Subgroups — #36561372

Order 22784.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029968	C₂	1	1	yes	maximal, characteristic
2	#26029153	C₂	1	2	yes	maximal, complemented
3	#26028677	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021151	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021040	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020918	C₂	1	2	yes	maximal, complemented
7	#26020756	C₂	1	2	yes	maximal, complemented
8	#26020307	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020136	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020052	C₂	1	2	yes	maximal, complemented
11	C₂×#444×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152396	C₂²	1	2	yes	—
13	C₂×#15668018	C₂²	1	1	yes	characteristic
14	C₂×#15668018	C₂²	1	1	yes	characteristic
15	C₄×#13083574	C₂²	1	1	yes	characteristic
16	#19151870	C₄	1	2	yes	complemented
17	#19151865	C₄	1	2	yes	complemented
18	#19151858	C₄	1	4	yes	complemented
19	#19151718	—	2	4	no	—
20	#19151713	—	2	4	no	—
21	#19151646	C₂²	1	2	yes	—
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	#19151636	C₂²	1	1	yes	characteristic
24	#19151615	C₂²	1	2	yes	—
25	#19151614	C₂²	1	2	yes	—
26	#19151582	C₂²	1	2	yes	—
27	#19151572	C₂²	1	2	yes	—
28	#19151555	—	2	1	no	—
29	#19151555	—	2	1	no	—
30	#19151553	C₂²	1	1	yes	characteristic
31	#19151553	C₂²	1	2	yes	—
32	#19151553	C₂²	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151550	—	2	1	no	—
35	#97×D₈₉	—	2	1	no	—
36	#19151369	C₂²	1	2	yes	—
37	#19151369	C₂²	1	2	yes	—
38	#19151358	C₂²	1	2	yes	—
39	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₈₉	C₂²	1	2	yes	—
41	#444×C₈₉	—	2	1	no	—
42	#444×C₈₉	—	2	1	no	—
43	#444×C₈₉	—	2	1	no	—
44	#444×C₈₉	—	2	1	no	—
45	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#104×C₈₉	C₂²	1	2	yes	—
47	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#13083574	C₂³	1	1	yes	characteristic
49	#15668043	C₂×C₄	1	4	yes	—
50	#15668042	—	2	2	no	—
51	#15668038	C₂×C₄	1	4	yes	—
52	#15668037	—	2	2	no	—
53	#15668032	—	2	4	no	—
54	#15668018	—	2	2	no	—
55	#15668018	—	2	1	no	—
56	#15668018	—	2	1	no	—
57	#15668018	C₂×C₄	1	2	yes	—
58	#15668018	C₂×C₄	1	2	yes	—
59	#15668018	D₄	1	4	yes	—
60	C₂×#13083558	C₂³	1	1	yes	characteristic
61	C₂×#13083558	C₂³	1	2	yes	—
62	C₂×#13083558	C₂³	1	1	yes	characteristic
63	C₂×#13083557	—	2	1	no	—
64	C₂×#13083557	—	2	1	no	—
65	C₂×C₈×D₈₉	—	2	1	no	—
66	C₂×C₈×D₈₉	—	2	1	no	—
67	C₄×Dic₁₇₈	—	2	1	no	—
68	C₄×D₃₅₆	—	2	1	no	—
69	C₄×C₂²⋊D₈₉	—	2	2	no	—
70	#15667971	C₂³	1	2	yes	—
71	#15667971	C₂³	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	C₄²×D₈₉	—	2	1	no	—
74	#15667948	C₂×C₄	1	2	yes	complemented
75	#15667948	C₂×C₄	1	2	yes	complemented
76	#15667947	—	2	4	no	—
77	#15667946	—	2	1	no	—
78	#15667944	—	2	1	no	—
79	#15667939	—	2	4	no	—
80	#15667938	—	2	4	no	—
81	#15667931	C₂×C₄	1	4	yes	complemented
82	#15667929	C₂×C₄	1	4	yes	complemented
83	#15667927	—	2	4	no	—
84	#15667923	—	2	1	no	—
85	#15667922	—	2	2	no	—
86	#15667922	—	2	1	no	—
87	#15667922	—	2	1	no	—
88	C₄×#10623494	—	2	1	no	—
89	C₈×Dic₈₉	—	2	2	no	—
