Subgroups — #36568339

Order 22784.

796 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030722	C₂	1	1	yes	maximal, characteristic
2	#26029168	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029112	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021150	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020787	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020782	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020776	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020771	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020744	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020737	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020735	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020728	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020377	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020007	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668043	C₂²	1	1	yes	characteristic
17	C₂×#15668038	C₂²	1	1	yes	characteristic
18	C₂×#15668034	C₂²	1	1	yes	characteristic
19	#19152364	C₂²	1	1	yes	characteristic
20	#19152364	C₂²	1	1	yes	characteristic
21	#19152172	C₂²	1	1	yes	characteristic
22	#19152165	C₂²	1	1	yes	characteristic
23	#19152076	C₂²	1	1	yes	characteristic
24	#19152073	C₂²	1	1	yes	characteristic
25	#19151989	C₄	1	2	yes	complemented
26	#19151984	C₄	1	2	yes	complemented
27	#19151979	C₄	1	2	yes	complemented
28	#19151969	C₄	1	2	yes	complemented
29	#19151719	—	2	2	no	—
30	#19151714	—	2	2	no	—
31	#19151699	—	2	2	no	—
32	SD₁₆×Dic₈₉	—	2	2	no	—
33	#19151636	C₂²	1	1	yes	characteristic
34	#19151614	C₂²	1	1	yes	characteristic
35	#19151614	C₂²	1	1	yes	characteristic
36	#19151614	C₂²	1	1	yes	characteristic
37	#19151614	C₂²	1	1	yes	characteristic
38	#19151607	C₂²	1	1	yes	characteristic
39	#19151603	C₂²	1	1	yes	characteristic
40	#19151571	C₂²	1	1	yes	characteristic
41	#19151571	C₂²	1	1	yes	characteristic
42	#19151553	C₂²	1	1	yes	characteristic
43	#19151553	C₂²	1	1	yes	characteristic
44	#19151370	C₂²	1	1	yes	characteristic
45	#19151370	C₂²	1	1	yes	characteristic
46	#19151356	C₂²	1	1	yes	characteristic
47	#19151355	C₂²	1	1	yes	characteristic
48	#19151355	C₂²	1	1	yes	characteristic
49	#19151355	C₂²	1	1	yes	characteristic
50	#19151354	C₂²	1	1	yes	characteristic
51	#19151354	C₂²	1	1	yes	characteristic
52	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
54	#419×C₈₉	C₂²	1	1	yes	characteristic
55	#418×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
58	#405×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083574	C₂³	1	1	yes	characteristic
60	C₂×#13083574	C₂³	1	1	yes	characteristic
61	#15668043	—	4	1	no	—
62	#15668043	—	4	1	no	—
63	#15668038	—	4	1	no	—
