Subgroups — #36605439

Order 22784.

884 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030711	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151872	C₂	1	2	yes	maximal, complemented
3	#26029724	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151808	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028998	C₂	1	1	yes	maximal, characteristic
6	#26021554	C₂	1	2	yes	maximal, complemented
7	#26021372	C₂	1	2	yes	maximal, complemented
8	#26021096	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020768	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668045	C₂²	1	2	yes	—
13	C₂×#15668045	C₂²	1	2	yes	—
14	C₂×#15668043	C₂²	1	2	yes	—
15	C₂²×#13083564	C₂²	1	2	yes	—
16	C₂×#15668020	C₂²	1	2	yes	—
17	#19152148	C₂²	1	1	yes	characteristic
18	C₂×#15668012	C₂²	1	1	yes	characteristic
19	#19151992	—	2	2	no	—
20	#19151978	—	2	1	no	—
21	#19151971	—	2	1	no	—
22	#19151872	—	2	8	no	—
23	#19151820	—	2	2	no	—
24	#19151808	—	2	1	no	—
25	#19151808	—	2	2	no	—
26	#19151808	—	2	1	no	—
27	#19151808	—	2	1	no	—
28	#19151798	—	2	1	no	—
29	#19151677	—	2	1	no	—
30	#19151671	—	2	2	no	—
31	C₈×D₃₅₆	—	2	1	no	—
32	C₂×#15667947	C₂²	1	2	yes	—
33	#19151622	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
35	#19151597	C₂²	1	2	yes	—
36	C₂×#15667935	C₂²	1	2	yes	—
37	C₂×#15667930	C₂²	1	2	yes	—
38	C₂×#15667930	C₂²	1	2	yes	—
39	#19151566	C₂²	1	2	yes	—
40	#19151362	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	#343×C₈₉	C₂²	1	1	yes	characteristic
47	#343×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#13083574	C₂³	1	2	yes	—
49	C₂²×Dic₁₇₈	C₂³	1	2	yes	—
50	#15668045	—	2	4	no	—
51	#15668045	—	2	4	no	—
52	#15668045	—	4	2	no	—
53	#15668045	—	4	2	no	—
54	#15668043	—	2	4	no	—
55	#15668043	—	4	2	no	—
56	C₂×Dic₃₅₆	—	2	2	no	—
57	C₂×Dic₃₅₆	—	2	2	no	—
58	C₂×#13083564	—	2	2	no	—
59	C₂×#13083564	—	2	2	no	—
60	C₂×#13083564	—	2	2	no	—
61	C₂×#13083564	—	2	4	no	—
62	C₂×#13083564	—	4	2	no	—
63	C₂×#13083563	—	2	2	no	—
64	C₂×#13083563	—	2	2	no	—
65	C₂×#13083561	—	2	2	no	—
66	#15668020	—	2	4	no	—
67	#15668020	—	4	2	no	—
68	C₂×#13083558	C₂³	1	2	yes	—
69	C₂×#13083557	—	2	2	no	—
70	C₂²×#10623494	C₂³	1	2	yes	—
71	C₂×C₈×D₈₉	—	2	2	no	—
72	#15668012	—	2	1	no	—
73	#15668012	—	2	1	no	—
74	#15668012	—	2	1	no	—
75	#15668012	—	2	1	no	—
76	#15668012	D₄	1	1	yes	characteristic
77	#15668009	D₄	1	1	yes	characteristic
78	#15668000	D₄	1	2	yes	—
