Subgroups — C₂×C₈₉×#3568 #36440584

Order 22784.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3568	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563×C₈₉	C₂	1	3	yes	maximal, complemented
3	C₂×H(3,𝔽₄)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#556×C₈₉	C₂	1	6	yes	maximal, complemented
5	C₂×#551×C₈₉	C₂	1	6	yes	maximal, complemented
6	C₂×#542×C₈₉	C₂	1	6	yes	maximal, complemented
7	C₂×#538×C₈₉	C₂	1	6	yes	maximal, complemented
8	C₂×#529×C₈₉	C₂	1	3	yes	maximal, complemented
9	#563×C₈₉	C₂²	1	48	yes	complemented
10	H(3,𝔽₄)×C₈₉	C₂²	1	16	yes	complemented
11	#556×C₈₉	C₂²	1	96	yes	complemented
12	#551×C₈₉	C₂²	1	96	yes	complemented
13	#542×C₈₉	C₂²	1	96	yes	complemented
14	#538×C₈₉	C₂²	1	96	yes	complemented
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
16	#529×C₈₉	C₂²	1	48	yes	complemented
17	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
18	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
19	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
20	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
22	C₂×#125×C₈₉	C₂²	1	3	yes	complemented
23	C₂×#124×C₈₉	C₂²	1	3	yes	—
24	C₂×#124×C₈₉	C₂²	1	6	yes	—
25	C₂×#124×C₈₉	C₂²	1	6	yes	—
26	C₂×#124×C₈₉	C₂²	1	6	yes	complemented
27	C₂×#123×C₈₉	C₂²	1	6	yes	—
28	C₂×#123×C₈₉	C₂²	1	6	yes	—
29	C₂×#123×C₈₉	C₂²	1	6	yes	complemented
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
31	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
34	C₂×#121×C₈₉	C₂²	1	3	yes	—
35	C₂×#121×C₈₉	C₂²	1	6	yes	—
36	C₂×#120×C₈₉	C₂²	1	6	yes	—
37	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
38	C₂×C₄×Q₈×C₈₉	C₂²	1	3	yes	complemented
39	C₂×C₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
40	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
41	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
42	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	complemented
43	C₂×#117×C₈₉	C₂²	1	6	yes	complemented
44	C₂×#117×C₈₉	C₂²	1	6	yes	complemented
45	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	complemented
46	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₈₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
49	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
51	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
52	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
56	C₄⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
57	#126×C₈₉	C₂³	1	48	yes	complemented
58	#126×C₈₉	C₂³	1	48	yes	complemented
59	#126×C₈₉	C₂³	1	48	yes	complemented
60	#126×C₈₉	C₂³	1	16	yes	complemented
61	#126×C₈₉	C₂³	1	48	yes	complemented
62	#125×C₈₉	C₂³	1	24	yes	complemented
63	#124×C₈₉	C₂³	1	24	yes	—
64	#124×C₈₉	C₂³	1	48	yes	—
65	#124×C₈₉	C₂³	1	48	yes	—
66	#124×C₈₉	C₂³	1	48	yes	complemented
67	#123×C₈₉	C₂³	1	48	yes	—
68	#123×C₈₉	C₂³	1	48	yes	—
69	#123×C₈₉	C₂³	1	48	yes	complemented
70	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	complemented
71	C₂²⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
72	C₂²⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
73	C₂²⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
74	#121×C₈₉	C₂³	1	24	yes	—
75	#121×C₈₉	C₂³	1	48	yes	—
76	#120×C₈₉	C₂³	1	48	yes	—
77	#120×C₈₉	C₂³	1	16	yes	complemented
78	C₄×Q₈×C₈₉	C₂³	1	24	yes	complemented
79	C₄×Q₈×C₈₉	C₂³	1	48	yes	complemented
80	C₄×D₄×C₈₉	C₂³	1	24	yes	—
81	C₄×D₄×C₈₉	C₂³	1	48	yes	—
82	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
83	#117×C₈₉	C₂³	1	48	yes	complemented
84	#117×C₈₉	C₂³	1	48	yes	complemented
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	48	yes	complemented
103	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
106	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
107	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₈₉	C₂³	1	8	yes	complemented
109	C₂⁴×C₈₉	—	4	12	no	—
110	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
