Subgroups — C₂×#26020494 #36555327

Order 22784.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152365	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151647	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151622	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151615	C₂	1	1	yes	maximal, characteristic
5	#26020494	C₂	1	8	yes	maximal, direct product factor
6	C₂×#19151370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₈₉	C₂	1	1	yes	maximal, characteristic
9	#19152365	—	2	2	no	—
10	#19152365	—	2	2	no	—
11	#19152365	—	2	2	no	—
12	#19152365	C₂²	1	4	yes	—
13	C₂×#15668019	—	2	2	no	—
14	C₂×#15668019	—	2	2	no	—
15	C₂²×#13083558	—	2	2	no	—
16	C₂²×#13083558	C₂²	1	1	yes	characteristic
17	C₂²×#13083558	C₂²	1	1	yes	characteristic
18	C₂²×#13083558	C₂²	1	1	yes	characteristic
19	C₂×#15667971	C₂²	1	1	yes	characteristic
20	#19151647	—	2	2	no	—
21	#19151647	C₂²	1	4	yes	complemented
22	C₂×#15667948	—	2	2	no	—
23	#19151622	—	2	2	no	—
24	#19151622	C₂²	1	4	yes	complemented
25	C₂×C₄⋊#10623494	—	2	2	no	—
26	#19151615	—	2	2	no	—
27	#19151615	C₂²	1	4	yes	—
28	C₂×#15667939	—	2	2	no	—
29	#19151370	C₂²	1	4	yes	complemented
30	#19151358	C₂²	1	4	yes	complemented
31	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#104×C₈₉	C₄	1	2	yes	complemented
35	C₂×#104×C₈₉	C₄	1	4	yes	complemented
36	C₂×#104×C₈₉	C₄	1	2	yes	complemented
37	C₂×#104×C₈₉	C₂²	1	4	yes	—
38	#15668019	—	2	8	no	—
39	#15668019	—	2	8	no	—
40	#15668019	—	2	8	no	—
41	#15668019	—	2	8	no	—
42	C₂×#13083558	—	2	4	no	—
43	C₂×#13083558	—	2	8	no	—
44	C₂×#13083558	—	2	8	no	—
45	C₂×#13083558	—	2	1	no	—
46	C₂×#13083558	—	2	1	no	—
47	C₂×#13083558	—	2	1	no	—
48	C₂×#13083558	—	2	1	no	—
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083558	—	2	1	no	—
54	C₂×#13083558	—	2	1	no	—
55	C₂×#13083558	—	2	1	no	—
56	C₂×#13083558	—	2	1	no	—
57	C₂×#13083558	D₄	1	2	yes	—
58	C₂×#13083558	D₄	1	2	yes	—
59	C₂×#13083558	D₄	1	2	yes	—
60	C₂×#13083558	C₂³	1	2	yes	—
61	C₂×#13083558	C₂³	1	2	yes	—
62	C₂×#13083558	C₂³	1	2	yes	—
63	C₂²×#10623494	—	2	4	no	—
64	C₂²×#10623494	—	2	1	no	—
65	C₂²×#10623494	—	2	1	no	—
66	C₂²×#10623494	D₄	1	2	yes	—
67	#15667971	—	2	1	no	—
68	#15667971	—	2	1	no	—
69	#15667971	—	2	1	no	—
70	#15667971	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₈₉	—	2	1	no	—
72	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
73	C₂×C₄×Dic₈₉	—	2	1	no	—
74	#15667948	—	2	8	no	—
75	C₄⋊#10623494	—	2	8	no	—
76	#15667939	—	2	8	no	—
77	C₂×#41×C₈₉	—	2	1	no	—
78	C₂×#41×C₈₉	—	2	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	C₂×#41×C₈₉	—	2	1	no	—
83	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
84	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
85	C₂×#41×C₈₉	D₄	1	2	yes	—
86	C₂×#41×C₈₉	D₄	1	2	yes	—
87	C₂×#41×C₈₉	Q₈	1	2	yes	—
88	C₂×#41×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	Q₈	1	1	yes	characteristic
