Subgroups — #36449676

Order 22784.

690 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	C₂×#19151945	C₂	1	1	yes	maximal, characteristic
2	#26023316	C₂	1	1	yes	maximal, characteristic
3	#26021204	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021174	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
6	#26018092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668012	C₂²	1	1	yes	characteristic
9	C₂×#15668009	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₅₆	—	2	1	no	—
11	C₂×#15667974	—	2	1	no	—
12	#19151945	—	2	2	no	—
13	#19151945	C₄	1	4	yes	complemented
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×#15667937	—	2	1	no	—
16	C₂×#15667937	—	2	1	no	—
17	C₂×#15667934	—	2	2	no	—
18	#19151500	—	2	1	no	—
19	#19151499	—	2	1	no	—
20	#19151476	—	2	2	no	—
21	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
22	#19151360	—	2	1	no	—
23	#19151360	—	2	1	no	—
24	#19151341	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₇₈	—	2	1	no	—
29	C₂²×D₃₅₆	—	2	1	no	—
30	C₂²×D₃₅₆	—	2	1	no	—
31	C₂²×D₃₅₆	D₄	1	2	yes	—
32	C₂²×C₄×D₈₉	—	2	2	no	—
33	C₂²×#10623494	—	2	1	no	—
34	#15668012	—	2	1	no	—
35	#15668012	—	2	1	no	—
36	#15668012	—	2	1	no	—
37	#15668012	C₂×C₄	1	2	yes	complemented
38	#15668009	—	2	1	no	—
39	#15668009	—	2	1	no	—
40	#15668009	C₂×C₄	1	2	yes	—
41	#15668009	D₄	1	2	yes	—
42	C₄×D₃₅₆	—	4	2	no	—
43	C₄×D₃₅₆	—	4	2	no	—
44	#15667974	—	4	2	no	—
45	#15667974	—	4	2	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
50	C₂×#13083551	—	2	2	no	—
51	C₂×#13083551	—	2	2	no	—
52	C₂×#13083551	—	2	2	no	—
53	C₂×C₄×Dic₈₉	—	2	1	no	—
54	C₄⋊#10623494	—	2	1	no	—
55	C₄⋊#10623494	—	2	1	no	—
56	#15667937	—	4	2	no	—
57	#15667937	—	4	2	no	—
58	#15667934	—	2	8	no	—
59	#15667919	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	—	2	1	no	—
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₈₉	—	2	1	no	—
67	C₄⋊C₈×C₈₉	—	2	1	no	—
68	C₄×C₈×C₈₉	—	2	1	no	—
69	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	complemented
70	#95×C₈₉	—	2	1	no	—
71	C₂³×D₈₉	—	2	2	no	—
72	C₂×Dic₁₇₈	—	2	2	no	—
73	C₂×Dic₁₇₈	—	4	1	no	—
74	C₂×Dic₁₇₈	—	4	1	no	—
75	C₂×Dic₁₇₈	—	4	1	no	—
76	C₂×Dic₁₇₈	—	4	1	no	—
77	C₂×Dic₁₇₈	—	4	1	no	—
78	C₂×D₃₅₆	—	2	2	no	—
79	C₂×D₃₅₆	—	2	2	no	—
80	C₂×D₃₅₆	—	2	2	no	—
81	C₂×D₃₅₆	—	2	2	no	—
82	C₂×D₃₅₆	—	2	2	no	—
83	C₂×D₃₅₆	—	4	1	no	—
84	C₂×D₃₅₆	—	4	1	no	—
85	C₂×D₃₅₆	—	4	1	no	—
86	C₂×D₃₅₆	—	4	1	no	—
87	C₂×D₃₅₆	—	4	1	no	—
88	C₂×D₃₅₆	—	4	1	no	—
89	C₂×D₃₅₆	—	4	1	no	—
90	C₂×D₃₅₆	—	4	1	no	—
91	C₂×D₃₅₆	—	4	2	no	—
92	C₂×D₃₅₆	—	4	2	no	—
93	C₂×D₃₅₆	C₂²⋊C₄	1	4	yes	—
94	C₂²×Dic₈₉	—	2	1	no	—
95	C₂²×Dic₈₉	—	2	1	no	—
96	C₂²×Dic₈₉	—	4	1	no	—
97	C₂×C₄×D₈₉	—	4	4	no	—
98	C₂×C₄×D₈₉	—	4	4	no	—
99	C₂×C₄×D₈₉	—	8	2	no	—
100	C₂×#10623494	—	4	1	no	—
101	C₂×#10623494	—	4	1	no	—
102	C₂×#10623494	—	4	1	no	—
103	C₄⋊Dic₈₉	—	2	1	no	—
104	C₄⋊Dic₈₉	—	2	2	no	—
105	C₄⋊Dic₈₉	—	2	2	no	—
106	C₄⋊Dic₈₉	—	2	1	no	—
107	C₄⋊Dic₈₉	—	2	1	no	—
108	C₄⋊Dic₈₉	—	4	1	no	—
109	C₄⋊Dic₈₉	—	4	1	no	—
110	C₄⋊Dic₈₉	D₈	1	2	yes	—
111	#13083551	—	4	4	no	—
112	#13083551	—	4	4	no	—
