Subgroups — C₄×#550×C₈₉ #36412008

Order 22784.

3420 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2366	C₂	1	3	yes	maximal, complemented
4	C₈₉×#2363	C₂	1	6	yes	maximal, complemented
5	C₈₉×#2354	C₂	1	3	yes	maximal, complemented
6	Q₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2341	C₂	1	2	yes	maximal, complemented
8	C₄×#127×C₈₉	C₂	1	3	yes	maximal, complemented
9	C₄×#121×C₈₉	C₂	1	6	yes	maximal, complemented
10	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₈₉	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₈₉	C₂²	1	2	yes	—
13	#550×C₈₉	C₄	1	16	yes	direct product factor
14	C₂×#127×C₈₉	C₂²	1	3	yes	—
15	C₂×#121×C₈₉	C₂²	1	6	yes	—
16	C₄×#41×C₈₉	—	2	16	no	—
17	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
24	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
27	C₂×#117×C₈₉	C₂²	1	6	yes	—
28	C₂²×C₄²×C₈₉	C₂²	1	6	yes	—
29	#390×C₈₉	C₂²	1	6	yes	—
30	#390×C₈₉	C₂²	1	6	yes	—
31	#390×C₈₉	C₂²	1	6	yes	—
32	#390×C₈₉	C₂²	1	6	yes	—
33	#389×C₈₉	C₂²	1	6	yes	—
34	#388×C₈₉	C₂²	1	12	yes	—
35	#386×C₈₉	C₂²	1	12	yes	—
36	#384×C₈₉	C₂²	1	3	yes	—
37	#380×C₈₉	C₂²	1	6	yes	—
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
41	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
42	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
43	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
45	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
46	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
47	C₄³×C₈₉	C₂²	1	3	yes	—
48	C₂×#41×C₈₉	—	2	8	no	—
49	C₂×#41×C₈₉	—	2	8	no	—
50	C₂×#41×C₈₉	C₂×C₄	1	16	yes	complemented
51	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
53	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
54	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
58	#127×C₈₉	C₂×C₄	1	24	yes	complemented
59	#121×C₈₉	C₂×C₄	1	48	yes	complemented
60	C₄×Q₈×C₈₉	—	2	8	no	—
61	C₄×Q₈×C₈₉	—	2	4	no	—
62	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
63	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
64	C₄×D₄×C₈₉	—	2	24	no	—
65	C₄×D₄×C₈₉	—	2	12	no	—
66	C₄×D₄×C₈₉	—	2	24	no	—
67	C₄×D₄×C₈₉	—	2	12	no	—
68	C₄×D₄×C₈₉	—	4	12	no	—
69	C₄×D₄×C₈₉	C₂×C₄	1	24	yes	complemented
70	#117×C₈₉	—	2	24	no	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
82	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
83	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
84	C₂×C₄²×C₈₉	—	2	24	no	—
85	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
86	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
87	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
88	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
92	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
93	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	#95×C₈₉	C₂³	1	2	yes	—
96	#95×C₈₉	C₂³	1	6	yes	—
97	#95×C₈₉	C₂³	1	6	yes	—
98	#95×C₈₉	C₂³	1	6	yes	—
99	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
100	#41×C₈₉	—	2	64	no	—
101	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
102	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₈₉	#41	1	4	yes	—
104	C₂×D₄×C₈₉	—	2	12	no	—
105	C₂×D₄×C₈₉	—	2	6	no	—
106	C₂×D₄×C₈₉	—	2	6	no	—
107	C₂×D₄×C₈₉	—	2	12	no	—
108	C₂×D₄×C₈₉	—	4	6	no	—
109	C₂×D₄×C₈₉	—	4	6	no	—
110	C₂×D₄×C₈₉	C₂²×C₄	1	12	yes	—
111	C₂×D₄×C₈₉	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₈₉	C₂²×C₄	1	24	yes	—
