Subgroups — C₂×C₈₉×#2847 #36414459

Order 22784.

8582 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₈₉	C₂	1	3	yes	maximal, complemented
3	C₂²×#120×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2847	C₂	1	16	yes	maximal, direct product factor
5	C₂×#386×C₈₉	C₂	1	6	yes	maximal, complemented
6	C₂×#380×C₈₉	C₂	1	3	yes	maximal, complemented
7	C₂⁶×C₈₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₈₉	C₂²	1	6	yes	—
9	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
10	C₂⁴×C₄×C₈₉	—	2	24	no	—
11	C₂⁴×C₄×C₈₉	C₂²	1	3	yes	—
12	C₂⁴×C₄×C₈₉	C₂²	1	3	yes	—
13	C₂⁴×C₄×C₈₉	C₂²	1	8	yes	complemented
14	C₂×#121×C₈₉	—	2	24	no	—
15	C₂×#121×C₈₉	C₂²	1	24	yes	complemented
16	C₂×#120×C₈₉	—	2	16	no	—
17	C₂×#120×C₈₉	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	3	yes	complemented
19	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	complemented
21	#386×C₈₉	C₂²	1	48	yes	complemented
22	#380×C₈₉	C₂²	1	24	yes	complemented
23	C₂×#95×C₈₉	C₂²	1	6	yes	complemented
24	C₂⁵×C₈₉	—	2	12	no	—
25	C₂⁵×C₈₉	—	2	12	no	—
26	C₂⁵×C₈₉	D₄	1	8	yes	complemented
27	C₂⁵×C₈₉	C₂³	1	2	yes	—
28	C₂⁵×C₈₉	C₂³	1	4	yes	—
29	C₂⁵×C₈₉	C₂³	1	3	yes	—
30	C₂²×D₄×C₈₉	—	2	24	no	—
31	C₂²×D₄×C₈₉	—	2	24	no	—
32	C₂²×D₄×C₈₉	—	2	24	no	—
33	C₂²×D₄×C₈₉	—	2	12	no	—
34	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
35	C₂²×D₄×C₈₉	C₂³	1	4	yes	complemented
36	C₂³×C₄×C₈₉	—	2	128	no	—
37	C₂³×C₄×C₈₉	—	2	12	no	—
38	C₂³×C₄×C₈₉	—	2	24	no	—
39	C₂³×C₄×C₈₉	—	2	24	no	—
40	C₂³×C₄×C₈₉	—	2	96	no	—
41	C₂³×C₄×C₈₉	D₄	1	24	yes	complemented
42	C₂³×C₄×C₈₉	C₂³	1	12	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
44	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
45	C₂³×C₄×C₈₉	C₂³	1	12	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
47	#121×C₈₉	—	2	96	no	—
48	#120×C₈₉	—	2	64	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	12	no	—
50	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	complemented
51	C₂×C₂²⋊C₄×C₈₉	—	2	24	no	—
52	C₂×C₂²⋊C₄×C₈₉	—	2	24	no	—
53	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	—
54	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	complemented
55	#95×C₈₉	C₂³	1	24	yes	complemented
56	C₂⁴×C₈₉	—	2	32	no	—
57	C₂⁴×C₈₉	—	2	96	no	—
58	C₂⁴×C₈₉	—	2	96	no	—
59	C₂⁴×C₈₉	—	2	24	no	—
60	C₂⁴×C₈₉	—	2	12	no	—
61	C₂⁴×C₈₉	—	2	24	no	—
62	C₂⁴×C₈₉	—	2	12	no	—
63	C₂⁴×C₈₉	—	2	12	no	—
64	C₂⁴×C₈₉	—	2	4	no	—
65	C₂⁴×C₈₉	—	2	12	no	—
66	C₂⁴×C₈₉	C₂×D₄	1	12	yes	—
67	C₂⁴×C₈₉	C₂×D₄	1	12	yes	—
68	C₂⁴×C₈₉	C₂×D₄	1	16	yes	complemented
69	C₂⁴×C₈₉	#41	1	12	yes	—
70	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
