Subgroups — C₈₉×#22803 #36400651

Order 22784.

710 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	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2925	C₂	1	2	yes	maximal, complemented
3	C₈₉×#1975	C₂	1	2	yes	maximal
4	C₈₉×#1929	C₂	1	4	yes	maximal, complemented
5	C₈₉×#1848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1806	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1773	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
10	C₄×#41×C₈₉	C₂²	1	2	yes	—
11	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
12	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
13	C₄×SD₁₆×C₈₉	C₄	1	2	yes	complemented
14	C₄×SD₁₆×C₈₉	C₄	1	2	yes	complemented
15	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
16	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
17	#433×C₈₉	—	2	4	no	—
18	#432×C₈₉	—	2	2	no	—
19	#431×C₈₉	—	2	2	no	—
20	C₂×#108×C₈₉	C₂²	1	2	yes	—
21	C₂×#108×C₈₉	C₂²	1	2	yes	—
22	#427×C₈₉	C₂²	1	1	yes	characteristic
23	#423×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#104×C₈₉	C₂²	1	4	yes	—
26	#416×C₈₉	C₂²	1	2	yes	—
27	#408×C₈₉	C₂²	1	4	yes	—
28	#405×C₈₉	C₂²	1	4	yes	—
29	C₂×#97×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	#339×C₈₉	C₂²	1	4	yes	—
33	#336×C₈₉	C₂²	1	2	yes	—
34	C₂×#41×C₈₉	C₂³	1	2	yes	—
35	#135×C₈₉	—	2	2	no	—
36	#135×C₈₉	—	2	2	no	—
37	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
39	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
41	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₈₉	—	2	2	no	—
47	C₄×D₄×C₈₉	—	2	2	no	—
48	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
50	#117×C₈₉	—	2	2	no	—
51	#117×C₈₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
53	C₂×C₄²×C₈₉	—	2	2	no	—
54	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
55	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
56	#108×C₈₉	—	2	4	no	—
57	#108×C₈₉	—	4	2	no	—
58	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
59	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
60	#106×C₈₉	C₂×C₄	1	2	yes	—
61	C₄⋊C₈×C₈₉	—	2	2	no	—
62	C₄⋊C₈×C₈₉	—	2	2	no	—
63	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
64	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
65	#104×C₈₉	—	4	4	no	—
66	#103×C₈₉	C₂×C₄	1	2	yes	—
67	#103×C₈₉	C₂×C₄	1	2	yes	—
68	#102×C₈₉	C₂×C₄	1	2	yes	—
69	#102×C₈₉	C₂×C₄	1	2	yes	—
70	C₂²⋊C₈×C₈₉	—	2	4	no	—
71	C₂²⋊C₈×C₈₉	—	2	4	no	—
72	#97×C₈₉	—	2	4	no	—
73	#97×C₈₉	—	2	4	no	—
74	C₄×C₈×C₈₉	—	2	4	no	—
75	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	#95×C₈₉	—	2	1	no	—
80	#41×C₈₉	—	2	2	no	—
81	#41×C₈₉	—	2	2	no	—
82	#41×C₈₉	—	2	2	no	—
83	#41×C₈₉	—	2	2	no	—
84	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₈₉	—	2	2	no	—
86	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₈₉	—	2	2	no	—
88	C₂²×C₄×C₈₉	—	2	2	no	—
89	C₂²×C₄×C₈₉	—	2	2	no	—
90	C₂²×C₄×C₈₉	—	2	2	no	—
91	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₈₉	—	2	2	no	—
95	SD₁₆×C₈₉	—	2	4	no	—
96	D₈×C₈₉	—	2	2	no	—
97	M₁₆×C₈₉	—	2	4	no	—
98	M₁₆×C₈₉	—	2	4	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	1	no	—
101	C₂×C₈×C₈₉	—	2	1	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	4	no	—
104	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₈₉	#41	1	2	yes	—
110	C₂×C₈×C₈₉	#41	1	2	yes	—
111	C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₄⋊C₄×C₈₉	—	2	2	no	—
