Subgroups — #36577298

Order 22784.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029169	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029162	C₂	1	2	yes	maximal, complemented
3	#26028863	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021146	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021043	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020923	C₂	1	2	yes	maximal, complemented
7	#26020616	C₂	1	2	yes	maximal, complemented
8	#26020474	C₂	1	2	yes	maximal, complemented
9	#26020160	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3067	C₂	1	1	yes	maximal, characteristic
12	#19152365	C₂²	1	2	yes	—
13	#19152365	C₂²	1	2	yes	—
14	#19151720	—	2	2	no	—
15	#19151720	—	2	4	no	—
16	#19151715	—	2	2	no	—
17	#19151715	—	2	4	no	—
18	#19151647	—	2	2	no	—
19	#19151647	C₂²	1	2	yes	—
20	#19151647	C₂²	1	2	yes	—
21	C₂×#15667948	—	2	2	no	—
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	#19151615	C₂²	1	2	yes	—
25	C₂×#15667939	C₂²	1	2	yes	—
26	C₂×#15667939	C₂²	1	1	yes	characteristic
27	#19151594	C₂²	1	1	yes	characteristic
28	#19151565	C₂²	1	2	yes	—
29	#19151553	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₈₉	C₂²	1	2	yes	—
31	C₂×#15667922	C₂²	1	1	yes	characteristic
32	#19151370	C₂²	1	2	yes	—
33	#19151362	C₂²	1	2	yes	—
34	#19151362	C₂²	1	1	yes	characteristic
35	#19151359	C₂²	1	1	yes	characteristic
36	#575×C₈₉	C₂²	1	2	yes	—
37	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
39	#473×C₈₉	C₄	1	2	yes	complemented
40	#472×C₈₉	C₄	1	2	yes	complemented
41	#471×C₈₉	C₄	1	4	yes	complemented
42	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
43	#413×C₈₉	C₂²	1	2	yes	—
44	#15668019	—	2	4	no	—
45	#15668019	—	2	4	no	—
46	#15668019	—	2	4	no	—
47	#15668019	—	4	2	no	—
48	C₂×#13083558	—	2	4	no	—
49	C₂×#13083558	—	4	2	no	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083558	C₂³	1	2	yes	—
52	C₂×#13083558	C₂³	1	1	yes	characteristic
53	C₂²×#10623494	C₂³	1	1	yes	characteristic
54	#15667971	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
56	#15667948	—	2	4	no	—
57	#15667948	—	2	4	no	—
58	#15667948	—	2	1	no	—
59	#15667948	—	2	1	no	—
60	#15667948	D₄	1	2	yes	—
61	#15667948	D₄	1	2	yes	—
62	#15667939	—	2	4	no	—
63	#15667939	—	2	2	no	—
64	#15667939	—	2	2	no	—
65	#15667939	D₄	1	4	yes	—
66	#15667936	—	2	1	no	—
67	#15667933	—	2	1	no	—
68	C₂²⋊#10623494	—	4	2	no	—
69	#15667922	—	2	2	no	—
70	#15667922	—	2	1	no	—
71	#15667922	—	2	1	no	—
72	#15667922	—	2	1	no	—
73	C₈×Dic₈₉	—	2	2	no	—
74	C₈×Dic₈₉	—	2	1	no	—
75	C₂×#41×C₈₉	C₂³	1	2	yes	—
76	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
77	#137×C₈₉	—	2	2	no	—
78	#137×C₈₉	C₂×C₄	1	4	yes	—
79	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
80	AGL(1,ℤ/8)×C₈₉	C₂×C₄	1	4	yes	—
81	#135×C₈₉	—	2	4	no	—
82	#135×C₈₉	—	2	1	no	—
83	#135×C₈₉	—	2	1	no	—
84	#135×C₈₉	—	2	1	no	—
85	#135×C₈₉	—	2	1	no	—
86	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
88	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#131×C₈₉	—	2	1	no	—
90	#131×C₈₉	—	2	1	no	—
91	#131×C₈₉	C₂×C₄	1	2	yes	—
92	#131×C₈₉	C₂×C₄	1	2	yes	—
93	C₂×M₁₆×C₈₉	—	2	1	no	—
94	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
95	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	—	2	1	no	—
