Subgroups — #36581013

Order 22784.

706 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030714	C₂	1	1	yes	maximal, characteristic
2	#26020745	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020743	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020741	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020737	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020735	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020726	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020725	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020652	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020638	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020635	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020632	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020402	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020400	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1903	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668045	C₂²	1	1	yes	characteristic
17	C₂×#15668042	C₂²	1	1	yes	characteristic
18	C₂×#15668038	C₂²	1	1	yes	characteristic
19	#19152364	C₂²	1	1	yes	characteristic
20	#19152144	C₂²	1	1	yes	characteristic
21	C₂×#15667999	C₂²	1	1	yes	characteristic
22	#19152075	C₂²	1	1	yes	characteristic
23	#19152073	C₂²	1	1	yes	characteristic
24	#19151989	C₄	1	2	yes	complemented
25	#19151986	C₄	1	2	yes	complemented
26	#19151981	C₄	1	2	yes	complemented
27	#19151979	C₄	1	2	yes	complemented
28	#19151615	C₂²	1	1	yes	characteristic
29	#19151614	C₂²	1	1	yes	characteristic
30	#19151614	C₂²	1	1	yes	characteristic
31	#19151608	C₂²	1	1	yes	characteristic
32	#19151608	C₂²	1	1	yes	characteristic
33	#19151603	C₂²	1	1	yes	characteristic
34	C₂×#15667930	C₂²	1	1	yes	characteristic
35	#19151572	C₂²	1	1	yes	characteristic
36	#19151571	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
38	#19151370	C₂²	1	1	yes	characteristic
39	#19151370	C₂²	1	1	yes	characteristic
40	#19151369	C₂²	1	1	yes	characteristic
41	#19151359	C₂²	1	1	yes	characteristic
42	#19151359	C₂²	1	1	yes	characteristic
43	#19151359	C₂²	1	1	yes	characteristic
44	#19151357	C₂²	1	1	yes	characteristic
45	#19151356	C₂²	1	1	yes	characteristic
46	#19151355	C₂²	1	1	yes	characteristic
47	#19151354	C₂²	1	1	yes	characteristic
48	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
49	#568×C₈₉	C₂²	1	1	yes	characteristic
50	#421×C₈₉	C₂²	1	1	yes	characteristic
51	#418×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
53	#344×C₈₉	C₂²	1	1	yes	characteristic
54	#338×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#13083574	C₂³	1	1	yes	characteristic
56	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
57	#15668045	—	4	1	no	—
58	#15668045	—	4	1	no	—
59	#15668042	—	4	1	no	—
60	#15668042	—	4	1	no	—
61	#15668038	—	4	1	no	—
62	#15668038	—	4	1	no	—
63	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	complemented
