Subgroups — C₂²×#535×C₈₉ #36440522

Order 22784.

14414 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#535×C₈₉	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#127×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂²×#124×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#121×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂²×#120×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₈₉	C₂²	1	2	yes	—
10	C₂²×#41×C₈₉	—	2	16	no	—
11	C₂²×#41×C₈₉	C₂²	1	24	yes	complemented
12	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₈₉	—	2	16	no	—
14	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
15	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
16	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
17	C₂³×D₄×C₈₉	C₂²	1	24	yes	complemented
18	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₈₉	C₂²	1	8	yes	complemented
20	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	complemented
22	#535×C₈₉	C₂²	1	256	yes	direct product factor
23	C₂×#127×C₈₉	C₂²	1	48	yes	complemented
24	C₂×#124×C₈₉	C₂²	1	48	yes	complemented
25	C₂×#121×C₈₉	C₂²	1	96	yes	complemented
26	C₂×#120×C₈₉	C₂²	1	96	yes	complemented
27	C₂×#117×C₈₉	C₂²	1	24	yes	complemented
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
31	C₂²×C₄²×C₈₉	C₂²	1	2	yes	complemented
32	C₂⁵×C₈₉	—	2	16	no	—
33	C₂⁵×C₈₉	—	4	16	no	—
34	C₂⁵×C₈₉	C₂³	1	4	yes	—
35	C₂⁵×C₈₉	C₂³	1	2	yes	—
36	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
37	C₂⁵×C₈₉	C₂³	1	24	yes	—
38	C₂×#41×C₈₉	—	2	192	no	—
39	C₂×#41×C₈₉	C₂³	1	64	yes	complemented
40	C₂²×Q₈×C₈₉	—	2	8	no	—
41	C₂²×Q₈×C₈₉	C₂³	1	12	yes	complemented
42	C₂²×D₄×C₈₉	—	2	16	no	—
43	C₂²×D₄×C₈₉	—	2	16	no	—
44	C₂²×D₄×C₈₉	—	2	16	no	—
45	C₂²×D₄×C₈₉	—	2	8	no	—
46	C₂²×D₄×C₈₉	—	2	192	no	—
47	C₂²×D₄×C₈₉	—	4	32	no	—
48	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
51	C₂²×D₄×C₈₉	C₂³	1	64	yes	complemented
52	C₂²×D₄×C₈₉	C₂³	1	12	yes	complemented
53	C₂²×D₄×C₈₉	C₂³	1	96	yes	complemented
54	C₂³×C₄×C₈₉	—	2	16	no	—
55	C₂³×C₄×C₈₉	D₄	1	16	yes	complemented
56	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	C₂³	1	12	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	24	yes	complemented
62	#127×C₈₉	C₂³	1	128	yes	complemented
63	#124×C₈₉	C₂³	1	128	yes	complemented
64	#121×C₈₉	C₂³	1	256	yes	complemented
65	#120×C₈₉	C₂³	1	256	yes	complemented
66	#117×C₈₉	C₂³	1	64	yes	complemented
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	24	yes	complemented
68	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	96	yes	complemented
70	C₂×C₄²×C₈₉	C₂³	1	24	yes	complemented
71	C₂⁴×C₈₉	—	2	8	no	—
72	C₂⁴×C₈₉	—	2	8	no	—
