Subgroups — #36553076

Order 22784.

938 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151727	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151726	C₂	1	1	yes	maximal, characteristic
3	C₄×#15667977	C₂	1	1	yes	maximal, characteristic
4	#26020128	C₂	1	1	yes	maximal, characteristic
5	#26020127	C₂	1	1	yes	maximal, characteristic
6	#26020125	C₂	1	1	yes	maximal, characteristic
7	C₈×#13083553	C₂	1	1	yes	maximal, characteristic
8	#26020113	C₂	1	1	yes	maximal, characteristic
9	#26020107	C₂	1	1	yes	maximal, characteristic
10	#26020104	C₂	1	1	yes	maximal, characteristic
11	#26020104	C₂	1	1	yes	maximal, characteristic
12	C₄×#15667922	C₂	1	1	yes	maximal, characteristic
13	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic
14	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
17	C₂×#15667977	C₄	1	2	yes	—
18	#19151727	C₄	1	8	yes	complemented
19	#19151726	C₄	1	8	yes	complemented
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×#15667941	C₂²	1	1	yes	characteristic
22	C₂×#15667941	C₂²	1	1	yes	characteristic
23	C₂×#15667941	C₂²	1	1	yes	characteristic
24	C₂×#15667941	C₂²	1	1	yes	characteristic
25	C₂×#15667923	C₂²	1	1	yes	characteristic
26	C₂×#15667923	C₂²	1	1	yes	characteristic
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×#15667922	C₂²	1	1	yes	characteristic
29	C₂×#15667922	C₂²	1	1	yes	characteristic
30	C₂×#15667922	C₂²	1	1	yes	characteristic
31	C₂×#15667922	C₂²	1	1	yes	characteristic
32	C₂×#15667922	C₂²	1	1	yes	characteristic
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₈₉	C₄	1	2	yes	—
39	C₄×#13083553	C₂²	1	1	yes	characteristic
40	C₄×#13083553	C₂²	1	1	yes	characteristic
41	#19151449	C₄	1	2	yes	—
42	#19151449	C₄	1	2	yes	—
43	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
44	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
45	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
46	#19151353	C₂²	1	1	yes	characteristic
47	#19151353	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
63	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
64	#15667977	—	2	8	no	—
65	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×#13083553	C₂×C₄	1	2	yes	—
67	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083553	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	C₂×C₄	1	4	yes	—
81	#15667941	C₂×C₄	1	4	yes	—
82	#15667941	C₂×C₄	1	4	yes	—
83	#15667941	C₂×C₄	1	4	yes	—
84	#15667941	C₂×C₄	1	4	yes	—
85	#15667923	—	2	2	no	—
86	#15667923	C₂×C₄	1	4	yes	—
87	#15667922	—	2	2	no	—
88	#15667922	—	2	2	no	—
89	#15667922	—	2	2	no	—
90	#15667922	C₂×C₄	1	4	yes	—
91	#15667922	C₂×C₄	1	4	yes	—
92	#15667922	Q₈	1	4	yes	complemented
93	C₄×#10623494	—	2	2	no	—
94	C₈×Dic₈₉	—	2	2	no	—
95	C₈×Dic₈₉	—	2	2	no	—
96	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
97	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
98	#15667919	C₂×C₄	1	2	yes	—
99	#15667919	C₂×C₄	1	2	yes	—
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
109	#97×C₈₉	—	2	2	no	—
110	#97×C₈₉	C₂×C₄	1	4	yes	—
111	C₄×C₈×C₈₉	—	2	2	no	—
112	#95×C₈₉	C₂×C₄	1	2	yes	—
113	C₂×Dic₁₇₈	—	2	4	no	—
114	C₂×Dic₁₇₈	C₄²	1	4	yes	—
115	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
119	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
120	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	1	no	—
