Subgroups — #36462339

Order 22784.

958 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151496	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151468	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151361	C₂	1	2	yes	maximal
4	C₂×#19151361	C₂	1	2	yes	maximal
5	C₂×#336×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₈₉	—	2	1	no	—
7	C₂²×C₄⋊Dic₈₉	—	2	1	no	—
8	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₈₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
11	C₂²×#13083553	—	2	1	no	—
12	#19151496	—	2	2	no	—
13	#19151496	C₄	1	4	yes	complemented
14	#19151468	—	2	4	no	—
15	C₂×#15667919	—	2	1	no	—
16	#19151361	—	2	4	no	—
17	#19151361	—	2	4	no	—
18	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
20	#336×C₈₉	—	2	2	no	—
21	C₂³×Dic₈₉	—	2	1	no	—
22	C₂³×Dic₈₉	—	2	1	no	—
23	C₂³×Dic₈₉	—	2	2	no	—
24	C₂×C₄⋊Dic₈₉	—	2	4	no	—
25	C₂×C₄⋊Dic₈₉	—	2	4	no	—
26	C₂×C₄⋊Dic₈₉	—	2	1	no	—
27	C₂×C₄⋊Dic₈₉	—	2	2	no	—
28	C₂×C₄⋊Dic₈₉	—	2	2	no	—
29	C₂×C₄⋊Dic₈₉	—	2	2	no	—
30	C₂×C₄⋊Dic₈₉	—	2	1	no	—
31	C₂×C₄⋊Dic₈₉	—	2	1	no	—
32	C₂×C₄⋊Dic₈₉	—	2	1	no	—
33	C₂×C₄⋊Dic₈₉	—	2	2	no	—
34	C₂×C₄⋊Dic₈₉	—	2	2	no	—
35	C₂×C₄⋊Dic₈₉	—	2	2	no	—
36	C₂×C₄⋊Dic₈₉	—	2	2	no	—
37	C₂×C₄⋊Dic₈₉	—	4	2	no	—
38	C₂×C₄⋊Dic₈₉	—	4	2	no	—
39	C₂×C₄⋊Dic₈₉	—	4	2	no	—
40	C₂×C₄⋊Dic₈₉	—	4	2	no	—
41	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊Dic₈₉	D₄	1	4	yes	—
44	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₈₉	Q₈	1	2	yes	—
46	C₂×#13083553	—	2	4	no	—
47	C₂×#13083553	—	4	2	no	—
48	C₂×#13083553	—	4	2	no	—
49	#15667919	—	2	4	no	—
50	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₈₉	—	2	2	no	—
54	C₂²×C₈×C₈₉	—	2	2	no	—
55	C₂²×C₈×C₈₉	—	2	2	no	—
56	C₂²×C₈×C₈₉	—	2	2	no	—
57	C₂²×C₈×C₈₉	—	2	2	no	—
58	C₂²×C₈×C₈₉	—	2	2	no	—
59	C₂²×C₈×C₈₉	Q₈	1	4	yes	—
60	C₂×C₄²×C₈₉	—	2	2	no	—
61	C₂×C₄²×C₈₉	—	2	2	no	—
62	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₈₉	D₄	1	2	yes	—
64	C₂²×Dic₈₉	—	2	2	no	—
65	C₂²×Dic₈₉	—	2	2	no	—
66	C₂²×Dic₈₉	—	2	2	no	—
67	C₂²×Dic₈₉	—	2	2	no	—
68	C₂²×Dic₈₉	—	2	4	no	—
69	C₂²×Dic₈₉	—	4	1	no	—
70	C₂²×Dic₈₉	—	4	1	no	—
71	C₂²×Dic₈₉	—	4	1	no	—
72	C₂²×Dic₈₉	—	4	1	no	—
73	C₂²×Dic₈₉	—	4	1	no	—
74	C₂²×Dic₈₉	—	4	2	no	—
75	C₂²×Dic₈₉	—	4	1	no	—
76	C₂²×Dic₈₉	—	4	2	no	—
77	C₂²×Dic₈₉	—	4	1	no	—
78	C₂²×Dic₈₉	—	4	2	no	—
79	C₂²×Dic₈₉	—	4	1	no	—
80	C₂²×Dic₈₉	—	4	2	no	—
81	C₂²×Dic₈₉	—	4	1	no	—
82	C₂²×Dic₈₉	—	4	2	no	—
83	C₂²×Dic₈₉	—	4	2	no	—
84	C₂²×Dic₈₉	—	4	1	no	—
85	C₄⋊Dic₈₉	—	2	2	no	—
86	C₄⋊Dic₈₉	—	2	2	no	—
87	C₄⋊Dic₈₉	—	2	2	no	—
88	C₄⋊Dic₈₉	—	2	4	no	—