64	C₂×#13083564	C₂×C₄	1	2	yes	complemented
65	C₂×#13083563	C₂×C₄	1	2	yes	complemented
66	C₂×#13083562	C₂×C₄	1	2	yes	—
67	C₂×#13083562	C₂×C₄	1	2	yes	complemented
68	C₂×#13083559	C₂×C₄	1	2	yes	—
69	#15668020	—	4	1	no	—
70	#15668018	—	4	1	no	—
71	C₂×#13083558	C₂³	1	1	yes	characteristic
72	C₂×#13083558	C₂³	1	1	yes	characteristic
73	M₁₆×D₈₉	—	4	1	no	—
74	#15668010	C₂×C₄	1	1	yes	characteristic, complemented
75	#15668008	C₂×C₄	1	1	yes	characteristic, complemented
76	#15668001	C₂×C₄	1	1	yes	characteristic, complemented
77	#15667999	—	4	1	no	—
78	#15667999	C₂×C₄	1	2	yes	—
79	#15667999	C₂×C₄	1	2	yes	—
80	#15667999	C₂×C₄	1	1	yes	characteristic, complemented
81	#15667984	—	4	1	no	—
82	C₄×Dic₁₇₈	—	4	1	no	—
83	#15667977	—	4	1	no	—
84	D₄×Dic₈₉	—	4	1	no	—
85	D₄×Dic₈₉	—	4	1	no	—
86	C₄×C₂²⋊D₈₉	—	4	1	no	—
87	#15667971	C₂³	1	1	yes	characteristic
88	#15667971	C₂³	1	1	yes	characteristic
89	#15667971	C₂³	1	1	yes	characteristic
90	#15667968	—	4	1	no	—
91	C₂×C₂²⋊Dic₈₉	—	4	1	no	—
92	C₂×C₂²⋊Dic₈₉	—	4	1	no	—
93	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
94	#15667939	—	4	1	no	—
95	#15667938	—	4	1	no	—
96	#15667938	—	4	1	no	—
97	#15667937	—	4	1	no	—
98	#15667937	—	4	1	no	—
99	#15667933	—	4	1	no	—
100	#15667930	—	4	1	no	—
101	#15667927	—	4	1	no	—
102	#15667926	—	4	1	no	—
103	#15667922	C₂×C₄	1	2	yes	complemented
104	C₈×Dic₈₉	C₂×C₄	1	2	yes	complemented
105	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
108	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
109	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
110	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
111	#131×C₈₉	—	4	1	no	—
112	#131×C₈₉	—	4	1	no	—
113	C₂×M₁₆×C₈₉	—	4	1	no	—
114	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	#117×C₈₉	C₂³	1	1	yes	characteristic
119	#104×C₈₉	—	4	1	no	—
120	#102×C₈₉	—	4	1	no	—
121	#100×C₈₉	—	4	1	no	—
122	#13083574	—	2	1	no	—
123	#13083574	—	2	1	no	—
124	#13083574	—	2	1	no	—
125	#13083574	—	2	1	no	—
126	C₂×Dic₁₇₈	—	2	1	no	—
127	C₂×Dic₁₇₈	—	2	1	no	—
128	C₂×Dic₁₇₈	—	2	1	no	—
129	C₂×Dic₁₇₈	—	2	1	no	—
130	C₂×Dic₁₇₈	—	2	1	no	—
131	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
132	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊D₈₉	—	2	1	no	—
135	C₂×C₂²⋊D₈₉	—	4	1	no	—
136	C₂²×Dic₈₉	—	2	1	no	—
137	C₂²×Dic₈₉	—	2	1	no	—
138	C₂²×Dic₈₉	—	4	2	no	—
139	C₂×C₄×D₈₉	—	2	1	no	—
140	Dic₃₅₆	—	4	2	no	—
141	#13083564	—	4	2	no	—
142	#13083563	—	4	2	no	—
143	#13083562	—	4	2	no	—
144	#13083562	—	4	2	no	—
145	#13083559	—	4	2	no	—
146	#13083558	—	2	1	no	—
147	#13083558	—	2	1	no	—
148	#13083558	—	2	1	no	—
149	#13083558	—	2	1	no	—
150	#13083557	—	4	2	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	C₂²×C₄	1	2	yes	—
153	C₈×D₈₉	—	4	2	no	—
154	C₄⋊Dic₈₉	—	2	1	no	—
155	C₄⋊Dic₈₉	—	2	1	no	—
156	C₄⋊Dic₈₉	—	2	1	no	—
157	#13083553	—	4	1	no	—
158	#13083553	—	4	2	no	—
159	C₂²⋊Dic₈₉	—	2	1	no	—
160	C₂²⋊Dic₈₉	—	2	1	no	—
161	C₂²⋊Dic₈₉	—	2	1	no	—
