Subgroups — C₈₉×#60399 #36438247

Order 22784.

5128 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3484	C₂	1	3	yes	maximal, complemented
3	C₈₉×#3027	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3026	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3025	C₂	1	4	yes	maximal, complemented
6	C₂×B(4,𝔽₂)×C₈₉	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2883	C₂	1	3	yes	maximal, complemented
8	#585×C₈₉	—	2	12	no	—
9	#585×C₈₉	C₂²	1	4	yes	complemented
10	C₂×H(5,𝔽₂)×C₈₉	—	2	12	no	—
11	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	3	yes	—
12	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	8	yes	complemented
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
14	#546×C₈₉	—	2	12	no	—
15	D₄²×C₈₉	—	2	12	no	—
16	#535×C₈₉	C₂²	1	6	yes	complemented
17	#534×C₈₉	C₂²	1	12	yes	complemented
18	#525×C₈₉	C₂²	1	6	yes	complemented
19	C₂×#120×C₈₉	C₂²	1	12	yes	complemented
20	#518×C₈₉	C₂²	1	3	yes	complemented
21	#458×C₈₉	C₂²	1	16	yes	complemented
22	B(4,𝔽₂)×C₈₉	C₂²	1	16	yes	complemented
23	B(4,𝔽₂)×C₈₉	C₂²	1	32	yes	complemented
24	#410×C₈₉	C₂²	1	12	yes	complemented
25	C₂×#99×C₈₉	C₂²	1	24	yes	complemented
26	C₂⁵×C₈₉	C₂³	1	2	yes	complemented
27	2₋¹⁺⁴×C₈₉	—	2	16	no	—
28	2₋¹⁺⁴×C₈₉	—	2	12	no	—
29	H(5,𝔽₂)×C₈₉	—	2	48	no	—
30	H(5,𝔽₂)×C₈₉	—	2	24	no	—
31	H(5,𝔽₂)×C₈₉	—	2	12	no	—
32	H(5,𝔽₂)×C₈₉	—	2	48	no	—
33	H(5,𝔽₂)×C₈₉	C₂³	1	16	yes	—
34	C₂×#41×C₈₉	—	2	48	no	—
35	C₂×#41×C₈₉	—	2	24	no	—
36	C₂×#41×C₈₉	—	2	24	no	—
37	C₂×#41×C₈₉	D₄	1	12	yes	complemented
38	C₂×#41×C₈₉	C₂³	1	6	yes	—
39	C₂²×D₄×C₈₉	—	2	16	no	—
40	C₂²×D₄×C₈₉	—	2	24	no	—
41	C₂²×D₄×C₈₉	—	2	12	no	—
42	C₂²×D₄×C₈₉	—	2	12	no	—
43	C₂²×D₄×C₈₉	D₄	1	12	yes	complemented
44	C₂²×D₄×C₈₉	C₂³	1	12	yes	—
45	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₈₉	C₂³	1	2	yes	complemented
47	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
48	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
49	#127×C₈₉	—	2	6	no	—
50	#124×C₈₉	—	2	6	no	—
51	#123×C₈₉	—	2	12	no	—
52	#123×C₈₉	C₂³	1	12	yes	complemented
53	C₂²⋊Q₈×C₈₉	—	2	6	no	—
54	#121×C₈₉	—	2	6	no	—
55	#121×C₈₉	—	2	24	no	—
56	#121×C₈₉	—	2	12	no	—
57	#120×C₈₉	—	2	12	no	—
58	#120×C₈₉	—	2	24	no	—
59	#120×C₈₉	C₂³	1	12	yes	complemented
60	#120×C₈₉	C₂³	1	24	yes	complemented
61	C₄×D₄×C₈₉	—	2	12	no	—
62	C₄×D₄×C₈₉	—	2	12	no	—
63	#117×C₈₉	C₂³	1	6	yes	complemented
64	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	complemented
66	#99×C₈₉	C₂³	1	48	yes	complemented
67	C₂⁴×C₈₉	—	2	8	no	—
68	C₂⁴×C₈₉	—	2	12	no	—
69	C₂⁴×C₈₉	—	8	4	no	—
70	C₂⁴×C₈₉	C₂×D₄	1	12	yes	complemented
71	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
72	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
73	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
74	#41×C₈₉	—	2	96	no	—
