Subgroups — #36538325

Order 22784.

702 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030060	C₂	1	2	yes	maximal
3	C₈×#13083573	C₂	1	1	yes	maximal, characteristic
4	#26019623	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019621	C₂	1	2	yes	maximal, complemented
6	#26019619	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019617	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019615	C₂	1	2	yes	maximal, complemented
9	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018935	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1669	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	—	2	1	no	—
13	C₂×Q₁₆×D₈₉	—	2	1	no	—
14	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
15	C₄×#13083573	C₂²	1	1	yes	characteristic
16	#19151978	C₂²	1	1	yes	characteristic
17	#19151977	C₂²	1	2	yes	—
18	#19151976	—	2	1	no	—
19	#19151976	—	2	1	no	—
20	#19151892	—	2	2	no	—
21	#19151886	—	2	2	no	—
22	#19151884	C₂²	1	2	yes	—
23	#19151880	C₂²	1	2	yes	—
24	#19151878	C₂²	1	2	yes	—
25	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	#19151722	C₂²	1	1	yes	characteristic
27	D₄×#10623494	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₈₉	—	2	1	no	—
29	#19151661	—	2	1	no	—
30	#19151650	C₂²	1	1	yes	characteristic
31	#19151648	—	2	1	no	—
32	#19151639	—	2	2	no	—
33	#19151620	C₂²	1	2	yes	—
34	#19151596	—	2	2	no	—
35	C₂×C₈×Dic₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151344	C₂²	1	2	yes	—
41	#19151343	C₂²	1	2	yes	—
42	#494×C₈₉	C₂²	1	1	yes	characteristic
43	#474×C₈₉	C₂²	1	2	yes	—
44	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083573	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₈₉	—	2	2	no	—
49	C₂×Dic₃₅₆	—	2	1	no	—
50	C₂×Dic₃₅₆	—	2	1	no	—
51	C₂×#13083564	—	2	2	no	—
52	C₂×#13083564	—	2	2	no	—
53	Q₁₆×D₈₉	—	4	4	no	—
54	Q₁₆×D₈₉	—	4	4	no	—
55	C₂×#13083557	—	2	2	no	—
56	C₂²×#10623494	—	2	1	no	—
57	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
59	#15668012	C₂³	1	2	yes	—
60	#15668011	—	2	2	no	—
61	#15668011	—	2	2	no	—
62	#15668010	—	2	2	no	—
63	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	#15667977	D₄	1	1	yes	characteristic
65	D₄×Dic₈₉	D₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	#15667972	—	2	1	no	—
68	#15667970	D₄	1	1	yes	characteristic
69	#15667968	—	2	1	no	—
70	C₄⋊C₄×D₈₉	—	2	2	no	—
71	C₄⋊C₄×D₈₉	—	2	2	no	—
72	C₂×C₄×Dic₈₉	—	2	1	no	—
73	C₄²×D₈₉	C₂³	1	1	yes	characteristic
74	#15667945	—	2	2	no	—
75	#15667944	—	2	2	no	—
76	#15667943	—	2	2	no	—
77	C₄⋊#10623494	C₂³	1	2	yes	—
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	#15667941	—	2	1	no	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	1	no	—
82	#15667937	—	2	2	no	—
83	#15667935	—	2	2	no	—
84	#15667933	—	2	2	no	—
85	C₂²⋊#10623494	—	2	1	no	—
86	#15667924	—	2	1	no	—
87	C₄×#10623494	C₂³	1	1	yes	characteristic
88	C₈×Dic₈₉	—	2	1	no	—
89	C₈×Dic₈₉	—	2	1	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	C₂²×C₈×C₈₉	—	2	1	no	—
96	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
97	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
98	#107×C₈₉	—	2	2	no	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	#102×C₈₉	—	2	2	no	—
