Subgroups — C₂×C₈₉×#3028 #36438245

Order 22784.

4790 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#536×C₈₉	C₂	1	3	yes	maximal, complemented
3	C₈₉×#3028	C₂	1	16	yes	maximal, direct product factor
4	C₂×#458×C₈₉	C₂	1	8	yes	maximal, complemented
5	C₂×#410×C₈₉	C₂	1	3	yes	maximal, complemented
6	#585×C₈₉	—	2	12	no	—
7	#585×C₈₉	C₂²	1	8	yes	—
8	C₂×2₋¹⁺⁴×C₈₉	—	2	3	no	—
9	C₂×H(5,𝔽₂)×C₈₉	—	2	3	no	—
10	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	4	yes	—
11	C₂²×#41×C₈₉	—	2	6	no	—
12	C₂²×#41×C₈₉	C₂²	1	3	yes	—
13	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
14	#536×C₈₉	—	2	12	no	—
15	#536×C₈₉	C₂²	1	24	yes	complemented
16	C₂×C₄⋊Q₈×C₈₉	—	2	3	no	—
17	C₂×#124×C₈₉	—	2	3	no	—
18	C₂×#123×C₈₉	C₂²	1	12	yes	complemented
19	C₂×C₂²⋊Q₈×C₈₉	—	2	6	no	—
20	C₂×#117×C₈₉	C₂²	1	3	yes	complemented
21	#458×C₈₉	C₂²	1	64	yes	complemented
22	#410×C₈₉	C₂²	1	24	yes	complemented
23	C₂×#99×C₈₉	C₂²	1	12	yes	complemented
24	2₋¹⁺⁴×C₈₉	—	2	24	no	—
25	2₋¹⁺⁴×C₈₉	—	2	24	no	—
26	H(5,𝔽₂)×C₈₉	—	2	24	no	—
27	H(5,𝔽₂)×C₈₉	—	2	24	no	—
28	H(5,𝔽₂)×C₈₉	—	2	24	no	—
29	H(5,𝔽₂)×C₈₉	C₂³	1	16	yes	—
30	C₂×#41×C₈₉	—	2	4	no	—
31	C₂×#41×C₈₉	—	2	12	no	—
32	C₂×#41×C₈₉	—	2	48	no	—
33	C₂×#41×C₈₉	—	2	6	no	—
34	C₂×#41×C₈₉	—	2	12	no	—
35	C₂×#41×C₈₉	—	2	48	no	—
36	C₂×#41×C₈₉	—	2	6	no	—
37	C₂×#41×C₈₉	—	2	12	no	—
38	C₂×#41×C₈₉	D₄	1	12	yes	—
39	C₂×#41×C₈₉	C₂³	1	12	yes	—
40	C₂²×Q₈×C₈₉	—	2	6	no	—
41	C₂²×Q₈×C₈₉	—	2	3	no	—
42	C₂²×Q₈×C₈₉	—	2	3	no	—
43	C₂²×Q₈×C₈₉	—	2	6	no	—
44	C₂²×Q₈×C₈₉	D₄	1	3	yes	—
45	C₂²×Q₈×C₈₉	C₂³	1	4	yes	complemented
46	C₂²×D₄×C₈₉	—	2	6	no	—
47	C₂²×D₄×C₈₉	—	2	12	no	—
48	C₂²×D₄×C₈₉	D₄	1	3	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
50	C₂³×C₄×C₈₉	—	2	4	no	—
51	C₂³×C₄×C₈₉	D₄	1	6	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₈₉	—	2	24	no	—
55	#124×C₈₉	—	2	24	no	—
56	#123×C₈₉	—	2	24	no	—
57	#123×C₈₉	C₂³	1	48	yes	complemented
58	C₂²⋊Q₈×C₈₉	—	2	48	no	—
59	#117×C₈₉	—	2	6	no	—
60	#117×C₈₉	C₂³	1	12	yes	complemented
61	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	12	no	—
63	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
64	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
65	C₂×C₄²×C₈₉	—	2	3	no	—
66	#99×C₈₉	C₂³	1	48	yes	complemented
67	C₂⁴×C₈₉	—	2	4	no	—
68	C₂⁴×C₈₉	C₂×D₄	1	6	yes	—
69	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
70	#41×C₈₉	—	2	32	no	—
71	#41×C₈₉	—	2	48	no	—
72	#41×C₈₉	—	2	96	no	—
73	#41×C₈₉	—	2	24	no	—
