Subgroups — C₂×C₈₉×#3170 #36438520

Order 22784.

2006 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	2	yes	maximal
2	C₈₉×#3170	C₂	1	16	yes	maximal, direct product factor
3	C₂×#500×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#494×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#487×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#467×C₈₉	C₂	1	4	yes	maximal
7	C₂×C₄×Q₁₆×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₈₉	C₂²	1	4	yes	—
10	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
11	#533×C₈₉	—	2	8	no	—
12	#533×C₈₉	C₂²	1	16	yes	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
15	C₂×#125×C₈₉	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₈₉	—	2	2	no	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
20	C₂×#117×C₈₉	—	2	2	no	—
21	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
22	#500×C₈₉	C₂²	1	8	yes	complemented
23	#494×C₈₉	C₂²	1	8	yes	complemented
24	#487×C₈₉	C₂²	1	16	yes	complemented
25	#467×C₈₉	C₂²	1	32	yes	—
26	C₄×Q₁₆×C₈₉	C₂²	1	32	yes	complemented
27	C₂×#107×C₈₉	C₂²	1	4	yes	—
28	C₂×#103×C₈₉	C₂²	1	8	yes	—
29	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₈₉	C₂²	1	8	yes	—
32	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
33	C₂²×Q₈×C₈₉	—	2	2	no	—
34	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
35	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₈₉	—	2	16	no	—
39	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
40	C₂²×C₈×C₈₉	—	2	8	no	—
41	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₈₉	C₂³	1	8	yes	—
43	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₈₉	—	2	4	no	—
45	C₄⋊Q₈×C₈₉	—	2	4	no	—
46	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
47	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
48	#125×C₈₉	—	2	16	no	—
49	C₂²⋊Q₈×C₈₉	—	2	16	no	—
50	C₂²⋊Q₈×C₈₉	—	2	8	no	—
51	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
52	C₄×Q₈×C₈₉	—	2	16	no	—
53	C₄×Q₈×C₈₉	—	2	8	no	—
54	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
55	#117×C₈₉	—	2	16	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
63	C₂×C₄²×C₈₉	—	2	4	no	—
64	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	D₄	1	4	yes	—
66	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#107×C₈₉	C₂³	1	16	yes	—
71	#103×C₈₉	C₂³	1	32	yes	—
72	C₄×C₈×C₈₉	C₂³	1	8	yes	—
73	C₄×C₈×C₈₉	C₂³	1	4	yes	—
74	C₄×C₈×C₈₉	C₂³	1	4	yes	—
75	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₈₉	—	2	4	no	—
77	C₂×Q₈×C₈₉	—	2	8	no	—
78	C₂×Q₈×C₈₉	—	2	16	no	—
79	C₂×Q₈×C₈₉	—	4	8	no	—
80	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
81	C₂²×C₄×C₈₉	—	2	4	no	—
82	C₂²×C₄×C₈₉	—	2	4	no	—
83	C₂²×C₄×C₈₉	—	2	4	no	—
84	C₂²×C₄×C₈₉	—	2	4	no	—
85	C₂²×C₄×C₈₉	Q₁₆	1	8	yes	complemented
86	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
96	Q₁₆×C₈₉	—	2	32	no	—
97	C₂×C₈×C₈₉	—	2	4	no	—
98	C₂×C₈×C₈₉	—	2	16	no	—
99	C₂×C₈×C₈₉	#41	1	8	yes	—
100	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
101	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
102	C₄⋊C₄×C₈₉	—	2	8	no	—
103	C₄⋊C₄×C₈₉	—	2	8	no	—
104	C₄⋊C₄×C₈₉	—	2	8	no	—
105	C₄⋊C₄×C₈₉	—	2	16	no	—
106	C₄⋊C₄×C₈₉	—	2	16	no	—
107	C₄⋊C₄×C₈₉	—	2	4	no	—
108	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₈₉	—	2	16	no	—
110	C₄²×C₈₉	—	2	16	no	—
111	C₄²×C₈₉	C₂×D₄	1	4	yes	—
112	C₄²×C₈₉	C₂×D₄	1	2	yes	—
113	C₄²×C₈₉	C₂×D₄	1	4	yes	—
114	C₄²×C₈₉	C₂×D₄	1	2	yes	—
115	C₄²×C₈₉	C₂⁴	1	2	yes	—
116	C₄²×C₈₉	C₂⁴	1	2	yes	—
117	C₂³×C₈₉	—	2	2	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	C₂×Q₁₆	1	4	yes	—