113	#13083551	—	8	2	no	—
114	C₄×Dic₈₉	—	4	1	no	—
115	C₄×Dic₈₉	—	4	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	—	2	1	no	—
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	—	4	1	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₂×C₈×C₈₉	—	4	1	no	—
125	C₂×C₈×C₈₉	—	4	1	no	—
126	C₂×C₈×C₈₉	—	4	1	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	SD₁₆	1	2	yes	—
131	C₄²×C₈₉	—	4	1	no	—
132	C₄²×C₈₉	—	4	1	no	—
133	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₈₉	#41	1	1	yes	characteristic
136	C₄²×C₈₉	#41	1	1	yes	characteristic
137	C₂³×C₈₉	#120	1	1	yes	characteristic
138	C₂²×D₈₉	—	2	4	no	—
139	C₂²×D₈₉	—	4	2	no	—
140	C₂²×D₈₉	—	4	2	no	—
141	C₂²×D₈₉	—	4	2	no	—
142	C₂²×D₈₉	—	4	2	no	—
143	C₂²×D₈₉	—	4	2	no	—
144	C₂²×D₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	4	1	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	—	4	1	no	—
172	C₂×Dic₈₉	—	4	1	no	—
173	C₂×Dic₈₉	—	4	1	no	—
174	C₂×Dic₈₉	—	8	1	no	—
175	C₂×Dic₈₉	—	8	1	no	—
176	D₃₅₆	—	4	4	no	—
177	D₃₅₆	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	8	2	no	—
186	C₄×D₈₉	—	8	8	no	—
187	Dic₁₇₈	—	4	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	Dic₁₇₈	—	8	1	no	—
190	Dic₁₇₈	—	8	1	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₈×C₈₉	—	8	1	no	—
193	#10623494	—	8	1	no	—
194	C₂²×C₈₉	#386	1	1	yes	characteristic
195	C₂²×C₈₉	#447	1	1	yes	characteristic
196	C₂²×C₈₉	#449	1	1	yes	characteristic
197	C₂²×C₈₉	#450	1	1	yes	characteristic
198	C₂²×C₈₉	#452	1	1	yes	characteristic
199	C₂²×C₈₉	#455	1	1	yes	characteristic
200	C₂²×C₈₉	#455	1	1	yes	characteristic
201	C₂×D₈₉	—	4	4	no	—
202	C₂×D₈₉	—	4	4	no	—
203	C₂×D₈₉	—	4	4	no	—
204	C₂×D₈₉	—	8	2	no	—
205	C₂×D₈₉	—	8	2	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₂×D₈₉	—	8	2	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	4	2	no	—
211	C₄×C₈₉	—	8	1	no	—
212	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
213	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
214	C₄×C₈₉	#440	1	1	yes	characteristic
215	C₄×C₈₉	#442	1	1	yes	characteristic
216	C₄×C₈₉	#459	1	1	yes	characteristic
217	C₄×C₈₉	#461	1	1	yes	characteristic
218	C₄×C₈₉	#463	1	1	yes	characteristic
219	C₄×C₈₉	#463	1	1	yes	characteristic
220	Dic₈₉	—	4	2	no	—
221	Dic₈₉	—	8	2	no	—
222	Dic₈₉	—	8	1	no	—
223	#9057	—	89	1	no	maximal, Sylow
224	C₂×C₈₉	#1639	1	1	yes	characteristic
225	C₂×C₈₉	#1640	1	1	yes	characteristic
226	C₂×C₈₉	#1641	1	1	yes	characteristic
227	C₂×C₈₉	#1642	1	1	yes	characteristic
228	C₂×C₈₉	#1877	1	1	yes	characteristic
229	C₂×C₈₉	#1879	1	1	yes	characteristic
230	C₂×C₈₉	#1885	1	1	yes	characteristic
231	D₈₉	—	8	4	no	—
232	C₂×#486	—	89	1	no	—
233	#2366	—	89	1	no	—
234	#1988	—	89	1	no	—
235	#1981	—	89	1	no	—
236	C₂×#331	—	89	1	no	—
237	#1279	—	89	1	no	—
238	#1279	D₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#9057	1	1	yes	characteristic, complemented, Sylow
240	C₂×C₄⋊Q₈	—	89	1	no	—
241	C₂×#127	—	89	1	no	—
242	C₂×C₄×D₄	—	178	1	no	—
243	C₂×C₄×D₄	—	178	1	no	—
244	#486	—	89	4	no	—
245	#486	—	178	2	no	—
246	C₂×C₄⋊C₈	—	89	1	no	—
