Subgroups — #36538229

Order 22784.

716 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030347	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030339	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019700	C₂	1	2	yes	maximal, complemented
5	#26019686	C₂	1	2	yes	maximal, complemented
6	#26019624	C₂	1	2	yes	maximal, complemented
7	#26019590	C₂	1	2	yes	maximal, complemented
8	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018952	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	—	2	1	no	—
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19151931	—	2	1	no	—
15	#19151914	—	2	1	no	—
16	#19151885	C₂²	1	2	yes	—
17	#19151875	C₂²	1	2	yes	—
18	#19151800	C₂²	1	2	yes	—
19	#19151790	C₂²	1	2	yes	—
20	#19151748	—	2	1	no	—
21	#19151731	—	2	1	no	—
22	#19151708	—	2	2	no	—
23	#19151696	—	2	2	no	—
24	C₈×D₃₅₆	—	2	1	no	—
25	C₈×D₃₅₆	—	2	1	no	—
26	C₈×D₃₅₆	C₂²	1	2	yes	—
27	C₈×D₃₅₆	C₂²	1	2	yes	—
28	#19151655	C₂²	1	1	yes	characteristic
29	#19151655	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
31	C₂×#15667924	—	2	1	no	—
32	#19151351	C₂²	1	2	yes	complemented
33	#19151349	C₂²	1	2	yes	complemented
34	#19151347	C₂²	1	2	yes	complemented
35	#19151344	C₂²	1	2	yes	complemented
36	#19151344	C₂²	1	2	yes	complemented
37	#19151342	C₂²	1	2	yes	complemented
38	#533×C₈₉	C₂²	1	1	yes	characteristic
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#465×C₈₉	—	2	1	no	—
45	#465×C₈₉	—	2	1	no	—
46	C₄×SD₁₆×C₈₉	—	2	1	no	—
47	C₄×SD₁₆×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	C₂×#13083561	—	2	2	no	—
52	C₂×#13083559	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	C₂×C₈×D₈₉	—	4	4	no	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	—	2	1	no	—
59	C₄×D₃₅₆	D₄	1	2	yes	—
60	C₄×D₃₅₆	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
62	C₂×#13083551	—	2	1	no	—
63	#15667945	—	2	2	no	—
64	#15667943	—	2	2	no	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667936	—	2	2	no	—
70	#15667933	—	2	2	no	—
71	#15667932	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	C₂²⋊#10623494	—	2	1	no	—
74	C₂²⋊#10623494	—	2	1	no	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667923	—	2	1	no	—
78	#15667923	—	2	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×SD₁₆×C₈₉	—	2	1	no	—
81	C₂×SD₁₆×C₈₉	—	2	1	no	—
82	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	#127×C₈₉	C₂³	1	1	yes	characteristic
88	#125×C₈₉	—	2	1	no	—
89	#124×C₈₉	—	2	1	no	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	—	2	1	no	—
92	#121×C₈₉	—	2	1	no	—
93	#121×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₄×D₄×C₈₉	—	2	1	no	—
97	C₄×D₄×C₈₉	—	2	1	no	—
98	#117×C₈₉	—	2	1	no	—
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	#106×C₈₉	—	2	1	no	—
101	#106×C₈₉	—	2	1	no	—
102	#103×C₈₉	—	2	1	no	—
103	#103×C₈₉	—	2	1	no	—
104	#102×C₈₉	—	2	1	no	—
105	#102×C₈₉	—	2	1	no	—
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×D₈₉	—	2	1	no	—
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×D₃₅₆	—	2	4	no	—