75	#41×C₈₉	—	2	48	no	—
76	#41×C₈₉	—	2	16	no	—
77	#41×C₈₉	—	2	48	no	—
78	#41×C₈₉	—	2	48	no	—
79	#41×C₈₉	—	2	24	no	—
80	C₂×Q₈×C₈₉	—	2	24	no	—
81	C₂×Q₈×C₈₉	—	2	8	no	—
82	C₂×Q₈×C₈₉	C₂×D₄	1	6	yes	complemented
83	C₂×D₄×C₈₉	—	2	96	no	—
84	C₂×D₄×C₈₉	—	2	24	no	—
85	C₂×D₄×C₈₉	—	2	24	no	—
86	C₂×D₄×C₈₉	—	2	48	no	—
87	C₂×D₄×C₈₉	—	2	48	no	—
88	C₂×D₄×C₈₉	—	2	48	no	—
89	C₂×D₄×C₈₉	—	2	12	no	—
90	C₂×D₄×C₈₉	—	2	12	no	—
91	C₂×D₄×C₈₉	—	2	24	no	—
92	C₂×D₄×C₈₉	—	2	6	no	—
93	C₂×D₄×C₈₉	—	4	16	no	—
94	C₂×D₄×C₈₉	—	8	24	no	—
95	C₂×D₄×C₈₉	C₂×D₄	1	12	yes	—
96	C₂×D₄×C₈₉	C₂×D₄	1	24	yes	complemented
97	C₂×D₄×C₈₉	C₂×D₄	1	6	yes	complemented
98	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
99	C₂²×C₄×C₈₉	—	2	24	no	—
100	C₂²×C₄×C₈₉	—	2	16	no	—
101	C₂²×C₄×C₈₉	—	2	12	no	—
102	C₂²×C₄×C₈₉	—	2	6	no	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	12	yes	complemented
104	C₂²×C₄×C₈₉	C₂×D₄	1	12	yes	complemented
105	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₈₉	—	2	6	no	—
108	C₄⋊C₄×C₈₉	—	2	12	no	—
109	C₂²⋊C₄×C₈₉	—	2	12	no	—
110	C₂²⋊C₄×C₈₉	—	2	12	no	—
111	C₂²⋊C₄×C₈₉	—	2	12	no	—
112	C₂²⋊C₄×C₈₉	—	2	24	no	—
113	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
114	C₄²×C₈₉	—	2	6	no	—
115	C₂³×C₈₉	—	2	16	no	—
116	C₂³×C₈₉	—	2	3	no	—
117	C₂³×C₈₉	—	2	24	no	—
118	C₂³×C₈₉	—	2	6	no	—
119	C₂³×C₈₉	—	4	2	no	—
120	C₂³×C₈₉	—	4	24	no	—
121	C₂³×C₈₉	—	4	8	no	—
122	C₂³×C₈₉	—	8	2	no	—
123	C₂³×C₈₉	—	8	2	no	—
124	C₂³×C₈₉	—	8	12	no	—
125	C₂³×C₈₉	—	8	12	no	—
126	C₂³×C₈₉	—	16	8	no	—
127	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
128	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
129	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
130	Q₈×C₈₉	—	2	16	no	—
131	Q₈×C₈₉	—	2	12	no	—
132	D₄×C₈₉	—	2	48	no	—
133	D₄×C₈₉	—	2	48	no	—
134	D₄×C₈₉	—	2	24	no	—
135	D₄×C₈₉	—	2	12	no	—
136	D₄×C₈₉	—	4	24	no	—
137	D₄×C₈₉	—	4	8	no	—
138	D₄×C₈₉	—	4	4	no	—
139	D₄×C₈₉	—	8	24	no	—
140	D₄×C₈₉	#120	1	16	yes	—
141	C₂×C₄×C₈₉	—	2	48	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	3	no	—
146	C₂×C₄×C₈₉	—	4	4	no	—
147	C₂×C₄×C₈₉	—	8	12	no	—
148	C₂×C₄×C₈₉	C₂²×D₄	1	12	yes	—
149	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
150	C₂²×C₈₉	—	2	6	no	—
151	C₂²×C₈₉	—	2	12	no	—
152	C₂²×C₈₉	—	4	12	no	—
153	C₂²×C₈₉	—	4	1	no	—
154	C₂²×C₈₉	—	4	3	no	—
155	C₂²×C₈₉	—	4	12	no	—
156	C₂²×C₈₉	—	4	12	no	—
157	C₂²×C₈₉	—	4	1	no	—
158	C₂²×C₈₉	—	4	2	no	—
159	C₂²×C₈₉	—	8	24	no	—
160	C₂²×C₈₉	—	8	16	no	—
161	C₂²×C₈₉	—	8	16	no	—
162	C₂²×C₈₉	C₂×#120	1	8	yes	—
163	C₂²×C₈₉	C₂³×D₄	1	3	yes	—
164	C₄×C₈₉	—	2	12	no	—
165	C₄×C₈₉	—	4	12	no	—
166	C₄×C₈₉	—	4	1	no	—
167	C₄×C₈₉	C₂×#120	1	4	yes	—
168	#60399	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂×C₈₉	—	2	3	no	—
170	C₂×C₈₉	—	2	8	no	—
171	C₂×C₈₉	—	4	2	no	—
172	C₂×C₈₉	—	4	12	no	—
173	C₂×C₈₉	—	8	2	no	—
