Subgroups — C₈₉×#61436 #36439284

Order 22784.

1960 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3483	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3362	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3341	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3305	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3287	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3169	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3106	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₈₉	C₂	1	3	yes	maximal, complemented
12	C₂×#135×C₈₉	C₂²	1	3	yes	—
13	Q₈²×C₈₉	C₂²	1	2	yes	—
14	#555×C₈₉	—	2	6	no	—
15	#555×C₈₉	C₂²	1	6	yes	—
16	#550×C₈₉	—	2	2	no	—
17	#550×C₈₉	C₂²	1	6	yes	—
18	#550×C₈₉	C₂²	1	2	yes	—
19	#532×C₈₉	—	2	6	no	—
20	#532×C₈₉	C₂²	1	6	yes	—
21	C₄×#41×C₈₉	—	2	2	no	—
22	C₄×#41×C₈₉	C₂²	1	6	yes	—
23	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
24	#500×C₈₉	C₂²	1	3	yes	—
25	#493×C₈₉	C₂²	1	3	yes	—
26	#486×C₈₉	C₂²	1	6	yes	—
27	#482×C₈₉	C₂²	1	12	yes	—
28	#477×C₈₉	C₂²	1	6	yes	—
29	#476×C₈₉	C₂²	1	6	yes	—
30	#466×C₈₉	C₂²	1	6	yes	—
31	#466×C₈₉	C₂²	1	6	yes	—
32	#460×C₈₉	C₂²	1	6	yes	—
33	#459×C₈₉	C₂²	1	6	yes	—
34	#449×C₈₉	C₂²	1	12	yes	—
35	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₈₉	C₂²	1	3	yes	—
38	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×SD₁₆×C₈₉	C₂²	1	6	yes	—
40	C₄×SD₁₆×C₈₉	C₂²	1	6	yes	—
41	C₄×D₈×C₈₉	C₂²	1	3	yes	—
42	C₄×D₈×C₈₉	C₂²	1	6	yes	—
43	C₄×D₈×C₈₉	C₂²	1	3	yes	—
44	C₈×D₄×C₈₉	C₂²	1	3	yes	—
45	C₈×D₄×C₈₉	C₂²	1	3	yes	—
46	#431×C₈₉	C₂²	1	3	yes	—
47	#427×C₈₉	C₂²	1	3	yes	—
48	#416×C₈₉	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
50	C₂×#41×C₈₉	—	2	2	no	—
51	C₂×#41×C₈₉	—	2	6	no	—
52	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
53	C₂×#41×C₈₉	C₂³	1	6	yes	—
54	#135×C₈₉	—	2	12	no	—
55	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
57	C₂×D₈×C₈₉	C₂³	1	3	yes	—
58	C₂×D₈×C₈₉	C₂³	1	6	yes	—
59	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
60	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
61	C₄⋊Q₈×C₈₉	—	2	6	no	—
62	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
63	#127×C₈₉	—	2	6	no	—
64	#127×C₈₉	C₂³	1	6	yes	—
65	#124×C₈₉	—	2	12	no	—
66	#124×C₈₉	—	2	6	no	—
67	#121×C₈₉	—	2	6	no	—
68	#121×C₈₉	—	2	6	no	—
69	#121×C₈₉	—	2	6	no	—
70	#121×C₈₉	—	2	12	no	—
71	#121×C₈₉	C₂³	1	12	yes	—
72	C₄×Q₈×C₈₉	—	2	2	no	—
73	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
75	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
76	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₈₉	—	2	6	no	—
78	C₄×D₄×C₈₉	—	2	6	no	—
79	C₄×D₄×C₈₉	—	2	6	no	—
80	C₄×D₄×C₈₉	—	2	6	no	—
81	C₄×D₄×C₈₉	D₄	1	3	yes	—
82	C₄×D₄×C₈₉	C₂³	1	6	yes	—
83	C₄×D₄×C₈₉	C₂³	1	6	yes	—
84	C₄×D₄×C₈₉	C₂³	1	3	yes	—
85	#117×C₈₉	—	2	6	no	—
86	#117×C₈₉	—	2	6	no	—
87	#117×C₈₉	D₄	1	3	yes	—
88	#117×C₈₉	C₂³	1	6	yes	—
89	C₂×C₄²×C₈₉	—	2	6	no	—
