Subgroups — #36524228

Order 22784.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029218	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668045	C₂	1	1	yes	maximal, characteristic
4	#26019162	C₂	1	2	yes	maximal, complemented
5	#26019156	C₂	1	2	yes	maximal, complemented
6	#26019150	C₂	1	2	yes	maximal, complemented
7	#26019144	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018648	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018640	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668045	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
15	#19151728	—	2	1	no	—
16	#19151728	—	2	1	no	—
17	#19151728	C₂²	1	2	yes	—
18	#19151728	C₂²	1	1	yes	characteristic
19	#19151728	C₂²	1	2	yes	—
20	#19151728	C₂²	1	1	yes	characteristic
21	#19151706	C₄	1	2	yes	—
22	#19151700	C₄	1	2	yes	—
23	C₄×Dic₃₅₆	C₂²	1	2	yes	—
24	C₄×#13083563	C₂²	1	2	yes	—
25	#19151677	C₂²	1	1	yes	characteristic
26	#19151677	C₂²	1	1	yes	characteristic
27	#19151669	—	2	1	no	—
28	#19151669	—	2	1	no	—
29	#19151651	C₂²	1	1	yes	characteristic
30	#19151649	—	2	1	no	—
31	#19151640	C₄	1	1	yes	characteristic
32	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
33	C₂×#15667941	—	2	1	no	—
34	#19151608	C₄	1	1	yes	characteristic
35	#19151600	C₄	1	1	yes	characteristic
36	C₄×#13083557	—	2	1	no	—
37	C₂×#15667922	—	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	#19151330	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	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
51	#15668045	—	2	4	no	—
52	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
53	C₂×#13083563	C₂×C₄	1	2	yes	—
54	C₂×#13083557	—	2	1	no	—
55	C₂×#13083557	—	2	1	no	—
56	C₂²×#10623494	—	2	1	no	—
57	C₄×Dic₁₇₈	—	2	1	no	—
58	C₄×Dic₁₇₈	—	2	1	no	—
59	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₇₈	C₂³	1	2	yes	—
62	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₈₉	—	2	1	no	—
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	#15667971	C₂×C₄	1	1	yes	characteristic
68	#15667969	—	2	1	no	—
69	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083553	—	2	1	no	—
71	C₂×C₄×Dic₈₉	—	2	1	no	—
72	C₄²×D₈₉	—	2	1	no	—
73	#15667946	C₂×C₄	1	2	yes	—
74	#15667944	C₂×C₄	1	2	yes	—
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	C₂³	1	2	yes	—
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	1	no	—
82	#15667941	—	2	1	no	—
83	#15667937	C₂×C₄	1	2	yes	—
84	#15667937	C₂×C₄	1	2	yes	—
85	#15667937	C₂×C₄	1	2	yes	—
86	#15667934	C₂×C₄	1	2	yes	—
87	C₂²⋊#10623494	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	#15667924	—	2	1	no	—
90	#15667922	—	2	1	no	—
91	#15667922	—	2	1	no	—
92	#15667922	—	2	2	no	—
93	#15667922	—	2	2	no	—
94	C₄×#10623494	—	2	1	no	—
95	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	—	2	1	no	—
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	#97×C₈₉	C₂×C₄	1	2	yes	—
103	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄×C₈×C₈₉	C₂³	1	2	yes	—
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	#13083574	—	2	2	no	—
110	#13083574	—	2	2	no	—
111	C₂×Dic₁₇₈	—	2	2	no	—
112	C₂×Dic₁₇₈	—	2	2	no	—
113	C₂×Dic₁₇₈	—	2	1	no	—
114	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
115	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊D₈₉	—	2	1	no	—
