Subgroups — #36460480

Order 22784.

906 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151468	C₂	1	1	yes	maximal, characteristic
2	#26022608	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151366	C₂	1	1	yes	maximal, characteristic
4	#26019973	C₂	1	1	yes	maximal, characteristic
5	#26019972	C₂	1	1	yes	maximal, characteristic
6	C₂×#19151358	C₂	1	1	yes	maximal, characteristic
7	C₂×#339×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#13083558	C₂²	1	1	yes	characteristic
9	C₂×#15667971	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₈₉	—	2	2	no	—
11	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
13	#19151468	—	2	2	no	—
14	#19151468	C₄	1	4	yes	complemented
15	C₄⋊C₄×Dic₈₉	—	2	2	no	—
16	C₄×C₄⋊Dic₈₉	—	2	2	no	—
17	C₂²⋊C₄×Dic₈₉	—	2	2	no	—
18	#19151366	—	2	2	no	—
19	#19151361	—	2	2	no	—
20	#19151360	—	2	2	no	—
21	#19151358	C₄	1	4	yes	complemented
22	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
25	#339×C₈₉	C₄	1	4	yes	complemented
26	C₂³×Dic₈₉	—	2	1	no	—
27	C₂³×Dic₈₉	D₄	1	2	yes	—
28	C₂×#13083558	—	2	1	no	—
29	C₂×#13083558	—	2	1	no	—
30	C₂×#13083558	—	2	1	no	—
31	C₂×#13083558	—	2	1	no	—
32	C₂×#13083558	—	2	1	no	—
33	C₂×#13083558	C₂×C₄	1	2	yes	—
34	C₂²×#10623494	—	2	1	no	—
35	#15667971	—	2	1	no	—
36	#15667971	—	2	1	no	—
37	#15667971	C₂×C₄	1	2	yes	—
38	#15667971	Q₈	1	2	yes	—
39	C₂×C₄⋊Dic₈₉	—	2	8	no	—
40	C₂×C₄⋊Dic₈₉	—	2	1	no	—
41	C₂×C₄⋊Dic₈₉	—	2	1	no	—
42	C₂×C₄⋊Dic₈₉	—	2	1	no	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	—	2	1	no	—
45	C₂×C₄⋊Dic₈₉	—	2	1	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄⋊Dic₈₉	—	2	1	no	—
49	C₂×C₄⋊Dic₈₉	—	4	8	no	—
50	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
53	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
54	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
55	C₂×C₄×Dic₈₉	—	2	4	no	—
56	C₂×C₄×Dic₈₉	—	2	1	no	—
57	#15667919	—	2	4	no	—
58	C₂³×C₄×C₈₉	—	2	1	no	—
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₈₉	—	2	1	no	—
61	C₂×M₁₆×C₈₉	—	2	1	no	—
62	C₂×M₁₆×C₈₉	—	2	1	no	—
63	C₂×M₁₆×C₈₉	—	2	1	no	—
64	C₂×M₁₆×C₈₉	—	2	1	no	—
65	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₈₉	—	2	1	no	—
67	#117×C₈₉	—	2	1	no	—
68	#117×C₈₉	—	2	1	no	—
69	#117×C₈₉	C₂×C₄	1	2	yes	—
70	#117×C₈₉	Q₈	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	1	no	—
75	C₂×C₄²×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	—	2	1	no	—
77	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
80	C₂²×Dic₈₉	—	2	2	no	—
81	C₂²×Dic₈₉	—	2	2	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂²×Dic₈₉	—	2	2	no	—
84	C₂²×Dic₈₉	—	4	4	no	—
85	C₂²×Dic₈₉	—	4	4	no	—
86	C₂²×Dic₈₉	—	4	1	no	—
87	C₂²×Dic₈₉	—	4	1	no	—
88	C₂²×Dic₈₉	C₂²⋊C₄	1	4	yes	—
89	#13083558	—	2	2	no	—
90	#13083558	—	2	2	no	—
91	#13083558	—	4	1	no	—
92	#13083558	—	4	1	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	4	1	no	—
95	C₂×#10623494	—	4	1	no	—
96	C₄⋊Dic₈₉	—	2	2	no	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	C₄⋊Dic₈₉	—	2	2	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	—	2	2	no	—
102	C₄⋊Dic₈₉	—	2	2	no	—
103	C₄⋊Dic₈₉	—	4	16	no	—
104	C₄⋊Dic₈₉	—	4	1	no	—
105	C₄⋊Dic₈₉	—	4	1	no	—
106	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	complemented
107	C₂²⋊Dic₈₉	—	2	2	no	—
108	C₂²⋊Dic₈₉	—	2	2	no	—
