Subgroups — #36560874

Order 22784.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029709	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151716	C₂	1	2	yes	maximal, complemented
3	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#15668018	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021170	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020901	C₂	1	2	yes	maximal, complemented
8	#26020578	C₂	1	2	yes	maximal, complemented
9	#26020273	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020089	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	2	yes	—
13	C₂×#15668018	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	1	yes	characteristic
15	C₂×#15668018	C₂²	1	1	yes	characteristic
16	#19152148	C₂²	1	1	yes	characteristic
17	C₄×#13083574	C₂²	1	1	yes	characteristic
18	#19151821	C₄	1	2	yes	complemented
19	#19151814	C₄	1	2	yes	complemented
20	#19151809	C₄	1	1	yes	characteristic, complemented
21	#19151804	C₄	1	1	yes	characteristic, complemented
22	#19151799	C₄	1	1	yes	characteristic, complemented
23	#19151794	C₄	1	1	yes	characteristic, complemented
24	#19151716	—	2	8	no	—
25	#19151677	—	2	1	no	—
26	#19151677	—	2	1	no	—
27	C₈×D₃₅₆	—	2	1	no	—
28	C₈×D₃₅₆	—	2	1	no	—
29	C₂×#15667948	C₂²	1	2	yes	—
30	#19151622	C₂²	1	1	yes	characteristic
31	C₂×#15667940	C₂²	1	2	yes	—
32	C₂×#15667940	C₂²	1	2	yes	—
33	C₂×#15667940	C₂²	1	2	yes	—
34	#19151595	C₂²	1	2	yes	—
35	#19151564	C₂²	1	2	yes	—
36	#19151553	C₂²	1	1	yes	characteristic
37	#19151553	C₂²	1	1	yes	characteristic
38	#19151552	—	2	1	no	—
39	#19151552	—	2	1	no	—
40	C₄×#13083558	C₂²	1	1	yes	characteristic
41	C₄×#13083557	—	2	1	no	—
42	C₄×C₈×D₈₉	—	2	1	no	—
43	#19151363	C₂²	1	2	yes	—
44	#19151358	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
49	#336×C₈₉	C₂²	1	2	yes	—
50	C₂×#13083574	C₂³	1	2	yes	—
51	C₂×#13083574	C₂³	1	1	yes	characteristic
52	#15668034	—	2	4	no	—
53	#15668034	—	2	4	no	—
54	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
55	C₂×#13083563	C₂×C₄	1	2	yes	—
56	C₂×#13083563	C₂×C₄	1	2	yes	—
57	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
58	#15668018	—	2	2	no	—
59	#15668018	—	2	2	no	—
60	#15668018	—	2	4	no	—
61	#15668018	—	2	2	no	—
62	#15668018	—	2	4	no	—
63	#15668018	D₄	1	4	yes	complemented
64	C₂×#13083558	C₂³	1	2	yes	—
65	C₂×#13083558	C₂³	1	1	yes	characteristic
66	C₂×#13083558	C₂³	1	1	yes	characteristic
67	C₂×#13083557	—	2	1	no	—
68	C₂×#13083557	—	2	1	no	—
69	C₂×#13083557	—	2	2	no	—
70	C₂×C₈×D₈₉	—	2	1	no	—
71	C₂×C₈×D₈₉	—	2	1	no	—
72	C₂×C₈×D₈₉	—	2	2	no	—
73	#15668012	C₂×C₄	1	1	yes	characteristic
74	#15668009	C₂×C₄	1	1	yes	characteristic
75	#15668000	C₂×C₄	1	2	yes	—
76	#15667986	—	2	1	no	—
77	#15667986	—	2	1	no	—
78	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
80	C₄×D₃₅₆	—	2	1	no	—
81	C₄×D₃₅₆	—	2	1	no	—
82	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
83	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₈₉	—	2	1	no	—
85	C₄×C₂²⋊D₈₉	—	2	1	no	—
86	#15667971	C₂³	1	1	yes	characteristic
87	#15667969	—	2	1	no	—
88	C₄²×D₈₉	—	2	1	no	—
89	#15667948	—	2	4	no	—
90	C₄⋊#10623494	—	2	1	no	—
91	C₄⋊#10623494	—	2	1	no	—
92	#15667940	—	2	4	no	—
93	#15667940	—	2	4	no	—
94	#15667940	—	2	4	no	—
95	#15667937	C₂×C₄	1	2	yes	—
