Subgroups — C₄×#428×C₈₉ #36398300

Order 22784.

1218 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₈₉	C₂	1	2	yes	maximal
2	C₂×C₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1776	C₂	1	4	yes	maximal, complemented
6	C₄×#107×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₄×#106×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1736	C₂	1	2	yes	maximal
9	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₈₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₈₉	—	2	1	no	—
14	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
15	#428×C₈₉	C₄	1	16	yes	direct product factor
16	C₂×#107×C₈₉	C₂²	1	4	yes	—
17	C₂×#106×C₈₉	C₂²	1	4	yes	—
18	C₄×M₁₆×C₈₉	C₄	1	8	yes	complemented
19	C₂×#97×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
30	#376×C₈₉	—	2	1	no	—
31	C₂×#95×C₈₉	—	2	1	no	—
32	C₄³×C₈₉	—	2	1	no	—
33	#340×C₈₉	C₂²	1	4	yes	—
34	#340×C₈₉	C₂²	1	4	yes	—
35	C₂³×C₄×C₈₉	—	2	2	no	—
36	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₈₉	—	2	4	no	—
40	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
41	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
42	C₂×M₁₆×C₈₉	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
45	#117×C₈₉	—	2	4	no	—
46	#117×C₈₉	C₂×C₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
54	C₂×C₄²×C₈₉	—	2	2	no	—
55	C₂×C₄²×C₈₉	—	2	2	no	—
56	C₂×C₄²×C₈₉	—	2	2	no	—
57	C₂×C₄²×C₈₉	—	2	1	no	—
58	C₂×C₄²×C₈₉	—	2	1	no	—
59	C₂×C₄²×C₈₉	—	2	2	no	—
60	C₂×C₄²×C₈₉	—	4	4	no	—
61	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	Q₈	1	4	yes	—
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	#107×C₈₉	C₂×C₄	1	16	yes	complemented
68	#106×C₈₉	C₂×C₄	1	16	yes	complemented
69	#97×C₈₉	C₂×C₄	1	8	yes	complemented
70	C₄×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
71	#95×C₈₉	—	2	2	no	—
72	#95×C₈₉	—	2	2	no	—
73	#95×C₈₉	—	2	1	no	—
74	#95×C₈₉	—	2	1	no	—
75	#95×C₈₉	—	2	2	no	—
76	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	—	2	2	no	—
78	C₂²×C₄×C₈₉	—	2	2	no	—
79	C₂²×C₄×C₈₉	—	2	8	no	—
80	C₂²×C₄×C₈₉	—	2	2	no	—
81	C₂²×C₄×C₈₉	—	2	2	no	—
82	C₂²×C₄×C₈₉	—	2	4	no	—
83	C₂²×C₄×C₈₉	—	4	2	no	—
84	C₂²×C₄×C₈₉	—	4	4	no	—
85	C₂²×C₄×C₈₉	—	4	4	no	—
86	C₂²×C₄×C₈₉	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₈₉	C₄⋊C₄	1	4	yes	—
88	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₈₉	#41	1	4	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₈₉	—	2	8	no	—
99	M₁₆×C₈₉	C₄²	1	16	yes	complemented
100	C₂×C₈×C₈₉	—	2	4	no	—
101	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
104	C₄⋊C₄×C₈₉	—	2	8	no	—
105	C₄⋊C₄×C₈₉	—	2	4	no	—
106	C₄⋊C₄×C₈₉	—	2	2	no	—
107	C₄⋊C₄×C₈₉	—	2	2	no	—
108	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
109	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
110	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
111	C₂²⋊C₄×C₈₉	—	2	8	no	—
112	C₄²×C₈₉	—	2	8	no	—
113	C₄²×C₈₉	—	4	4	no	—
114	C₄²×C₈₉	—	4	4	no	—
115	C₄²×C₈₉	—	4	2	no	—
116	C₄²×C₈₉	—	4	4	no	—
117	C₄²×C₈₉	—	4	2	no	—
118	C₄²×C₈₉	C₄⋊C₄	1	4	yes	—
119	C₄²×C₈₉	C₄⋊C₄	1	4	yes	—
120	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
123	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	2	2	no	—
127	C₂³×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₈₉	C₄×D₄	1	4	yes	—
129	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	8	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	8	no	—
138	C₂×C₄×C₈₉	—	4	4	no	—
139	C₂×C₄×C₈₉	—	4	16	no	—
140	C₂×C₄×C₈₉	—	4	4	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	4	no	—
146	C₂×C₄×C₈₉	C₂×C₄²	1	4	yes	—
147	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₈₉	#117	1	4	yes	—