64	#15668038	—	4	1	no	—
65	#15668034	—	2	1	no	—
66	#15668034	—	2	1	no	—
67	#15668034	—	2	1	no	—
68	#15668034	—	2	1	no	—
69	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×#13083564	C₂×C₄	1	2	yes	complemented
71	C₂×#13083563	C₂×C₄	1	1	yes	characteristic, complemented
72	C₂×#13083563	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×#13083562	C₂×C₄	1	2	yes	—
74	C₂×#13083561	C₂×C₄	1	2	yes	complemented
75	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×#13083559	C₂×C₄	1	2	yes	—
77	#15668020	—	2	2	no	—
78	#15668020	—	2	2	no	—
79	#15668018	—	4	1	no	—
80	#15668018	—	4	1	no	—
81	C₂×#13083558	C₂³	1	1	yes	characteristic
82	C₂×#13083558	C₂³	1	1	yes	characteristic
83	M₁₆×D₈₉	—	4	1	no	—
84	M₁₆×D₈₉	—	4	1	no	—
85	#15668010	C₂×C₄	1	2	yes	complemented
86	#15668008	C₂×C₄	1	2	yes	—
87	#15668001	C₂×C₄	1	2	yes	complemented
88	#15667999	C₂×C₄	1	2	yes	—
89	#15667995	—	4	1	no	—
90	#15667988	—	4	1	no	—
91	#15667983	—	4	1	no	—
92	#15667981	—	4	1	no	—
93	Q₈×Dic₈₉	—	2	2	no	—
94	Q₈×Dic₈₉	—	4	1	no	—
95	D₄×Dic₈₉	—	2	2	no	—
96	D₄×Dic₈₉	—	4	1	no	—
97	#15667971	—	4	1	no	—
98	#15667971	C₂³	1	1	yes	characteristic
99	#15667971	C₂³	1	1	yes	characteristic
100	#15667971	C₂³	1	1	yes	characteristic
101	#15667971	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊Dic₈₉	—	4	1	no	—
103	#15667946	—	2	1	no	—
104	#15667944	—	2	1	no	—
105	#15667938	—	2	2	no	—
106	#15667938	—	2	2	no	—
107	#15667938	—	4	1	no	—
108	#15667938	—	4	1	no	—
109	#15667936	—	2	2	no	—
110	#15667933	—	2	2	no	—
111	#15667926	—	4	1	no	—
112	#15667926	—	4	1	no	—
113	#15667922	C₂×C₄	1	2	yes	complemented
114	#15667922	D₄	1	2	yes	complemented
115	C₈×Dic₈₉	C₂×C₄	1	2	yes	complemented
116	C₈×Dic₈₉	D₄	1	2	yes	complemented
117	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×SD₁₆×C₈₉	—	2	1	no	—
120	C₂×SD₁₆×C₈₉	—	2	1	no	—
121	C₂×SD₁₆×C₈₉	—	2	1	no	—
122	C₂×SD₁₆×C₈₉	—	2	1	no	—
123	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
124	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
125	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
129	#117×C₈₉	C₂³	1	1	yes	characteristic
130	#108×C₈₉	—	2	1	no	—
131	#108×C₈₉	—	2	1	no	—
132	#103×C₈₉	—	4	1	no	—
133	#102×C₈₉	—	4	1	no	—
134	#101×C₈₉	—	4	1	no	—
135	#100×C₈₉	—	4	1	no	—
136	#97×C₈₉	—	2	1	no	—
137	C₄×C₈×C₈₉	—	2	1	no	—
138	#13083574	—	2	1	no	—
139	#13083574	—	2	1	no	—
140	#13083574	—	2	1	no	—
141	#13083574	—	2	1	no	—
142	#13083574	—	2	1	no	—
143	#13083574	—	2	1	no	—
144	#13083574	—	2	1	no	—
145	#13083574	—	2	1	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₂²⋊D₈₉	—	2	1	no	—
151	C₂×C₂²⋊D₈₉	—	2	1	no	—
152	C₂×C₂²⋊D₈₉	—	4	2	no	—
153	C₂²×Dic₈₉	—	4	2	no	—
154	C₂×C₄×D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	Dic₃₅₆	—	2	1	no	—