89	C₄⋊Dic₈₉	—	2	4	no	—
90	C₄⋊Dic₈₉	—	2	4	no	—
91	C₄⋊Dic₈₉	—	4	8	no	—
92	C₄⋊Dic₈₉	—	4	8	no	—
93	C₄⋊Dic₈₉	—	4	2	no	—
94	C₄⋊Dic₈₉	—	4	2	no	—
95	C₄⋊Dic₈₉	—	4	2	no	—
96	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	complemented
97	#13083553	—	4	8	no	—
98	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	2	1	no	—
101	C₂²×C₄×C₈₉	—	2	1	no	—
102	C₂²×C₄×C₈₉	—	2	1	no	—
103	C₂²×C₄×C₈₉	—	2	1	no	—
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	C₂²×C₄×C₈₉	—	2	1	no	—
106	C₂²×C₄×C₈₉	—	2	1	no	—
107	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₈₉	D₈	1	2	yes	—
110	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
111	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
112	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	#41	1	2	yes	—
122	C₂²×C₄×C₈₉	#41	1	2	yes	—
123	C₂×C₈×C₈₉	—	2	4	no	—
124	C₂×C₈×C₈₉	—	2	4	no	—
125	C₂×C₈×C₈₉	—	2	4	no	—
126	C₂×C₈×C₈₉	—	4	2	no	—
127	C₂×C₈×C₈₉	—	4	2	no	—
128	C₂×C₈×C₈₉	—	4	2	no	—
129	C₂×C₈×C₈₉	—	4	2	no	—
130	C₄²×C₈₉	—	2	4	no	—
131	C₄²×C₈₉	—	2	4	no	—
132	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₈₉	#120	1	1	yes	characteristic
134	C₂³×C₈₉	#121	1	1	yes	characteristic
135	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
136	C₂³×C₈₉	#123	1	1	yes	characteristic
137	C₂³×C₈₉	#124	1	1	yes	characteristic
138	C₂³×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
139	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
140	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
143	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂³×C₈₉	#137	1	1	yes	characteristic
146	C₂³×C₈₉	#137	1	1	yes	characteristic
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	#102	1	4	yes	—
160	C₂×C₄×C₈₉	#103	1	4	yes	—
161	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	2	yes	—
167	C₂×C₄×C₈₉	#121	1	2	yes	—
168	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₈₉	#123	1	2	yes	—
173	C₂×C₄×C₈₉	#125	1	2	yes	—
174	C₂×C₄×C₈₉	#125	1	2	yes	—
175	C₂×C₄×C₈₉	#126	1	2	yes	—
176	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
177	C₂×Dic₈₉	—	2	4	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	4	2	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	C₂×Dic₈₉	—	4	2	no	—
183	C₂×Dic₈₉	—	4	2	no	—
184	C₂×Dic₈₉	—	4	2	no	—
185	C₂×Dic₈₉	—	4	4	no	—
186	C₂×Dic₈₉	—	4	2	no	—
187	C₂×Dic₈₉	—	4	2	no	—
188	C₂×Dic₈₉	—	4	4	no	—
189	C₂×Dic₈₉	—	4	4	no	—
190	C₂×Dic₈₉	—	8	1	no	—
191	C₂×Dic₈₉	—	8	1	no	—
192	C₂×Dic₈₉	—	8	2	no	—
193	C₂×Dic₈₉	—	8	2	no	—
194	C₂×Dic₈₉	—	8	1	no	—