109	C₄×Dic₈₉	—	2	2	no	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₄×Dic₈₉	—	8	4	no	—
112	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	—	2	4	no	—
114	C₂²×C₄×C₈₉	—	2	4	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	2	2	no	—
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	M₁₆×C₈₉	—	2	2	no	—
134	M₁₆×C₈₉	—	2	2	no	—
135	M₁₆×C₈₉	—	4	1	no	—
136	M₁₆×C₈₉	—	4	1	no	—
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₂×C₈×C₈₉	—	4	1	no	—
139	C₂×C₈×C₈₉	—	4	1	no	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	complemented
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₂²⋊C₄×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	C₄²	1	4	yes	complemented
150	C₂³×C₈₉	—	2	2	no	—
151	C₂³×C₈₉	—	2	2	no	—
152	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₂³×C₈₉	#120	1	1	yes	characteristic
156	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂³×C₈₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₈₉	—	2	8	no	—
160	C₂×C₄×C₈₉	—	2	8	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
190	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
191	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
192	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
193	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
195	C₂×Dic₈₉	—	2	4	no	—
196	C₂×Dic₈₉	—	2	4	no	—
197	C₂×Dic₈₉	—	4	2	no	—
198	C₂×Dic₈₉	—	4	4	no	—
199	C₂×Dic₈₉	—	4	2	no	—
200	C₂×Dic₈₉	—	4	4	no	—
201	C₂×Dic₈₉	—	4	4	no	—
202	C₂×Dic₈₉	—	4	2	no	—
203	C₂×Dic₈₉	—	8	2	no	—
204	C₂×Dic₈₉	—	8	2	no	—
205	C₂×Dic₈₉	—	8	2	no	—
206	C₈×C₈₉	—	4	2	no	—
207	#10623494	—	4	2	no	—
208	C₂²×C₈₉	—	2	2	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	2	2	no	—
211	C₂²×C₈₉	—	2	2	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	2	1	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₈₉	#385	1	1	yes	characteristic
218	C₂²×C₈₉	#385	1	1	yes	characteristic
219	C₂²×C₈₉	#386	1	1	yes	characteristic
220	C₂²×C₈₉	#387	1	1	yes	characteristic
221	C₂²×C₈₉	#387	1	1	yes	characteristic
222	C₂²×C₈₉	#391	1	1	yes	characteristic
223	C₂²×C₈₉	#453	1	2	yes	—
224	C₂²×C₈₉	#456	1	2	yes	—
225	C₄×C₈₉	—	2	8	no	—
226	C₄×C₈₉	—	4	4	no	—
227	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₄×C₈₉	#387	1	1	yes	characteristic
230	C₄×C₈₉	#387	1	1	yes	characteristic
231	C₄×C₈₉	#388	1	1	yes	characteristic
232	C₄×C₈₉	#388	1	1	yes	characteristic
233	C₄×C₈₉	#389	1	1	yes	characteristic
234	C₄×C₈₉	#389	1	1	yes	characteristic
235	Dic₈₉	—	4	4	no	—
236	Dic₈₉	—	4	4	no	—
237	Dic₈₉	—	8	2	no	—
238	#10891	—	89	1	no	maximal, Sylow
239	C₂×C₈₉	—	2	1	no	—
240	C₂×C₈₉	—	2	1	no	—
241	C₂×C₈₉	—	2	1	no	—
242	C₂×C₈₉	—	2	1	no	—
243	C₂×C₈₉	#1436	1	1	yes	characteristic
244	C₂×C₈₉	#1859	1	2	yes	—
245	C₂×C₈₉	#1859	1	2	yes	—
246	C₂×C₈₉	#1886	1	1	yes	characteristic
247	C₂×C₈₉	#1887	1	1	yes	characteristic
248	C₂×#384	—	89	1	no	—
249	#2274	—	89	1	no	—
250	C₂×#343	—	89	1	no	—
251	#1736	—	89	1	no	—
252	#1736	—	89	1	no	—
253	C₂×#339	—	89	1	no	—
254	C₂×#339	D₈₉	1	1	yes	characteristic
255	C₈₉	#10891	1	1	yes	characteristic, complemented, Sylow
256	C₂²×M₁₆	—	89	1	no	—
257	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
258	C₂×#117	—	89	1	no	—
259	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	—	89	1	no	—
261	C₂²×C₄⋊C₄	—	89	1	no	—
262	C₂²×C₄⋊C₄	—	178	2	no	—
263	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
