Subgroups — C₈₉×#25588 #36403436

Order 22784.

1448 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2867	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2002	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1887	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
11	#559×C₈₉	—	2	2	no	—
12	#550×C₈₉	—	2	2	no	—
13	#546×C₈₉	—	2	4	no	—
14	#540×C₈₉	—	2	2	no	—
15	#535×C₈₉	C₂²	1	2	yes	—
16	#533×C₈₉	C₂²	1	1	yes	characteristic
17	#532×C₈₉	—	2	2	no	—
18	C₂×#127×C₈₉	—	2	4	no	—
19	C₂×#127×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
22	#518×C₈₉	C₂²	1	2	yes	—
23	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
24	#490×C₈₉	—	2	2	no	—
25	#486×C₈₉	—	2	2	no	—
26	#460×C₈₉	—	2	2	no	—
27	#459×C₈₉	—	2	2	no	—
28	#423×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#104×C₈₉	C₂²	1	2	yes	—
30	#418×C₈₉	C₂²	1	4	yes	—
31	#418×C₈₉	C₂²	1	2	yes	—
32	C₂×#100×C₈₉	C₂²	1	4	yes	—
33	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
34	C₄³×C₈₉	C₂²	1	1	yes	characteristic
35	#339×C₈₉	C₂²	1	2	yes	—
36	#339×C₈₉	C₂²	1	4	yes	—
37	C₂×#41×C₈₉	—	2	4	no	—
38	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₈₉	—	2	8	no	—
40	C₂²×D₄×C₈₉	—	2	2	no	—
41	C₂²×D₄×C₈₉	D₄	1	4	yes	—
42	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
43	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
44	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
45	C₂×SD₁₆×C₈₉	—	2	2	no	—
46	C₂×D₈×C₈₉	—	2	2	no	—
47	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
48	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₈₉	D₄	1	2	yes	complemented
50	#127×C₈₉	—	2	2	no	—
51	#127×C₈₉	—	2	1	no	—
52	#127×C₈₉	—	2	1	no	—
53	#127×C₈₉	—	2	2	no	—
54	#127×C₈₉	—	2	2	no	—
55	#127×C₈₉	—	2	1	no	—
56	#127×C₈₉	—	2	1	no	—
57	#127×C₈₉	—	2	8	no	—
58	#127×C₈₉	—	4	4	no	—
59	#127×C₈₉	—	4	16	no	—
60	#125×C₈₉	D₄	1	2	yes	complemented
61	#124×C₈₉	—	2	4	no	—
62	#124×C₈₉	—	2	2	no	—
63	#123×C₈₉	—	2	8	no	—
64	C₂²⋊Q₈×C₈₉	—	2	2	no	—
65	#121×C₈₉	—	2	4	no	—
66	#121×C₈₉	—	2	8	no	—
67	#121×C₈₉	—	2	4	no	—
68	#120×C₈₉	—	2	4	no	—
69	C₄×Q₈×C₈₉	—	2	2	no	—
70	C₄×Q₈×C₈₉	D₄	1	2	yes	complemented
71	C₄×D₄×C₈₉	—	2	4	no	—
72	C₄×D₄×C₈₉	—	2	2	no	—
73	C₄×D₄×C₈₉	—	2	4	no	—
74	C₄×D₄×C₈₉	—	2	4	no	—
75	C₄×D₄×C₈₉	D₄	1	2	yes	complemented
76	#117×C₈₉	—	2	1	no	—
77	#117×C₈₉	C₂³	1	1	yes	characteristic
78	#117×C₈₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
80	C₂×C₄²×C₈₉	—	2	2	no	—
81	C₂×C₄²×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₈₉	—	2	2	no	—
85	#104×C₈₉	—	2	4	no	—
86	#102×C₈₉	—	2	4	no	—
87	#102×C₈₉	—	2	8	no	—
88	#100×C₈₉	—	4	4	no	—
89	#97×C₈₉	—	2	1	no	—
90	C₄×C₈×C₈₉	—	2	1	no	—
91	C₂⁴×C₈₉	—	2	2	no	—
92	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
93	#41×C₈₉	—	2	2	no	—
94	#41×C₈₉	—	2	2	no	—
95	#41×C₈₉	—	8	8	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₈₉	—	2	1	no	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	4	no	—
101	C₂×D₄×C₈₉	—	2	4	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	2	2	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	4	no	—
107	C₂×D₄×C₈₉	—	2	4	no	—
108	C₂×D₄×C₈₉	—	2	4	no	—
109	C₂×D₄×C₈₉	—	2	4	no	—
110	C₂×D₄×C₈₉	—	4	8	no	—
111	C₂×D₄×C₈₉	—	4	16	no	—
112	C₂×D₄×C₈₉	—	4	32	no	—
113	C₂×D₄×C₈₉	—	4	8	no	—
114	C₂×D₄×C₈₉	—	4	2	no	—
115	C₂×D₄×C₈₉	—	4	2	no	—
116	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	2	8	no	—
119	C₂²×C₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
123	SD₁₆×C₈₉	—	4	4	no	—
124	D₈×C₈₉	—	4	4	no	—
125	M₁₆×C₈₉	—	2	2	no	—
126	M₁₆×C₈₉	—	2	2	no	—
127	M₁₆×C₈₉	—	2	4	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	2	2	no	—
132	C₄⋊C₄×C₈₉	—	2	4	no	—
133	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
135	C₂²⋊C₄×C₈₉	—	2	8	no	—
136	C₂²⋊C₄×C₈₉	—	2	8	no	—
137	C₂²⋊C₄×C₈₉	—	2	1	no	—