79	#15667986	—	2	1	no	—
80	#15667986	—	2	1	no	—
81	C₄×D₃₅₆	—	2	1	no	—
82	C₄×D₃₅₆	—	2	1	no	—
83	C₂×C₄⋊Dic₈₉	—	2	1	no	—
84	C₂×C₄⋊Dic₈₉	—	2	1	no	—
85	#15667947	—	2	4	no	—
86	C₄⋊#10623494	—	2	1	no	—
87	C₄⋊#10623494	—	2	1	no	—
88	C₄⋊#10623494	D₄	1	1	yes	characteristic
89	C₄⋊#10623494	D₄	1	2	yes	—
90	C₄⋊#10623494	D₄	1	1	yes	characteristic
91	#15667935	—	2	2	no	—
92	#15667935	—	2	2	no	—
93	#15667935	—	2	2	no	—
94	#15667932	—	2	2	no	—
95	#15667930	—	2	4	no	—
96	#15667930	—	4	2	no	—
97	#15667924	—	2	2	no	—
98	#15667924	—	2	2	no	—
99	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₈₉	—	2	1	no	—
105	C₄×Q₈×C₈₉	—	2	1	no	—
106	C₄×Q₈×C₈₉	—	2	1	no	—
107	C₄×Q₈×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	—	2	1	no	—
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	#101×C₈₉	—	2	2	no	—
113	#101×C₈₉	D₄	1	4	yes	complemented
114	#97×C₈₉	—	2	1	no	—
115	#97×C₈₉	—	2	1	no	—
116	C₄×C₈×C₈₉	—	2	1	no	—
117	C₄×C₈×C₈₉	—	2	1	no	—
118	#13083574	—	2	2	no	—
119	#13083574	—	2	2	no	—
120	#13083574	—	2	2	no	—
121	#13083574	—	2	2	no	—
122	C₂×Dic₁₇₈	—	2	2	no	—
123	C₂×Dic₁₇₈	—	2	2	no	—
124	C₂×Dic₁₇₈	—	2	2	no	—
125	C₂×Dic₁₇₈	—	2	2	no	—
126	C₂×Dic₁₇₈	—	2	2	no	—
127	C₂×Dic₁₇₈	—	2	2	no	—
128	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
129	C₂×D₃₅₆	—	2	1	no	—
130	C₂×D₃₅₆	—	2	1	no	—
131	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
132	C₂×C₂²⋊D₈₉	—	2	2	no	—
133	C₂²×Dic₈₉	—	2	2	no	—
134	C₂×C₄×D₈₉	—	2	2	no	—
135	Dic₃₅₆	—	4	4	no	—
136	Dic₃₅₆	—	4	4	no	—
137	#13083564	—	4	4	no	—
138	#13083564	—	4	4	no	—
139	#13083564	—	4	4	no	—
140	#13083563	—	4	4	no	—
141	#13083563	—	4	4	no	—
142	#13083561	—	4	4	no	—
143	#13083558	—	2	2	no	—
144	#13083558	—	2	2	no	—
145	#13083557	—	4	4	no	—
146	C₂×#10623494	—	2	2	no	—
147	C₂×#10623494	—	2	2	no	—
148	C₂×#10623494	—	2	2	no	—
149	C₂×#10623494	C₂×D₄	1	2	yes	—
150	C₂×#10623494	C₂×D₄	1	2	yes	—
151	C₈×D₈₉	—	4	4	no	—
152	C₄⋊Dic₈₉	—	2	1	no	—
153	C₄⋊Dic₈₉	—	2	1	no	—
154	C₄⋊Dic₈₉	—	4	1	no	—
155	C₄⋊Dic₈₉	—	4	1	no	—
156	C₄⋊Dic₈₉	—	4	1	no	—
157	C₄⋊Dic₈₉	—	4	1	no	—
158	#13083551	—	2	2	no	—
159	#13083551	—	2	2	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	1	no	—
168	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₈₉	—	2	1	no	—
172	M₁₆×C₈₉	—	2	1	no	—
173	M₁₆×C₈₉	—	2	1	no	—
174	M₁₆×C₈₉	—	2	1	no	—
175	M₁₆×C₈₉	—	2	1	no	—
176	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
