Subgroups — C₂×C₈₉×#3097 #36438361

Order 22784.

2170 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3097	C₂	1	16	yes	maximal, direct product factor
4	C₂×#484×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#485×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#485×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#483×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#419×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#408×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	#536×C₈₉	—	2	4	no	—
18	#536×C₈₉	C₂²	1	8	yes	—
19	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
20	C₂×#124×C₈₉	—	2	1	no	—
21	C₂×#123×C₈₉	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	#520×C₈₉	—	2	4	no	—
25	#520×C₈₉	C₂²	1	8	yes	—
26	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
27	C₂×C₄×D₄×C₈₉	—	2	2	no	—
28	C₂×C₄×D₄×C₈₉	—	2	1	no	—
29	C₂×#117×C₈₉	C₂²	1	2	yes	—
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#485×C₈₉	C₂²	1	16	yes	complemented
35	#485×C₈₉	C₂²	1	16	yes	complemented
36	#484×C₈₉	C₂²	1	16	yes	complemented
37	#483×C₈₉	C₂²	1	16	yes	complemented
38	#428×C₈₉	C₂²	1	8	yes	complemented
39	#427×C₈₉	C₂²	1	8	yes	complemented
40	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#107×C₈₉	C₂²	1	2	yes	—
42	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#106×C₈₉	C₂²	1	2	yes	—
45	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
46	#419×C₈₉	C₂²	1	8	yes	complemented
47	C₂×#103×C₈₉	C₂²	1	2	yes	—
48	C₂×#103×C₈₉	C₂²	1	2	yes	—
49	C₂×#103×C₈₉	C₂²	1	2	yes	—
50	C₂×#103×C₈₉	C₂²	1	2	yes	—
51	C₂×#103×C₈₉	C₂²	1	8	yes	complemented
52	#408×C₈₉	C₂²	1	8	yes	—
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
54	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
55	C₂×#41×C₈₉	—	2	4	no	—
56	C₂×#41×C₈₉	—	2	4	no	—
57	C₂×#41×C₈₉	D₄	1	4	yes	—
58	C₂×#41×C₈₉	C₂³	1	4	yes	—
59	C₂²×Q₈×C₈₉	—	2	1	no	—
60	C₂²×Q₈×C₈₉	—	2	2	no	—
61	C₂²×Q₈×C₈₉	—	2	4	no	—
62	C₂²×Q₈×C₈₉	—	2	4	no	—
63	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
65	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
66	C₂²×D₄×C₈₉	D₄	1	2	yes	—
67	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₈₉	—	2	1	no	—
69	C₂³×C₄×C₈₉	—	2	2	no	—
70	C₂³×C₄×C₈₉	—	2	1	no	—
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₈₉	—	2	4	no	—
74	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
75	C₂²×C₈×C₈₉	—	2	4	no	—
76	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
78	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
80	C₄⋊Q₈×C₈₉	—	2	8	no	—
81	#124×C₈₉	—	2	8	no	—
82	#123×C₈₉	—	2	16	no	—
83	C₂²⋊Q₈×C₈₉	—	2	4	no	—
84	C₂²⋊Q₈×C₈₉	—	2	4	no	—
85	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
86	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
87	C₄×Q₈×C₈₉	—	2	8	no	—
88	C₄×D₄×C₈₉	—	2	16	no	—
89	C₄×D₄×C₈₉	—	2	8	no	—
90	#117×C₈₉	—	2	4	no	—
91	#117×C₈₉	—	2	2	no	—
92	#117×C₈₉	—	2	2	no	—
93	#117×C₈₉	C₂³	1	4	yes	—
94	#117×C₈₉	C₂³	1	4	yes	—
95	#117×C₈₉	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
114	C₂×C₄²×C₈₉	—	2	2	no	—
115	C₂×C₄²×C₈₉	—	2	1	no	—
116	C₂×C₄²×C₈₉	—	2	1	no	—
117	#107×C₈₉	C₂³	1	4	yes	—
118	#107×C₈₉	C₂³	1	4	yes	—
