Subgroups — C₂×C₈₉×#3243 #36438705

Order 22784.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3243	C₂	1	16	yes	maximal, direct product factor
4	C₂×#501×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#500×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#488×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#484×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#485×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#482×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂×#480×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#479×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#477×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#478×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#433×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#544×C₈₉	—	2	4	no	—
18	#544×C₈₉	C₂²	1	8	yes	complemented
19	#542×C₈₉	—	2	4	no	—
20	#542×C₈₉	C₂²	1	8	yes	—
21	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₈₉	—	2	1	no	—
26	C₂×#125×C₈₉	—	2	1	no	—
27	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₈₉	—	2	1	no	—
30	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₈₉	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	#501×C₈₉	C₂²	1	8	yes	complemented
43	#500×C₈₉	C₂²	1	8	yes	complemented
44	#489×C₈₉	C₂²	1	8	yes	complemented
45	#488×C₈₉	C₂²	1	8	yes	complemented
46	#485×C₈₉	C₂²	1	8	yes	complemented
47	#484×C₈₉	C₂²	1	8	yes	complemented
48	#482×C₈₉	C₂²	1	8	yes	—
49	#480×C₈₉	C₂²	1	8	yes	—
50	#479×C₈₉	C₂²	1	8	yes	complemented
51	#478×C₈₉	C₂²	1	8	yes	complemented
52	#477×C₈₉	C₂²	1	8	yes	complemented
53	#474×C₈₉	C₂²	1	8	yes	complemented
54	#433×C₈₉	C₂²	1	8	yes	complemented
55	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
68	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
71	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₈₉	—	2	1	no	—
78	C₂²×Q₈×C₈₉	—	2	1	no	—
79	C₂²×Q₈×C₈₉	—	2	1	no	—
80	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	—	2	1	no	—
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₉	—	2	8	no	—
91	C₄⋊Q₈×C₈₉	—	2	2	no	—
92	C₄⋊Q₈×C₈₉	—	2	2	no	—
93	C₄⋊Q₈×C₈₉	—	2	2	no	—
94	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
97	#126×C₈₉	—	2	8	no	—
98	#125×C₈₉	—	2	8	no	—
99	#125×C₈₉	—	2	2	no	—
100	#125×C₈₉	—	2	2	no	—
101	#125×C₈₉	C₂³	1	4	yes	—
102	#125×C₈₉	C₂³	1	4	yes	—
103	#124×C₈₉	—	2	8	no	—
104	#124×C₈₉	—	2	2	no	—
105	#124×C₈₉	C₂³	1	4	yes	—
106	#123×C₈₉	—	2	8	no	—
107	C₂²⋊Q₈×C₈₉	—	2	2	no	—
108	C₂²⋊Q₈×C₈₉	—	2	8	no	—
109	C₂²⋊Q₈×C₈₉	—	2	8	no	—
110	C₂²⋊Q₈×C₈₉	—	2	8	no	—
111	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
112	#121×C₈₉	—	2	2	no	—
113	#121×C₈₉	C₂³	1	4	yes	—
114	C₄×Q₈×C₈₉	—	2	2	no	—
115	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
116	C₄×D₄×C₈₉	—	2	2	no	—
117	C₄×D₄×C₈₉	C₂³	1	4	yes	—
118	#117×C₈₉	—	2	2	no	—
119	#117×C₈₉	D₄	1	4	yes	—
120	#117×C₈₉	C₂³	1	4	yes	—
121	#117×C₈₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
150	C₂×C₄²×C₈₉	—	2	1	no	—
151	C₂×C₄²×C₈₉	—	2	1	no	—
152	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
154	#107×C₈₉	C₂³	1	4	yes	—
155	#107×C₈₉	C₂³	1	4	yes	—
156	#107×C₈₉	C₂³	1	4	yes	—
157	#107×C₈₉	C₂³	1	4	yes	—
158	#107×C₈₉	C₂³	1	4	yes	—
159	#107×C₈₉	C₂³	1	4	yes	—
160	#106×C₈₉	C₂³	1	4	yes	—
161	#106×C₈₉	C₂³	1	4	yes	—