157	Dic₃₅₆	—	2	1	no	—
158	#13083564	—	4	2	no	—
159	#13083563	—	2	1	no	—
160	#13083563	—	2	1	no	—
161	#13083563	—	2	1	no	—
162	#13083563	—	2	1	no	—
163	#13083562	—	4	2	no	—
164	#13083561	—	4	2	no	—
165	D₇₁₂	—	2	1	no	—
166	D₇₁₂	—	2	1	no	—
167	#13083559	—	4	2	no	—
168	#13083558	—	2	1	no	—
169	#13083558	—	2	1	no	—
170	#13083558	—	2	1	no	—
171	#13083558	—	2	1	no	—
172	#13083557	—	4	2	no	—
173	#13083557	—	4	2	no	—
174	C₂×#10623494	C₂²×C₄	1	2	yes	—
175	C₂×#10623494	C₂×D₄	1	2	yes	—
176	C₈×D₈₉	—	4	2	no	—
177	C₈×D₈₉	—	4	2	no	—
178	C₄⋊Dic₈₉	—	2	1	no	—
179	C₄⋊Dic₈₉	—	2	1	no	—
180	C₄⋊Dic₈₉	—	2	1	no	—
181	C₄⋊Dic₈₉	—	2	1	no	—
182	C₄⋊Dic₈₉	—	4	2	no	—
183	#13083553	—	4	2	no	—
184	C₂²⋊Dic₈₉	—	2	1	no	—
185	C₂²⋊Dic₈₉	—	2	1	no	—
186	C₂²⋊Dic₈₉	—	2	1	no	—
187	C₂²⋊Dic₈₉	—	2	1	no	—
188	C₂²⋊Dic₈₉	—	4	2	no	—
189	C₂²⋊Dic₈₉	—	4	2	no	—
190	#13083551	—	4	2	no	—
191	C₄×Dic₈₉	—	2	1	no	—
192	C₄×Dic₈₉	—	2	1	no	—
193	C₄×Dic₈₉	—	4	2	no	—
194	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
195	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
196	C₂⁴×C₈₉	—	2	1	no	—
197	C₂×Q₈×C₈₉	—	2	1	no	—
198	C₂×Q₈×C₈₉	—	2	1	no	—
199	C₂×Q₈×C₈₉	—	2	1	no	—
200	C₂×Q₈×C₈₉	—	2	1	no	—
201	C₂×Q₈×C₈₉	—	2	1	no	—
202	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	2	1	no	—
205	C₂×D₄×C₈₉	—	2	1	no	—
206	C₂×D₄×C₈₉	—	2	1	no	—
207	C₂×D₄×C₈₉	—	2	1	no	—
208	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	SD₁₆×C₈₉	—	2	2	no	—
212	SD₁₆×C₈₉	—	2	2	no	—
213	SD₁₆×C₈₉	—	2	2	no	—
214	SD₁₆×C₈₉	—	2	2	no	—
215	M₁₆×C₈₉	—	2	1	no	—
216	M₁₆×C₈₉	—	2	1	no	—
217	M₁₆×C₈₉	—	2	1	no	—
218	M₁₆×C₈₉	—	2	1	no	—
219	M₁₆×C₈₉	—	2	1	no	—
220	M₁₆×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
229	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₂²⋊C₄×C₈₉	—	2	1	no	—
232	C₄²×C₈₉	—	2	1	no	—
233	C₂³×C₈₉	—	2	2	no	—
234	C₂³×C₈₉	—	4	1	no	—
235	C₂³×C₈₉	—	4	1	no	—
236	C₂³×C₈₉	—	16	1	no	—
237	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂²×D₈₉	—	2	1	no	—
239	C₂²×D₈₉	—	2	1	no	—
240	Q₈×C₈₉	—	2	2	no	—
241	Q₈×C₈₉	—	2	2	no	—
242	Q₈×C₈₉	—	4	1	no	—
243	Q₈×C₈₉	—	4	1	no	—
244	D₄×C₈₉	—	2	2	no	—
245	D₄×C₈₉	—	2	2	no	—
246	D₄×C₈₉	—	4	1	no	—
247	D₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	4	1	no	—
250	C₂×C₄×C₈₉	—	4	1	no	—
251	C₂×C₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂²⋊D₈₉	—	4	1	no	—
259	C₂²⋊D₈₉	—	4	1	no	—
260	C₂²⋊D₈₉	—	4	1	no	—
261	C₂²⋊D₈₉	—	4	1	no	—
262	C₂²⋊D₈₉	—	16	2	no	—
263	C₂×Dic₈₉	—	2	2	no	—
264	C₂×Dic₈₉	—	2	1	no	—
265	C₂×Dic₈₉	—	2	1	no	—
266	C₂×Dic₈₉	—	2	2	no	—
267	C₂×Dic₈₉	—	4	1	no	—
268	C₂×Dic₈₉	—	4	1	no	—
269	C₂×Dic₈₉	—	16	2	no	—
270	D₃₅₆	—	2	1	no	—
271	D₃₅₆	—	2	1	no	—
272	D₃₅₆	—	2	1	no	—
273	D₃₅₆	—	2	1	no	—
