Subgroups — C₂×C₈₉×#3095 #36438358

Order 22784.

2326 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3095	C₂	1	16	yes	maximal, direct product factor
4	C₂×#484×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#485×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₂×#483×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#428×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#419×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₈₉	—	2	4	no	—
15	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	—
19	C₂×#117×C₈₉	—	2	1	no	—
20	C₂×#117×C₈₉	—	2	4	no	—
21	C₂×#117×C₈₉	—	2	1	no	—
22	C₂×#117×C₈₉	C₂²	1	2	yes	—
23	C₂×#117×C₈₉	C₂²	1	8	yes	—
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
30	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
31	C₂²×C₄²×C₈₉	—	2	1	no	—
32	#485×C₈₉	C₂²	1	32	yes	complemented
33	#484×C₈₉	C₂²	1	16	yes	complemented
34	#483×C₈₉	C₂²	1	16	yes	complemented
35	#428×C₈₉	C₂²	1	16	yes	complemented
36	C₂×#107×C₈₉	C₂²	1	4	yes	complemented
37	C₂×#106×C₈₉	C₂²	1	4	yes	complemented
38	#419×C₈₉	C₂²	1	16	yes	complemented
39	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
40	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
41	#407×C₈₉	C₂²	1	8	yes	—
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₈₉	—	2	2	no	—
46	C₂²×Q₈×C₈₉	—	2	1	no	—
47	C₂²×Q₈×C₈₉	—	2	8	no	—
48	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
49	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₈₉	—	2	8	no	—
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	C₂³×C₄×C₈₉	—	2	1	no	—
53	C₂³×C₄×C₈₉	—	2	1	no	—
54	C₂³×C₄×C₈₉	—	2	1	no	—
55	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₈₉	D₄	1	4	yes	—
58	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₈₉	—	2	8	no	—
64	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
65	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
66	C₂²⋊Q₈×C₈₉	—	2	8	no	—
67	C₂²⋊Q₈×C₈₉	—	2	4	no	—
68	C₂²⋊Q₈×C₈₉	—	2	4	no	—
69	C₂²⋊Q₈×C₈₉	—	2	8	no	—
70	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
71	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
72	#117×C₈₉	—	2	8	no	—
73	#117×C₈₉	—	2	4	no	—
74	#117×C₈₉	—	2	8	no	—
75	#117×C₈₉	—	2	4	no	—
76	#117×C₈₉	C₂³	1	8	yes	—
77	#117×C₈₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
99	C₂×C₄²×C₈₉	—	2	8	no	—
100	C₂×C₄²×C₈₉	—	2	2	no	—
101	C₂×C₄²×C₈₉	—	2	2	no	—
102	#107×C₈₉	C₂³	1	16	yes	complemented
103	#106×C₈₉	C₂³	1	16	yes	complemented
104	#103×C₈₉	C₂³	1	16	yes	complemented
105	#103×C₈₉	C₂³	1	16	yes	complemented
106	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
107	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
108	C₂⁴×C₈₉	—	2	4	no	—
109	C₂⁴×C₈₉	—	2	4	no	—
110	C₂⁴×C₈₉	—	4	2	no	—
111	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
113	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₈₉	—	2	4	no	—
116	C₂×Q₈×C₈₉	—	2	2	no	—
117	C₂×Q₈×C₈₉	—	2	8	no	—
118	C₂×Q₈×C₈₉	—	2	16	no	—
119	C₂×Q₈×C₈₉	—	4	8	no	—
120	C₂×Q₈×C₈₉	—	4	4	no	—
121	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	16	no	—
125	C₂²×C₄×C₈₉	—	2	4	no	—
126	C₂²×C₄×C₈₉	—	2	4	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	2	16	no	—
129	C₂²×C₄×C₈₉	—	2	4	no	—
130	C₂²×C₄×C₈₉	—	2	4	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	—	2	4	no	—