90	C₂²×D₄×C₈₉	—	2	1	no	—
91	C₂²×D₄×C₈₉	Q₈	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	—	2	1	no	—
93	C₂³×C₄×C₈₉	—	2	1	no	—
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₈₉	—	2	1	no	—
96	C₂×M₁₆×C₈₉	—	2	1	no	—
97	C₂×M₁₆×C₈₉	—	2	1	no	—
98	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
99	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₈₉	—	2	1	no	—
102	C₂×C₄²×C₈₉	—	2	1	no	—
103	C₂×C₄²×C₈₉	—	2	1	no	—
104	C₂×C₄²×C₈₉	—	2	1	no	—
105	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
109	#104×C₈₉	C₂×C₄	1	8	yes	complemented
110	#104×C₈₉	C₂×C₄	1	8	yes	complemented
111	C₂²×Dic₈₉	—	4	1	no	—
112	#13083558	—	2	16	no	—
113	#13083558	—	2	2	no	—
114	#13083558	—	2	2	no	—
115	#13083558	—	2	2	no	—
116	#13083558	—	2	2	no	—
117	#13083558	—	2	2	no	—
118	#13083558	—	2	2	no	—
119	#13083558	—	2	2	no	—
120	#13083558	—	2	2	no	—
121	#13083558	—	2	2	no	—
122	#13083558	—	4	1	no	—
123	#13083558	—	4	1	no	—
124	#13083558	C₂×D₄	1	4	yes	—
125	C₂×#10623494	—	2	16	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₂×#10623494	—	2	2	no	—
131	C₂×#10623494	—	2	2	no	—
132	C₂×#10623494	—	4	1	no	—
133	C₂×#10623494	—	4	1	no	—
134	C₂×#10623494	C₂×D₄	1	4	yes	—
135	C₄⋊Dic₈₉	—	2	2	no	—
136	C₄⋊Dic₈₉	—	4	1	no	—
137	C₂²⋊Dic₈₉	—	2	2	no	—
138	C₂²⋊Dic₈₉	—	4	1	no	—
139	C₄×Dic₈₉	—	2	2	no	—
140	C₄×Dic₈₉	—	4	1	no	—
141	C₂⁴×C₈₉	—	2	1	no	—
142	C₂⁴×C₈₉	#41	1	1	yes	characteristic
143	#41×C₈₉	—	2	2	no	—
144	#41×C₈₉	—	2	2	no	—
145	#41×C₈₉	—	2	2	no	—
146	#41×C₈₉	—	2	2	no	—
147	#41×C₈₉	—	2	2	no	—
148	#41×C₈₉	—	2	2	no	—
149	#41×C₈₉	—	2	2	no	—
150	#41×C₈₉	—	2	2	no	—
151	#41×C₈₉	—	2	2	no	—
152	#41×C₈₉	—	2	2	no	—
153	#41×C₈₉	—	2	2	no	—
154	#41×C₈₉	—	2	2	no	—
155	#41×C₈₉	C₄⋊C₄	1	4	yes	—
156	#41×C₈₉	C₄⋊C₄	1	4	yes	—
157	#41×C₈₉	C₂²×C₄	1	4	yes	—
158	#41×C₈₉	C₂×D₄	1	4	yes	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	C₄⋊C₄	1	2	yes	—
163	C₂×Q₈×C₈₉	C₄⋊C₄	1	2	yes	—
164	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
165	C₂×D₄×C₈₉	—	2	2	no	—
166	C₂×D₄×C₈₉	—	2	2	no	—
167	C₂×D₄×C₈₉	—	2	2	no	—
168	C₂×D₄×C₈₉	—	2	2	no	—
169	C₂×D₄×C₈₉	—	2	2	no	—
170	C₂×D₄×C₈₉	—	2	2	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	C₄⋊C₄	1	2	yes	—
175	C₂×D₄×C₈₉	C₄⋊C₄	1	2	yes	—
176	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	2	no	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	2	no	—
188	C₂²×C₄×C₈₉	—	4	4	no	—
189	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
201	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	M₁₆×C₈₉	—	2	2	no	—
204	M₁₆×C₈₉	—	2	2	no	—
205	M₁₆×C₈₉	—	2	2	no	—
206	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
207	C₂×C₈×C₈₉	—	2	2	no	—
208	C₂×C₈×C₈₉	—	2	2	no	—
209	C₂×C₈×C₈₉	—	2	2	no	—
210	C₄²×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	—	2	2	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	—	2	2	no	—
214	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