162	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
163	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
164	#103×C₈₉	C₂³	1	4	yes	—
165	#103×C₈₉	C₂³	1	4	yes	—
166	#103×C₈₉	C₂³	1	4	yes	—
167	#103×C₈₉	C₂³	1	4	yes	—
168	#102×C₈₉	C₂³	1	4	yes	—
169	#102×C₈₉	C₂³	1	4	yes	—
170	#102×C₈₉	C₂³	1	4	yes	—
171	#102×C₈₉	C₂³	1	4	yes	—
172	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
173	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
174	#97×C₈₉	C₂³	1	4	yes	—
175	C₄×C₈×C₈₉	C₂³	1	4	yes	—
176	C₂⁴×C₈₉	—	2	1	no	—
177	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₈₉	—	2	1	no	—
179	C₂×Q₈×C₈₉	—	2	4	no	—
180	C₂×Q₈×C₈₉	—	2	4	no	—
181	C₂×Q₈×C₈₉	—	2	4	no	—
182	C₂×Q₈×C₈₉	—	2	2	no	—
183	C₂×Q₈×C₈₉	—	2	2	no	—
184	C₂×Q₈×C₈₉	—	8	2	no	—
185	C₂×Q₈×C₈₉	—	8	2	no	—
186	C₂×Q₈×C₈₉	—	8	2	no	—
187	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	2	no	—
191	C₂×D₄×C₈₉	—	2	2	no	—
192	C₂×D₄×C₈₉	—	8	2	no	—
193	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₈₉	—	2	2	no	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	8	2	no	—
206	C₂²×C₄×C₈₉	—	8	2	no	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₈×C₈₉	—	2	2	no	—
216	C₂×C₈×C₈₉	—	2	2	no	—
217	C₂×C₈×C₈₉	—	2	2	no	—
218	C₂×C₈×C₈₉	—	2	2	no	—
219	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
220	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
221	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
222	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
223	C₄⋊C₄×C₈₉	—	2	4	no	—
224	C₄⋊C₄×C₈₉	—	2	1	no	—
225	C₄⋊C₄×C₈₉	—	2	1	no	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	4	no	—
228	C₄⋊C₄×C₈₉	—	2	4	no	—
229	C₄⋊C₄×C₈₉	—	2	4	no	—
230	C₄⋊C₄×C₈₉	—	2	4	no	—
231	C₄⋊C₄×C₈₉	—	2	4	no	—
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	no	—
235	C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₄⋊C₄×C₈₉	—	2	1	no	—
237	C₄⋊C₄×C₈₉	—	2	1	no	—
238	C₄⋊C₄×C₈₉	—	2	1	no	—
239	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
240	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
241	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
246	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂²⋊C₄×C₈₉	—	2	4	no	—
248	C₂²⋊C₄×C₈₉	—	2	4	no	—
249	C₂²⋊C₄×C₈₉	—	2	4	no	—
250	C₂²⋊C₄×C₈₉	—	2	4	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
254	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
255	C₄²×C₈₉	—	2	4	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	C₂×D₄	1	2	yes	—
258	C₄²×C₈₉	C₂×D₄	1	2	yes	—
259	C₄²×C₈₉	C₂⁴	1	2	yes	—
260	C₄²×C₈₉	C₂⁴	1	2	yes	—
261	C₂³×C₈₉	—	2	2	no	—
262	C₂³×C₈₉	—	2	2	no	—
263	C₂³×C₈₉	—	2	2	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	4	2	no	—
266	C₂³×C₈₉	—	4	2	no	—
267	C₂³×C₈₉	—	4	2	no	—
268	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
269	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
270	Q₈×C₈₉	—	2	2	no	—
271	Q₈×C₈₉	—	2	2	no	—
272	Q₈×C₈₉	—	4	2	no	—
273	Q₈×C₈₉	—	8	4	no	—
274	Q₈×C₈₉	—	8	4	no	—
275	Q₈×C₈₉	—	8	4	no	—
276	D₄×C₈₉	—	2	2	no	—
277	D₄×C₈₉	—	2	2	no	—
278	D₄×C₈₉	—	4	2	no	—
279	D₄×C₈₉	—	8	4	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	4	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	4	2	no	—
296	C₂×C₄×C₈₉	—	4	2	no	—
297	C₂×C₄×C₈₉	—	4	2	no	—
298	C₂×C₄×C₈₉	—	4	2	no	—
299	C₂×C₄×C₈₉	—	4	2	no	—
