Subgroups — C₄×#19151868 #36561308

Order 22784.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151868	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668037	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021162	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021037	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020914	C₂	1	2	yes	maximal, complemented
7	#26020760	C₂	1	2	yes	maximal, complemented
8	#26020316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#15667948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#15667928	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	C₂²	1	2	yes	—
13	C₂²×D₇₁₂	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₃₅₆	C₂²	1	2	yes	—
15	#19151868	C₄	1	8	yes	direct product factor
16	#19151708	—	2	2	no	—
17	#19151696	—	2	2	no	—
18	C₄×#13083561	—	2	2	no	—
19	C₄×D₇₁₂	—	2	1	no	—
20	C₄×D₇₁₂	—	2	1	no	—
21	C₄×D₇₁₂	—	2	1	no	—
22	C₄×D₇₁₂	—	2	1	no	—
23	C₄×#13083559	—	2	2	no	—
24	C₂×#15667948	C₂²	1	1	yes	characteristic
25	C₂×#15667948	C₂²	1	1	yes	characteristic
26	#19151641	C₂²	1	2	yes	—
27	C₂×#15667946	C₂²	1	1	yes	characteristic
28	#19151602	C₂²	1	2	yes	—
29	#19151599	C₂²	1	2	yes	—
30	C₂×#15667934	C₂²	1	2	yes	—
31	C₂×#15667928	C₂²	1	2	yes	—
32	C₂×#15667928	C₂²	1	2	yes	—
33	C₄×#13083558	C₂²	1	2	yes	—
34	#19151366	C₂²	1	2	yes	—
35	#19151366	C₂²	1	2	yes	—
36	#19151363	C₂²	1	2	yes	—
37	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	#405×C₈₉	—	2	1	no	—
41	#405×C₈₉	—	2	1	no	—
42	#405×C₈₉	C₂²	1	1	yes	characteristic
43	#405×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₈₉	—	2	1	no	—
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	—	2	1	no	—
47	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×D₃₅₆	C₂³	1	2	yes	—
49	C₂²×C₄×D₈₉	—	2	2	no	—
50	#15668037	—	2	4	no	—
51	#15668037	C₂×C₄	1	8	yes	complemented
52	C₂×#13083561	—	2	2	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	—	2	2	no	—
56	C₂×D₇₁₂	C₂×C₄	1	4	yes	complemented
57	C₂×#13083559	—	2	2	no	—
58	C₂×#13083558	C₂³	1	2	yes	—
59	C₂×#13083558	C₂³	1	2	yes	—
60	C₄×D₃₅₆	—	2	2	no	—
61	C₄×D₃₅₆	—	2	2	no	—
62	C₄×D₃₅₆	—	2	2	no	—
63	C₄×D₃₅₆	—	2	2	no	—
64	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
65	C₂×#13083551	—	2	2	no	—
66	#15667948	—	2	2	no	—
67	#15667948	C₂×C₄	1	4	yes	complemented
68	#15667946	—	2	1	no	—
69	#15667946	—	2	1	no	—
70	#15667945	—	2	2	no	—
71	#15667943	—	2	2	no	—
72	#15667936	—	2	2	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667933	—	2	2	no	—
76	#15667932	—	2	2	no	—
77	#15667932	—	2	2	no	—
78	#15667928	—	2	4	no	—
79	#15667928	C₂×C₄	1	8	yes	complemented
80	#15667923	—	2	2	no	—
81	C₄×#10623494	—	2	2	no	—
82	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
83	#131×C₈₉	—	2	2	no	—
84	#131×C₈₉	—	2	2	no	—
85	#131×C₈₉	—	2	2	no	—
86	#131×C₈₉	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₈₉	—	2	1	no	—
88	C₂×M₁₆×C₈₉	—	2	1	no	—
89	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	—	2	1	no	—
92	C₂²×C₈×C₈₉	—	2	1	no	—
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
97	C₄×D₄×C₈₉	—	2	1	no	—
98	C₄×D₄×C₈₉	—	2	1	no	—
99	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
100	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
101	#117×C₈₉	—	2	1	no	—
102	#117×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	—	2	1	no	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	#97×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	#97×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	—	2	1	no	—
110	C₄×C₈×C₈₉	—	2	1	no	—
111	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
114	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
115	C₂³×D₈₉	—	2	2	no	—
116	C₂×D₃₅₆	—	2	2	no	—
117	C₂×D₃₅₆	—	2	2	no	—