153	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₈₉	C₄×Q₈	1	8	yes	—
155	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₈₉	#137	1	2	yes	—
157	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
159	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
161	C₈×C₈₉	—	2	4	no	—
162	C₈×C₈₉	C₂×C₄²	1	8	yes	complemented
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	4	no	—
166	C₂²×C₈₉	—	2	4	no	—
167	C₂²×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
168	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×C₄×D₄	1	2	yes	—
170	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
172	C₂²×C₈₉	#575	1	2	yes	—
173	C₄×C₈₉	—	2	2	no	—
174	C₄×C₈₉	—	2	2	no	—
175	C₄×C₈₉	—	2	2	no	—
176	C₄×C₈₉	—	4	4	no	—
177	C₄×C₈₉	—	4	8	no	—
178	C₄×C₈₉	—	4	4	no	—
179	C₄×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
180	C₄×C₈₉	#428	1	4	yes	direct product factor
181	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
182	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
183	C₄×C₈₉	C₂×C₄×Q₈	1	2	yes	—
184	C₄×#428	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₈₉	—	2	4	no	—
186	C₂×C₈₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
188	C₂×C₈₉	#2911	1	1	yes	characteristic
189	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₈₉	C₄×#137	1	2	yes	—
191	C₂×#428	C₂×C₈₉	1	2	yes	—
192	C₂×C₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic
193	C₄×#117	C₂×C₈₉	1	1	yes	characteristic
194	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
195	#1776	C₂×C₈₉	1	4	yes	complemented
196	C₄×#107	C₂×C₈₉	1	2	yes	complemented
197	C₄×#106	C₂×C₈₉	1	2	yes	complemented
198	#1736	C₂×C₈₉	1	2	yes	—
199	C₈₉	C₄×#428	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
202	C₂×#117	C₂²×C₈₉	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
204	C₂²×C₄²	—	2	1	no	—
205	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
206	#428	C₄×C₈₉	1	16	yes	direct product factor
207	C₂×#107	C₂²×C₈₉	1	4	yes	—
208	C₂×#106	C₂²×C₈₉	1	4	yes	—
209	C₄×M₁₆	C₄×C₈₉	1	8	yes	complemented
210	C₂×#97	C₂²×C₈₉	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
219	C₄×C₂²⋊C₄	—	2	1	no	—
220	C₄×C₂²⋊C₄	—	2	1	no	—
221	#376	—	2	1	no	—
222	C₂×#95	—	2	1	no	—
223	C₄³	—	2	1	no	—
224	#340	C₂²×C₈₉	1	4	yes	—
225	#340	C₂²×C₈₉	1	4	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
230	C₂×M₁₆	—	2	4	no	—
231	C₂×M₁₆	C₂×C₄×C₈₉	1	4	yes	—
232	C₂×M₁₆	C₂×C₄×C₈₉	1	4	yes	—
233	C₂×M₁₆	C₂×C₄×C₈₉	1	8	yes	—
234	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
235	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
236	#117	—	2	4	no	—
237	#117	C₂×C₄×C₈₉	1	8	yes	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	8	yes	—
241	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
242	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	4	4	no	—
252	C₂×C₄²	C₂×C₄×C₈₉	1	4	yes	—
253	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
255	C₂×C₄²	Q₈×C₈₉	1	4	yes	—
256	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
258	#107	C₂×C₄×C₈₉	1	16	yes	complemented
259	#106	C₂×C₄×C₈₉	1	16	yes	complemented
260	#97	C₂×C₄×C₈₉	1	8	yes	complemented
261	C₄×C₈	C₂×C₄×C₈₉	1	8	yes	complemented
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	2	no	—
267	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₄⋊C₄×C₈₉	1	4	yes	—
278	C₂²×C₄	C₄⋊C₄×C₈₉	1	4	yes	—
279	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
281	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
287	C₂²×C₄	#41×C₈₉	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
289	M₁₆	—	2	8	no	—
290	M₁₆	C₄²×C₈₉	1	16	yes	complemented