71	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
72	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
73	C₂×D₄×C₈₉	—	2	48	no	—
74	C₂×D₄×C₈₉	—	2	48	no	—
75	C₂×D₄×C₈₉	—	2	48	no	—
76	C₂×D₄×C₈₉	—	2	24	no	—
77	C₂×D₄×C₈₉	—	4	96	no	—
78	C₂×D₄×C₈₉	—	4	16	no	—
79	C₂²×C₄×C₈₉	—	2	96	no	—
80	C₂²×C₄×C₈₉	—	2	256	no	—
81	C₂²×C₄×C₈₉	—	2	24	no	—
82	C₂²×C₄×C₈₉	—	2	12	no	—
83	C₂²×C₄×C₈₉	—	2	96	no	—
84	C₂²×C₄×C₈₉	—	2	48	no	—
85	C₂²×C₄×C₈₉	—	2	48	no	—
86	C₂²×C₄×C₈₉	—	2	12	no	—
87	C₂²×C₄×C₈₉	—	2	12	no	—
88	C₂²×C₄×C₈₉	—	2	12	no	—
89	C₂²×C₄×C₈₉	C₂×D₄	1	12	yes	—
90	C₂²×C₄×C₈₉	C₂×D₄	1	12	yes	—
91	C₂²×C₄×C₈₉	C₂×D₄	1	48	yes	complemented
92	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
93	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
95	C₄⋊C₄×C₈₉	—	2	24	no	—
96	C₂²⋊C₄×C₈₉	—	2	48	no	—
97	C₂²⋊C₄×C₈₉	—	2	48	no	—
98	C₂³×C₈₉	—	2	32	no	—
99	C₂³×C₈₉	—	2	256	no	—
100	C₂³×C₈₉	—	2	96	no	—
101	C₂³×C₈₉	—	2	24	no	—
102	C₂³×C₈₉	—	2	48	no	—
103	C₂³×C₈₉	—	2	96	no	—
104	C₂³×C₈₉	—	2	24	no	—
105	C₂³×C₈₉	—	2	48	no	—
106	C₂³×C₈₉	—	2	12	no	—
107	C₂³×C₈₉	—	2	12	no	—
108	C₂³×C₈₉	—	2	12	no	—
109	C₂³×C₈₉	—	2	4	no	—
110	C₂³×C₈₉	—	2	12	no	—
111	C₂³×C₈₉	—	4	8	no	—
112	C₂³×C₈₉	—	4	24	no	—
113	C₂³×C₈₉	—	4	24	no	—
114	C₂³×C₈₉	#121	1	48	yes	complemented
115	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
116	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
117	C₂³×C₈₉	C₂²×D₄	1	6	yes	—
118	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
119	C₂³×C₈₉	C₂×#41	1	12	yes	—
120	C₂³×C₈₉	C₂×#41	1	6	yes	—
121	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
122	D₄×C₈₉	—	4	96	no	—
123	D₄×C₈₉	—	4	16	no	—
124	C₂×C₄×C₈₉	—	2	96	no	—
125	C₂×C₄×C₈₉	—	2	24	no	—
126	C₂×C₄×C₈₉	—	2	12	no	—
127	C₂×C₄×C₈₉	—	2	96	no	—
128	C₂×C₄×C₈₉	—	2	12	no	—
129	C₂×C₄×C₈₉	—	2	12	no	—
130	C₂×C₄×C₈₉	—	2	12	no	—
131	C₂×C₄×C₈₉	—	4	24	no	—
132	C₂×C₄×C₈₉	#120	1	16	yes	complemented
133	C₂×C₄×C₈₉	C₂²×D₄	1	12	yes	—
134	C₂×C₄×C₈₉	C₂²×D₄	1	12	yes	—
135	C₂²×C₈₉	—	2	128	no	—
136	C₂²×C₈₉	—	2	96	no	—
137	C₂²×C₈₉	—	2	12	no	—
138	C₂²×C₈₉	—	2	24	no	—
139	C₂²×C₈₉	—	2	12	no	—
140	C₂²×C₈₉	—	2	24	no	—
141	C₂²×C₈₉	—	4	4	no	—
142	C₂²×C₈₉	—	4	12	no	—
143	C₂²×C₈₉	—	4	12	no	—
144	C₂²×C₈₉	—	8	16	no	—
145	C₂²×C₈₉	C₂×#120	1	4	yes	—
146	C₂²×C₈₉	C₂×#121	1	12	yes	—
147	C₂²×C₈₉	C₂×#121	1	24	yes	complemented
148	C₂²×C₈₉	#525	1	12	yes	—
149	C₂²×C₈₉	C₂³×D₄	1	3	yes	—
150	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
151	C₂²×C₈₉	C₂²×#41	1	3	yes	—
152	C₄×C₈₉	—	2	12	no	—
153	C₄×C₈₉	—	4	12	no	—
154	C₄×C₈₉	C₂×#120	1	8	yes	complemented