90	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
91	#107×C₈₉	C₂³	1	1	yes	characteristic
92	#107×C₈₉	C₂³	1	3	yes	—
93	#107×C₈₉	C₂³	1	6	yes	—
94	#106×C₈₉	C₂³	1	6	yes	—
95	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
96	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
97	#103×C₈₉	C₂³	1	2	yes	—
98	#103×C₈₉	C₂³	1	6	yes	—
99	#102×C₈₉	C₂³	1	6	yes	—
100	#102×C₈₉	C₂³	1	6	yes	—
101	#102×C₈₉	C₂³	1	12	yes	—
102	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₄×C₈×C₈₉	C₂³	1	3	yes	—
105	C₄×C₈×C₈₉	C₂³	1	3	yes	—
106	C₄×C₈×C₈₉	C₂³	1	3	yes	—
107	#41×C₈₉	—	2	4	no	—
108	#41×C₈₉	—	2	12	no	—
109	#41×C₈₉	—	4	6	no	—
110	#41×C₈₉	—	4	8	no	—
111	#41×C₈₉	—	8	12	no	—
112	C₂×Q₈×C₈₉	—	2	6	no	—
113	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
115	C₂×D₄×C₈₉	—	2	6	no	—
116	C₂×D₄×C₈₉	—	2	12	no	—
117	C₂×D₄×C₈₉	—	2	6	no	—
118	C₂×D₄×C₈₉	—	2	6	no	—
119	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
120	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₈₉	—	2	6	no	—
122	C₂²×C₄×C₈₉	—	2	6	no	—
123	C₂²×C₄×C₈₉	—	2	6	no	—
124	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
125	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
126	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
127	Q₁₆×C₈₉	#41	1	4	yes	complemented
128	SD₁₆×C₈₉	—	2	12	no	—
129	D₈×C₈₉	—	2	6	no	—
130	D₈×C₈₉	—	4	6	no	—
131	C₂×C₈×C₈₉	—	2	6	no	—
132	C₂×C₈×C₈₉	—	4	3	no	—
133	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
135	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
136	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	6	no	—
139	C₄⋊C₄×C₈₉	—	2	6	no	—
140	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
143	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
144	C₂²⋊C₄×C₈₉	—	2	6	no	—
145	C₂²⋊C₄×C₈₉	—	2	12	no	—
146	C₂²⋊C₄×C₈₉	—	2	6	no	—
147	C₂²⋊C₄×C₈₉	—	2	6	no	—
148	C₂²⋊C₄×C₈₉	C₂×D₄	1	6	yes	—
149	C₄²×C₈₉	—	2	6	no	—
150	C₄²×C₈₉	—	2	6	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	C₂×D₄	1	3	yes	—
153	C₄²×C₈₉	C₂×D₄	1	3	yes	—
154	C₄²×C₈₉	C₂⁴	1	3	yes	—
155	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₈₉	—	2	6	no	—
157	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
158	Q₈×C₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	8	6	no	—
160	Q₈×C₈₉	#135	1	4	yes	complemented
161	Q₈×C₈₉	C₂×#41	1	4	yes	—
162	D₄×C₈₉	—	2	6	no	—
163	D₄×C₈₉	—	2	6	no	—
164	D₄×C₈₉	—	2	6	no	—
165	D₄×C₈₉	—	4	12	no	—
166	D₄×C₈₉	—	4	12	no	—
167	D₄×C₈₉	—	8	6	no	—
168	D₄×C₈₉	—	8	12	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	6	no	—
171	C₂×C₄×C₈₉	—	2	6	no	—
172	C₂×C₄×C₈₉	—	2	3	no	—
173	C₂×C₄×C₈₉	—	2	3	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	6	no	—
176	C₂×C₄×C₈₉	—	4	12	no	—
177	C₂×C₄×C₈₉	—	4	12	no	—
178	C₂×C₄×C₈₉	—	4	12	no	—
179	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
182	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