113	C₂²×C₄×C₈₉	—	2	12	no	—
114	C₂²×C₄×C₈₉	—	2	12	no	—
115	C₂²×C₄×C₈₉	—	2	12	no	—
116	C₂²×C₄×C₈₉	—	2	12	no	—
117	C₂²×C₄×C₈₉	—	2	12	no	—
118	C₂²×C₄×C₈₉	—	2	12	no	—
119	C₂²×C₄×C₈₉	—	2	12	no	—
120	C₂²×C₄×C₈₉	—	4	6	no	—
121	C₂²×C₄×C₈₉	C₂²×C₄	1	24	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₈₉	—	2	12	no	—
133	C₄⋊C₄×C₈₉	—	2	6	no	—
134	C₄⋊C₄×C₈₉	—	2	6	no	—
135	C₄⋊C₄×C₈₉	—	4	6	no	—
136	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
137	C₄⋊C₄×C₈₉	C₂²×C₄	1	12	yes	—
138	C₄⋊C₄×C₈₉	C₂×D₄	1	12	yes	—
139	C₄⋊C₄×C₈₉	#41	1	4	yes	complemented
140	C₂²⋊C₄×C₈₉	—	2	24	no	—
141	C₂²⋊C₄×C₈₉	—	2	12	no	—
142	C₂²⋊C₄×C₈₉	—	2	12	no	—
143	C₂²⋊C₄×C₈₉	—	4	12	no	—
144	C₂²⋊C₄×C₈₉	C₂²×C₄	1	24	yes	—
145	C₄²×C₈₉	—	2	4	no	—
146	C₄²×C₈₉	—	2	12	no	—
147	C₄²×C₈₉	—	2	12	no	—
148	C₄²×C₈₉	—	2	6	no	—
149	C₄²×C₈₉	—	2	6	no	—
150	C₄²×C₈₉	—	2	6	no	—
151	C₄²×C₈₉	—	4	3	no	—
152	C₄²×C₈₉	C₂²×C₄	1	12	yes	—
153	C₄²×C₈₉	C₂×D₄	1	12	yes	—
154	C₄²×C₈₉	#41	1	4	yes	complemented
155	C₂³×C₈₉	—	2	6	no	—
156	C₂³×C₈₉	—	2	6	no	—
157	C₂³×C₈₉	—	2	6	no	—
158	C₂³×C₈₉	—	2	6	no	—
159	C₂³×C₈₉	—	2	6	no	—
160	C₂³×C₈₉	—	2	6	no	—
161	C₂³×C₈₉	C₂³×C₄	1	12	yes	—
162	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
163	Q₈×C₈₉	C₄×D₄	1	16	yes	complemented
164	D₄×C₈₉	—	2	48	no	—
165	D₄×C₈₉	—	2	24	no	—
166	D₄×C₈₉	—	4	24	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	3	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	3	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	3	no	—
175	C₂×C₄×C₈₉	—	2	3	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	48	no	—
178	C₂×C₄×C₈₉	—	2	6	no	—
179	C₂×C₄×C₈₉	—	2	3	no	—
180	C₂×C₄×C₈₉	—	2	3	no	—
181	C₂×C₄×C₈₉	—	2	6	no	—
182	C₂×C₄×C₈₉	—	2	3	no	—
183	C₂×C₄×C₈₉	—	2	6	no	—
184	C₂×C₄×C₈₉	—	4	24	no	—
185	C₂×C₄×C₈₉	—	4	24	no	—
186	C₂×C₄×C₈₉	C₂³×C₄	1	6	yes	—
187	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₈₉	C₂³×C₄	1	6	yes	—
189	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
191	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
192	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
194	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
195	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
196	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
197	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
198	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
199	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
200	C₂²×C₈₉	—	2	12	no	—
201	C₂²×C₈₉	—	2	12	no	—
202	C₂²×C₈₉	—	2	12	no	—
203	C₂²×C₈₉	—	4	6	no	—
204	C₂²×C₈₉	—	4	6	no	—
205	C₂²×C₈₉	—	4	6	no	—
206	C₂²×C₈₉	—	4	6	no	—
207	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
208	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
209	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
210	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
211	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
212	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×C₈₉	#585	1	1	yes	characteristic
214	C₄×C₈₉	—	2	4	no	—
215	C₄×C₈₉	—	2	6	no	—
216	C₄×C₈₉	—	2	4	no	—
217	C₄×C₈₉	—	2	6	no	—
218	C₄×C₈₉	—	2	2	no	—
219	C₄×C₈₉	—	4	6	no	—
220	C₄×C₈₉	—	4	3	no	—
221	C₄×C₈₉	C₂×C₄×D₄	1	12	yes	—
222	C₄×C₈₉	C₄×#41	1	4	yes	complemented
223	C₄×C₈₉	#550	1	4	yes	direct product factor
224	C₄×#550	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₈₉	—	4	12	no	—
