Subgroups — C₂×C₈₉×#3093 #36438356

Order 22784.

2346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3093	C₂	1	16	yes	maximal, direct product factor
4	C₂×#485×C₈₉	C₂	1	4	yes	maximal, complemented
5	C₂×#482×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₂×#428×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#417×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
12	#525×C₈₉	—	2	4	no	—
13	#525×C₈₉	C₂²	1	8	yes	—
14	C₂×#123×C₈₉	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×#121×C₈₉	C₂²	1	2	yes	—
17	C₂×#120×C₈₉	—	2	1	no	—
18	C₂×C₄×D₄×C₈₉	—	2	2	no	—
19	C₂×#117×C₈₉	—	2	2	no	—
20	C₂×#117×C₈₉	—	2	4	no	—
21	C₂×#117×C₈₉	C₂²	1	4	yes	—
22	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₉	C₂²	1	8	yes	complemented
24	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
26	C₂²×C₄²×C₈₉	—	2	1	no	—
27	#485×C₈₉	C₂²	1	32	yes	complemented
28	#482×C₈₉	C₂²	1	32	yes	complemented
29	#428×C₈₉	C₂²	1	16	yes	complemented
30	C₂×#107×C₈₉	C₂²	1	4	yes	complemented
31	C₂×#106×C₈₉	C₂²	1	4	yes	complemented
32	#417×C₈₉	C₂²	1	16	yes	complemented
33	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#102×C₈₉	C₂²	1	4	yes	complemented
35	#407×C₈₉	C₂²	1	8	yes	complemented
36	C₂×C₂²⋊C₈×C₈₉	C₂²	1	4	yes	—
37	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
38	C₂×#41×C₈₉	—	2	2	no	—
39	C₂×#41×C₈₉	—	2	8	no	—
40	C₂×#41×C₈₉	C₂³	1	4	yes	—
41	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₈₉	—	2	2	no	—
43	C₂²×D₄×C₈₉	—	2	1	no	—
44	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	—	2	8	no	—
46	C₂³×C₄×C₈₉	—	2	2	no	—
47	C₂³×C₄×C₈₉	—	2	1	no	—
48	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₈₉	D₄	1	2	yes	—
50	C₂³×C₄×C₈₉	D₄	1	4	yes	—
51	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₈₉	—	2	8	no	—
55	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
56	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
57	#123×C₈₉	—	2	8	no	—
58	C₂²⋊Q₈×C₈₉	—	2	4	no	—
59	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
60	#121×C₈₉	—	2	4	no	—
61	#121×C₈₉	C₂³	1	8	yes	—
62	#120×C₈₉	—	2	8	no	—
63	C₄×D₄×C₈₉	—	2	16	no	—
64	#117×C₈₉	—	2	8	no	—
65	#117×C₈₉	—	2	16	no	—
66	#117×C₈₉	—	2	2	no	—
67	#117×C₈₉	C₂³	1	4	yes	—
68	#117×C₈₉	C₂³	1	16	yes	—
69	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
80	C₂×C₄²×C₈₉	—	2	4	no	—
81	C₂×C₄²×C₈₉	—	2	8	no	—
82	C₂×C₄²×C₈₉	—	2	1	no	—
83	#107×C₈₉	C₂³	1	16	yes	complemented
84	#106×C₈₉	C₂³	1	16	yes	complemented
85	#103×C₈₉	C₂³	1	16	yes	complemented
86	#102×C₈₉	C₂³	1	16	yes	complemented
87	C₂²⋊C₈×C₈₉	C₂³	1	16	yes	—
88	C₂⁴×C₈₉	—	2	4	no	—
89	C₂⁴×C₈₉	—	2	1	no	—
90	C₂⁴×C₈₉	—	4	4	no	—
91	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
92	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
94	#41×C₈₉	—	2	16	no	—
95	#41×C₈₉	—	4	8	no	—
96	C₂×Q₈×C₈₉	—	2	1	no	—
97	C₂×Q₈×C₈₉	—	2	4	no	—
98	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	4	no	—
101	C₂×D₄×C₈₉	—	2	1	no	—
102	C₂×D₄×C₈₉	—	2	4	no	—
103	C₂×D₄×C₈₉	—	4	8	no	—
104	C₂×D₄×C₈₉	—	4	4	no	—
105	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₈₉	—	2	4	no	—
107	C₂²×C₄×C₈₉	—	2	8	no	—
108	C₂²×C₄×C₈₉	—	2	16	no	—