90	C₈×Dic₈₉	—	2	1	no	—
91	C₈×Dic₈₉	—	2	1	no	—
92	C₂×#41×C₈₉	C₂³	1	2	yes	—
93	#135×C₈₉	—	2	1	no	—
94	#135×C₈₉	—	2	1	no	—
95	#135×C₈₉	—	2	1	no	—
96	#135×C₈₉	—	2	1	no	—
97	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
99	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
100	#131×C₈₉	—	2	2	no	—
101	#131×C₈₉	—	2	2	no	—
102	#131×C₈₉	—	2	2	no	—
103	#131×C₈₉	—	2	2	no	—
104	C₂×M₁₆×C₈₉	—	2	2	no	—
105	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₈₉	—	2	2	no	—
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	#108×C₈₉	—	2	1	no	—
111	#108×C₈₉	—	2	1	no	—
112	#104×C₈₉	—	2	2	no	—
113	#104×C₈₉	—	2	2	no	—
114	#97×C₈₉	D₄	1	1	yes	characteristic
115	#97×C₈₉	D₄	1	1	yes	characteristic
116	#97×C₈₉	D₄	1	1	yes	characteristic
117	#97×C₈₉	D₄	1	1	yes	characteristic
118	#13083574	—	2	1	no	—
119	#13083574	—	2	1	no	—
120	#13083574	C₂²×C₄	1	2	yes	—
121	#13083574	C₂×D₄	1	2	yes	—
122	C₂×Dic₁₇₈	#41	1	1	yes	characteristic
123	C₂×D₃₅₆	#41	1	1	yes	characteristic
124	C₂×C₂²⋊D₈₉	—	2	1	no	—
125	C₂×C₄×D₈₉	—	2	1	no	—
126	C₂×C₄×D₈₉	—	2	2	no	—
127	#13083564	—	2	4	no	—
128	#13083562	—	2	4	no	—
129	#13083561	—	2	4	no	—
130	#13083559	—	2	4	no	—
131	#13083558	—	2	1	no	—
132	#13083558	—	2	1	no	—
133	#13083558	—	2	2	no	—
134	#13083558	C₂²×C₄	1	2	yes	—
135	#13083558	C₂²×C₄	1	4	yes	—
136	#13083558	C₂×D₄	1	2	yes	—
137	#13083557	—	2	2	no	—
138	#13083557	—	2	2	no	—
139	#13083557	—	2	4	no	—
140	C₂×#10623494	—	2	1	no	—
141	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	2	no	—
143	C₈×D₈₉	—	2	2	no	—
144	C₈×D₈₉	—	2	2	no	—
145	C₈×D₈₉	—	2	4	no	—
146	C₄⋊Dic₈₉	—	2	1	no	—
147	C₄⋊Dic₈₉	—	2	2	no	—
148	#13083553	—	2	2	no	—
149	C₂²⋊Dic₈₉	—	2	2	no	—
150	C₂²⋊Dic₈₉	#41	1	2	yes	—
151	#13083551	—	2	2	no	—
152	C₄×Dic₈₉	—	2	2	no	—
153	C₄×Dic₈₉	—	2	1	no	—
154	C₄×Dic₈₉	—	2	2	no	—
155	#41×C₈₉	—	2	2	no	—
156	#41×C₈₉	—	2	2	no	—
157	#41×C₈₉	—	2	2	no	—
158	#41×C₈₉	—	2	2	no	—
159	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₈₉	—	2	2	no	—
161	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	2	2	no	—
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₈₉	—	2	1	no	—
166	Q₁₆×C₈₉	—	2	1	no	—
167	SD₁₆×C₈₉	—	2	2	no	—
168	SD₁₆×C₈₉	—	2	2	no	—
169	D₈×C₈₉	—	2	1	no	—
170	D₈×C₈₉	—	2	1	no	—
171	M₁₆×C₈₉	—	2	2	no	—
172	M₁₆×C₈₉	—	2	2	no	—
173	M₁₆×C₈₉	—	4	2	no	—
174	M₁₆×C₈₉	—	4	2	no	—
175	C₂×C₈×C₈₉	—	2	2	no	—
176	C₂×C₈×C₈₉	—	4	2	no	—
177	C₂×C₈×C₈₉	—	4	2	no	—
178	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
186	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
187	C₂×C₈×C₈₉	#41	1	2	yes	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₈₉	—	2	2	no	—
192	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
193	C₂²×D₈₉	—	2	1	no	—
194	Q₈×C₈₉	—	2	2	no	—
195	Q₈×C₈₉	—	2	2	no	—
196	D₄×C₈₉	—	2	2	no	—
197	D₄×C₈₉	—	2	2	no	—
198	D₄×C₈₉	—	4	2	no	—
199	D₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	4	2	no	—
204	C₂×C₄×C₈₉	—	4	2	no	—
205	C₂×C₄×C₈₉	—	8	1	no	—
206	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
212	C₂²⋊D₈₉	—	2	2	no	—
213	C₂²⋊D₈₉	—	2	2	no	—
214	C₂×Dic₈₉	—	2	1	no	—
