Subgroups — C₈₉×#21043 #36398891

Order 22784.

790 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2905	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2873	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1922	C₂	1	8	yes	maximal, complemented
5	C₂×#341×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1733	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1733	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1729	C₂	1	1	yes	maximal, characteristic
9	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	#427×C₈₉	C₄	1	4	yes	complemented
17	#427×C₈₉	C₂²	1	4	yes	—
18	C₂×#107×C₈₉	C₄	1	2	yes	complemented
19	C₂×#106×C₈₉	C₄	1	2	yes	complemented
20	#424×C₈₉	—	2	2	no	—
21	#424×C₈₉	C₂²	1	4	yes	—
22	#423×C₈₉	—	2	2	no	—
23	#405×C₈₉	—	2	2	no	—
24	#405×C₈₉	C₂²	1	4	yes	—
25	C₄×M₁₆×C₈₉	—	2	2	no	—
26	#341×C₈₉	C₂²	1	4	yes	—
27	#339×C₈₉	C₂²	1	4	yes	—
28	#339×C₈₉	C₂²	1	4	yes	—
29	#336×C₈₉	C₂²	1	4	yes	—
30	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
31	C₂×M₁₆×C₈₉	—	2	1	no	—
32	C₂×M₁₆×C₈₉	—	2	2	no	—
33	C₂×M₁₆×C₈₉	—	2	2	no	—
34	C₂×M₁₆×C₈₉	—	2	2	no	—
35	C₂×M₁₆×C₈₉	—	2	1	no	—
36	C₂×M₁₆×C₈₉	—	2	2	no	—
37	C₂×M₁₆×C₈₉	—	2	2	no	—
38	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
39	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
40	C₂×M₁₆×C₈₉	Q₈	1	4	yes	—
41	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
42	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₈₉	—	2	1	no	—
44	C₂²×C₈×C₈₉	—	2	2	no	—
45	C₂²×C₈×C₈₉	—	2	2	no	—
46	C₂²×C₈×C₈₉	—	2	1	no	—
47	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
52	#117×C₈₉	—	2	1	no	—
53	#117×C₈₉	—	2	1	no	—
54	#117×C₈₉	—	2	1	no	—
55	#117×C₈₉	—	2	1	no	—
56	#117×C₈₉	—	2	2	no	—
57	#117×C₈₉	—	2	2	no	—
58	#117×C₈₉	C₂×C₄	1	2	yes	—
59	#117×C₈₉	C₂×C₄	1	2	yes	—
60	#117×C₈₉	C₂³	1	2	yes	—
61	#117×C₈₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₄²×C₈₉	—	2	1	no	—
69	C₂×C₄²×C₈₉	—	2	1	no	—
70	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
71	#107×C₈₉	C₂×C₄	1	8	yes	—
72	#106×C₈₉	C₂×C₄	1	8	yes	—
73	C₄⋊C₈×C₈₉	—	2	8	no	—
74	#97×C₈₉	—	2	4	no	—
75	C₄×C₈×C₈₉	—	2	4	no	—
76	C₂⁴×C₈₉	#41	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	—	2	2	no	—
78	C₂²×C₄×C₈₉	—	2	2	no	—
79	C₂²×C₄×C₈₉	—	2	2	no	—
80	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₈₉	#41	1	2	yes	—
86	C₂²×C₄×C₈₉	#41	1	2	yes	—
87	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	#41	1	2	yes	—
89	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
90	M₁₆×C₈₉	—	2	4	no	—
91	M₁₆×C₈₉	—	2	4	no	—
92	M₁₆×C₈₉	—	2	4	no	—
93	M₁₆×C₈₉	—	2	2	no	—
94	M₁₆×C₈₉	—	2	2	no	—
95	M₁₆×C₈₉	—	2	2	no	—
96	M₁₆×C₈₉	—	4	2	no	—
97	M₁₆×C₈₉	C₂×Q₈	1	4	yes	—
98	C₂×C₈×C₈₉	—	2	2	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	4	no	—
101	C₂×C₈×C₈₉	—	2	4	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	2	2	no	—
107	C₂×C₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	—	4	2	no	—
109	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₈₉	—	2	2	no	—
113	C₄⋊C₄×C₈₉	—	2	2	no	—
114	C₄⋊C₄×C₈₉	—	4	2	no	—
115	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
117	C₂²⋊C₄×C₈₉	—	2	2	no	—
118	C₂²⋊C₄×C₈₉	—	2	2	no	—
119	C₂²⋊C₄×C₈₉	—	2	2	no	—
120	C₂²⋊C₄×C₈₉	—	2	2	no	—