155	C₂×#2847	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂×C₈₉	—	2	24	no	—
157	C₂×C₈₉	—	8	4	no	—
158	C₂×C₈₉	#2847	1	8	yes	direct product factor
159	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
160	C₂×C₈₉	C₂²×#121	1	3	yes	—
161	C₂×C₈₉	C₂×#525	1	3	yes	—
162	C₂⁵×C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
163	C₂²×#121	C₂×C₈₉	1	3	yes	complemented
164	C₂²×#120	C₂×C₈₉	1	2	yes	complemented
165	#2847	C₂×C₈₉	1	16	yes	direct product factor
166	C₂×#386	C₂×C₈₉	1	6	yes	complemented
167	C₂×#380	C₂×C₈₉	1	3	yes	complemented
168	C₈₉	C₂×#2847	1	1	yes	characteristic, direct product factor, Sylow
169	C₂⁶	C₂²×C₈₉	1	1	yes	characteristic
170	C₂³×D₄	C₂²×C₈₉	1	6	yes	—
171	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
172	C₂⁴×C₄	—	2	24	no	—
173	C₂⁴×C₄	C₂²×C₈₉	1	3	yes	—
174	C₂⁴×C₄	C₂²×C₈₉	1	3	yes	—
175	C₂⁴×C₄	C₂²×C₈₉	1	8	yes	complemented
176	C₂×#121	—	2	24	no	—
177	C₂×#121	C₂²×C₈₉	1	24	yes	complemented
178	C₂×#120	—	2	16	no	—
179	C₂×#120	C₂²×C₈₉	1	16	yes	complemented
180	C₂²×C₄⋊C₄	C₂²×C₈₉	1	3	yes	complemented
181	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	complemented
183	#386	C₂²×C₈₉	1	48	yes	complemented
184	#380	C₂²×C₈₉	1	24	yes	complemented
185	C₂×#95	C₂²×C₈₉	1	6	yes	complemented
186	C₂⁵	—	2	12	no	—
187	C₂⁵	—	2	12	no	—
188	C₂⁵	D₄×C₈₉	1	8	yes	complemented
189	C₂⁵	C₂³×C₈₉	1	2	yes	—
190	C₂⁵	C₂³×C₈₉	1	4	yes	—
191	C₂⁵	C₂³×C₈₉	1	3	yes	—
192	C₂²×D₄	—	2	24	no	—
193	C₂²×D₄	—	2	24	no	—
194	C₂²×D₄	—	2	24	no	—
195	C₂²×D₄	—	2	12	no	—
196	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
197	C₂²×D₄	C₂³×C₈₉	1	4	yes	complemented
198	C₂³×C₄	—	2	128	no	—
199	C₂³×C₄	—	2	12	no	—
200	C₂³×C₄	—	2	24	no	—
201	C₂³×C₄	—	2	24	no	—
202	C₂³×C₄	—	2	96	no	—
203	C₂³×C₄	D₄×C₈₉	1	24	yes	complemented
204	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
205	C₂³×C₄	C₂³×C₈₉	1	12	yes	—
206	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
207	C₂³×C₄	C₂³×C₈₉	1	12	yes	—
208	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
209	#121	—	2	96	no	—
210	#120	—	2	64	no	—
211	C₂×C₄⋊C₄	—	2	12	no	—
212	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	complemented
213	C₂×C₂²⋊C₄	—	2	24	no	—
214	C₂×C₂²⋊C₄	—	2	24	no	—
215	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	—
216	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	complemented
217	#95	C₂³×C₈₉	1	24	yes	complemented
218	C₂⁴	—	2	32	no	—
219	C₂⁴	—	2	96	no	—
220	C₂⁴	—	2	96	no	—
221	C₂⁴	—	2	24	no	—
222	C₂⁴	—	2	12	no	—
223	C₂⁴	—	2	24	no	—
224	C₂⁴	—	2	12	no	—
225	C₂⁴	—	2	12	no	—