74	#41×C₈₉	—	2	24	no	—
75	#41×C₈₉	—	2	24	no	—
76	#41×C₈₉	—	2	48	no	—
77	#41×C₈₉	—	2	24	no	—
78	C₂×Q₈×C₈₉	—	2	4	no	—
79	C₂×Q₈×C₈₉	—	2	48	no	—
80	C₂×Q₈×C₈₉	—	2	6	no	—
81	C₂×Q₈×C₈₉	—	2	6	no	—
82	C₂×Q₈×C₈₉	—	2	12	no	—
83	C₂×Q₈×C₈₉	—	2	12	no	—
84	C₂×Q₈×C₈₉	—	4	6	no	—
85	C₂×Q₈×C₈₉	—	4	6	no	—
86	C₂×Q₈×C₈₉	—	4	1	no	—
87	C₂×Q₈×C₈₉	—	4	3	no	—
88	C₂×Q₈×C₈₉	C₂×D₄	1	12	yes	—
89	C₂×D₄×C₈₉	—	2	12	no	—
90	C₂×D₄×C₈₉	—	2	48	no	—
91	C₂×D₄×C₈₉	—	2	48	no	—
92	C₂×D₄×C₈₉	—	2	12	no	—
93	C₂×D₄×C₈₉	—	2	48	no	—
94	C₂×D₄×C₈₉	—	2	12	no	—
95	C₂×D₄×C₈₉	—	2	6	no	—
96	C₂×D₄×C₈₉	—	2	6	no	—
97	C₂×D₄×C₈₉	C₂×D₄	1	12	yes	—
98	C₂×D₄×C₈₉	C₂×D₄	1	12	yes	—
99	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
100	C₂²×C₄×C₈₉	—	2	12	no	—
101	C₂²×C₄×C₈₉	—	2	32	no	—
102	C₂²×C₄×C₈₉	—	2	6	no	—
103	C₂²×C₄×C₈₉	—	2	6	no	—
104	C₂²×C₄×C₈₉	—	2	12	no	—
105	C₂²×C₄×C₈₉	—	2	6	no	—
106	C₂²×C₄×C₈₉	—	2	6	no	—
107	C₂²×C₄×C₈₉	—	2	6	no	—
108	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	24	yes	—
110	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
113	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₈₉	—	2	12	no	—
116	C₄⋊C₄×C₈₉	—	2	48	no	—
117	C₂²⋊C₄×C₈₉	—	2	48	no	—
118	C₂²⋊C₄×C₈₉	—	2	6	no	—
119	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
120	C₄²×C₈₉	—	2	12	no	—
121	C₂³×C₈₉	—	2	16	no	—
122	C₂³×C₈₉	—	2	6	no	—
123	C₂³×C₈₉	—	2	6	no	—
124	C₂³×C₈₉	—	4	2	no	—
125	C₂³×C₈₉	—	4	12	no	—
126	C₂³×C₈₉	—	8	8	no	—
127	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
128	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
129	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
130	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
131	Q₈×C₈₉	—	2	16	no	—
132	Q₈×C₈₉	—	2	24	no	—
133	Q₈×C₈₉	—	4	4	no	—
134	Q₈×C₈₉	—	4	12	no	—
135	D₄×C₈₉	—	2	48	no	—
136	D₄×C₈₉	—	2	24	no	—
137	D₄×C₈₉	—	2	24	no	—
138	D₄×C₈₉	—	2	24	no	—
139	C₂×C₄×C₈₉	—	2	48	no	—
140	C₂×C₄×C₈₉	—	2	6	no	—
141	C₂×C₄×C₈₉	—	2	6	no	—
142	C₂×C₄×C₈₉	—	2	24	no	—
143	C₂×C₄×C₈₉	—	2	24	no	—
144	C₂×C₄×C₈₉	—	2	12	no	—
145	C₂×C₄×C₈₉	—	2	12	no	—
146	C₂×C₄×C₈₉	—	4	12	no	—
147	C₂×C₄×C₈₉	—	4	6	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	#120	1	6	yes	—
150	C₂×C₄×C₈₉	#120	1	6	yes	—
151	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#120	1	3	yes	—
153	C₂×C₄×C₈₉	C₂²×D₄	1	12	yes	—
154	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
155	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
156	C₂²×C₈₉	—	2	6	no	—
