Subgroups — C₈₉×#35242 #36413090

Order 22784.

5090 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#536×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2849	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2614	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2436	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2434	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2409	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2310	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₈₉	—	2	16	no	—
13	C₂³×Q₈×C₈₉	—	2	8	no	—
14	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
15	C₂³×Q₈×C₈₉	C₂²	1	4	yes	—
16	C₂³×Q₈×C₈₉	C₂²	1	4	yes	—
17	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
20	#536×C₈₉	—	2	16	no	—
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
22	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
23	#525×C₈₉	—	2	8	no	—
24	C₂×#123×C₈₉	C₂²	1	8	yes	—
25	C₂×#123×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#120×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	2	yes	—
33	#395×C₈₉	C₂²	1	16	yes	complemented
34	#393×C₈₉	C₂²	1	16	yes	complemented
35	#391×C₈₉	C₂²	1	8	yes	complemented
36	#391×C₈₉	C₂²	1	8	yes	complemented
37	#386×C₈₉	C₂²	1	16	yes	—
38	#385×C₈₉	C₂²	1	16	yes	—
39	#381×C₈₉	C₂²	1	8	yes	—
40	#381×C₈₉	C₂²	1	2	yes	—
41	#380×C₈₉	C₂²	1	4	yes	—
42	#379×C₈₉	C₂²	1	2	yes	—
43	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
44	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
45	C₂×#41×C₈₉	—	2	4	no	—
46	C₂×#41×C₈₉	—	2	8	no	—
47	C₂²×Q₈×C₈₉	—	2	128	no	—
48	C₂²×Q₈×C₈₉	—	2	32	no	—
49	C₂²×Q₈×C₈₉	—	2	32	no	—
50	C₂²×Q₈×C₈₉	—	2	16	no	—
51	C₂²×Q₈×C₈₉	—	2	16	no	—
52	C₂²×Q₈×C₈₉	—	2	16	no	—
53	C₂²×Q₈×C₈₉	—	2	8	no	—
54	C₂²×Q₈×C₈₉	—	2	8	no	—
55	C₂²×Q₈×C₈₉	—	2	8	no	—
56	C₂²×Q₈×C₈₉	D₄	1	16	yes	complemented
57	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
58	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
60	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	—	2	8	no	—
65	C₂³×C₄×C₈₉	—	2	16	no	—
66	C₂³×C₄×C₈₉	—	2	8	no	—
67	C₂³×C₄×C₈₉	D₄	1	8	yes	—
68	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
69	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₈₉	—	2	16	no	—
76	#124×C₈₉	—	2	16	no	—
77	#123×C₈₉	—	2	8	no	—
78	#123×C₈₉	—	2	32	no	—
79	C₂²⋊Q₈×C₈₉	—	2	32	no	—
80	C₂²⋊Q₈×C₈₉	—	2	8	no	—
81	#121×C₈₉	—	2	8	no	—
82	#120×C₈₉	—	2	8	no	—
83	C₄×D₄×C₈₉	—	2	16	no	—
84	#117×C₈₉	—	2	4	no	—
85	#117×C₈₉	—	2	8	no	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
98	#95×C₈₉	C₂³	1	8	yes	—
99	#95×C₈₉	C₂³	1	32	yes	—
100	C₂⁴×C₈₉	—	2	4	no	—
101	C₂⁴×C₈₉	—	2	8	no	—
102	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
103	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
104	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
105	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
106	#41×C₈₉	—	4	16	no	—
107	C₂×Q₈×C₈₉	—	2	128	no	—
108	C₂×Q₈×C₈₉	—	2	128	no	—
109	C₂×Q₈×C₈₉	—	2	64	no	—
110	C₂×Q₈×C₈₉	—	2	64	no	—
111	C₂×Q₈×C₈₉	—	2	32	no	—
112	C₂×Q₈×C₈₉	—	2	16	no	—
113	C₂×Q₈×C₈₉	—	2	8	no	—
114	C₂×Q₈×C₈₉	—	2	8	no	—
115	C₂×Q₈×C₈₉	—	2	8	no	—
116	C₂×Q₈×C₈₉	—	2	8	no	—
117	C₂×Q₈×C₈₉	—	2	2	no	—
118	C₂×Q₈×C₈₉	—	2	4	no	—
119	C₂×Q₈×C₈₉	C₂×D₄	1	16	yes	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	16	yes	—
121	C₂×D₄×C₈₉	—	2	8	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	8	no	—
124	C₂×D₄×C₈₉	—	2	16	no	—
125	C₂×D₄×C₈₉	—	2	2	no	—
126	C₂×D₄×C₈₉	—	2	4	no	—
127	C₂²×C₄×C₈₉	—	2	64	no	—
128	C₂²×C₄×C₈₉	—	2	16	no	—