264	#384	—	89	4	no	—
265	#384	—	178	2	no	—
266	C₄×C₄⋊C₄	—	178	2	no	—
267	C₄×C₄⋊C₄	—	178	2	no	—
268	C₄×C₂²⋊C₄	—	178	2	no	—
269	#343	—	178	2	no	—
270	#340	—	178	2	no	—
271	#340	—	178	2	no	—
272	#339	—	89	4	no	—
273	#339	Dic₈₉	1	4	yes	complemented
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	89	2	no	—
276	C₂³×C₄	—	178	1	no	—
277	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	89	2	no	—
284	C₂×M₁₆	—	178	1	no	—
285	C₂×M₁₆	—	178	1	no	—
286	C₂×M₁₆	—	178	1	no	—
287	C₂×M₁₆	—	178	1	no	—
288	C₂×M₁₆	—	178	1	no	—
289	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	178	1	no	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	89	2	no	—
295	#117	—	89	2	no	—
296	#117	—	178	1	no	—
297	#117	—	178	1	no	—
298	#117	Dic₁₇₈	1	2	yes	—
299	#117	C₂×Dic₈₉	1	2	yes	—
300	C₂×C₄⋊C₄	—	89	2	no	—
301	C₂×C₄⋊C₄	—	89	2	no	—
302	C₂×C₄⋊C₄	—	89	2	no	—
303	C₂×C₄⋊C₄	—	89	2	no	—
304	C₂×C₄⋊C₄	—	356	8	no	—
305	C₂×C₄⋊C₄	—	178	8	no	—
306	C₂×C₄⋊C₄	—	178	1	no	—
307	C₂×C₄⋊C₄	—	178	1	no	—
308	C₂×C₄⋊C₄	—	178	1	no	—
309	C₂×C₄⋊C₄	—	178	1	no	—
310	C₂×C₄⋊C₄	—	178	1	no	—
311	C₂×C₄⋊C₄	—	178	1	no	—
312	C₂×C₄⋊C₄	—	178	1	no	—
313	C₂×C₄⋊C₄	—	178	1	no	—
314	C₂×C₄⋊C₄	—	178	1	no	—
315	C₂×C₄⋊C₄	D₃₅₆	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	178	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	178	1	no	—
323	C₂×C₄²	—	178	4	no	—
324	C₂×C₄²	C₄×D₈₉	1	2	yes	—
325	C₂×C₄²	C₄×D₈₉	1	2	yes	—
326	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
327	#95	—	178	4	no	—
328	C₂⁴	D₄×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	89	4	no	—
336	C₂²×C₄	—	356	4	no	—
337	C₂²×C₄	—	356	4	no	—
338	C₂²×C₄	—	356	1	no	—
339	C₂²×C₄	—	356	1	no	—
340	C₂²×C₄	—	178	2	no	—
341	C₂²×C₄	—	178	2	no	—
342	C₂²×C₄	—	178	2	no	—
343	C₂²×C₄	—	178	2	no	—
344	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
350	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
352	C₂²×C₄	#13083573	1	1	yes	characteristic
353	C₂²×C₄	#13083573	1	1	yes	characteristic
354	C₂²×C₄	#13083573	1	1	yes	characteristic
355	C₂²×C₄	#13083574	1	1	yes	characteristic
356	C₂²×C₄	#13083574	1	1	yes	characteristic
357	C₂²×C₄	#13083575	1	1	yes	characteristic
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	4	1	no	—
361	M₁₆	—	4	1	no	—
362	M₁₆	—	356	1	no	—
363	M₁₆	—	356	1	no	—
364	M₁₆	—	178	2	no	—
365	M₁₆	—	178	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	356	1	no	—
370	C₂×C₈	—	356	1	no	—
371	C₂×C₈	—	178	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	89	4	no	—
374	C₄⋊C₄	—	356	16	no	—
375	C₄⋊C₄	—	356	1	no	—
376	C₄⋊C₄	—	356	1	no	—
377	C₄⋊C₄	—	178	2	no	—
378	C₄⋊C₄	—	178	2	no	—
379	C₄⋊C₄	—	178	2	no	—
380	C₄⋊C₄	—	178	2	no	—
381	C₄⋊C₄	—	178	2	no	—
382	C₄⋊C₄	—	178	2	no	—
383	C₄⋊C₄	—	178	2	no	—
384	C₄⋊C₄	C₄⋊Dic₈₉	1	4	yes	complemented
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	178	2	no	—
388	C₂²⋊C₄	—	178	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	178	2	no	—
395	C₄²	—	178	2	no	—
396	C₄²	—	712	4	no	—
397	C₄²	C₄×Dic₈₉	1	4	yes	complemented
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
401	C₂³	#15667972	1	1	yes	characteristic
402	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
403	C₂³	#15667982	1	1	yes	characteristic
404	C₂³	#15667989	1	1	yes	characteristic
405	C₂³	#15667990	1	1	yes	characteristic