195	C₂×Dic₈₉	—	8	1	no	—
196	C₂×Dic₈₉	—	8	2	no	—
197	C₂×Dic₈₉	—	8	2	no	—
198	C₈×C₈₉	—	4	4	no	—
199	C₂²×C₈₉	#380	1	1	yes	characteristic
200	C₂²×C₈₉	#386	1	1	yes	characteristic
201	C₂²×C₈₉	#391	1	1	yes	characteristic
202	C₂²×C₈₉	#394	1	1	yes	characteristic
203	C₂²×C₈₉	#395	1	1	yes	characteristic
204	C₂²×C₈₉	#398	1	1	yes	characteristic
205	C₂²×C₈₉	#400	1	1	yes	characteristic
206	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
207	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
208	C₂²×C₈₉	#417	1	1	yes	characteristic
209	C₂²×C₈₉	#417	1	1	yes	characteristic
210	C₂²×C₈₉	#447	1	1	yes	characteristic
211	C₂²×C₈₉	#448	1	1	yes	characteristic
212	C₂²×C₈₉	#450	1	1	yes	characteristic
213	C₂²×C₈₉	#451	1	1	yes	characteristic
214	C₂²×C₈₉	#459	1	1	yes	characteristic
215	C₂²×C₈₉	#460	1	1	yes	characteristic
216	C₂²×C₈₉	#461	1	1	yes	characteristic
217	C₂²×C₈₉	#462	1	1	yes	characteristic
218	C₂²×C₈₉	#474	1	1	yes	characteristic
219	C₂²×C₈₉	#475	1	1	yes	characteristic
220	C₂²×C₈₉	#476	1	1	yes	characteristic
221	C₂²×C₈₉	#477	1	1	yes	characteristic
222	C₂²×C₈₉	#480	1	1	yes	characteristic
223	C₂²×C₈₉	#481	1	1	yes	characteristic
224	C₂²×C₈₉	#483	1	1	yes	characteristic
225	C₂²×C₈₉	#484	1	1	yes	characteristic
226	C₂²×C₈₉	#486	1	1	yes	characteristic
227	C₂²×C₈₉	#487	1	1	yes	characteristic
228	C₂²×C₈₉	#490	1	1	yes	characteristic
229	C₂²×C₈₉	#491	1	1	yes	characteristic
230	C₂²×C₈₉	#498	1	1	yes	characteristic
231	C₂²×C₈₉	#500	1	1	yes	characteristic
232	C₂²×C₈₉	#501	1	1	yes	characteristic
233	C₂²×C₈₉	#501	1	1	yes	characteristic
234	C₄×C₈₉	—	2	4	no	—
235	C₄×C₈₉	—	2	4	no	—
236	C₄×C₈₉	#387	1	2	yes	—
237	C₄×C₈₉	#389	1	2	yes	—
238	C₄×C₈₉	#396	1	2	yes	—
239	C₄×C₈₉	#398	1	2	yes	—
240	Dic₈₉	—	4	4	no	—
241	Dic₈₉	—	8	2	no	—
242	Dic₈₉	—	8	4	no	—
243	#11207	—	89	1	no	maximal, Sylow
244	C₂×C₈₉	#1441	1	1	yes	characteristic
245	C₂×C₈₉	#1802	1	1	yes	characteristic
246	C₂×C₈₉	#1803	1	1	yes	characteristic
247	C₂×C₈₉	#1872	1	1	yes	characteristic
248	C₂×C₈₉	#1874	1	1	yes	characteristic
249	C₂×C₈₉	#1990	1	1	yes	characteristic
250	C₂×C₈₉	#1992	1	1	yes	characteristic
251	C₂×C₈₉	#2041	1	1	yes	characteristic
252	C₂×C₈₉	#2043	1	1	yes	characteristic
253	C₂×C₈₉	#2057	1	1	yes	characteristic
254	C₂×C₈₉	#2058	1	1	yes	characteristic
255	C₂×C₈₉	#2083	1	1	yes	characteristic
256	C₂×C₈₉	#2084	1	1	yes	characteristic
257	C₂×C₈₉	#2099	1	1	yes	characteristic
258	C₂×C₈₉	#2100	1	1	yes	characteristic
259	C₂×#389	—	89	1	no	—
260	C₂×#384	—	89	1	no	—
261	C₂×#340	—	89	2	no	—