73	C₂⁴×C₈₉	—	2	96	no	—
74	C₂⁴×C₈₉	—	2	16	no	—
75	C₂⁴×C₈₉	—	2	16	no	—
76	C₂⁴×C₈₉	—	2	32	no	—
77	C₂⁴×C₈₉	—	4	96	no	—
78	C₂⁴×C₈₉	—	4	128	no	—
79	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
80	C₂⁴×C₈₉	C₂⁴	1	24	yes	—
81	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
82	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
83	C₂⁴×C₈₉	C₂⁴	1	32	yes	—
84	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
85	#41×C₈₉	—	2	256	no	—
86	C₂×Q₈×C₈₉	—	2	48	no	—
87	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	complemented
88	C₂×D₄×C₈₉	—	2	96	no	—
89	C₂×D₄×C₈₉	—	2	96	no	—
90	C₂×D₄×C₈₉	—	2	96	no	—
91	C₂×D₄×C₈₉	—	2	48	no	—
92	C₂×D₄×C₈₉	—	2	256	no	—
93	C₂×D₄×C₈₉	—	4	192	no	—
94	C₂×D₄×C₈₉	C₂⁴	1	32	yes	—
95	C₂×D₄×C₈₉	C₂⁴	1	32	yes	—
96	C₂×D₄×C₈₉	C₂⁴	1	32	yes	—
97	C₂×D₄×C₈₉	C₂⁴	1	16	yes	complemented
98	C₂×D₄×C₈₉	C₂⁴	1	128	yes	complemented
99	C₂²×C₄×C₈₉	—	2	8	no	—
100	C₂²×C₄×C₈₉	—	2	16	no	—
101	C₂²×C₄×C₈₉	—	2	96	no	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₈₉	C₂×D₄	1	96	yes	complemented
105	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
106	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
108	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
109	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
110	C₂²×C₄×C₈₉	C₂⁴	1	32	yes	complemented
111	C₄⋊C₄×C₈₉	C₂⁴	1	32	yes	complemented
112	C₂²⋊C₄×C₈₉	C₂⁴	1	32	yes	—
113	C₂²⋊C₄×C₈₉	C₂⁴	1	128	yes	complemented
114	C₄²×C₈₉	C₂⁴	1	32	yes	complemented
115	C₂³×C₈₉	—	2	32	no	—
116	C₂³×C₈₉	—	2	24	no	—
117	C₂³×C₈₉	—	2	24	no	—
118	C₂³×C₈₉	—	2	64	no	—
119	C₂³×C₈₉	—	2	48	no	—
120	C₂³×C₈₉	—	2	48	no	—
121	C₂³×C₈₉	—	2	96	no	—
122	C₂³×C₈₉	—	4	64	no	—
123	C₂³×C₈₉	—	4	384	no	—
124	C₂³×C₈₉	—	4	32	no	—
125	C₂³×C₈₉	—	4	64	no	—
126	C₂³×C₈₉	C₂²×D₄	1	24	yes	—
127	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
128	C₂³×C₈₉	H(5,𝔽₂)	1	8	yes	—
129	C₂³×C₈₉	C₂⁵	1	16	yes	—
130	C₂³×C₈₉	C₂⁵	1	8	yes	—
131	C₂³×C₈₉	C₂⁵	1	4	yes	—
132	C₂³×C₈₉	C₂⁵	1	3	yes	—
133	Q₈×C₈₉	—	2	32	no	—
134	D₄×C₈₉	—	2	64	no	—
135	D₄×C₈₉	—	2	64	no	—
136	D₄×C₈₉	—	2	64	no	—
137	D₄×C₈₉	—	2	32	no	—
138	D₄×C₈₉	—	4	128	no	—
139	C₂×C₄×C₈₉	—	2	24	no	—
140	C₂×C₄×C₈₉	—	2	48	no	—
141	C₂×C₄×C₈₉	—	2	64	no	—
142	C₂×C₄×C₈₉	C₂²×D₄	1	24	yes	—
143	C₂×C₄×C₈₉	C₂²×D₄	1	24	yes	—
144	C₂×C₄×C₈₉	C₂²×D₄	1	64	yes	complemented
145	C₂×C₄×C₈₉	C₂⁵	1	16	yes	—
146	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
147	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
148	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
149	C₂²×C₈₉	—	2	8	no	—
150	C₂²×C₈₉	—	2	48	no	—
151	C₂²×C₈₉	—	2	8	no	—
152	C₂²×C₈₉	—	2	16	no	—