157	C₂²×C₈₉	—	2	12	no	—
158	C₂²×C₈₉	—	4	3	no	—
159	C₂²×C₈₉	—	4	1	no	—
160	C₂²×C₈₉	—	4	12	no	—
161	C₂²×C₈₉	—	4	12	no	—
162	C₂²×C₈₉	—	8	6	no	—
163	C₂²×C₈₉	—	8	16	no	—
164	C₂²×C₈₉	C₂×#120	1	3	yes	—
165	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
166	C₂²×C₈₉	C₂³×D₄	1	3	yes	—
167	C₄×C₈₉	—	2	12	no	—
168	C₄×C₈₉	—	4	12	no	—
169	C₄×C₈₉	—	4	4	no	—
170	C₄×C₈₉	C₂×#120	1	2	yes	—
171	C₄×C₈₉	C₂×#120	1	6	yes	—
172	C₂×#3028	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₈₉	—	2	3	no	—
174	C₂×C₈₉	—	2	3	no	—
175	C₂×C₈₉	—	4	12	no	—
176	C₂×C₈₉	#3028	1	2	yes	direct product factor
177	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
178	C₂×#585	C₂×C₈₉	1	1	yes	characteristic
179	C₂×#536	C₂×C₈₉	1	3	yes	complemented
180	#3028	C₂×C₈₉	1	16	yes	direct product factor
181	C₂×#458	C₂×C₈₉	1	8	yes	complemented
182	C₂×#410	C₂×C₈₉	1	3	yes	complemented
183	C₈₉	C₂×#3028	1	1	yes	characteristic, direct product factor, Sylow
184	#585	—	2	12	no	—
185	#585	C₂²×C₈₉	1	8	yes	—
186	C₂×2₋¹⁺⁴	—	2	3	no	—
187	C₂×H(5,𝔽₂)	—	2	3	no	—
188	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	4	yes	—
189	C₂²×#41	—	2	6	no	—
190	C₂²×#41	C₂²×C₈₉	1	3	yes	—
191	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
192	#536	—	2	12	no	—
193	#536	C₂²×C₈₉	1	24	yes	complemented
194	C₂×C₄⋊Q₈	—	2	3	no	—
195	C₂×#124	—	2	3	no	—
196	C₂×#123	C₂²×C₈₉	1	12	yes	complemented
197	C₂×C₂²⋊Q₈	—	2	6	no	—
198	C₂×#117	C₂²×C₈₉	1	3	yes	complemented
199	#458	C₂²×C₈₉	1	64	yes	complemented
200	#410	C₂²×C₈₉	1	24	yes	complemented
201	C₂×#99	C₂²×C₈₉	1	12	yes	complemented
202	2₋¹⁺⁴	—	2	24	no	—
203	2₋¹⁺⁴	—	2	24	no	—
204	H(5,𝔽₂)	—	2	24	no	—
205	H(5,𝔽₂)	—	2	24	no	—
206	H(5,𝔽₂)	—	2	24	no	—
207	H(5,𝔽₂)	C₂³×C₈₉	1	16	yes	—
208	C₂×#41	—	2	4	no	—
209	C₂×#41	—	2	12	no	—
210	C₂×#41	—	2	48	no	—
211	C₂×#41	—	2	6	no	—
212	C₂×#41	—	2	12	no	—
213	C₂×#41	—	2	48	no	—
214	C₂×#41	—	2	6	no	—
215	C₂×#41	—	2	12	no	—
216	C₂×#41	D₄×C₈₉	1	12	yes	—
217	C₂×#41	C₂³×C₈₉	1	12	yes	—
218	C₂²×Q₈	—	2	6	no	—
219	C₂²×Q₈	—	2	3	no	—
220	C₂²×Q₈	—	2	3	no	—
221	C₂²×Q₈	—	2	6	no	—
222	C₂²×Q₈	D₄×C₈₉	1	3	yes	—
223	C₂²×Q₈	C₂³×C₈₉	1	4	yes	complemented
224	C₂²×D₄	—	2	6	no	—
225	C₂²×D₄	—	2	12	no	—
226	C₂²×D₄	D₄×C₈₉	1	3	yes	—
227	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	D₄×C₈₉	1	6	yes	—
230	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	24	no	—
233	#124	—	2	24	no	—
234	#123	—	2	24	no	—
235	#123	C₂³×C₈₉	1	48	yes	complemented
