Subgroups — #36536771

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030681	C₂	1	1	yes	maximal, characteristic
2	#26030285	C₂	1	2	yes	maximal, complemented
3	C₈×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019619	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019613	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019603	C₂	1	2	yes	maximal, complemented
8	#26019602	C₂	1	2	yes	maximal, complemented
9	#26018999	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018900	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668035	—	2	1	no	—
13	C₂×#15668035	—	2	1	no	—
14	#19152149	C₂²	1	2	yes	—
15	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
16	#19151983	—	2	1	no	—
17	#19151983	—	2	1	no	—
18	#19151975	C₂²	1	1	yes	characteristic
19	#19151972	C₂²	1	2	yes	—
20	#19151918	—	2	2	no	—
21	#19151880	C₂²	1	2	yes	—
22	#19151799	C₂²	1	2	yes	—
23	#19151798	C₂²	1	2	yes	—
24	#19151738	—	2	2	no	—
25	Q₈×#10623494	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₇₈	—	2	1	no	—
27	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
28	#19151722	—	2	1	no	—
29	#19151722	C₂²	1	1	yes	characteristic
30	#19151685	—	2	2	no	—
31	#19151683	—	2	2	no	—
32	#19151650	C₂²	1	2	yes	—
33	C₄⋊C₈×D₈₉	—	2	1	no	—
34	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151348	C₂²	1	2	yes	—
39	#19151344	C₂²	1	2	yes	—
40	#19151341	C₂²	1	2	yes	—
41	#19151341	C₂²	1	2	yes	—
42	#494×C₈₉	C₂²	1	1	yes	characteristic
43	#475×C₈₉	C₂²	1	2	yes	—
44	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083575	—	2	2	no	—
48	C₂×Q₈×D₈₉	D₄	1	1	yes	characteristic
49	#15668035	—	4	4	no	—
50	#15668035	—	4	4	no	—
51	C₂×#13083563	—	2	2	no	—
52	C₂×#13083561	—	2	2	no	—
53	C₂×#13083561	—	2	2	no	—
54	C₂×#13083561	—	2	2	no	—
55	C₂×D₇₁₂	—	2	1	no	—
56	C₂×D₇₁₂	—	2	1	no	—
57	C₂×C₈×D₈₉	—	2	1	no	—
58	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
59	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
60	#15668009	C₂³	1	2	yes	—
61	#15668001	—	2	2	no	—
62	#15667987	—	2	2	no	—
63	#15667987	—	2	2	no	—
64	Q₈×Dic₈₉	D₄	1	1	yes	characteristic
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	#15667977	—	2	1	no	—
68	#15667977	D₄	1	1	yes	characteristic
69	#15667974	—	2	2	no	—
70	#15667974	—	2	2	no	—
71	C₄⋊C₄×D₈₉	—	2	1	no	—
72	C₄⋊C₄×D₈₉	D₄	1	1	yes	characteristic
73	C₄²×D₈₉	—	2	1	no	—
74	C₄²×D₈₉	C₂³	1	1	yes	characteristic
75	#15667943	—	2	2	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	#15667941	—	2	1	no	—
80	#15667941	—	2	1	no	—
81	#15667941	—	2	1	no	—
82	#15667935	—	2	2	no	—
83	#15667934	—	2	2	no	—
84	#15667932	—	2	2	no	—
85	#15667924	—	2	2	no	—
86	C₄×#10623494	—	2	1	no	—
87	C₄×#10623494	C₂³	1	1	yes	characteristic
88	C₈×Dic₈₉	—	2	1	no	—
89	C₈×Dic₈₉	—	2	2	no	—
90	C₈×Dic₈₉	—	2	1	no	—
91	C₈×Dic₈₉	D₄	1	1	yes	characteristic
92	C₈×Dic₈₉	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₈₉	—	2	1	no	—
94	C₂×Q₁₆×C₈₉	—	2	1	no	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	2	no	—
98	C₄⋊C₈×C₈₉	—	2	1	no	—
99	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
101	#103×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	#13083575	—	4	4	no	—
105	#13083575	—	4	4	no	—