174	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
175	H(7,𝔽₂)	C₂×C₈₉	1	1	yes	characteristic, complemented
176	#3484	C₂×C₈₉	1	3	yes	complemented
177	#3027	C₂×C₈₉	1	4	yes	complemented
178	#3026	C₂×C₈₉	1	8	yes	complemented
179	#3025	C₂×C₈₉	1	4	yes	complemented
180	C₂×B(4,𝔽₂)	C₂×C₈₉	1	8	yes	complemented
181	#2883	C₂×C₈₉	1	3	yes	complemented
182	C₈₉	#60399	1	1	yes	characteristic, direct product factor, Sylow
183	#585	—	2	12	no	—
184	#585	C₂²×C₈₉	1	4	yes	complemented
185	C₂×H(5,𝔽₂)	—	2	12	no	—
186	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	3	yes	—
187	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	8	yes	complemented
188	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
189	#546	—	2	12	no	—
190	D₄²	—	2	12	no	—
191	#535	C₂²×C₈₉	1	6	yes	complemented
192	#534	C₂²×C₈₉	1	12	yes	complemented
193	#525	C₂²×C₈₉	1	6	yes	complemented
194	C₂×#120	C₂²×C₈₉	1	12	yes	complemented
195	#518	C₂²×C₈₉	1	3	yes	complemented
196	#458	C₂²×C₈₉	1	16	yes	complemented
197	B(4,𝔽₂)	C₂²×C₈₉	1	16	yes	complemented
198	B(4,𝔽₂)	C₂²×C₈₉	1	32	yes	complemented
199	#410	C₂²×C₈₉	1	12	yes	complemented
200	C₂×#99	C₂²×C₈₉	1	24	yes	complemented
201	C₂⁵	C₂³×C₈₉	1	2	yes	complemented
202	2₋¹⁺⁴	—	2	16	no	—
203	2₋¹⁺⁴	—	2	12	no	—
204	H(5,𝔽₂)	—	2	48	no	—
205	H(5,𝔽₂)	—	2	24	no	—
206	H(5,𝔽₂)	—	2	12	no	—
207	H(5,𝔽₂)	—	2	48	no	—
208	H(5,𝔽₂)	C₂³×C₈₉	1	16	yes	—
209	C₂×#41	—	2	48	no	—
210	C₂×#41	—	2	24	no	—
211	C₂×#41	—	2	24	no	—
212	C₂×#41	D₄×C₈₉	1	12	yes	complemented
213	C₂×#41	C₂³×C₈₉	1	6	yes	—
214	C₂²×D₄	—	2	16	no	—
215	C₂²×D₄	—	2	24	no	—
216	C₂²×D₄	—	2	12	no	—
217	C₂²×D₄	—	2	12	no	—
218	C₂²×D₄	D₄×C₈₉	1	12	yes	complemented
219	C₂²×D₄	C₂³×C₈₉	1	12	yes	—
220	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
221	C₂²×D₄	C₂³×C₈₉	1	2	yes	complemented
222	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic, complemented
223	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic, complemented
224	#127	—	2	6	no	—
225	#124	—	2	6	no	—
226	#123	—	2	12	no	—
227	#123	C₂³×C₈₉	1	12	yes	complemented
228	C₂²⋊Q₈	—	2	6	no	—
229	#121	—	2	6	no	—
230	#121	—	2	24	no	—
231	#121	—	2	12	no	—
232	#120	—	2	12	no	—
233	#120	—	2	24	no	—
234	#120	C₂³×C₈₉	1	12	yes	complemented
235	#120	C₂³×C₈₉	1	24	yes	complemented
236	C₄×D₄	—	2	12	no	—
237	C₄×D₄	—	2	12	no	—
238	#117	C₂³×C₈₉	1	6	yes	complemented
239	C₂×C₂²⋊C₄	—	2	12	no	—
240	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	complemented
241	#99	C₂³×C₈₉	1	48	yes	complemented
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	12	no	—
244	C₂⁴	—	8	4	no	—
245	C₂⁴	C₂×D₄×C₈₉	1	12	yes	complemented
246	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
247	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
248	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