109	C₂²×C₄×C₈₉	—	2	8	no	—
110	C₂²×C₄×C₈₉	—	2	16	no	—
111	C₂²×C₄×C₈₉	—	2	8	no	—
112	C₂²×C₄×C₈₉	—	2	4	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	2	4	no	—
116	C₂²×C₄×C₈₉	—	4	8	no	—
117	C₂²×C₄×C₈₉	—	4	4	no	—
118	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
120	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	#41	1	8	yes	—
125	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₈₉	—	2	16	no	—
129	C₂×C₈×C₈₉	—	2	8	no	—
130	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
131	C₄⋊C₄×C₈₉	—	2	8	no	—
132	C₄⋊C₄×C₈₉	—	2	4	no	—
133	C₄⋊C₄×C₈₉	—	2	8	no	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
136	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²⋊C₄×C₈₉	—	2	16	no	—
138	C₂²⋊C₄×C₈₉	—	2	4	no	—
139	C₂²⋊C₄×C₈₉	—	2	8	no	—
140	C₂²⋊C₄×C₈₉	—	2	8	no	—
141	C₄²×C₈₉	—	2	16	no	—
142	C₄²×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	2	4	no	—
144	C₂³×C₈₉	—	2	8	no	—
145	C₂³×C₈₉	—	2	4	no	—
146	C₂³×C₈₉	—	2	4	no	—
147	C₂³×C₈₉	—	2	4	no	—
148	C₂³×C₈₉	—	2	2	no	—
149	C₂³×C₈₉	—	4	8	no	—
150	C₂³×C₈₉	—	4	16	no	—
151	C₂³×C₈₉	—	4	2	no	—
152	C₂³×C₈₉	—	4	4	no	—
153	C₂³×C₈₉	#123	1	4	yes	—
154	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
155	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
156	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₈₉	—	2	4	no	—
158	Q₈×C₈₉	—	4	2	no	—
159	D₄×C₈₉	—	2	4	no	—
160	D₄×C₈₉	—	4	16	no	—
161	D₄×C₈₉	—	4	8	no	—
162	D₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	2	8	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	2	16	no	—
166	C₂×C₄×C₈₉	—	2	8	no	—
167	C₂×C₄×C₈₉	—	2	8	no	—
168	C₂×C₄×C₈₉	—	2	8	no	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	4	16	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	8	no	—
174	C₂×C₄×C₈₉	—	4	4	no	—
175	C₂×C₄×C₈₉	—	4	8	no	—
176	C₂×C₄×C₈₉	#123	1	4	yes	—
177	C₂×C₄×C₈₉	#123	1	8	yes	—
178	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
179	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
182	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
183	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
184	C₈×C₈₉	—	2	8	no	—
185	C₂²×C₈₉	—	2	8	no	—
186	C₂²×C₈₉	—	2	4	no	—
187	C₂²×C₈₉	—	2	4	no	—
188	C₂²×C₈₉	—	2	4	no	—
189	C₂²×C₈₉	—	2	4	no	—
190	C₂²×C₈₉	—	4	16	no	—
191	C₂²×C₈₉	—	4	8	no	—
192	C₂²×C₈₉	—	4	2	no	—
193	C₂²×C₈₉	—	4	4	no	—
194	C₂²×C₈₉	—	8	4	no	—
195	C₂²×C₈₉	C₂×#123	1	4	yes	—
196	C₂²×C₈₉	C₂×#123	1	2	yes	—
197	C₂²×C₈₉	#575	1	4	yes	—
198	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
199	C₄×C₈₉	—	2	4	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	8	no	—
202	C₄×C₈₉	—	4	4	no	—
203	C₄×C₈₉	C₂×#123	1	4	yes	—
204	C₄×C₈₉	C₂×#123	1	2	yes	—
205	C₄×C₈₉	C₂²×#41	1	2	yes	—
206	C₂×#3093	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	—	2	4	no	—
208	C₂×C₈₉	—	4	4	no	—
209	C₂×C₈₉	—	8	2	no	—
210	C₂×C₈₉	#3093	1	4	yes	direct product factor
211	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
212	C₂×C₈₉	C₂×#575	1	2	yes	—
213	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
214	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
215	#3093	C₂×C₈₉	1	16	yes	direct product factor