121	C₂²⋊C₄×C₈₉	—	4	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	—	2	2	no	—
126	C₄²×C₈₉	—	2	2	no	—
127	C₄²×C₈₉	—	2	2	no	—
128	C₂³×C₈₉	—	4	2	no	—
129	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
130	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
131	C₂³×C₈₉	#125	1	2	yes	—
132	C₂³×C₈₉	#126	1	2	yes	—
133	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₈₉	—	2	4	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	4	4	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	8	2	no	—
139	C₂×C₄×C₈₉	—	8	2	no	—
140	C₂×C₄×C₈₉	#117	1	2	yes	—
141	C₂×C₄×C₈₉	#117	1	2	yes	—
142	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₈₉	#123	1	2	yes	—
149	C₂×C₄×C₈₉	#123	1	2	yes	—
150	C₂×C₄×C₈₉	#125	1	2	yes	—
151	C₂×C₄×C₈₉	#126	1	2	yes	—
152	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
158	C₈×C₈₉	—	2	2	no	—
159	C₈×C₈₉	—	2	2	no	—
160	C₈×C₈₉	—	2	4	no	—
161	C₈×C₈₉	—	2	4	no	—
162	C₈×C₈₉	—	4	2	no	—
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	4	2	no	—
167	C₂²×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	#387	1	2	yes	—
169	C₂²×C₈₉	#387	1	2	yes	—
170	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₈₉	C₂×#125	1	1	yes	characteristic
172	C₂²×C₈₉	C₂×#126	1	1	yes	characteristic
173	C₄×C₈₉	—	4	4	no	—
174	C₄×C₈₉	—	4	4	no	—
175	C₄×C₈₉	—	8	2	no	—
176	C₄×C₈₉	#387	1	2	yes	—
177	C₄×C₈₉	#387	1	2	yes	—
178	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
179	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
180	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
182	#21043	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₈₉	—	2	1	no	—
184	C₂×C₈₉	—	2	1	no	—
185	C₂×C₈₉	—	2	2	no	—
186	C₂×C₈₉	—	2	2	no	—
187	C₂×C₈₉	C₂×#387	1	1	yes	characteristic
188	C₂×C₈₉	#2957	1	2	yes	—
189	C₂×#427	C₂×C₈₉	1	1	yes	characteristic
190	#2905	C₂×C₈₉	1	1	yes	characteristic
191	#2873	C₂×C₈₉	1	1	yes	characteristic
192	#1922	C₂×C₈₉	1	8	yes	complemented
193	C₂×#341	C₂×C₈₉	1	1	yes	characteristic
194	#1733	C₂×C₈₉	1	1	yes	characteristic
195	#1733	C₂×C₈₉	1	1	yes	characteristic
196	#1729	C₂×C₈₉	1	1	yes	characteristic
197	C₈₉	#21043	1	1	yes	characteristic, direct product factor, Sylow
198	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
200	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
202	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
203	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
204	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
205	#427	C₄×C₈₉	1	4	yes	complemented
206	#427	C₂²×C₈₉	1	4	yes	—
207	C₂×#107	C₄×C₈₉	1	2	yes	complemented
208	C₂×#106	C₄×C₈₉	1	2	yes	complemented
209	#424	—	2	2	no	—
210	#424	C₂²×C₈₉	1	4	yes	—
211	#423	—	2	2	no	—
212	#405	—	2	2	no	—
213	#405	C₂²×C₈₉	1	4	yes	—
214	C₄×M₁₆	—	2	2	no	—
215	#341	C₂²×C₈₉	1	4	yes	—
216	#339	C₂²×C₈₉	1	4	yes	—
217	#339	C₂²×C₈₉	1	4	yes	—
218	#336	C₂²×C₈₉	1	4	yes	—
219	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
228	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
229	C₂×M₁₆	Q₈×C₈₉	1	4	yes	—
230	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
231	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
237	C₂²×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