133	C₂²×C₄×C₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	—	2	2	no	—
136	C₂²×C₄×C₈₉	—	2	2	no	—
137	C₂²×C₄×C₈₉	—	4	4	no	—
138	C₂²×C₄×C₈₉	—	4	4	no	—
139	C₂²×C₄×C₈₉	—	4	4	no	—
140	C₂²×C₄×C₈₉	—	4	4	no	—
141	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	#41	1	8	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₈₉	—	2	16	no	—
156	C₂×C₈×C₈₉	—	2	8	no	—
157	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₈₉	—	2	8	no	—
159	C₄⋊C₄×C₈₉	—	2	8	no	—
160	C₄⋊C₄×C₈₉	—	2	4	no	—
161	C₄⋊C₄×C₈₉	—	2	4	no	—
162	C₄⋊C₄×C₈₉	—	2	2	no	—
163	C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₄⋊C₄×C₈₉	—	2	4	no	—
165	C₄⋊C₄×C₈₉	—	2	2	no	—
166	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
167	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₈₉	—	2	8	no	—
170	C₂²⋊C₄×C₈₉	—	2	8	no	—
171	C₂²⋊C₄×C₈₉	—	2	8	no	—
172	C₂²⋊C₄×C₈₉	—	2	8	no	—
173	C₄²×C₈₉	—	2	8	no	—
174	C₄²×C₈₉	—	2	8	no	—
175	C₂³×C₈₉	—	2	2	no	—
176	C₂³×C₈₉	—	2	2	no	—
177	C₂³×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	2	2	no	—
179	C₂³×C₈₉	—	2	8	no	—
180	C₂³×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	8	no	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	—	2	2	no	—
184	C₂³×C₈₉	—	4	4	no	—
185	C₂³×C₈₉	—	4	16	no	—
186	C₂³×C₈₉	#123	1	4	yes	—
187	C₂³×C₈₉	#137	1	4	yes	—
188	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
189	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
190	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₈₉	—	2	8	no	—
193	Q₈×C₈₉	—	4	8	no	—
194	Q₈×C₈₉	—	4	4	no	—
195	C₂×C₄×C₈₉	—	2	8	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	—	2	8	no	—
199	C₂×C₄×C₈₉	—	2	4	no	—
200	C₂×C₄×C₈₉	—	2	4	no	—
201	C₂×C₄×C₈₉	—	2	8	no	—
202	C₂×C₄×C₈₉	—	2	4	no	—
203	C₂×C₄×C₈₉	—	2	4	no	—
204	C₂×C₄×C₈₉	—	2	4	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	2	4	no	—
208	C₂×C₄×C₈₉	—	4	8	no	—
209	C₂×C₄×C₈₉	—	4	8	no	—
210	C₂×C₄×C₈₉	—	4	8	no	—
211	C₂×C₄×C₈₉	—	4	4	no	—
212	C₂×C₄×C₈₉	—	4	8	no	—
213	C₂×C₄×C₈₉	—	4	4	no	—
214	C₂×C₄×C₈₉	—	4	4	no	—
215	C₂×C₄×C₈₉	—	4	4	no	—
216	C₂×C₄×C₈₉	#123	1	8	yes	—
217	C₂×C₄×C₈₉	#123	1	4	yes	—
218	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
223	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
224	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
225	C₈×C₈₉	—	2	8	no	—
226	C₂²×C₈₉	—	2	8	no	—
227	C₂²×C₈₉	—	2	8	no	—
228	C₂²×C₈₉	—	2	2	no	—
229	C₂²×C₈₉	—	2	2	no	—
230	C₂²×C₈₉	—	2	2	no	—
231	C₂²×C₈₉	—	2	2	no	—
232	C₂²×C₈₉	—	2	2	no	—
233	C₂²×C₈₉	—	2	2	no	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	4	16	no	—
236	C₂²×C₈₉	—	4	4	no	—
237	C₂²×C₈₉	C₂×#123	1	4	yes	—
238	C₂²×C₈₉	C₂×#123	1	2	yes	—
239	C₂²×C₈₉	C₂×#137	1	4	yes	—
240	C₂²×C₈₉	C₂×#137	1	2	yes	—
241	C₂²×C₈₉	#575	1	2	yes	—
242	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
243	C₄×C₈₉	—	2	2	no	—
244	C₄×C₈₉	—	2	2	no	—
245	C₄×C₈₉	—	4	4	no	—
246	C₄×C₈₉	—	4	4	no	—
247	C₄×C₈₉	—	4	4	no	—
248	C₄×C₈₉	—	4	4	no	—
249	C₄×C₈₉	C₂×#123	1	4	yes	—
250	C₄×C₈₉	C₂×#123	1	2	yes	—
251	C₄×C₈₉	C₂²×#41	1	2	yes	—
252	C₂×#3095	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂×C₈₉	—	2	4	no	—
254	C₂×C₈₉	—	2	4	no	—
255	C₂×C₈₉	—	4	2	no	—
256	C₂×C₈₉	#3095	1	4	yes	direct product factor
257	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
258	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
