Subgroups — C₈₉×#35274 #36413122

Order 22784.

4510 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	4	yes	maximal, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2867	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2858	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2657	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2541	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2433	C₂	1	8	yes	maximal, complemented
9	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
12	C₂³×D₄×C₈₉	C₂²	1	4	yes	—
13	#535×C₈₉	—	2	32	no	—
14	#532×C₈₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×#127×C₈₉	—	2	8	no	—
17	C₂×#127×C₈₉	C₂²	1	2	yes	—
18	C₂×#127×C₈₉	C₂²	1	2	yes	—
19	C₂×#127×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#127×C₈₉	C₂²	1	8	yes	complemented
22	C₂×#127×C₈₉	C₂²	1	16	yes	complemented
23	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
24	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
25	C₂×#121×C₈₉	C₂²	1	4	yes	—
26	C₂×#121×C₈₉	C₂²	1	16	yes	complemented
27	C₂×#120×C₈₉	C₂²	1	16	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
29	C₂×#117×C₈₉	C₂²	1	2	yes	—
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#392×C₈₉	C₂²	1	32	yes	complemented
32	#390×C₈₉	C₂²	1	16	yes	complemented
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
34	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
35	#376×C₈₉	C₂²	1	2	yes	complemented
36	C₄³×C₈₉	C₂²	1	2	yes	complemented
37	C₂⁵×C₈₉	C₂³	1	4	yes	—
38	C₂×#41×C₈₉	—	2	8	no	—
39	C₂×#41×C₈₉	—	2	16	no	—
40	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₈₉	—	2	16	no	—
42	C₂²×D₄×C₈₉	—	2	8	no	—
43	C₂²×D₄×C₈₉	—	2	16	no	—
44	C₂²×D₄×C₈₉	—	4	16	no	—
45	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
47	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
52	C₂²×D₄×C₈₉	C₂³	1	32	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	—	2	4	no	—
57	#127×C₈₉	—	2	16	no	—
58	#127×C₈₉	—	2	8	no	—
59	#127×C₈₉	—	2	8	no	—
60	#127×C₈₉	—	2	4	no	—
61	#127×C₈₉	—	2	32	no	—
62	#127×C₈₉	—	4	32	no	—
63	#124×C₈₉	—	2	8	no	—
64	#124×C₈₉	—	2	32	no	—
65	#121×C₈₉	—	2	16	no	—
66	#121×C₈₉	—	2	64	no	—
67	#120×C₈₉	—	2	64	no	—
68	C₄×D₄×C₈₉	—	2	16	no	—
69	#117×C₈₉	D₄	1	16	yes	complemented
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
75	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
76	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
80	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	C₂⁴×C₈₉	—	2	8	no	—
83	C₂⁴×C₈₉	—	2	16	no	—
84	C₂⁴×C₈₉	—	4	16	no	—
85	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
86	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
87	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
88	#41×C₈₉	—	4	32	no	—
89	C₂×Q₈×C₈₉	—	2	8	no	—
90	C₂×Q₈×C₈₉	—	2	4	no	—
91	C₂×D₄×C₈₉	—	2	16	no	—
92	C₂×D₄×C₈₉	—	2	8	no	—
93	C₂×D₄×C₈₉	—	2	8	no	—
94	C₂×D₄×C₈₉	—	2	16	no	—
95	C₂×D₄×C₈₉	—	2	16	no	—
96	C₂×D₄×C₈₉	—	2	4	no	—
97	C₂×D₄×C₈₉	—	2	16	no	—
98	C₂×D₄×C₈₉	—	2	8	no	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	16	no	—
101	C₂×D₄×C₈₉	—	2	8	no	—
102	C₂×D₄×C₈₉	—	2	64	no	—
103	C₂×D₄×C₈₉	—	2	16	no	—
104	C₂×D₄×C₈₉	—	2	32	no	—
105	C₂×D₄×C₈₉	—	4	16	no	—
106	C₂×D₄×C₈₉	—	4	64	no	—
107	C₂×D₄×C₈₉	—	4	64	no	—
108	C₂×D₄×C₈₉	—	4	32	no	—
109	C₂²×C₄×C₈₉	—	2	8	no	—
110	C₂²×C₄×C₈₉	—	2	8	no	—
111	C₂²×C₄×C₈₉	—	2	16	no	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
121	C₄⋊C₄×C₈₉	—	2	8	no	—
