Subgroups — C₂×C₈₉×#3192 #36438583

Order 22784.

3010 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3192	C₂	1	16	yes	maximal, direct product factor
3	C₂×#481×C₈₉	C₂	1	4	yes	maximal, complemented
4	C₂×#469×C₈₉	C₂	1	4	yes	maximal, complemented
5	C₂×#447×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₈₉	—	2	2	no	—
8	C₂³×D₄×C₈₉	C₂²	1	2	yes	complemented
9	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₈₉	C₂²	1	4	yes	complemented
11	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	complemented
12	C₂×#121×C₈₉	—	2	2	no	—
13	C₂×#121×C₈₉	—	2	8	no	—
14	C₂×#121×C₈₉	—	2	2	no	—
15	C₂×#121×C₈₉	C₂²	1	4	yes	—
16	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
17	C₂×#121×C₈₉	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊C₄×C₈₉	—	2	2	no	—
20	#481×C₈₉	C₂²	1	32	yes	complemented
21	#469×C₈₉	C₂²	1	32	yes	complemented
22	#447×C₈₉	C₂²	1	32	yes	complemented
23	C₂×#106×C₈₉	C₂²	1	4	yes	complemented
24	C₂×#102×C₈₉	C₂²	1	8	yes	complemented
25	#407×C₈₉	C₂²	1	8	yes	complemented
26	C₂×C₂²⋊C₈×C₈₉	C₂²	1	4	yes	complemented
27	C₂⁵×C₈₉	—	2	2	no	—
28	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₈₉	—	2	4	no	—
30	C₂²×D₄×C₈₉	—	2	16	no	—
31	C₂²×D₄×C₈₉	—	2	4	no	—
32	C₂²×D₄×C₈₉	—	2	4	no	—
33	C₂²×D₄×C₈₉	—	2	2	no	—
34	C₂²×D₄×C₈₉	—	4	8	no	—
35	C₂²×D₄×C₈₉	—	4	16	no	—
36	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
37	C₂²×D₄×C₈₉	C₂³	1	8	yes	complemented
38	C₂³×C₄×C₈₉	—	2	2	no	—
39	C₂³×C₄×C₈₉	—	4	4	no	—
40	C₂³×C₄×C₈₉	D₄	1	2	yes	—
41	C₂³×C₄×C₈₉	D₄	1	4	yes	—
42	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
46	C₂×D₈×C₈₉	—	4	8	no	—
47	C₂×D₈×C₈₉	C₂³	1	16	yes	complemented
48	C₂×M₁₆×C₈₉	—	4	4	no	—
49	C₂×M₁₆×C₈₉	C₂³	1	8	yes	complemented
50	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
51	#121×C₈₉	—	2	8	no	—
52	#121×C₈₉	—	2	16	no	—
53	#121×C₈₉	—	2	8	no	—
54	#121×C₈₉	—	2	16	no	—
55	#121×C₈₉	C₂³	1	16	yes	—
56	#121×C₈₉	C₂³	1	16	yes	complemented
57	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
61	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
63	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
64	#106×C₈₉	C₂³	1	16	yes	complemented
65	#102×C₈₉	C₂³	1	32	yes	complemented
66	C₂²⋊C₈×C₈₉	C₂³	1	16	yes	complemented
67	C₂⁴×C₈₉	—	2	8	no	—
68	C₂⁴×C₈₉	—	2	8	no	—
69	C₂⁴×C₈₉	—	2	4	no	—
70	C₂⁴×C₈₉	—	4	2	no	—
71	C₂⁴×C₈₉	—	4	8	no	—
72	C₂⁴×C₈₉	—	4	8	no	—
73	C₂⁴×C₈₉	—	4	8	no	—
74	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
76	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
77	C₂×D₄×C₈₉	—	2	16	no	—
78	C₂×D₄×C₈₉	—	2	16	no	—
79	C₂×D₄×C₈₉	—	2	4	no	—
80	C₂×D₄×C₈₉	—	2	8	no	—
81	C₂×D₄×C₈₉	—	2	16	no	—
82	C₂×D₄×C₈₉	—	4	16	no	—
83	C₂×D₄×C₈₉	—	4	8	no	—
84	C₂×D₄×C₈₉	—	4	16	no	—
85	C₂×D₄×C₈₉	—	4	64	no	—
86	C₂×D₄×C₈₉	—	4	16	no	—
87	C₂×D₄×C₈₉	—	4	16	no	—
88	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₈₉	—	2	4	no	—
90	C₂²×C₄×C₈₉	—	2	8	no	—
91	C₂²×C₄×C₈₉	—	2	8	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	4	8	no	—
94	C₂²×C₄×C₈₉	—	4	8	no	—
95	C₂²×C₄×C₈₉	—	4	4	no	—