226	C₂×C₈₉	C₂²×C₄×D₄	1	1	yes	characteristic
227	C₂×C₈₉	C₂×C₄×#41	1	1	yes	characteristic
228	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
230	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
231	C₂×C₈₉	#3480	1	1	yes	characteristic
232	C₂×C₈₉	#3483	1	1	yes	characteristic
233	C₂×#550	C₂×C₈₉	1	1	yes	characteristic
234	C₂×C₄×#41	C₂×C₈₉	1	2	yes	complemented
235	#2366	C₂×C₈₉	1	3	yes	complemented
236	#2363	C₂×C₈₉	1	6	yes	complemented
237	#2354	C₂×C₈₉	1	3	yes	complemented
238	Q₈×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
239	#2341	C₂×C₈₉	1	2	yes	complemented
240	C₄×#127	C₂×C₈₉	1	3	yes	complemented
241	C₄×#121	C₂×C₈₉	1	6	yes	complemented
242	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
243	C₄²×D₄	C₂×C₈₉	1	3	yes	complemented
244	C₈₉	C₄×#550	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×#41	C₂²×C₈₉	1	2	yes	—
246	#550	C₄×C₈₉	1	16	yes	direct product factor
247	C₂×#127	C₂²×C₈₉	1	3	yes	—
248	C₂×#121	C₂²×C₈₉	1	6	yes	—
249	C₄×#41	—	2	16	no	—
250	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
255	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
256	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
257	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
258	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
259	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
260	C₂×#117	C₂²×C₈₉	1	6	yes	—
261	C₂²×C₄²	C₂²×C₈₉	1	6	yes	—
262	#390	C₂²×C₈₉	1	6	yes	—
263	#390	C₂²×C₈₉	1	6	yes	—
264	#390	C₂²×C₈₉	1	6	yes	—
265	#390	C₂²×C₈₉	1	6	yes	—
266	#389	C₂²×C₈₉	1	6	yes	—
267	#388	C₂²×C₈₉	1	12	yes	—
268	#386	C₂²×C₈₉	1	12	yes	—
269	#384	C₂²×C₈₉	1	3	yes	—
270	#380	C₂²×C₈₉	1	6	yes	—
271	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
272	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
273	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
274	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
275	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
279	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
280	C₄³	C₂²×C₈₉	1	3	yes	—
281	C₂×#41	—	2	8	no	—
282	C₂×#41	—	2	8	no	—
283	C₂×#41	C₂×C₄×C₈₉	1	16	yes	complemented
284	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
286	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
287	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
288	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
289	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
290	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
291	#127	C₂×C₄×C₈₉	1	24	yes	complemented
292	#121	C₂×C₄×C₈₉	1	48	yes	complemented
293	C₄×Q₈	—	2	8	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
296	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
297	C₄×D₄	—	2	24	no	—
298	C₄×D₄	—	2	12	no	—
299	C₄×D₄	—	2	24	no	—
300	C₄×D₄	—	2	12	no	—
301	C₄×D₄	—	4	12	no	—
302	C₄×D₄	C₂×C₄×C₈₉	1	24	yes	complemented
303	#117	—	2	24	no	—
304	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
305	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
306	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
308	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
310	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
317	C₂×C₄²	—	2	24	no	—
318	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