247	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
248	C₂×#103	—	178	1	no	—
249	C₂×#103	—	178	1	no	—
250	C₂×#102	—	178	2	no	—
251	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
252	#390	—	178	1	no	—
253	#390	—	178	1	no	—
254	#386	—	178	2	no	—
255	C₄×C₄⋊C₄	—	89	1	no	—
256	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
257	#340	—	178	1	no	—
258	#340	—	178	1	no	—
259	#331	—	178	2	no	—
260	C₂²×Q₈	—	178	1	no	—
261	C₂²×D₄	—	89	2	no	—
262	C₂²×D₄	—	178	1	no	—
263	C₂²×D₄	—	178	1	no	—
264	C₂³×C₄	—	178	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	178	1	no	—
268	C₄⋊Q₈	—	89	2	no	—
269	C₄⋊Q₈	—	178	1	no	—
270	C₄⋊Q₈	—	178	1	no	—
271	C₄⋊Q₈	—	178	1	no	—
272	#127	—	89	2	no	—
273	#127	—	89	2	no	—
274	#127	—	178	1	no	—
275	#127	—	178	1	no	—
276	C₄×D₄	—	356	2	no	—
277	C₄×D₄	—	356	2	no	—
278	C₄×D₄	—	356	2	no	—
279	C₄×D₄	—	356	2	no	—
280	C₂×C₄⋊C₄	—	89	1	no	—
281	C₂×C₄⋊C₄	—	89	1	no	—
282	C₂×C₄⋊C₄	—	178	1	no	—
283	C₂×C₄⋊C₄	—	178	1	no	—
284	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
285	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	178	2	no	—
287	C₂×C₂²⋊C₄	—	178	2	no	—
288	C₂×C₂²⋊C₄	—	178	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	178	1	no	—
291	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	178	1	no	—
295	C₄⋊C₈	—	178	1	no	—
296	#103	—	356	2	no	—
297	#103	—	356	2	no	—
298	#102	—	178	8	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	C₄×D₈₉	1	2	yes	complemented
301	#95	—	2	1	no	—
302	#95	—	178	1	no	—
303	C₂⁴	—	178	2	no	—
304	C₂×Q₈	—	356	1	no	—
305	C₂×Q₈	—	356	1	no	—
306	C₂×Q₈	—	356	1	no	—
307	C₂×Q₈	—	356	1	no	—
308	C₂×Q₈	—	356	1	no	—
309	C₂×Q₈	—	178	2	no	—
310	C₂×D₄	—	89	4	no	—
311	C₂×D₄	—	356	2	no	—
312	C₂×D₄	—	356	2	no	—
313	C₂×D₄	—	356	1	no	—
314	C₂×D₄	—	356	1	no	—
315	C₂×D₄	—	356	1	no	—
316	C₂×D₄	—	356	1	no	—
317	C₂×D₄	—	356	1	no	—
318	C₂×D₄	—	356	1	no	—
319	C₂×D₄	—	356	1	no	—
320	C₂×D₄	—	356	1	no	—
321	C₂×D₄	—	178	2	no	—
322	C₂×D₄	—	178	2	no	—
323	C₂×D₄	—	178	2	no	—
324	C₂×D₄	—	178	2	no	—
325	C₂×D₄	—	178	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	356	4	no	—
329	C₂²×C₄	—	356	4	no	—
330	C₂²×C₄	—	356	1	no	—
331	C₂²×C₄	—	178	1	no	—
332	C₂²×C₄	—	178	1	no	—
333	C₂²×C₄	—	712	2	no	—
334	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	356	1	no	—
344	C₂×C₈	—	356	1	no	—
345	C₂×C₈	—	356	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	89	2	no	—
350	C₄⋊C₄	—	356	1	no	—
351	C₄⋊C₄	—	356	1	no	—
352	C₄⋊C₄	—	178	2	no	—
353	C₄⋊C₄	—	178	1	no	—
354	C₄⋊C₄	—	178	1	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	—	178	1	no	—
357	C₄⋊C₄	#13083563	1	2	yes	—
358	C₂²⋊C₄	—	356	4	no	—
359	C₂²⋊C₄	—	356	4	no	—
360	C₂²⋊C₄	—	712	2	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	356	1	no	—
364	C₄²	—	356	1	no	—
365	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₄²	D₄×D₈₉	1	1	yes	characteristic
367	C₄²	#13083574	1	1	yes	characteristic
368	C₄²	#13083575	1	1	yes	characteristic
369	C₂³	—	356	2	no	—
370	C₂³	—	356	2	no	—
371	C₂³	—	356	2	no	—
372	C₂³	—	356	2	no	—
373	C₂³	—	356	2	no	—