118	C₂×D₃₅₆	—	2	2	no	—
119	C₂×D₃₅₆	—	2	2	no	—
120	C₂×D₃₅₆	—	2	2	no	—
121	C₂×D₃₅₆	C₂²×C₄	1	4	yes	—
122	C₂²×Dic₈₉	—	2	2	no	—
123	C₂×C₄×D₈₉	—	4	2	no	—
124	C₂×C₄×D₈₉	—	4	2	no	—
125	C₂×C₄×D₈₉	—	8	4	no	—
126	#13083561	—	2	8	no	—
127	D₇₁₂	—	2	4	no	—
128	D₇₁₂	—	2	4	no	—
129	#13083559	—	2	8	no	—
130	#13083558	—	2	2	no	—
131	#13083558	—	2	2	no	—
132	#13083558	—	2	2	no	—
133	#13083558	C₂²×C₄	1	4	yes	—
134	C₂×#10623494	—	2	2	no	—
135	C₂×#10623494	—	2	2	no	—
136	C₄⋊Dic₈₉	—	2	2	no	—
137	C₄⋊Dic₈₉	—	2	2	no	—
138	#13083551	—	4	2	no	—
139	#13083551	—	4	2	no	—
140	#41×C₈₉	—	2	1	no	—
141	#41×C₈₉	—	2	1	no	—
142	#41×C₈₉	C₂²×C₄	1	2	yes	—
143	#41×C₈₉	#41	1	2	yes	—
144	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	M₁₆×C₈₉	—	2	4	no	—
154	M₁₆×C₈₉	—	2	1	no	—
155	M₁₆×C₈₉	—	2	1	no	—
156	M₁₆×C₈₉	—	2	4	no	—
157	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
158	M₁₆×C₈₉	#41	1	2	yes	—
159	C₂×C₈×C₈₉	—	2	4	no	—
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	—	2	4	no	—
165	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₈₉	#41	1	2	yes	—
171	C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂²⋊C₄×C₈₉	—	2	1	no	—
176	C₂²⋊C₄×C₈₉	—	2	1	no	—
177	C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₄²×C₈₉	—	2	1	no	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₄²×C₈₉	—	2	1	no	—
181	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₈₉	—	2	1	no	—
186	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂²×D₈₉	—	2	4	no	—
188	C₂²×D₈₉	—	4	2	no	—
189	C₂²×D₈₉	—	4	2	no	—
190	C₂²×D₈₉	—	8	2	no	—
191	C₂²×D₈₉	—	8	2	no	—
192	Q₈×C₈₉	—	2	1	no	—
193	Q₈×C₈₉	C₄×D₄	1	2	yes	—
194	D₄×C₈₉	—	2	2	no	—
195	D₄×C₈₉	—	2	2	no	—
196	D₄×C₈₉	—	2	1	no	—
197	D₄×C₈₉	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	2	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	4	2	no	—
206	C₂×C₄×C₈₉	—	4	2	no	—
207	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂²×D₄	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	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
217	C₂×Dic₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	8	2	no	—
219	D₃₅₆	—	2	4	no	—
220	D₃₅₆	—	2	4	no	—
221	D₃₅₆	—	4	2	no	—
222	D₃₅₆	—	4	2	no	—
223	C₄×D₈₉	—	8	4	no	—
224	C₄×D₈₉	—	8	4	no	—
225	C₈×C₈₉	—	2	2	no	—
226	C₈×C₈₉	—	2	1	no	—
227	C₈×C₈₉	—	2	2	no	—
228	C₈×C₈₉	—	2	1	no	—
229	C₈×C₈₉	C₄×D₄	1	2	yes	—
230	C₈×C₈₉	C₄×D₄	1	2	yes	—
231	#10623494	—	2	4	no	—
232	#10623494	—	4	2	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	—	2	1	no	—
235	C₂²×C₈₉	—	2	2	no	—
236	C₂²×C₈₉	—	4	1	no	—
237	C₂²×C₈₉	—	4	1	no	—
238	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
239	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
240	C₂²×C₈₉	#529	1	1	yes	characteristic
241	C₂×D₈₉	—	4	4	no	—
242	C₂×D₈₉	—	8	4	no	—
243	C₂×D₈₉	—	8	2	no	—
244	C₂×D₈₉	—	8	2	no	—
245	C₂×D₈₉	—	8	4	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	2	1	no	—
248	C₄×C₈₉	—	2	1	no	—
249	C₄×C₈₉	—	2	2	no	—
250	C₄×C₈₉	—	4	1	no	—
251	C₄×C₈₉	—	4	1	no	—
252	C₄×C₈₉	#472	1	2	yes	complemented
253	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₈₉	#525	1	1	yes	characteristic
256	C₄×C₈₉	#532	1	1	yes	characteristic
257	Dic₈₉	—	8	2	no	—
258	C₄×#472	—	89	1	no	maximal, Sylow
259	C₂×C₈₉	—	2	1	no	—
260	C₂×C₈₉	—	2	1	no	—
261	C₂×C₈₉	—	4	2	no	—
262	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
263	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
264	C₂×C₈₉	#3067	1	1	yes	characteristic
265	D₈₉	—	8	4	no	—
266	C₂×#472	—	89	1	no	—
267	C₄×AGL(1,ℤ/8)	—	89	2	no	—
268	C₂×C₄×D₈	—	89	1	no	—
269	C₄×#131	D₈₉	1	1	yes	characteristic, complemented
270	#1978	—	89	1	no	—
271	#1952	—	89	1	no	—
272	#1931	—	89	2	no	—
273	#1907	—	89	2	no	—
274	#1816	—	89	1	no	—
275	C₄×#108	—	89	1	no	—
276	C₄×#100	—	89	2	no	—