300	C₂×C₄×C₈₉	—	4	2	no	—
301	C₂×C₄×C₈₉	—	4	2	no	—
302	C₂×C₄×C₈₉	—	8	4	no	—
303	C₂×C₄×C₈₉	—	8	4	no	—
304	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
311	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
313	C₈×C₈₉	—	2	2	no	—
314	C₈×C₈₉	—	2	2	no	—
315	C₈×C₈₉	—	2	2	no	—
316	C₈×C₈₉	—	2	2	no	—
317	C₂²×C₈₉	—	2	2	no	—
318	C₂²×C₈₉	—	2	2	no	—
319	C₂²×C₈₉	—	2	2	no	—
320	C₂²×C₈₉	—	4	4	no	—
321	C₂²×C₈₉	—	4	2	no	—
322	C₂²×C₈₉	—	4	2	no	—
323	C₂²×C₈₉	—	4	2	no	—
324	C₂²×C₈₉	—	8	4	no	—
325	C₂²×C₈₉	#536	1	2	yes	—
326	C₂²×C₈₉	#576	1	2	yes	—
327	C₂²×C₈₉	#578	1	2	yes	—
328	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
329	C₄×C₈₉	—	2	2	no	—
330	C₄×C₈₉	—	2	2	no	—
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	2	no	—
333	C₄×C₈₉	—	2	2	no	—
334	C₄×C₈₉	—	4	2	no	—
335	C₄×C₈₉	—	4	2	no	—
336	C₄×C₈₉	—	4	2	no	—
337	C₄×C₈₉	—	4	2	no	—
338	C₄×C₈₉	—	4	2	no	—
339	C₄×C₈₉	—	4	2	no	—
340	C₄×C₈₉	—	4	2	no	—
341	C₄×C₈₉	#536	1	2	yes	—
342	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
343	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂×#3243	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₈₉	—	4	2	no	—
346	C₂×C₈₉	—	8	2	no	—
347	C₂×C₈₉	#3243	1	4	yes	direct product factor
348	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
349	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
350	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
351	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
352	C₂×#542	C₂×C₈₉	1	1	yes	characteristic
353	#3243	C₂×C₈₉	1	16	yes	direct product factor
354	C₂×#501	C₂×C₈₉	1	1	yes	characteristic, complemented
355	C₂×#500	C₂×C₈₉	1	1	yes	characteristic, complemented
356	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
357	C₂×#488	C₂×C₈₉	1	1	yes	characteristic, complemented
358	C₂×#484	C₂×C₈₉	1	1	yes	characteristic, complemented
359	C₂×#485	C₂×C₈₉	1	1	yes	characteristic, complemented
360	C₂×#482	C₂×C₈₉	1	1	yes	characteristic
361	C₂×#480	C₂×C₈₉	1	1	yes	characteristic
362	C₂×#479	C₂×C₈₉	1	1	yes	characteristic, complemented
363	C₂×#477	C₂×C₈₉	1	1	yes	characteristic, complemented
364	C₂×#478	C₂×C₈₉	1	1	yes	characteristic, complemented
365	C₂×#474	C₂×C₈₉	1	1	yes	characteristic, complemented
366	C₂×#433	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₈₉	C₂×#3243	1	1	yes	characteristic, direct product factor, Sylow
368	#544	—	2	4	no	—
369	#544	C₂²×C₈₉	1	8	yes	complemented
370	#542	—	2	4	no	—
371	#542	C₂²×C₈₉	1	8	yes	—
372	C₂×C₄⋊Q₈	—	2	1	no	—
373	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
374	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
376	C₂×#126	—	2	1	no	—
377	C₂×#125	—	2	1	no	—
378	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
379	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
380	C₂×#124	—	2	1	no	—
381	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
382	C₂×#123	—	2	1	no	—
383	C₂×C₂²⋊Q₈	—	2	1	no	—
384	C₂×C₂²⋊Q₈	—	2	1	no	—
385	C₂×C₂²⋊Q₈	—	2	1	no	—
386	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
387	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
390	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
391	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
393	#501	C₂²×C₈₉	1	8	yes	complemented
394	#500	C₂²×C₈₉	1	8	yes	complemented