185	C₈×C₈₉	—	2	3	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	3	no	—
188	C₈×C₈₉	C₂×#41	1	2	yes	—
189	C₂²×C₈₉	—	2	3	no	—
190	C₂²×C₈₉	—	2	3	no	—
191	C₂²×C₈₉	—	2	3	no	—
192	C₂²×C₈₉	—	4	6	no	—
193	C₂²×C₈₉	—	4	6	no	—
194	C₂²×C₈₉	—	4	6	no	—
195	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
196	C₄×C₈₉	—	2	3	no	—
197	C₄×C₈₉	—	2	4	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	3	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	6	no	—
202	C₄×C₈₉	C₂×#135	1	6	yes	—
203	C₄×C₈₉	#576	1	2	yes	—
204	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
205	C₄×C₈₉	#585	1	1	yes	characteristic
206	#61436	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	—	4	3	no	—
208	C₂×C₈₉	—	8	6	no	—
209	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
210	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
211	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
212	#3483	C₂×C₈₉	1	2	yes	complemented
213	#3391	C₂×C₈₉	1	1	yes	characteristic, complemented
214	Q₈×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
215	#3362	C₂×C₈₉	1	2	yes	complemented
216	#3341	C₂×C₈₉	1	3	yes	complemented
217	#3305	C₂×C₈₉	1	6	yes	complemented
218	#3287	C₂×C₈₉	1	3	yes	complemented
219	#3169	C₂×C₈₉	1	3	yes	complemented
220	#3106	C₂×C₈₉	1	6	yes	complemented
221	C₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
222	C₄×#135	C₂×C₈₉	1	3	yes	complemented
223	C₈₉	#61436	1	1	yes	characteristic, direct product factor, Sylow
224	C₂×#135	C₂²×C₈₉	1	3	yes	—
225	Q₈²	C₂²×C₈₉	1	2	yes	—
226	#555	—	2	6	no	—
227	#555	C₂²×C₈₉	1	6	yes	—
228	#550	—	2	2	no	—
229	#550	C₂²×C₈₉	1	6	yes	—
230	#550	C₂²×C₈₉	1	2	yes	—
231	#532	—	2	6	no	—
232	#532	C₂²×C₈₉	1	6	yes	—
233	C₄×#41	—	2	2	no	—
234	C₄×#41	C₂²×C₈₉	1	6	yes	—
235	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
236	#500	C₂²×C₈₉	1	3	yes	—
237	#493	C₂²×C₈₉	1	3	yes	—
238	#486	C₂²×C₈₉	1	6	yes	—
239	#482	C₂²×C₈₉	1	12	yes	—
240	#477	C₂²×C₈₉	1	6	yes	—
241	#476	C₂²×C₈₉	1	6	yes	—
242	#466	C₂²×C₈₉	1	6	yes	—
243	#466	C₂²×C₈₉	1	6	yes	—
244	#460	C₂²×C₈₉	1	6	yes	—
245	#459	C₂²×C₈₉	1	6	yes	—
246	#449	C₂²×C₈₉	1	12	yes	—
247	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
248	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
249	C₄×Q₁₆	C₂²×C₈₉	1	3	yes	—
250	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
251	C₄×SD₁₆	C₂²×C₈₉	1	6	yes	—
252	C₄×SD₁₆	C₂²×C₈₉	1	6	yes	—
253	C₄×D₈	C₂²×C₈₉	1	3	yes	—
254	C₄×D₈	C₂²×C₈₉	1	6	yes	—
255	C₄×D₈	C₂²×C₈₉	1	3	yes	—
256	C₈×D₄	C₂²×C₈₉	1	3	yes	—
257	C₈×D₄	C₂²×C₈₉	1	3	yes	—
258	#431	C₂²×C₈₉	1	3	yes	—
259	#427	C₂²×C₈₉	1	3	yes	—
260	#416	C₂²×C₈₉	1	6	yes	—
261	C₂×C₄×C₈	C₂²×C₈₉	1	3	yes	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	6	no	—
264	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
265	C₂×#41	C₂³×C₈₉	1	6	yes	—
266	#135	—	2	12	no	—