125	C₂×#10623494	—	2	1	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	C₂²×C₄	1	2	yes	—
128	C₂×#10623494	C₂²×C₄	1	2	yes	—
129	C₂×#10623494	C₂²×C₄	1	2	yes	—
130	C₂×#10623494	C₂²×C₄	1	2	yes	—
131	C₂×#10623494	C₂×Q₈	1	2	yes	—
132	C₂×#10623494	#41	1	2	yes	—
133	C₄⋊Dic₈₉	C₄²	1	4	yes	—
134	#13083553	—	2	4	no	—
135	#13083553	C₄²	1	4	yes	—
136	#13083553	C₄²	1	4	yes	—
137	#13083553	M₁₆	1	8	yes	—
138	C₄×Dic₈₉	—	2	4	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	4	no	—
142	C₄×Dic₈₉	—	2	4	no	—
143	C₄×Dic₈₉	—	4	2	no	—
144	C₄×Dic₈₉	—	4	2	no	—
145	C₄×Dic₈₉	—	4	2	no	—
146	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
147	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
148	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
149	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
150	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
151	C₄×Dic₈₉	#41	1	2	yes	—
152	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	1	no	—
159	C₂×C₈×C₈₉	—	2	1	no	—
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
168	C₂×C₈×C₈₉	#41	1	2	yes	—
169	C₄⋊C₄×C₈₉	—	2	4	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	—	2	1	no	—
172	C₄²×C₈₉	—	2	1	no	—
173	C₄²×C₈₉	—	2	1	no	—
174	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
175	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
176	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	2	2	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
185	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
186	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
187	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
193	C₂×Dic₈₉	—	2	2	no	—
194	C₂×Dic₈₉	—	2	2	no	—
195	C₂×Dic₈₉	—	2	2	no	—
196	C₂×Dic₈₉	—	2	2	no	—
197	C₂×Dic₈₉	—	2	2	no	—
198	C₂×Dic₈₉	—	2	2	no	—
199	C₂×Dic₈₉	—	2	2	no	—
200	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
201	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
202	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
203	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
204	C₂×Dic₈₉	C₄×Q₈	1	4	yes	—
205	C₂×Dic₈₉	C₂×M₁₆	1	4	yes	—
206	C₂×Dic₈₉	C₂×M₁₆	1	4	yes	—
207	Dic₁₇₈	—	2	8	no	—
208	C₈×C₈₉	—	2	2	no	—
209	C₈×C₈₉	—	2	2	no	—
210	C₈×C₈₉	—	2	2	no	—
211	C₈×C₈₉	C₄×Q₈	1	4	yes	complemented
212	#10623494	—	2	2	no	—
213	#10623494	—	2	2	no	—
214	#10623494	—	2	2	no	—
215	#10623494	C₄×Q₈	1	4	yes	complemented
216	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
217	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
219	C₂²×C₈₉	C₂²×M₁₆	1	2	yes	—
220	C₂²×C₈₉	#568	1	2	yes	—
221	C₄×C₈₉	—	2	2	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	4	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
227	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
228	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
229	Dic₈₉	—	2	2	no	—
230	Dic₈₉	—	2	2	no	—
231	Dic₈₉	—	2	2	no	—
232	Dic₈₉	—	2	4	no	—
233	Dic₈₉	—	2	4	no	—
234	Dic₈₉	C₄×M₁₆	1	4	yes	—
235	#20520	—	89	1	no	maximal, Sylow
236	C₂×C₈₉	C₄²×Q₈	1	1	yes	characteristic
237	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
238	C₂×C₈₉	#2875	1	1	yes	characteristic
239	C₂×C₈₉	Q₈×M₁₆	1	2	yes	—
240	C₂×C₈₉	#2970	1	2	yes	—
241	C₂×#446	—	89	1	no	—
242	C₂×#446	—	89	1	no	—
243	C₄²×Q₈	—	89	1	no	—