113	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
114	C₂²×Dic₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	2	no	—
116	C₂×C₄×D₈₉	—	2	2	no	—
117	C₂×C₄×D₈₉	—	4	2	no	—
118	C₂×C₄×D₈₉	—	4	2	no	—
119	#13083561	—	4	4	no	—
120	#13083559	—	4	4	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	4	2	no	—
125	C₈×D₈₉	—	4	4	no	—
126	C₈×D₈₉	—	4	4	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
129	#13083551	—	2	2	no	—
130	#13083551	—	2	2	no	—
131	#41×C₈₉	—	8	2	no	—
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	1	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	—	4	1	no	—
139	C₂²×C₄×C₈₉	—	4	1	no	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
143	SD₁₆×C₈₉	—	4	2	no	—
144	SD₁₆×C₈₉	—	4	2	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	4	1	no	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	4	1	no	—
158	C₄⋊C₄×C₈₉	—	4	1	no	—
159	C₂²⋊C₄×C₈₉	—	4	1	no	—
160	C₂²⋊C₄×C₈₉	—	4	1	no	—
161	C₂²⋊C₄×C₈₉	—	4	1	no	—
162	C₄²×C₈₉	—	4	1	no	—
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₈₉	#41	1	1	yes	characteristic
166	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂³×C₈₉	—	4	1	no	—
168	C₂³×C₈₉	#121	1	1	yes	characteristic
169	C₂²×D₈₉	—	2	4	no	—
170	C₂²×D₈₉	—	2	2	no	—
171	C₂²×D₈₉	—	4	2	no	—
172	C₂²×D₈₉	—	4	2	no	—
173	Q₈×C₈₉	—	4	2	no	—
174	Q₈×C₈₉	—	4	1	no	—
175	Q₈×C₈₉	—	4	1	no	—
176	Q₈×C₈₉	—	8	1	no	—
177	D₄×C₈₉	—	4	2	no	—
178	D₄×C₈₉	—	4	1	no	—
179	D₄×C₈₉	—	4	1	no	—
180	D₄×C₈₉	—	8	1	no	—
181	D₄×C₈₉	—	8	2	no	—
182	C₂×C₄×C₈₉	—	2	2	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	4	1	no	—
187	C₂×C₄×C₈₉	—	4	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	8	2	no	—
190	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
196	C₂×Dic₈₉	—	2	2	no	—
197	C₂×Dic₈₉	—	4	2	no	—
198	D₃₅₆	—	2	4	no	—
199	D₃₅₆	—	2	2	no	—
200	D₃₅₆	#135	1	4	yes	—
201	C₄×D₈₉	—	4	4	no	—
202	C₄×D₈₉	—	4	2	no	—
203	C₄×D₈₉	—	4	2	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
208	#10623494	—	4	2	no	—
209	#10623494	—	4	2	no	—
210	#10623494	—	4	2	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	8	1	no	—
214	C₂²×C₈₉	—	8	1	no	—
215	C₂²×C₈₉	—	8	1	no	—
216	C₂²×C₈₉	#471	1	2	yes	—
217	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
218	C₂×D₈₉	—	2	4	no	—
219	C₂×D₈₉	—	4	8	no	—
220	C₂×D₈₉	—	4	2	no	—
221	C₂×D₈₉	—	4	2	no	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	8	1	no	—
227	C₄×C₈₉	—	8	1	no	—
228	C₄×C₈₉	—	8	1	no	—
229	C₄×C₈₉	C₂×#135	1	2	yes	—
230	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₈₉	#575	1	1	yes	characteristic
232	Dic₈₉	—	4	2	no	—
233	#19257	—	89	1	no	maximal, Sylow
234	C₂×C₈₉	—	2	2	no	—
235	C₂×C₈₉	—	16	1	no	—
236	C₂×C₈₉	#3036	1	1	yes	characteristic
237	C₂×C₈₉	#3050	1	1	yes	characteristic
238	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
239	D₈₉	—	4	4	no	—
240	#3167	D₈₉	1	1	yes	characteristic, complemented
241	#3110	—	89	1	no	—
242	#3109	—	89	1	no	—
243	C₂×C₈×D₄	—	89	1	no	—
244	#1683	—	89	2	no	—
245	#1681	—	89	2	no	—
246	#1671	—	89	2	no	—
247	#1665	—	89	2	no	—
248	#1568	—	89	1	no	—