274	C₄×D₈₉	—	4	1	no	—
275	C₄×D₈₉	—	4	1	no	—
276	C₄×D₈₉	—	4	1	no	—
277	C₄×D₈₉	—	4	1	no	—
278	Dic₁₇₈	—	2	1	no	—
279	Dic₁₇₈	—	2	1	no	—
280	Dic₁₇₈	—	2	1	no	—
281	Dic₁₇₈	—	2	1	no	—
282	C₈×C₈₉	—	4	1	no	—
283	C₈×C₈₉	—	4	1	no	—
284	C₈×C₈₉	—	4	1	no	—
285	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
286	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
287	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
288	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
289	#10623494	—	2	2	no	—
290	#10623494	—	2	2	no	—
291	C₂²×C₈₉	—	4	1	no	—
292	C₂²×C₈₉	—	4	2	no	—
293	C₂²×C₈₉	—	8	2	no	—
294	C₂²×C₈₉	—	8	2	no	—
295	C₂²×C₈₉	—	16	1	no	—
296	C₂²×C₈₉	#518	1	1	yes	characteristic
297	C₂²×C₈₉	#535	1	1	yes	characteristic
298	C₂²×C₈₉	#540	1	1	yes	characteristic
299	C₂×D₈₉	—	4	1	no	—
300	C₂×D₈₉	—	4	1	no	—
301	C₂×D₈₉	—	8	1	no	—
302	C₂×D₈₉	—	8	1	no	—
303	C₄×C₈₉	—	4	2	no	—
304	C₄×C₈₉	—	8	1	no	—
305	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₈₉	#518	1	1	yes	characteristic
307	C₄×C₈₉	#535	1	1	yes	characteristic
308	C₄×C₈₉	#540	1	1	yes	characteristic
309	Dic₈₉	—	4	2	no	—
310	Dic₈₉	—	4	2	no	—
311	Dic₈₉	—	4	1	no	—
312	Dic₈₉	—	4	1	no	—
313	Dic₈₉	—	8	1	no	—
314	Dic₈₉	—	8	1	no	—
315	#22284	—	89	1	no	maximal, Sylow
316	C₂×C₈₉	—	2	1	no	—
317	C₂×C₈₉	—	2	1	no	—
318	C₂×C₈₉	—	2	1	no	—
319	C₂×C₈₉	—	8	2	no	—
320	C₂×C₈₉	#2328	1	1	yes	characteristic
321	D₈₉	—	8	1	no	—
322	D₈₉	—	8	1	no	—
323	#3154	—	89	1	no	—
324	#2957	—	89	1	no	—
325	#2949	—	89	1	no	—
326	#1977	D₈₉	1	1	yes	characteristic, complemented
327	#1976	—	89	1	no	—
328	#1912	—	89	1	no	—
329	#1911	—	89	1	no	—
330	#1910	—	89	1	no	—
331	#1909	—	89	1	no	—
332	#1905	—	89	1	no	—
333	#1904	—	89	1	no	—
334	#1903	—	89	1	no	—
335	#1902	—	89	1	no	—
336	#1833	—	89	1	no	—
337	#1747	—	89	1	no	—
338	C₈₉	#22284	1	1	yes	characteristic, complemented, Sylow
339	C₂×#137	—	89	1	no	—
340	C₂×AGL(1,ℤ/8)	—	89	1	no	—
341	C₂×#135	—	89	1	no	—
342	C₂²×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
343	#568	—	89	1	no	—
344	#568	—	89	1	no	—
345	#536	—	89	1	no	—
346	#535	—	89	1	no	—
347	#519	—	89	1	no	—
348	#518	—	89	1	no	—
349	#497	—	89	2	no	—
350	#496	—	89	2	no	—
351	#495	—	89	2	no	—
352	#492	—	89	2	no	—
353	#444	—	178	2	no	—
354	#443	—	178	2	no	—
355	#440	—	178	2	no	—
356	C₄×SD₁₆	—	178	2	no	—
357	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
358	#427	—	89	1	no	—
359	#421	—	89	1	no	—
360	#421	—	89	1	no	—
361	#421	—	89	1	no	—
362	#421	—	89	1	no	—
363	#419	—	89	1	no	—
364	#419	C₂×D₈₉	1	1	yes	characteristic
365	#418	—	89	1	no	—
366	#418	C₂×D₈₉	1	1	yes	characteristic
367	C₂×#101	C₂×D₈₉	1	1	yes	characteristic
368	C₂×#100	C₂×D₈₉	1	1	yes	characteristic
369	#410	—	89	1	no	—
370	#410	—	89	1	no	—