374	C₂³	—	356	2	no	—
375	C₂³	—	178	4	no	—
376	C₂³	#15667982	1	1	yes	characteristic
377	Q₈	—	356	2	no	—
378	Q₈	—	356	2	no	—
379	Q₈	—	712	1	no	—
380	Q₈	—	712	1	no	—
381	D₄	—	356	4	no	—
382	D₄	—	356	2	no	—
383	D₄	—	356	2	no	—
384	D₄	—	356	2	no	—
385	D₄	—	356	2	no	—
386	D₄	—	356	2	no	—
387	D₄	—	356	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	356	2	no	—
390	D₄	—	712	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	2	no	—
402	C₂×C₄	—	356	1	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	1	no	—
405	C₂×C₄	—	178	2	no	—
406	C₂×C₄	—	712	8	no	—
407	C₂×C₄	—	712	1	no	—
408	C₂×C₄	—	712	1	no	—
409	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
410	C₂×C₄	#15667974	1	1	yes	characteristic
411	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
412	C₂×C₄	#15667985	1	1	yes	characteristic
413	C₂×C₄	#15667987	1	1	yes	characteristic
414	C₂×C₄	#15667997	1	1	yes	characteristic
415	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
417	C₂×C₄	#15668034	1	1	yes	characteristic
418	C₂×C₄	#15668035	1	1	yes	characteristic
419	C₂×C₄	#15668039	1	1	yes	characteristic
420	C₂×C₄	#15668039	1	1	yes	characteristic
421	C₂×C₄	#15668040	1	1	yes	characteristic
422	C₂×C₄	#15668045	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	8	1	no	—
425	C₈	—	712	1	no	—
426	C₂²	—	356	4	no	—
427	C₂²	—	356	4	no	—
428	C₂²	—	356	4	no	—
429	C₂²	—	712	2	no	—
430	C₂²	—	712	2	no	—
431	C₂²	—	712	2	no	—
432	C₂²	—	712	2	no	—
433	C₂²	#19151476	1	1	yes	characteristic
434	C₂²	#19151733	1	1	yes	characteristic
435	C₂²	#19151746	1	1	yes	characteristic
436	C₂²	#19151751	1	1	yes	characteristic
437	C₂²	#19151762	1	1	yes	characteristic
438	C₂²	#19151777	1	1	yes	characteristic
439	C₂²	#19151777	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	356	2	no	—
445	C₄	—	712	1	no	—
446	C₄	—	712	2	no	—
447	C₄	#19151680	1	1	yes	characteristic
448	C₄	C₄×#13083563	1	1	yes	characteristic
449	C₄	#19151700	1	1	yes	characteristic
450	C₄	#19151709	1	1	yes	characteristic
451	C₄	#19151792	1	1	yes	characteristic
452	C₄	#19151804	1	1	yes	characteristic
453	C₄	#19151814	1	1	yes	characteristic
454	C₄	#19151816	1	1	yes	characteristic
455	C₂	—	712	4	no	—
456	C₂	#26019434	1	1	yes	characteristic
457	C₂	#26019441	1	1	yes	characteristic
458	C₂	#26019448	1	1	yes	characteristic
459	C₂	#26019455	1	1	yes	characteristic
460	C₂	#26020585	1	1	yes	characteristic
461	C₂	#26020601	1	1	yes	characteristic
462	C₂	#26020639	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1279	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1279	D₈₉
hypocenter	C₈₉	#9057
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
3. #26021204	C₂	semidirect
4. #26021174	C₂	semidirect
6. #26018092	C₂	semidirect
7. C₈₉×#1279	C₂	semidirect
13. #19151945	C₄	semidirect
37. #15668012	C₂×C₄	semidirect
69. C₄×C₈×C₈₉	C₂×C₄	semidirect
238. #1279	D₈₉	semidirect
239. C₈₉	#9057	semidirect
300. C₄×C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151945	2
#26023316	2
#26021204	2
#26021174	2
C₂×#19151341	2
#26018092	2
C₈₉×#1279	2
#9057	89