113	C₄⋊C₄×C₈₉	—	4	2	no	—
114	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
115	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
116	C₂²⋊C₄×C₈₉	—	2	2	no	—
117	C₂²⋊C₄×C₈₉	—	2	2	no	—
118	C₂²⋊C₄×C₈₉	—	2	2	no	—
119	C₄²×C₈₉	—	2	2	no	—
120	C₄²×C₈₉	—	2	2	no	—
121	C₄²×C₈₉	—	2	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₈₉	—	2	2	no	—
129	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
130	Q₈×C₈₉	—	2	2	no	—
131	Q₈×C₈₉	—	2	2	no	—
132	D₄×C₈₉	—	2	2	no	—
133	D₄×C₈₉	—	2	2	no	—
134	D₄×C₈₉	—	4	2	no	—
135	D₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	4	4	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	—	4	2	no	—
147	C₂×C₄×C₈₉	—	8	2	no	—
148	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
158	C₈×C₈₉	—	2	1	no	—
159	C₈×C₈₉	—	2	1	no	—
160	C₈×C₈₉	—	2	4	no	—
161	C₈×C₈₉	—	4	4	no	—
162	C₈×C₈₉	#117	1	2	yes	—
163	C₈×C₈₉	#117	1	2	yes	—
164	C₂²×C₈₉	—	2	1	no	—
165	C₂²×C₈₉	—	2	1	no	—
166	C₂²×C₈₉	—	4	2	no	—
167	C₂²×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	—	4	2	no	—
169	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₈₉	#555	1	1	yes	characteristic
171	C₂²×C₈₉	#556	1	1	yes	characteristic
172	C₄×C₈₉	—	2	1	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	4	2	no	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	—	4	2	no	—
178	C₄×C₈₉	—	8	2	no	—
179	C₄×C₈₉	#444	1	2	yes	—
180	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
181	C₄×C₈₉	#520	1	1	yes	characteristic
182	C₄×C₈₉	#547	1	1	yes	characteristic
183	C₄×C₈₉	#550	1	1	yes	characteristic
184	#22803	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₈₉	—	2	1	no	—
186	C₂×C₈₉	—	2	1	no	—
187	C₂×C₈₉	—	8	2	no	—
188	C₂×C₈₉	#2354	1	1	yes	characteristic
189	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
190	C₂×C₈₉	#2957	1	1	yes	characteristic
191	C₄×#135	C₂×C₈₉	1	1	yes	characteristic
192	#2925	C₂×C₈₉	1	2	yes	complemented
193	#1975	C₂×C₈₉	1	2	yes	—
194	#1929	C₂×C₈₉	1	4	yes	complemented
195	#1848	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#1806	C₂×C₈₉	1	2	yes	complemented
197	#1773	C₂×C₈₉	1	2	yes	complemented
198	#1770	C₂×C₈₉	1	1	yes	characteristic, complemented
199	C₈₉	#22803	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
201	C₄×#41	C₂²×C₈₉	1	2	yes	—
202	C₄×Q₁₆	C₄×C₈₉	1	1	yes	characteristic, complemented
203	C₄×Q₁₆	C₄×C₈₉	1	1	yes	characteristic, complemented
204	C₄×SD₁₆	C₄×C₈₉	1	2	yes	complemented
205	C₄×SD₁₆	C₄×C₈₉	1	2	yes	complemented
206	C₄×D₈	C₄×C₈₉	1	1	yes	characteristic, complemented
207	C₄×D₈	C₄×C₈₉	1	1	yes	characteristic, complemented
208	#433	—	2	4	no	—
209	#432	—	2	2	no	—
210	#431	—	2	2	no	—
211	C₂×#108	C₂²×C₈₉	1	2	yes	—
212	C₂×#108	C₂²×C₈₉	1	2	yes	—
213	#427	C₂²×C₈₉	1	1	yes	characteristic
214	#423	C₂²×C₈₉	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×#104	C₂²×C₈₉	1	4	yes	—
217	#416	C₂²×C₈₉	1	2	yes	—
218	#408	C₂²×C₈₉	1	4	yes	—
219	#405	C₂²×C₈₉	1	4	yes	—
220	C₂×#97	C₂²×C₈₉	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
222	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
223	#339	C₂²×C₈₉	1	4	yes	—
224	#336	C₂²×C₈₉	1	2	yes	—
225	C₂×#41	C₂³×C₈₉	1	2	yes	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	C₂×Q₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×C₄×C₈₉	1	2	yes	—
230	C₂×D₈	C₂×C₄×C₈₉	1	1	yes	characteristic