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#108×C₈₉	C₂×C₄	1	2	yes	—
99	#108×C₈₉	C₂×C₄	1	2	yes	—
100	#101×C₈₉	C₂×C₄	1	4	yes	—
101	#100×C₈₉	C₂×C₄	1	4	yes	—
102	C₂²×Dic₈₉	—	2	1	no	—
103	#13083558	—	2	1	no	—
104	#13083558	—	2	2	no	—
105	#13083558	—	2	2	no	—
106	#13083558	—	2	2	no	—
107	#13083558	—	4	4	no	—
108	#13083558	—	4	4	no	—
109	#13083558	C₂×D₄	1	4	yes	—
110	#13083558	C₂×D₄	1	2	yes	—
111	C₂×#10623494	—	2	2	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	4	4	no	—
118	C₂×#10623494	—	4	4	no	—
119	C₄⋊Dic₈₉	—	2	1	no	—
120	C₂²⋊Dic₈₉	—	2	1	no	—
121	C₄×Dic₈₉	—	2	1	no	—
122	C₄×Dic₈₉	—	2	1	no	—
123	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
124	#41×C₈₉	—	2	1	no	—
125	#41×C₈₉	—	2	1	no	—
126	#41×C₈₉	—	2	2	no	—
127	#41×C₈₉	—	2	2	no	—
128	#41×C₈₉	—	2	2	no	—
129	#41×C₈₉	—	2	2	no	—
130	#41×C₈₉	C₂²×C₄	1	2	yes	—
131	#41×C₈₉	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
133	C₂×Q₈×C₈₉	#41	1	1	yes	characteristic
134	C₂×D₄×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
137	C₂×D₄×C₈₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	—	2	2	no	—
140	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
141	Q₁₆×C₈₉	—	2	4	no	—
142	Q₁₆×C₈₉	—	2	1	no	—
143	Q₁₆×C₈₉	—	2	1	no	—
144	SD₁₆×C₈₉	—	2	4	no	—
145	SD₁₆×C₈₉	—	2	4	no	—
146	SD₁₆×C₈₉	—	2	2	no	—
147	SD₁₆×C₈₉	—	2	2	no	—
148	D₈×C₈₉	—	2	4	no	—
149	D₈×C₈₉	—	2	1	no	—
150	D₈×C₈₉	—	2	1	no	—
151	M₁₆×C₈₉	—	2	1	no	—
152	M₁₆×C₈₉	—	2	2	no	—
153	M₁₆×C₈₉	—	2	2	no	—
154	M₁₆×C₈₉	—	2	2	no	—
155	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
156	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
166	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
167	C₂³×C₈₉	—	2	1	no	—
168	C₂³×C₈₉	—	2	2	no	—
169	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
170	Q₈×C₈₉	—	2	1	no	—
171	Q₈×C₈₉	—	2	2	no	—
172	Q₈×C₈₉	—	2	2	no	—
173	Q₈×C₈₉	C₄×D₄	1	2	yes	—
174	D₄×C₈₉	—	2	2	no	—
175	D₄×C₈₉	—	2	2	no	—
176	D₄×C₈₉	—	2	2	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	2	1	no	—
179	D₄×C₈₉	—	4	2	no	—
180	D₄×C₈₉	—	4	2	no	—
181	D₄×C₈₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×Dic₈₉	—	2	2	no	—
195	C₂×Dic₈₉	—	4	1	no	—
196	C₂×Dic₈₉	—	8	1	no	—
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	2	4	no	—
199	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
200	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
201	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
202	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
203	#10623494	—	2	2	no	—
204	#10623494	—	2	4	no	—
205	#10623494	—	4	2	no	—
206	#10623494	—	4	1	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	—	8	1	no	—
211	C₂²×C₈₉	—	8	2	no	—
212	C₂²×C₈₉	#520	1	1	yes	characteristic
213	C₂²×C₈₉	#547	1	1	yes	characteristic
214	C₂²×C₈₉	#548	1	1	yes	characteristic
215	C₄×C₈₉	—	2	2	no	—
216	C₄×C₈₉	—	4	2	no	—
217	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₈₉	D₄²	1	1	yes	characteristic
220	C₄×C₈₉	#553	1	1	yes	characteristic
221	Dic₈₉	—	4	2	no	—
222	Dic₈₉	—	8	1	no	—
223	#23043	—	89	1	no	maximal, Sylow
224	C₂×C₈₉	—	2	1	no	—
225	C₂×C₈₉	—	2	1	no	—
226	C₂×C₈₉	—	2	1	no	—
227	C₂×C₈₉	—	4	2	no	—
228	C₂×C₈₉	—	8	2	no	—
229	C₂×C₈₉	#2361	1	1	yes	characteristic
230	#3067	D₈₉	1	1	yes	characteristic
231	#2957	—	89	1	no	—
