Subgroups — C₈₉×#35166 #36413014

Order 22784.

3714 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	C₂×#537×C₈₉	C₂	1	4	yes	maximal, complemented
2	C₂×#532×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2856	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2656	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2542	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2541	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2540	C₂	1	8	yes	maximal, complemented
8	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₈₉	C₂²	1	4	yes	—
10	#537×C₈₉	—	2	32	no	—
11	#532×C₈₉	—	2	16	no	—
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
13	C₂×#127×C₈₉	C₂²	1	2	yes	—
14	C₂×#127×C₈₉	C₂²	1	4	yes	—
15	C₂×#124×C₈₉	C₂²	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	16	yes	—
17	C₂×#121×C₈₉	C₂²	1	4	yes	—
18	C₂×#121×C₈₉	C₂²	1	16	yes	—
19	C₂×#121×C₈₉	C₂²	1	4	yes	—
20	C₂×#121×C₈₉	C₂²	1	16	yes	—
21	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
26	#399×C₈₉	C₂²	1	16	yes	—
27	#392×C₈₉	C₂²	1	16	yes	—
28	#390×C₈₉	C₂²	1	16	yes	—
29	#390×C₈₉	C₂²	1	8	yes	—
30	#384×C₈₉	C₂²	1	4	yes	—
31	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
32	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
33	C₂×#95×C₈₉	C₂²	1	2	yes	—
34	C₂×#41×C₈₉	—	2	16	no	—
35	C₂×#41×C₈₉	—	2	32	no	—
36	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
37	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
38	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
39	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
40	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
41	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₈₉	—	2	8	no	—
48	#127×C₈₉	—	2	8	no	—
49	#127×C₈₉	—	4	8	no	—
50	#124×C₈₉	—	2	16	no	—
51	C₂²⋊Q₈×C₈₉	—	2	64	no	—
52	#121×C₈₉	—	2	16	no	—
53	#121×C₈₉	—	2	16	no	—
54	#121×C₈₉	—	2	64	no	—
55	#121×C₈₉	—	2	64	no	—
56	C₄×D₄×C₈₉	—	2	16	no	—
57	C₄×D₄×C₈₉	—	2	16	no	—
58	C₂×C₄⋊C₄×C₈₉	D₄	1	16	yes	complemented
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
64	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
66	C₂×C₄²×C₈₉	—	4	4	no	—
67	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
68	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
72	#95×C₈₉	C₂³	1	8	yes	—
73	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
74	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
75	#41×C₈₉	—	4	64	no	—
76	C₂×Q₈×C₈₉	—	2	16	no	—
77	C₂×Q₈×C₈₉	—	2	8	no	—
78	C₂×D₄×C₈₉	—	2	16	no	—
79	C₂×D₄×C₈₉	—	2	32	no	—
80	C₂×D₄×C₈₉	—	2	8	no	—
81	C₂×D₄×C₈₉	—	2	8	no	—
82	C₂×D₄×C₈₉	—	2	16	no	—
83	C₂×D₄×C₈₉	—	2	8	no	—
84	C₂×D₄×C₈₉	—	2	32	no	—
85	C₂×D₄×C₈₉	—	2	8	no	—
86	C₂×D₄×C₈₉	—	2	8	no	—
87	C₂×D₄×C₈₉	—	4	8	no	—
88	C₂×D₄×C₈₉	—	4	16	no	—
89	C₂×D₄×C₈₉	—	4	16	no	—
90	C₂²×C₄×C₈₉	—	2	2	no	—
91	C₂²×C₄×C₈₉	—	2	2	no	—
92	C₂²×C₄×C₈₉	—	2	16	no	—
93	C₂²×C₄×C₈₉	—	2	32	no	—
94	C₂²×C₄×C₈₉	—	4	4	no	—
95	C₂²×C₄×C₈₉	—	4	2	no	—
96	C₂²×C₄×C₈₉	—	4	4	no	—
97	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	—
100	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₈₉	—	2	8	no	—
109	C₄⋊C₄×C₈₉	—	2	8	no	—
110	C₄⋊C₄×C₈₉	—	2	32	no	—
111	C₄⋊C₄×C₈₉	C₂×D₄	1	32	yes	—
112	C₂²⋊C₄×C₈₉	—	2	16	no	—
113	C₂²⋊C₄×C₈₉	—	2	16	no	—
114	C₂²⋊C₄×C₈₉	—	2	64	no	—
115	C₄²×C₈₉	—	2	8	no	—
116	C₄²×C₈₉	—	4	4	no	—
117	C₄²×C₈₉	C₂×D₄	1	8	yes	—
118	C₄²×C₈₉	C₂×D₄	1	8	yes	—
119	C₂³×C₈₉	—	2	1	no	—
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	—	2	8	no	—
123	C₂³×C₈₉	—	2	16	no	—
124	C₂³×C₈₉	—	2	8	no	—
125	C₂³×C₈₉	—	2	8	no	—
126	C₂³×C₈₉	—	2	16	no	—
127	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
128	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
129	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
130	Q₈×C₈₉	—	4	16	no	—
131	D₄×C₈₉	—	4	16	no	—
132	D₄×C₈₉	—	4	32	no	—
133	D₄×C₈₉	—	4	16	no	—
134	D₄×C₈₉	—	4	16	no	—
135	D₄×C₈₉	—	8	32	no	—
136	C₂×C₄×C₈₉	—	2	8	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	2	8	no	—
141	C₂×C₄×C₈₉	—	2	8	no	—
142	C₂×C₄×C₈₉	—	2	8	no	—
143	C₂×C₄×C₈₉	—	2	16	no	—