122	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	complemented
123	C₂²⋊C₄×C₈₉	—	2	16	no	—
124	C₂²⋊C₄×C₈₉	—	2	64	no	—
125	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
126	C₄²×C₈₉	—	2	16	no	—
127	C₄²×C₈₉	C₂×D₄	1	8	yes	—
128	C₄²×C₈₉	C₂×D₄	1	4	yes	—
129	C₄²×C₈₉	C₂×D₄	1	4	yes	—
130	C₄²×C₈₉	C₂×D₄	1	16	yes	complemented
131	C₂³×C₈₉	—	2	4	no	—
132	C₂³×C₈₉	—	2	4	no	—
133	C₂³×C₈₉	—	2	16	no	—
134	C₂³×C₈₉	—	2	8	no	—
135	C₂³×C₈₉	—	2	8	no	—
136	C₂³×C₈₉	—	2	16	no	—
137	C₂³×C₈₉	—	2	32	no	—
138	C₂³×C₈₉	—	4	32	no	—
139	C₂³×C₈₉	—	4	16	no	—
140	C₂³×C₈₉	—	8	32	no	—
141	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
142	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
143	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
144	Q₈×C₈₉	—	4	8	no	—
145	D₄×C₈₉	—	4	32	no	—
146	D₄×C₈₉	—	4	16	no	—
147	D₄×C₈₉	—	4	16	no	—
148	D₄×C₈₉	—	4	16	no	—
149	D₄×C₈₉	—	4	8	no	—
150	D₄×C₈₉	—	4	16	no	—
151	D₄×C₈₉	—	4	32	no	—
152	D₄×C₈₉	—	8	64	no	—
153	C₂×C₄×C₈₉	—	2	16	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	16	no	—
156	C₂×C₄×C₈₉	—	2	8	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	4	16	no	—
159	C₂×C₄×C₈₉	#127	1	16	yes	complemented
160	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
162	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
167	C₂×C₄×C₈₉	H(5,𝔽₂)	1	8	yes	—
168	C₂²×C₈₉	—	2	4	no	—
169	C₂²×C₈₉	—	2	8	no	—
170	C₂²×C₈₉	—	4	4	no	—
171	C₂²×C₈₉	—	4	8	no	—
172	C₂²×C₈₉	—	4	16	no	—
173	C₂²×C₈₉	—	4	8	no	—
174	C₂²×C₈₉	—	4	16	no	—
175	C₂²×C₈₉	—	4	32	no	—
176	C₂²×C₈₉	—	8	32	no	—
177	C₂²×C₈₉	C₂×#127	1	4	yes	—
178	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
179	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
180	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
181	C₄×C₈₉	—	2	4	no	—
182	C₄×C₈₉	—	2	16	no	—
183	C₄×C₈₉	—	4	4	no	—
184	C₄×C₈₉	C₂×#127	1	4	yes	—
185	C₄×C₈₉	C₂×#127	1	4	yes	—
186	C₄×C₈₉	#535	1	8	yes	complemented
187	#35274	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₈₉	—	2	4	no	—
189	C₂×C₈₉	—	8	4	no	—
190	C₂×C₈₉	—	8	8	no	—
191	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
192	C₂×C₈₉	C₂×#535	1	2	yes	—
193	C₂×C₈₉	#3498	1	4	yes	—
194	C₂×#535	C₂×C₈₉	1	4	yes	complemented
195	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
196	C₂²×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
197	#2867	C₂×C₈₉	1	2	yes	complemented
198	#2858	C₂×C₈₉	1	2	yes	complemented
199	#2657	C₂×C₈₉	1	4	yes	complemented
200	#2541	C₂×C₈₉	1	8	yes	complemented
201	#2433	C₂×C₈₉	1	8	yes	complemented
202	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
203	C₈₉	#35274	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×#41	C₂²×C₈₉	1	2	yes	—
205	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
206	C₂³×D₄	C₂²×C₈₉	1	4	yes	—
207	#535	—	2	32	no	—
208	#532	—	2	8	no	—
209	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
210	C₂×#127	—	2	8	no	—
211	C₂×#127	C₂²×C₈₉	1	2	yes	—
212	C₂×#127	C₂²×C₈₉	1	2	yes	—
213	C₂×#127	C₂²×C₈₉	1	4	yes	—
214	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
215	C₂×#127	C₂²×C₈₉	1	8	yes	complemented
216	C₂×#127	C₂²×C₈₉	1	16	yes	complemented
217	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
218	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
219	C₂×#121	C₂²×C₈₉	1	4	yes	—
220	C₂×#121	C₂²×C₈₉	1	16	yes	complemented
221	C₂×#120	C₂²×C₈₉	1	16	yes	—
222	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
223	C₂×#117	C₂²×C₈₉	1	2	yes	—