215	C₂×Dic₈₉	—	2	2	no	—
216	C₂×Dic₈₉	—	4	2	no	—
217	D₃₅₆	—	2	1	no	—
218	D₃₅₆	C₄×D₄	1	2	yes	—
219	C₄×D₈₉	—	2	2	no	—
220	C₄×D₈₉	—	2	2	no	—
221	C₄×D₈₉	—	8	2	no	—
222	Dic₁₇₈	—	2	1	no	—
223	Dic₁₇₈	C₄×D₄	1	2	yes	—
224	C₈×C₈₉	—	4	2	no	—
225	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
226	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
227	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
228	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
229	C₈×C₈₉	#121	1	2	yes	—
230	C₈×C₈₉	#121	1	2	yes	—
231	#10623494	—	2	2	no	—
232	#10623494	—	2	4	no	—
233	#10623494	—	2	2	no	—
234	C₂²×C₈₉	—	4	1	no	—
235	C₂²×C₈₉	—	4	2	no	—
236	C₂²×C₈₉	—	8	2	no	—
237	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
238	C₂²×C₈₉	#525	1	1	yes	characteristic
239	C₂²×C₈₉	#532	1	1	yes	characteristic
240	C₂×D₈₉	—	2	2	no	—
241	C₂×D₈₉	—	4	2	no	—
242	C₄×C₈₉	—	4	1	no	—
243	C₄×C₈₉	—	4	1	no	—
244	C₄×C₈₉	—	4	2	no	—
245	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
248	C₄×C₈₉	#529	1	1	yes	characteristic
249	Dic₈₉	—	2	2	no	—
250	Dic₈₉	—	4	2	no	—
251	Dic₈₉	—	8	2	no	—
252	#21559	—	89	1	no	maximal, Sylow
253	C₂×C₈₉	—	2	1	no	—
254	C₂×C₈₉	—	2	1	no	—
255	C₂×C₈₉	—	2	1	no	—
256	C₂×C₈₉	—	8	2	no	—
257	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
258	D₈₉	—	4	2	no	—
259	#3067	—	89	1	no	—
260	#2955	—	89	2	no	—
261	C₂×#444	D₈₉	1	1	yes	characteristic, complemented
262	#2875	—	89	1	no	—
263	#1976	—	89	1	no	—
264	#1953	—	89	1	no	—
265	#1932	—	89	2	no	—
266	#1906	—	89	2	no	—
267	#1814	—	89	1	no	—
268	#1773	—	89	1	no	—
269	#1757	—	89	2	no	—
270	C₈₉	#21559	1	1	yes	characteristic, complemented, Sylow
271	#575	—	89	2	no	—
272	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
273	C₂×#131	—	89	1	no	—
274	C₂×#131	—	89	1	no	—
275	C₂×#131	C₂×D₈₉	1	2	yes	—
276	C₄×#41	—	89	1	no	—
277	#473	—	89	2	no	—
278	#472	—	89	2	no	—
279	#471	—	89	4	no	—
280	#444	—	2	1	no	—
281	#444	—	2	1	no	—
282	#444	—	2	1	no	—
283	#444	—	2	1	no	—
284	#444	—	178	4	no	—
285	#443	—	178	4	no	—
286	#430	—	89	2	no	—
287	C₂×#108	—	89	1	no	—
288	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
289	#427	—	89	1	no	—
290	#421	—	89	2	no	—
291	#421	—	89	2	no	—
292	C₂×#104	C₂×D₈₉	1	2	yes	—
293	#413	—	89	2	no	—
294	#410	—	89	2	no	—
295	#405	—	89	1	no	—
296	#405	—	89	1	no	—
297	#405	—	89	2	no	—
298	#405	—	178	1	no	—
299	#405	—	178	1	no	—
300	C₄×M₁₆	—	89	1	no	—
301	C₄×M₁₆	—	178	1	no	—
302	C₂×#97	—	178	1	no	—
303	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
304	#344	—	89	2	no	—
305	#344	—	89	2	no	—
306	#339	—	89	2	no	—
307	C₂×#41	—	89	1	no	—
308	C₂×#41	C₂²×D₈₉	1	2	yes	—
309	#137	—	89	4	no	—
310	#137	—	178	2	no	—
311	AGL(1,ℤ/8)	—	89	4	no	—
312	AGL(1,ℤ/8)	—	178	2	no	—
313	#135	—	2	1	no	—
314	#135	—	2	1	no	—
315	#135	—	2	1	no	—
316	#135	—	2	1	no	—
317	#135	—	178	4	no	—
318	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic, complemented
319	C₂×SD₁₆	C₄×D₈₉	1	2	yes	complemented
320	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic, complemented
321	#131	—	2	2	no	—
322	#131	—	2	2	no	—