259	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
260	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
261	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic
262	#3095	C₂×C₈₉	1	16	yes	direct product factor
263	C₂×#484	C₂×C₈₉	1	2	yes	complemented
264	C₂×#485	C₂×C₈₉	1	4	yes	complemented
265	C₂×#483	C₂×C₈₉	1	2	yes	complemented
266	C₂×#428	C₂×C₈₉	1	2	yes	complemented
267	C₂×#419	C₂×C₈₉	1	2	yes	complemented
268	C₂×#407	C₂×C₈₉	1	1	yes	characteristic
269	C₈₉	C₂×#3095	1	1	yes	characteristic, direct product factor, Sylow
270	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
272	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
273	C₂×C₂²⋊Q₈	—	2	1	no	—
274	C₂×C₂²⋊Q₈	—	2	4	no	—
275	C₂×C₂²⋊Q₈	—	2	1	no	—
276	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
277	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	—
279	C₂×#117	—	2	1	no	—
280	C₂×#117	—	2	4	no	—
281	C₂×#117	—	2	1	no	—
282	C₂×#117	C₂²×C₈₉	1	2	yes	—
283	C₂×#117	C₂²×C₈₉	1	8	yes	—
284	C₂×#117	C₂²×C₈₉	1	2	yes	—
285	C₂²×C₄⋊C₄	—	2	1	no	—
286	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	—	2	1	no	—
290	C₂²×C₂²⋊C₄	—	2	1	no	—
291	C₂²×C₄²	—	2	1	no	—
292	#485	C₂²×C₈₉	1	32	yes	complemented
293	#484	C₂²×C₈₉	1	16	yes	complemented
294	#483	C₂²×C₈₉	1	16	yes	complemented
295	#428	C₂²×C₈₉	1	16	yes	complemented
296	C₂×#107	C₂²×C₈₉	1	4	yes	complemented
297	C₂×#106	C₂²×C₈₉	1	4	yes	complemented
298	#419	C₂²×C₈₉	1	16	yes	complemented
299	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
300	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
301	#407	C₂²×C₈₉	1	8	yes	—
302	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
304	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	2	8	no	—
308	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
309	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
310	C₂³×C₄	—	2	8	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₈₉	1	4	yes	—
317	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
318	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
322	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
323	C₂×M₁₆	—	2	8	no	—
324	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
325	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
331	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
332	#117	—	2	8	no	—
333	#117	—	2	4	no	—
334	#117	—	2	8	no	—
335	#117	—	2	4	no	—
336	#117	C₂³×C₈₉	1	8	yes	—
337	#117	C₂³×C₈₉	1	8	yes	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	8	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	8	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	8	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	8	no	—
361	C₂×C₄²	—	2	2	no	—
362	#107	C₂³×C₈₉	1	16	yes	complemented
363	#106	C₂³×C₈₉	1	16	yes	complemented
364	#103	C₂³×C₈₉	1	16	yes	complemented
365	#103	C₂³×C₈₉	1	16	yes	complemented
366	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
367	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
372	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
373	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
374	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	16	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	16	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	16	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