371	#405	—	89	1	no	—
372	#405	—	89	1	no	—
373	#405	C₂×D₈₉	1	1	yes	characteristic
374	#344	—	89	1	no	—
375	#344	—	89	1	no	—
376	#338	—	89	1	no	—
377	H(3,ℤ/4)	—	89	1	no	—
378	H(3,ℤ/4)	—	89	1	no	—
379	H(3,ℤ/4)	—	89	1	no	—
380	H(3,ℤ/4)	—	89	1	no	—
381	H(3,ℤ/4)	—	89	1	no	—
382	C₂×#41	—	89	1	no	—
383	C₂×#41	—	89	1	no	—
384	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
385	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
386	#137	—	356	1	no	—
387	#137	—	356	1	no	—
388	AGL(1,ℤ/8)	—	356	1	no	—
389	AGL(1,ℤ/8)	—	356	1	no	—
390	#135	—	178	1	no	—
391	#135	—	178	1	no	—
392	#135	—	178	1	no	—
393	#135	—	178	1	no	—
394	C₂×Q₁₆	—	89	2	no	—
395	C₂×Q₁₆	—	89	1	no	—
396	C₂×SD₁₆	—	2	1	no	—
397	C₂×SD₁₆	—	2	1	no	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×SD₁₆	—	2	1	no	—
400	C₂×SD₁₆	—	89	2	no	—
401	C₂×SD₁₆	—	89	2	no	—
402	C₂×SD₁₆	—	89	1	no	—
403	C₂×SD₁₆	—	89	1	no	—
404	C₂×SD₁₆	C₄×D₈₉	1	2	yes	—
405	C₂×SD₁₆	C₄×D₈₉	1	2	yes	—
406	C₂×D₈	—	89	2	no	—
407	C₂×D₈	—	89	1	no	—
408	#131	—	356	1	no	—
409	#131	—	356	1	no	—
410	#131	—	178	2	no	—
411	#131	—	178	2	no	—
412	C₂×M₁₆	—	89	1	no	—
413	C₂×M₁₆	—	89	1	no	—
414	C₂×M₁₆	—	356	1	no	—
415	C₂×M₁₆	—	356	1	no	—
416	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
417	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
418	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
419	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	89	2	no	—
421	#127	—	89	2	no	—
422	#124	—	89	2	no	—
423	#124	—	89	2	no	—
424	#123	—	356	1	no	—
425	C₂²⋊Q₈	—	356	1	no	—
426	#121	—	356	1	no	—
427	#120	—	356	1	no	—
428	C₄×Q₈	—	356	1	no	—
429	C₄×Q₈	—	178	2	no	—
430	C₄×D₄	—	356	1	no	—
431	C₄×D₄	—	178	2	no	—
432	#117	—	89	1	no	—
433	#117	—	89	1	no	—
434	#117	—	89	1	no	—
435	#117	—	89	1	no	—
436	#117	—	356	1	no	—
437	#117	C₂²×D₈₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	356	1	no	—
439	#108	—	2	1	no	—
440	#108	—	2	1	no	—
441	#107	—	178	1	no	—
442	#106	—	178	1	no	—
443	#104	—	356	1	no	—
444	#104	—	356	1	no	—
445	#104	—	178	2	no	—
446	#104	—	178	2	no	—
447	#103	—	4	1	no	—
448	#103	—	178	2	no	—
449	#102	—	4	1	no	—
450	#102	—	178	2	no	—
451	#101	—	4	1	no	—
452	#100	—	4	1	no	—
453	#99	—	356	1	no	—
454	#99	—	356	1	no	—
455	#97	—	2	1	no	—
456	#97	—	89	2	no	—
457	#97	—	89	2	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	89	2	no	—
460	C₄×C₈	—	89	2	no	—
461	C₂⁴	—	2	1	no	—
462	#41	—	178	1	no	—
463	#41	—	178	1	no	—
464	#41	—	178	1	no	—
465	#41	—	178	1	no	—
466	#41	—	178	1	no	—
467	#41	—	178	1	no	—
468	#41	—	178	1	no	—
469	#41	—	178	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	89	1	no	—
476	C₂×Q₈	—	89	1	no	—
477	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	89	1	no	—
