Subgroups — #36525038

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030847	C₂	1	1	yes	maximal, characteristic
2	#26029227	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019144	C₂	1	2	yes	maximal, complemented
5	#26019138	C₂	1	2	yes	maximal, complemented
6	#26019077	C₂	1	2	yes	maximal, complemented
7	#26019066	C₂	1	2	yes	maximal, complemented
8	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018722	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018718	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19152132	C₂²	1	1	yes	characteristic
15	#19152007	C₄	1	1	yes	characteristic
16	#19151987	C₄	1	1	yes	characteristic
17	#19151963	C₄	1	1	yes	characteristic
18	#19151958	C₄	1	1	yes	characteristic
19	#19151851	C₄	1	2	yes	—
20	#19151844	C₄	1	2	yes	—
21	#19151728	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
23	C₄×#13083563	C₂²	1	2	yes	—
24	C₄×D₇₁₂	C₂²	1	2	yes	—
25	#19151677	—	2	1	no	—
26	#19151677	C₂²	1	1	yes	characteristic
27	#19151677	C₂²	1	2	yes	—
28	#19151669	—	2	1	no	—
29	C₈×D₃₅₆	—	2	1	no	—
30	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
31	C₈×D₃₅₆	C₂²	1	2	yes	—
32	C₈×C₂²⋊D₈₉	—	2	1	no	—
33	#19151657	—	2	1	no	—
34	#19151655	C₂²	1	1	yes	characteristic
35	#19151622	C₂²	1	1	yes	characteristic
36	#19151564	—	2	1	no	—
37	#19151552	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	—
39	#19151349	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151327	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	—	2	1	no	—
50	C₂×#13083563	C₂×C₄	1	2	yes	—
51	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
52	#15668018	—	4	4	no	—
53	C₂×#13083558	—	2	1	no	—
54	C₂×#13083557	—	2	1	no	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×C₈×D₈₉	—	2	1	no	—
57	C₂×C₈×D₈₉	—	2	2	no	—
58	#15668012	C₂×C₄	1	1	yes	characteristic
59	#15668009	C₂×C₄	1	1	yes	characteristic
60	#15668006	—	2	1	no	—
61	#15668004	C₂×C₄	1	1	yes	characteristic
62	#15668000	—	2	1	no	—
63	#15668000	C₂×C₄	1	1	yes	characteristic
64	#15667995	—	2	1	no	—
65	#15667991	C₂×C₄	1	1	yes	characteristic
66	#15667986	—	2	1	no	—
67	#15667986	C₂×C₄	1	1	yes	characteristic
68	#15667986	C₂×C₄	1	2	yes	—
69	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
70	C₄×D₃₅₆	—	2	1	no	—
71	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
72	C₄×D₃₅₆	C₂³	1	2	yes	—
73	C₄×C₂²⋊D₈₉	—	2	1	no	—
74	#15667969	—	2	1	no	—
75	#15667946	C₂×C₄	1	2	yes	—
76	#15667944	C₂×C₄	1	2	yes	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	#15667941	—	2	1	no	—
82	#15667941	—	2	1	no	—
83	#15667937	C₂×C₄	1	2	yes	—
84	#15667934	C₂×C₄	1	2	yes	—
85	#15667934	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	#15667924	—	2	2	no	—
91	#15667924	—	2	2	no	—
92	#15667923	—	2	1	no	—
93	#15667922	—	2	1	no	—
94	C₈×Dic₈₉	—	2	1	no	—
95	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
96	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	—	2	1	no	—
100	C₂²⋊C₈×C₈₉	—	2	1	no	—
101	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