120	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
121	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₈₉	—	2	16	no	—
123	Q₈×C₈₉	—	4	8	no	—
124	Q₈×C₈₉	—	4	16	no	—
125	C₂×C₄×C₈₉	—	2	2	no	—
126	C₂×C₄×C₈₉	—	2	2	no	—
127	C₂×C₄×C₈₉	—	2	4	no	—
128	C₂×C₄×C₈₉	—	2	8	no	—
129	C₂×C₄×C₈₉	—	2	4	no	—
130	C₂×C₄×C₈₉	—	2	8	no	—
131	C₂×C₄×C₈₉	—	2	8	no	—
132	C₂×C₄×C₈₉	—	4	8	no	—
133	C₂×C₄×C₈₉	—	4	8	no	—
134	C₂×C₄×C₈₉	C₂×Q₁₆	1	4	yes	—
135	C₂×C₄×C₈₉	C₂×Q₁₆	1	4	yes	—
136	C₂×C₄×C₈₉	C₂×Q₁₆	1	16	yes	complemented
137	C₂×C₄×C₈₉	#135	1	4	yes	—
138	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
139	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
145	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
146	C₈×C₈₉	—	2	4	no	—
147	C₈×C₈₉	C₂×#41	1	8	yes	—
148	C₂²×C₈₉	—	2	8	no	—
149	C₂²×C₈₉	—	2	2	no	—
150	C₂²×C₈₉	—	2	2	no	—
151	C₂²×C₈₉	#532	1	2	yes	—
152	C₂²×C₈₉	C₂²×Q₁₆	1	4	yes	—
153	C₂²×C₈₉	C₂²×Q₁₆	1	2	yes	—
154	C₂²×C₈₉	C₂×#135	1	2	yes	—
155	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
156	C₄×C₈₉	—	2	2	no	—
157	C₄×C₈₉	—	2	2	no	—
158	C₄×C₈₉	—	4	8	no	—
159	C₄×C₈₉	—	4	8	no	—
160	C₄×C₈₉	#532	1	2	yes	—
161	C₄×C₈₉	C₂²×Q₁₆	1	4	yes	—
162	C₄×C₈₉	C₂²×Q₁₆	1	4	yes	—
163	C₄×C₈₉	C₂×#135	1	4	yes	—
164	C₄×C₈₉	C₂²×#41	1	2	yes	—
165	C₂×#3170	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₈₉	—	2	4	no	—
167	C₂×C₈₉	#3170	1	4	yes	direct product factor
168	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
169	C₂×C₈₉	C₂³×Q₁₆	1	1	yes	characteristic
170	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
171	C₂×#533	C₂×C₈₉	1	2	yes	—
172	#3170	C₂×C₈₉	1	16	yes	direct product factor
173	C₂×#500	C₂×C₈₉	1	1	yes	characteristic, complemented
174	C₂×#494	C₂×C₈₉	1	1	yes	characteristic, complemented
175	C₂×#487	C₂×C₈₉	1	2	yes	complemented
176	C₂×#467	C₂×C₈₉	1	4	yes	—
177	C₂×C₄×Q₁₆	C₂×C₈₉	1	4	yes	complemented
178	C₂²×C₄×C₈	C₂×C₈₉	1	1	yes	characteristic
179	C₈₉	C₂×#3170	1	1	yes	characteristic, direct product factor, Sylow
180	C₂²×Q₁₆	C₂²×C₈₉	1	4	yes	—
181	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
182	#533	—	2	8	no	—
183	#533	C₂²×C₈₉	1	16	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
186	C₂×#125	—	2	2	no	—
187	C₂×C₂²⋊Q₈	—	2	2	no	—
188	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
189	C₂×C₄×Q₈	—	2	2	no	—
190	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
191	C₂×#117	—	2	2	no	—
192	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
193	#500	C₂²×C₈₉	1	8	yes	complemented
194	#494	C₂²×C₈₉	1	8	yes	complemented
195	#487	C₂²×C₈₉	1	16	yes	complemented
196	#467	C₂²×C₈₉	1	32	yes	—
197	C₄×Q₁₆	C₂²×C₈₉	1	32	yes	complemented
198	C₂×#107	C₂²×C₈₉	1	4	yes	—
199	C₂×#103	C₂²×C₈₉	1	8	yes	—
200	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₈₉	1	8	yes	—
203	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
206	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
207	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
209	C₂×Q₁₆	—	2	16	no	—
210	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
211	C₂²×C₈	—	2	8	no	—
212	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
213	C₂²×C₈	C₂³×C₈₉	1	8	yes	—
214	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
215	C₄⋊Q₈	—	2	4	no	—
216	C₄⋊Q₈	—	2	4	no	—
217	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
218	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
219	#125	—	2	16	no	—
220	C₂²⋊Q₈	—	2	16	no	—
221	C₂²⋊Q₈	—	2	8	no	—
222	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