118	C₂²×Dic₈₉	—	2	1	no	—
119	C₂²×Dic₈₉	—	2	1	no	—
120	C₂×C₄×D₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	Dic₃₅₆	—	2	4	no	—
124	#13083563	—	2	4	no	—
125	#13083557	—	4	2	no	—
126	#13083557	—	4	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	4	2	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
135	#13083553	—	2	1	no	—
136	#13083553	—	2	2	no	—
137	#13083553	—	2	1	no	—
138	#13083553	—	2	2	no	—
139	C₂²⋊Dic₈₉	—	2	1	no	—
140	#13083551	—	2	1	no	—
141	#13083551	—	2	1	no	—
142	C₄×Dic₈₉	—	2	1	no	—
143	C₄×Dic₈₉	—	2	1	no	—
144	C₄×Dic₈₉	—	2	2	no	—
145	C₄×Dic₈₉	—	2	1	no	—
146	C₄×Dic₈₉	—	2	2	no	—
147	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
150	M₁₆×C₈₉	—	2	2	no	—
151	M₁₆×C₈₉	M₁₆	1	4	yes	complemented
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	4	1	no	—
155	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	#41	1	1	yes	characteristic
164	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
174	C₂×C₄×C₈₉	#131	1	2	yes	—
175	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	2	1	no	—
180	C₂×Dic₈₉	—	2	1	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	C₂×Dic₈₉	—	2	1	no	—
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	4	2	no	—
185	C₂×Dic₈₉	—	4	2	no	—
186	D₃₅₆	—	2	1	no	—
187	D₃₅₆	—	2	1	no	—
188	C₄×D₈₉	—	4	2	no	—
189	C₄×D₈₉	—	4	1	no	—
190	C₄×D₈₉	—	4	1	no	—
191	C₄×D₈₉	—	4	2	no	—
192	Dic₁₇₈	—	2	2	no	—
193	Dic₁₇₈	—	2	1	no	—
194	Dic₁₇₈	—	2	2	no	—
195	Dic₁₇₈	—	2	1	no	—
196	Dic₁₇₈	—	4	2	no	—
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	2	1	no	—
199	C₈×C₈₉	—	2	1	no	—
200	C₈×C₈₉	—	2	1	no	—
201	C₈×C₈₉	—	4	2	no	—
202	C₈×C₈₉	C₂×M₁₆	1	4	yes	—
203	C₈×C₈₉	#137	1	2	yes	complemented
204	#10623494	—	4	1	no	—
205	#10623494	—	4	2	no	—
206	#10623494	—	4	1	no	—
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	#436	1	2	yes	—
210	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₈₉	—	4	1	no	—
212	C₂×D₈₉	—	4	1	no	—
213	C₂×D₈₉	—	4	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	#436	1	2	yes	—
218	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
219	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
220	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
221	C₄×C₈₉	#575	1	1	yes	characteristic
222	Dic₈₉	—	4	2	no	—
223	Dic₈₉	—	4	1	no	—
224	Dic₈₉	—	4	1	no	—
225	Dic₈₉	—	4	1	no	—
226	Dic₈₉	—	4	2	no	—
227	#17892	—	89	1	no	maximal, Sylow
228	C₂×C₈₉	—	2	2	no	—
229	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
230	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
231	C₂×C₈₉	#2955	1	1	yes	characteristic
232	D₈₉	—	8	1	no	—
233	#2965	—	89	1	no	—
234	C₂×#446	—	89	1	no	—
235	C₄×#137	—	89	1	no	—
236	#1593	—	89	2	no	—
237	#1592	—	89	2	no	—
238	#1591	—	89	2	no	—
239	#1590	—	89	2	no	—
240	#1565	—	89	1	no	—
241	#1479	—	89	1	no	—
242	#1477	—	89	1	no	—
243	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
244	C₈₉	#17892	1	1	yes	characteristic, complemented, Sylow
245	C₂×#137	—	89	1	no	—
246	C₄×#41	—	89	1	no	—
247	C₂×C₄×Q₈	—	89	1	no	—
248	#446	—	89	2	no	—
249	#446	—	89	1	no	—
250	#446	—	89	2	no	—
251	#446	—	89	1	no	—
252	#446	—	178	1	no	—
253	#446	—	178	1	no	—
254	#441	—	89	2	no	—
255	#440	—	89	2	no	—
256	C₄×Q₁₆	—	89	2	no	—