215	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
216	C₂³×C₈₉	—	2	2	no	—
217	C₂³×C₈₉	—	2	2	no	—
218	C₂³×C₈₉	—	2	2	no	—
219	C₂³×C₈₉	—	4	2	no	—
220	C₂³×C₈₉	—	8	2	no	—
221	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
222	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₈₉	#123	1	1	yes	characteristic
226	C₂³×C₈₉	#123	1	1	yes	characteristic
227	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
228	Q₈×C₈₉	—	2	2	no	—
229	Q₈×C₈₉	—	2	2	no	—
230	Q₈×C₈₉	—	2	2	no	—
231	Q₈×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
232	D₄×C₈₉	—	2	4	no	—
233	D₄×C₈₉	—	2	4	no	—
234	D₄×C₈₉	—	2	4	no	—
235	D₄×C₈₉	—	2	4	no	—
236	D₄×C₈₉	—	2	2	no	—
237	D₄×C₈₉	—	2	2	no	—
238	D₄×C₈₉	—	2	2	no	—
239	D₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
240	C₂×C₄×C₈₉	—	2	4	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	4	no	—
246	C₂×C₄×C₈₉	—	2	4	no	—
247	C₂×C₄×C₈₉	—	2	4	no	—
248	C₂×C₄×C₈₉	—	2	4	no	—
249	C₂×C₄×C₈₉	—	2	2	no	—
250	C₂×C₄×C₈₉	—	4	4	no	—
251	C₂×C₄×C₈₉	—	4	4	no	—
252	C₂×C₄×C₈₉	—	4	2	no	—
253	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
274	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
275	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
280	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
281	C₂×Dic₈₉	—	4	2	no	—
282	C₂×Dic₈₉	—	8	2	no	—
283	C₈×C₈₉	—	2	4	no	—
284	#10623494	—	2	4	no	—
285	#10623494	—	2	4	no	—
286	#10623494	—	4	2	no	—
287	C₂²×C₈₉	—	2	2	no	—
288	C₂²×C₈₉	—	2	2	no	—
289	C₂²×C₈₉	—	2	2	no	—
290	C₂²×C₈₉	—	2	4	no	—
291	C₂²×C₈₉	—	4	1	no	—
292	C₂²×C₈₉	—	4	1	no	—
293	C₂²×C₈₉	—	4	1	no	—
294	C₂²×C₈₉	—	4	1	no	—
295	C₂²×C₈₉	—	4	4	no	—
296	C₂²×C₈₉	—	8	2	no	—
297	C₂²×C₈₉	—	8	2	no	—
298	C₂²×C₈₉	#385	1	1	yes	characteristic
299	C₂²×C₈₉	#385	1	1	yes	characteristic
300	C₂²×C₈₉	#385	1	1	yes	characteristic
301	C₂²×C₈₉	#385	1	1	yes	characteristic
302	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
305	C₄×C₈₉	—	2	4	no	—
306	C₄×C₈₉	—	2	4	no	—
307	C₄×C₈₉	—	4	2	no	—
308	C₄×C₈₉	#385	1	1	yes	characteristic
309	C₄×C₈₉	#385	1	1	yes	characteristic
310	C₄×C₈₉	#385	1	1	yes	characteristic
311	C₄×C₈₉	#385	1	1	yes	characteristic
312	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
313	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
315	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
316	Dic₈₉	—	8	2	no	—
317	C₂×#1861	—	89	1	no	maximal, Sylow
318	C₂×C₈₉	—	2	1	no	—
319	C₂×C₈₉	—	2	1	no	—
320	C₂×C₈₉	—	2	1	no	—
321	C₂×C₈₉	—	2	1	no	—
322	C₂×C₈₉	—	2	1	no	—
323	C₂×C₈₉	—	2	1	no	—
324	C₂×C₈₉	—	4	4	no	—
325	C₂×C₈₉	#1861	1	2	yes	complemented
326	C₂×C₈₉	C₂×#385	1	1	yes	characteristic
327	C₂×#568	—	89	1	no	—
328	C₂×#430	—	89	1	no	—
329	C₂×#423	—	89	1	no	—
330	C₂×#421	—	89	1	no	—
331	C₂²×#104	D₈₉	1	1	yes	characteristic
332	#1861	—	89	8	no	—
333	C₂×#344	—	89	1	no	—
334	C₂×#339	—	89	1	no	—
