Subgroups — #36525384

Order 22784.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030260	C₂	1	1	yes	maximal, characteristic
2	#26029195	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#13083558	C₂	1	1	yes	maximal, characteristic
4	#26019151	C₂	1	2	yes	maximal, complemented
5	#26019133	C₂	1	2	yes	maximal, complemented
6	#26019106	C₂	1	2	yes	maximal, complemented
7	#26019061	C₂	1	2	yes	maximal, complemented
8	#26019026	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018708	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#13083558	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	#19151928	C₄	1	2	yes	—
15	#19151888	C₄	1	1	yes	characteristic
16	#19151888	C₄	1	1	yes	characteristic
17	#19151803	C₄	1	1	yes	characteristic
18	#19151803	C₄	1	1	yes	characteristic
19	#19151749	C₄	1	2	yes	—
20	#19151727	—	2	2	no	—
21	#19151725	C₂²	1	2	yes	complemented
22	#19151722	C₂²	1	2	yes	complemented
23	C₄×#13083562	C₂²	1	2	yes	—
24	C₄×#13083562	C₂²	1	2	yes	—
25	#19151676	C₂²	1	2	yes	—
26	#19151670	—	2	2	no	—
27	D₄×#10623494	C₂²	1	2	yes	—
28	#19151651	C₂²	1	1	yes	characteristic
29	#19151624	—	2	1	no	—
30	#19151622	C₂²	1	1	yes	characteristic
31	#19151562	—	2	1	no	—
32	#19151553	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151350	C₂²	1	2	yes	complemented
35	#19151350	C₂²	1	2	yes	complemented
36	#19151330	C₂²	1	2	yes	complemented
37	#19151330	C₂²	1	2	yes	complemented
38	#19151320	C₂²	1	2	yes	complemented
39	#19151319	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083562	C₂×C₄	1	2	yes	—
48	C₂×#13083562	C₂×C₄	1	2	yes	—
49	C₂×#13083558	—	2	2	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083558	—	4	4	no	—
52	C₂×#13083558	D₄	1	1	yes	characteristic
53	C₂×#13083558	D₄	1	1	yes	characteristic
54	C₂²×#10623494	—	2	2	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668004	—	2	1	no	—
58	#15667991	—	2	1	no	—
59	#15667991	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₇₈	—	2	1	no	—
61	C₄×Dic₁₇₈	C₂³	1	2	yes	—
62	#15667971	—	2	1	no	—
63	#15667943	C₂×C₄	1	2	yes	—
64	#15667943	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667941	—	2	2	no	—
70	#15667941	—	2	2	no	—
71	#15667935	C₂×C₄	1	2	yes	—
72	#15667935	C₂×C₄	1	2	yes	—
73	#15667933	C₂×C₄	1	2	yes	—
74	#15667933	C₂×C₄	1	2	yes	—
75	C₂²⋊#10623494	—	2	2	no	—
76	C₂²⋊#10623494	—	2	2	no	—
77	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
78	#15667923	D₄	1	2	yes	—
79	#15667922	—	2	2	no	—
80	C₄×#10623494	C₂³	1	2	yes	—
81	C₄×#10623494	C₂³	1	2	yes	—
82	C₈×Dic₈₉	—	2	2	no	—
83	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂²×C₈×C₈₉	—	2	1	no	—
86	C₂²×C₈×C₈₉	—	2	1	no	—
87	C₄×D₄×C₈₉	—	2	1	no	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₈₉	—	2	1	no	—
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₇₈	—	2	1	no	—
103	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
104	#13083562	—	2	4	no	—
105	#13083562	—	4	2	no	—
106	#13083558	—	2	2	no	—
107	#13083558	—	2	2	no	—
108	#13083558	—	4	4	no	—
109	#13083558	—	4	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	4	4	no	—
112	C₂×#10623494	C₂²×C₄	1	2	yes	—
113	C₂×#10623494	C₂²×C₄	1	2	yes	—
114	C₂×#10623494	C₂×D₄	1	2	yes	—
115	C₂×#10623494	C₂×D₄	1	2	yes	—
116	C₄⋊Dic₈₉	—	2	1	no	—
117	C₄⋊Dic₈₉	—	2	1	no	—
118	C₄⋊Dic₈₉	—	2	1	no	—
119	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
120	#13083553	—	2	2	no	—
121	#13083553	—	2	2	no	—
122	C₂²⋊Dic₈₉	—	2	2	no	—
123	C₄×Dic₈₉	—	2	2	no	—
124	C₂⁴×C₈₉	—	2	1	no	—
125	C₂×D₄×C₈₉	—	2	2	no	—
126	C₂×D₄×C₈₉	—	2	1	no	—
127	C₂×D₄×C₈₉	—	4	1	no	—
128	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	—	4	2	no	—
136	C₂²×C₄×C₈₉	—	4	2	no	—
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	4	2	no	—