162	C₂²⋊Dic₈₉	—	4	1	no	—
163	C₂²⋊Dic₈₉	—	4	2	no	—
164	C₂²⋊Dic₈₉	—	4	2	no	—
165	C₂²⋊Dic₈₉	—	4	2	no	—
166	#13083551	—	4	1	no	—
167	C₄×Dic₈₉	—	2	1	no	—
168	C₄×Dic₈₉	—	2	1	no	—
169	C₄×Dic₈₉	—	2	1	no	—
170	C₄×Dic₈₉	—	2	1	no	—
171	C₄×Dic₈₉	—	4	2	no	—
172	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂⁴×C₈₉	—	2	1	no	—
175	#41×C₈₉	—	2	1	no	—
176	#41×C₈₉	—	2	1	no	—
177	#41×C₈₉	—	2	1	no	—
178	#41×C₈₉	—	2	1	no	—
179	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
187	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
190	SD₁₆×C₈₉	—	4	2	no	—
191	D₈×C₈₉	—	4	2	no	—
192	M₁₆×C₈₉	—	2	1	no	—
193	M₁₆×C₈₉	—	2	1	no	—
194	M₁₆×C₈₉	—	2	1	no	—
195	M₁₆×C₈₉	—	2	1	no	—
196	M₁₆×C₈₉	—	2	1	no	—
197	M₁₆×C₈₉	—	2	1	no	—
198	M₁₆×C₈₉	—	2	1	no	—
199	M₁₆×C₈₉	—	2	1	no	—
200	M₁₆×C₈₉	—	4	2	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	4	2	no	—
205	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
206	C₄⋊C₄×C₈₉	—	2	1	no	—
207	C₂²⋊C₄×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	2	1	no	—
209	C₂³×C₈₉	—	2	1	no	—
210	C₂³×C₈₉	—	2	2	no	—
211	C₂³×C₈₉	—	4	1	no	—
212	C₂³×C₈₉	—	4	1	no	—
213	C₂³×C₈₉	—	8	2	no	—
214	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×D₈₉	—	2	1	no	—
216	Q₈×C₈₉	—	2	1	no	—
217	Q₈×C₈₉	—	2	1	no	—
218	D₄×C₈₉	—	2	1	no	—
219	D₄×C₈₉	—	2	2	no	—
220	D₄×C₈₉	—	2	2	no	—
221	D₄×C₈₉	—	2	1	no	—
222	D₄×C₈₉	—	4	1	no	—
223	D₄×C₈₉	—	4	1	no	—
224	D₄×C₈₉	—	4	1	no	—
225	D₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²⋊D₈₉	—	4	1	no	—
237	C₂²⋊D₈₉	—	4	1	no	—
238	C₂²⋊D₈₉	—	8	2	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	2	2	no	—
242	C₂×Dic₈₉	—	2	1	no	—
243	C₂×Dic₈₉	—	4	1	no	—
244	C₂×Dic₈₉	—	4	1	no	—
245	C₂×Dic₈₉	—	4	1	no	—
246	C₂×Dic₈₉	—	4	1	no	—
247	C₂×Dic₈₉	—	4	1	no	—
248	C₂×Dic₈₉	—	8	1	no	—
249	C₂×Dic₈₉	—	16	2	no	—
250	D₃₅₆	—	2	1	no	—
251	D₃₅₆	—	2	1	no	—
252	C₄×D₈₉	—	4	1	no	—
253	C₄×D₈₉	—	4	1	no	—
254	Dic₁₇₈	—	2	1	no	—
255	Dic₁₇₈	—	2	2	no	—
256	Dic₁₇₈	—	2	2	no	—
257	Dic₁₇₈	—	2	1	no	—
258	Dic₁₇₈	—	4	1	no	—
259	Dic₁₇₈	—	4	1	no	—
260	C₈×C₈₉	—	2	2	no	—
261	C₈×C₈₉	—	4	1	no	—
262	C₈×C₈₉	—	4	1	no	—
263	C₈×C₈₉	—	4	1	no	—
264	#10623494	—	2	2	no	—
265	#10623494	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	4	2	no	—
269	C₂²×C₈₉	—	8	2	no	—
270	C₂²×C₈₉	—	8	1	no	—
271	C₂²×C₈₉	—	8	2	no	—
272	C₂²×C₈₉	—	16	1	no	—
273	C₂²×C₈₉	#518	1	1	yes	characteristic
274	C₂²×C₈₉	#560	1	1	yes	characteristic
275	C₂²×C₈₉	#560	1	1	yes	characteristic
276	C₂×D₈₉	—	4	1	no	—
277	C₂×D₈₉	—	8	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	8	1	no	—
280	C₄×C₈₉	#518	1	1	yes	characteristic
281	C₄×C₈₉	#518	1	1	yes	characteristic
282	C₄×C₈₉	#560	1	1	yes	characteristic
283	C₄×C₈₉	#560	1	1	yes	characteristic
284	Dic₈₉	—	4	1	no	—
285	Dic₈₉	—	4	1	no	—
286	Dic₈₉	—	4	2	no	—
287	Dic₈₉	—	4	1	no	—
288	Dic₈₉	—	8	1	no	—
289	Dic₈₉	—	8	1	no	—
290	Dic₈₉	—	8	1	no	—
291	#23362	—	89	1	no	maximal, Sylow
292	C₂×C₈₉	—	2	1	no	—