408	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
410	C₂²×C₄	#41×C₈₉	1	8	yes	—
411	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
415	M₁₆	—	2	16	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
428	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	8	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	16	no	—
446	C₂³	#123×C₈₉	1	4	yes	—
447	C₂³	#137×C₈₉	1	4	yes	—
448	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
449	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
450	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
451	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
452	Q₈	—	2	8	no	—
453	Q₈	—	4	8	no	—
454	Q₈	—	4	4	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	#123×C₈₉	1	8	yes	—
477	C₂×C₄	#123×C₈₉	1	4	yes	—
478	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
483	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
484	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
485	C₈	—	2	8	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	8	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	16	no	—
496	C₂²	—	4	4	no	—
497	C₂²	C₂×#123×C₈₉	1	4	yes	—
498	C₂²	C₂×#123×C₈₉	1	2	yes	—
499	C₂²	C₂×#137×C₈₉	1	4	yes	—
500	C₂²	C₂×#137×C₈₉	1	2	yes	—
501	C₂²	#575×C₈₉	1	2	yes	—
502	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	C₂×#123×C₈₉	1	4	yes	—
510	C₄	C₂×#123×C₈₉	1	2	yes	—
511	C₄	C₂²×#41×C₈₉	1	2	yes	—
512	C₂	—	2	4	no	—
513	C₂	—	2	4	no	—
514	C₂	—	4	2	no	—
515	C₂	C₈₉×#3095	1	4	yes	direct product factor
516	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
517	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
518	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₉×#3095	C₂	direct (N × H)
4. C₂×#484×C₈₉	C₂	semidirect
5. C₂×#485×C₈₉	C₂	semidirect
6. C₂×#483×C₈₉	C₂	semidirect
7. C₂×#428×C₈₉	C₂	semidirect
8. C₂×#419×C₈₉	C₂	semidirect
32. #485×C₈₉	C₂²	semidirect
33. #484×C₈₉	C₂²	semidirect
34. #483×C₈₉	C₂²	semidirect
35. #428×C₈₉	C₂²	semidirect
36. C₂×#107×C₈₉	C₂²	semidirect
37. C₂×#106×C₈₉	C₂²	semidirect
38. #419×C₈₉	C₂²	semidirect
39. C₂×#103×C₈₉	C₂²	semidirect
40. C₂×#103×C₈₉	C₂²	semidirect
102. #107×C₈₉	C₂³	semidirect
103. #106×C₈₉	C₂³	semidirect
104. #103×C₈₉	C₂³	semidirect
105. #103×C₈₉	C₂³	semidirect
252. C₂×#3095	C₈₉	direct (N × H)
256. C₂×C₈₉	#3095	direct (N × H)
262. #3095	C₂×C₈₉	direct (N × H)
263. C₂×#484	C₂×C₈₉	semidirect
264. C₂×#485	C₂×C₈₉	semidirect
265. C₂×#483	C₂×C₈₉	semidirect
266. C₂×#428	C₂×C₈₉	semidirect
267. C₂×#419	C₂×C₈₉	semidirect
269. C₈₉	C₂×#3095	direct (N × H)
292. #485	C₂²×C₈₉	semidirect
293. #484	C₂²×C₈₉	semidirect
294. #483	C₂²×C₈₉	semidirect
295. #428	C₂²×C₈₉	semidirect
296. C₂×#107	C₂²×C₈₉	semidirect
297. C₂×#106	C₂²×C₈₉	semidirect
298. #419	C₂²×C₈₉	semidirect
299. C₂×#103	C₂²×C₈₉	semidirect
300. C₂×#103	C₂²×C₈₉	semidirect
362. #107	C₂³×C₈₉	semidirect
363. #106	C₂³×C₈₉	semidirect
364. #103	C₂³×C₈₉	semidirect
365. #103	C₂³×C₈₉	semidirect
515. C₂	C₈₉×#3095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#3095	2
C₂×#484×C₈₉	2
C₂×#485×C₈₉	2
C₂×#483×C₈₉	2
C₂×#428×C₈₉	2
C₂×#419×C₈₉	2
C₂×#407×C₈₉	2
C₂×#3095	89

Subgroups — C2×C89×#3095 #36438358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3095 #36438358