484	C₂×D₄	—	89	1	no	—
485	C₂×D₄	—	356	2	no	—
486	C₂×D₄	—	178	1	no	—
487	C₂×D₄	—	178	1	no	—
488	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	356	2	no	—
491	C₂²×C₄	—	178	1	no	—
492	C₂²×C₄	—	178	1	no	—
493	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
494	Q₁₆	—	356	2	no	—
495	Q₁₆	—	178	1	no	—
496	Q₁₆	—	178	1	no	—
497	SD₁₆	—	2	2	no	—
498	SD₁₆	—	2	2	no	—
499	SD₁₆	—	2	2	no	—
500	SD₁₆	—	2	2	no	—
501	SD₁₆	—	356	2	no	—
502	SD₁₆	—	356	2	no	—
503	SD₁₆	—	178	1	no	—
504	SD₁₆	—	178	1	no	—
505	SD₁₆	—	178	1	no	—
506	SD₁₆	—	178	1	no	—
507	D₈	—	356	2	no	—
508	D₈	—	178	1	no	—
509	D₈	—	178	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	356	2	no	—
517	M₁₆	—	356	2	no	—
518	M₁₆	—	178	1	no	—
519	M₁₆	—	178	1	no	—
520	M₁₆	—	178	1	no	—
521	M₁₆	—	178	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	89	2	no	—
526	C₂×C₈	—	89	2	no	—
527	C₂×C₈	—	356	2	no	—
528	C₂×C₈	—	356	2	no	—
529	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
530	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
531	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
532	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
533	C₂×C₈	#13083573	1	1	yes	characteristic
534	C₂×C₈	#13083573	1	1	yes	characteristic
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	356	2	no	—
537	C₄⋊C₄	—	356	2	no	—
538	C₄⋊C₄	—	178	1	no	—
539	C₄⋊C₄	—	178	1	no	—
540	C₄⋊C₄	—	178	1	no	—
541	C₄⋊C₄	—	178	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	356	2	no	—
544	C₂²⋊C₄	—	356	2	no	—
545	C₂²⋊C₄	—	356	2	no	—
546	C₂²⋊C₄	—	178	1	no	—
547	C₂²⋊C₄	—	178	1	no	—
548	C₂²⋊C₄	—	178	1	no	—
549	C₂²⋊C₄	—	178	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	89	2	no	—
552	C₄²	—	89	2	no	—
553	C₄²	—	356	2	no	—
554	C₄²	—	178	1	no	—
555	C₄²	—	178	1	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	16	1	no	—
560	C₂³	—	178	1	no	—
561	C₂³	—	178	1	no	—
562	C₂³	#15668058	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	178	1	no	—
568	Q₈	—	178	1	no	—
569	Q₈	—	178	1	no	—
570	Q₈	—	178	1	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	356	1	no	—
576	D₄	—	356	1	no	—
577	D₄	—	356	1	no	—
578	D₄	—	356	1	no	—
579	D₄	—	1424	2	no	—
580	D₄	—	178	1	no	—
581	D₄	—	178	1	no	—
582	D₄	—	178	1	no	—
583	D₄	—	178	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	356	1	no	—
589	C₂×C₄	—	356	1	no	—
590	C₂×C₄	—	356	1	no	—
591	C₂×C₄	—	356	1	no	—
592	C₂×C₄	—	356	1	no	—
593	C₂×C₄	—	356	1	no	—
594	C₂×C₄	—	1424	2	no	—
595	C₂×C₄	—	178	2	no	—
596	C₂×C₄	—	178	2	no	—
597	C₂×C₄	—	178	1	no	—
598	C₂×C₄	—	178	1	no	—
599	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
600	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
602	C₂×C₄	#15668057	1	1	yes	characteristic