395	#489	C₂²×C₈₉	1	8	yes	complemented
396	#488	C₂²×C₈₉	1	8	yes	complemented
397	#485	C₂²×C₈₉	1	8	yes	complemented
398	#484	C₂²×C₈₉	1	8	yes	complemented
399	#482	C₂²×C₈₉	1	8	yes	—
400	#480	C₂²×C₈₉	1	8	yes	—
401	#479	C₂²×C₈₉	1	8	yes	complemented
402	#478	C₂²×C₈₉	1	8	yes	complemented
403	#477	C₂²×C₈₉	1	8	yes	complemented
404	#474	C₂²×C₈₉	1	8	yes	complemented
405	#433	C₂²×C₈₉	1	8	yes	complemented
406	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
441	C₄⋊Q₈	—	2	8	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
446	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
447	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
448	#126	—	2	8	no	—
449	#125	—	2	8	no	—
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	#125	C₂³×C₈₉	1	4	yes	—
453	#125	C₂³×C₈₉	1	4	yes	—
454	#124	—	2	8	no	—
455	#124	—	2	2	no	—
456	#124	C₂³×C₈₉	1	4	yes	—
457	#123	—	2	8	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	8	no	—
460	C₂²⋊Q₈	—	2	8	no	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
463	#121	—	2	2	no	—
464	#121	C₂³×C₈₉	1	4	yes	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	C₂³×C₈₉	1	4	yes	—
469	#117	—	2	2	no	—
470	#117	D₄×C₈₉	1	4	yes	—
471	#117	C₂³×C₈₉	1	4	yes	—
472	#117	C₂³×C₈₉	1	4	yes	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
505	#107	C₂³×C₈₉	1	4	yes	—
506	#107	C₂³×C₈₉	1	4	yes	—
507	#107	C₂³×C₈₉	1	4	yes	—
508	#107	C₂³×C₈₉	1	4	yes	—
509	#107	C₂³×C₈₉	1	4	yes	—
510	#107	C₂³×C₈₉	1	4	yes	—
511	#106	C₂³×C₈₉	1	4	yes	—
512	#106	C₂³×C₈₉	1	4	yes	—
513	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
514	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
515	#103	C₂³×C₈₉	1	4	yes	—
516	#103	C₂³×C₈₉	1	4	yes	—
517	#103	C₂³×C₈₉	1	4	yes	—
518	#103	C₂³×C₈₉	1	4	yes	—
519	#102	C₂³×C₈₉	1	4	yes	—
520	#102	C₂³×C₈₉	1	4	yes	—
521	#102	C₂³×C₈₉	1	4	yes	—
522	#102	C₂³×C₈₉	1	4	yes	—
523	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
524	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
525	#97	C₂³×C₈₉	1	4	yes	—
526	C₄×C₈	C₂³×C₈₉	1	4	yes	—
527	C₂⁴	—	2	1	no	—
528	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	8	2	no	—
536	C₂×Q₈	—	8	2	no	—
537	C₂×Q₈	—	8	2	no	—
538	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	8	2	no	—
544	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	8	2	no	—
557	C₂²×C₄	—	8	2	no	—
558	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
566	C₂×C₈	—	2	2	no	—
567	C₂×C₈	—	2	2	no	—
568	C₂×C₈	—	2	2	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
571	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
572	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
573	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
591	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
592	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
593	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
594	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
595	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
596	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
597	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
605	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	C₂×D₄×C₈₉	1	2	yes	—
609	C₄²	C₂×D₄×C₈₉	1	2	yes	—
610	C₄²	C₂⁴×C₈₉	1	2	yes	—
