Subgroups — #36459624

Order 22784.

886 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151556	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151554	C₂	1	1	yes	maximal, characteristic
3	C₂²×#15667923	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151362	C₂	1	1	yes	maximal, characteristic
5	#26019968	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	C₂³×#10623494	C₂²	1	1	yes	characteristic
10	C₂³×#10623494	C₂²	1	1	yes	characteristic
11	C₂×#15667971	C₂²	1	1	yes	characteristic
12	#19151556	—	2	2	no	—
13	#19151556	C₄	1	4	yes	complemented
14	#19151554	—	2	2	no	—
15	#19151554	C₄	1	4	yes	complemented
16	C₂×#15667923	—	2	2	no	—
17	C₂×#15667923	—	2	2	no	—
18	C₂×#15667923	—	2	1	no	—
19	C₂×#15667923	C₄	1	4	yes	complemented
20	C₂×#15667922	—	2	1	no	—
21	C₂×C₄×#10623494	—	2	1	no	—
22	C₂×C₈×Dic₈₉	—	2	1	no	—
23	#19151362	C₄	1	4	yes	complemented
24	#19151360	C₄	1	4	yes	complemented
25	#19151358	C₄	1	4	yes	complemented
26	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
29	#339×C₈₉	C₄	1	4	yes	complemented
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	C₂×#13083558	C₂×C₄	1	2	yes	—
35	C₂×#13083558	C₂×C₄	1	2	yes	—
36	C₂²×#10623494	—	2	1	no	—
37	C₂²×#10623494	—	2	1	no	—
38	C₂²×#10623494	—	2	1	no	—
39	C₂²×#10623494	—	2	1	no	—
40	C₂²×#10623494	—	2	1	no	—
41	C₂²×#10623494	C₂×C₄	1	2	yes	—
42	C₂²×#10623494	C₂×C₄	1	2	yes	—
43	C₂²×#10623494	C₂×C₄	1	2	yes	—
44	C₂²×#10623494	C₂×C₄	1	2	yes	—
45	C₂²×#10623494	C₂×C₄	1	2	yes	—
46	C₂²×#10623494	C₂×C₄	1	2	yes	—
47	C₂²×#10623494	D₄	1	1	yes	characteristic
48	C₂²×#10623494	D₄	1	1	yes	characteristic
49	C₂²×#10623494	D₄	1	2	yes	—
50	C₂²×#10623494	D₄	1	2	yes	—
51	C₂²×#10623494	Q₈	1	2	yes	—
52	#15667971	—	2	1	no	—
53	#15667971	—	2	1	no	—
54	#15667971	C₂×C₄	1	2	yes	—
55	#15667971	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
58	C₂×C₄×Dic₈₉	—	2	1	no	—
59	#15667923	—	2	8	no	—
60	#15667923	—	2	4	no	—
61	#15667922	—	2	4	no	—
62	C₄×#10623494	—	2	4	no	—
63	C₈×Dic₈₉	—	2	4	no	—
64	C₂³×C₄×C₈₉	—	2	1	no	—
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₈₉	—	2	1	no	—
67	C₂×M₁₆×C₈₉	—	2	1	no	—
68	C₂×M₁₆×C₈₉	—	2	1	no	—
69	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₈₉	—	2	1	no	—
73	#117×C₈₉	—	2	1	no	—
74	#117×C₈₉	—	2	1	no	—
75	#117×C₈₉	C₂×C₄	1	2	yes	—
76	#117×C₈₉	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
79	C₂×C₄²×C₈₉	—	2	1	no	—
80	C₂×C₄²×C₈₉	—	2	1	no	—
81	C₂×C₄²×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	—	2	1	no	—
83	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	#13083558	—	2	2	no	—
88	#13083558	—	2	2	no	—
89	#13083558	—	2	2	no	—
90	#13083558	C₄²	1	4	yes	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	2	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	C₄²	1	4	yes	—
101	C₂×#10623494	C₄²	1	4	yes	—
102	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
103	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
104	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
105	C₂×#10623494	C₂²⋊C₄	1	4	yes	—
106	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
107	C₂×#10623494	C₄⋊C₄	1	2	yes	—
108	C₂×#10623494	C₄⋊C₄	1	2	yes	—
109	C₂×#10623494	C₄⋊C₄	1	4	yes	—
110	C₂×#10623494	C₄⋊C₄	1	4	yes	—
111	C₄⋊Dic₈₉	—	2	2	no	—
112	C₄⋊Dic₈₉	C₄²	1	4	yes	—
113	C₂²⋊Dic₈₉	—	2	2	no	—
114	C₂²⋊Dic₈₉	—	2	2	no	—
115	C₄×Dic₈₉	—	2	2	no	—
116	C₄×Dic₈₉	—	2	2	no	—
117	C₂⁴×C₈₉	#41	1	1	yes	characteristic
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	—	2	2	no	—
122	C₂²×C₄×C₈₉	—	4	4	no	—
123	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	2	2	no	—
139	M₁₆×C₈₉	—	2	2	no	—
140	M₁₆×C₈₉	C₄²	1	4	yes	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	C₄²	1	4	yes	—
146	C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	C₄²	1	4	yes	—
154	C₂³×C₈₉	—	2	4	no	—
155	C₂³×C₈₉	#117	1	1	yes	characteristic
156	C₂³×C₈₉	#117	1	1	yes	characteristic