236	C₂²⋊Q₈	—	2	48	no	—
237	#117	—	2	6	no	—
238	#117	C₂³×C₈₉	1	12	yes	complemented
239	C₂×C₄⋊C₄	—	2	3	no	—
240	C₂×C₄⋊C₄	—	2	12	no	—
241	C₂×C₂²⋊C₄	—	2	12	no	—
242	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
243	C₂×C₄²	—	2	3	no	—
244	#99	C₂³×C₈₉	1	48	yes	complemented
245	C₂⁴	—	2	4	no	—
246	C₂⁴	C₂×D₄×C₈₉	1	6	yes	—
247	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
248	#41	—	2	32	no	—
249	#41	—	2	48	no	—
250	#41	—	2	96	no	—
251	#41	—	2	24	no	—
252	#41	—	2	24	no	—
253	#41	—	2	24	no	—
254	#41	—	2	48	no	—
255	#41	—	2	24	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	48	no	—
258	C₂×Q₈	—	2	6	no	—
259	C₂×Q₈	—	2	6	no	—
260	C₂×Q₈	—	2	12	no	—
261	C₂×Q₈	—	2	12	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	3	no	—
264	C₂×Q₈	—	4	6	no	—
265	C₂×Q₈	—	4	6	no	—
266	C₂×Q₈	C₂×D₄×C₈₉	1	12	yes	—
267	C₂×D₄	—	2	12	no	—
268	C₂×D₄	—	2	48	no	—
269	C₂×D₄	—	2	48	no	—
270	C₂×D₄	—	2	12	no	—
271	C₂×D₄	—	2	48	no	—
272	C₂×D₄	—	2	12	no	—
273	C₂×D₄	—	2	6	no	—
274	C₂×D₄	—	2	6	no	—
275	C₂×D₄	C₂×D₄×C₈₉	1	12	yes	—
276	C₂×D₄	C₂×D₄×C₈₉	1	12	yes	—
277	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
278	C₂²×C₄	—	2	12	no	—
279	C₂²×C₄	—	2	32	no	—
280	C₂²×C₄	—	2	6	no	—
281	C₂²×C₄	—	2	6	no	—
282	C₂²×C₄	—	2	12	no	—
283	C₂²×C₄	—	2	6	no	—
284	C₂²×C₄	—	2	6	no	—
285	C₂²×C₄	—	2	6	no	—
286	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
287	C₂²×C₄	C₂×D₄×C₈₉	1	24	yes	—
288	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
289	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
290	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
291	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
292	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
293	C₄⋊C₄	—	2	12	no	—
294	C₄⋊C₄	—	2	48	no	—
295	C₂²⋊C₄	—	2	48	no	—
296	C₂²⋊C₄	—	2	6	no	—
297	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
298	C₄²	—	2	12	no	—
299	C₂³	—	2	16	no	—
300	C₂³	—	2	6	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	12	no	—
304	C₂³	—	8	8	no	—
305	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
306	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
307	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
308	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
309	Q₈	—	2	16	no	—
310	Q₈	—	2	24	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	4	12	no	—
313	D₄	—	2	48	no	—
314	D₄	—	2	24	no	—
315	D₄	—	2	24	no	—
316	D₄	—	2	24	no	—