111	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
112	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₈₉	—	4	12	no	—
114	C₂×Q₈×C₈₉	—	4	6	no	—
115	C₂×Q₈×C₈₉	C₂⁴	1	24	yes	—
116	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
117	C₂×D₄×C₈₉	—	4	12	no	—
118	C₂×D₄×C₈₉	—	4	6	no	—
119	C₂×D₄×C₈₉	—	4	12	no	—
120	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
121	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
122	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
123	C₂²×C₄×C₈₉	—	4	12	no	—
124	C₂²×C₄×C₈₉	—	4	6	no	—
125	C₂²×C₄×C₈₉	—	4	12	no	—
126	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
132	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
134	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
135	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
136	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
137	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
138	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
139	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
140	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
141	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
142	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
143	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
144	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
145	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
146	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
147	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
148	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
149	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
150	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
151	C₄²×C₈₉	C₂⁴	1	12	yes	—
152	C₄²×C₈₉	C₂⁴	1	4	yes	—
153	C₄²×C₈₉	C₂⁴	1	24	yes	—
154	C₄²×C₈₉	C₂⁴	1	24	yes	—
155	C₄²×C₈₉	C₂⁴	1	8	yes	—
156	C₂³×C₈₉	—	2	6	no	—
157	C₂³×C₈₉	—	2	12	no	—
158	C₂³×C₈₉	—	2	12	no	—
159	C₂³×C₈₉	—	2	12	no	—
160	C₂³×C₈₉	—	4	24	no	—
161	C₂³×C₈₉	—	8	16	no	—
162	C₂³×C₈₉	C₂⁵	1	12	yes	—
163	C₂³×C₈₉	C₂⁵	1	2	yes	—
164	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
165	Q₈×C₈₉	—	4	24	no	—
166	Q₈×C₈₉	—	4	12	no	—
167	D₄×C₈₉	—	4	24	no	—
168	D₄×C₈₉	—	4	12	no	—
169	D₄×C₈₉	—	4	24	no	—
170	C₂×C₄×C₈₉	—	2	6	no	—
171	C₂×C₄×C₈₉	—	2	12	no	—
172	C₂×C₄×C₈₉	—	2	6	no	—
173	C₂×C₄×C₈₉	—	2	12	no	—
174	C₂×C₄×C₈₉	—	2	12	no	—
175	C₂×C₄×C₈₉	—	4	24	no	—
176	C₂×C₄×C₈₉	—	4	12	no	—
177	C₂×C₄×C₈₉	—	4	24	no	—
178	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
179	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
180	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
181	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
182	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
183	C₂²×C₈₉	—	2	6	no	—
184	C₂²×C₈₉	—	2	12	no	—
185	C₂²×C₈₉	—	2	12	no	—
186	C₂²×C₈₉	—	2	12	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	—	4	24	no	—
189	C₂²×C₈₉	—	8	16	no	—
190	C₂²×C₈₉	#585	1	6	yes	—
191	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
192	C₄×C₈₉	—	2	6	no	—
193	C₄×C₈₉	—	2	12	no	—
194	C₄×C₈₉	—	2	6	no	—
195	C₄×C₈₉	—	2	12	no	—
196	C₄×C₈₉	—	2	12	no	—
197	C₂×#3568	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂×C₈₉	—	4	2	no	—
199	C₂×C₈₉	—	4	12	no	—
200	C₂×C₈₉	#3568	1	4	yes	direct product factor
201	C₂×C₈₉	C₂×#585	1	3	yes	—
202	#3568	C₂×C₈₉	1	32	yes	direct product factor
203	C₂×#563	C₂×C₈₉	1	3	yes	complemented
204	C₂×H(3,𝔽₄)	C₂×C₈₉	1	1	yes	characteristic, complemented
205	C₂×#556	C₂×C₈₉	1	6	yes	complemented
206	C₂×#551	C₂×C₈₉	1	6	yes	complemented
207	C₂×#542	C₂×C₈₉	1	6	yes	complemented
208	C₂×#538	C₂×C₈₉	1	6	yes	complemented
209	C₂×#529	C₂×C₈₉	1	3	yes	complemented
210	C₈₉	C₂×#3568	1	1	yes	characteristic, direct product factor, Sylow
211	#563	C₂²×C₈₉	1	48	yes	complemented
212	H(3,𝔽₄)	C₂²×C₈₉	1	16	yes	complemented
213	#556	C₂²×C₈₉	1	96	yes	complemented
214	#551	C₂²×C₈₉	1	96	yes	complemented
215	#542	C₂²×C₈₉	1	96	yes	complemented