335	C₈₉	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
336	C₂²×#41	C₂×D₈₉	1	1	yes	characteristic
337	#568	—	89	4	no	—
338	#568	—	178	2	no	—
339	#568	—	178	2	no	—
340	#568	—	178	2	no	—
341	C₂×#131	—	178	2	no	—
342	C₂×#131	—	178	2	no	—
343	C₂²×M₁₆	—	89	1	no	—
344	C₂²×M₁₆	—	89	1	no	—
345	C₂²×M₁₆	—	89	1	no	—
346	C₂²×M₁₆	—	178	2	no	—
347	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
348	C₂×#117	—	89	1	no	—
349	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
350	#430	—	89	4	no	—
351	#430	—	178	2	no	—
352	C₂×#108	—	178	2	no	—
353	#423	—	89	4	no	—
354	#423	—	178	2	no	—
355	C₂×C₄⋊C₈	—	178	2	no	—
356	#421	—	89	4	no	—
357	#421	—	178	2	no	—
358	C₂×#104	—	178	2	no	—
359	C₂×#104	Dic₈₉	1	2	yes	complemented
360	C₂×#104	Dic₈₉	1	4	yes	complemented
361	C₂×#104	Dic₈₉	1	2	yes	complemented
362	C₂×#104	C₂×D₈₉	1	4	yes	—
363	#344	—	89	4	no	—
364	#339	—	89	4	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	Dic₁₇₈	1	2	yes	—
372	C₂×#41	D₃₅₆	1	2	yes	—
373	C₂×#41	D₃₅₆	1	2	yes	—
374	C₂×#41	C₂×Dic₈₉	1	2	yes	—
375	C₂×#41	C₂×Dic₈₉	1	2	yes	—
376	C₂×#41	C₂²×D₈₉	1	2	yes	—
377	C₂²×Q₈	Dic₁₇₈	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	Dic₁₇₈	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
383	#131	—	178	8	no	—
384	#131	—	178	8	no	—
385	#131	—	178	8	no	—
386	#131	—	178	8	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	89	2	no	—
391	C₂×M₁₆	—	89	2	no	—
392	C₂×M₁₆	—	89	2	no	—
393	C₂×M₁₆	—	89	2	no	—
394	C₂×M₁₆	—	89	2	no	—
395	C₂×M₁₆	—	89	2	no	—
396	C₂×M₁₆	—	178	1	no	—
397	C₂×M₁₆	—	178	1	no	—
398	C₂×M₁₆	—	178	1	no	—
399	C₂×M₁₆	—	178	1	no	—
400	C₂×M₁₆	—	178	8	no	—
401	C₂×M₁₆	—	178	1	no	—
402	C₂×M₁₆	—	178	4	no	—
403	C₂×M₁₆	—	178	8	no	—
404	C₂×M₁₆	—	178	1	no	—
405	C₂×M₁₆	—	178	1	no	—
406	C₂×M₁₆	—	178	1	no	—
407	C₂×M₁₆	—	178	1	no	—
408	C₂×M₁₆	—	178	1	no	—
409	C₂×M₁₆	—	178	1	no	—
410	C₂×M₁₆	—	178	1	no	—
411	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
412	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
413	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	89	2	no	—
416	C₂²×C₈	—	178	1	no	—
417	C₂²×C₈	—	178	4	no	—
418	C₂²×C₈	—	178	1	no	—
419	#117	—	89	2	no	—
420	#117	—	178	1	no	—
421	#117	—	178	1	no	—
422	#117	—	178	1	no	—
423	C₂×C₄⋊C₄	—	178	1	no	—
424	C₂×C₂²⋊C₄	—	178	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	178	1	no	—
429	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
430	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
431	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
432	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
433	#108	—	178	8	no	—
434	C₄⋊C₈	—	178	8	no	—
435	#104	—	178	8	no	—
436	#104	C₂×Dic₈₉	1	8	yes	complemented
437	#104	C₂×Dic₈₉	1	8	yes	complemented
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#13083573	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	C₄⋊Dic₈₉	1	4	yes	—
453	#41	C₄⋊Dic₈₉	1	4	yes	—