138	C₂²⋊C₄×C₈₉	—	2	2	no	—
139	C₂²⋊C₄×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	—	2	8	no	—
141	C₄²×C₈₉	—	2	2	no	—
142	C₄²×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₈₉	C₂×D₄	1	2	yes	—
148	C₄²×C₈₉	#41	1	4	yes	complemented
149	C₂³×C₈₉	—	2	4	no	—
150	C₂³×C₈₉	—	2	1	no	—
151	C₂³×C₈₉	—	2	8	no	—
152	C₂³×C₈₉	—	4	8	no	—
153	C₂³×C₈₉	—	4	8	no	—
154	C₂³×C₈₉	—	4	2	no	—
155	C₂³×C₈₉	—	4	4	no	—
156	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₈₉	—	2	1	no	—
158	Q₈×C₈₉	—	2	1	no	—
159	Q₈×C₈₉	—	4	4	no	—
160	D₄×C₈₉	—	2	1	no	—
161	D₄×C₈₉	—	2	1	no	—
162	D₄×C₈₉	—	4	2	no	—
163	D₄×C₈₉	—	4	2	no	—
164	D₄×C₈₉	—	4	2	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	—	4	4	no	—
168	D₄×C₈₉	—	4	4	no	—
169	D₄×C₈₉	—	4	8	no	—
170	D₄×C₈₉	—	8	4	no	—
171	D₄×C₈₉	—	8	32	no	—
172	D₄×C₈₉	—	8	4	no	—
173	D₄×C₈₉	—	8	8	no	—
174	D₄×C₈₉	—	8	4	no	—
175	C₂×C₄×C₈₉	—	2	8	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	4	no	—
183	C₂×C₄×C₈₉	—	8	8	no	—
184	C₂×C₄×C₈₉	#120	1	2	yes	—
185	C₂×C₄×C₈₉	#120	1	2	yes	—
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
189	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
190	C₈×C₈₉	—	4	2	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₂²×C₈₉	—	2	2	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	4	no	—
195	C₂²×C₈₉	—	4	2	no	—
196	C₂²×C₈₉	—	4	8	no	—
197	C₂²×C₈₉	—	8	8	no	—
198	C₂²×C₈₉	—	8	8	no	—
199	C₂²×C₈₉	—	8	2	no	—
200	C₂²×C₈₉	—	8	4	no	—
201	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
202	C₂²×C₈₉	#546	1	2	yes	—
203	C₄×C₈₉	—	2	8	no	—
204	C₄×C₈₉	—	2	2	no	—
205	C₄×C₈₉	—	4	1	no	—
206	C₄×C₈₉	—	4	2	no	—
207	C₄×C₈₉	—	4	4	no	—
208	C₄×C₈₉	#453	1	4	yes	—
209	C₄×C₈₉	#532	1	1	yes	characteristic
210	C₄×C₈₉	#535	1	1	yes	characteristic
211	C₄×C₈₉	#550	1	2	yes	—
212	#25588	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂×C₈₉	—	2	2	no	—
214	C₂×C₈₉	—	8	1	no	—
215	C₂×C₈₉	—	8	4	no	—
216	C₂×C₈₉	—	16	2	no	—
217	C₂×C₈₉	#2431	1	1	yes	characteristic
218	C₂×C₈₉	C₂×#453	1	2	yes	—
219	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
220	#3138	C₂×C₈₉	1	1	yes	characteristic, complemented
221	#3038	C₂×C₈₉	1	1	yes	characteristic, complemented
222	#2867	C₂×C₈₉	1	1	yes	characteristic, complemented
223	#2002	C₂×C₈₉	1	4	yes	complemented
224	#1994	C₂×C₈₉	1	1	yes	characteristic, complemented
225	#1965	C₂×C₈₉	1	1	yes	characteristic, complemented
226	#1887	C₂×C₈₉	1	4	yes	complemented
227	C₄×#104	C₂×C₈₉	1	1	yes	characteristic, complemented
228	C₈₉	#25588	1	1	yes	characteristic, direct product factor, Sylow
229	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
230	#559	—	2	2	no	—
231	#550	—	2	2	no	—
232	#546	—	2	4	no	—
233	#540	—	2	2	no	—
234	#535	C₂²×C₈₉	1	2	yes	—
235	#533	C₂²×C₈₉	1	1	yes	characteristic
236	#532	—	2	2	no	—
237	C₂×#127	—	2	4	no	—
238	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
239	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
240	C₂×#127	C₂²×C₈₉	1	4	yes	—
241	#518	C₂²×C₈₉	1	2	yes	—
242	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
243	#490	—	2	2	no	—
244	#486	—	2	2	no	—
245	#460	—	2	2	no	—
246	#459	—	2	2	no	—
247	#423	C₂²×C₈₉	1	1	yes	characteristic
248	C₂×#104	C₂²×C₈₉	1	2	yes	—
249	#418	C₂²×C₈₉	1	4	yes	—
250	#418	C₂²×C₈₉	1	2	yes	—
251	C₂×#100	C₂²×C₈₉	1	4	yes	—
252	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
253	C₄³	C₂²×C₈₉	1	1	yes	characteristic
254	#339	C₂²×C₈₉	1	2	yes	—
255	#339	C₂²×C₈₉	1	4	yes	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
258	C₂²×D₄	—	2	8	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	D₄×C₈₉	1	4	yes	—
261	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
262	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
263	AGL(1,ℤ/8)	—	4	4	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