216	C₂×#485	C₂×C₈₉	1	4	yes	complemented
217	C₂×#482	C₂×C₈₉	1	4	yes	complemented
218	C₂×#428	C₂×C₈₉	1	2	yes	complemented
219	C₂×#417	C₂×C₈₉	1	2	yes	complemented
220	C₂×#407	C₂×C₈₉	1	1	yes	characteristic, complemented
221	C₈₉	C₂×#3093	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
223	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
225	#525	—	2	4	no	—
226	#525	C₂²×C₈₉	1	8	yes	—
227	C₂×#123	—	2	1	no	—
228	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
229	C₂×#121	C₂²×C₈₉	1	2	yes	—
230	C₂×#120	—	2	1	no	—
231	C₂×C₄×D₄	—	2	2	no	—
232	C₂×#117	—	2	2	no	—
233	C₂×#117	—	2	4	no	—
234	C₂×#117	C₂²×C₈₉	1	4	yes	—
235	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
236	C₂×#117	C₂²×C₈₉	1	8	yes	complemented
237	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
238	C₂²×C₂²⋊C₄	—	2	1	no	—
239	C₂²×C₄²	—	2	1	no	—
240	#485	C₂²×C₈₉	1	32	yes	complemented
241	#482	C₂²×C₈₉	1	32	yes	complemented
242	#428	C₂²×C₈₉	1	16	yes	complemented
243	C₂×#107	C₂²×C₈₉	1	4	yes	complemented
244	C₂×#106	C₂²×C₈₉	1	4	yes	complemented
245	#417	C₂²×C₈₉	1	16	yes	complemented
246	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
247	C₂×#102	C₂²×C₈₉	1	4	yes	complemented
248	#407	C₂²×C₈₉	1	8	yes	complemented
249	C₂×C₂²⋊C₈	C₂²×C₈₉	1	4	yes	—
250	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	8	no	—
253	C₂×#41	C₂³×C₈₉	1	4	yes	—
254	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
258	C₂³×C₄	—	2	8	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	D₄×C₈₉	1	2	yes	—
262	C₂³×C₄	D₄×C₈₉	1	4	yes	—
263	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
265	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
266	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
267	C₂×M₁₆	—	2	8	no	—
268	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
269	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
270	#123	—	2	8	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
273	#121	—	2	4	no	—
274	#121	C₂³×C₈₉	1	8	yes	—
275	#120	—	2	8	no	—
276	C₄×D₄	—	2	16	no	—
277	#117	—	2	8	no	—
278	#117	—	2	16	no	—
279	#117	—	2	2	no	—
280	#117	C₂³×C₈₉	1	16	yes	—
281	#117	C₂³×C₈₉	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
287	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	—	2	8	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	—	2	1	no	—
296	#107	C₂³×C₈₉	1	16	yes	complemented
297	#106	C₂³×C₈₉	1	16	yes	complemented
298	#103	C₂³×C₈₉	1	16	yes	complemented
299	#102	C₂³×C₈₉	1	16	yes	complemented
300	C₂²⋊C₈	C₂³×C₈₉	1	16	yes	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
305	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
306	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
307	#41	—	2	16	no	—
308	#41	—	4	8	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	4	8	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	16	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
334	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
337	C₂²×C₄	#41×C₈₉	1	8	yes	—
338	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
341	M₁₆	—	2	16	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