145	C₂×C₈×C₈₉	—	4	2	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₂²⋊C₄×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	—	2	1	no	—
158	C₂³×C₈₉	—	2	1	no	—
159	C₂³×C₈₉	—	4	2	no	—
160	C₂³×C₈₉	—	4	2	no	—
161	C₂³×C₈₉	—	8	1	no	—
162	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
163	D₄×C₈₉	—	2	1	no	—
164	D₄×C₈₉	—	2	1	no	—
165	D₄×C₈₉	—	2	1	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	#131	1	2	yes	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	1	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	1	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₂×C₄×C₈₉	#137	1	2	yes	—
185	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₈₉	—	2	2	no	—
189	C₂×Dic₈₉	—	2	2	no	—
190	Dic₁₇₈	—	2	2	no	—
191	Dic₁₇₈	—	2	2	no	—
192	Dic₁₇₈	—	8	1	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	—	4	1	no	—
197	#10623494	—	2	2	no	—
198	#10623494	—	2	2	no	—
199	#10623494	—	2	2	no	—
200	#10623494	—	2	2	no	—
201	#10623494	—	4	2	no	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	4	1	no	—
206	C₂²×C₈₉	—	4	1	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	8	4	no	—
211	C₂²×C₈₉	#440	1	2	yes	—
212	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	4	1	no	—
217	C₄×C₈₉	—	4	1	no	—
218	C₄×C₈₉	#440	1	2	yes	—
219	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
220	C₄×C₈₉	#568	1	1	yes	characteristic
221	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
223	Dic₈₉	—	4	2	no	—
224	Dic₈₉	—	4	2	no	—
225	#18000	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	2	2	no	—
227	C₂×C₈₉	—	4	2	no	—
228	C₂×C₈₉	—	8	1	no	—
229	C₂×C₈₉	#2933	1	1	yes	characteristic
230	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
231	C₂×C₈₉	#2956	1	1	yes	characteristic
232	#3101	—	89	1	no	—
233	#2962	—	89	1	no	—
234	D₄×M₁₆	—	89	1	no	—
235	#1592	—	89	2	no	—
236	#1588	—	89	2	no	—
237	#1585	—	89	2	no	—
238	SD₁₆⋊C₈	—	89	2	no	—
239	#1571	—	89	1	no	—
240	#1493	—	89	1	no	—
241	C₂×D₄⋊C₈	D₈₉	1	1	yes	characteristic
242	#1451	—	89	1	no	—
243	C₈₉	#18000	1	1	yes	characteristic, complemented, Sylow
244	C₂²×M₁₆	—	178	1	no	—
245	#533	—	89	1	no	—
246	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
247	#483	—	89	2	no	—
248	#476	—	89	1	no	—
249	#476	—	89	1	no	—
250	#461	—	89	1	no	—
251	#461	—	89	1	no	—
252	#450	—	89	2	no	—
253	#446	—	89	2	no	—
254	#446	—	178	2	no	—
255	C₈×Q₈	—	89	2	no	—
256	C₄×SD₁₆	—	89	2	no	—
257	C₄×SD₁₆	—	89	2	no	—
258	#436	—	89	2	no	—
259	#435	—	178	2	no	—
260	C₈×D₄	—	89	2	no	—
261	#431	—	89	1	no	—
262	#424	—	178	1	no	—
263	#423	—	89	1	no	—
264	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
265	#407	—	178	1	no	—
266	#405	—	178	1	no	—
267	C₄×M₁₆	—	89	1	no	—
268	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
269	#335	—	89	2	no	—
270	#335	—	89	2	no	—
271	Q₈⋊C₈	—	89	2	no	—
272	Q₈⋊C₈	—	89	2	no	—
273	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
274	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
275	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
276	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
277	#322	—	89	2	no	—
278	#322	—	89	2	no	—
279	C₂²×D₄	C₄×D₈₉	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	—	89	2	no	—
282	C₂×SD₁₆	—	89	2	no	—
283	C₂×M₁₆	—	89	1	no	—
284	C₂×M₁₆	—	89	1	no	—
285	C₂×M₁₆	—	356	4	no	—
286	C₂×M₁₆	—	178	2	no	—
287	C₂×M₁₆	—	178	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	178	2	no	—
291	C₄⋊Q₈	—	89	1	no	—
292	C₄⋊Q₈	—	89	1	no	—
293	#125	—	178	1	no	—
294	C₂²⋊Q₈	—	89	2	no	—
295	C₂²⋊Q₈	—	178	1	no	—
296	C₄×Q₈	—	89	2	no	—
297	C₄×Q₈	—	178	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
301	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
302	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