129	C₂²×C₄×C₈₉	—	2	8	no	—
130	C₂²×C₄×C₈₉	—	2	8	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	—	2	32	no	—
133	C₂²×C₄×C₈₉	—	2	32	no	—
134	C₂²×C₄×C₈₉	—	2	8	no	—
135	C₂²×C₄×C₈₉	—	2	8	no	—
136	C₂²×C₄×C₈₉	—	2	4	no	—
137	C₂²×C₄×C₈₉	—	2	8	no	—
138	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
139	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	—
141	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
146	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	—	2	8	no	—
154	C₄⋊C₄×C₈₉	—	2	32	no	—
155	C₂²⋊C₄×C₈₉	—	2	4	no	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₂²⋊C₄×C₈₉	—	2	16	no	—
159	C₂²⋊C₄×C₈₉	—	2	8	no	—
160	C₂²⋊C₄×C₈₉	—	2	32	no	—
161	C₄²×C₈₉	—	2	4	no	—
162	C₄²×C₈₉	—	2	8	no	—
163	C₂³×C₈₉	—	2	32	no	—
164	C₂³×C₈₉	—	2	8	no	—
165	C₂³×C₈₉	—	2	16	no	—
166	C₂³×C₈₉	—	2	4	no	—
167	C₂³×C₈₉	—	2	4	no	—
168	C₂³×C₈₉	—	2	4	no	—
169	C₂³×C₈₉	—	2	4	no	—
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	—	2	8	no	—
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
174	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
175	C₂³×C₈₉	2₋¹⁺⁴	1	8	yes	—
176	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
177	Q₈×C₈₉	—	2	64	no	—
178	Q₈×C₈₉	—	2	32	no	—
179	Q₈×C₈₉	—	2	32	no	—
180	Q₈×C₈₉	—	4	4	no	—
181	D₄×C₈₉	—	4	8	no	—
182	D₄×C₈₉	—	4	16	no	—
183	D₄×C₈₉	—	4	4	no	—
184	C₂×C₄×C₈₉	—	2	64	no	—
185	C₂×C₄×C₈₉	—	2	32	no	—
186	C₂×C₄×C₈₉	—	2	8	no	—
187	C₂×C₄×C₈₉	—	2	8	no	—
188	C₂×C₄×C₈₉	—	2	8	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	2	16	no	—
191	C₂×C₄×C₈₉	—	2	16	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	4	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	4	no	—
196	C₂×C₄×C₈₉	—	2	16	no	—
197	C₂×C₄×C₈₉	—	2	8	no	—
198	C₂×C₄×C₈₉	—	4	8	no	—
199	C₂×C₄×C₈₉	#120	1	16	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
206	C₂²×C₈₉	—	2	32	no	—
207	C₂²×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	4	no	—
209	C₂²×C₈₉	—	2	4	no	—
210	C₂²×C₈₉	—	2	8	no	—
211	C₂²×C₈₉	—	2	16	no	—
212	C₂²×C₈₉	—	4	2	no	—
213	C₂²×C₈₉	—	4	4	no	—
214	C₂²×C₈₉	—	4	8	no	—
215	C₂²×C₈₉	C₂×#120	1	4	yes	—
216	C₂²×C₈₉	#536	1	8	yes	complemented
217	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
218	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
219	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	4	yes	—
220	C₄×C₈₉	—	2	16	no	—
221	C₄×C₈₉	—	2	4	no	—
222	C₄×C₈₉	—	4	2	no	—
223	C₄×C₈₉	—	4	4	no	—
224	C₄×C₈₉	—	4	8	no	—
225	C₄×C₈₉	C₂×#120	1	4	yes	—
226	C₄×C₈₉	C₂×#120	1	4	yes	—
227	#35242	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₈₉	—	2	4	no	—
229	C₂×C₈₉	—	2	8	no	—
230	C₂×C₈₉	—	8	2	no	—
231	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#536	1	2	yes	—
233	C₂×C₈₉	#3486	1	4	yes	—
234	C₂⁴×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
235	C₂×#536	C₂×C₈₉	1	2	yes	complemented
236	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
237	#2849	C₂×C₈₉	1	4	yes	complemented
238	#2614	C₂×C₈₉	1	4	yes	complemented
239	#2436	C₂×C₈₉	1	4	yes	complemented
240	#2434	C₂×C₈₉	1	4	yes	complemented
241	#2409	C₂×C₈₉	1	8	yes	complemented
242	#2310	C₂×C₈₉	1	2	yes	complemented
243	#2280	C₂×C₈₉	1	1	yes	characteristic, complemented
244	C₈₉	#35242	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
246	C₂³×Q₈	—	2	16	no	—
247	C₂³×Q₈	—	2	8	no	—
248	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
249	C₂³×Q₈	C₂²×C₈₉	1	4	yes	—
250	C₂³×Q₈	C₂²×C₈₉	1	4	yes	—
251	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
252	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