102	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
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	—	4	2	no	—
110	#13083574	—	4	2	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	—	2	1	no	—
115	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
117	C₂×C₂²⋊D₈₉	—	2	1	no	—
118	C₂×C₂²⋊D₈₉	—	2	2	no	—
119	C₂×C₄×D₈₉	—	2	1	no	—
120	C₂×C₄×D₈₉	—	2	2	no	—
121	#13083563	—	2	4	no	—
122	D₇₁₂	—	2	4	no	—
123	#13083558	—	4	2	no	—
124	#13083557	—	4	2	no	—
125	#13083557	—	4	4	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₈×D₈₉	—	4	2	no	—
130	C₈×D₈₉	—	4	4	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
133	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
135	#13083553	—	2	1	no	—
136	#13083553	—	2	1	no	—
137	#13083553	—	2	1	no	—
138	#13083553	—	2	1	no	—
139	C₂²⋊Dic₈₉	—	2	1	no	—
140	#13083551	—	2	1	no	—
141	#13083551	—	2	1	no	—
142	#13083551	—	2	1	no	—
143	#13083551	—	2	2	no	—
144	#13083551	—	2	2	no	—
145	#13083551	—	2	1	no	—
146	C₄×Dic₈₉	—	2	1	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	4	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	4	1	no	—
154	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₈₉	#41	1	1	yes	characteristic
163	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
164	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₈₉	—	2	1	no	—
166	C₂²×D₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₈₉	—	4	2	no	—
178	C₂²⋊D₈₉	—	4	4	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	D₃₅₆	—	2	2	no	—
184	D₃₅₆	—	2	2	no	—
185	D₃₅₆	—	2	2	no	—
186	D₃₅₆	—	4	2	no	—
187	D₃₅₆	—	4	2	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	—	4	2	no	—
194	C₈×C₈₉	—	2	2	no	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	2	1	no	—
198	C₈×C₈₉	—	4	2	no	—
199	C₈×C₈₉	#131	1	4	yes	complemented
200	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
201	#10623494	—	4	2	no	—
202	#10623494	—	4	1	no	—
203	#10623494	—	4	1	no	—
204	C₂²×C₈₉	—	2	1	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂×D₈₉	—	4	1	no	—
209	C₂×D₈₉	—	4	2	no	—
210	C₂×D₈₉	—	4	2	no	—
211	C₂×D₈₉	—	4	1	no	—
212	C₂×D₈₉	—	4	2	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	—	2	1	no	—
218	C₄×C₈₉	C₂×#131	1	2	yes	—
219	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₄×C₈₉	#575	1	1	yes	characteristic
221	Dic₈₉	—	4	1	no	—
222	Dic₈₉	—	4	2	no	—
223	Dic₈₉	—	4	1	no	—
224	Dic₈₉	—	4	1	no	—
225	#17966	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	4	1	no	—
227	C₂×C₈₉	#2931	1	1	yes	characteristic
228	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×C₈₉	#2955	1	1	yes	characteristic
230	D₈₉	—	8	2	no	—
231	D₈₉	—	8	1	no	—
232	#3171	—	89	1	no	—
233	#2966	—	89	1	no	—
234	#2931	—	89	1	no	—
235	#1590	—	89	2	no	—
236	#1589	—	89	2	no	—
237	#1580	—	89	2	no	—
238	SD₁₆⋊C₈	—	89	2	no	—
239	#1569	—	89	1	no	—
240	#1496	—	89	1	no	—
241	#1495	—	89	1	no	—
242	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
243	C₈₉	#17966	1	1	yes	characteristic, complemented, Sylow
244	C₂×#131	—	178	1	no	—
245	#532	—	89	1	no	—