406	C₂³	#15667997	1	1	yes	characteristic
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	356	4	no	—
417	C₂×C₄	—	356	2	no	—
418	C₂×C₄	—	356	4	no	—
419	C₂×C₄	—	356	4	no	—
420	C₂×C₄	—	356	2	no	—
421	C₂×C₄	—	178	4	no	—
422	C₂×C₄	—	178	4	no	—
423	C₂×C₄	—	712	2	no	—
424	C₂×C₄	—	712	2	no	—
425	C₂×C₄	—	712	2	no	—
426	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
429	C₂×C₄	#15667968	1	1	yes	characteristic
430	C₂×C₄	#15667970	1	1	yes	characteristic
431	C₂×C₄	#15667971	1	1	yes	characteristic
432	C₂×C₄	#15667972	1	1	yes	characteristic
433	C₂×C₄	#15667974	1	1	yes	characteristic
434	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
435	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
436	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
437	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
438	C₂×C₄	#15667977	1	1	yes	characteristic
439	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
440	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
441	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
442	C₂×C₄	#15667985	1	1	yes	characteristic
443	C₂×C₄	#15667987	1	1	yes	characteristic
444	C₂×C₄	#15667989	1	1	yes	characteristic
445	C₂×C₄	#15667992	1	1	yes	characteristic
446	C₂×C₄	#15667994	1	1	yes	characteristic
447	C₂×C₄	#15667996	1	1	yes	characteristic
448	C₂×C₄	#15667998	1	1	yes	characteristic
449	C₂×C₄	#15668002	1	1	yes	characteristic
450	C₂×C₄	#15668003	1	1	yes	characteristic
451	C₂×C₄	#15668005	1	1	yes	characteristic
452	C₂×C₄	#15668007	1	1	yes	characteristic
453	C₂×C₄	#15668011	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	356	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
465	C₂²	#19151472	1	1	yes	characteristic
466	C₂²	#19151473	1	1	yes	characteristic
467	C₂²	#19151476	1	1	yes	characteristic
468	C₂²	#19151484	1	1	yes	characteristic
469	C₂²	#19151485	1	1	yes	characteristic
470	C₂²	#19151502	1	1	yes	characteristic
471	C₂²	#19151767	1	2	yes	—
472	C₂²	#19151782	1	2	yes	—
473	C₄	—	2	8	no	—
474	C₄	—	4	4	no	—
475	C₄	—	356	4	no	—
476	C₄	—	356	4	no	—
477	C₄	—	712	2	no	—
478	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
479	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
480	C₄	#19151481	1	1	yes	characteristic
481	C₄	#19151483	1	1	yes	characteristic
482	C₄	#19151490	1	1	yes	characteristic
483	C₄	#19151491	1	1	yes	characteristic
484	C₄	#19151495	1	1	yes	characteristic
485	C₄	#19151497	1	1	yes	characteristic
486	C₂	—	2	1	no	—
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	#26018486	1	1	yes	characteristic
491	C₂	#26020479	1	2	yes	—
492	C₂	#26020480	1	2	yes	—
493	C₂	#26020644	1	1	yes	characteristic
494	C₂	#26020649	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#339×C₈₉	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#339	D₈₉
hypocenter	C₈₉	#10891
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
14. #19151468	C₄	semidirect
21. #19151358	C₄	semidirect
25. #339×C₈₉	C₄	semidirect
106. C₄⋊Dic₈₉	C₄⋊C₄	semidirect
141. C₄⋊C₄×C₈₉	C₄⋊C₄	semidirect
149. C₄²×C₈₉	C₄²	semidirect
255. C₈₉	#10891	semidirect
273. #339	Dic₈₉	semidirect
384. C₄⋊C₄	C₄⋊Dic₈₉	semidirect
397. C₄²	C₄×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151468	2
#26022608	2
C₂×#19151366	2
#26019973	2
#26019972	2
C₂×#19151358	2
C₂×#339×C₈₉	2
#10891	89