319	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
320	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
321	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
322	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
323	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
324	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
325	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
326	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
327	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
328	#95	C₂³×C₈₉	1	2	yes	—
329	#95	C₂³×C₈₉	1	6	yes	—
330	#95	C₂³×C₈₉	1	6	yes	—
331	#95	C₂³×C₈₉	1	6	yes	—
332	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
333	#41	—	2	64	no	—
334	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
335	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
336	C₂×Q₈	#41×C₈₉	1	4	yes	—
337	C₂×D₄	—	2	12	no	—
338	C₂×D₄	—	2	6	no	—
339	C₂×D₄	—	2	6	no	—
340	C₂×D₄	—	2	12	no	—
341	C₂×D₄	—	4	6	no	—
342	C₂×D₄	—	4	6	no	—
343	C₂×D₄	C₂²×C₄×C₈₉	1	12	yes	—
344	C₂×D₄	C₂²×C₄×C₈₉	1	24	yes	—
345	C₂×D₄	C₂²×C₄×C₈₉	1	24	yes	—
346	C₂²×C₄	—	2	12	no	—
347	C₂²×C₄	—	2	12	no	—
348	C₂²×C₄	—	2	12	no	—
349	C₂²×C₄	—	2	12	no	—
350	C₂²×C₄	—	2	12	no	—
351	C₂²×C₄	—	2	12	no	—
352	C₂²×C₄	—	2	12	no	—
353	C₂²×C₄	—	4	6	no	—
354	C₂²×C₄	C₂²×C₄×C₈₉	1	24	yes	—
355	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
356	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
357	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
360	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
363	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
365	C₄⋊C₄	—	2	12	no	—
366	C₄⋊C₄	—	2	6	no	—
367	C₄⋊C₄	—	2	6	no	—
368	C₄⋊C₄	—	4	6	no	—
369	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
370	C₄⋊C₄	C₂²×C₄×C₈₉	1	12	yes	—
371	C₄⋊C₄	C₂×D₄×C₈₉	1	12	yes	—
372	C₄⋊C₄	#41×C₈₉	1	4	yes	complemented
373	C₂²⋊C₄	—	2	24	no	—
374	C₂²⋊C₄	—	2	12	no	—
375	C₂²⋊C₄	—	2	12	no	—
376	C₂²⋊C₄	—	4	12	no	—
377	C₂²⋊C₄	C₂²×C₄×C₈₉	1	24	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	12	no	—
380	C₄²	—	2	12	no	—
381	C₄²	—	2	6	no	—
382	C₄²	—	2	6	no	—
383	C₄²	—	2	6	no	—
384	C₄²	—	4	3	no	—
385	C₄²	C₂²×C₄×C₈₉	1	12	yes	—
386	C₄²	C₂×D₄×C₈₉	1	12	yes	—
387	C₄²	#41×C₈₉	1	4	yes	complemented
388	C₂³	—	2	6	no	—
389	C₂³	—	2	6	no	—
390	C₂³	—	2	6	no	—
391	C₂³	—	2	6	no	—
392	C₂³	—	2	6	no	—
393	C₂³	—	2	6	no	—
394	C₂³	C₂³×C₄×C₈₉	1	12	yes	—
395	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
396	Q₈	C₄×D₄×C₈₉	1	16	yes	complemented
397	D₄	—	2	48	no	—
398	D₄	—	2	24	no	—
399	D₄	—	4	24	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	3	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	3	no	—
408	C₂×C₄	—	2	3	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	48	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	3	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	2	3	no	—
416	C₂×C₄	—	2	6	no	—
417	C₂×C₄	—	4	24	no	—
418	C₂×C₄	—	4	24	no	—
419	C₂×C₄	C₂³×C₄×C₈₉	1	6	yes	—
420	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₈₉	1	6	yes	—
422	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
424	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
425	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
426	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
427	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