96	#15667937	C₂×C₄	1	2	yes	—
97	#15667934	C₂×C₄	1	2	yes	—
98	#15667934	C₂×C₄	1	2	yes	—
99	#15667924	—	2	2	no	—
100	#15667924	—	2	2	no	—
101	#15667923	—	2	1	no	—
102	#15667922	—	2	1	no	—
103	#15667922	—	2	1	no	—
104	C₄×#10623494	—	2	1	no	—
105	C₈×Dic₈₉	—	2	1	no	—
106	C₈×Dic₈₉	—	2	1	no	—
107	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
116	C₄×C₈×C₈₉	—	2	4	no	—
117	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
118	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
119	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
120	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
121	#95×C₈₉	—	2	1	no	—
122	#13083574	—	2	1	no	—
123	#13083574	—	2	1	no	—
124	#13083574	—	2	2	no	—
125	#13083574	—	2	2	no	—
126	#13083574	—	2	2	no	—
127	#13083574	—	2	2	no	—
128	#13083574	C₂×D₄	1	2	yes	—
129	#13083574	#41	1	2	yes	—
130	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
131	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₃₅₆	—	2	1	no	—
133	C₂×D₃₅₆	—	2	1	no	—
134	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
135	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊D₈₉	—	2	1	no	—
137	C₂×C₂²⋊D₈₉	—	2	2	no	—
138	C₂×C₄×D₈₉	—	2	1	no	—
139	C₂×C₄×D₈₉	—	2	1	no	—
140	C₂×C₄×D₈₉	—	2	1	no	—
141	C₂×C₄×D₈₉	—	2	2	no	—
142	Dic₃₅₆	—	2	4	no	—
143	#13083563	—	2	4	no	—
144	#13083563	—	2	4	no	—
145	D₇₁₂	—	2	4	no	—
146	#13083558	—	2	1	no	—
147	#13083558	—	2	1	no	—
148	#13083558	—	2	2	no	—
149	#13083558	—	2	2	no	—
150	#13083558	C₂×D₄	1	2	yes	—
151	#13083558	#41	1	2	yes	—
152	#13083557	—	2	4	no	—
153	#13083557	—	2	4	no	—
154	#13083557	—	4	4	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	2	no	—
158	C₈×D₈₉	—	2	4	no	—
159	C₈×D₈₉	—	2	4	no	—
160	C₈×D₈₉	—	4	4	no	—
161	C₄⋊Dic₈₉	—	2	1	no	—
162	C₄⋊Dic₈₉	—	2	1	no	—
163	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
165	#13083553	—	2	1	no	—
166	#13083553	—	2	1	no	—
167	C₂²⋊Dic₈₉	—	2	1	no	—
168	#13083551	—	2	1	no	—
169	#13083551	—	2	1	no	—
170	#13083551	—	2	2	no	—
171	#13083551	—	2	2	no	—
172	C₄×Dic₈₉	—	2	1	no	—
173	C₄×Dic₈₉	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	2	no	—
176	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₈₉	—	2	2	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	2	no	—
183	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
185	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	#41	1	2	yes	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄²×C₈₉	—	2	2	no	—
193	C₄²×C₈₉	—	2	2	no	—
194	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂²×D₈₉	—	2	1	no	—
200	C₂²×D₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	2	no	—
202	C₂×C₄×C₈₉	—	2	4	no	—
203	C₂×C₄×C₈₉	—	4	1	no	—
204	C₂×C₄×C₈₉	—	4	2	no	—
205	C₂×C₄×C₈₉	—	4	2	no	—
206	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
216	C₂²⋊D₈₉	—	2	2	no	—
217	C₂²⋊D₈₉	—	2	2	no	—
218	C₂²⋊D₈₉	—	4	2	no	—
219	C₂²⋊D₈₉	—	4	2	no	—
220	C₂×Dic₈₉	—	2	1	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	2	1	no	—
223	C₂×Dic₈₉	—	2	2	no	—
224	D₃₅₆	—	2	2	no	—
225	D₃₅₆	—	2	1	no	—
226	D₃₅₆	—	2	2	no	—
227	D₃₅₆	—	4	2	no	—
228	D₃₅₆	—	4	2	no	—
229	D₃₅₆	C₄×D₄	1	2	yes	—
230	C₄×D₈₉	—	2	2	no	—
231	C₄×D₈₉	—	2	2	no	—
232	C₄×D₈₉	—	4	2	no	—
233	C₄×D₈₉	—	4	2	no	—
234	C₄×D₈₉	—	4	2	no	—