102	C₂²⋊C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	#13083573	—	2	2	no	—
105	#13083573	Q₁₆	1	4	yes	complemented
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×Dic₁₇₈	—	4	2	no	—
108	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
109	Q₈×D₈₉	—	4	4	no	—
110	Q₈×D₈₉	—	4	4	no	—
111	C₂×C₂²⋊D₈₉	—	2	1	no	—
112	C₂²×Dic₈₉	—	2	1	no	—
113	C₂²×Dic₈₉	—	2	1	no	—
114	C₂×C₄×D₈₉	—	4	2	no	—
115	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
118	Dic₃₅₆	—	4	2	no	—
119	Dic₃₅₆	—	4	2	no	—
120	#13083564	—	4	4	no	—
121	#13083564	—	4	4	no	—
122	#13083557	—	4	4	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	—	4	2	no	—
126	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
127	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
128	C₈×D₈₉	—	2	2	no	—
129	C₈×D₈₉	—	2	2	no	—
130	C₄⋊Dic₈₉	—	2	2	no	—
131	C₄⋊Dic₈₉	—	2	2	no	—
132	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
133	#13083553	—	2	1	no	—
134	#13083553	—	2	1	no	—
135	#13083553	—	4	2	no	—
136	#13083553	—	4	2	no	—
137	C₂²⋊Dic₈₉	—	2	1	no	—
138	#13083551	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₈₉	#41	1	1	yes	characteristic
145	C₂×Q₈×C₈₉	—	2	2	no	—
146	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	Q₁₆×C₈₉	—	4	2	no	—
149	Q₁₆×C₈₉	—	4	2	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	2	1	no	—
152	C₂×C₈×C₈₉	—	4	2	no	—
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	—	2	1	no	—
161	C₂²×D₈₉	#121	1	1	yes	characteristic
162	Q₈×C₈₉	—	4	2	no	—
163	Q₈×C₈₉	—	4	2	no	—
164	D₄×C₈₉	—	2	1	no	—
165	D₄×C₈₉	C₂×Q₁₆	1	2	yes	complemented
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₈₉	—	2	4	no	—
174	C₂×Dic₈₉	—	2	1	no	—
175	C₂×Dic₈₉	—	2	4	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	4	2	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	#121	1	1	yes	characteristic
180	C₂×Dic₈₉	#121	1	1	yes	characteristic
181	C₂×Dic₈₉	#121	1	1	yes	characteristic
182	C₄×D₈₉	—	2	1	no	—
183	C₄×D₈₉	—	2	1	no	—
184	C₄×D₈₉	—	2	2	no	—
185	C₄×D₈₉	—	8	4	no	—
186	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
187	C₄×D₈₉	#135	1	2	yes	—
188	Dic₁₇₈	—	2	1	no	—
189	Dic₁₇₈	—	4	2	no	—
190	Dic₁₇₈	—	4	2	no	—
191	Dic₁₇₈	—	8	4	no	—
192	Dic₁₇₈	C₂×Q₁₆	1	2	yes	complemented
193	C₈×C₈₉	—	2	1	no	—
194	C₈×C₈₉	—	4	2	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
197	#10623494	—	2	1	no	—
198	#10623494	—	4	2	no	—
199	#10623494	—	4	1	no	—
200	#10623494	AGL(1,ℤ/8)	1	2	yes	—
201	C₂²×C₈₉	—	2	2	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	—	4	1	no	—
204	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
205	C₂×D₈₉	—	2	1	no	—
206	C₂×D₈₉	—	2	1	no	—
207	C₂×D₈₉	#467	1	2	yes	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	8	2	no	—
211	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
212	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
213	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	Dic₈₉	—	2	1	no	—
216	Dic₈₉	—	2	2	no	—
217	Dic₈₉	—	4	1	no	—
218	Dic₈₉	—	8	2	no	—
219	Dic₈₉	#467	1	2	yes	—
220	Dic₈₉	#473	1	2	yes	—
221	#19268	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	4	2	no	—
223	C₂×C₈₉	#3038	1	1	yes	characteristic
224	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