153	C₂²×C₈₉	—	2	16	no	—
154	C₂²×C₈₉	—	2	32	no	—
155	C₂²×C₈₉	—	4	128	no	—
156	C₂²×C₈₉	—	4	48	no	—
157	C₂²×C₈₉	—	4	96	no	—
158	C₂²×C₈₉	#535	1	16	yes	direct product factor
159	C₂²×C₈₉	C₂³×D₄	1	8	yes	—
160	C₂²×C₈₉	C₂³×D₄	1	6	yes	—
161	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	12	yes	—
162	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
163	C₄×C₈₉	—	2	8	no	—
164	C₄×C₈₉	—	2	16	no	—
165	C₄×C₈₉	C₂³×D₄	1	8	yes	—
166	C₄×C₈₉	C₂³×D₄	1	8	yes	—
167	C₂²×#535	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₈₉	—	2	8	no	—
169	C₂×C₈₉	—	4	8	no	—
170	C₂×C₈₉	—	4	16	no	—
171	C₂×C₈₉	C₂×#535	1	12	yes	direct product factor
172	C₂×C₈₉	C₂⁴×D₄	1	1	yes	characteristic
173	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	2	yes	—
174	C₂³×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
175	C₂⁴×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
176	C₂×#535	C₂×C₈₉	1	48	yes	direct product factor
177	C₂²×#127	C₂×C₈₉	1	2	yes	complemented
178	C₂²×#124	C₂×C₈₉	1	2	yes	complemented
179	C₂²×#121	C₂×C₈₉	1	4	yes	complemented
180	C₂²×#120	C₂×C₈₉	1	4	yes	complemented
181	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
182	C₈₉	C₂²×#535	1	1	yes	characteristic, direct product factor, Sylow
183	C₂⁶	C₂²×C₈₉	1	2	yes	—
184	C₂²×#41	—	2	16	no	—
185	C₂²×#41	C₂²×C₈₉	1	24	yes	complemented
186	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
187	C₂³×D₄	—	2	16	no	—
188	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
189	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
190	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
191	C₂³×D₄	C₂²×C₈₉	1	24	yes	complemented
192	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
193	C₂³×D₄	C₂²×C₈₉	1	8	yes	complemented
194	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
195	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	complemented
196	#535	C₂²×C₈₉	1	256	yes	direct product factor
197	C₂×#127	C₂²×C₈₉	1	48	yes	complemented
198	C₂×#124	C₂²×C₈₉	1	48	yes	complemented
199	C₂×#121	C₂²×C₈₉	1	96	yes	complemented
200	C₂×#120	C₂²×C₈₉	1	96	yes	complemented
201	C₂×#117	C₂²×C₈₉	1	24	yes	complemented
202	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
203	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
205	C₂²×C₄²	C₂²×C₈₉	1	2	yes	complemented
206	C₂⁵	—	2	16	no	—
207	C₂⁵	—	4	16	no	—
208	C₂⁵	C₂³×C₈₉	1	4	yes	—
209	C₂⁵	C₂³×C₈₉	1	2	yes	—
210	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
211	C₂⁵	C₂³×C₈₉	1	24	yes	—
212	C₂×#41	—	2	192	no	—
213	C₂×#41	C₂³×C₈₉	1	64	yes	complemented
214	C₂²×Q₈	—	2	8	no	—
215	C₂²×Q₈	C₂³×C₈₉	1	12	yes	complemented