157	C₂³×C₈₉	#117	1	1	yes	characteristic
158	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₈₉	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	4	4	no	—
165	C₂×C₄×C₈₉	—	4	4	no	—
166	C₂×C₄×C₈₉	—	4	4	no	—
167	C₂×C₄×C₈₉	—	4	4	no	—
168	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×Dic₈₉	—	2	4	no	—
197	C₂×Dic₈₉	—	4	4	no	—
198	C₈×C₈₉	—	2	4	no	—
199	#10623494	—	2	4	no	—
200	#10623494	—	2	4	no	—
201	#10623494	#95	1	4	yes	—
202	#10623494	#95	1	4	yes	—
203	C₂²×C₈₉	—	2	2	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	2	2	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	2	2	no	—
209	C₂²×C₈₉	#376	1	1	yes	characteristic
210	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₈₉	#444	1	4	yes	—
217	C₄×C₈₉	—	4	4	no	—
218	C₄×C₈₉	—	4	4	no	—
219	C₄×C₈₉	C₄³	1	1	yes	characteristic
220	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
221	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
222	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
227	Dic₈₉	—	4	4	no	—
228	#10707	—	89	1	no	maximal, Sylow
229	C₂×C₈₉	—	2	1	no	—
230	C₂×C₈₉	—	2	1	no	—
231	C₂×C₈₉	—	2	1	no	—
232	C₂×C₈₉	—	2	1	no	—
233	C₂×C₈₉	C₄×#95	1	1	yes	characteristic
234	C₂×C₈₉	#1765	1	2	yes	—
235	C₂×C₈₉	#1765	1	2	yes	—
236	C₂×C₈₉	#1773	1	2	yes	—
237	C₂×#405	—	89	1	no	—
238	C₂×#405	—	89	1	no	—
239	C₂²×#97	—	89	1	no	—
240	C₂×#341	—	89	1	no	—
241	#1735	—	89	1	no	—
242	C₂×#339	—	89	1	no	—
243	C₂×#339	D₈₉	1	1	yes	characteristic
244	C₈₉	#10707	1	1	yes	characteristic, complemented, Sylow
245	C₂²×M₁₆	—	89	1	no	—
246	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
247	C₂³×C₈	—	89	1	no	—
248	C₂³×C₈	—	89	1	no	—
249	C₂×#117	—	89	1	no	—
250	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
251	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
252	#405	—	89	4	no	—
253	#405	—	89	4	no	—
254	#405	—	178	2	no	—
255	#405	—	178	2	no	—
256	C₂×#97	—	89	4	no	—
257	C₂×#97	—	178	2	no	—
258	C₂×#97	—	178	2	no	—
259	C₂×#97	—	178	1	no	—
260	C₂×#97	—	178	1	no	—
261	C₂×C₄×C₈	—	178	1	no	—
262	C₂×C₄×C₈	—	178	1	no	—
263	#341	—	89	4	no	—
264	#340	—	89	4	no	—
265	#339	—	89	4	no	—
266	#339	Dic₈₉	1	4	yes	complemented
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	89	2	no	—
273	C₂×M₁₆	—	89	2	no	—
274	C₂×M₁₆	—	89	2	no	—
275	C₂×M₁₆	—	178	1	no	—
276	C₂×M₁₆	—	178	1	no	—
277	C₂×M₁₆	—	178	1	no	—
278	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
279	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
280	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	89	2	no	—
283	C₂²×C₈	—	89	2	no	—
284	C₂²×C₈	—	89	2	no	—
285	C₂²×C₈	—	89	2	no	—
286	C₂²×C₈	—	89	2	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	89	1	no	—
289	C₂²×C₈	—	89	2	no	—
290	C₂²×C₈	—	89	2	no	—
291	C₂²×C₈	—	89	2	no	—
292	C₂²×C₈	—	89	2	no	—
293	C₂²×C₈	—	178	1	no	—
294	C₂²×C₈	—	178	1	no	—
295	C₂²×C₈	—	178	1	no	—
296	C₂²×C₈	—	178	1	no	—
297	C₂²×C₈	—	178	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	89	2	no	—
301	#117	—	89	2	no	—
302	#117	—	178	1	no	—
303	#117	—	178	1	no	—
304	#117	C₄×D₈₉	1	2	yes	—
305	#117	C₂×Dic₈₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	89	2	no	—
307	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	178	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	178	1	no	—
315	C₂×C₄²	C₄×D₈₉	1	2	yes	—
316	C₂×C₄²	C₄×D₈₉	1	2	yes	—
317	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
318	#97	—	178	8	no	—
319	#97	—	178	4	no	—
320	#97	—	178	4	no	—
321	C₄×C₈	—	178	4	no	—
322	C₄×C₈	—	178	4	no	—
323	C₂⁴	#13083573	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	178	2	no	—
330	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083573	1	1	yes	characteristic
342	C₂²×C₄	#13083573	1	1	yes	characteristic
343	C₂²×C₄	#13083575	1	1	yes	characteristic
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	89	4	no	—
348	M₁₆	—	178	2	no	—
349	M₁₆	—	178	2	no	—
350	M₁₆	—	178	2	no	—