317	C₂×C₄	—	2	48	no	—
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	6	no	—
320	C₂×C₄	—	2	24	no	—
321	C₂×C₄	—	2	24	no	—
322	C₂×C₄	—	2	12	no	—
323	C₂×C₄	—	2	12	no	—
324	C₂×C₄	—	4	12	no	—
325	C₂×C₄	—	4	6	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
328	C₂×C₄	#120×C₈₉	1	3	yes	—
329	C₂×C₄	#120×C₈₉	1	6	yes	—
330	C₂×C₄	#120×C₈₉	1	6	yes	—
331	C₂×C₄	C₂²×D₄×C₈₉	1	12	yes	—
332	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
333	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
334	C₂²	—	2	6	no	—
335	C₂²	—	2	12	no	—
336	C₂²	—	4	3	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	12	no	—
339	C₂²	—	4	12	no	—
340	C₂²	—	8	6	no	—
341	C₂²	—	8	16	no	—
342	C₂²	C₂×#120×C₈₉	1	3	yes	—
343	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
344	C₂²	C₂³×D₄×C₈₉	1	3	yes	—
345	C₄	—	2	12	no	—
346	C₄	—	4	12	no	—
347	C₄	—	4	4	no	—
348	C₄	C₂×#120×C₈₉	1	2	yes	—
349	C₄	C₂×#120×C₈₉	1	6	yes	—
350	C₂	—	2	3	no	—
351	C₂	—	2	3	no	—
352	C₂	—	4	12	no	—
353	C₂	C₈₉×#3028	1	2	yes	direct product factor
354	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#585×C₈₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#536×C₈₉	C₂	semidirect
3. C₈₉×#3028	C₂	direct (N × H)
4. C₂×#458×C₈₉	C₂	semidirect
5. C₂×#410×C₈₉	C₂	semidirect
13. C₂³×Q₈×C₈₉	C₂²	semidirect
15. #536×C₈₉	C₂²	semidirect
18. C₂×#123×C₈₉	C₂²	semidirect
20. C₂×#117×C₈₉	C₂²	semidirect
21. #458×C₈₉	C₂²	semidirect
22. #410×C₈₉	C₂²	semidirect
23. C₂×#99×C₈₉	C₂²	semidirect
45. C₂²×Q₈×C₈₉	C₂³	semidirect
57. #123×C₈₉	C₂³	semidirect
60. #117×C₈₉	C₂³	semidirect
66. #99×C₈₉	C₂³	semidirect
172. C₂×#3028	C₈₉	direct (N × H)
176. C₂×C₈₉	#3028	direct (N × H)
179. C₂×#536	C₂×C₈₉	semidirect
180. #3028	C₂×C₈₉	direct (N × H)
181. C₂×#458	C₂×C₈₉	semidirect
182. C₂×#410	C₂×C₈₉	semidirect
183. C₈₉	C₂×#3028	direct (N × H)
191. C₂³×Q₈	C₂²×C₈₉	semidirect
193. #536	C₂²×C₈₉	semidirect
196. C₂×#123	C₂²×C₈₉	semidirect
198. C₂×#117	C₂²×C₈₉	semidirect
199. #458	C₂²×C₈₉	semidirect
200. #410	C₂²×C₈₉	semidirect
201. C₂×#99	C₂²×C₈₉	semidirect
223. C₂²×Q₈	C₂³×C₈₉	semidirect
235. #123	C₂³×C₈₉	semidirect
238. #117	C₂³×C₈₉	semidirect
244. #99	C₂³×C₈₉	semidirect
353. C₂	C₈₉×#3028	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×#585×C₈₉	2
C₂×#536×C₈₉	2
C₈₉×#3028	2
C₂×#458×C₈₉	2
C₂×#410×C₈₉	2
C₂×#3028	89

Subgroups — C2×C89×#3028 #36438245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3028 #36438245