119	#107×C₈₉	C₂³	1	8	yes	—
120	#106×C₈₉	C₂³	1	4	yes	—
121	#106×C₈₉	C₂³	1	4	yes	—
122	#106×C₈₉	C₂³	1	8	yes	—
123	#103×C₈₉	C₂³	1	8	yes	—
124	#103×C₈₉	C₂³	1	8	yes	—
125	#103×C₈₉	C₂³	1	8	yes	—
126	#103×C₈₉	C₂³	1	8	yes	—
127	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
128	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
129	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
130	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
131	#41×C₈₉	—	2	16	no	—
132	#41×C₈₉	—	2	8	no	—
133	#41×C₈₉	—	2	8	no	—
134	C₂×Q₈×C₈₉	—	2	4	no	—
135	C₂×Q₈×C₈₉	—	2	2	no	—
136	C₂×Q₈×C₈₉	—	2	4	no	—
137	C₂×Q₈×C₈₉	—	2	4	no	—
138	C₂×Q₈×C₈₉	—	2	4	no	—
139	C₂×Q₈×C₈₉	—	2	8	no	—
140	C₂×Q₈×C₈₉	—	2	8	no	—
141	C₂×Q₈×C₈₉	—	4	4	no	—
142	C₂×Q₈×C₈₉	—	4	8	no	—
143	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
144	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
145	C₂×D₄×C₈₉	—	2	8	no	—
146	C₂×D₄×C₈₉	—	2	4	no	—
147	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
148	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	4	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	2	no	—
156	C₂²×C₄×C₈₉	—	2	1	no	—
157	C₂²×C₄×C₈₉	—	2	2	no	—
158	C₂²×C₄×C₈₉	—	2	8	no	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	4	4	no	—
161	C₂²×C₄×C₈₉	—	8	2	no	—
162	C₂²×C₄×C₈₉	—	8	4	no	—
163	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	#41	1	4	yes	—
168	C₂²×C₄×C₈₉	#41	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₈₉	—	2	8	no	—
173	C₂×C₈×C₈₉	—	2	2	no	—
174	C₂×C₈×C₈₉	—	2	2	no	—
175	C₂×C₈×C₈₉	—	2	8	no	—
176	C₂×C₈×C₈₉	—	2	4	no	—
177	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
178	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
179	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₄⋊C₄×C₈₉	—	2	2	no	—
182	C₄⋊C₄×C₈₉	—	2	8	no	—
183	C₄⋊C₄×C₈₉	—	2	4	no	—
184	C₄⋊C₄×C₈₉	—	2	8	no	—
185	C₄⋊C₄×C₈₉	—	2	8	no	—
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
190	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
191	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
192	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
193	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
194	C₂²⋊C₄×C₈₉	—	2	8	no	—
195	C₂²⋊C₄×C₈₉	—	2	4	no	—
196	C₂²⋊C₄×C₈₉	—	2	4	no	—
197	C₂²⋊C₄×C₈₉	—	2	8	no	—
198	C₂²⋊C₄×C₈₉	—	2	8	no	—
199	C₄²×C₈₉	—	2	8	no	—
200	C₄²×C₈₉	—	2	4	no	—
201	C₄²×C₈₉	—	2	4	no	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	2	no	—
204	C₂³×C₈₉	—	2	4	no	—
205	C₂³×C₈₉	—	2	4	no	—
206	C₂³×C₈₉	—	2	4	no	—
207	C₂³×C₈₉	#123	1	4	yes	—
208	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
209	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
210	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₈₉	—	2	8	no	—
212	Q₈×C₈₉	—	2	4	no	—
213	Q₈×C₈₉	—	2	4	no	—
214	Q₈×C₈₉	—	4	4	no	—
215	Q₈×C₈₉	—	4	8	no	—
216	D₄×C₈₉	—	2	16	no	—
217	D₄×C₈₉	—	2	8	no	—
218	C₂×C₄×C₈₉	—	2	4	no	—
219	C₂×C₄×C₈₉	—	2	8	no	—
220	C₂×C₄×C₈₉	—	2	4	no	—
221	C₂×C₄×C₈₉	—	2	4	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	2	no	—
224	C₂×C₄×C₈₉	—	2	2	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	4	no	—
228	C₂×C₄×C₈₉	—	4	8	no	—
229	C₂×C₄×C₈₉	—	4	4	no	—
230	C₂×C₄×C₈₉	—	4	2	no	—