96	C₂²×C₄×C₈₉	—	4	2	no	—
97	C₂²×C₄×C₈₉	—	4	8	no	—
98	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
107	D₈×C₈₉	—	4	16	no	—
108	M₁₆×C₈₉	—	4	8	no	—
109	C₂×C₈×C₈₉	—	2	8	no	—
110	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
111	C₄⋊C₄×C₈₉	—	2	4	no	—
112	C₄⋊C₄×C₈₉	—	2	8	no	—
113	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
114	C₂²⋊C₄×C₈₉	—	2	16	no	—
115	C₂²⋊C₄×C₈₉	—	2	16	no	—
116	C₂³×C₈₉	—	2	4	no	—
117	C₂³×C₈₉	—	2	4	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	—	2	16	no	—
120	C₂³×C₈₉	—	2	4	no	—
121	C₂³×C₈₉	—	2	8	no	—
122	C₂³×C₈₉	—	4	4	no	—
123	C₂³×C₈₉	—	4	16	no	—
124	C₂³×C₈₉	—	4	16	no	—
125	C₂³×C₈₉	—	4	16	no	—
126	C₂³×C₈₉	—	4	8	no	—
127	C₂³×C₈₉	—	4	8	no	—
128	C₂³×C₈₉	—	4	16	no	—
129	C₂³×C₈₉	—	4	8	no	—
130	C₂³×C₈₉	—	8	32	no	—
131	C₂³×C₈₉	AGL(1,ℤ/8)	1	8	yes	—
132	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
133	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
134	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
135	D₄×C₈₉	—	2	16	no	—
136	D₄×C₈₉	—	4	16	no	—
137	D₄×C₈₉	—	4	32	no	—
138	D₄×C₈₉	—	4	32	no	—
139	D₄×C₈₉	—	4	8	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	4	no	—
142	C₂×C₄×C₈₉	—	2	4	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	2	4	no	—
145	C₂×C₄×C₈₉	—	2	8	no	—
146	C₂×C₄×C₈₉	—	2	8	no	—
147	C₂×C₄×C₈₉	—	4	8	no	—
148	C₂×C₄×C₈₉	—	4	4	no	—
149	C₂×C₄×C₈₉	—	4	16	no	—
150	C₂×C₄×C₈₉	—	4	8	no	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
155	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
156	C₈×C₈₉	—	2	8	no	—
157	C₂²×C₈₉	—	2	4	no	—
158	C₂²×C₈₉	—	2	16	no	—
159	C₂²×C₈₉	—	2	4	no	—
160	C₂²×C₈₉	—	2	2	no	—
161	C₂²×C₈₉	—	2	4	no	—
162	C₂²×C₈₉	—	4	16	no	—
163	C₂²×C₈₉	—	4	4	no	—
164	C₂²×C₈₉	—	4	8	no	—
165	C₂²×C₈₉	—	4	8	no	—
166	C₂²×C₈₉	—	4	8	no	—
167	C₂²×C₈₉	—	8	32	no	—
168	C₂²×C₈₉	—	8	16	no	—
169	C₂²×C₈₉	#534	1	2	yes	—
170	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	8	yes	—
171	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
172	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₈₉	—	2	2	no	—
174	C₄×C₈₉	—	2	4	no	—
175	C₄×C₈₉	—	4	8	no	—
176	C₄×C₈₉	#534	1	2	yes	—
177	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
178	C₂×#3192	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₈₉	—	2	8	no	—
180	C₂×C₈₉	—	4	2	no	—
181	C₂×C₈₉	—	8	8	no	—
182	C₂×C₈₉	#3192	1	4	yes	direct product factor
183	C₂×C₈₉	C₂×#534	1	1	yes	characteristic
184	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	2	yes	—
185	C₂²×#121	C₂×C₈₉	1	2	yes	complemented
186	#3192	C₂×C₈₉	1	16	yes	direct product factor
187	C₂×#481	C₂×C₈₉	1	4	yes	complemented
188	C₂×#469	C₂×C₈₉	1	4	yes	complemented
189	C₂×#447	C₂×C₈₉	1	4	yes	complemented
190	C₂×#407	C₂×C₈₉	1	1	yes	characteristic, complemented
191	C₈₉	C₂×#3192	1	1	yes	characteristic, direct product factor, Sylow
192	C₂³×D₄	—	2	2	no	—
193	C₂³×D₄	C₂²×C₈₉	1	2	yes	complemented
194	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
195	C₂²×D₈	C₂²×C₈₉	1	4	yes	complemented