249	#41	—	2	96	no	—
250	#41	—	2	48	no	—
251	#41	—	2	16	no	—
252	#41	—	2	48	no	—
253	#41	—	2	48	no	—
254	#41	—	2	24	no	—
255	C₂×Q₈	—	2	24	no	—
256	C₂×Q₈	—	2	8	no	—
257	C₂×Q₈	C₂×D₄×C₈₉	1	6	yes	complemented
258	C₂×D₄	—	2	96	no	—
259	C₂×D₄	—	2	24	no	—
260	C₂×D₄	—	2	24	no	—
261	C₂×D₄	—	2	48	no	—
262	C₂×D₄	—	2	48	no	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	—	2	12	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	24	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	4	16	no	—
269	C₂×D₄	—	8	24	no	—
270	C₂×D₄	C₂×D₄×C₈₉	1	12	yes	—
271	C₂×D₄	C₂×D₄×C₈₉	1	24	yes	complemented
272	C₂×D₄	C₂×D₄×C₈₉	1	6	yes	complemented
273	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
274	C₂²×C₄	—	2	24	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	12	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	C₂×D₄×C₈₉	1	12	yes	complemented
279	C₂²×C₄	C₂×D₄×C₈₉	1	12	yes	complemented
280	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
282	C₄⋊C₄	—	2	6	no	—
283	C₄⋊C₄	—	2	12	no	—
284	C₂²⋊C₄	—	2	12	no	—
285	C₂²⋊C₄	—	2	12	no	—
286	C₂²⋊C₄	—	2	12	no	—
287	C₂²⋊C₄	—	2	24	no	—
288	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
289	C₄²	—	2	6	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	3	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	2	6	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	24	no	—
296	C₂³	—	4	8	no	—
297	C₂³	—	8	2	no	—
298	C₂³	—	8	2	no	—
299	C₂³	—	8	12	no	—
300	C₂³	—	8	12	no	—
301	C₂³	—	16	8	no	—
302	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
303	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
304	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
305	Q₈	—	2	16	no	—
306	Q₈	—	2	12	no	—
307	D₄	—	2	48	no	—
308	D₄	—	2	48	no	—
309	D₄	—	2	24	no	—
310	D₄	—	2	12	no	—
311	D₄	—	4	24	no	—
312	D₄	—	4	8	no	—
313	D₄	—	4	4	no	—
314	D₄	—	8	24	no	—
315	D₄	#120×C₈₉	1	16	yes	—
316	C₂×C₄	—	2	48	no	—
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	24	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	8	12	no	—
323	C₂×C₄	C₂²×D₄×C₈₉	1	12	yes	—
324	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
325	C₂²	—	2	6	no	—
326	C₂²	—	2	12	no	—
327	C₂²	—	4	12	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	12	no	—
330	C₂²	—	4	3	no	—
331	C₂²	—	4	12	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	8	24	no	—
335	C₂²	—	8	16	no	—
336	C₂²	—	8	16	no	—
337	C₂²	C₂×#120×C₈₉	1	8	yes	—
338	C₂²	C₂³×D₄×C₈₉	1	3	yes	—
339	C₄	—	2	12	no	—
340	C₄	—	4	12	no	—
341	C₄	—	4	1	no	—
342	C₄	C₂×#120×C₈₉	1	4	yes	—
343	C₂	—	2	3	no	—
344	C₂	—	2	8	no	—
345	C₂	—	4	2	no	—
346	C₂	—	4	12	no	—
347	C₂	—	8	2	no	—
348	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	C₂²×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂²×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×H(7,𝔽₂)	C₂	semidirect