257	C₄×SD₁₆	—	89	2	no	—
258	#436	—	89	1	no	—
259	#436	—	89	1	no	—
260	#435	—	178	1	no	—
261	#435	—	178	1	no	—
262	#431	—	89	1	no	—
263	#431	—	178	1	no	—
264	#431	C₂×D₈₉	1	1	yes	characteristic
265	#428	—	89	1	no	—
266	C₂×C₄⋊C₈	—	89	1	no	—
267	C₂×C₄⋊C₈	—	178	1	no	—
268	#419	—	89	1	no	—
269	#417	—	89	1	no	—
270	C₄×M₁₆	—	178	1	no	—
271	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
272	C₂×#97	—	178	1	no	—
273	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
274	#335	—	89	2	no	—
275	#334	—	89	2	no	—
276	Q₈⋊C₈	—	89	2	no	—
277	Q₈⋊C₈	—	89	2	no	—
278	Q₈⋊C₈	—	89	2	no	—
279	D₄⋊C₈	—	89	2	no	—
280	#322	C₂×D₈₉	1	2	yes	—
281	C₈²	C₂×D₈₉	1	2	yes	—
282	C₂×#41	—	89	1	no	—
283	C₂²×Q₈	—	89	1	no	—
284	#137	—	178	4	no	—
285	C₂×Q₁₆	—	89	2	no	—
286	C₂×SD₁₆	—	89	2	no	—
287	C₂×M₁₆	—	178	1	no	—
288	C₂×M₁₆	—	178	1	no	—
289	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
290	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
291	C₂²×C₈	—	178	1	no	—
292	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
293	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
294	C₄×Q₈	—	89	2	no	—
295	C₄×Q₈	—	89	1	no	—
296	C₄×Q₈	—	89	2	no	—
297	C₄×Q₈	—	89	1	no	—
298	C₄×Q₈	—	178	1	no	—
299	C₄×Q₈	—	178	1	no	—
300	C₄×D₄	—	89	1	no	—
301	C₄×D₄	—	89	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	—	178	1	no	—
304	#117	—	89	1	no	—
305	#117	—	178	1	no	—
306	C₂×C₄⋊C₄	—	89	1	no	—
307	C₂×C₄⋊C₄	—	178	1	no	—
308	C₂×C₄²	—	178	1	no	—
309	C₂×C₄²	—	178	1	no	—
310	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
311	#107	—	89	2	no	—
312	#106	—	89	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	89	2	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	89	1	no	—
317	C₄⋊C₈	—	178	2	no	—
318	C₄⋊C₈	—	178	2	no	—
319	C₄⋊C₈	—	178	1	no	—
320	C₄⋊C₈	—	178	1	no	—
321	C₄⋊C₈	—	178	1	no	—
322	#103	—	89	2	no	—
323	#103	—	89	2	no	—
324	#103	—	89	2	no	—
325	#102	—	89	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	178	1	no	—
328	C₂²⋊C₈	—	178	1	no	—
329	C₂²⋊C₈	—	178	1	no	—
330	#97	—	178	2	no	—
331	#97	—	178	2	no	—
332	#97	—	178	1	no	—
333	#97	—	178	1	no	—
334	#97	C₄×D₈₉	1	2	yes	—
335	C₄×C₈	—	178	1	no	—
336	C₄×C₈	D₃₅₆	1	1	yes	characteristic
337	C₄×C₈	D₃₅₆	1	1	yes	characteristic
338	C₄×C₈	C₂²×D₈₉	1	2	yes	—
339	C₄×C₈	C₂²×D₈₉	1	2	yes	—
340	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
342	#41	—	178	2	no	—
343	#41	—	178	2	no	—
344	C₂×Q₈	—	89	2	no	—
345	C₂×Q₈	—	89	1	no	—
346	C₂×Q₈	—	178	2	no	—
347	C₂×Q₈	—	178	2	no	—
348	C₂×Q₈	—	178	1	no	—
349	C₂×D₄	—	89	1	no	—
350	C₂×D₄	—	178	1	no	—
351	C₂²×C₄	—	178	1	no	—
352	C₂²×C₄	—	178	1	no	—
353	C₂²×C₄	—	178	1	no	—
354	C₂²×C₄	—	178	1	no	—
355	C₂²×C₄	—	178	1	no	—
356	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
358	C₂²×C₄	#13083574	1	1	yes	characteristic
359	Q₁₆	—	178	4	no	—
360	SD₁₆	—	178	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	356	2	no	—
363	M₁₆	—	356	2	no	—
364	M₁₆	#13083557	1	4	yes	complemented
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	356	2	no	—
369	C₂×C₈	—	178	1	no	—
370	C₂×C₈	—	178	1	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
373	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
374	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