293	C₂×C₈₉	—	2	1	no	—
294	C₂×C₈₉	—	2	1	no	—
295	C₂×C₈₉	—	8	1	no	—
296	C₂×C₈₉	—	8	2	no	—
297	C₂×C₈₉	#2380	1	1	yes	characteristic
298	D₈₉	—	8	1	no	—
299	#3153	—	89	1	no	—
300	#1905	—	89	1	no	—
301	#1905	—	89	1	no	—
302	#1904	—	89	1	no	—
303	#1904	—	89	1	no	—
304	#1903	—	89	1	no	—
305	#1903	D₈₉	1	1	yes	characteristic, complemented
306	#1902	—	89	1	no	—
307	#1902	—	89	1	no	—
308	#1888	—	89	1	no	—
309	#1885	—	89	1	no	—
310	#1884	—	89	1	no	—
311	#1884	—	89	1	no	—
312	#1841	—	89	1	no	—
313	#1841	—	89	1	no	—
314	C₈₉	#23362	1	1	yes	characteristic, complemented, Sylow
315	C₂×#137	—	89	1	no	—
316	C₂×#137	—	89	1	no	—
317	C₂×AGL(1,ℤ/8)	—	89	1	no	—
318	C₂×AGL(1,ℤ/8)	C₂×D₈₉	1	1	yes	characteristic
319	#568	—	89	1	no	—
320	#568	C₂×D₈₉	1	1	yes	characteristic
321	#532	—	89	1	no	—
322	C₂×#124	—	89	1	no	—
323	#519	—	89	1	no	—
324	#518	—	89	1	no	—
325	#497	—	89	2	no	—
326	#496	—	89	2	no	—
327	#495	—	89	2	no	—
328	#495	—	89	2	no	—
329	#421	—	89	1	no	—
330	#421	—	89	1	no	—
331	#421	—	89	1	no	—
332	#421	C₂×D₈₉	1	1	yes	characteristic
333	#419	—	89	1	no	—
334	#419	—	89	1	no	—
335	#418	—	89	1	no	—
336	#418	C₂×D₈₉	1	1	yes	characteristic
337	C₂×#101	—	89	1	no	—
338	C₂×#100	C₂×D₈₉	1	1	yes	characteristic
339	#410	—	89	1	no	—
340	#410	—	89	1	no	—
341	C₄×M₁₆	—	89	1	no	—
342	#344	—	89	1	no	—
343	#344	—	89	1	no	—
344	#344	—	89	1	no	—
345	#344	C₂×D₈₉	1	1	yes	characteristic
346	#339	—	89	1	no	—
347	#339	—	89	1	no	—
348	#339	—	89	1	no	—
349	#339	—	89	1	no	—
350	#338	—	89	1	no	—
351	#338	C₂×D₈₉	1	1	yes	characteristic
352	H(3,ℤ/4)	—	89	1	no	—
353	H(3,ℤ/4)	—	89	1	no	—
354	C₂×#41	—	89	1	no	—
355	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
356	C₂²×Q₈	—	89	1	no	—
357	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
358	#137	—	356	1	no	—
359	#137	—	356	1	no	—
360	#137	—	356	1	no	—
361	#137	—	356	1	no	—
362	AGL(1,ℤ/8)	—	4	1	no	—
363	AGL(1,ℤ/8)	—	4	1	no	—
364	AGL(1,ℤ/8)	—	356	1	no	—
365	AGL(1,ℤ/8)	—	356	1	no	—
366	C₂×Q₁₆	—	89	2	no	—
367	C₂×Q₁₆	—	89	2	no	—
368	C₂×SD₁₆	—	89	2	no	—
369	C₂×SD₁₆	—	89	2	no	—
370	C₂×SD₁₆	—	89	2	no	—
371	C₂×SD₁₆	C₄×D₈₉	1	2	yes	—
372	C₂×D₈	—	89	2	no	—
373	C₂×D₈	C₄×D₈₉	1	2	yes	—
374	#131	—	4	1	no	—
375	#131	—	4	1	no	—
376	#131	—	356	1	no	—
377	#131	—	356	1	no	—
378	C₂×M₁₆	—	4	1	no	—
379	C₂×M₁₆	—	89	1	no	—
380	C₂×M₁₆	—	89	1	no	—
381	C₂×M₁₆	—	356	1	no	—
382	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
383	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
384	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
385	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
386	C₄⋊Q₈	—	89	1	no	—
387	#127	—	89	1	no	—
388	#124	—	89	1	no	—
389	#124	—	89	2	no	—
390	#124	—	89	2	no	—
391	#124	—	89	1	no	—
392	#124	—	356	1	no	—
393	#121	—	356	1	no	—
394	C₄×Q₈	—	356	1	no	—
395	C₄×Q₈	—	356	1	no	—
396	C₄×D₄	—	356	1	no	—
397	C₄×D₄	—	356	1	no	—
398	C₄×D₄	—	356	1	no	—
399	#117	—	89	1	no	—
400	#117	—	89	1	no	—
401	#117	—	89	1	no	—