351	M₁₆	C₄×Dic₈₉	1	4	yes	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	89	4	no	—
356	C₂×C₈	—	89	2	no	—
357	C₂×C₈	—	89	2	no	—
358	C₂×C₈	—	89	4	no	—
359	C₂×C₈	—	89	2	no	—
360	C₂×C₈	—	89	2	no	—
361	C₂×C₈	—	89	4	no	—
362	C₂×C₈	—	89	4	no	—
363	C₂×C₈	—	89	2	no	—
364	C₂×C₈	—	89	2	no	—
365	C₂×C₈	—	89	4	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	2	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	—	178	2	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	—	178	2	no	—
373	C₂×C₈	—	178	2	no	—
374	C₂×C₈	—	178	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	89	4	no	—
377	C₄⋊C₄	—	178	2	no	—
378	C₄⋊C₄	C₄×Dic₈₉	1	4	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	178	2	no	—
382	C₂²⋊C₄	—	178	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	178	2	no	—
389	C₄²	—	178	2	no	—
390	C₄²	C₄×Dic₈₉	1	4	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	#15667968	1	1	yes	characteristic
393	C₂³	#15667968	1	1	yes	characteristic
394	C₂³	#15667970	1	1	yes	characteristic
395	C₂³	#15667972	1	1	yes	characteristic
396	C₂³	#15667972	1	1	yes	characteristic
397	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
398	C₂³	#15667977	1	1	yes	characteristic
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	356	4	no	—
406	C₂×C₄	—	178	4	no	—
407	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
414	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
420	C₂×C₄	#15667968	1	1	yes	characteristic
421	C₂×C₄	#15667970	1	1	yes	characteristic
422	C₂×C₄	#15667970	1	1	yes	characteristic
423	C₂×C₄	#15667972	1	1	yes	characteristic
424	C₂×C₄	#15667972	1	1	yes	characteristic
425	C₂×C₄	#15667972	1	1	yes	characteristic
426	C₂×C₄	#15667972	1	1	yes	characteristic
427	C₂×C₄	#15667974	1	1	yes	characteristic
428	C₂×C₄	#15667974	1	1	yes	characteristic
429	C₂×C₄	#15667974	1	1	yes	characteristic
430	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
431	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
432	C₂×C₄	#15667977	1	1	yes	characteristic
433	C₂×C₄	#15667977	1	1	yes	characteristic
434	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	89	4	no	—
437	C₈	—	89	4	no	—
438	C₈	—	178	4	no	—
439	C₈	—	178	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	#19151443	1	1	yes	characteristic
447	C₂²	#19151445	1	1	yes	characteristic
448	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
449	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
450	C₂²	#19151449	1	1	yes	characteristic
451	C₂²	#19151449	1	1	yes	characteristic
452	C₂²	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
453	C₂²	#19151717	1	4	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	356	4	no	—
457	C₄	C₄²×Dic₈₉	1	1	yes	characteristic
458	C₄	#95×D₈₉	1	1	yes	characteristic
459	C₄	#19151445	1	1	yes	characteristic
460	C₄	#19151445	1	1	yes	characteristic
461	C₄	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
462	C₄	#19151449	1	1	yes	characteristic
463	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
464	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	#95×Dic₈₉	1	1	yes	characteristic
470	C₂	#26020093	1	2	yes	—
471	C₂	#26020097	1	2	yes	—
472	C₂	#26020135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₄×C₈₉	C₄³
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#339×C₈₉	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂⁴×C₈₉	#41
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#339	D₈₉
hypocenter	C₈₉	#10707
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #19151556	C₄	semidirect
15. #19151554	C₄	semidirect
19. C₂×#15667923	C₄	semidirect
23. #19151362	C₄	semidirect
24. #19151360	C₄	semidirect
25. #19151358	C₄	semidirect
29. #339×C₈₉	C₄	semidirect
244. C₈₉	#10707	semidirect
266. #339	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151556	2
C₂×#19151554	2
C₂²×#15667923	2
C₂×#19151362	2
#26019968	2
C₂×#19151358	2
C₂×#339×C₈₉	2
#10707	89