223	C₄×Q₈	—	2	16	no	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
226	#117	—	2	16	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₈₉	1	4	yes	—
238	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
241	#107	C₂³×C₈₉	1	16	yes	—
242	#103	C₂³×C₈₉	1	32	yes	—
243	C₄×C₈	C₂³×C₈₉	1	8	yes	—
244	C₄×C₈	C₂³×C₈₉	1	4	yes	—
245	C₄×C₈	C₂³×C₈₉	1	4	yes	—
246	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	4	8	no	—
251	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	Q₁₆×C₈₉	1	8	yes	complemented
257	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
264	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
265	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
267	Q₁₆	—	2	32	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	16	no	—
270	C₂×C₈	#41×C₈₉	1	8	yes	—
271	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
272	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
280	C₂²⋊C₄	—	2	16	no	—
281	C₄²	—	2	16	no	—
282	C₄²	C₂×D₄×C₈₉	1	4	yes	—
283	C₄²	C₂×D₄×C₈₉	1	2	yes	—
284	C₄²	C₂×D₄×C₈₉	1	4	yes	—
285	C₄²	C₂×D₄×C₈₉	1	2	yes	—
286	C₄²	C₂⁴×C₈₉	1	2	yes	—
287	C₄²	C₂⁴×C₈₉	1	2	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂×Q₁₆×C₈₉	1	4	yes	—
291	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
292	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
293	Q₈	—	2	16	no	—
294	Q₈	—	4	8	no	—
295	Q₈	—	4	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂×Q₁₆×C₈₉	1	4	yes	—
306	C₂×C₄	C₂×Q₁₆×C₈₉	1	4	yes	—
307	C₂×C₄	C₂×Q₁₆×C₈₉	1	16	yes	complemented
308	C₂×C₄	#135×C₈₉	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
315	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
316	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
317	C₈	—	2	4	no	—
318	C₈	C₂×#41×C₈₉	1	8	yes	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	2	no	—
322	C₂²	#532×C₈₉	1	2	yes	—
323	C₂²	C₂²×Q₁₆×C₈₉	1	4	yes	—
324	C₂²	C₂²×Q₁₆×C₈₉	1	2	yes	—
325	C₂²	C₂×#135×C₈₉	1	2	yes	—
326	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	8	no	—
331	C₄	#532×C₈₉	1	2	yes	—
332	C₄	C₂²×Q₁₆×C₈₉	1	4	yes	—
333	C₄	C₂²×Q₁₆×C₈₉	1	4	yes	—
334	C₄	C₂×#135×C₈₉	1	4	yes	—
335	C₄	C₂²×#41×C₈₉	1	2	yes	—
336	C₂	—	2	4	no	—
337	C₂	C₈₉×#3170	1	4	yes	direct product factor
338	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
339	C₂	C₂³×Q₁₆×C₈₉	1	1	yes	characteristic
340	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3170	C₂	direct (N × H)
3. C₂×#500×C₈₉	C₂	semidirect
4. C₂×#494×C₈₉	C₂	semidirect
5. C₂×#487×C₈₉	C₂	semidirect
7. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
22. #500×C₈₉	C₂²	semidirect
23. #494×C₈₉	C₂²	semidirect
24. #487×C₈₉	C₂²	semidirect
26. C₄×Q₁₆×C₈₉	C₂²	semidirect
85. C₂²×C₄×C₈₉	Q₁₆	semidirect
136. C₂×C₄×C₈₉	C₂×Q₁₆	semidirect
165. C₂×#3170	C₈₉	direct (N × H)
167. C₂×C₈₉	#3170	direct (N × H)
172. #3170	C₂×C₈₉	direct (N × H)
173. C₂×#500	C₂×C₈₉	semidirect
174. C₂×#494	C₂×C₈₉	semidirect
175. C₂×#487	C₂×C₈₉	semidirect
177. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
179. C₈₉	C₂×#3170	direct (N × H)
193. #500	C₂²×C₈₉	semidirect
194. #494	C₂²×C₈₉	semidirect
195. #487	C₂²×C₈₉	semidirect
197. C₄×Q₁₆	C₂²×C₈₉	semidirect
256. C₂²×C₄	Q₁₆×C₈₉	semidirect
307. C₂×C₄	C₂×Q₁₆×C₈₉	semidirect
337. C₂	C₈₉×#3170	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×#533×C₈₉	2
C₈₉×#3170	2
C₂×#500×C₈₉	2
C₂×#494×C₈₉	2
C₂×#487×C₈₉	2
C₂×#467×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₂²×C₄×C₈×C₈₉	2
C₂×#3170	89

Subgroups — C2×C89×#3170 #36438520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3170 #36438520