402	#117	—	356	1	no	—
403	#117	C₂²×D₈₉	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	—	356	1	no	—
405	C₂×C₂²⋊C₄	—	356	1	no	—
406	C₂×C₄²	—	89	1	no	—
407	#104	—	4	1	no	—
408	#104	—	356	1	no	—
409	#104	—	356	1	no	—
410	#104	—	356	1	no	—
411	#103	—	356	1	no	—
412	#103	—	356	1	no	—
413	#102	—	4	1	no	—
414	#102	—	356	1	no	—
415	#101	—	356	1	no	—
416	#100	—	4	1	no	—
417	#99	—	356	1	no	—
418	#99	—	356	1	no	—
419	#97	—	89	2	no	—
420	C₄×C₈	—	89	2	no	—
421	C₂⁴	—	2	1	no	—
422	#41	—	2	1	no	—
423	#41	—	2	1	no	—
424	#41	—	2	1	no	—
425	#41	—	2	1	no	—
426	#41	—	178	1	no	—
427	#41	—	178	1	no	—
428	#41	—	178	1	no	—
429	#41	—	178	1	no	—
430	C₂×Q₈	—	89	2	no	—
431	C₂×Q₈	—	89	1	no	—
432	C₂×Q₈	—	178	1	no	—
433	C₂×Q₈	—	178	1	no	—
434	C₂×Q₈	—	178	1	no	—
435	C₂×Q₈	—	178	1	no	—
436	C₂×Q₈	—	178	1	no	—
437	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	89	1	no	—
445	C₂×D₄	—	356	1	no	—
446	C₂×D₄	—	178	1	no	—
447	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
448	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	356	2	no	—
451	C₂²×C₄	—	178	1	no	—
452	C₂²×C₄	—	178	1	no	—
453	C₂²×C₄	—	178	1	no	—
454	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
455	Q₁₆	—	356	2	no	—
456	Q₁₆	—	356	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	—	356	2	no	—
459	SD₁₆	—	356	2	no	—
460	SD₁₆	—	356	2	no	—
461	D₈	—	4	2	no	—
462	D₈	—	356	2	no	—
463	M₁₆	—	2	1	no	—
464	M₁₆	—	2	1	no	—
465	M₁₆	—	2	1	no	—
466	M₁₆	—	2	1	no	—
467	M₁₆	—	2	1	no	—
468	M₁₆	—	2	1	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	356	2	no	—
473	M₁₆	—	178	1	no	—
474	M₁₆	—	178	1	no	—
475	M₁₆	—	178	1	no	—
476	M₁₆	—	178	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	89	2	no	—
482	C₂×C₈	—	356	2	no	—
483	C₂×C₈	—	178	1	no	—
484	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	356	1	no	—
487	C₄⋊C₄	—	356	2	no	—
488	C₄⋊C₄	—	178	1	no	—
489	C₄⋊C₄	—	178	1	no	—
490	C₄⋊C₄	—	178	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	356	1	no	—
493	C₂²⋊C₄	—	356	2	no	—
494	C₂²⋊C₄	—	356	2	no	—
495	C₂²⋊C₄	—	356	2	no	—
496	C₂²⋊C₄	—	356	1	no	—
497	C₂²⋊C₄	—	178	1	no	—
498	C₂²⋊C₄	—	178	1	no	—
499	C₂²⋊C₄	—	178	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	89	1	no	—
502	C₄²	—	89	1	no	—
503	C₄²	—	356	2	no	—
504	C₄²	—	178	1	no	—
505	C₄²	—	178	1	no	—
506	C₄²	—	178	1	no	—
507	C₄²	—	178	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	8	2	no	—
513	C₂³	—	178	1	no	—
514	C₂³	#15668058	1	1	yes	characteristic
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	356	1	no	—
518	Q₈	—	356	1	no	—
519	Q₈	—	178	1	no	—
520	Q₈	—	178	2	no	—
521	Q₈	—	178	2	no	—
522	Q₈	—	178	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	2	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	356	1	no	—
532	D₄	—	356	1	no	—
533	D₄	—	178	1	no	—
534	D₄	—	178	1	no	—
535	D₄	—	712	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	356	1	no	—
541	C₂×C₄	—	356	1	no	—