253	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
254	#536	—	2	16	no	—
255	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
256	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
257	#525	—	2	8	no	—
258	C₂×#123	C₂²×C₈₉	1	8	yes	—
259	C₂×#123	C₂²×C₈₉	1	2	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
262	C₂×#121	C₂²×C₈₉	1	2	yes	—
263	C₂×#120	C₂²×C₈₉	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
265	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#117	C₂²×C₈₉	1	2	yes	—
267	#395	C₂²×C₈₉	1	16	yes	complemented
268	#393	C₂²×C₈₉	1	16	yes	complemented
269	#391	C₂²×C₈₉	1	8	yes	complemented
270	#391	C₂²×C₈₉	1	8	yes	complemented
271	#386	C₂²×C₈₉	1	16	yes	—
272	#385	C₂²×C₈₉	1	16	yes	—
273	#381	C₂²×C₈₉	1	8	yes	—
274	#381	C₂²×C₈₉	1	2	yes	—
275	#380	C₂²×C₈₉	1	4	yes	—
276	#379	C₂²×C₈₉	1	2	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
278	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	2	8	no	—
281	C₂²×Q₈	—	2	128	no	—
282	C₂²×Q₈	—	2	32	no	—
283	C₂²×Q₈	—	2	32	no	—
284	C₂²×Q₈	—	2	16	no	—
285	C₂²×Q₈	—	2	16	no	—
286	C₂²×Q₈	—	2	16	no	—
287	C₂²×Q₈	—	2	8	no	—
288	C₂²×Q₈	—	2	8	no	—
289	C₂²×Q₈	—	2	8	no	—
290	C₂²×Q₈	D₄×C₈₉	1	16	yes	complemented
291	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
293	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
294	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
295	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
296	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
297	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	8	no	—
299	C₂³×C₄	—	2	16	no	—
300	C₂³×C₄	—	2	8	no	—
301	C₂³×C₄	D₄×C₈₉	1	8	yes	—
302	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
303	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
304	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
305	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
306	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
307	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
309	C₄⋊Q₈	—	2	16	no	—
310	#124	—	2	16	no	—
311	#123	—	2	8	no	—
312	#123	—	2	32	no	—
313	C₂²⋊Q₈	—	2	32	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	#121	—	2	8	no	—
316	#120	—	2	8	no	—
317	C₄×D₄	—	2	16	no	—
318	#117	—	2	4	no	—
319	#117	—	2	8	no	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
330	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
332	#95	C₂³×C₈₉	1	8	yes	—
333	#95	C₂³×C₈₉	1	32	yes	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	8	no	—
336	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
337	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
338	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
339	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
340	#41	—	4	16	no	—
341	C₂×Q₈	—	2	128	no	—
342	C₂×Q₈	—	2	128	no	—
343	C₂×Q₈	—	2	64	no	—
344	C₂×Q₈	—	2	64	no	—
345	C₂×Q₈	—	2	32	no	—
346	C₂×Q₈	—	2	16	no	—
347	C₂×Q₈	—	2	8	no	—
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	2	8	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	C₂×D₄×C₈₉	1	16	yes	—
354	C₂×Q₈	C₂×D₄×C₈₉	1	16	yes	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂²×C₄	—	2	64	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	32	no	—
367	C₂²×C₄	—	2	32	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
373	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
374	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	—
375	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