267	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
268	C₄⋊Q₈	D₄×C₈₉	1	2	yes	complemented
269	#127	—	2	2	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	2	no	—
273	#127	—	2	2	no	—
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	8	no	—
277	#127	—	4	4	no	—
278	#127	—	4	16	no	—
279	#125	D₄×C₈₉	1	2	yes	complemented
280	#124	—	2	4	no	—
281	#124	—	2	2	no	—
282	#123	—	2	8	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	#121	—	2	4	no	—
285	#121	—	2	8	no	—
286	#121	—	2	4	no	—
287	#120	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	D₄×C₈₉	1	2	yes	complemented
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	D₄×C₈₉	1	2	yes	complemented
295	#117	—	2	1	no	—
296	#117	C₂³×C₈₉	1	1	yes	characteristic
297	#117	C₂³×C₈₉	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
302	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
303	C₄⋊C₈	—	2	2	no	—
304	#104	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	8	no	—
307	#100	—	4	4	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	8	8	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	—	4	16	no	—
331	C₂×D₄	—	4	32	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
342	SD₁₆	—	4	4	no	—
343	D₈	—	4	4	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
353	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₄²	—	2	8	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
365	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₈₉	1	2	yes	—
367	C₄²	#41×C₈₉	1	4	yes	complemented
368	C₂³	—	2	4	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	4	no	—
375	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	2	1	no	—
378	Q₈	—	4	4	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	8	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	8	4	no	—
390	D₄	—	8	32	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	8	no	—
393	D₄	—	8	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	#120×C₈₉	1	2	yes	—
404	C₂×C₄	#120×C₈₉	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
408	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	8	8	no	—
417	C₂²	—	8	8	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	4	no	—
420	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
421	C₂²	#546×C₈₉	1	2	yes	—
422	C₄	—	2	8	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	#453×C₈₉	1	4	yes	—
428	C₄	#532×C₈₉	1	1	yes	characteristic
429	C₄	#535×C₈₉	1	1	yes	characteristic
430	C₄	#550×C₈₉	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	8	4	no	—
434	C₂	—	16	2	no	—
435	C₂	C₈₉×#2431	1	1	yes	characteristic
436	C₂	C₂×#453×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3508	C₂	semidirect
2. C₈₉×#3138	C₂	semidirect
3. C₈₉×#3038	C₂	semidirect
4. C₈₉×#2867	C₂	semidirect
5. C₈₉×#2002	C₂	semidirect
6. C₈₉×#1994	C₂	semidirect
7. C₈₉×#1965	C₂	semidirect
8. C₈₉×#1887	C₂	semidirect
9. C₄×#104×C₈₉	C₂	semidirect
49. C₄⋊Q₈×C₈₉	D₄	semidirect
60. #125×C₈₉	D₄	semidirect
70. C₄×Q₈×C₈₉	D₄	semidirect
75. C₄×D₄×C₈₉	D₄	semidirect
148. C₄²×C₈₉	#41	semidirect
212. #25588	C₈₉	direct (N × H)
219. #3508	C₂×C₈₉	semidirect
220. #3138	C₂×C₈₉	semidirect
221. #3038	C₂×C₈₉	semidirect
222. #2867	C₂×C₈₉	semidirect
223. #2002	C₂×C₈₉	semidirect
224. #1994	C₂×C₈₉	semidirect
225. #1965	C₂×C₈₉	semidirect
226. #1887	C₂×C₈₉	semidirect
227. C₄×#104	C₂×C₈₉	semidirect
228. C₈₉	#25588	direct (N × H)
268. C₄⋊Q₈	D₄×C₈₉	semidirect
279. #125	D₄×C₈₉	semidirect
289. C₄×Q₈	D₄×C₈₉	semidirect
294. C₄×D₄	D₄×C₈₉	semidirect
367. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3138	2
C₈₉×#3038	2
C₈₉×#2867	2
C₈₉×#2002	2
C₈₉×#1994	2
C₈₉×#1965	2
C₈₉×#1887	2
C₄×#104×C₈₉	2
#25588	89

Subgroups — C89×#25588 #36403436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25588 #36403436