216	C₂²×D₄	—	2	16	no	—
217	C₂²×D₄	—	2	16	no	—
218	C₂²×D₄	—	2	16	no	—
219	C₂²×D₄	—	2	8	no	—
220	C₂²×D₄	—	2	192	no	—
221	C₂²×D₄	—	4	32	no	—
222	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
223	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
224	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
225	C₂²×D₄	C₂³×C₈₉	1	64	yes	complemented
226	C₂²×D₄	C₂³×C₈₉	1	12	yes	complemented
227	C₂²×D₄	C₂³×C₈₉	1	96	yes	complemented
228	C₂³×C₄	—	2	16	no	—
229	C₂³×C₄	D₄×C₈₉	1	16	yes	complemented
230	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₈₉	1	12	yes	—
235	C₂³×C₄	C₂³×C₈₉	1	24	yes	complemented
236	#127	C₂³×C₈₉	1	128	yes	complemented
237	#124	C₂³×C₈₉	1	128	yes	complemented
238	#121	C₂³×C₈₉	1	256	yes	complemented
239	#120	C₂³×C₈₉	1	256	yes	complemented
240	#117	C₂³×C₈₉	1	64	yes	complemented
241	C₂×C₄⋊C₄	C₂³×C₈₉	1	24	yes	complemented
242	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₈₉	1	96	yes	complemented
244	C₂×C₄²	C₂³×C₈₉	1	24	yes	complemented
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	96	no	—
248	C₂⁴	—	2	16	no	—
249	C₂⁴	—	2	16	no	—
250	C₂⁴	—	2	32	no	—
251	C₂⁴	—	4	96	no	—
252	C₂⁴	—	4	128	no	—
253	C₂⁴	C₂×D₄×C₈₉	1	8	yes	—
254	C₂⁴	C₂⁴×C₈₉	1	24	yes	—
255	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
256	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
257	C₂⁴	C₂⁴×C₈₉	1	32	yes	—
258	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
259	#41	—	2	256	no	—
260	C₂×Q₈	—	2	48	no	—
261	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	complemented
262	C₂×D₄	—	2	96	no	—
263	C₂×D₄	—	2	96	no	—
264	C₂×D₄	—	2	96	no	—
265	C₂×D₄	—	2	48	no	—
266	C₂×D₄	—	2	256	no	—
267	C₂×D₄	—	4	192	no	—
268	C₂×D₄	C₂⁴×C₈₉	1	32	yes	—
269	C₂×D₄	C₂⁴×C₈₉	1	32	yes	—
270	C₂×D₄	C₂⁴×C₈₉	1	32	yes	—
271	C₂×D₄	C₂⁴×C₈₉	1	16	yes	complemented
272	C₂×D₄	C₂⁴×C₈₉	1	128	yes	complemented
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	96	no	—
276	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
277	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
278	C₂²×C₄	C₂×D₄×C₈₉	1	96	yes	complemented
279	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
280	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
281	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
282	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
283	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
284	C₂²×C₄	C₂⁴×C₈₉	1	32	yes	complemented
285	C₄⋊C₄	C₂⁴×C₈₉	1	32	yes	complemented
286	C₂²⋊C₄	C₂⁴×C₈₉	1	32	yes	—
287	C₂²⋊C₄	C₂⁴×C₈₉	1	128	yes	complemented
288	C₄²	C₂⁴×C₈₉	1	32	yes	complemented
289	C₂³	—	2	32	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	64	no	—