232	#2956	—	89	2	no	—
233	#2916	—	89	1	no	—
234	#1975	—	89	1	no	—
235	#1953	—	89	1	no	—
236	#1932	—	89	2	no	—
237	#1881	—	89	2	no	—
238	#1858	—	89	2	no	—
239	#1778	—	89	1	no	—
240	#1765	—	89	1	no	—
241	C₈₉	#23043	1	1	yes	characteristic, complemented, Sylow
242	#575	C₂×D₈₉	1	2	yes	—
243	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
244	#568	—	89	2	no	—
245	#568	—	89	2	no	—
246	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
247	#473	Dic₈₉	1	2	yes	complemented
248	#472	Dic₈₉	1	2	yes	complemented
249	#471	Dic₈₉	1	4	yes	complemented
250	#444	—	178	4	no	—
251	#444	—	178	2	no	—
252	#443	—	178	4	no	—
253	#443	—	178	2	no	—
254	#430	—	89	2	no	—
255	#430	—	89	2	no	—
256	#430	—	178	2	no	—
257	C₂×#108	—	89	1	no	—
258	C₂×#108	—	89	1	no	—
259	C₂×#108	—	178	2	no	—
260	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
261	#421	—	89	2	no	—
262	C₂×#104	—	89	1	no	—
263	C₂×#104	—	89	2	no	—
264	#416	—	89	1	no	—
265	#413	C₂×D₈₉	1	2	yes	—
266	#408	—	89	2	no	—
267	#405	—	89	1	no	—
268	C₄×M₁₆	—	89	2	no	—
269	C₂×#97	—	89	1	no	—
270	#344	—	89	2	no	—
271	#341	—	89	1	no	—
272	#341	—	89	2	no	—
273	#339	—	89	1	no	—
274	C₂×#41	C₂²×D₈₉	1	2	yes	—
275	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
276	#137	—	2	2	no	—
277	#137	C₂×Dic₈₉	1	4	yes	—
278	AGL(1,ℤ/8)	—	2	2	no	—
279	AGL(1,ℤ/8)	C₂×Dic₈₉	1	4	yes	—
280	#135	—	2	4	no	—
281	#135	—	2	1	no	—
282	#135	—	2	1	no	—
283	#135	—	2	1	no	—
284	#135	—	2	1	no	—
285	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
286	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
287	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
288	#131	—	2	1	no	—
289	#131	—	2	1	no	—
290	#131	—	356	2	no	—
291	#131	—	178	4	no	—
292	#131	—	178	4	no	—
293	#131	—	178	4	no	—
294	#131	C₂×Dic₈₉	1	2	yes	—
295	#131	C₂×Dic₈₉	1	2	yes	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	89	2	no	—
298	C₂×M₁₆	—	89	1	no	—
299	C₂×M₁₆	—	89	2	no	—
300	C₂×M₁₆	—	356	2	no	—
301	C₂×M₁₆	—	178	4	no	—
302	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
303	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	89	1	no	—
306	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	#117	—	89	1	no	—
308	C₂×C₄²	—	89	1	no	—
309	#108	—	89	2	no	—
310	#108	—	89	2	no	—
311	#108	—	178	4	no	—
312	#108	—	178	4	no	—
313	#108	—	178	1	no	—
314	#108	—	178	1	no	—
315	#108	C₂×Dic₈₉	1	2	yes	—
316	#108	C₂×Dic₈₉	1	2	yes	—
317	#104	—	89	4	no	—
318	#104	—	178	2	no	—
319	#104	—	178	2	no	—
320	#104	—	178	4	no	—
321	#103	—	178	1	no	—
322	#102	—	178	1	no	—
323	#101	C₂×Dic₈₉	1	4	yes	—
324	#100	C₂×Dic₈₉	1	4	yes	—
325	C₂²⋊C₈	—	356	2	no	—
326	#97	—	178	2	no	—
327	#97	—	178	1	no	—
328	#97	—	178	1	no	—
329	#97	—	178	1	no	—
330	C₄×C₈	—	178	2	no	—
331	C₄×C₈	—	178	1	no	—
332	#41	—	2	1	no	—
333	#41	—	2	1	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	C₂²×Dic₈₉	1	2	yes	—
339	#41	D₄×D₈₉	1	2	yes	—
340	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
341	C₂×Q₈	#13083573	1	1	yes	characteristic
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
345	C₂×D₄	#13083573	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
350	Q₁₆	—	2	4	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	2	1	no	—
353	SD₁₆	—	2	4	no	—
354	SD₁₆	—	2	4	no	—