323	#131	—	2	2	no	—
324	#131	—	2	2	no	—
325	#131	—	89	2	no	—
326	#131	—	89	2	no	—
327	#131	—	89	4	no	—
328	#131	—	178	2	no	—
329	#131	—	178	1	no	—
330	#131	—	178	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	89	1	no	—
333	C₂×M₁₆	—	89	1	no	—
334	C₂×M₁₆	—	89	2	no	—
335	C₂×M₁₆	—	178	1	no	—
336	C₂×M₁₆	—	178	1	no	—
337	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	178	1	no	—
340	C₂²×C₈	—	178	1	no	—
341	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
342	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
343	C₄×Q₈	—	178	1	no	—
344	C₄×D₄	—	178	1	no	—
345	C₄×D₄	—	178	2	no	—
346	#117	—	89	1	no	—
347	#117	—	89	2	no	—
348	#117	—	178	1	no	—
349	C₂×C₄²	—	178	1	no	—
350	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
351	#108	—	2	1	no	—
352	#108	—	2	1	no	—
353	#108	—	89	2	no	—
354	#108	—	89	2	no	—
355	#108	—	178	4	no	—
356	#107	—	178	1	no	—
357	#106	—	178	1	no	—
358	#104	—	2	2	no	—
359	#104	—	2	2	no	—
360	#104	—	178	4	no	—
361	#104	—	178	4	no	—
362	#101	—	89	4	no	—
363	#100	—	89	4	no	—
364	#99	—	178	4	no	—
365	#97	—	178	2	no	—
366	#97	—	178	1	no	—
367	#97	—	178	1	no	—
368	#97	—	178	1	no	—
369	#97	C₂²⋊D₈₉	1	1	yes	characteristic
370	#97	C₂²⋊D₈₉	1	1	yes	characteristic
371	#97	C₂²⋊D₈₉	1	1	yes	characteristic
372	#97	C₂²⋊D₈₉	1	1	yes	characteristic
373	C₄×C₈	—	178	2	no	—
374	C₄×C₈	—	178	1	no	—
375	C₄×C₈	—	178	1	no	—
376	C₄×C₈	—	178	1	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	89	2	no	—
382	#41	—	89	2	no	—
383	#41	—	178	1	no	—
384	#41	—	178	1	no	—
385	C₂×Q₈	—	89	1	no	—
386	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	89	1	no	—
389	C₂×D₄	—	178	1	no	—
390	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	178	2	no	—
394	C₂²×C₄	—	178	1	no	—
395	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
396	Q₁₆	—	2	1	no	—
397	Q₁₆	—	2	1	no	—
398	Q₁₆	—	178	4	no	—
399	SD₁₆	—	2	2	no	—
400	SD₁₆	—	2	2	no	—
401	SD₁₆	—	178	4	no	—
402	SD₁₆	—	178	4	no	—
403	D₈	—	2	1	no	—
404	D₈	—	2	1	no	—
405	D₈	—	178	4	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	4	2	no	—
409	M₁₆	—	4	2	no	—
410	M₁₆	—	89	2	no	—
411	M₁₆	—	89	4	no	—
412	M₁₆	—	89	2	no	—
413	M₁₆	—	178	2	no	—
414	M₁₆	—	178	1	no	—
415	M₁₆	—	178	1	no	—
416	M₁₆	—	178	2	no	—
417	M₁₆	—	178	2	no	—
418	M₁₆	—	178	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	178	2	no	—
423	C₂×C₈	—	178	1	no	—
424	C₂×C₈	—	178	1	no	—
425	C₂×C₈	—	178	2	no	—
426	C₂×C₈	—	178	2	no	—
427	C₂×C₈	—	178	4	no	—
428	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
430	C₂×C₈	D₄×D₈₉	1	2	yes	—
431	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
433	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
434	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
435	C₂×C₈	#13083573	1	2	yes	—
436	C₂×C₈	#13083574	1	1	yes	characteristic
437	C₂×C₈	#13083574	1	1	yes	characteristic
438	C₄⋊C₄	—	178	2	no	—
439	C₄⋊C₄	—	178	2	no	—
440	C₄⋊C₄	—	178	1	no	—
441	C₂²⋊C₄	—	89	2	no	—
442	C₂²⋊C₄	—	178	2	no	—
443	C₂²⋊C₄	—	178	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	178	2	no	—
446	C₄²	—	178	2	no	—