375	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
376	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
377	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
378	C₄⋊C₄	—	89	2	no	—
379	C₄⋊C₄	—	89	1	no	—
380	C₄⋊C₄	—	89	1	no	—
381	C₄⋊C₄	—	178	1	no	—
382	C₄⋊C₄	—	178	2	no	—
383	C₄⋊C₄	—	178	1	no	—
384	C₄⋊C₄	—	178	2	no	—
385	C₄⋊C₄	—	178	1	no	—
386	C₂²⋊C₄	—	178	1	no	—
387	C₂²⋊C₄	—	178	1	no	—
388	C₂²⋊C₄	—	178	1	no	—
389	C₄²	—	178	1	no	—
390	C₄²	—	178	1	no	—
391	C₄²	—	178	2	no	—
392	C₄²	—	178	1	no	—
393	C₄²	—	178	2	no	—
394	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
395	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
396	C₄²	#13083574	1	1	yes	characteristic
397	C₄²	C₂³×D₈₉	1	1	yes	characteristic
398	C₂³	—	178	1	no	—
399	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
400	Q₈	—	356	2	no	—
401	Q₈	—	178	2	no	—
402	Q₈	—	178	1	no	—
403	Q₈	—	178	2	no	—
404	Q₈	—	178	1	no	—
405	D₄	—	356	2	no	—
406	D₄	—	178	1	no	—
407	D₄	—	178	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	356	2	no	—
412	C₂×C₄	—	356	2	no	—
413	C₂×C₄	—	356	2	no	—
414	C₂×C₄	—	356	1	no	—
415	C₂×C₄	—	356	1	no	—
416	C₂×C₄	—	356	2	no	—
417	C₂×C₄	—	178	1	no	—
418	C₂×C₄	—	178	1	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	178	1	no	—
421	C₂×C₄	—	178	2	no	—
422	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
423	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
424	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083557	1	2	yes	—
426	C₂×C₄	#15668018	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
429	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	356	1	no	—
436	C₈	—	356	2	no	—
437	C₈	—	356	1	no	—
438	C₈	C₂×#13083557	1	4	yes	—
439	C₈	#15668045	1	2	yes	complemented
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	356	1	no	—
443	C₂²	—	356	1	no	—
444	C₂²	—	356	1	no	—
445	C₂²	#19151677	1	2	yes	—
446	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	356	1	no	—
451	C₄	—	356	1	no	—
452	C₄	—	356	2	no	—
453	C₄	—	356	1	no	—
454	C₄	—	356	2	no	—
455	C₄	#19151677	1	2	yes	—
456	C₄	C₂²×#13083557	1	1	yes	characteristic
457	C₄	C₂×#15668018	1	1	yes	characteristic
458	C₄	C₂×#15668045	1	1	yes	characteristic
459	C₄	#19152398	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	712	1	no	—
462	C₂	C₂×#19151677	1	1	yes	characteristic
463	C₂	C₄×#15668045	1	1	yes	characteristic
464	C₂	#26029156	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×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17892
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#19151728	C₂	semidirect
4. #26019162	C₂	semidirect
5. #26019156	C₂	semidirect
6. #26019150	C₂	semidirect
7. #26019144	C₂	semidirect
8. #26019004	C₂	semidirect
9. #26018648	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
151. M₁₆×C₈₉	M₁₆	semidirect
203. C₈×C₈₉	#137	semidirect
243. C₈×M₁₆	D₈₉	semidirect
244. C₈₉	#17892	semidirect
364. M₁₆	#13083557	semidirect
439. C₈	#15668045	semidirect

Maximal subgroups

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

subgroup	index
#26029218	2
C₂×#19151728	2
C₄×#15668045	2
#26019162	2
#26019156	2
#26019150	2
#26019144	2
#26019004	2
#26018648	2
#26018640	2
C₈×M₁₆×C₈₉	2
#17892	89