235	C₄×D₈₉	—	4	2	no	—
236	Dic₁₇₈	—	2	1	no	—
237	Dic₁₇₈	—	2	2	no	—
238	Dic₁₇₈	—	2	2	no	—
239	Dic₁₇₈	C₄×D₄	1	2	yes	—
240	C₈×C₈₉	—	2	2	no	—
241	C₈×C₈₉	—	2	2	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	#121	1	2	yes	—
245	C₈×C₈₉	#121	1	2	yes	—
246	#10623494	—	2	2	no	—
247	#10623494	—	2	2	no	—
248	#10623494	—	4	2	no	—
249	C₂²×C₈₉	—	2	1	no	—
250	C₂²×C₈₉	—	2	1	no	—
251	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₈₉	#529	1	1	yes	characteristic
253	C₂²×C₈₉	#532	1	1	yes	characteristic
254	C₂×D₈₉	—	2	2	no	—
255	C₂×D₈₉	—	4	1	no	—
256	C₂×D₈₉	—	4	1	no	—
257	C₂×D₈₉	—	4	2	no	—
258	C₂×D₈₉	—	4	2	no	—
259	C₂×D₈₉	—	4	2	no	—
260	C₄×C₈₉	—	2	1	no	—
261	C₄×C₈₉	—	2	1	no	—
262	C₄×C₈₉	—	2	1	no	—
263	C₄×C₈₉	—	4	4	no	—
264	C₄×C₈₉	#443	1	2	yes	complemented
265	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
266	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
267	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
268	C₄×C₈₉	#525	1	1	yes	characteristic
269	Dic₈₉	—	2	2	no	—
270	Dic₈₉	—	4	1	no	—
271	Dic₈₉	—	4	1	no	—
272	Dic₈₉	—	4	2	no	—
273	#21517	—	89	1	no	maximal, Sylow
274	C₂×C₈₉	—	2	1	no	—
275	C₂×C₈₉	—	2	1	no	—
276	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
277	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
278	C₂×C₈₉	#2955	1	1	yes	characteristic
279	D₈₉	—	4	2	no	—
280	D₈₉	—	8	2	no	—
281	#3035	—	89	1	no	—
282	C₂×#443	—	89	2	no	—
283	#2931	—	89	1	no	—
284	C₄×#131	—	89	1	no	—
285	#1980	—	89	1	no	—
286	#1950	—	89	1	no	—
287	#1929	—	89	2	no	—
288	#1876	—	89	2	no	—
289	#1806	—	89	1	no	—
290	C₈×C₄⋊C₄	D₈₉	1	1	yes	characteristic, complemented
291	#1764	—	89	2	no	—
292	C₈₉	#21517	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	—	89	2	no	—
294	C₂×#131	—	89	1	no	—
295	C₂×#131	—	89	1	no	—
296	C₂×#131	—	89	2	no	—
297	#532	—	89	1	no	—
298	C₄×#41	—	89	1	no	—
299	#464	—	89	2	no	—
300	#463	—	89	2	no	—
301	#462	—	89	1	no	—
302	#461	—	89	1	no	—
303	#460	—	89	1	no	—
304	#459	—	89	1	no	—
305	#443	—	178	8	no	—
306	#436	—	178	1	no	—
307	#436	—	178	1	no	—
308	C₈×D₄	—	178	1	no	—
309	C₈×D₄	—	178	1	no	—
310	C₂×#108	—	89	2	no	—
311	#423	—	89	1	no	—
312	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
313	C₂×#104	—	89	2	no	—
314	C₂×#104	—	89	2	no	—
315	C₂×#104	—	89	2	no	—
316	#416	—	89	2	no	—
317	#408	—	89	2	no	—
318	#405	—	89	1	no	—
319	#405	—	89	1	no	—
320	#405	—	178	1	no	—
321	#405	—	178	1	no	—
322	C₄×M₁₆	—	89	1	no	—
323	C₄×M₁₆	—	178	1	no	—
324	C₂×C₄×C₈	—	178	1	no	—
325	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
326	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
328	#341	—	89	2	no	—
329	#339	—	89	2	no	—
330	#336	C₂×D₈₉	1	2	yes	—
331	C₂×#41	—	89	1	no	—
332	C₂×#41	—	89	2	no	—
333	#135	—	178	4	no	—
334	#135	—	178	4	no	—
335	C₂×Q₁₆	—	89	2	no	—
336	C₂×SD₁₆	—	89	2	no	—
337	C₂×SD₁₆	—	89	2	no	—
338	C₂×D₈	—	89	2	no	—
339	#131	—	89	4	no	—
340	#131	—	178	2	no	—
341	#131	—	178	2	no	—
342	#131	—	178	4	no	—
343	#131	—	178	4	no	—
344	#131	—	178	2	no	—
345	C₂×M₁₆	—	89	1	no	—
346	C₂×M₁₆	—	89	1	no	—
347	C₂×M₁₆	—	89	2	no	—
348	C₂×M₁₆	—	178	2	no	—
349	C₂×M₁₆	—	178	1	no	—
350	C₂×M₁₆	—	178	1	no	—
351	C₂²×C₈	—	178	2	no	—
352	C₂²×C₈	—	178	1	no	—
353	C₂²×C₈	—	178	1	no	—