246	#529	—	89	1	no	—
247	#501	—	89	1	no	—
248	#496	—	89	1	no	—
249	#490	—	89	1	no	—
250	#489	—	89	1	no	—
251	#469	—	89	2	no	—
252	#468	—	89	2	no	—
253	#446	—	89	1	no	—
254	C₈×Q₈	—	89	1	no	—
255	C₄×SD₁₆	—	89	2	no	—
256	C₄×D₈	—	89	2	no	—
257	#436	—	89	1	no	—
258	#436	—	89	2	no	—
259	#436	—	178	1	no	—
260	#435	—	178	1	no	—
261	C₈×D₄	—	89	2	no	—
262	C₈×D₄	—	89	1	no	—
263	C₈×D₄	—	178	1	no	—
264	C₈×D₄	—	178	1	no	—
265	#433	—	178	1	no	—
266	#432	—	89	1	no	—
267	#431	C₂×D₈₉	1	1	yes	characteristic
268	#423	—	89	1	no	—
269	#408	—	178	1	no	—
270	#405	—	178	1	no	—
271	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
273	#335	—	89	2	no	—
274	#334	—	89	2	no	—
275	Q₈⋊C₈	—	89	2	no	—
276	D₄⋊C₈	—	89	2	no	—
277	D₄⋊C₈	—	89	2	no	—
278	D₄⋊C₈	—	89	2	no	—
279	#322	C₂×D₈₉	1	2	yes	—
280	C₈²	C₂×D₈₉	1	2	yes	—
281	C₂×#41	—	178	1	no	—
282	C₂×SD₁₆	—	89	2	no	—
283	C₂×D₈	—	89	2	no	—
284	#131	—	356	4	no	—
285	C₂×M₁₆	—	178	1	no	—
286	C₂×M₁₆	—	178	2	no	—
287	C₂×M₁₆	—	178	1	no	—
288	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
289	C₂²×C₈	—	178	2	no	—
290	C₂²×C₈	—	178	1	no	—
291	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
292	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
293	C₄⋊Q₈	—	89	1	no	—
294	#127	—	89	1	no	—
295	#126	—	178	1	no	—
296	#125	—	89	1	no	—
297	#124	—	89	1	no	—
298	#124	—	178	1	no	—
299	#123	—	178	1	no	—
300	C₂²⋊Q₈	—	89	1	no	—
301	#121	—	89	1	no	—
302	#121	—	89	2	no	—
303	#121	—	178	1	no	—
304	C₄×Q₈	—	89	1	no	—
305	C₄×D₄	—	89	1	no	—
306	C₄×D₄	—	89	2	no	—
307	C₄×D₄	—	178	1	no	—
308	C₄×D₄	—	178	1	no	—
309	#117	—	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	1	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	89	2	no	—
317	C₄⋊C₈	—	178	1	no	—
318	C₄⋊C₈	—	178	1	no	—
319	C₄⋊C₈	—	178	1	no	—
320	#103	—	89	2	no	—
321	#102	—	89	2	no	—
322	#102	—	89	2	no	—
323	#102	—	89	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	178	1	no	—
326	C₂²⋊C₈	—	178	2	no	—
327	C₂²⋊C₈	—	178	2	no	—
328	C₂²⋊C₈	—	178	1	no	—
329	C₂²⋊C₈	—	178	1	no	—
330	#97	—	178	1	no	—
331	#97	—	178	1	no	—
332	#97	C₄×D₈₉	1	1	yes	characteristic
333	#97	C₄×D₈₉	1	1	yes	characteristic
334	C₄×C₈	—	178	1	no	—
335	C₄×C₈	D₃₅₆	1	1	yes	characteristic
336	C₄×C₈	D₃₅₆	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₈₉	1	2	yes	—
338	C₄×C₈	C₂²×D₈₉	1	2	yes	—
339	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
341	#41	—	356	2	no	—
342	#41	—	356	2	no	—
343	C₂×Q₈	—	89	1	no	—
344	C₂×Q₈	—	178	1	no	—
345	C₂×D₄	—	89	1	no	—
346	C₂×D₄	—	89	2	no	—
347	C₂×D₄	—	178	1	no	—
348	C₂×D₄	—	178	2	no	—
349	C₂×D₄	—	178	1	no	—
350	C₂×D₄	—	178	1	no	—
351	C₂²×C₄	—	178	1	no	—
352	C₂²×C₄	—	178	2	no	—
353	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
355	C₂²×C₄	#13083574	1	1	yes	characteristic
356	SD₁₆	—	178	4	no	—
357	D₈	—	178	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	356	2	no	—
360	M₁₆	—	356	4	no	—
361	M₁₆	—	356	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	356	4	no	—
366	C₂×C₈	—	356	2	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