428	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
429	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
430	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
431	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
432	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
433	C₂²	—	2	12	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	2	12	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	4	6	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	6	no	—
440	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
441	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
442	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
443	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
444	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
445	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
446	C₂²	#585×C₈₉	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	2	6	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	6	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	6	no	—
453	C₄	—	4	3	no	—
454	C₄	C₂×C₄×D₄×C₈₉	1	12	yes	—
455	C₄	C₄×#41×C₈₉	1	4	yes	complemented
456	C₄	#550×C₈₉	1	4	yes	direct product factor
457	C₂	—	4	12	no	—
458	C₂	C₂²×C₄×D₄×C₈₉	1	1	yes	characteristic
459	C₂	C₂×C₄×#41×C₈₉	1	1	yes	characteristic
460	C₂	C₄×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
461	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
462	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
463	C₂	C₈₉×#3480	1	1	yes	characteristic
464	C₂	C₈₉×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂⁵
prime radical	C₂×#550×C₈₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#2366	C₂	semidirect
4. C₈₉×#2363	C₂	semidirect
5. C₈₉×#2354	C₂	semidirect
6. Q₈×C₄⋊C₄×C₈₉	C₂	semidirect
7. C₈₉×#2341	C₂	semidirect
8. C₄×#127×C₈₉	C₂	semidirect
9. C₄×#121×C₈₉	C₂	semidirect
10. C₄²×Q₈×C₈₉	C₂	semidirect
11. C₄²×D₄×C₈₉	C₂	semidirect
13. #550×C₈₉	C₄	direct (N × H)
50. C₂×#41×C₈₉	C₂×C₄	semidirect
58. #127×C₈₉	C₂×C₄	semidirect
59. #121×C₈₉	C₂×C₄	semidirect
62. C₄×Q₈×C₈₉	C₂×C₄	semidirect
63. C₄×Q₈×C₈₉	D₄	semidirect
69. C₄×D₄×C₈₉	C₂×C₄	semidirect
139. C₄⋊C₄×C₈₉	#41	semidirect
154. C₄²×C₈₉	#41	semidirect
163. Q₈×C₈₉	C₄×D₄	semidirect
222. C₄×C₈₉	C₄×#41	semidirect
223. C₄×C₈₉	#550	direct (N × H)
224. C₄×#550	C₈₉	direct (N × H)
234. C₂×C₄×#41	C₂×C₈₉	semidirect
235. #2366	C₂×C₈₉	semidirect
236. #2363	C₂×C₈₉	semidirect
237. #2354	C₂×C₈₉	semidirect
238. Q₈×C₄⋊C₄	C₂×C₈₉	semidirect
239. #2341	C₂×C₈₉	semidirect
240. C₄×#127	C₂×C₈₉	semidirect
241. C₄×#121	C₂×C₈₉	semidirect
242. C₄²×Q₈	C₂×C₈₉	semidirect
243. C₄²×D₄	C₂×C₈₉	semidirect
244. C₈₉	C₄×#550	direct (N × H)
246. #550	C₄×C₈₉	direct (N × H)
283. C₂×#41	C₂×C₄×C₈₉	semidirect
291. #127	C₂×C₄×C₈₉	semidirect
292. #121	C₂×C₄×C₈₉	semidirect
295. C₄×Q₈	C₂×C₄×C₈₉	semidirect
296. C₄×Q₈	D₄×C₈₉	semidirect
302. C₄×D₄	C₂×C₄×C₈₉	semidirect
372. C₄⋊C₄	#41×C₈₉	semidirect
387. C₄²	#41×C₈₉	semidirect
396. Q₈	C₄×D₄×C₈₉	semidirect
455. C₄	C₄×#41×C₈₉	semidirect
456. C₄	#550×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×#550×C₈₉	2
C₂×C₄×#41×C₈₉	2
C₈₉×#2366	2
C₈₉×#2363	2
C₈₉×#2354	2
Q₈×C₄⋊C₄×C₈₉	2
C₈₉×#2341	2
C₄×#127×C₈₉	2
C₄×#121×C₈₉	2
C₄²×Q₈×C₈₉	2
C₄²×D₄×C₈₉	2
C₄×#550	89

Subgroups — C4×#550×C89 #36412008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#550×C₈₉ #36412008