂²×C₄	—	178	1	no	—
375	C₂²×C₄	—	178	1	no	—
376	C₂²×C₄	—	178	1	no	—
377	C₂²×C₄	—	178	1	no	—
378	C₂²×C₄	—	178	1	no	—
379	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
381	C₂²×C₄	#13083574	1	1	yes	characteristic
382	Q₁₆	—	178	2	no	—
383	SD₁₆	—	89	4	no	—
384	SD₁₆	—	178	2	no	—
385	D₈	—	178	2	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	356	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	1	no	—
391	C₂×C₈	—	356	4	no	—
392	C₂×C₈	—	178	2	no	—
393	C₂×C₈	—	178	2	no	—
394	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
395	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
396	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
397	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
398	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
399	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
400	C₄⋊C₄	—	89	1	no	—
401	C₄⋊C₄	—	89	1	no	—
402	C₄⋊C₄	—	89	1	no	—
403	C₄⋊C₄	—	89	1	no	—
404	C₄⋊C₄	—	178	1	no	—
405	C₄⋊C₄	—	178	1	no	—
406	C₄⋊C₄	—	178	1	no	—
407	C₄⋊C₄	—	178	1	no	—
408	C₂²⋊C₄	—	178	1	no	—
409	C₂²⋊C₄	—	178	1	no	—
410	C₂²⋊C₄	—	178	1	no	—
411	C₂²⋊C₄	—	178	1	no	—
412	C₂²⋊C₄	—	178	1	no	—
413	C₂²⋊C₄	—	178	1	no	—
414	C₄²	—	178	1	no	—
415	C₄²	—	178	1	no	—
416	C₄²	—	178	1	no	—
417	C₄²	—	178	1	no	—
418	C₄²	—	178	1	no	—
419	C₄²	—	178	1	no	—
420	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
421	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
422	C₄²	#13083574	1	1	yes	characteristic
423	C₄²	C₂³×D₈₉	1	1	yes	characteristic
424	C₂³	—	178	1	no	—
425	C₂³	—	178	1	no	—
426	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
427	Q₈	—	89	2	no	—
428	Q₈	—	178	1	no	—
429	Q₈	—	178	1	no	—
430	Q₈	—	178	1	no	—
431	D₄	—	89	2	no	—
432	D₄	—	356	2	no	—
433	D₄	—	356	2	no	—
434	D₄	—	178	1	no	—
435	D₄	—	178	1	no	—
436	D₄	—	178	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	356	2	no	—
442	C₂×C₄	—	356	2	no	—
443	C₂×C₄	—	356	2	no	—
444	C₂×C₄	—	356	2	no	—
445	C₂×C₄	—	178	1	no	—
446	C₂×C₄	—	178	1	no	—
447	C₂×C₄	—	178	1	no	—
448	C₂×C₄	—	178	1	no	—
449	C₂×C₄	—	178	1	no	—
450	C₂×C₄	—	178	1	no	—
451	C₂×C₄	—	712	1	no	—
452	C₂×C₄	—	712	1	no	—
453	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
454	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
455	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
458	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	356	2	no	—
465	C₈	—	356	2	no	—
466	C₈	M₁₆×D₈₉	1	2	yes	—
467	C₈	#15668034	1	4	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	356	1	no	—
472	C₂²	—	356	1	no	—
473	C₂²	—	356	1	no	—
474	C₂²	—	356	1	no	—
475	C₂²	—	356	1	no	—
476	C₂²	—	178	2	no	—
477	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	356	1	no	—
483	C₄	—	356	1	no	—
484	C₄	—	356	1	no	—
485	C₄	—	356	1	no	—
486	C₄	—	356	1	no	—
487	C₄	—	178	2	no	—
488	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
489	C₄	#19152364	1	1	yes	characteristic
490	C₄	C₂×#15668034	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	356	2	no	—
493	C₂	—	712	1	no	—
494	C₂	M₁₆×D₃₅₆	1	1	yes	characteristic
495	C₂	C₄×#15668034	1	1	yes	characteristic
496	C₂	#26029170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#18037
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
1. #26029270	C₂	semidirect
2. #26029267	C₂	semidirect
4. #26019144	C₂	semidirect
5. #26019104	C₂	semidirect
6. #26019083	C₂	semidirect
7. C₈×#13083563	C₂	semidirect
8. #26019015	C₂	semidirect
9. #26018687	C₂	semidirect
10. #26018687	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
132. #13083563	M₁₆	semidirect
216. C₈×C₈₉	#135	semidirect
259. C₈×M₁₆	D₈₉	semidirect
260. C₈₉	#18037	semidirect
467. C₈	#15668034	semidirect

Maximal subgroups

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

subgroup	index
#26029270	2
#26029267	2
C₄×#15668034	2
#26019144	2
#26019104	2
#26019083	2
C₈×#13083563	2
#26019015	2
#26018687	2
C₈×M₁₆×C₈₉	2
#18037	89