542	C₂×C₄	—	356	1	no	—
543	C₂×C₄	—	356	1	no	—
544	C₂×C₄	—	356	1	no	—
545	C₂×C₄	—	356	1	no	—
546	C₂×C₄	—	356	1	no	—
547	C₂×C₄	—	1424	2	no	—
548	C₂×C₄	—	178	1	no	—
549	C₂×C₄	—	178	1	no	—
550	C₂×C₄	—	178	2	no	—
551	C₂×C₄	—	178	1	no	—
552	C₂×C₄	—	712	1	no	—
553	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
554	C₂×C₄	#15668057	1	1	yes	characteristic
555	C₂×C₄	#15668057	1	1	yes	characteristic
556	C₂×C₄	#15668057	1	1	yes	characteristic
557	C₂×C₄	#15668057	1	1	yes	characteristic
558	C₂×C₄	#15668058	1	1	yes	characteristic
559	C₈	—	2	2	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	356	1	no	—
564	C₈	—	178	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	16	1	no	—
572	C₂²	—	356	1	no	—
573	C₂²	—	712	1	no	—
574	C₂²	#19152070	1	1	yes	characteristic
575	C₂²	#19152336	1	1	yes	characteristic
576	C₂²	#19152338	1	1	yes	characteristic
577	C₄	—	4	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	356	1	no	—
580	C₄	—	356	1	no	—
581	C₄	—	356	1	no	—
582	C₄	—	356	2	no	—
583	C₄	—	712	1	no	—
584	C₄	—	712	1	no	—
585	C₄	—	712	1	no	—
586	C₄	#19152070	1	1	yes	characteristic
587	C₄	#19152071	1	1	yes	characteristic
588	C₄	#19152336	1	1	yes	characteristic
589	C₄	#19152337	1	1	yes	characteristic
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	8	1	no	—
594	C₂	—	8	2	no	—
595	C₂	—	712	1	no	—
596	C₂	#26023427	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26023427
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1903	C₂
socle	C₂×C₈₉	#2380
prime radical	#26030714	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1903	D₈₉
hypocenter	C₈₉	#23362
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1903

Complements

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

N	H ≅ G/N	type
2. #26020745	C₂	semidirect
3. #26020743	C₂	semidirect
4. #26020741	C₂	semidirect
5. #26020737	C₂	semidirect
6. #26020735	C₂	semidirect
7. #26020726	C₂	semidirect
8. #26020725	C₂	semidirect
9. #26020652	C₂	semidirect
10. #26020638	C₂	semidirect
11. #26020635	C₂	semidirect
12. #26020632	C₂	semidirect
13. #26020402	C₂	semidirect
14. #26020400	C₂	semidirect
15. C₈₉×#1903	C₂	semidirect
24. #19151989	C₄	semidirect
25. #19151986	C₄	semidirect
26. #19151981	C₄	semidirect
27. #19151979	C₄	semidirect
63. C₂×Dic₃₅₆	C₂×C₄	semidirect
64. C₂×#13083564	C₂×C₄	semidirect
65. C₂×#13083563	C₂×C₄	semidirect
67. C₂×#13083562	C₂×C₄	semidirect
74. #15668010	C₂×C₄	semidirect
75. #15668008	C₂×C₄	semidirect
76. #15668001	C₂×C₄	semidirect
80. #15667999	C₂×C₄	semidirect
103. #15667922	C₂×C₄	semidirect
104. C₈×Dic₈₉	C₂×C₄	semidirect
305. #1903	D₈₉	semidirect
314. C₈₉	#23362	semidirect

Maximal subgroups

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

subgroup	index
#26030714	2
#26020745	2
#26020743	2
#26020741	2
#26020737	2
#26020735	2
#26020726	2
#26020725	2
#26020652	2
#26020638	2
#26020635	2
#26020632	2
#26020402	2
#26020400	2
C₈₉×#1903	2
#23362	89