106	C₂×Dic₁₇₈	—	2	1	no	—
107	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₈₉	—	2	2	no	—
109	Q₈×D₈₉	—	2	2	no	—
110	C₂×D₃₅₆	—	2	2	no	—
111	C₂×D₃₅₆	—	2	2	no	—
112	C₂×D₃₅₆	—	2	2	no	—
113	C₂×D₃₅₆	—	4	2	no	—
114	C₂×C₄×D₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	4	2	no	—
117	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
120	#13083563	—	4	4	no	—
121	#13083561	—	4	4	no	—
122	#13083561	—	4	4	no	—
123	#13083561	—	4	4	no	—
124	D₇₁₂	—	4	2	no	—
125	D₇₁₂	—	4	2	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
129	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
130	C₈×D₈₉	—	2	2	no	—
131	C₈×D₈₉	—	4	2	no	—
132	C₈×D₈₉	SD₁₆	1	4	yes	complemented
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
135	#13083553	—	2	1	no	—
136	#13083553	—	2	1	no	—
137	#13083553	—	2	1	no	—
138	#13083551	—	4	2	no	—
139	#13083551	—	4	2	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	1	no	—
143	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₈₉	#41	1	1	yes	characteristic
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	Q₁₆×C₈₉	—	4	2	no	—
149	Q₁₆×C₈₉	—	4	2	no	—
150	C₂×C₈×C₈₉	—	2	1	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	2	no	—
156	C₄⋊C₄×C₈₉	—	2	2	no	—
157	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂²×D₈₉	—	4	2	no	—
161	C₂²×D₈₉	#121	1	1	yes	characteristic
162	Q₈×C₈₉	—	2	1	no	—
163	Q₈×C₈₉	—	4	2	no	—
164	Q₈×C₈₉	—	4	2	no	—
165	Q₈×C₈₉	#135	1	2	yes	complemented
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₈₉	—	2	1	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	#121	1	1	yes	characteristic
175	C₂×Dic₈₉	#121	1	1	yes	characteristic
176	C₂×Dic₈₉	#121	1	1	yes	characteristic
177	D₃₅₆	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	8	2	no	—
182	D₃₅₆	—	8	4	no	—
183	C₄×D₈₉	—	2	4	no	—
184	C₄×D₈₉	—	2	1	no	—
185	C₄×D₈₉	—	2	1	no	—
186	C₄×D₈₉	—	4	1	no	—
187	C₄×D₈₉	—	4	2	no	—
188	C₄×D₈₉	—	8	4	no	—
189	C₄×D₈₉	C₂×SD₁₆	1	2	yes	—
190	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
191	Dic₁₇₈	—	2	4	no	—
192	Dic₁₇₈	—	2	1	no	—
193	Dic₁₇₈	#135	1	2	yes	complemented
194	C₈×C₈₉	—	2	1	no	—
195	C₈×C₈₉	—	4	2	no	—
196	C₈×C₈₉	—	4	1	no	—
197	C₈×C₈₉	C₂×SD₁₆	1	2	yes	—
198	#10623494	—	2	1	no	—
199	#10623494	—	4	2	no	—
200	#10623494	—	4	1	no	—
201	#10623494	C₂×SD₁₆	1	2	yes	—
202	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
203	C₂×D₈₉	—	2	1	no	—
204	C₂×D₈₉	—	2	1	no	—
205	C₂×D₈₉	—	8	2	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₂×D₈₉	—	8	2	no	—
208	C₂×D₈₉	#460	1	2	yes	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	4	1	no	—
212	C₄×C₈₉	—	8	2	no	—
213	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
215	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
216	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	Dic₈₉	—	2	1	no	—
218	Dic₈₉	—	2	2	no	—
219	Dic₈₉	—	2	1	no	—
220	Dic₈₉	—	4	1	no	—
221	Dic₈₉	#460	1	2	yes	—
222	#19114	—	89	1	no	maximal, Sylow
223	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
224	C₂×C₈₉	#3050	1	1	yes	characteristic
225	C₂×C₈₉	#3067	1	1	yes	characteristic
226	D₈₉	—	2	2	no	—
227	D₈₉	—	16	2	no	—
228	#3147	—	89	1	no	—
229	#3103	—	89	2	no	—
230	C₂×C₈×Q₈	—	89	1	no	—