277	C₈₉	C₄×#472	1	1	yes	characteristic, complemented, Sylow
278	C₂×AGL(1,ℤ/8)	—	89	2	no	—
279	C₂²×D₈	—	89	1	no	—
280	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
281	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
282	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
283	C₂×C₄×D₄	—	89	2	no	—
284	#472	—	89	8	no	—
285	#442	—	178	2	no	—
286	#440	—	178	2	no	—
287	C₄×SD₁₆	—	178	2	no	—
288	C₄×D₈	—	178	2	no	—
289	C₄×D₈	—	178	1	no	—
290	C₄×D₈	—	178	1	no	—
291	C₄×D₈	—	178	1	no	—
292	C₄×D₈	—	178	1	no	—
293	C₂×#108	—	89	1	no	—
294	C₂×#108	—	89	1	no	—
295	#428	—	89	2	no	—
296	C₂×#107	—	89	1	no	—
297	#418	—	89	2	no	—
298	#417	—	89	2	no	—
299	C₂×#102	—	89	2	no	—
300	C₂×#100	—	89	2	no	—
301	C₂×#100	—	89	2	no	—
302	#405	—	2	1	no	—
303	#405	—	2	1	no	—
304	#405	C₂×D₈₉	1	1	yes	characteristic
305	#405	C₂×D₈₉	1	1	yes	characteristic
306	C₄×M₁₆	—	2	1	no	—
307	C₄×M₁₆	—	89	2	no	—
308	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
309	C₂×C₄×C₈	—	2	1	no	—
310	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
311	#343	—	89	2	no	—
312	#343	—	89	2	no	—
313	#341	—	89	2	no	—
314	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
315	C₂²×D₄	—	89	2	no	—
316	C₂³×C₄	—	178	2	no	—
317	AGL(1,ℤ/8)	—	89	8	no	—
318	AGL(1,ℤ/8)	—	178	4	no	—
319	C₂×SD₁₆	—	178	2	no	—
320	C₂×D₈	—	89	4	no	—
321	C₂×D₈	—	178	2	no	—
322	C₂×D₈	—	178	1	no	—
323	C₂×D₈	—	178	1	no	—
324	C₂×D₈	—	178	2	no	—
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	#131	—	2	2	no	—
328	#131	C₄×D₈₉	1	4	yes	complemented
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	89	2	no	—
332	C₂×M₁₆	—	89	2	no	—
333	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
338	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
339	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
340	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	178	2	no	—
344	C₄×D₄	—	178	2	no	—
345	C₄×D₄	—	178	2	no	—
346	C₄×D₄	—	178	2	no	—
347	C₄×D₄	D₃₅₆	1	1	yes	characteristic
348	C₄×D₄	D₃₅₆	1	1	yes	characteristic
349	#117	—	2	1	no	—
350	#117	C₂²×D₈₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	—	89	2	no	—
352	C₂×C₂²⋊C₄	—	178	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
355	#108	—	89	4	no	—
356	#108	—	178	2	no	—
357	#107	—	178	1	no	—
358	#107	—	178	1	no	—
359	#107	—	178	2	no	—
360	#106	—	178	2	no	—
361	#103	—	178	2	no	—
362	#102	—	178	2	no	—
363	#102	—	178	2	no	—
364	#102	—	178	2	no	—
365	#102	—	178	2	no	—
366	#102	—	178	2	no	—
367	#100	—	89	8	no	—
368	#100	—	178	4	no	—
369	#97	—	2	1	no	—
370	#97	—	2	1	no	—
371	#97	—	2	1	no	—
372	#97	—	178	2	no	—
373	C₄×C₈	—	2	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	—	178	2	no	—
377	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
378	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
379	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
380	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂⁴	—	178	2	no	—
382	#41	—	2	1	no	—
383	#41	—	2	1	no	—
384	#41	C₂×C₄×D₈₉	1	2	yes	—
385	#41	#13083574	1	2	yes	—
386	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	89	4	no	—
389	C₂×D₄	—	178	2	no	—
390	C₂×D₄	—	178	2	no	—
391	C₂×D₄	—	178	2	no	—
392	C₂×D₄	—	178	2	no	—
393	C₂×D₄	—	178	2	no	—
394	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	356	2	no	—
399	C₂²×C₄	—	356	2	no	—
400	C₂²×C₄	—	178	2	no	—
401	C₂²×C₄	—	712	4	no	—
402	C₂²×C₄	#13083574	1	1	yes	characteristic
403	C₂²×C₄	#13083574	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
405	SD₁₆	—	178	8	no	—
406	D₈	—	178	8	no	—
407	D₈	—	178	4	no	—
408	D₈	—	178	4	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	1	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	2	4	no	—
413	M₁₆	—	89	4	no	—
414	M₁₆	—	178	2	no	—