249	#1552	—	89	1	no	—
250	#1551	—	89	1	no	—
251	C₈₉	#19257	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₈	—	178	1	no	—
253	#533	C₂×D₈₉	1	1	yes	characteristic
254	#532	C₂×D₈₉	1	1	yes	characteristic
255	C₂×C₄×D₄	—	89	1	no	—
256	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#492	C₂×D₈₉	1	1	yes	characteristic, complemented
258	#487	C₂×D₈₉	1	1	yes	characteristic, complemented
259	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
260	#484	—	178	1	no	—
261	#481	—	178	1	no	—
262	#476	—	89	2	no	—
263	#474	—	89	2	no	—
264	#465	—	2	1	no	—
265	#465	—	2	1	no	—
266	#461	—	89	2	no	—
267	#459	—	89	2	no	—
268	#450	—	178	1	no	—
269	#447	—	178	1	no	—
270	#442	—	178	2	no	—
271	#440	—	178	2	no	—
272	C₄×SD₁₆	—	2	1	no	—
273	C₄×SD₁₆	—	2	1	no	—
274	C₈×D₄	—	89	2	no	—
275	C₈×D₄	—	89	2	no	—
276	C₈×D₄	—	178	1	no	—
277	C₈×D₄	—	178	1	no	—
278	#432	—	89	1	no	—
279	#432	—	89	1	no	—
280	C₂×C₄⋊C₈	—	89	1	no	—
281	C₂×C₂²⋊C₈	—	178	1	no	—
282	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
283	#335	—	89	2	no	—
284	#334	—	89	2	no	—
285	#333	—	89	2	no	—
286	#332	—	89	2	no	—
287	#332	—	89	2	no	—
288	#331	—	89	2	no	—
289	C₂×#41	—	2	1	no	—
290	C₂²×D₄	—	89	1	no	—
291	C₂³×C₄	—	178	1	no	—
292	C₂×SD₁₆	—	2	1	no	—
293	C₂×SD₁₆	—	2	1	no	—
294	C₂×SD₁₆	—	178	2	no	—
295	C₂×D₈	—	178	2	no	—
296	C₂²×C₈	—	356	4	no	—
297	C₂²×C₈	—	178	1	no	—
298	C₂²×C₈	—	178	2	no	—
299	C₂²×C₈	—	178	2	no	—
300	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
305	#127	C₂²×D₈₉	1	1	yes	characteristic
306	#125	—	2	1	no	—
307	#124	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	89	2	no	—
317	C₄×D₄	—	89	2	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	#117	—	2	1	no	—
321	C₂×C₄⋊C₄	—	89	1	no	—
322	C₂×C₂²⋊C₄	—	178	1	no	—
323	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
324	#107	—	178	2	no	—
325	#106	—	2	1	no	—
326	#106	—	2	1	no	—
327	#106	—	178	2	no	—
328	C₄⋊C₈	—	89	2	no	—
329	C₄⋊C₈	—	89	2	no	—
330	C₄⋊C₈	—	89	2	no	—
331	C₄⋊C₈	—	178	1	no	—
332	#103	—	2	1	no	—
333	#103	—	2	1	no	—
334	#103	—	178	2	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	#102	—	178	2	no	—
338	#102	—	178	2	no	—
339	#102	—	178	2	no	—
340	C₂²⋊C₈	—	178	1	no	—
341	C₂²⋊C₈	—	178	1	no	—
342	C₂²⋊C₈	—	178	2	no	—
343	C₂²⋊C₈	—	178	2	no	—
344	#97	—	178	1	no	—
345	#97	—	178	1	no	—
346	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
347	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
349	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
350	C₂⁴	—	178	1	no	—
351	#41	—	8	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	89	2	no	—
360	C₂×D₄	—	178	4	no	—
361	C₂×D₄	—	178	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	356	2	no	—
364	C₂²×C₄	—	356	2	no	—
365	C₂²×C₄	—	178	1	no	—
366	C₂²×C₄	—	178	2	no	—
367	C₂²×C₄	—	178	2	no	—
368	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₂²×C₄	#13083573	1	1	yes	characteristic
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	356	4	no	—
374	D₈	—	356	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	356	4	no	—