244	#1771	—	89	1	no	—
245	#1771	—	89	1	no	—
246	#1771	—	89	1	no	—
247	#1771	D₈₉	1	1	yes	characteristic
248	C₈×C₄⋊C₄	—	89	1	no	—
249	C₈×C₄⋊C₄	—	89	1	no	—
250	#1767	—	89	1	no	—
251	#1767	—	89	1	no	—
252	#1767	—	89	1	no	—
253	C₄×#97	—	89	1	no	—
254	C₄×#97	—	89	1	no	—
255	C₄×#97	—	89	1	no	—
256	C₈₉	#20520	1	1	yes	characteristic, complemented, Sylow
257	C₂×C₄×Q₈	—	89	2	no	—
258	C₂×C₄×Q₈	—	89	1	no	—
259	#446	—	89	8	no	—
260	#446	—	89	8	no	—
261	C₂×C₄⋊C₈	—	89	1	no	—
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×C₄⋊C₈	—	89	1	no	—
264	C₂×C₄⋊C₈	—	89	1	no	—
265	C₂×C₄⋊C₈	—	89	1	no	—
266	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
267	C₂×#97	—	89	1	no	—
268	C₂×#97	—	89	1	no	—
269	C₂×#97	—	89	1	no	—
270	C₂×#97	—	89	1	no	—
271	C₂×#97	—	89	1	no	—
272	C₂×#97	—	89	1	no	—
273	C₂×#97	—	89	1	no	—
274	C₂×#97	—	89	1	no	—
275	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
276	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
277	C₂×C₄×C₈	—	89	1	no	—
278	C₂×C₄×C₈	—	89	1	no	—
279	C₂×C₄×C₈	—	89	1	no	—
280	C₂×C₄×C₈	—	89	1	no	—
281	C₂×C₄×C₈	—	89	1	no	—
282	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
283	C₄×C₄⋊C₄	—	89	2	no	—
284	C₄×C₄⋊C₄	—	89	1	no	—
285	C₄×C₄⋊C₄	—	89	1	no	—
286	C₄×C₄⋊C₄	—	89	2	no	—
287	C₄×C₄⋊C₄	—	89	2	no	—
288	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
289	C₄³	—	89	1	no	—
290	C₄³	—	89	1	no	—
291	C₄³	—	89	1	no	—
292	#336	—	89	1	no	—
293	#336	—	89	1	no	—
294	#336	—	89	1	no	—
295	#336	—	89	1	no	—
296	#336	C₂×D₈₉	1	1	yes	characteristic
297	#336	C₂×D₈₉	1	1	yes	characteristic
298	C₂²×Q₈	—	89	1	no	—
299	C₂²×C₈	—	89	1	no	—
300	C₂²×C₈	—	89	1	no	—
301	C₂²×C₈	—	89	1	no	—
302	C₂²×C₈	—	89	1	no	—
303	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₄×Q₈	—	89	4	no	—
308	C₄×Q₈	—	89	4	no	—
309	C₄×Q₈	—	178	8	no	—
310	C₂×C₄⋊C₄	—	89	2	no	—
311	C₂×C₄⋊C₄	—	89	1	no	—
312	C₂×C₄⋊C₄	—	89	1	no	—
313	C₂×C₄⋊C₄	—	89	1	no	—
314	C₂×C₄⋊C₄	—	89	2	no	—
315	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
316	C₂×C₄²	—	89	1	no	—
317	C₂×C₄²	—	89	1	no	—
318	C₂×C₄²	—	89	1	no	—
319	C₂×C₄²	—	89	2	no	—
320	C₂×C₄²	—	89	2	no	—
321	C₂×C₄²	—	89	2	no	—
322	C₂×C₄²	—	89	2	no	—
323	C₂×C₄²	—	89	2	no	—
324	C₂×C₄²	—	89	2	no	—
325	C₂×C₄²	—	89	1	no	—
326	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
329	C₄⋊C₈	—	89	4	no	—
330	C₄⋊C₈	—	89	4	no	—
331	C₄⋊C₈	—	89	4	no	—
332	C₄⋊C₈	—	89	4	no	—
333	C₄⋊C₈	—	89	4	no	—
334	C₄⋊C₈	C₄×D₈₉	1	4	yes	—
335	#97	—	2	2	no	—
336	#97	—	89	4	no	—
337	#97	—	89	4	no	—
338	#97	—	89	4	no	—
339	#97	—	89	4	no	—
340	#97	—	178	2	no	—
341	#97	—	178	2	no	—
342	#97	—	178	2	no	—
343	#97	—	178	2	no	—
344	#97	C₄×D₈₉	1	4	yes	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	89	4	no	—
347	C₄×C₈	—	89	4	no	—
348	C₄×C₈	—	178	2	no	—
349	C₄×C₈	—	178	2	no	—
350	C₄×C₈	—	178	2	no	—
351	#95	—	89	2	no	—
352	#95	—	89	2	no	—
353	#95	C₄×D₈₉	1	2	yes	—
354	C₂×Q₈	—	89	4	no	—
355	C₂×Q₈	—	178	4	no	—
356	C₂²×C₄	—	89	1	no	—
357	C₂²×C₄	—	89	1	no	—
358	C₂²×C₄	—	89	1	no	—
359	C₂²×C₄	—	89	2	no	—
360	C₂²×C₄	—	89	2	no	—
361	C₂²×C₄	—	89	1	no	—
362	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
363	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
364	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	89	2	no	—
374	C₂×C₈	—	89	2	no	—