224	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
225	#392	C₂²×C₈₉	1	32	yes	complemented
226	#390	C₂²×C₈₉	1	16	yes	complemented
227	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
228	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
229	#376	C₂²×C₈₉	1	2	yes	complemented
230	C₄³	C₂²×C₈₉	1	2	yes	complemented
231	C₂⁵	C₂³×C₈₉	1	4	yes	—
232	C₂×#41	—	2	8	no	—
233	C₂×#41	—	2	16	no	—
234	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
235	C₂²×D₄	—	2	16	no	—
236	C₂²×D₄	—	2	8	no	—
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	4	16	no	—
239	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
240	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
241	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
242	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
243	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
244	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
245	C₂²×D₄	C₂³×C₈₉	1	32	yes	—
246	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
247	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
248	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
249	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	4	no	—
251	#127	—	2	16	no	—
252	#127	—	2	8	no	—
253	#127	—	2	8	no	—
254	#127	—	2	4	no	—
255	#127	—	2	32	no	—
256	#127	—	4	32	no	—
257	#124	—	2	8	no	—
258	#124	—	2	32	no	—
259	#121	—	2	16	no	—
260	#121	—	2	64	no	—
261	#120	—	2	64	no	—
262	C₄×D₄	—	2	16	no	—
263	#117	D₄×C₈₉	1	16	yes	complemented
264	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
269	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
270	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
271	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
272	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
275	#95	C₂³×C₈₉	1	8	yes	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	16	no	—
278	C₂⁴	—	4	16	no	—
279	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
280	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
281	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
282	#41	—	4	32	no	—
283	C₂×Q₈	—	2	8	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×D₄	—	2	16	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	16	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	16	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	64	no	—
297	C₂×D₄	—	2	16	no	—
298	C₂×D₄	—	2	32	no	—
299	C₂×D₄	—	4	16	no	—
300	C₂×D₄	—	4	64	no	—
301	C₂×D₄	—	4	64	no	—
302	C₂×D₄	—	4	32	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
307	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
309	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
312	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	complemented
317	C₂²⋊C₄	—	2	16	no	—
318	C₂²⋊C₄	—	2	64	no	—
319	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
320	C₄²	—	2	16	no	—
321	C₄²	C₂×D₄×C₈₉	1	8	yes	—
322	C₄²	C₂×D₄×C₈₉	1	4	yes	—
323	C₄²	C₂×D₄×C₈₉	1	4	yes	—
324	C₄²	C₂×D₄×C₈₉	1	16	yes	complemented
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	16	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	8	no	—
330	C₂³	—	2	16	no	—
331	C₂³	—	2	32	no	—
332	C₂³	—	4	32	no	—
333	C₂³	—	4	16	no	—
334	C₂³	—	8	32	no	—
335	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
336	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
337	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
338	Q₈	—	4	8	no	—