216	#538	C₂²×C₈₉	1	96	yes	complemented
217	C₂×C₄⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
218	#529	C₂²×C₈₉	1	48	yes	complemented
219	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
220	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
221	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
222	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
223	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
224	C₂×#125	C₂²×C₈₉	1	3	yes	complemented
225	C₂×#124	C₂²×C₈₉	1	3	yes	—
226	C₂×#124	C₂²×C₈₉	1	6	yes	—
227	C₂×#124	C₂²×C₈₉	1	6	yes	—
228	C₂×#124	C₂²×C₈₉	1	6	yes	complemented
229	C₂×#123	C₂²×C₈₉	1	6	yes	—
230	C₂×#123	C₂²×C₈₉	1	6	yes	—
231	C₂×#123	C₂²×C₈₉	1	6	yes	complemented
232	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
233	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
234	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
235	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
236	C₂×#121	C₂²×C₈₉	1	3	yes	—
237	C₂×#121	C₂²×C₈₉	1	6	yes	—
238	C₂×#120	C₂²×C₈₉	1	6	yes	—
239	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
240	C₂×C₄×Q₈	C₂²×C₈₉	1	3	yes	complemented
241	C₂×C₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
242	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
243	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
244	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	complemented
245	C₂×#117	C₂²×C₈₉	1	6	yes	complemented
246	C₂×#117	C₂²×C₈₉	1	6	yes	complemented
247	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	complemented
248	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
249	C₂⁵	C₂³×C₈₉	1	2	yes	—
250	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
251	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
252	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
253	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
254	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
255	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
256	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
257	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
258	C₄⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
259	#126	C₂³×C₈₉	1	48	yes	complemented
260	#126	C₂³×C₈₉	1	48	yes	complemented
261	#126	C₂³×C₈₉	1	48	yes	complemented
262	#126	C₂³×C₈₉	1	16	yes	complemented
263	#126	C₂³×C₈₉	1	48	yes	complemented
264	#125	C₂³×C₈₉	1	24	yes	complemented
265	#124	C₂³×C₈₉	1	24	yes	—
266	#124	C₂³×C₈₉	1	48	yes	—
267	#124	C₂³×C₈₉	1	48	yes	—
268	#124	C₂³×C₈₉	1	48	yes	complemented
269	#123	C₂³×C₈₉	1	48	yes	—
270	#123	C₂³×C₈₉	1	48	yes	—
271	#123	C₂³×C₈₉	1	48	yes	complemented
272	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	complemented
273	C₂²⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
274	C₂²⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
275	C₂²⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
276	#121	C₂³×C₈₉	1	24	yes	—
277	#121	C₂³×C₈₉	1	48	yes	—
278	#120	C₂³×C₈₉	1	48	yes	—
279	#120	C₂³×C₈₉	1	16	yes	complemented
280	C₄×Q₈	C₂³×C₈₉	1	24	yes	complemented
281	C₄×Q₈	C₂³×C₈₉	1	48	yes	complemented
282	C₄×D₄	C₂³×C₈₉	1	24	yes	—
283	C₄×D₄	C₂³×C₈₉	1	48	yes	—
284	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
285	#117	C₂³×C₈₉	1	48	yes	complemented
286	#117	C₂³×C₈₉	1	48	yes	complemented
287	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
288	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
289	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
290	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
291	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
292	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
293	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
294	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₈₉	1	48	yes	complemented
305	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