354	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
355	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	C₄⋊Q₈	—	89	1	no	—
358	#127	—	89	1	no	—
359	#124	—	89	2	no	—
360	#121	—	178	1	no	—
361	#121	—	178	1	no	—
362	C₄×Q₈	—	89	1	no	—
363	C₄×Q₈	—	89	1	no	—
364	C₄×D₄	—	89	1	no	—
365	C₄×D₄	—	89	1	no	—
366	C₄×D₄	—	178	1	no	—
367	C₄×D₄	—	178	1	no	—
368	C₄×D₄	—	178	1	no	—
369	C₄×D₄	—	178	1	no	—
370	#117	—	89	1	no	—
371	#117	—	178	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	178	1	no	—
374	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
375	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
376	#108	—	178	4	no	—
377	C₄⋊C₈	—	178	1	no	—
378	C₄⋊C₈	—	178	1	no	—
379	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
380	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
381	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
382	#104	—	178	4	no	—
383	#104	—	178	4	no	—
384	#104	—	178	4	no	—
385	#103	—	89	2	no	—
386	#103	—	89	2	no	—
387	#102	—	89	2	no	—
388	#102	—	89	2	no	—
389	C₂²⋊C₈	—	178	2	no	—
390	C₂²⋊C₈	—	178	2	no	—
391	#97	—	178	1	no	—
392	#97	—	178	1	no	—
393	#97	—	178	1	no	—
394	C₄×C₈	—	2	4	no	—
395	C₄×C₈	—	178	1	no	—
396	C₄×C₈	—	178	1	no	—
397	C₄×C₈	—	178	1	no	—
398	C₄×C₈	D₃₅₆	1	1	yes	characteristic
399	C₄×C₈	D₃₅₆	1	1	yes	characteristic
400	C₄×C₈	D₃₅₆	1	1	yes	characteristic
401	C₄×C₈	D₃₅₆	1	1	yes	characteristic
402	#95	—	2	1	no	—
403	#41	—	89	2	no	—
404	#41	—	89	2	no	—
405	#41	—	178	2	no	—
406	#41	—	178	2	no	—
407	#41	—	178	2	no	—
408	#41	—	178	2	no	—
409	#41	—	178	1	no	—
410	#41	—	178	1	no	—
411	C₂×Q₈	—	89	1	no	—
412	C₂×Q₈	—	89	2	no	—
413	C₂×D₄	—	89	1	no	—
414	C₂×D₄	—	89	2	no	—
415	C₂×D₄	—	178	2	no	—
416	C₂×D₄	—	178	1	no	—
417	C₂×D₄	—	178	1	no	—
418	C₂×D₄	—	178	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	178	1	no	—
421	C₂²×C₄	—	178	1	no	—
422	C₂²×C₄	—	178	2	no	—
423	C₂²×C₄	—	178	1	no	—
424	C₂²×C₄	#13083574	1	1	yes	characteristic
425	C₂²×C₄	#13083574	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
427	Q₁₆	—	178	4	no	—
428	SD₁₆	—	178	4	no	—
429	SD₁₆	—	178	4	no	—
430	D₈	—	178	4	no	—
431	M₁₆	—	89	2	no	—
432	M₁₆	—	89	2	no	—
433	M₁₆	—	356	4	no	—
434	M₁₆	—	178	4	no	—
435	M₁₆	—	178	2	no	—
436	M₁₆	—	178	2	no	—
437	M₁₆	—	178	1	no	—
438	M₁₆	—	178	1	no	—
439	M₁₆	—	178	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	356	4	no	—
445	C₂×C₈	—	178	4	no	—
446	C₂×C₈	—	178	2	no	—
447	C₂×C₈	—	178	1	no	—
448	C₂×C₈	—	178	1	no	—
449	C₂×C₈	—	178	4	no	—
450	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
451	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
452	C₂×C₈	D₄×D₈₉	1	2	yes	—
453	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
454	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
455	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
456	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
457	C₂×C₈	#13083575	1	2	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	89	1	no	—
460	C₄⋊C₄	—	89	1	no	—
461	C₄⋊C₄	—	178	1	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₂²⋊C₄	—	178	1	no	—
466	C₂²⋊C₄	—	178	1	no	—
467	C₂²⋊C₄	—	178	1	no	—
468	C₂²⋊C₄	—	178	2	no	—
469	C₂²⋊C₄	—	178	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	178	1	no	—
473	C₄²	—	178	1	no	—