225	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
226	D₈₉	—	2	2	no	—
227	C₂×#494	—	89	1	no	—
228	#3079	—	89	2	no	—
229	C₈×#41	—	89	1	no	—
230	#1670	—	89	1	no	—
231	#1670	—	89	1	no	—
232	#1670	—	89	2	no	—
233	#1669	—	89	2	no	—
234	#1669	—	89	1	no	—
235	#1669	D₈₉	1	1	yes	characteristic, complemented
236	#1567	—	89	1	no	—
237	#1549	—	89	2	no	—
238	C₈₉	#19268	1	1	yes	characteristic, complemented, Sylow
239	C₂²×Q₁₆	—	178	1	no	—
240	C₂²×Q₁₆	—	178	1	no	—
241	C₂×C₄⋊Q₈	—	89	2	no	—
242	C₄×#41	—	89	1	no	—
243	#494	—	89	2	no	—
244	#494	—	89	1	no	—
245	#494	—	178	1	no	—
246	#494	—	178	1	no	—
247	#494	C₂×D₈₉	1	1	yes	characteristic
248	#477	—	178	2	no	—
249	#476	—	178	2	no	—
250	#475	—	89	2	no	—
251	#475	—	89	2	no	—
252	#474	—	89	2	no	—
253	#474	C₂×D₈₉	1	2	yes	—
254	C₈×Q₈	—	89	1	no	—
255	C₈×Q₈	—	89	1	no	—
256	C₈×D₄	—	89	1	no	—
257	C₈×D₄	—	178	1	no	—
258	C₈×D₄	—	178	1	no	—
259	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
260	#431	—	89	1	no	—
261	#431	—	178	1	no	—
262	#428	—	178	2	no	—
263	#423	—	89	2	no	—
264	#417	—	178	2	no	—
265	C₂×C₄×C₈	—	89	1	no	—
266	C₂×C₄×C₈	—	178	1	no	—
267	#335	—	89	2	no	—
268	#335	—	89	1	no	—
269	#335	C₂×D₈₉	1	1	yes	characteristic
270	#332	—	89	2	no	—
271	#332	—	89	2	no	—
272	#332	—	89	2	no	—
273	#332	C₂×D₈₉	1	2	yes	—
274	C₂×#41	—	89	1	no	—
275	C₂²×Q₈	—	178	2	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	356	4	no	—
279	C₂×Q₁₆	—	356	4	no	—
280	C₂×Q₁₆	—	178	2	no	—
281	C₂×Q₁₆	—	178	2	no	—
282	C₂×Q₁₆	—	178	1	no	—
283	C₂×Q₁₆	—	178	1	no	—
284	C₂×M₁₆	—	178	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	89	1	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	178	1	no	—
289	C₄⋊Q₈	—	89	2	no	—
290	C₄⋊Q₈	—	178	2	no	—
291	C₄⋊Q₈	—	178	2	no	—
292	C₄⋊Q₈	—	178	2	no	—
293	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
294	C₄×Q₈	—	89	1	no	—
295	C₄×Q₈	—	89	1	no	—
296	C₄×D₄	—	89	1	no	—
297	C₄×D₄	—	178	1	no	—
298	C₄×D₄	—	178	1	no	—
299	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
300	#117	—	89	1	no	—
301	#117	—	178	1	no	—
302	C₂×C₄⋊C₄	—	178	2	no	—
303	C₂×C₄⋊C₄	—	178	2	no	—
304	C₂×C₄²	—	89	1	no	—
305	C₂×C₄²	—	178	1	no	—
306	#107	—	2	2	no	—
307	#107	—	178	2	no	—
308	#106	—	178	2	no	—
309	#106	—	178	2	no	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	2	no	—
312	C₄⋊C₈	—	178	2	no	—
313	C₄⋊C₈	—	178	1	no	—
314	C₄⋊C₈	—	178	1	no	—
315	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
317	#103	—	178	2	no	—
318	#103	—	178	2	no	—
319	#102	—	2	2	no	—
320	#102	—	178	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	178	1	no	—
323	C₂²⋊C₈	—	178	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	1	no	—
329	C₄×C₈	—	178	1	no	—
330	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
331	#41	—	89	4	no	—
332	#41	—	178	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	89	1	no	—
335	C₂×Q₈	—	356	2	no	—
336	C₂×Q₈	—	356	4	no	—
337	C₂×Q₈	—	356	4	no	—
338	C₂×Q₈	—	178	2	no	—
339	C₂×D₄	—	178	1	no	—
340	C₂×D₄	D₄×D₈₉	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	89	1	no	—
343	C₂²×C₄	—	89	1	no	—
344	C₂²×C₄	—	89	1	no	—
345	C₂²×C₄	—	356	2	no	—
346	C₂²×C₄	—	178	1	no	—
347	C₂²×C₄	—	178	1	no	—
348	Q₁₆	—	4	2	no	—
349	Q₁₆	—	4	2	no	—
350	Q₁₆	—	356	2	no	—