415	M₁₆	—	178	2	no	—
416	M₁₆	—	178	2	no	—
417	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
418	M₁₆	#13083574	1	2	yes	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	4	no	—
425	C₂×C₈	—	178	2	no	—
426	C₂×C₈	—	178	2	no	—
427	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
428	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂×C₈	#13083574	1	2	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	178	2	no	—
436	C₄⋊C₄	—	178	2	no	—
437	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
438	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	356	2	no	—
443	C₂²⋊C₄	—	356	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
450	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
451	C₂³	—	2	1	no	—
452	C₂³	—	356	2	no	—
453	C₂³	—	356	2	no	—
454	C₂³	—	178	4	no	—
455	C₂³	—	712	2	no	—
456	C₂³	—	712	2	no	—
457	C₂³	C₂×#13083574	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	C₄×D₃₅₆	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	356	2	no	—
464	D₄	—	356	2	no	—
465	D₄	—	178	4	no	—
466	D₄	—	178	4	no	—
467	D₄	C₄×D₃₅₆	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	356	2	no	—
478	C₂×C₄	—	712	4	no	—
479	C₂×C₄	—	712	4	no	—
480	C₂×C₄	—	712	2	no	—
481	C₂×C₄	#15667986	1	1	yes	characteristic
482	C₂×C₄	#15667986	1	1	yes	characteristic
483	C₂×C₄	#15667986	1	1	yes	characteristic
484	C₂×C₄	#15667986	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
488	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
489	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
490	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	1	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	1	no	—
495	C₈	—	356	2	no	—
496	C₈	—	178	4	no	—
497	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
498	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	356	4	no	—
505	C₂²	—	712	4	no	—
506	C₂²	—	712	4	no	—
507	C₂²	—	712	2	no	—
508	C₂²	—	712	2	no	—
509	C₂²	C₄×#13083574	1	1	yes	characteristic
510	C₂²	C₂×#15667986	1	1	yes	characteristic
511	C₂²	#19152132	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	712	2	no	—
519	C₄	#19151868	1	2	yes	direct product factor
520	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
521	C₄	C₂×C₄×D₃₅₆	1	1	yes	characteristic
522	C₄	#19152109	1	1	yes	characteristic
523	C₄	#19152148	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	712	4	no	—
528	C₂	C₄×#15667986	1	1	yes	characteristic
529	C₂	C₂×#19151868	1	1	yes	characteristic
530	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667986
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#131×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#19151868	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#131	D₈₉
hypocenter	C₈₉	C₄×#472
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₄×#15668037	C₂	semidirect
3. C₂×C₄×D₇₁₂	C₂	semidirect
4. #26021162	C₂	semidirect
5. #26021037	C₂	semidirect
6. #26020914	C₂	semidirect
7. #26020760	C₂	semidirect
8. #26020316	C₂	semidirect
9. C₄×#15667948	C₂	semidirect
10. C₄×#15667928	C₂	semidirect
11. C₄×#131×C₈₉	C₂	semidirect
15. #19151868	C₄	direct (N × H)
51. #15668037	C₂×C₄	semidirect
56. C₂×D₇₁₂	C₂×C₄	semidirect
67. #15667948	C₂×C₄	semidirect
79. #15667928	C₂×C₄	semidirect
86. #131×C₈₉	C₂×C₄	semidirect
252. C₄×C₈₉	#472	semidirect
269. C₄×#131	D₈₉	semidirect
277. C₈₉	C₄×#472	semidirect
328. #131	C₄×D₈₉	semidirect
519. C₄	#19151868	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19151868	2
C₄×#15668037	2
C₂×C₄×D₇₁₂	2
#26021162	2
#26021037	2
#26020914	2
#26020760	2
#26020316	2
C₄×#15667948	2
C₄×#15667928	2
C₄×#131×C₈₉	2
C₄×#472	89

Subgroups — C4×#19151868 #36561308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151868 #36561308