226	C₂⁴	—	2	4	no	—
227	C₂⁴	—	2	12	no	—
228	C₂⁴	C₂×D₄×C₈₉	1	12	yes	—
229	C₂⁴	C₂×D₄×C₈₉	1	12	yes	—
230	C₂⁴	C₂×D₄×C₈₉	1	16	yes	complemented
231	C₂⁴	#41×C₈₉	1	12	yes	—
232	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
233	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
234	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
235	C₂×D₄	—	2	48	no	—
236	C₂×D₄	—	2	48	no	—
237	C₂×D₄	—	2	48	no	—
238	C₂×D₄	—	2	24	no	—
239	C₂×D₄	—	4	96	no	—
240	C₂×D₄	—	4	16	no	—
241	C₂²×C₄	—	2	96	no	—
242	C₂²×C₄	—	2	256	no	—
243	C₂²×C₄	—	2	24	no	—
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	96	no	—
246	C₂²×C₄	—	2	48	no	—
247	C₂²×C₄	—	2	48	no	—
248	C₂²×C₄	—	2	12	no	—
249	C₂²×C₄	—	2	12	no	—
250	C₂²×C₄	—	2	12	no	—
251	C₂²×C₄	C₂×D₄×C₈₉	1	12	yes	—
252	C₂²×C₄	C₂×D₄×C₈₉	1	12	yes	—
253	C₂²×C₄	C₂×D₄×C₈₉	1	48	yes	complemented
254	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
255	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
256	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
257	C₄⋊C₄	—	2	24	no	—
258	C₂²⋊C₄	—	2	48	no	—
259	C₂²⋊C₄	—	2	48	no	—
260	C₂³	—	2	32	no	—
261	C₂³	—	2	256	no	—
262	C₂³	—	2	96	no	—
263	C₂³	—	2	24	no	—
264	C₂³	—	2	48	no	—
265	C₂³	—	2	96	no	—
266	C₂³	—	2	24	no	—
267	C₂³	—	2	48	no	—
268	C₂³	—	2	12	no	—
269	C₂³	—	2	12	no	—
270	C₂³	—	2	12	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	12	no	—
273	C₂³	—	4	8	no	—
274	C₂³	—	4	24	no	—
275	C₂³	—	4	24	no	—
276	C₂³	#121×C₈₉	1	48	yes	complemented
277	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
278	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
279	C₂³	C₂²×D₄×C₈₉	1	6	yes	—
280	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
281	C₂³	C₂×#41×C₈₉	1	12	yes	—
282	C₂³	C₂×#41×C₈₉	1	6	yes	—
283	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
284	D₄	—	4	96	no	—
285	D₄	—	4	16	no	—
286	C₂×C₄	—	2	96	no	—
287	C₂×C₄	—	2	24	no	—
288	C₂×C₄	—	2	12	no	—
289	C₂×C₄	—	2	96	no	—
290	C₂×C₄	—	2	12	no	—
291	C₂×C₄	—	2	12	no	—
292	C₂×C₄	—	2	12	no	—
293	C₂×C₄	—	4	24	no	—
294	C₂×C₄	#120×C₈₉	1	16	yes	complemented
295	C₂×C₄	C₂²×D₄×C₈₉	1	12	yes	—
296	C₂×C₄	C₂²×D₄×C₈₉	1	12	yes	—
297	C₂²	—	2	128	no	—
298	C₂²	—	2	96	no	—
299	C₂²	—	2	12	no	—
300	C₂²	—	2	24	no	—
301	C₂²	—	2	12	no	—
302	C₂²	—	2	24	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	12	no	—
305	C₂²	—	4	12	no	—
306	C₂²	—	8	16	no	—
307	C₂²	C₂×#120×C₈₉	1	4	yes	—
308	C₂²	C₂×#121×C₈₉	1	12	yes	—
309	C₂²	C₂×#121×C₈₉	1	24	yes	complemented
310	C₂²	#525×C₈₉	1	12	yes	—
311	C₂²	C₂³×D₄×C₈₉	1	3	yes	—
312	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