377	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
380	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
382	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	32	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	16	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	32	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	8	no	—
397	C₂³	—	2	32	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	8	no	—
406	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
407	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
408	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
409	C₂³	2₋¹⁺⁴×C₈₉	1	8	yes	—
410	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
411	Q₈	—	2	64	no	—
412	Q₈	—	2	32	no	—
413	Q₈	—	2	32	no	—
414	Q₈	—	4	4	no	—
415	D₄	—	4	8	no	—
416	D₄	—	4	16	no	—
417	D₄	—	4	4	no	—
418	C₂×C₄	—	2	64	no	—
419	C₂×C₄	—	2	32	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	16	no	—
425	C₂×C₄	—	2	16	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	16	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	#120×C₈₉	1	16	yes	—
434	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
435	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
440	C₂²	—	2	32	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	8	no	—
445	C₂²	—	2	16	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	C₂×#120×C₈₉	1	4	yes	—
450	C₂²	#536×C₈₉	1	8	yes	complemented
451	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
452	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
453	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	4	yes	—
454	C₄	—	2	16	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	8	no	—
459	C₄	C₂×#120×C₈₉	1	4	yes	—
460	C₄	C₂×#120×C₈₉	1	4	yes	—
461	C₂	—	2	4	no	—
462	C₂	—	2	8	no	—
463	C₂	—	8	2	no	—
464	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic
465	C₂	C₂×#536×C₈₉	1	2	yes	—
466	C₂	C₈₉×#3486	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#525×C₈₉	C₂
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. C₂⁴×Q₈×C₈₉	C₂	semidirect
2. C₂×#536×C₈₉	C₂	semidirect
4. C₈₉×#2849	C₂	semidirect
5. C₈₉×#2614	C₂	semidirect
6. C₈₉×#2436	C₂	semidirect
7. C₈₉×#2434	C₂	semidirect
8. C₈₉×#2409	C₂	semidirect
9. C₈₉×#2310	C₂	semidirect
10. C₈₉×#2280	C₂	semidirect
21. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#124×C₈₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. #395×C₈₉	C₂²	semidirect
34. #393×C₈₉	C₂²	semidirect
35. #391×C₈₉	C₂²	semidirect
36. #391×C₈₉	C₂²	semidirect
56. C₂²×Q₈×C₈₉	D₄	semidirect
216. C₂²×C₈₉	#536	semidirect
227. #35242	C₈₉	direct (N × H)
234. C₂⁴×Q₈	C₂×C₈₉	semidirect
235. C₂×#536	C₂×C₈₉	semidirect
237. #2849	C₂×C₈₉	semidirect
238. #2614	C₂×C₈₉	semidirect
239. #2436	C₂×C₈₉	semidirect
240. #2434	C₂×C₈₉	semidirect
241. #2409	C₂×C₈₉	semidirect
242. #2310	C₂×C₈₉	semidirect
243. #2280	C₂×C₈₉	semidirect
244. C₈₉	#35242	direct (N × H)
255. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
256. C₂×#124	C₂²×C₈₉	semidirect
261. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
267. #395	C₂²×C₈₉	semidirect
268. #393	C₂²×C₈₉	semidirect
269. #391	C₂²×C₈₉	semidirect
270. #391	C₂²×C₈₉	semidirect
290. C₂²×Q₈	D₄×C₈₉	semidirect
450. C₂²	#536×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₈₉	2
C₂×#536×C₈₉	2
C₂×#525×C₈₉	2
C₈₉×#2849	2
C₈₉×#2614	2
C₈₉×#2436	2
C₈₉×#2434	2
C₈₉×#2409	2
C₈₉×#2310	2
C₈₉×#2280	2
#35242	89

Subgroups — C89×#35242 #36413090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35242 #36413090