611	C₄²	C₂⁴×C₈₉	1	2	yes	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
620	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
621	Q₈	—	2	2	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	4	2	no	—
624	Q₈	—	8	4	no	—
625	Q₈	—	8	4	no	—
626	Q₈	—	8	4	no	—
627	D₄	—	2	2	no	—
628	D₄	—	2	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	8	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
661	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
662	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
663	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
664	C₈	—	2	2	no	—
665	C₈	—	2	2	no	—
666	C₈	—	2	2	no	—
667	C₈	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	8	4	no	—
676	C₂²	#536×C₈₉	1	2	yes	—
677	C₂²	#576×C₈₉	1	2	yes	—
678	C₂²	#578×C₈₉	1	2	yes	—
679	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	#536×C₈₉	1	2	yes	—
693	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
694	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
695	C₂	—	4	2	no	—
696	C₂	—	8	2	no	—
697	C₂	C₈₉×#3243	1	4	yes	direct product factor
698	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
699	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
700	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	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#3243	C₂	direct (N × H)
4. C₂×#501×C₈₉	C₂	semidirect
5. C₂×#500×C₈₉	C₂	semidirect
6. C₂×#489×C₈₉	C₂	semidirect
7. C₂×#488×C₈₉	C₂	semidirect
8. C₂×#484×C₈₉	C₂	semidirect
9. C₂×#485×C₈₉	C₂	semidirect
12. C₂×#479×C₈₉	C₂	semidirect
13. C₂×#477×C₈₉	C₂	semidirect
14. C₂×#478×C₈₉	C₂	semidirect
15. C₂×#474×C₈₉	C₂	semidirect
16. C₂×#433×C₈₉	C₂	semidirect
18. #544×C₈₉	C₂²	semidirect
42. #501×C₈₉	C₂²	semidirect
43. #500×C₈₉	C₂²	semidirect
44. #489×C₈₉	C₂²	semidirect
45. #488×C₈₉	C₂²	semidirect
46. #485×C₈₉	C₂²	semidirect
47. #484×C₈₉	C₂²	semidirect
50. #479×C₈₉	C₂²	semidirect
51. #478×C₈₉	C₂²	semidirect
52. #477×C₈₉	C₂²	semidirect
53. #474×C₈₉	C₂²	semidirect
54. #433×C₈₉	C₂²	semidirect
344. C₂×#3243	C₈₉	direct (N × H)
347. C₂×C₈₉	#3243	direct (N × H)
351. C₂×#544	C₂×C₈₉	semidirect
353. #3243	C₂×C₈₉	direct (N × H)
354. C₂×#501	C₂×C₈₉	semidirect
355. C₂×#500	C₂×C₈₉	semidirect
356. C₂×#489	C₂×C₈₉	semidirect
357. C₂×#488	C₂×C₈₉	semidirect
358. C₂×#484	C₂×C₈₉	semidirect
359. C₂×#485	C₂×C₈₉	semidirect
362. C₂×#479	C₂×C₈₉	semidirect
363. C₂×#477	C₂×C₈₉	semidirect
364. C₂×#478	C₂×C₈₉	semidirect
365. C₂×#474	C₂×C₈₉	semidirect
366. C₂×#433	C₂×C₈₉	semidirect
367. C₈₉	C₂×#3243	direct (N × H)
369. #544	C₂²×C₈₉	semidirect
393. #501	C₂²×C₈₉	semidirect
394. #500	C₂²×C₈₉	semidirect
395. #489	C₂²×C₈₉	semidirect
396. #488	C₂²×C₈₉	semidirect
397. #485	C₂²×C₈₉	semidirect
398. #484	C₂²×C₈₉	semidirect
401. #479	C₂²×C₈₉	semidirect
402. #478	C₂²×C₈₉	semidirect
403. #477	C₂²×C₈₉	semidirect
404. #474	C₂²×C₈₉	semidirect
405. #433	C₂²×C₈₉	semidirect
697. C₂	C₈₉×#3243	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×#544×C₈₉	2
C₂×#542×C₈₉	2
C₈₉×#3243	2
C₂×#501×C₈₉	2
C₂×#500×C₈₉	2
C₂×#489×C₈₉	2
C₂×#488×C₈₉	2
C₂×#484×C₈₉	2
C₂×#485×C₈₉	2
C₂×#482×C₈₉	2
C₂×#480×C₈₉	2
C₂×#479×C₈₉	2
C₂×#477×C₈₉	2
C₂×#478×C₈₉	2
C₂×#474×C₈₉	2
C₂×#433×C₈₉	2
C₂×#3243	89

Subgroups — C2×C89×#3243 #36438705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3243 #36438705