378	C₂×C₈	—	356	2	no	—
379	C₂×C₈	—	356	4	no	—
380	C₂×C₈	—	178	2	no	—
381	C₂×C₈	—	178	2	no	—
382	C₂×C₈	—	178	2	no	—
383	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	89	2	no	—
396	C₄⋊C₄	—	178	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	178	2	no	—
401	C₂²⋊C₄	—	178	2	no	—
402	C₄²	—	4	1	no	—
403	C₄²	D₄×D₈₉	1	1	yes	characteristic
404	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₄²	#13083573	1	1	yes	characteristic
406	C₄²	C₂³×D₈₉	1	1	yes	characteristic
407	C₂³	—	4	1	no	—
408	C₂³	—	356	2	no	—
409	C₂³	—	356	2	no	—
410	C₂³	—	178	4	no	—
411	C₂³	—	178	2	no	—
412	C₂³	#15667983	1	1	yes	characteristic
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	8	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	2	no	—
422	D₄	—	89	4	no	—
423	D₄	—	178	4	no	—
424	D₄	—	178	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	356	4	no	—
434	C₂×C₄	—	356	2	no	—
435	C₂×C₄	—	356	2	no	—
436	C₂×C₄	—	356	2	no	—
437	C₂×C₄	—	178	2	no	—
438	C₂×C₄	#15667983	1	1	yes	characteristic
439	C₂×C₄	#15667983	1	1	yes	characteristic
440	C₂×C₄	#15667983	1	1	yes	characteristic
441	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
443	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	356	2	no	—
448	C₈	—	356	2	no	—
449	C₈	—	356	2	no	—
450	C₈	#15668037	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	356	8	no	—
457	C₂²	—	356	2	no	—
458	C₂²	—	356	2	no	—
459	C₂²	—	178	4	no	—
460	C₂²	#19151858	1	2	yes	—
461	C₂²	C₂×#15667983	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	8	1	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	356	2	no	—
470	C₄	#135×D₈₉	1	2	yes	—
471	C₄	C₂×#15668037	1	1	yes	characteristic
472	C₄	#19152396	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	16	1	no	—
475	C₂	—	356	4	no	—
476	C₂	#26029712	1	1	yes	characteristic
477	C₂	#26029829	1	1	yes	characteristic
478	C₂	C₂×#19151858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3167	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26030339	C₂
hypercenter	#3167	D₈₉
hypocenter	C₈₉	#19257
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #26030347	C₂	semidirect
3. C₂×C₈×D₃₅₆	C₂	semidirect
4. #26019700	C₂	semidirect
5. #26019686	C₂	semidirect
6. #26019624	C₂	semidirect
7. #26019590	C₂	semidirect
8. #26019015	C₂	semidirect
9. #26018952	C₂	semidirect
10. #26018947	C₂	semidirect
11. C₈₉×#3167	C₂	semidirect
32. #19151351	C₂²	semidirect
33. #19151349	C₂²	semidirect
34. #19151347	C₂²	semidirect
35. #19151344	C₂²	semidirect
36. #19151344	C₂²	semidirect
37. #19151342	C₂²	semidirect
40. #498×C₈₉	C₂²	semidirect
41. #492×C₈₉	C₂²	semidirect
42. #487×C₈₉	C₂²	semidirect
43. #486×C₈₉	C₂²	semidirect
240. #3167	D₈₉	semidirect
251. C₈₉	#19257	semidirect
256. #498	C₂×D₈₉	semidirect
257. #492	C₂×D₈₉	semidirect
258. #487	C₂×D₈₉	semidirect
259. #486	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030347	2
#26030339	2
C₂×C₈×D₃₅₆	2
#26019700	2
#26019686	2
#26019624	2
#26019590	2
#26019015	2
#26018952	2
#26018947	2
C₈₉×#3167	2
#19257	89