262	C₂×#340	—	89	2	no	—
263	C₂×#336	D₈₉	1	1	yes	characteristic
264	C₈₉	#11207	1	1	yes	characteristic, complemented, Sylow
265	C₂³×C₈	C₂×D₈₉	1	2	yes	—
266	C₂²×C₄⋊C₄	—	89	1	no	—
267	C₂²×C₄⋊C₄	—	89	2	no	—
268	C₂²×C₄⋊C₄	—	89	1	no	—
269	C₂²×C₄⋊C₄	—	178	1	no	—
270	C₂²×C₄⋊C₄	—	178	1	no	—
271	C₂²×C₄⋊C₄	—	178	1	no	—
272	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
273	#389	—	89	4	no	—
274	#389	—	178	2	no	—
275	#384	—	178	4	no	—
276	C₂×#95	—	178	1	no	—
277	#340	—	178	4	no	—
278	#340	—	178	4	no	—
279	#336	—	2	2	no	—
280	C₂³×C₄	—	178	2	no	—
281	C₂³×C₄	—	178	1	no	—
282	C₂³×C₄	—	178	1	no	—
283	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
284	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	Dic₁₇₈	1	4	yes	—
293	C₂×C₄⋊C₄	—	89	2	no	—
294	C₂×C₄⋊C₄	—	89	2	no	—
295	C₂×C₄⋊C₄	—	89	2	no	—
296	C₂×C₄⋊C₄	—	89	2	no	—
297	C₂×C₄⋊C₄	—	89	4	no	—
298	C₂×C₄⋊C₄	—	356	2	no	—
299	C₂×C₄⋊C₄	—	356	2	no	—
300	C₂×C₄⋊C₄	—	356	2	no	—
301	C₂×C₄⋊C₄	—	356	2	no	—
302	C₂×C₄⋊C₄	—	356	2	no	—
303	C₂×C₄⋊C₄	—	356	2	no	—
304	C₂×C₄⋊C₄	—	178	4	no	—
305	C₂×C₄⋊C₄	—	178	4	no	—
306	C₂×C₄⋊C₄	—	178	4	no	—
307	C₂×C₄⋊C₄	—	178	2	no	—
308	C₂×C₄⋊C₄	—	178	1	no	—
309	C₂×C₄⋊C₄	—	178	2	no	—
310	C₂×C₄⋊C₄	—	178	2	no	—
311	C₂×C₄⋊C₄	—	178	2	no	—
312	C₂×C₄⋊C₄	—	178	2	no	—
313	C₂×C₄⋊C₄	—	178	2	no	—
314	C₂×C₄⋊C₄	—	178	2	no	—
315	C₂×C₄⋊C₄	—	178	1	no	—
316	C₂×C₄⋊C₄	—	178	1	no	—
317	C₂×C₄⋊C₄	—	178	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₄×D₈₉	1	2	yes	—
321	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
322	#95	—	178	4	no	—
323	C₂⁴	C₂×D₃₅₆	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	356	1	no	—
333	C₂²×C₄	—	356	1	no	—
334	C₂²×C₄	—	356	1	no	—
335	C₂²×C₄	—	356	1	no	—
336	C₂²×C₄	—	356	1	no	—
337	C₂²×C₄	—	356	2	no	—
338	C₂²×C₄	—	356	1	no	—
339	C₂²×C₄	—	356	2	no	—
340	C₂²×C₄	—	356	2	no	—
341	C₂²×C₄	—	356	1	no	—
342	C₂²×C₄	—	356	2	no	—
343	C₂²×C₄	—	356	1	no	—
344	C₂²×C₄	—	356	2	no	—
345	C₂²×C₄	—	356	2	no	—
346	C₂²×C₄	—	356	1	no	—
347	C₂²×C₄	—	356	1	no	—
348	C₂²×C₄	—	178	4	no	—
349	C₂²×C₄	—	178	2	no	—
350	C₂²×C₄	—	178	2	no	—
351	C₂²×C₄	—	178	2	no	—
352	C₂²×C₄	—	178	2	no	—
353	C₂²×C₄	#13083551	1	2	yes	—
354	C₂²×C₄	#13083551	1	2	yes	—
355	C₂²×C₄	D₇₁₂	1	2	yes	—
356	C₂²×C₄	#13083563	1	2	yes	—
357	C₂²×C₄	#13083563	1	2	yes	—
358	C₂²×C₄	Dic₃₅₆	1	2	yes	—
359	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₄	D₄×D₈₉	1	2	yes	—
361	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
365	C₂²×C₄	#13083573	1	1	yes	characteristic
366	C₂²×C₄	#13083573	1	2	yes	—