355	SD₁₆	—	2	2	no	—
356	SD₁₆	—	2	2	no	—
357	D₈	—	2	4	no	—
358	D₈	—	2	1	no	—
359	D₈	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	89	2	no	—
365	M₁₆	—	89	4	no	—
366	M₁₆	—	356	4	no	—
367	M₁₆	—	356	4	no	—
368	M₁₆	—	178	2	no	—
369	M₁₆	—	178	2	no	—
370	M₁₆	—	178	1	no	—
371	M₁₆	—	178	2	no	—
372	M₁₆	C₂²×Dic₈₉	1	2	yes	—
373	M₁₆	C₂²×Dic₈₉	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	356	4	no	—
379	C₂×C₈	—	356	4	no	—
380	C₂×C₈	—	178	1	no	—
381	C₂×C₈	—	178	1	no	—
382	C₂×C₈	—	178	1	no	—
383	C₂×C₈	—	178	2	no	—
384	C₂×C₈	—	178	2	no	—
385	C₂×C₈	—	178	1	no	—
386	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
387	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
388	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
389	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
390	C₂×C₈	#13083573	1	1	yes	characteristic
391	C₂×C₈	#13083573	1	1	yes	characteristic
392	C₄⋊C₄	—	178	1	no	—
393	C₂²⋊C₄	—	178	1	no	—
394	C₄²	—	89	2	no	—
395	C₄²	—	178	1	no	—
396	C₄²	—	178	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	2	no	—
399	C₂³	#15668059	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	D₄×Dic₈₉	1	2	yes	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	1	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	D₄×Dic₈₉	1	2	yes	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	356	1	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	712	1	no	—
421	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
426	C₂×C₄	#15668058	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	2	4	no	—
429	C₈	—	356	2	no	—
430	C₈	—	356	1	no	—
431	C₈	—	178	4	no	—
432	C₈	—	178	2	no	—
433	C₈	D₄×Dic₈₉	1	1	yes	characteristic
434	C₈	D₄×Dic₈₉	1	1	yes	characteristic
435	C₈	D₄×Dic₈₉	1	1	yes	characteristic
436	C₈	D₄×Dic₈₉	1	1	yes	characteristic
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	#19152081	1	1	yes	characteristic
443	C₂²	#19152248	1	1	yes	characteristic
444	C₂²	#19152254	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	356	2	no	—
448	C₄	—	712	1	no	—
449	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
450	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
451	C₄	#19152232	1	1	yes	characteristic
452	C₄	#19152300	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	4	2	no	—
457	C₂	—	8	2	no	—
458	C₂	#26023272	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19152232
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3067	C₂
socle	C₂×C₈₉	#2361
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3067	D₈₉
hypocenter	C₈₉	#23043
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #26029169	C₂	semidirect
2. #26029162	C₂	semidirect
3. #26028863	C₂	semidirect
4. #26021146	C₂	semidirect
5. #26021043	C₂	semidirect
6. #26020923	C₂	semidirect
7. #26020616	C₂	semidirect
8. #26020474	C₂	semidirect
9. #26020160	C₂	semidirect
10. #26020094	C₂	semidirect
39. #473×C₈₉	C₄	semidirect
40. #472×C₈₉	C₄	semidirect
41. #471×C₈₉	C₄	semidirect
241. C₈₉	#23043	semidirect
247. #473	Dic₈₉	semidirect
248. #472	Dic₈₉	semidirect
249. #471	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029169	2
#26029162	2
#26028863	2
#26021146	2
#26021043	2
#26020923	2
#26020616	2
#26020474	2
#26020160	2
#26020094	2
C₈₉×#3067	2
#23043	89