238	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
240	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
241	#117	—	2	1	no	—
242	#117	—	2	1	no	—
243	#117	—	2	1	no	—
244	#117	—	2	1	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	C₂×C₄×C₈₉	1	2	yes	—
248	#117	C₂×C₄×C₈₉	1	2	yes	—
249	#117	C₂³×C₈₉	1	2	yes	—
250	#117	C₂³×C₈₉	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
260	#107	C₂×C₄×C₈₉	1	8	yes	—
261	#106	C₂×C₄×C₈₉	1	8	yes	—
262	C₄⋊C₈	—	2	8	no	—
263	#97	—	2	4	no	—
264	C₄×C₈	—	2	4	no	—
265	C₂⁴	#41×C₈₉	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
274	C₂²×C₄	#41×C₈₉	1	2	yes	—
275	C₂²×C₄	#41×C₈₉	1	2	yes	—
276	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
277	C₂²×C₄	#41×C₈₉	1	2	yes	—
278	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
279	M₁₆	—	2	4	no	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	C₂×Q₈×C₈₉	1	4	yes	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
299	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
300	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
305	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
319	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
320	C₂³	#125×C₈₉	1	2	yes	—
321	C₂³	#126×C₈₉	1	2	yes	—
322	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	#117×C₈₉	1	2	yes	—
330	C₂×C₄	#117×C₈₉	1	2	yes	—
331	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
333	C₂×C₄	C₄×Q₈×C₈₉	1	2	yes	—
334	C₂×C₄	C₄×Q₈×C₈₉	1	2	yes	—
335	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
336	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
337	C₂×C₄	#123×C₈₉	1	2	yes	—
338	C₂×C₄	#123×C₈₉	1	2	yes	—
339	C₂×C₄	#125×C₈₉	1	2	yes	—
340	C₂×C₄	#126×C₈₉	1	2	yes	—
341	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×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	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	#387×C₈₉	1	2	yes	—
358	C₂²	#387×C₈₉	1	2	yes	—
359	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
360	C₂²	C₂×#125×C₈₉	1	1	yes	characteristic
361	C₂²	C₂×#126×C₈₉	1	1	yes	characteristic
362	C₄	—	4	4	no	—
363	C₄	—	4	4	no	—
364	C₄	—	8	2	no	—
365	C₄	#387×C₈₉	1	2	yes	—
366	C₄	#387×C₈₉	1	2	yes	—
367	C₄	C₂×#117×C₈₉	1	1	yes	characteristic
368	C₄	C₂×C₄×Q₈×C₈₉	1	1	yes	characteristic
369	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
370	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	2	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	C₂×#387×C₈₉	1	1	yes	characteristic
376	C₂	C₈₉×#2957	1	2	yes	—

	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	C₂⁴×C₈₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂²×M₁₆×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1922	C₂	semidirect
16. #427×C₈₉	C₄	semidirect
18. C₂×#107×C₈₉	C₄	semidirect
19. C₂×#106×C₈₉	C₄	semidirect
182. #21043	C₈₉	direct (N × H)
192. #1922	C₂×C₈₉	semidirect
197. C₈₉	#21043	direct (N × H)
205. #427	C₄×C₈₉	semidirect
207. C₂×#107	C₄×C₈₉	semidirect
208. C₂×#106	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#427×C₈₉	2
C₈₉×#2905	2
C₈₉×#2873	2
C₈₉×#1922	2
C₂×#341×C₈₉	2
C₈₉×#1733	2
C₈₉×#1729	2
#21043	89

Subgroups — C89×#21043 #36398891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#21043 #36398891