367	C₂²×C₄	#13083574	1	2	yes	—
368	C₂²×C₄	#13083575	1	1	yes	characteristic
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₄⋊C₄	—	89	4	no	—
377	C₄⋊C₄	—	356	8	no	—
378	C₄⋊C₄	—	356	8	no	—
379	C₄⋊C₄	—	356	2	no	—
380	C₄⋊C₄	—	356	2	no	—
381	C₄⋊C₄	—	356	2	no	—
382	C₄⋊C₄	—	356	8	no	—
383	C₄⋊C₄	—	178	4	no	—
384	C₄⋊C₄	—	178	4	no	—
385	C₄⋊C₄	—	178	4	no	—
386	C₄⋊C₄	—	178	2	no	—
387	C₄⋊C₄	—	178	2	no	—
388	C₄⋊C₄	—	178	2	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₂³	C₂×#13083551	1	1	yes	characteristic
392	C₂³	#15667982	1	1	yes	characteristic
393	C₂³	#15667987	1	1	yes	characteristic
394	C₂³	#15667992	1	1	yes	characteristic
395	C₂³	#15667996	1	1	yes	characteristic
396	C₂³	#15668000	1	1	yes	characteristic
397	C₂³	#15668012	1	1	yes	characteristic
398	C₂³	C₂×D₇₁₂	1	1	yes	characteristic
399	C₂³	C₂×#13083563	1	1	yes	characteristic
400	C₂³	C₂×#13083563	1	1	yes	characteristic
401	C₂³	C₂×Dic₃₅₆	1	1	yes	characteristic
402	C₂³	#15668040	1	1	yes	characteristic
403	C₂³	#15668040	1	1	yes	characteristic
404	C₂³	#15668045	1	1	yes	characteristic
405	C₂³	#15668045	1	1	yes	characteristic
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	356	2	no	—
419	C₂×C₄	—	356	2	no	—
420	C₂×C₄	—	356	2	no	—
421	C₂×C₄	—	356	2	no	—
422	C₂×C₄	—	356	2	no	—
423	C₂×C₄	—	356	2	no	—
424	C₂×C₄	—	356	2	no	—
425	C₂×C₄	—	356	4	no	—
426	C₂×C₄	—	356	4	no	—
427	C₂×C₄	—	356	4	no	—
428	C₂×C₄	—	356	2	no	—
429	C₂×C₄	—	356	2	no	—
430	C₂×C₄	—	178	4	no	—
431	C₂×C₄	—	712	1	no	—
432	C₂×C₄	—	712	1	no	—
433	C₂×C₄	—	712	2	no	—
434	C₂×C₄	—	712	2	no	—
435	C₂×C₄	—	712	1	no	—
436	C₂×C₄	—	712	1	no	—
437	C₂×C₄	—	712	2	no	—
438	C₂×C₄	—	712	2	no	—
439	C₂×C₄	#15667934	1	4	yes	—
440	C₂×C₄	#15667937	1	4	yes	—
441	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
442	C₂×C₄	#15667970	1	1	yes	characteristic
443	C₂×C₄	#15667972	1	2	yes	—
444	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
445	C₂×C₄	#15667983	1	1	yes	characteristic
446	C₂×C₄	#15667984	1	2	yes	—
447	C₂×C₄	#15667985	1	2	yes	—
448	C₂×C₄	#15667988	1	1	yes	characteristic
449	C₂×C₄	#15667989	1	2	yes	—
450	C₂×C₄	#15667989	1	2	yes	—
451	C₂×C₄	#15667991	1	2	yes	—
452	C₂×C₄	#15667997	1	2	yes	—
453	C₂×C₄	#15668002	1	2	yes	—
454	C₂×C₄	#15668003	1	2	yes	—
455	C₂×C₄	#15668005	1	2	yes	—
456	C₂×C₄	#15668011	1	2	yes	—
457	C₈	—	4	4	no	—
458	C₂²	#19151455	1	1	yes	characteristic
459	C₂²	#19151475	1	1	yes	characteristic
460	C₂²	#19151504	1	1	yes	characteristic
461	C₂²	#19151516	1	1	yes	characteristic
462	C₂²	#19151519	1	1	yes	characteristic