231	#1670	—	89	1	no	—
232	#1670	D₈₉	1	1	yes	characteristic, complemented
233	#1668	—	89	1	no	—
234	#1668	—	89	1	no	—
235	#1666	—	89	2	no	—
236	#1666	—	89	2	no	—
237	#1564	—	89	1	no	—
238	#1540	—	89	2	no	—
239	C₈₉	#19114	1	1	yes	characteristic, complemented, Sylow
240	C₂×#135	—	178	1	no	—
241	C₂×#135	—	178	1	no	—
242	#532	—	89	2	no	—
243	C₂×C₄×Q₈	—	89	1	no	—
244	#495	—	178	1	no	—
245	#495	—	178	1	no	—
246	#494	C₂×D₈₉	1	1	yes	characteristic
247	#493	—	89	1	no	—
248	#492	—	89	2	no	—
249	#481	—	178	2	no	—
250	#475	—	89	2	no	—
251	#475	C₂×D₈₉	1	2	yes	—
252	#460	—	89	2	no	—
253	#460	—	89	2	no	—
254	#448	—	178	2	no	—
255	C₈×Q₈	—	89	1	no	—
256	C₈×Q₈	—	89	1	no	—
257	C₈×Q₈	—	89	1	no	—
258	C₈×Q₈	—	178	1	no	—
259	C₈×Q₈	—	178	1	no	—
260	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
261	C₄×SD₁₆	—	178	2	no	—
262	C₄×SD₁₆	—	178	2	no	—
263	#431	—	89	2	no	—
264	C₂×C₄⋊C₈	—	89	1	no	—
265	C₂×C₄⋊C₈	—	178	1	no	—
266	C₂×C₄×C₈	—	89	1	no	—
267	C₂×C₄×C₈	—	178	1	no	—
268	#335	—	89	1	no	—
269	#335	C₂×D₈₉	1	1	yes	characteristic
270	#334	—	89	2	no	—
271	#332	—	89	2	no	—
272	#332	C₂×D₈₉	1	2	yes	—
273	#331	—	89	2	no	—
274	#331	—	89	2	no	—
275	C₂×#41	—	178	2	no	—
276	C₂²×Q₈	—	89	1	no	—
277	#135	—	356	4	no	—
278	#135	—	356	4	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	178	2	no	—
282	C₂×SD₁₆	—	178	2	no	—
283	C₂×SD₁₆	—	178	2	no	—
284	C₂×SD₁₆	—	178	2	no	—
285	C₂×D₈	—	178	1	no	—
286	C₂×D₈	—	178	1	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	89	1	no	—
289	C₂²×C₈	—	178	1	no	—
290	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
291	#127	—	89	2	no	—
292	#124	—	178	2	no	—
293	#121	—	178	2	no	—
294	#121	—	178	2	no	—
295	C₄×Q₈	—	89	1	no	—
296	C₄×Q₈	—	89	1	no	—
297	C₄×Q₈	—	89	1	no	—
298	C₄×Q₈	—	178	1	no	—
299	C₄×Q₈	—	178	1	no	—
300	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
301	C₄×D₄	—	178	2	no	—
302	C₄×D₄	—	178	2	no	—
303	C₂×C₄⋊C₄	—	89	1	no	—
304	C₂×C₄⋊C₄	—	178	1	no	—
305	C₂×C₄²	—	89	1	no	—
306	C₂×C₄²	—	178	1	no	—
307	#106	—	2	2	no	—
308	#106	—	178	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	2	no	—
312	C₄⋊C₈	—	178	1	no	—
313	C₄⋊C₈	—	178	1	no	—
314	C₄⋊C₈	—	178	1	no	—
315	C₄⋊C₈	—	178	1	no	—
316	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
318	#103	—	2	2	no	—
319	#103	—	178	2	no	—
320	#102	—	178	2	no	—
321	#102	—	178	2	no	—
322	C₂²⋊C₈	—	178	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	89	1	no	—
326	C₄×C₈	—	89	1	no	—
327	C₄×C₈	—	178	1	no	—
328	C₄×C₈	—	178	2	no	—
329	C₄×C₈	—	178	1	no	—
330	C₄×C₈	—	178	1	no	—
331	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
332	#41	—	356	4	no	—
333	#41	—	356	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	89	1	no	—
336	C₂×Q₈	—	178	1	no	—
337	C₂×Q₈	—	178	2	no	—
338	C₂×Q₈	—	178	2	no	—
339	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
340	C₂×D₄	—	356	2	no	—
341	C₂×D₄	—	178	2	no	—
342	C₂×D₄	—	178	2	no	—
343	C₂×D₄	—	178	2	no	—
344	C₂²×C₄	—	89	1	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	89	1	no	—
347	C₂²×C₄	—	356	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	—	178	1	no	—
350	Q₁₆	—	4	2	no	—
351	Q₁₆	—	4	2	no	—
352	SD₁₆	—	356	4	no	—
353	SD₁₆	—	356	4	no	—