306	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
307	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
308	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
309	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₈₉	1	8	yes	complemented
311	C₂⁴	—	4	12	no	—
312	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
313	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
314	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
315	C₂×Q₈	—	4	12	no	—
316	C₂×Q₈	—	4	6	no	—
317	C₂×Q₈	C₂⁴×C₈₉	1	24	yes	—
318	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
319	C₂×D₄	—	4	12	no	—
320	C₂×D₄	—	4	6	no	—
321	C₂×D₄	—	4	12	no	—
322	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
323	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
324	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
325	C₂²×C₄	—	4	12	no	—
326	C₂²×C₄	—	4	6	no	—
327	C₂²×C₄	—	4	12	no	—
328	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
329	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
332	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
333	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
334	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
335	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
336	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
337	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
338	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
339	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
340	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
341	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
342	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
343	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
344	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
345	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
346	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
347	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
348	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
349	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
350	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
351	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
352	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
353	C₄²	C₂⁴×C₈₉	1	12	yes	—
354	C₄²	C₂⁴×C₈₉	1	4	yes	—
355	C₄²	C₂⁴×C₈₉	1	24	yes	—
356	C₄²	C₂⁴×C₈₉	1	24	yes	—
357	C₄²	C₂⁴×C₈₉	1	8	yes	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	2	12	no	—
362	C₂³	—	4	24	no	—
363	C₂³	—	8	16	no	—
364	C₂³	C₂⁵×C₈₉	1	12	yes	—
365	C₂³	C₂⁵×C₈₉	1	2	yes	—
366	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
367	Q₈	—	4	24	no	—
368	Q₈	—	4	12	no	—
369	D₄	—	4	24	no	—
370	D₄	—	4	12	no	—
371	D₄	—	4	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	2	12	no	—
377	C₂×C₄	—	4	24	no	—
378	C₂×C₄	—	4	12	no	—
379	C₂×C₄	—	4	24	no	—
380	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
381	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
382	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
383	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
384	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
385	C₂²	—	2	6	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	2	12	no	—
389	C₂²	—	4	24	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	16	no	—
392	C₂²	#585×C₈₉	1	6	yes	—
393	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	2	6	no	—
397	C₄	—	2	12	no	—
398	C₄	—	2	12	no	—
399	C₂	—	4	2	no	—
400	C₂	—	4	12	no	—
401	C₂	C₈₉×#3568	1	4	yes	direct product factor
402	C₂	C₂×#585×C₈₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3568	C₂	direct (N × H)
2. C₂×#563×C₈₉	C₂	semidirect
3. C₂×H(3,𝔽₄)×C₈₉	C₂	semidirect
4. C₂×#556×C₈₉	C₂	semidirect
5. C₂×#551×C₈₉	C₂	semidirect
6. C₂×#542×C₈₉	C₂	semidirect
7. C₂×#538×C₈₉	C₂	semidirect
8. C₂×#529×C₈₉	C₂	semidirect
9. #563×C₈₉	C₂²	semidirect
10. H(3,𝔽₄)×C₈₉	C₂²	semidirect