454	#41	C₂²×Dic₈₉	1	4	yes	—
455	#41	C₂×D₃₅₆	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₄⋊Dic₈₉	1	2	yes	—
460	C₂×Q₈	C₄⋊Dic₈₉	1	2	yes	—
461	C₂×Q₈	C₂×Dic₁₇₈	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₄⋊Dic₈₉	1	2	yes	—
472	C₂×D₄	C₄⋊Dic₈₉	1	2	yes	—
473	C₂×D₄	C₂×Dic₁₇₈	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	356	1	no	—
487	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
489	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
490	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
491	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
492	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
495	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
496	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
497	C₂²×C₄	#13083573	1	1	yes	characteristic
498	C₂²×C₄	#13083573	1	1	yes	characteristic
499	C₂²×C₄	#13083573	1	1	yes	characteristic
500	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	89	4	no	—
505	M₁₆	—	356	1	no	—
506	M₁₆	—	356	1	no	—
507	M₁₆	—	178	2	no	—
508	M₁₆	—	178	2	no	—
509	M₁₆	—	178	16	no	—
510	M₁₆	—	178	2	no	—
511	M₁₆	—	178	2	no	—
512	M₁₆	—	178	2	no	—
513	M₁₆	—	178	2	no	—
514	M₁₆	—	178	2	no	—
515	M₁₆	—	178	2	no	—
516	M₁₆	—	178	2	no	—
517	M₁₆	C₂²×Dic₈₉	1	4	yes	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	89	4	no	—
522	C₂×C₈	—	356	1	no	—
523	C₂×C₈	—	356	1	no	—
524	C₂×C₈	—	178	2	no	—
525	C₂×C₈	—	178	16	no	—
526	C₂×C₈	—	178	2	no	—
527	C₂×C₈	—	178	2	no	—
528	C₂×C₈	—	178	2	no	—
529	C₂×C₈	—	178	2	no	—
530	C₂×C₈	—	178	2	no	—
531	C₄⋊C₄	—	356	1	no	—
532	C₄⋊C₄	—	178	2	no	—
533	C₂²⋊C₄	—	356	1	no	—
534	C₂²⋊C₄	—	178	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	356	1	no	—
540	C₄²	—	178	2	no	—
541	C₄²	C₂²×Dic₈₉	1	2	yes	—
542	C₄²	C₂²×Dic₈₉	1	2	yes	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
549	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
550	C₂³	#15667989	1	1	yes	characteristic
551	C₂³	#15667989	1	1	yes	characteristic
552	C₂³	#15667996	1	1	yes	characteristic
553	C₂³	#15667996	1	1	yes	characteristic
554	C₂³	C₂×#13083573	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×C₄⋊Dic₈₉	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	356	2	no	—
581	C₂×C₄	—	712	2	no	—
582	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
584	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
586	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
587	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
588	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
589	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
590	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
591	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
592	C₂×C₄	#15667982	1	1	yes	characteristic
593	C₂×C₄	#15667982	1	1	yes	characteristic
594	C₂×C₄	#15667982	1	1	yes	characteristic