293	C₂³	—	2	48	no	—
294	C₂³	—	2	48	no	—
295	C₂³	—	2	96	no	—
296	C₂³	—	4	64	no	—
297	C₂³	—	4	384	no	—
298	C₂³	—	4	32	no	—
299	C₂³	—	4	64	no	—
300	C₂³	C₂²×D₄×C₈₉	1	24	yes	—
301	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
302	C₂³	H(5,𝔽₂)×C₈₉	1	8	yes	—
303	C₂³	C₂⁵×C₈₉	1	16	yes	—
304	C₂³	C₂⁵×C₈₉	1	8	yes	—
305	C₂³	C₂⁵×C₈₉	1	4	yes	—
306	C₂³	C₂⁵×C₈₉	1	3	yes	—
307	Q₈	—	2	32	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	64	no	—
310	D₄	—	2	64	no	—
311	D₄	—	2	32	no	—
312	D₄	—	4	128	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	48	no	—
315	C₂×C₄	—	2	64	no	—
316	C₂×C₄	C₂²×D₄×C₈₉	1	24	yes	—
317	C₂×C₄	C₂²×D₄×C₈₉	1	24	yes	—
318	C₂×C₄	C₂²×D₄×C₈₉	1	64	yes	complemented
319	C₂×C₄	C₂⁵×C₈₉	1	16	yes	—
320	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
321	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
322	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	2	16	no	—
328	C₂²	—	2	32	no	—
329	C₂²	—	4	128	no	—
330	C₂²	—	4	96	no	—
331	C₂²	—	4	48	no	—
332	C₂²	#535×C₈₉	1	16	yes	direct product factor
333	C₂²	C₂³×D₄×C₈₉	1	8	yes	—
334	C₂²	C₂³×D₄×C₈₉	1	6	yes	—
335	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	12	yes	—
336	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
337	C₄	—	2	8	no	—
338	C₄	—	2	16	no	—
339	C₄	C₂³×D₄×C₈₉	1	8	yes	—
340	C₄	C₂³×D₄×C₈₉	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	8	no	—
343	C₂	—	4	16	no	—
344	C₂	C₂×#535×C₈₉	1	12	yes	direct product factor
345	C₂	C₂⁴×D₄×C₈₉	1	1	yes	characteristic
346	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₈₉	C₂	semidirect
2. C₂⁴×D₄×C₈₉	C₂	semidirect
3. C₂×#535×C₈₉	C₂	direct (N × H)
4. C₂²×#127×C₈₉	C₂	semidirect
5. C₂²×#124×C₈₉	C₂	semidirect
6. C₂²×#121×C₈₉	C₂	semidirect
7. C₂²×#120×C₈₉	C₂	semidirect
8. C₂²×#117×C₈₉	C₂	semidirect
11. C₂²×#41×C₈₉	C₂²	semidirect
12. C₂³×Q₈×C₈₉	C₂²	semidirect
17. C₂³×D₄×C₈₉	C₂²	semidirect
18. C₂³×D₄×C₈₉	C₂²	semidirect
19. C₂³×D₄×C₈₉	C₂²	semidirect
21. C₂⁴×C₄×C₈₉	C₂²	semidirect
22. #535×C₈₉	C₂²	direct (N × H)
23. C₂×#127×C₈₉	C₂²	semidirect
24. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×#121×C₈₉	C₂²	semidirect
26. C₂×#120×C₈₉	C₂²	semidirect
27. C₂×#117×C₈₉	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
30. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
31. C₂²×C₄²×C₈₉	C₂²	semidirect
39. C₂×#41×C₈₉	C₂³	semidirect
41. C₂²×Q₈×C₈₉	C₂³	semidirect
51. C₂²×D₄×C₈₉	C₂³	semidirect
52. C₂²×D₄×C₈₉	C₂³	semidirect
53. C₂²×D₄×C₈₉	C₂³	semidirect
55. C₂³×C₄×C₈₉	D₄	semidirect
61. C₂³×C₄×C₈₉	C₂³	semidirect
62. #127×C₈₉	C₂³	semidirect