375	C₂×C₈	—	89	2	no	—
376	C₂×C₈	—	89	2	no	—
377	C₂×C₈	—	89	2	no	—
378	C₂×C₈	—	89	2	no	—
379	C₂×C₈	—	178	1	no	—
380	C₂×C₈	—	178	1	no	—
381	C₂×C₈	—	178	1	no	—
382	C₂×C₈	—	178	1	no	—
383	C₂×C₈	—	178	1	no	—
384	C₂×C₈	—	178	1	no	—
385	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
386	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
387	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
388	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
389	C₂×C₈	Q₈×D₈₉	1	2	yes	—
390	C₂×C₈	#13083573	1	2	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	89	8	no	—
393	C₄⋊C₄	—	89	4	no	—
394	C₄⋊C₄	—	89	4	no	—
395	C₄⋊C₄	—	89	4	no	—
396	C₄⋊C₄	—	178	4	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	89	2	no	—
402	C₄²	—	89	2	no	—
403	C₄²	—	89	2	no	—
404	C₄²	—	89	2	no	—
405	C₄²	—	89	2	no	—
406	C₄²	—	89	2	no	—
407	C₄²	—	356	2	no	—
408	C₄²	—	356	2	no	—
409	C₄²	—	356	2	no	—
410	C₄²	—	178	4	no	—
411	C₄²	—	178	4	no	—
412	C₄²	—	178	4	no	—
413	C₄²	—	178	1	no	—
414	C₄²	—	178	1	no	—
415	C₄²	C₂×C₄×D₈₉	1	2	yes	—
416	C₄²	C₂×C₄×D₈₉	1	2	yes	—
417	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
418	Q₈	—	178	8	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	89	2	no	—
427	C₂×C₄	—	89	4	no	—
428	C₂×C₄	—	89	2	no	—
429	C₂×C₄	—	89	2	no	—
430	C₂×C₄	—	89	2	no	—
431	C₂×C₄	—	89	4	no	—
432	C₂×C₄	—	89	4	no	—
433	C₂×C₄	—	178	2	no	—
434	C₂×C₄	—	178	2	no	—
435	C₂×C₄	—	178	2	no	—
436	C₂×C₄	—	178	2	no	—
437	C₂×C₄	—	178	2	no	—
438	C₂×C₄	—	178	2	no	—
439	C₂×C₄	—	178	2	no	—
440	C₂×C₄	C₄²×D₈₉	1	2	yes	—
441	C₂×C₄	C₄²×D₈₉	1	2	yes	—
442	C₂×C₄	M₁₆×D₈₉	1	4	yes	—
443	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
446	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
447	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	89	4	no	—
453	C₈	—	178	2	no	—
454	C₈	—	178	2	no	—
455	C₈	—	178	2	no	—
456	C₈	#15667977	1	4	yes	complemented
457	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
458	C₂²	C₄×Q₈×D₈₉	1	1	yes	characteristic
459	C₂²	C₄×#13083573	1	1	yes	characteristic
460	C₂²	C₂×M₁₆×D₈₉	1	2	yes	—
461	C₂²	#19152363	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	89	4	no	—
467	C₄	—	178	2	no	—
468	C₄	—	178	2	no	—
469	C₄	—	178	2	no	—
470	C₄	—	178	4	no	—
471	C₄	—	178	4	no	—
472	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
473	C₄	C₂×#15667977	1	1	yes	characteristic
474	C₄	C₄×#13083573	1	1	yes	characteristic
475	C₄	#19152066	1	1	yes	characteristic
476	C₂	C₄×#15667977	1	1	yes	characteristic
477	C₂	C₄×M₁₆×D₈₉	1	1	yes	characteristic
478	C₂	#26028679	1	1	yes	characteristic
479	C₂	#26029204	1	2	yes	—
480	C₂	#26029262	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#1771	C₂
socle, prime radical	C₂³×C₈₉	C₂³×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1771	D₈₉
hypocenter	C₈₉	#20520
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
18. #19151727	C₄	semidirect
19. #19151726	C₄	semidirect
92. #15667922	Q₈	semidirect
211. C₈×C₈₉	C₄×Q₈	semidirect
215. #10623494	C₄×Q₈	semidirect
256. C₈₉	#20520	semidirect
456. C₈	#15667977	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151727	2
C₂×#19151726	2
C₄×#15667977	2
#26020128	2
#26020127	2
#26020125	2
C₈×#13083553	2
#26020113	2
#26020107	2
#26020104	2
C₄×#15667922	2
#97×Dic₈₉	2
C₈₉×#1771	2
#20520	89