595	C₂×C₄	#15667982	1	1	yes	characteristic
596	C₂×C₄	#15667989	1	1	yes	characteristic
597	C₂×C₄	#15667989	1	1	yes	characteristic
598	C₂×C₄	#15667989	1	1	yes	characteristic
599	C₂×C₄	#15667989	1	1	yes	characteristic
600	C₂×C₄	#15667989	1	1	yes	characteristic
601	C₂×C₄	#15667989	1	1	yes	characteristic
602	C₂×C₄	#15667996	1	1	yes	characteristic
603	C₂×C₄	#15667996	1	1	yes	characteristic
604	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
605	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
606	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
608	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
609	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	356	2	no	—
612	C₈	—	178	4	no	—
613	C₈	—	178	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	#19151473	1	1	yes	characteristic
626	C₂²	#19151473	1	1	yes	characteristic
627	C₂²	#19151473	1	1	yes	characteristic
628	C₂²	#19151473	1	1	yes	characteristic
629	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
630	C₂²	C₂×#15667989	1	1	yes	characteristic
631	C₂²	C₂×#15667996	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	712	2	no	—
636	C₄	#19151473	1	1	yes	characteristic
637	C₄	#19151473	1	1	yes	characteristic
638	C₄	#19151473	1	1	yes	characteristic
639	C₄	#19151473	1	1	yes	characteristic
640	C₄	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
641	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
642	C₄	C₂×#15667982	1	1	yes	characteristic
643	C₄	C₂×#15667989	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	#26020494	1	2	yes	direct product factor
652	C₂	C₂×#19151473	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667982
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂²×#104×C₈₉	C₂
socle	C₂²×C₈₉	#385
prime radical	C₂²×#41×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂²×#104	D₈₉
hypocenter	C₈₉	C₂×#1861
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
2. C₂×#19151647	C₂	semidirect
3. C₂×#19151622	C₂	semidirect
5. #26020494	C₂	direct (N × H)
6. C₂×#19151370	C₂	semidirect
7. C₂×#19151358	C₂	semidirect
21. #19151647	C₂²	semidirect
24. #19151622	C₂²	semidirect
29. #19151370	C₂²	semidirect
30. #19151358	C₂²	semidirect
34. C₂×#104×C₈₉	C₄	semidirect
35. C₂×#104×C₈₉	C₄	semidirect
36. C₂×#104×C₈₉	C₄	semidirect
109. #104×C₈₉	C₂×C₄	semidirect
110. #104×C₈₉	C₂×C₄	semidirect
325. C₂×C₈₉	#1861	semidirect
335. C₈₉	C₂×#1861	semidirect
359. C₂×#104	Dic₈₉	semidirect
360. C₂×#104	Dic₈₉	semidirect
361. C₂×#104	Dic₈₉	semidirect
436. #104	C₂×Dic₈₉	semidirect
437. #104	C₂×Dic₈₉	semidirect
651. C₂	#26020494	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×#19152365	2
C₂×#19151647	2
C₂×#19151622	2
C₂×#19151615	2
#26020494	2
C₂×#19151370	2
C₂×#19151358	2
C₂²×#104×C₈₉	2
C₂×#1861	89

Subgroups — C2×#26020494 #36555327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26020494 #36555327