447	C₄²	—	178	1	no	—
448	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
450	C₂³	—	2	2	no	—
451	C₂³	—	178	1	no	—
452	C₂³	#41×D₈₉	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	89	2	no	—
456	Q₈	—	178	1	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	89	2	no	—
462	D₄	—	178	2	no	—
463	D₄	—	178	2	no	—
464	D₄	—	178	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	356	2	no	—
472	C₂×C₄	—	178	2	no	—
473	C₂×C₄	—	178	1	no	—
474	C₂×C₄	—	178	2	no	—
475	C₂×C₄	—	178	2	no	—
476	C₂×C₄	—	712	2	no	—
477	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
479	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
480	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
481	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
482	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	178	4	no	—
485	C₈	—	178	2	no	—
486	C₈	—	178	2	no	—
487	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
488	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
489	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
490	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
491	C₈	#15667983	1	2	yes	—
492	C₈	#15667983	1	2	yes	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	356	2	no	—
497	C₂²	—	178	2	no	—
498	C₂²	C₄×#13083573	1	1	yes	characteristic
499	C₂²	#19152105	1	1	yes	characteristic
500	C₂²	#19152145	1	1	yes	characteristic
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	356	2	no	—
505	C₄	—	178	2	no	—
506	C₄	—	712	2	no	—
507	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
508	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
509	C₄	C₂×#15667983	1	1	yes	characteristic
510	C₄	#19152130	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	8	2	no	—
515	C₂	—	356	2	no	—
516	C₂	C₄×#15667983	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#15667983
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×#444×C₈₉	C₂
socle	C₂×C₈₉	C₄×#121
prime radical	#26029968	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×#444	D₈₉
hypocenter	C₈₉	#21559
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. #26029153	C₂	semidirect
3. #26028677	C₂	semidirect
4. #26021151	C₂	semidirect
5. #26021040	C₂	semidirect
6. #26020918	C₂	semidirect
7. #26020756	C₂	semidirect
8. #26020307	C₂	semidirect
9. #26020136	C₂	semidirect
10. #26020052	C₂	semidirect
11. C₂×#444×C₈₉	C₂	semidirect
16. #19151870	C₄	semidirect
17. #19151865	C₄	semidirect
18. #19151858	C₄	semidirect
74. #15667948	C₂×C₄	semidirect
75. #15667948	C₂×C₄	semidirect
81. #15667931	C₂×C₄	semidirect
82. #15667929	C₂×C₄	semidirect
97. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
98. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
99. C₂×D₈×C₈₉	C₂×C₄	semidirect
261. C₂×#444	D₈₉	semidirect
270. C₈₉	#21559	semidirect
318. C₂×Q₁₆	C₄×D₈₉	semidirect
319. C₂×SD₁₆	C₄×D₈₉	semidirect
320. C₂×D₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029968	2
#26029153	2
#26028677	2
#26021151	2
#26021040	2
#26020918	2
#26020756	2
#26020307	2
#26020136	2
#26020052	2
C₂×#444×C₈₉	2
#21559	89