231	C₂×C₄×C₈₉	—	4	4	no	—
232	C₂×C₄×C₈₉	—	4	2	no	—
233	C₂×C₄×C₈₉	—	4	2	no	—
234	C₂×C₄×C₈₉	—	4	2	no	—
235	C₂×C₄×C₈₉	—	8	4	no	—
236	C₂×C₄×C₈₉	—	8	8	no	—
237	C₂×C₄×C₈₉	#123	1	4	yes	—
238	C₂×C₄×C₈₉	#123	1	8	yes	—
239	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
243	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
245	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
246	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
247	C₈×C₈₉	—	2	2	no	—
248	C₈×C₈₉	—	2	2	no	—
249	C₈×C₈₉	—	2	4	no	—
250	C₂²×C₈₉	—	2	8	no	—
251	C₂²×C₈₉	—	2	2	no	—
252	C₂²×C₈₉	—	2	2	no	—
253	C₂²×C₈₉	—	2	4	no	—
254	C₂²×C₈₉	—	2	4	no	—
255	C₂²×C₈₉	—	2	4	no	—
256	C₂²×C₈₉	—	4	8	no	—
257	C₂²×C₈₉	C₂×#123	1	4	yes	—
258	C₂²×C₈₉	C₂×#123	1	2	yes	—
259	C₂²×C₈₉	#577	1	2	yes	—
260	C₂²×C₈₉	#578	1	2	yes	—
261	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
262	C₄×C₈₉	—	2	4	no	—
263	C₄×C₈₉	—	4	4	no	—
264	C₄×C₈₉	—	4	2	no	—
265	C₄×C₈₉	—	4	4	no	—
266	C₄×C₈₉	—	4	2	no	—
267	C₄×C₈₉	—	4	2	no	—
268	C₄×C₈₉	—	4	2	no	—
269	C₄×C₈₉	C₂×#123	1	2	yes	—
270	C₄×C₈₉	C₂×#123	1	4	yes	—
271	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
272	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
273	C₂×#3097	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂×C₈₉	—	2	4	no	—
275	C₂×C₈₉	—	4	4	no	—
276	C₂×C₈₉	#3097	1	4	yes	direct product factor
277	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
278	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
279	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
280	C₂×#536	C₂×C₈₉	1	1	yes	characteristic
281	C₂×#520	C₂×C₈₉	1	1	yes	characteristic
282	#3097	C₂×C₈₉	1	16	yes	direct product factor
283	C₂×#484	C₂×C₈₉	1	2	yes	complemented
284	C₂×#485	C₂×C₈₉	1	2	yes	complemented
285	C₂×#485	C₂×C₈₉	1	2	yes	complemented
286	C₂×#483	C₂×C₈₉	1	2	yes	complemented
287	C₂×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
288	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
289	C₂×#419	C₂×C₈₉	1	1	yes	characteristic, complemented
290	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
291	C₂×#408	C₂×C₈₉	1	1	yes	characteristic
292	C₈₉	C₂×#3097	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
297	#536	—	2	4	no	—
298	#536	C₂²×C₈₉	1	8	yes	—
299	C₂×C₄⋊Q₈	—	2	1	no	—
300	C₂×#124	—	2	1	no	—
301	C₂×#123	—	2	2	no	—
302	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
304	#520	—	2	4	no	—
305	#520	C₂²×C₈₉	1	8	yes	—
306	C₂×C₄×Q₈	—	2	1	no	—
307	C₂×C₄×D₄	—	2	2	no	—
308	C₂×C₄×D₄	—	2	1	no	—
309	C₂×#117	C₂²×C₈₉	1	2	yes	—
310	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
311	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
312	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
313	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
314	#485	C₂²×C₈₉	1	16	yes	complemented
315	#485	C₂²×C₈₉	1	16	yes	complemented
316	#484	C₂²×C₈₉	1	16	yes	complemented
317	#483	C₂²×C₈₉	1	16	yes	complemented
318	#428	C₂²×C₈₉	1	8	yes	complemented
319	#427	C₂²×C₈₉	1	8	yes	complemented
320	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
321	C₂×#107	C₂²×C₈₉	1	2	yes	—
322	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