11. #556×C₈₉	C₂²	semidirect
12. #551×C₈₉	C₂²	semidirect
13. #542×C₈₉	C₂²	semidirect
14. #538×C₈₉	C₂²	semidirect
15. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
16. #529×C₈₉	C₂²	semidirect
17. C₂×#126×C₈₉	C₂²	semidirect
18. C₂×#126×C₈₉	C₂²	semidirect
19. C₂×#126×C₈₉	C₂²	semidirect
20. C₂×#126×C₈₉	C₂²	semidirect
21. C₂×#126×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
26. C₂×#124×C₈₉	C₂²	semidirect
29. C₂×#123×C₈₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
37. C₂×#120×C₈₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
39. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
42. C₂×C₄×D₄×C₈₉	C₂²	semidirect
43. C₂×#117×C₈₉	C₂²	semidirect
44. C₂×#117×C₈₉	C₂²	semidirect
45. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
46. C₂²×C₄²×C₈₉	C₂²	semidirect
56. C₄⋊Q₈×C₈₉	C₂³	semidirect
57. #126×C₈₉	C₂³	semidirect
58. #126×C₈₉	C₂³	semidirect
59. #126×C₈₉	C₂³	semidirect
60. #126×C₈₉	C₂³	semidirect
61. #126×C₈₉	C₂³	semidirect
62. #125×C₈₉	C₂³	semidirect
66. #124×C₈₉	C₂³	semidirect
69. #123×C₈₉	C₂³	semidirect
70. C₂²⋊Q₈×C₈₉	C₂³	semidirect
71. C₂²⋊Q₈×C₈₉	C₂³	semidirect
72. C₂²⋊Q₈×C₈₉	C₂³	semidirect
73. C₂²⋊Q₈×C₈₉	C₂³	semidirect
77. #120×C₈₉	C₂³	semidirect
78. C₄×Q₈×C₈₉	C₂³	semidirect
79. C₄×Q₈×C₈₉	C₂³	semidirect
82. C₄×D₄×C₈₉	C₂³	semidirect
83. #117×C₈₉	C₂³	semidirect
84. #117×C₈₉	C₂³	semidirect
102. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
108. C₂×C₄²×C₈₉	C₂³	semidirect
197. C₂×#3568	C₈₉	direct (N × H)
200. C₂×C₈₉	#3568	direct (N × H)
202. #3568	C₂×C₈₉	direct (N × H)
203. C₂×#563	C₂×C₈₉	semidirect
204. C₂×H(3,𝔽₄)	C₂×C₈₉	semidirect
205. C₂×#556	C₂×C₈₉	semidirect
206. C₂×#551	C₂×C₈₉	semidirect
207. C₂×#542	C₂×C₈₉	semidirect
208. C₂×#538	C₂×C₈₉	semidirect
209. C₂×#529	C₂×C₈₉	semidirect
210. C₈₉	C₂×#3568	direct (N × H)
211. #563	C₂²×C₈₉	semidirect
212. H(3,𝔽₄)	C₂²×C₈₉	semidirect
213. #556	C₂²×C₈₉	semidirect
214. #551	C₂²×C₈₉	semidirect
215. #542	C₂²×C₈₉	semidirect
216. #538	C₂²×C₈₉	semidirect
217. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
218. #529	C₂²×C₈₉	semidirect
219. C₂×#126	C₂²×C₈₉	semidirect
220. C₂×#126	C₂²×C₈₉	semidirect
221. C₂×#126	C₂²×C₈₉	semidirect
222. C₂×#126	C₂²×C₈₉	semidirect
223. C₂×#126	C₂²×C₈₉	semidirect
224. C₂×#125	C₂²×C₈₉	semidirect
228. C₂×#124	C₂²×C₈₉	semidirect
231. C₂×#123	C₂²×C₈₉	semidirect
232. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
233. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
234. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
235. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
239. C₂×#120	C₂²×C₈₉	semidirect
240. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
241. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
244. C₂×C₄×D₄	C₂²×C₈₉	semidirect
245. C₂×#117	C₂²×C₈₉	semidirect
246. C₂×#117	C₂²×C₈₉	semidirect
247. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
248. C₂²×C₄²	C₂²×C₈₉	semidirect
258. C₄⋊Q₈	C₂³×C₈₉	semidirect
259. #126	C₂³×C₈₉	semidirect
260. #126	C₂³×C₈₉	semidirect
261. #126	C₂³×C₈₉	semidirect
262. #126	C₂³×C₈₉	semidirect
263. #126	C₂³×C₈₉	semidirect
264. #125	C₂³×C₈₉	semidirect
268. #124	C₂³×C₈₉	semidirect
271. #123	C₂³×C₈₉	semidirect
272. C₂²⋊Q₈	C₂³×C₈₉	semidirect
273. C₂²⋊Q₈	C₂³×C₈₉	semidirect
274. C₂²⋊Q₈	C₂³×C₈₉	semidirect
275. C₂²⋊Q₈	C₂³×C₈₉	semidirect
279. #120	C₂³×C₈₉	semidirect
280. C₄×Q₈	C₂³×C₈₉	semidirect
281. C₄×Q₈	C₂³×C₈₉	semidirect
284. C₄×D₄	C₂³×C₈₉	semidirect
285. #117	C₂³×C₈₉	semidirect
286. #117	C₂³×C₈₉	semidirect
304. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
310. C₂×C₄²	C₂³×C₈₉	semidirect
401. C₂	C₈₉×#3568	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3568	2
C₂×#563×C₈₉	2
C₂×H(3,𝔽₄)×C₈₉	2
C₂×#556×C₈₉	2
C₂×#551×C₈₉	2
C₂×#542×C₈₉	2
C₂×#538×C₈₉	2
C₂×#529×C₈₉	2
C₂×#3568	89

Subgroups — C2×C89×#3568 #36440584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3568 #36440584