267	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
268	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
269	C₂×D₈	C₂³×C₈₉	1	3	yes	—
270	C₂×D₈	C₂³×C₈₉	1	6	yes	—
271	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
272	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
273	C₄⋊Q₈	—	2	6	no	—
274	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
275	#127	—	2	6	no	—
276	#127	C₂³×C₈₉	1	6	yes	—
277	#124	—	2	12	no	—
278	#124	—	2	6	no	—
279	#121	—	2	6	no	—
280	#121	—	2	6	no	—
281	#121	—	2	6	no	—
282	#121	—	2	12	no	—
283	#121	C₂³×C₈₉	1	12	yes	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
286	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
287	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
288	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
289	C₄×D₄	—	2	6	no	—
290	C₄×D₄	—	2	6	no	—
291	C₄×D₄	—	2	6	no	—
292	C₄×D₄	—	2	6	no	—
293	C₄×D₄	D₄×C₈₉	1	3	yes	—
294	C₄×D₄	C₂³×C₈₉	1	6	yes	—
295	C₄×D₄	C₂³×C₈₉	1	6	yes	—
296	C₄×D₄	C₂³×C₈₉	1	3	yes	—
297	#117	—	2	6	no	—
298	#117	—	2	6	no	—
299	#117	D₄×C₈₉	1	3	yes	—
300	#117	C₂³×C₈₉	1	6	yes	—
301	C₂×C₄²	—	2	6	no	—
302	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
303	#107	C₂³×C₈₉	1	1	yes	characteristic
304	#107	C₂³×C₈₉	1	3	yes	—
305	#107	C₂³×C₈₉	1	6	yes	—
306	#106	C₂³×C₈₉	1	6	yes	—
307	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
308	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
309	#103	C₂³×C₈₉	1	2	yes	—
310	#103	C₂³×C₈₉	1	6	yes	—
311	#102	C₂³×C₈₉	1	6	yes	—
312	#102	C₂³×C₈₉	1	6	yes	—
313	#102	C₂³×C₈₉	1	12	yes	—
314	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
315	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₈₉	1	3	yes	—
317	C₄×C₈	C₂³×C₈₉	1	3	yes	—
318	C₄×C₈	C₂³×C₈₉	1	3	yes	—
319	#41	—	2	4	no	—
320	#41	—	2	12	no	—
321	#41	—	4	6	no	—
322	#41	—	4	8	no	—
323	#41	—	8	12	no	—
324	C₂×Q₈	—	2	6	no	—
325	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
327	C₂×D₄	—	2	6	no	—
328	C₂×D₄	—	2	12	no	—
329	C₂×D₄	—	2	6	no	—
330	C₂×D₄	—	2	6	no	—
331	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
332	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
333	C₂²×C₄	—	2	6	no	—
334	C₂²×C₄	—	2	6	no	—
335	C₂²×C₄	—	2	6	no	—
336	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
337	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
338	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
339	Q₁₆	#41×C₈₉	1	4	yes	complemented
340	SD₁₆	—	2	12	no	—
341	D₈	—	2	6	no	—
342	D₈	—	4	6	no	—
343	C₂×C₈	—	2	6	no	—
344	C₂×C₈	—	4	3	no	—
345	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
347	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
348	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	—	2	6	no	—
352	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
353	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
354	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