474	C₄²	—	178	1	no	—
475	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
477	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
478	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
479	C₂³	—	178	2	no	—
480	C₂³	—	178	1	no	—
481	C₂³	C₂×#13083574	1	1	yes	characteristic
482	Q₈	—	89	2	no	—
483	Q₈	—	178	2	no	—
484	Q₈	—	178	2	no	—
485	Q₈	—	178	1	no	—
486	D₄	—	89	2	no	—
487	D₄	—	356	2	no	—
488	D₄	—	356	2	no	—
489	D₄	—	356	2	no	—
490	D₄	—	356	2	no	—
491	D₄	—	178	2	no	—
492	D₄	—	178	2	no	—
493	D₄	—	178	2	no	—
494	D₄	—	178	2	no	—
495	D₄	—	178	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	356	2	no	—
502	C₂×C₄	—	356	2	no	—
503	C₂×C₄	—	356	2	no	—
504	C₂×C₄	—	356	2	no	—
505	C₂×C₄	—	178	1	no	—
506	C₂×C₄	—	178	1	no	—
507	C₂×C₄	—	178	2	no	—
508	C₂×C₄	—	178	1	no	—
509	C₂×C₄	—	178	2	no	—
510	C₂×C₄	—	178	2	no	—
511	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
512	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
513	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
514	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
518	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
519	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	356	2	no	—
526	C₈	—	178	2	no	—
527	C₈	—	178	2	no	—
528	C₈	#15667987	1	2	yes	—
529	C₈	#15667987	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	356	1	no	—
533	C₂²	—	356	1	no	—
534	C₂²	—	356	2	no	—
535	C₂²	—	356	2	no	—
536	C₂²	—	356	2	no	—
537	C₂²	—	178	2	no	—
538	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
539	C₂²	#19152135	1	1	yes	characteristic
540	C₂²	#19152145	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	4	no	—
545	C₄	—	356	1	no	—
546	C₄	—	356	1	no	—
547	C₄	—	356	2	no	—
548	C₄	—	178	2	no	—
549	C₄	#19151716	1	2	yes	complemented
550	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
551	C₄	C₄×#13083575	1	1	yes	characteristic
552	C₄	C₂×#15667987	1	1	yes	characteristic
553	C₄	#19152110	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	356	2	no	—
557	C₂	—	712	2	no	—
558	C₂	C₄×#15667987	1	1	yes	characteristic
559	C₂	C₂×#19151716	1	1	yes	characteristic
560	C₂	#26029156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈×C₄⋊C₄×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26029709	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₈₉
hypocenter	C₈₉	#21517
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#19151716	C₂	semidirect
3. #26028965	C₂	semidirect
4. C₄×#15668018	C₂	semidirect
5. #26021170	C₂	semidirect
6. #26021028	C₂	semidirect
7. #26020901	C₂	semidirect
8. #26020578	C₂	semidirect
9. #26020273	C₂	semidirect
10. #26020089	C₂	semidirect
11. C₈×C₄⋊C₄×C₈₉	C₂	semidirect
18. #19151821	C₄	semidirect
19. #19151814	C₄	semidirect
20. #19151809	C₄	semidirect
21. #19151804	C₄	semidirect
22. #19151799	C₄	semidirect
23. #19151794	C₄	semidirect
63. #15668018	D₄	semidirect
264. C₄×C₈₉	#443	semidirect
290. C₈×C₄⋊C₄	D₈₉	semidirect
292. C₈₉	#21517	semidirect
549. C₄	#19151716	semidirect

Maximal subgroups

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

subgroup	index
#26029709	2
C₂×#19151716	2
#26028965	2
C₄×#15668018	2
#26021170	2
#26021028	2
#26020901	2
#26020578	2
#26020273	2
#26020089	2
C₈×C₄⋊C₄×C₈₉	2
#21517	89