463	C₂²	#19151530	1	1	yes	characteristic
464	C₂²	#19151538	1	1	yes	characteristic
465	C₂²	C₂×#15667934	1	1	yes	characteristic
466	C₂²	C₂×#15667937	1	1	yes	characteristic
467	C₂²	#19151600	1	1	yes	characteristic
468	C₂²	#19151600	1	1	yes	characteristic
469	C₂²	#19151734	1	1	yes	characteristic
470	C₂²	#19151739	1	1	yes	characteristic
471	C₂²	#19151751	1	1	yes	characteristic
472	C₂²	#19151756	1	1	yes	characteristic
473	C₂²	#19151794	1	1	yes	characteristic
474	C₂²	#19151799	1	1	yes	characteristic
475	C₂²	#19151804	1	1	yes	characteristic
476	C₂²	#19151809	1	1	yes	characteristic
477	C₂²	#19151879	1	1	yes	characteristic
478	C₂²	#19151884	1	1	yes	characteristic
479	C₂²	#19151889	1	1	yes	characteristic
480	C₂²	#19151894	1	1	yes	characteristic
481	C₂²	#19151912	1	1	yes	characteristic
482	C₂²	#19151917	1	1	yes	characteristic
483	C₂²	#19151929	1	1	yes	characteristic
484	C₂²	#19151934	1	1	yes	characteristic
485	C₂²	#19151945	1	1	yes	characteristic
486	C₂²	#19151949	1	1	yes	characteristic
487	C₂²	#19151963	1	1	yes	characteristic
488	C₂²	#19151967	1	1	yes	characteristic
489	C₂²	#19151996	1	1	yes	characteristic
490	C₂²	#19152003	1	1	yes	characteristic
491	C₂²	#19152007	1	1	yes	characteristic
492	C₂²	#19152007	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	356	4	no	—
496	C₄	—	712	4	no	—
497	C₄	—	712	2	no	—
498	C₄	#19151485	1	2	yes	—
499	C₄	#19151495	1	2	yes	—
500	C₄	#19151521	1	2	yes	—
501	C₄	#19151531	1	2	yes	—
502	C₂	#26018506	1	1	yes	characteristic
503	C₂	#26020253	1	1	yes	characteristic
504	C₂	#26020258	1	1	yes	characteristic
505	C₂	#26020557	1	1	yes	characteristic
506	C₂	#26020567	1	1	yes	characteristic
507	C₂	#26021213	1	1	yes	characteristic
508	C₂	#26021221	1	1	yes	characteristic
509	C₂	#26021487	1	1	yes	characteristic
510	C₂	#26021499	1	1	yes	characteristic
511	C₂	#26021581	1	1	yes	characteristic
512	C₂	#26021586	1	1	yes	characteristic
513	C₂	#26021725	1	1	yes	characteristic
514	C₂	#26021730	1	1	yes	characteristic
515	C₂	#26021811	1	1	yes	characteristic
516	C₂	#26021816	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃₅₆
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#336×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#336	D₈₉
hypocenter	C₈₉	#11207
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
13. #19151496	C₄	semidirect
96. C₄⋊Dic₈₉	C₄⋊C₄	semidirect
264. C₈₉	#11207	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151496	2
C₂×#19151468	2
C₂×#19151361	2
C₂×#336×C₈₉	2
#11207	89