324	C₂×#106	C₂²×C₈₉	1	2	yes	—
325	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
326	#419	C₂²×C₈₉	1	8	yes	complemented
327	C₂×#103	C₂²×C₈₉	1	2	yes	—
328	C₂×#103	C₂²×C₈₉	1	2	yes	—
329	C₂×#103	C₂²×C₈₉	1	2	yes	—
330	C₂×#103	C₂²×C₈₉	1	2	yes	—
331	C₂×#103	C₂²×C₈₉	1	8	yes	complemented
332	#408	C₂²×C₈₉	1	8	yes	—
333	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
334	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
335	C₂×#41	—	2	4	no	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	D₄×C₈₉	1	4	yes	—
338	C₂×#41	C₂³×C₈₉	1	4	yes	—
339	C₂²×Q₈	—	2	1	no	—
340	C₂²×Q₈	—	2	2	no	—
341	C₂²×Q₈	—	2	4	no	—
342	C₂²×Q₈	—	2	4	no	—
343	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
344	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
345	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
346	C₂²×D₄	D₄×C₈₉	1	2	yes	—
347	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
352	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
355	C₂²×C₈	—	2	4	no	—
356	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
359	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
360	C₄⋊Q₈	—	2	8	no	—
361	#124	—	2	8	no	—
362	#123	—	2	16	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
366	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
367	C₄×Q₈	—	2	8	no	—
368	C₄×D₄	—	2	16	no	—
369	C₄×D₄	—	2	8	no	—
370	#117	—	2	4	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	C₂³×C₈₉	1	4	yes	—
374	#117	C₂³×C₈₉	1	8	yes	—
375	#117	C₂³×C₈₉	1	4	yes	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
386	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	#107	C₂³×C₈₉	1	4	yes	—
398	#107	C₂³×C₈₉	1	4	yes	—
399	#107	C₂³×C₈₉	1	8	yes	—
400	#106	C₂³×C₈₉	1	4	yes	—
401	#106	C₂³×C₈₉	1	4	yes	—
402	#106	C₂³×C₈₉	1	8	yes	—
403	#103	C₂³×C₈₉	1	8	yes	—
404	#103	C₂³×C₈₉	1	8	yes	—
405	#103	C₂³×C₈₉	1	8	yes	—
406	#103	C₂³×C₈₉	1	8	yes	—
407	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
408	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
409	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
410	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
411	#41	—	2	16	no	—
412	#41	—	2	8	no	—
413	#41	—	2	8	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	2	8	no	—
420	C₂×Q₈	—	2	8	no	—
421	C₂×Q₈	—	4	4	no	—
422	C₂×Q₈	—	4	8	no	—
423	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
424	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
428	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	8	2	no	—
442	C₂²×C₄	—	8	4	no	—
443	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
445	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
447	C₂²×C₄	#41×C₈₉	1	4	yes	—
448	C₂²×C₄	#41×C₈₉	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
452	M₁₆	—	2	8	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	8	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
458	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
459	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
471	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
472	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