144	C₂×C₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	—	4	16	no	—
146	C₂×C₄×C₈₉	—	4	32	no	—
147	C₂×C₄×C₈₉	#127	1	16	yes	complemented
148	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
153	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
155	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
156	C₂²×C₈₉	—	2	2	no	—
157	C₂²×C₈₉	—	2	2	no	—
158	C₂²×C₈₉	—	2	4	no	—
159	C₂²×C₈₉	—	2	4	no	—
160	C₂²×C₈₉	—	4	8	no	—
161	C₂²×C₈₉	—	4	8	no	—
162	C₂²×C₈₉	—	4	8	no	—
163	C₂²×C₈₉	—	4	16	no	—
164	C₂²×C₈₉	—	4	16	no	—
165	C₂²×C₈₉	C₂×#127	1	4	yes	—
166	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
167	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
168	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
170	C₂²×C₈₉	#585	1	2	yes	—
171	C₄×C₈₉	—	2	2	no	—
172	C₄×C₈₉	—	2	4	no	—
173	C₄×C₈₉	—	2	16	no	—
174	C₄×C₈₉	—	4	8	no	—
175	C₄×C₈₉	C₂×#127	1	8	yes	—
176	C₄×C₈₉	#537	1	4	yes	complemented
177	#35166	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₈₉	—	2	4	no	—
179	C₂×C₈₉	—	8	8	no	—
180	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
181	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
182	C₂×C₈₉	#3449	1	1	yes	characteristic
183	C₂×C₈₉	#3496	1	2	yes	—
184	C₂×C₈₉	#3497	1	2	yes	—
185	C₂×#537	C₂×C₈₉	1	4	yes	complemented
186	C₂×#532	C₂×C₈₉	1	2	yes	complemented
187	#2856	C₂×C₈₉	1	4	yes	complemented
188	#2656	C₂×C₈₉	1	4	yes	complemented
189	#2542	C₂×C₈₉	1	4	yes	complemented
190	#2541	C₂×C₈₉	1	4	yes	complemented
191	#2540	C₂×C₈₉	1	8	yes	complemented
192	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
193	C₈₉	#35166	1	1	yes	characteristic, direct product factor, Sylow
194	C₂²×#41	C₂²×C₈₉	1	4	yes	—
195	#537	—	2	32	no	—
196	#532	—	2	16	no	—
197	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
198	C₂×#127	C₂²×C₈₉	1	2	yes	—
199	C₂×#127	C₂²×C₈₉	1	4	yes	—
200	C₂×#124	C₂²×C₈₉	1	4	yes	—
201	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	16	yes	—
202	C₂×#121	C₂²×C₈₉	1	4	yes	—
203	C₂×#121	C₂²×C₈₉	1	16	yes	—
204	C₂×#121	C₂²×C₈₉	1	4	yes	—
205	C₂×#121	C₂²×C₈₉	1	16	yes	—
206	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
207	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
209	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
210	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
211	#399	C₂²×C₈₉	1	16	yes	—
212	#392	C₂²×C₈₉	1	16	yes	—
213	#390	C₂²×C₈₉	1	16	yes	—
214	#390	C₂²×C₈₉	1	8	yes	—
215	#384	C₂²×C₈₉	1	4	yes	—
216	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
217	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
218	C₂×#95	C₂²×C₈₉	1	2	yes	—
219	C₂×#41	—	2	16	no	—
220	C₂×#41	—	2	32	no	—
221	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
222	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
223	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
224	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
225	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
226	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
227	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
228	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
230	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	8	no	—
233	#127	—	2	8	no	—
234	#127	—	4	8	no	—
235	#124	—	2	16	no	—
236	C₂²⋊Q₈	—	2	64	no	—
237	#121	—	2	16	no	—
238	#121	—	2	16	no	—
239	#121	—	2	64	no	—
240	#121	—	2	64	no	—
241	C₄×D₄	—	2	16	no	—
242	C₄×D₄	—	2	16	no	—
243	C₂×C₄⋊C₄	D₄×C₈₉	1	16	yes	complemented
244	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
245	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
246	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
247	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
249	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	—
251	C₂×C₄²	—	4	4	no	—
252	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
253	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
254	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
255	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