603	C₂×C₄	#15668057	1	1	yes	characteristic
604	C₂×C₄	#15668058	1	1	yes	characteristic
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	178	2	no	—
609	C₈	—	178	2	no	—
610	C₈	#15667972	1	1	yes	characteristic
611	C₈	#15667972	1	1	yes	characteristic
612	C₈	#15667972	1	1	yes	characteristic
613	C₈	#15667972	1	1	yes	characteristic
614	C₂²	—	4	1	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	2	no	—
618	C₂²	—	16	1	no	—
619	C₂²	—	356	1	no	—
620	C₂²	—	356	1	no	—
621	C₂²	—	712	1	no	—
622	C₂²	—	712	1	no	—
623	C₂²	#19152070	1	1	yes	characteristic
624	C₂²	#19152166	1	1	yes	characteristic
625	C₂²	#19152201	1	1	yes	characteristic
626	C₄	—	4	2	no	—
627	C₄	—	8	1	no	—
628	C₄	—	356	2	no	—
629	C₄	—	356	2	no	—
630	C₄	—	356	1	no	—
631	C₄	—	356	1	no	—
632	C₄	—	712	1	no	—
633	C₄	—	712	1	no	—
634	C₄	C₂×#15667972	1	1	yes	characteristic
635	C₄	#19152070	1	1	yes	characteristic
636	C₄	#19152161	1	1	yes	characteristic
637	C₄	#19152201	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	8	2	no	—
642	C₂	—	712	1	no	—
643	C₂	—	712	1	no	—
644	C₂	#26022976	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26022976
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1977	C₂
socle	C₂×C₈₉	#2328
prime radical	#26030722	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1977	D₈₉
hypocenter	C₈₉	#22284
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1977

Complements

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

N	H ≅ G/N	type
2. #26029168	C₂	semidirect
3. #26029112	C₂	semidirect
4. #26021150	C₂	semidirect
5. #26020787	C₂	semidirect
6. #26020782	C₂	semidirect
7. #26020776	C₂	semidirect
8. #26020771	C₂	semidirect
9. #26020744	C₂	semidirect
10. #26020737	C₂	semidirect
11. #26020735	C₂	semidirect
12. #26020728	C₂	semidirect
13. #26020377	C₂	semidirect
14. #26020007	C₂	semidirect
15. C₈₉×#1977	C₂	semidirect
25. #19151989	C₄	semidirect
26. #19151984	C₄	semidirect
27. #19151979	C₄	semidirect
28. #19151969	C₄	semidirect
69. C₂×Dic₃₅₆	C₂×C₄	semidirect
70. C₂×#13083564	C₂×C₄	semidirect
71. C₂×#13083563	C₂×C₄	semidirect
72. C₂×#13083563	C₂×C₄	semidirect
74. C₂×#13083561	C₂×C₄	semidirect
75. C₂×D₇₁₂	C₂×C₄	semidirect
85. #15668010	C₂×C₄	semidirect
87. #15668001	C₂×C₄	semidirect
113. #15667922	C₂×C₄	semidirect
114. #15667922	D₄	semidirect
115. C₈×Dic₈₉	C₂×C₄	semidirect
116. C₈×Dic₈₉	D₄	semidirect
326. #1977	D₈₉	semidirect
338. C₈₉	#22284	semidirect

Maximal subgroups

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

subgroup	index
#26030722	2
#26029168	2
#26029112	2
#26021150	2
#26020787	2
#26020782	2
#26020776	2
#26020771	2
#26020744	2
#26020737	2
#26020735	2
#26020728	2
#26020377	2
#26020007	2
C₈₉×#1977	2
#22284	89