354	SD₁₆	—	356	4	no	—
355	SD₁₆	—	356	4	no	—
356	D₈	—	356	2	no	—
357	D₈	—	356	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	89	4	no	—
362	C₂×C₈	—	89	1	no	—
363	C₂×C₈	—	356	2	no	—
364	C₂×C₈	—	178	2	no	—
365	C₂×C₈	—	178	1	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
368	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	89	1	no	—
373	C₄⋊C₄	—	178	1	no	—
374	C₄⋊C₄	—	178	1	no	—
375	C₄⋊C₄	—	178	1	no	—
376	C₄⋊C₄	—	178	1	no	—
377	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
378	C₂²⋊C₄	—	356	2	no	—
379	C₂²⋊C₄	—	356	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	89	1	no	—
382	C₄²	—	89	1	no	—
383	C₄²	—	89	1	no	—
384	C₄²	—	178	1	no	—
385	C₄²	—	178	1	no	—
386	C₄²	—	178	1	no	—
387	C₄²	C₂³×D₈₉	1	1	yes	characteristic
388	C₂³	—	89	1	no	—
389	C₂³	—	356	2	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	89	2	no	—
394	Q₈	—	178	4	no	—
395	Q₈	—	178	1	no	—
396	Q₈	#15668035	1	2	yes	complemented
397	D₄	—	356	2	no	—
398	D₄	—	356	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	356	2	no	—
401	D₄	—	712	2	no	—
402	D₄	—	712	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	89	1	no	—
407	C₂×C₄	—	89	2	no	—
408	C₂×C₄	—	89	2	no	—
409	C₂×C₄	—	89	1	no	—
410	C₂×C₄	—	89	1	no	—
411	C₂×C₄	—	356	1	no	—
412	C₂×C₄	—	356	2	no	—
413	C₂×C₄	—	178	4	no	—
414	C₂×C₄	—	178	1	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	—	178	1	no	—
418	C₂×C₄	—	712	4	no	—
419	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
421	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	89	2	no	—
426	C₈	—	356	2	no	—
427	C₈	—	356	1	no	—
428	C₈	—	178	1	no	—
429	C₈	SD₁₆×D₈₉	1	2	yes	—
430	C₂²	—	89	2	no	—
431	C₂²	—	178	1	no	—
432	C₂²	—	178	1	no	—
433	C₂²	—	712	2	no	—
434	C₂²	—	712	2	no	—
435	C₂²	—	712	2	no	—
436	C₂²	#121×D₈₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	89	2	no	—
442	C₄	—	356	1	no	—
443	C₄	—	178	1	no	—
444	C₄	—	178	2	no	—
445	C₄	—	178	1	no	—
446	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
447	C₄	#135×D₈₉	1	1	yes	characteristic
448	C₄	C₂×#15668035	1	1	yes	characteristic
449	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
450	C₂	—	1424	2	no	—
451	C₂	—	178	2	no	—
452	C₂	#460×D₈₉	1	1	yes	characteristic
453	C₂	#26029835	1	1	yes	characteristic
454	C₂	#26029974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1670	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26030681	C₂
hypercenter	#1670	D₈₉
hypocenter	C₈₉	#19114
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
2. #26030285	C₂	semidirect
3. C₈×Q₈×D₈₉	C₂	semidirect
4. #26019619	C₂	semidirect
5. #26019613	C₂	semidirect
6. #26019612	C₂	semidirect
7. #26019603	C₂	semidirect
8. #26019602	C₂	semidirect
9. #26018999	C₂	semidirect
10. #26018900	C₂	semidirect
11. C₈₉×#1670	C₂	semidirect
132. C₈×D₈₉	SD₁₆	semidirect
165. Q₈×C₈₉	#135	semidirect
193. Dic₁₇₈	#135	semidirect
232. #1670	D₈₉	semidirect
239. C₈₉	#19114	semidirect
396. Q₈	#15668035	semidirect

Maximal subgroups

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

subgroup	index
#26030681	2
#26030285	2
C₈×Q₈×D₈₉	2
#26019619	2
#26019613	2
#26019612	2
#26019603	2
#26019602	2
#26018999	2
#26018900	2
C₈₉×#1670	2
#19114	89