256	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
257	#95	C₂³×C₈₉	1	8	yes	—
258	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
259	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
260	#41	—	4	64	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	8	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	32	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	16	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	2	32	no	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	16	no	—
274	C₂×D₄	—	4	16	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	—	2	32	no	—
279	C₂²×C₄	—	4	4	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
283	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
284	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	—
285	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
287	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
290	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	32	no	—
296	C₄⋊C₄	C₂×D₄×C₈₉	1	32	yes	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₂²⋊C₄	—	2	64	no	—
300	C₄²	—	2	8	no	—
301	C₄²	—	4	4	no	—
302	C₄²	C₂×D₄×C₈₉	1	8	yes	—
303	C₄²	C₂×D₄×C₈₉	1	8	yes	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	16	no	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	2	16	no	—
312	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
313	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
314	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
315	Q₈	—	4	16	no	—
316	D₄	—	4	16	no	—
317	D₄	—	4	32	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	16	no	—
320	D₄	—	8	32	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	16	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	—	4	32	no	—
332	C₂×C₄	#127×C₈₉	1	16	yes	complemented
333	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
336	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
338	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
339	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
340	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	8	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	16	no	—
349	C₂²	—	4	16	no	—
350	C₂²	C₂×#127×C₈₉	1	4	yes	—
351	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
352	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
353	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
354	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
355	C₂²	#585×C₈₉	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	16	no	—
359	C₄	—	4	8	no	—
360	C₄	C₂×#127×C₈₉	1	8	yes	—
361	C₄	#537×C₈₉	1	4	yes	complemented
362	C₂	—	2	4	no	—
363	C₂	—	8	8	no	—
364	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
365	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
366	C₂	C₈₉×#3449	1	1	yes	characteristic
367	C₂	C₈₉×#3496	1	2	yes	—
368	C₂	C₈₉×#3497	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#537×C₈₉	C₂	semidirect
2. C₂×#532×C₈₉	C₂	semidirect
3. C₈₉×#2856	C₂	semidirect
4. C₈₉×#2656	C₂	semidirect
5. C₈₉×#2542	C₂	semidirect
6. C₈₉×#2541	C₂	semidirect
7. C₈₉×#2540	C₂	semidirect
8. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
58. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
67. C₂×C₄²×C₈₉	D₄	semidirect
147. C₂×C₄×C₈₉	#127	semidirect
176. C₄×C₈₉	#537	semidirect
177. #35166	C₈₉	direct (N × H)
185. C₂×#537	C₂×C₈₉	semidirect
186. C₂×#532	C₂×C₈₉	semidirect
187. #2856	C₂×C₈₉	semidirect
188. #2656	C₂×C₈₉	semidirect
189. #2542	C₂×C₈₉	semidirect
190. #2541	C₂×C₈₉	semidirect
191. #2540	C₂×C₈₉	semidirect
192. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
193. C₈₉	#35166	direct (N × H)
243. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
252. C₂×C₄²	D₄×C₈₉	semidirect
332. C₂×C₄	#127×C₈₉	semidirect
361. C₄	#537×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#2856	2
C₈₉×#2656	2
C₈₉×#2542	2
C₈₉×#2541	2
C₈₉×#2540	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#35166	89

Subgroups — C89×#35166 #36413014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35166 #36413014