355	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
356	C₂²⋊C₄	—	2	6	no	—
357	C₂²⋊C₄	—	2	12	no	—
358	C₂²⋊C₄	—	2	6	no	—
359	C₂²⋊C₄	—	2	6	no	—
360	C₂²⋊C₄	C₂×D₄×C₈₉	1	6	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	6	no	—
363	C₄²	—	2	6	no	—
364	C₄²	C₂×D₄×C₈₉	1	3	yes	—
365	C₄²	C₂×D₄×C₈₉	1	3	yes	—
366	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
367	C₄²	C₂⁴×C₈₉	1	3	yes	—
368	C₂³	—	2	6	no	—
369	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
370	Q₈	—	2	2	no	—
371	Q₈	—	8	6	no	—
372	Q₈	#135×C₈₉	1	4	yes	complemented
373	Q₈	C₂×#41×C₈₉	1	4	yes	—
374	D₄	—	2	6	no	—
375	D₄	—	2	6	no	—
376	D₄	—	2	6	no	—
377	D₄	—	4	12	no	—
378	D₄	—	4	12	no	—
379	D₄	—	8	6	no	—
380	D₄	—	8	12	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	3	no	—
385	C₂×C₄	—	2	3	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	4	12	no	—
389	C₂×C₄	—	4	12	no	—
390	C₂×C₄	—	4	12	no	—
391	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
394	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
395	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	3	no	—
400	C₈	C₂×#41×C₈₉	1	2	yes	—
401	C₂²	—	2	3	no	—
402	C₂²	—	2	3	no	—
403	C₂²	—	2	3	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	—	4	6	no	—
407	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	3	no	—
410	C₄	—	2	3	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₂×#135×C₈₉	1	6	yes	—
415	C₄	#576×C₈₉	1	2	yes	—
416	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
417	C₄	#585×C₈₉	1	1	yes	characteristic
418	C₂	—	4	3	no	—
419	C₂	—	8	6	no	—
420	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
421	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
422	C₂	C₂×#576×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3483	C₂	semidirect
2. C₈₉×#3391	C₂	semidirect
3. Q₈×Q₁₆×C₈₉	C₂	semidirect
4. C₈₉×#3362	C₂	semidirect
5. C₈₉×#3341	C₂	semidirect
6. C₈₉×#3305	C₂	semidirect
7. C₈₉×#3287	C₂	semidirect
8. C₈₉×#3169	C₂	semidirect
9. C₈₉×#3106	C₂	semidirect
10. C₈×#41×C₈₉	C₂	semidirect
11. C₄×#135×C₈₉	C₂	semidirect
127. Q₁₆×C₈₉	#41	semidirect
160. Q₈×C₈₉	#135	semidirect
206. #61436	C₈₉	direct (N × H)
212. #3483	C₂×C₈₉	semidirect
213. #3391	C₂×C₈₉	semidirect
214. Q₈×Q₁₆	C₂×C₈₉	semidirect
215. #3362	C₂×C₈₉	semidirect
216. #3341	C₂×C₈₉	semidirect
217. #3305	C₂×C₈₉	semidirect
218. #3287	C₂×C₈₉	semidirect
219. #3169	C₂×C₈₉	semidirect
220. #3106	C₂×C₈₉	semidirect
221. C₈×#41	C₂×C₈₉	semidirect
222. C₄×#135	C₂×C₈₉	semidirect
223. C₈₉	#61436	direct (N × H)
339. Q₁₆	#41×C₈₉	semidirect
372. Q₈	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3483	2
C₈₉×#3391	2
Q₈×Q₁₆×C₈₉	2
C₈₉×#3362	2
C₈₉×#3341	2
C₈₉×#3305	2
C₈₉×#3287	2
C₈₉×#3169	2
C₈₉×#3106	2
C₈×#41×C₈₉	2
C₄×#135×C₈₉	2
#61436	89

Subgroups — C89×#61436 #36439284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61436 #36439284