349	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	—	2	16	no	—
355	C₄²	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	#123×C₈₉	1	4	yes	—
367	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
368	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
369	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	16	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	#123×C₈₉	1	4	yes	—
390	C₂×C₄	#123×C₈₉	1	8	yes	—
391	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
392	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
395	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
396	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
397	C₈	—	2	8	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	16	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	4	no	—
408	C₂²	C₂×#123×C₈₉	1	4	yes	—
409	C₂²	C₂×#123×C₈₉	1	2	yes	—
410	C₂²	#575×C₈₉	1	4	yes	—
411	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	4	8	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	2	no	—
416	C₄	C₂×#123×C₈₉	1	4	yes	—
417	C₄	C₂×#123×C₈₉	1	2	yes	—
418	C₄	C₂²×#41×C₈₉	1	2	yes	—
419	C₂	—	2	4	no	—
420	C₂	—	4	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₈₉×#3093	1	4	yes	direct product factor
423	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
424	C₂	C₂×#575×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#525×C₈₉	C₂
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
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#3093	C₂	direct (N × H)
4. C₂×#485×C₈₉	C₂	semidirect
5. C₂×#482×C₈₉	C₂	semidirect
6. C₂×#428×C₈₉	C₂	semidirect
7. C₂×#417×C₈₉	C₂	semidirect
8. C₂×#407×C₈₉	C₂	semidirect
23. C₂×#117×C₈₉	C₂²	semidirect
27. #485×C₈₉	C₂²	semidirect
28. #482×C₈₉	C₂²	semidirect
29. #428×C₈₉	C₂²	semidirect
30. C₂×#107×C₈₉	C₂²	semidirect
31. C₂×#106×C₈₉	C₂²	semidirect
32. #417×C₈₉	C₂²	semidirect
33. C₂×#103×C₈₉	C₂²	semidirect
34. C₂×#102×C₈₉	C₂²	semidirect
35. #407×C₈₉	C₂²	semidirect
83. #107×C₈₉	C₂³	semidirect
84. #106×C₈₉	C₂³	semidirect
85. #103×C₈₉	C₂³	semidirect
86. #102×C₈₉	C₂³	semidirect
206. C₂×#3093	C₈₉	direct (N × H)
210. C₂×C₈₉	#3093	direct (N × H)
214. C₂²×#117	C₂×C₈₉	semidirect
215. #3093	C₂×C₈₉	direct (N × H)
216. C₂×#485	C₂×C₈₉	semidirect
217. C₂×#482	C₂×C₈₉	semidirect
218. C₂×#428	C₂×C₈₉	semidirect
219. C₂×#417	C₂×C₈₉	semidirect
220. C₂×#407	C₂×C₈₉	semidirect
221. C₈₉	C₂×#3093	direct (N × H)
236. C₂×#117	C₂²×C₈₉	semidirect
240. #485	C₂²×C₈₉	semidirect
241. #482	C₂²×C₈₉	semidirect
242. #428	C₂²×C₈₉	semidirect
243. C₂×#107	C₂²×C₈₉	semidirect
244. C₂×#106	C₂²×C₈₉	semidirect
245. #417	C₂²×C₈₉	semidirect
246. C₂×#103	C₂²×C₈₉	semidirect
247. C₂×#102	C₂²×C₈₉	semidirect
248. #407	C₂²×C₈₉	semidirect
296. #107	C₂³×C₈₉	semidirect
297. #106	C₂³×C₈₉	semidirect
298. #103	C₂³×C₈₉	semidirect
299. #102	C₂³×C₈₉	semidirect
422. C₂	C₈₉×#3093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#525×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#3093	2
C₂×#485×C₈₉	2
C₂×#482×C₈₉	2
C₂×#428×C₈₉	2
C₂×#417×C₈₉	2
C₂×#407×C₈₉	2
C₂×#3093	89

Subgroups — C2×C89×#3093 #36438356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3093 #36438356