196	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	complemented
197	C₂×#121	—	2	2	no	—
198	C₂×#121	—	2	8	no	—
199	C₂×#121	—	2	2	no	—
200	C₂×#121	C₂²×C₈₉	1	4	yes	—
201	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
202	C₂×#121	C₂²×C₈₉	1	16	yes	complemented
203	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
204	C₂²×C₂²⋊C₄	—	2	2	no	—
205	#481	C₂²×C₈₉	1	32	yes	complemented
206	#469	C₂²×C₈₉	1	32	yes	complemented
207	#447	C₂²×C₈₉	1	32	yes	complemented
208	C₂×#106	C₂²×C₈₉	1	4	yes	complemented
209	C₂×#102	C₂²×C₈₉	1	8	yes	complemented
210	#407	C₂²×C₈₉	1	8	yes	complemented
211	C₂×C₂²⋊C₈	C₂²×C₈₉	1	4	yes	complemented
212	C₂⁵	—	2	2	no	—
213	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
214	C₂²×D₄	—	2	4	no	—
215	C₂²×D₄	—	2	4	no	—
216	C₂²×D₄	—	2	16	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	4	8	no	—
220	C₂²×D₄	—	4	16	no	—
221	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
222	C₂²×D₄	C₂³×C₈₉	1	8	yes	complemented
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	—	4	4	no	—
225	C₂³×C₄	D₄×C₈₉	1	2	yes	—
226	C₂³×C₄	D₄×C₈₉	1	4	yes	—
227	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
229	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
231	C₂×D₈	—	4	8	no	—
232	C₂×D₈	C₂³×C₈₉	1	16	yes	complemented
233	C₂×M₁₆	—	4	4	no	—
234	C₂×M₁₆	C₂³×C₈₉	1	8	yes	complemented
235	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
236	#121	—	2	8	no	—
237	#121	—	2	16	no	—
238	#121	—	2	8	no	—
239	#121	—	2	16	no	—
240	#121	C₂³×C₈₉	1	16	yes	—
241	#121	C₂³×C₈₉	1	16	yes	complemented
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
245	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₂²⋊C₄	—	2	16	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	#106	C₂³×C₈₉	1	16	yes	complemented
250	#102	C₂³×C₈₉	1	32	yes	complemented
251	C₂²⋊C₈	C₂³×C₈₉	1	16	yes	complemented
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	2	4	no	—
254	C₂⁴	—	2	8	no	—
255	C₂⁴	—	4	2	no	—
256	C₂⁴	—	4	8	no	—
257	C₂⁴	—	4	8	no	—
258	C₂⁴	—	4	8	no	—
259	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
260	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
261	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
262	C₂×D₄	—	2	16	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	16	no	—
267	C₂×D₄	—	4	16	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	—	4	16	no	—
270	C₂×D₄	—	4	64	no	—
271	C₂×D₄	—	4	16	no	—
272	C₂×D₄	—	4	16	no	—
273	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	8	no	—
283	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
288	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
292	D₈	—	4	16	no	—
293	M₁₆	—	4	8	no	—
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	16	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	8	32	no	—
316	C₂³	AGL(1,ℤ/8)×C₈₉	1	8	yes	—
317	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
318	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
319	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
320	D₄	—	2	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	32	no	—