2. C₈₉×#3484	C₂	semidirect
3. C₈₉×#3027	C₂	semidirect
4. C₈₉×#3026	C₂	semidirect
5. C₈₉×#3025	C₂	semidirect
6. C₂×B(4,𝔽₂)×C₈₉	C₂	semidirect
7. C₈₉×#2883	C₂	semidirect
9. #585×C₈₉	C₂²	semidirect
12. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
13. C₂³×D₄×C₈₉	C₂²	semidirect
16. #535×C₈₉	C₂²	semidirect
17. #534×C₈₉	C₂²	semidirect
18. #525×C₈₉	C₂²	semidirect
19. C₂×#120×C₈₉	C₂²	semidirect
20. #518×C₈₉	C₂²	semidirect
21. #458×C₈₉	C₂²	semidirect
22. B(4,𝔽₂)×C₈₉	C₂²	semidirect
23. B(4,𝔽₂)×C₈₉	C₂²	semidirect
24. #410×C₈₉	C₂²	semidirect
25. C₂×#99×C₈₉	C₂²	semidirect
26. C₂⁵×C₈₉	C₂³	semidirect
37. C₂×#41×C₈₉	D₄	semidirect
43. C₂²×D₄×C₈₉	D₄	semidirect
46. C₂²×D₄×C₈₉	C₂³	semidirect
47. C₂²×D₄×C₈₉	C₂³	semidirect
48. C₂³×C₄×C₈₉	C₂³	semidirect
52. #123×C₈₉	C₂³	semidirect
59. #120×C₈₉	C₂³	semidirect
60. #120×C₈₉	C₂³	semidirect
63. #117×C₈₉	C₂³	semidirect
65. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
66. #99×C₈₉	C₂³	semidirect
70. C₂⁴×C₈₉	C₂×D₄	semidirect
82. C₂×Q₈×C₈₉	C₂×D₄	semidirect
96. C₂×D₄×C₈₉	C₂×D₄	semidirect
97. C₂×D₄×C₈₉	C₂×D₄	semidirect
103. C₂²×C₄×C₈₉	C₂×D₄	semidirect
104. C₂²×C₄×C₈₉	C₂×D₄	semidirect
168. #60399	C₈₉	direct (N × H)
175. H(7,𝔽₂)	C₂×C₈₉	semidirect
176. #3484	C₂×C₈₉	semidirect
177. #3027	C₂×C₈₉	semidirect
178. #3026	C₂×C₈₉	semidirect
179. #3025	C₂×C₈₉	semidirect
180. C₂×B(4,𝔽₂)	C₂×C₈₉	semidirect
181. #2883	C₂×C₈₉	semidirect
182. C₈₉	#60399	direct (N × H)
184. #585	C₂²×C₈₉	semidirect
187. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
188. C₂³×D₄	C₂²×C₈₉	semidirect
191. #535	C₂²×C₈₉	semidirect
192. #534	C₂²×C₈₉	semidirect
193. #525	C₂²×C₈₉	semidirect
194. C₂×#120	C₂²×C₈₉	semidirect
195. #518	C₂²×C₈₉	semidirect
196. #458	C₂²×C₈₉	semidirect
197. B(4,𝔽₂)	C₂²×C₈₉	semidirect
198. B(4,𝔽₂)	C₂²×C₈₉	semidirect
199. #410	C₂²×C₈₉	semidirect
200. C₂×#99	C₂²×C₈₉	semidirect
201. C₂⁵	C₂³×C₈₉	semidirect
212. C₂×#41	D₄×C₈₉	semidirect
218. C₂²×D₄	D₄×C₈₉	semidirect
221. C₂²×D₄	C₂³×C₈₉	semidirect
222. C₂²×D₄	C₂³×C₈₉	semidirect
223. C₂³×C₄	C₂³×C₈₉	semidirect
227. #123	C₂³×C₈₉	semidirect
234. #120	C₂³×C₈₉	semidirect
235. #120	C₂³×C₈₉	semidirect
238. #117	C₂³×C₈₉	semidirect
240. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
241. #99	C₂³×C₈₉	semidirect
245. C₂⁴	C₂×D₄×C₈₉	semidirect
257. C₂×Q₈	C₂×D₄×C₈₉	semidirect
271. C₂×D₄	C₂×D₄×C₈₉	semidirect
272. C₂×D₄	C₂×D₄×C₈₉	semidirect
278. C₂²×C₄	C₂×D₄×C₈₉	semidirect
279. C₂²×C₄	C₂×D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×H(7,𝔽₂)	2
C₈₉×#3484	2
C₈₉×#3027	2
C₈₉×#3026	2
C₈₉×#3025	2
C₂×B(4,𝔽₂)×C₈₉	2
C₈₉×#2883	2
#60399	89

Subgroups — C89×#60399 #36438247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60399 #36438247