63. #124×C₈₉	C₂³	semidirect
64. #121×C₈₉	C₂³	semidirect
65. #120×C₈₉	C₂³	semidirect
66. #117×C₈₉	C₂³	semidirect
67. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
69. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
70. C₂×C₄²×C₈₉	C₂³	semidirect
87. C₂×Q₈×C₈₉	C₂⁴	semidirect
97. C₂×D₄×C₈₉	C₂⁴	semidirect
98. C₂×D₄×C₈₉	C₂⁴	semidirect
104. C₂²×C₄×C₈₉	C₂×D₄	semidirect
110. C₂²×C₄×C₈₉	C₂⁴	semidirect
111. C₄⋊C₄×C₈₉	C₂⁴	semidirect
113. C₂²⋊C₄×C₈₉	C₂⁴	semidirect
114. C₄²×C₈₉	C₂⁴	semidirect
144. C₂×C₄×C₈₉	C₂²×D₄	semidirect
158. C₂²×C₈₉	#535	direct (N × H)
167. C₂²×#535	C₈₉	direct (N × H)
171. C₂×C₈₉	C₂×#535	direct (N × H)
174. C₂³×#41	C₂×C₈₉	semidirect
175. C₂⁴×D₄	C₂×C₈₉	semidirect
176. C₂×#535	C₂×C₈₉	direct (N × H)
177. C₂²×#127	C₂×C₈₉	semidirect
178. C₂²×#124	C₂×C₈₉	semidirect
179. C₂²×#121	C₂×C₈₉	semidirect
180. C₂²×#120	C₂×C₈₉	semidirect
181. C₂²×#117	C₂×C₈₉	semidirect
182. C₈₉	C₂²×#535	direct (N × H)
185. C₂²×#41	C₂²×C₈₉	semidirect
186. C₂³×Q₈	C₂²×C₈₉	semidirect
191. C₂³×D₄	C₂²×C₈₉	semidirect
192. C₂³×D₄	C₂²×C₈₉	semidirect
193. C₂³×D₄	C₂²×C₈₉	semidirect
195. C₂⁴×C₄	C₂²×C₈₉	semidirect
196. #535	C₂²×C₈₉	direct (N × H)
197. C₂×#127	C₂²×C₈₉	semidirect
198. C₂×#124	C₂²×C₈₉	semidirect
199. C₂×#121	C₂²×C₈₉	semidirect
200. C₂×#120	C₂²×C₈₉	semidirect
201. C₂×#117	C₂²×C₈₉	semidirect
202. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
204. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
205. C₂²×C₄²	C₂²×C₈₉	semidirect
213. C₂×#41	C₂³×C₈₉	semidirect
215. C₂²×Q₈	C₂³×C₈₉	semidirect
225. C₂²×D₄	C₂³×C₈₉	semidirect
226. C₂²×D₄	C₂³×C₈₉	semidirect
227. C₂²×D₄	C₂³×C₈₉	semidirect
229. C₂³×C₄	D₄×C₈₉	semidirect
235. C₂³×C₄	C₂³×C₈₉	semidirect
236. #127	C₂³×C₈₉	semidirect
237. #124	C₂³×C₈₉	semidirect
238. #121	C₂³×C₈₉	semidirect
239. #120	C₂³×C₈₉	semidirect
240. #117	C₂³×C₈₉	semidirect
241. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
243. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
244. C₂×C₄²	C₂³×C₈₉	semidirect
261. C₂×Q₈	C₂⁴×C₈₉	semidirect
271. C₂×D₄	C₂⁴×C₈₉	semidirect
272. C₂×D₄	C₂⁴×C₈₉	semidirect
278. C₂²×C₄	C₂×D₄×C₈₉	semidirect
284. C₂²×C₄	C₂⁴×C₈₉	semidirect
285. C₄⋊C₄	C₂⁴×C₈₉	semidirect
287. C₂²⋊C₄	C₂⁴×C₈₉	semidirect
288. C₄²	C₂⁴×C₈₉	semidirect
318. C₂×C₄	C₂²×D₄×C₈₉	semidirect
332. C₂²	#535×C₈₉	direct (N × H)
344. C₂	C₂×#535×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₈₉	2
C₂⁴×D₄×C₈₉	2
C₂×#535×C₈₉	2
C₂²×#127×C₈₉	2
C₂²×#124×C₈₉	2
C₂²×#121×C₈₉	2
C₂²×#120×C₈₉	2
C₂²×#117×C₈₉	2
C₂²×#535	89

Subgroups — C22×#535×C89 #36440522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#535×C₈₉ #36440522