473	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₄²	—	2	8	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	2	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	#123×C₈₉	1	4	yes	—
488	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
489	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
490	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
491	Q₈	—	2	8	no	—
492	Q₈	—	2	4	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	4	4	no	—
495	Q₈	—	4	8	no	—
496	D₄	—	2	16	no	—
497	D₄	—	2	8	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	4	no	—
516	C₂×C₄	—	8	8	no	—
517	C₂×C₄	#123×C₈₉	1	4	yes	—
518	C₂×C₄	#123×C₈₉	1	8	yes	—
519	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
520	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
524	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
525	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
526	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	4	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	8	no	—
537	C₂²	C₂×#123×C₈₉	1	4	yes	—
538	C₂²	C₂×#123×C₈₉	1	2	yes	—
539	C₂²	#577×C₈₉	1	2	yes	—
540	C₂²	#578×C₈₉	1	2	yes	—
541	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
542	C₄	—	2	4	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	C₂×#123×C₈₉	1	2	yes	—
550	C₄	C₂×#123×C₈₉	1	4	yes	—
551	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
552	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
553	C₂	—	2	4	no	—
554	C₂	—	4	4	no	—
555	C₂	C₈₉×#3097	1	4	yes	direct product factor
556	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
557	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
558	C₂	C₂×#578×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₉×#3097	C₂	direct (N × H)
4. C₂×#484×C₈₉	C₂	semidirect
5. C₂×#485×C₈₉	C₂	semidirect
6. C₂×#485×C₈₉	C₂	semidirect
7. C₂×#483×C₈₉	C₂	semidirect
8. C₂×#428×C₈₉	C₂	semidirect
9. C₂×#427×C₈₉	C₂	semidirect
10. C₂×#419×C₈₉	C₂	semidirect
11. C₂²×#103×C₈₉	C₂	semidirect
34. #485×C₈₉	C₂²	semidirect
35. #485×C₈₉	C₂²	semidirect
36. #484×C₈₉	C₂²	semidirect
37. #483×C₈₉	C₂²	semidirect
38. #428×C₈₉	C₂²	semidirect
39. #427×C₈₉	C₂²	semidirect
46. #419×C₈₉	C₂²	semidirect
51. C₂×#103×C₈₉	C₂²	semidirect
273. C₂×#3097	C₈₉	direct (N × H)
276. C₂×C₈₉	#3097	direct (N × H)
282. #3097	C₂×C₈₉	direct (N × H)
283. C₂×#484	C₂×C₈₉	semidirect
284. C₂×#485	C₂×C₈₉	semidirect
285. C₂×#485	C₂×C₈₉	semidirect
286. C₂×#483	C₂×C₈₉	semidirect
287. C₂×#428	C₂×C₈₉	semidirect
288. C₂×#427	C₂×C₈₉	semidirect
289. C₂×#419	C₂×C₈₉	semidirect
290. C₂²×#103	C₂×C₈₉	semidirect
292. C₈₉	C₂×#3097	direct (N × H)
314. #485	C₂²×C₈₉	semidirect
315. #485	C₂²×C₈₉	semidirect
316. #484	C₂²×C₈₉	semidirect
317. #483	C₂²×C₈₉	semidirect
318. #428	C₂²×C₈₉	semidirect
319. #427	C₂²×C₈₉	semidirect
326. #419	C₂²×C₈₉	semidirect
331. C₂×#103	C₂²×C₈₉	semidirect
555. C₂	C₈₉×#3097	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×#536×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#3097	2
C₂×#484×C₈₉	2
C₂×#485×C₈₉	2
C₂×#483×C₈₉	2
C₂×#428×C₈₉	2
C₂×#427×C₈₉	2
C₂×#419×C₈₉	2
C₂²×#103×C₈₉	2
C₂×#408×C₈₉	2
C₂×#3097	89

Subgroups — C2×C89×#3097 #36438361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3097 #36438361