304	#117	—	178	1	no	—
305	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
308	#106	—	89	2	no	—
309	#106	—	89	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	1	no	—
313	C₄⋊C₈	—	89	2	no	—
314	C₄⋊C₈	—	178	2	no	—
315	C₄⋊C₈	—	178	2	no	—
316	C₄⋊C₈	—	178	1	no	—
317	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
319	#103	—	89	2	no	—
320	#103	—	89	2	no	—
321	#102	—	89	2	no	—
322	#102	—	89	2	no	—
323	C₂²⋊C₈	—	89	2	no	—
324	C₂²⋊C₈	—	178	2	no	—
325	C₂²⋊C₈	—	178	2	no	—
326	#97	—	89	2	no	—
327	#97	—	178	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	89	2	no	—
330	C₄×C₈	—	89	2	no	—
331	C₄×C₈	—	178	2	no	—
332	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	89	2	no	—
336	C₂×Q₈	—	178	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	#13083573	1	1	yes	characteristic
352	SD₁₆	—	356	2	no	—
353	SD₁₆	—	178	4	no	—
354	M₁₆	—	356	2	no	—
355	M₁₆	—	356	4	no	—
356	M₁₆	—	178	2	no	—
357	M₁₆	—	178	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	89	2	no	—
365	C₂×C₈	—	89	2	no	—
366	C₂×C₈	—	89	2	no	—
367	C₂×C₈	—	89	2	no	—
368	C₂×C₈	—	356	4	no	—
369	C₂×C₈	—	178	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	89	2	no	—
372	C₄⋊C₄	—	178	1	no	—
373	C₄⋊C₄	—	178	1	no	—
374	C₄⋊C₄	—	178	2	no	—
375	C₄⋊C₄	—	178	1	no	—
376	C₄⋊C₄	—	178	2	no	—
377	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	178	2	no	—
384	C₄²	—	178	2	no	—
385	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
386	C₄²	D₄×D₈₉	1	1	yes	characteristic
387	C₄²	#13083573	1	1	yes	characteristic
388	C₄²	C₂³×D₈₉	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	#15667972	1	1	yes	characteristic
395	Q₈	—	178	2	no	—
396	Q₈	—	178	2	no	—
397	Q₈	—	712	1	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	2	1	no	—
401	D₄	—	4	2	no	—
402	D₄	#15668018	1	2	yes	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	178	2	no	—
416	C₂×C₄	—	178	2	no	—
417	C₂×C₄	#15667972	1	1	yes	characteristic
418	C₂×C₄	#15667972	1	1	yes	characteristic
419	C₂×C₄	#15667972	1	1	yes	characteristic
420	C₂×C₄	#15668036	1	2	yes	—
421	C₂×C₄	#15668041	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	356	2	no	—
430	C₈	—	178	2	no	—
431	C₈	—	178	2	no	—
432	C₈	—	178	2	no	—
433	C₈	—	178	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	8	4	no	—
443	C₂²	#19151695	1	2	yes	—
444	C₂²	C₂×#15667972	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	356	2	no	—
451	C₄	—	356	2	no	—
452	C₄	#19151695	1	2	yes	—
453	C₄	C₂×#15668018	1	1	yes	characteristic
454	C₄	#19152364	1	1	yes	characteristic
455	C₄	C₂×#15668036	1	1	yes	characteristic
456	C₄	C₂×#15668041	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#26028973	1	1	yes	characteristic
461	C₂	C₂×#19151695	1	1	yes	characteristic
462	C₂	#26029158	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×D₄⋊C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×D₄⋊C₈	D₈₉
hypocenter	C₈₉	#18000
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #26029195	C₂	semidirect
4. #26019151	C₂	semidirect
5. #26019133	C₂	semidirect
6. #26019106	C₂	semidirect
7. #26019061	C₂	semidirect
8. #26019026	C₂	semidirect
9. #26018708	C₂	semidirect
10. #26018541	C₂	semidirect
21. #19151725	C₂²	semidirect
22. #19151722	C₂²	semidirect
34. #19151350	C₂²	semidirect
35. #19151350	C₂²	semidirect
36. #19151330	C₂²	semidirect
37. #19151330	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. #19151319	C₂²	semidirect
243. C₈₉	#18000	semidirect

Maximal subgroups

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

subgroup	index
#26030260	2
#26029195	2
D₄×#13083558	2
#26019151	2
#26019133	2
#26019106	2
#26019061	2
#26019026	2
#26018708	2
#26018541	2
C₂×D₄⋊C₈×C₈₉	2
#18000	89