231	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
232	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
234	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
235	C₄×Q₈	C₂×C₄×C₈₉	1	2	yes	—
236	C₄×Q₈	C₂×C₄×C₈₉	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
240	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
241	#117	—	2	2	no	—
242	#117	C₂³×C₈₉	1	2	yes	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
246	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
247	#108	—	2	4	no	—
248	#108	—	4	2	no	—
249	#107	C₂×C₄×C₈₉	1	1	yes	characteristic
250	#107	C₂×C₄×C₈₉	1	1	yes	characteristic
251	#106	C₂×C₄×C₈₉	1	2	yes	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
255	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
256	#104	—	4	4	no	—
257	#103	C₂×C₄×C₈₉	1	2	yes	—
258	#103	C₂×C₄×C₈₉	1	2	yes	—
259	#102	C₂×C₄×C₈₉	1	2	yes	—
260	#102	C₂×C₄×C₈₉	1	2	yes	—
261	C₂²⋊C₈	—	2	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
267	C₄×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
268	C₄×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
269	C₄×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
270	#95	—	2	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	2	4	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
298	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
300	C₂×C₈	#41×C₈₉	1	2	yes	—
301	C₂×C₈	#41×C₈₉	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
306	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
316	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
347	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
348	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	4	no	—
353	C₈	#117×C₈₉	1	2	yes	—
354	C₈	#117×C₈₉	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
361	C₂²	#555×C₈₉	1	1	yes	characteristic
362	C₂²	#556×C₈₉	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	#444×C₈₉	1	2	yes	—
371	C₄	C₂×#117×C₈₉	1	1	yes	characteristic
372	C₄	#520×C₈₉	1	1	yes	characteristic
373	C₄	#547×C₈₉	1	1	yes	characteristic
374	C₄	#550×C₈₉	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₈₉×#2354	1	1	yes	characteristic
379	C₂	C₂×#444×C₈₉	1	1	yes	characteristic
380	C₂	C₈₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂×C₄⋊C₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2925	C₂	semidirect
4. C₈₉×#1929	C₂	semidirect
5. C₈₉×#1848	C₂	semidirect
6. C₈₉×#1806	C₂	semidirect
7. C₈₉×#1773	C₂	semidirect
8. C₈₉×#1770	C₂	semidirect
11. C₄×Q₁₆×C₈₉	C₄	semidirect
12. C₄×Q₁₆×C₈₉	C₄	semidirect
13. C₄×SD₁₆×C₈₉	C₄	semidirect
14. C₄×SD₁₆×C₈₉	C₄	semidirect
15. C₄×D₈×C₈₉	C₄	semidirect
16. C₄×D₈×C₈₉	C₄	semidirect
184. #22803	C₈₉	direct (N × H)
192. #2925	C₂×C₈₉	semidirect
194. #1929	C₂×C₈₉	semidirect
195. #1848	C₂×C₈₉	semidirect
196. #1806	C₂×C₈₉	semidirect
197. #1773	C₂×C₈₉	semidirect
198. #1770	C₂×C₈₉	semidirect
199. C₈₉	#22803	direct (N × H)
202. C₄×Q₁₆	C₄×C₈₉	semidirect
203. C₄×Q₁₆	C₄×C₈₉	semidirect
204. C₄×SD₁₆	C₄×C₈₉	semidirect
205. C₄×SD₁₆	C₄×C₈₉	semidirect
206. C₄×D₈	C₄×C₈₉	semidirect
207. C₄×D₈	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×#135×C₈₉	2
C₈₉×#2925	2
C₈₉×#1975	2
C₈₉×#1929	2
C₈₉×#1848	2
C₈₉×#1806	2
C₈₉×#1773	2
C₈₉×#1770	2
#22803	89

Subgroups — C89×#22803 #36400651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22803 #36400651