351	Q₁₆	—	356	4	no	—
352	Q₁₆	—	356	4	no	—
353	Q₁₆	—	356	2	no	—
354	M₁₆	—	356	4	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	89	1	no	—
359	C₂×C₈	—	89	1	no	—
360	C₂×C₈	—	356	2	no	—
361	C₂×C₈	—	178	2	no	—
362	C₂×C₈	—	178	1	no	—
363	C₂×C₈	—	178	2	no	—
364	C₂×C₈	—	178	2	no	—
365	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
366	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	89	1	no	—
370	C₄⋊C₄	—	356	2	no	—
371	C₄⋊C₄	—	356	2	no	—
372	C₄⋊C₄	—	178	1	no	—
373	C₄⋊C₄	—	178	2	no	—
374	C₄⋊C₄	—	178	2	no	—
375	C₄⋊C₄	—	178	1	no	—
376	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	178	1	no	—
379	C₂²⋊C₄	—	178	1	no	—
380	C₄²	—	89	1	no	—
381	C₄²	—	89	1	no	—
382	C₄²	—	89	1	no	—
383	C₄²	—	178	1	no	—
384	C₄²	—	178	1	no	—
385	C₄²	—	178	1	no	—
386	C₄²	C₂³×D₈₉	1	1	yes	characteristic
387	C₂³	—	2	1	no	—
388	C₂³	—	89	1	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	89	2	no	—
392	Q₈	—	356	2	no	—
393	Q₈	—	356	2	no	—
394	Q₈	—	178	1	no	—
395	Q₈	—	712	4	no	—
396	D₄	—	2	1	no	—
397	D₄	—	178	4	no	—
398	D₄	Q₁₆×D₈₉	1	2	yes	complemented
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	89	1	no	—
404	C₂×C₄	—	89	1	no	—
405	C₂×C₄	—	89	2	no	—
406	C₂×C₄	—	89	2	no	—
407	C₂×C₄	—	89	1	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	—	178	4	no	—
412	C₂×C₄	—	178	1	no	—
413	C₂×C₄	—	178	1	no	—
414	C₂×C₄	—	178	1	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	712	4	no	—
417	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
419	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	89	2	no	—
424	C₈	—	356	2	no	—
425	C₈	—	356	1	no	—
426	C₈	—	178	1	no	—
427	C₈	#15668036	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	89	2	no	—
432	C₂²	—	178	1	no	—
433	C₂²	—	178	1	no	—
434	C₂²	#121×D₈₉	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	89	2	no	—
439	C₄	—	89	2	no	—
440	C₄	—	356	1	no	—
441	C₄	—	178	1	no	—
442	C₄	—	178	2	no	—
443	C₄	—	712	2	no	—
444	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
445	C₄	#135×D₈₉	1	1	yes	characteristic
446	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
447	C₄	C₂×#15668036	1	1	yes	characteristic
448	C₂	—	4	2	no	—
449	C₂	—	178	2	no	—
450	C₂	#26029727	1	1	yes	characteristic
451	C₂	#467×D₈₉	1	1	yes	characteristic
452	C₂	#473×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1669	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#13083573	D₄
hypercenter	#1669	D₈₉
hypocenter	C₈₉	#19268
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1669

Complements

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

N	H ≅ G/N	type
1. #494×D₈₉	C₂	semidirect
4. #26019623	C₂	semidirect
5. #26019621	C₂	semidirect
6. #26019619	C₂	semidirect
7. #26019617	C₂	semidirect
8. #26019615	C₂	semidirect
9. #26019009	C₂	semidirect
10. #26018935	C₂	semidirect
11. C₈₉×#1669	C₂	semidirect
105. #13083573	Q₁₆	semidirect
165. D₄×C₈₉	C₂×Q₁₆	semidirect
192. Dic₁₇₈	C₂×Q₁₆	semidirect
235. #1669	D₈₉	semidirect
238. C₈₉	#19268	semidirect
398. D₄	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#494×D₈₉	2
#26030060	2
C₈×#13083573	2
#26019623	2
#26019621	2
#26019619	2
#26019617	2
#26019615	2
#26019009	2
#26018935	2
C₈₉×#1669	2
#19268	89