371	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
372	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
373	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
374	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
375	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
376	C₄⋊C₄	—	89	1	no	—
377	C₄⋊C₄	—	89	1	no	—
378	C₄⋊C₄	—	89	2	no	—
379	C₄⋊C₄	—	178	1	no	—
380	C₄⋊C₄	—	178	1	no	—
381	C₄⋊C₄	—	178	1	no	—
382	C₄⋊C₄	—	178	1	no	—
383	C₄⋊C₄	—	178	1	no	—
384	C₂²⋊C₄	—	178	1	no	—
385	C₂²⋊C₄	—	178	1	no	—
386	C₂²⋊C₄	—	178	1	no	—
387	C₂²⋊C₄	—	178	2	no	—
388	C₂²⋊C₄	—	178	1	no	—
389	C₂²⋊C₄	—	178	2	no	—
390	C₂²⋊C₄	—	178	1	no	—
391	C₄²	—	178	1	no	—
392	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
393	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
394	C₄²	#13083574	1	1	yes	characteristic
395	C₄²	C₂³×D₈₉	1	1	yes	characteristic
396	C₂³	—	178	1	no	—
397	C₂³	—	178	2	no	—
398	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
399	Q₈	—	356	2	no	—
400	Q₈	—	178	2	no	—
401	D₄	—	356	2	no	—
402	D₄	—	356	2	no	—
403	D₄	—	356	2	no	—
404	D₄	—	356	4	no	—
405	D₄	—	178	2	no	—
406	D₄	—	178	2	no	—
407	D₄	—	178	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	356	2	no	—
413	C₂×C₄	—	356	1	no	—
414	C₂×C₄	—	356	1	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	—	178	1	no	—
418	C₂×C₄	—	178	1	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
421	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
422	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	2	no	—
431	C₈	—	356	2	no	—
432	C₈	—	356	1	no	—
433	C₈	—	356	1	no	—
434	C₈	#15668018	1	4	yes	complemented
435	C₈	#15668040	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	356	2	no	—
440	C₂²	—	356	1	no	—
441	C₂²	—	356	2	no	—
442	C₂²	—	356	1	no	—
443	C₂²	—	356	1	no	—
444	C₂²	—	356	2	no	—
445	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	356	2	no	—
451	C₄	—	356	1	no	—
452	C₄	—	356	1	no	—
453	C₄	—	356	1	no	—
454	C₄	C₂×#15668018	1	2	yes	—
455	C₄	C₂×#15668040	1	1	yes	characteristic
456	C₄	#19152398	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	712	2	no	—
459	C₂	—	712	1	no	—
460	C₂	#26028965	1	1	yes	characteristic
461	C₂	C₄×#15668040	1	1	yes	characteristic
462	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	#26030847	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17966
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. #26029227	C₂	semidirect
3. #26028965	C₂	semidirect
4. #26019144	C₂	semidirect
5. #26019138	C₂	semidirect
6. #26019077	C₂	semidirect
7. #26019066	C₂	semidirect
8. #26019019	C₂	semidirect
9. #26018722	C₂	semidirect
10. #26018718	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
199. C₈×C₈₉	#131	semidirect
242. C₈×M₁₆	D₈₉	semidirect
243. C₈₉	#17966	semidirect
434. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26030847	2
#26029227	2
#26028965	2
#26019144	2
#26019138	2
#26019077	2
#26019066	2
#26019019	2
#26018722	2
#26018718	2
C₈×M₁₆×C₈₉	2
#17966	89