323	D₄	—	4	32	no	—
324	D₄	—	4	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
339	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
340	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	16	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	16	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	#534×C₈₉	1	2	yes	—
355	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	8	yes	—
356	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
357	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	#534×C₈₉	1	2	yes	—
362	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
363	C₂	—	2	8	no	—
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₈₉×#3192	1	4	yes	direct product factor
367	C₂	C₂×#534×C₈₉	1	1	yes	characteristic
368	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#121×C₈₉	C₂	semidirect
2. C₈₉×#3192	C₂	direct (N × H)
3. C₂×#481×C₈₉	C₂	semidirect
4. C₂×#469×C₈₉	C₂	semidirect
5. C₂×#447×C₈₉	C₂	semidirect
6. C₂×#407×C₈₉	C₂	semidirect
8. C₂³×D₄×C₈₉	C₂²	semidirect
10. C₂²×D₈×C₈₉	C₂²	semidirect
11. C₂²×M₁₆×C₈₉	C₂²	semidirect
16. C₂×#121×C₈₉	C₂²	semidirect
17. C₂×#121×C₈₉	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
20. #481×C₈₉	C₂²	semidirect
21. #469×C₈₉	C₂²	semidirect
22. #447×C₈₉	C₂²	semidirect
23. C₂×#106×C₈₉	C₂²	semidirect
24. C₂×#102×C₈₉	C₂²	semidirect
25. #407×C₈₉	C₂²	semidirect
26. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
37. C₂²×D₄×C₈₉	C₂³	semidirect
47. C₂×D₈×C₈₉	C₂³	semidirect
49. C₂×M₁₆×C₈₉	C₂³	semidirect
56. #121×C₈₉	C₂³	semidirect
60. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
64. #106×C₈₉	C₂³	semidirect
65. #102×C₈₉	C₂³	semidirect
66. C₂²⋊C₈×C₈₉	C₂³	semidirect
178. C₂×#3192	C₈₉	direct (N × H)
182. C₂×C₈₉	#3192	direct (N × H)
185. C₂²×#121	C₂×C₈₉	semidirect
186. #3192	C₂×C₈₉	direct (N × H)
187. C₂×#481	C₂×C₈₉	semidirect
188. C₂×#469	C₂×C₈₉	semidirect
189. C₂×#447	C₂×C₈₉	semidirect
190. C₂×#407	C₂×C₈₉	semidirect
191. C₈₉	C₂×#3192	direct (N × H)
193. C₂³×D₄	C₂²×C₈₉	semidirect
195. C₂²×D₈	C₂²×C₈₉	semidirect
196. C₂²×M₁₆	C₂²×C₈₉	semidirect
201. C₂×#121	C₂²×C₈₉	semidirect
202. C₂×#121	C₂²×C₈₉	semidirect
203. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
205. #481	C₂²×C₈₉	semidirect
206. #469	C₂²×C₈₉	semidirect
207. #447	C₂²×C₈₉	semidirect
208. C₂×#106	C₂²×C₈₉	semidirect
209. C₂×#102	C₂²×C₈₉	semidirect
210. #407	C₂²×C₈₉	semidirect
211. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
222. C₂²×D₄	C₂³×C₈₉	semidirect
232. C₂×D₈	C₂³×C₈₉	semidirect
234. C₂×M₁₆	C₂³×C₈₉	semidirect
241. #121	C₂³×C₈₉	semidirect
245. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
249. #106	C₂³×C₈₉	semidirect
250. #102	C₂³×C₈₉	semidirect
251. C₂²⋊C₈	C₂³×C₈₉	semidirect
366. C₂	C₈₉×#3192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₈₉	2
C₈₉×#3192	2
C₂×#481×C₈₉	2
C₂×#469×C₈₉	2
C₂×#447×C₈₉	2
C₂×#407×C₈₉	2
C₂×#3192	89

Subgroups — C2×C89×#3192 #36438583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3192 #36438583