339	D₄	—	4	32	no	—
340	D₄	—	4	16	no	—
341	D₄	—	4	16	no	—
342	D₄	—	4	16	no	—
343	D₄	—	4	8	no	—
344	D₄	—	4	16	no	—
345	D₄	—	4	32	no	—
346	D₄	—	8	64	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	16	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	#127×C₈₉	1	16	yes	complemented
354	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
355	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
356	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
360	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
361	C₂×C₄	H(5,𝔽₂)×C₈₉	1	8	yes	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	8	no	—
366	C₂²	—	4	16	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	16	no	—
369	C₂²	—	4	32	no	—
370	C₂²	—	8	32	no	—
371	C₂²	C₂×#127×C₈₉	1	4	yes	—
372	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
373	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
374	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	2	16	no	—
377	C₄	—	4	4	no	—
378	C₄	C₂×#127×C₈₉	1	4	yes	—
379	C₄	C₂×#127×C₈₉	1	4	yes	—
380	C₄	#535×C₈₉	1	8	yes	complemented
381	C₂	—	2	4	no	—
382	C₂	—	8	4	no	—
383	C₂	—	8	8	no	—
384	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
385	C₂	C₂×#535×C₈₉	1	2	yes	—
386	C₂	C₈₉×#3498	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₈₉	C₂	semidirect
2. C₂×#532×C₈₉	C₂	semidirect
3. C₂²×#127×C₈₉	C₂	semidirect
4. C₈₉×#2867	C₂	semidirect
5. C₈₉×#2858	C₂	semidirect
6. C₈₉×#2657	C₂	semidirect
7. C₈₉×#2541	C₂	semidirect
8. C₈₉×#2433	C₂	semidirect
9. C₄×#117×C₈₉	C₂	semidirect
15. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
20. C₂×#127×C₈₉	C₂²	semidirect
21. C₂×#127×C₈₉	C₂²	semidirect
22. C₂×#127×C₈₉	C₂²	semidirect
23. C₂×#124×C₈₉	C₂²	semidirect
24. C₂×#124×C₈₉	C₂²	semidirect
26. C₂×#121×C₈₉	C₂²	semidirect
28. C₂×C₄×D₄×C₈₉	C₂²	semidirect
31. #392×C₈₉	C₂²	semidirect
32. #390×C₈₉	C₂²	semidirect
33. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
35. #376×C₈₉	C₂²	semidirect
36. C₄³×C₈₉	C₂²	semidirect
69. #117×C₈₉	D₄	semidirect
75. C₂×C₄²×C₈₉	D₄	semidirect
122. C₄⋊C₄×C₈₉	C₂×D₄	semidirect
130. C₄²×C₈₉	C₂×D₄	semidirect
159. C₂×C₄×C₈₉	#127	semidirect
186. C₄×C₈₉	#535	semidirect
187. #35274	C₈₉	direct (N × H)
194. C₂×#535	C₂×C₈₉	semidirect
195. C₂×#532	C₂×C₈₉	semidirect
196. C₂²×#127	C₂×C₈₉	semidirect
197. #2867	C₂×C₈₉	semidirect
198. #2858	C₂×C₈₉	semidirect
199. #2657	C₂×C₈₉	semidirect
200. #2541	C₂×C₈₉	semidirect
201. #2433	C₂×C₈₉	semidirect
202. C₄×#117	C₂×C₈₉	semidirect
203. C₈₉	#35274	direct (N × H)
209. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
214. C₂×#127	C₂²×C₈₉	semidirect
215. C₂×#127	C₂²×C₈₉	semidirect
216. C₂×#127	C₂²×C₈₉	semidirect
217. C₂×#124	C₂²×C₈₉	semidirect
218. C₂×#124	C₂²×C₈₉	semidirect
220. C₂×#121	C₂²×C₈₉	semidirect
222. C₂×C₄×D₄	C₂²×C₈₉	semidirect
225. #392	C₂²×C₈₉	semidirect
226. #390	C₂²×C₈₉	semidirect
227. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
229. #376	C₂²×C₈₉	semidirect
230. C₄³	C₂²×C₈₉	semidirect
263. #117	D₄×C₈₉	semidirect
269. C₂×C₄²	D₄×C₈₉	semidirect
316. C₄⋊C₄	C₂×D₄×C₈₉	semidirect
324. C₄²	C₂×D₄×C₈₉	semidirect
353. C₂×C₄	#127×C₈₉	semidirect
380. C₄	#535×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₈₉	2
C₂×#532×C₈₉	2
C₂²×#127×C₈₉	2
C₈₉×#2867	2
C₈₉×#2858	2
C₈₉×#2657	2
C₈₉×#2541	2
C₈₉×#2433	2
C₄×#117×C₈₉	2
#35274	89

Subgroups — C89×#35274 #36413122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35274 #36413122