313	C₂²	C₂²×#41×C₈₉	1	3	yes	—
314	C₄	—	2	12	no	—
315	C₄	—	4	12	no	—
316	C₄	C₂×#120×C₈₉	1	8	yes	complemented
317	C₂	—	2	24	no	—
318	C₂	—	8	4	no	—
319	C₂	C₈₉×#2847	1	8	yes	direct product factor
320	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic
321	C₂	C₂²×#121×C₈₉	1	3	yes	—
322	C₂	C₂×#525×C₈₉	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₄×C₈₉	C₂	semidirect
2. C₂²×#121×C₈₉	C₂	semidirect
3. C₂²×#120×C₈₉	C₂	semidirect
4. C₈₉×#2847	C₂	direct (N × H)
5. C₂×#386×C₈₉	C₂	semidirect
6. C₂×#380×C₈₉	C₂	semidirect
9. C₂³×D₄×C₈₉	C₂²	semidirect
13. C₂⁴×C₄×C₈₉	C₂²	semidirect
15. C₂×#121×C₈₉	C₂²	semidirect
17. C₂×#120×C₈₉	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
21. #386×C₈₉	C₂²	semidirect
22. #380×C₈₉	C₂²	semidirect
23. C₂×#95×C₈₉	C₂²	semidirect
26. C₂⁵×C₈₉	D₄	semidirect
35. C₂²×D₄×C₈₉	C₂³	semidirect
41. C₂³×C₄×C₈₉	D₄	semidirect
50. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
54. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
55. #95×C₈₉	C₂³	semidirect
68. C₂⁴×C₈₉	C₂×D₄	semidirect
91. C₂²×C₄×C₈₉	C₂×D₄	semidirect
114. C₂³×C₈₉	#121	semidirect
132. C₂×C₄×C₈₉	#120	semidirect
147. C₂²×C₈₉	C₂×#121	semidirect
154. C₄×C₈₉	C₂×#120	semidirect
155. C₂×#2847	C₈₉	direct (N × H)
158. C₂×C₈₉	#2847	direct (N × H)
162. C₂⁵×C₄	C₂×C₈₉	semidirect
163. C₂²×#121	C₂×C₈₉	semidirect
164. C₂²×#120	C₂×C₈₉	semidirect
165. #2847	C₂×C₈₉	direct (N × H)
166. C₂×#386	C₂×C₈₉	semidirect
167. C₂×#380	C₂×C₈₉	semidirect
168. C₈₉	C₂×#2847	direct (N × H)
171. C₂³×D₄	C₂²×C₈₉	semidirect
175. C₂⁴×C₄	C₂²×C₈₉	semidirect
177. C₂×#121	C₂²×C₈₉	semidirect
179. C₂×#120	C₂²×C₈₉	semidirect
180. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
182. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
183. #386	C₂²×C₈₉	semidirect
184. #380	C₂²×C₈₉	semidirect
185. C₂×#95	C₂²×C₈₉	semidirect
188. C₂⁵	D₄×C₈₉	semidirect
197. C₂²×D₄	C₂³×C₈₉	semidirect
203. C₂³×C₄	D₄×C₈₉	semidirect
212. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
216. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
217. #95	C₂³×C₈₉	semidirect
230. C₂⁴	C₂×D₄×C₈₉	semidirect
253. C₂²×C₄	C₂×D₄×C₈₉	semidirect
276. C₂³	#121×C₈₉	semidirect
294. C₂×C₄	#120×C₈₉	semidirect
309. C₂²	C₂×#121×C₈₉	semidirect
316. C₄	C₂×#120×C₈₉	semidirect
319. C₂	C₈₉×#2847	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₈₉	2
C₂²×#121×C₈₉	2
C₂²×#120×C₈₉	2
C₈₉×#2847	2
C₂×#386×C₈₉	2
C₂×#380×C₈₉	2
C₂×#2847	89

Subgroups — C2×C89×#2847 #36414459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2847 #36414459