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
293	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
294	C₂×C₈	C₂²×C₄×C₈₉	1	8	yes	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
300	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
301	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
302	C₂²⋊C₄	—	2	8	no	—
303	C₄²	—	2	8	no	—
304	C₄²	—	4	4	no	—
305	C₄²	—	4	4	no	—
306	C₄²	—	4	4	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	C₄⋊C₄×C₈₉	1	4	yes	—
310	C₄²	C₄⋊C₄×C₈₉	1	4	yes	—
311	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
312	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
313	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
314	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	2	no	—
318	C₂³	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
319	C₂³	C₄×D₄×C₈₉	1	4	yes	—
320	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	C₂×C₄²×C₈₉	1	4	yes	—
338	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
339	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
340	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
341	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
342	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
343	C₂×C₄	#117×C₈₉	1	4	yes	—
344	C₂×C₄	C₄×D₄×C₈₉	1	4	yes	—
345	C₂×C₄	C₄×Q₈×C₈₉	1	8	yes	—
346	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
347	C₂×C₄	#137×C₈₉	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
350	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
352	C₈	—	2	4	no	—
353	C₈	C₂×C₄²×C₈₉	1	8	yes	complemented
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	C₄×C₄⋊C₄×C₈₉	1	4	yes	—
359	C₂²	C₂²×C₄⋊C₄×C₈₉	1	1	yes	characteristic
360	C₂²	C₂×C₄×D₄×C₈₉	1	2	yes	—
361	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
362	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
363	C₂²	#575×C₈₉	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	8	no	—
368	C₄	—	4	4	no	—
369	C₄	—	4	4	no	—
370	C₄	C₄×C₄⋊C₄×C₈₉	1	4	yes	—
371	C₄	#428×C₈₉	1	4	yes	direct product factor
372	C₄	C₂²×C₄²×C₈₉	1	1	yes	characteristic
373	C₄	C₂×#117×C₈₉	1	1	yes	characteristic
374	C₄	C₂×C₄×Q₈×C₈₉	1	2	yes	—
375	C₂	—	2	4	no	—
376	C₂	C₂×C₄×C₄⋊C₄×C₈₉	1	1	yes	characteristic
377	C₂	C₂×#428×C₈₉	1	1	yes	characteristic
378	C₂	C₈₉×#2911	1	1	yes	characteristic
379	C₂	C₄×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
380	C₂	C₄×#137×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator	C₄	C₂²×C₄²×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈₉×#1776	C₂	semidirect
6. C₄×#107×C₈₉	C₂	semidirect
7. C₄×#106×C₈₉	C₂	semidirect
15. #428×C₈₉	C₄	direct (N × H)
18. C₄×M₁₆×C₈₉	C₄	semidirect
67. #107×C₈₉	C₂×C₄	semidirect
68. #106×C₈₉	C₂×C₄	semidirect
69. #97×C₈₉	C₂×C₄	semidirect
70. C₄×C₈×C₈₉	C₂×C₄	semidirect
99. M₁₆×C₈₉	C₄²	semidirect
162. C₈×C₈₉	C₂×C₄²	semidirect
180. C₄×C₈₉	#428	direct (N × H)
184. C₄×#428	C₈₉	direct (N × H)
195. #1776	C₂×C₈₉	semidirect
196. C₄×#107	C₂×C₈₉	semidirect
197. C₄×#106	C₂×C₈₉	semidirect
199. C₈₉	C₄×#428	direct (N × H)
206. #428	C₄×C₈₉	direct (N × H)
209. C₄×M₁₆	C₄×C₈₉	semidirect
258. #107	C₂×C₄×C₈₉	semidirect
259. #106	C₂×C₄×C₈₉	semidirect
260. #97	C₂×C₄×C₈₉	semidirect
261. C₄×C₈	C₂×C₄×C₈₉	semidirect
290. M₁₆	C₄²×C₈₉	semidirect
353. C₈	C₂×C₄²×C₈₉	semidirect
371. C₄	#428×C₈₉	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×#428×C₈₉	2
C₂×C₄×M₁₆×C₈₉	2
C₄×#117×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₈₉×#1776	2
C₄×#107×C₈₉	2
C₄×#106×C₈₉	2
C₈₉×#1736	2
C₄×#428	89

Subgroups — C4×#428×C89 #36398300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#428×C₈₉ #36398300