177	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
178	M₁₆×C₈₉	#41	1	2	yes	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	4	1	no	—
186	C₄⋊C₄×C₈₉	—	4	1	no	—
187	C₄²×C₈₉	—	4	1	no	—
188	C₄²×C₈₉	—	4	1	no	—
189	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
194	C₂²×D₈₉	—	2	2	no	—
195	Q₈×C₈₉	—	2	2	no	—
196	Q₈×C₈₉	—	2	2	no	—
197	Q₈×C₈₉	—	4	1	no	—
198	Q₈×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	4	1	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	8	1	no	—
206	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²⋊D₈₉	—	4	2	no	—
217	C₂²⋊D₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	2	2	no	—
219	C₂×Dic₈₉	—	4	2	no	—
220	C₂×Dic₈₉	—	4	2	no	—
221	C₂×Dic₈₉	—	4	2	no	—
222	D₃₅₆	—	2	2	no	—
223	D₃₅₆	—	2	2	no	—
224	D₃₅₆	—	4	2	no	—
225	D₃₅₆	—	8	1	no	—
226	C₄×D₈₉	—	4	2	no	—
227	C₄×D₈₉	—	4	2	no	—
228	Dic₁₇₈	—	2	2	no	—
229	Dic₁₇₈	—	2	2	no	—
230	Dic₁₇₈	—	4	2	no	—
231	Dic₁₇₈	—	4	2	no	—
232	Dic₁₇₈	—	4	2	no	—
233	Dic₁₇₈	—	4	2	no	—
234	C₈×C₈₉	—	2	2	no	—
235	C₈×C₈₉	—	2	2	no	—
236	C₈×C₈₉	—	2	2	no	—
237	C₈×C₈₉	—	4	1	no	—
238	#10623494	—	2	2	no	—
239	#10623494	—	2	2	no	—
240	#10623494	—	4	2	no	—
241	C₂²×C₈₉	—	2	1	no	—
242	C₂²×C₈₉	—	2	1	no	—
243	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
244	C₂²×C₈₉	#532	1	1	yes	characteristic
245	C₂²×C₈₉	#540	1	1	yes	characteristic
246	C₂×D₈₉	—	4	2	no	—
247	C₂×D₈₉	—	4	2	no	—
248	C₂×D₈₉	—	4	2	no	—
249	C₄×C₈₉	—	2	1	no	—
250	C₄×C₈₉	—	2	1	no	—
251	C₄×C₈₉	—	2	1	no	—
252	C₄×C₈₉	—	4	2	no	—
253	C₄×C₈₉	—	8	1	no	—
254	C₄×C₈₉	#473	1	2	yes	complemented
255	C₄×C₈₉	D₄²	1	1	yes	characteristic
256	C₄×C₈₉	D₄²	1	1	yes	characteristic
257	C₄×C₈₉	#546	1	1	yes	characteristic
258	C₄×C₈₉	#550	1	1	yes	characteristic
259	Dic₈₉	—	4	2	no	—
260	Dic₈₉	—	8	2	no	—
261	#25406	—	89	1	no	maximal, Sylow
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	2	1	no	—
264	C₂×C₈₉	#2428	1	1	yes	characteristic
265	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
266	C₂×C₈₉	#3069	1	1	yes	characteristic
267	D₈₉	—	8	2	no	—
268	#3152	—	89	1	no	—
269	C₂×#473	—	89	2	no	—
270	#3037	—	89	1	no	—
271	C₂×#462	—	89	1	no	—
272	#2935	—	89	1	no	—
273	#2052	—	89	2	no	—
274	#2020	—	89	2	no	—
275	#1966	—	89	1	no	—
276	#1950	—	89	1	no	—
277	#1908	—	89	2	no	—
278	C₄×#101	D₈₉	1	1	yes	characteristic, complemented
279	C₈₉	#25406	1	1	yes	characteristic, complemented, Sylow
280	C₂×#137	—	89	2	no	—
281	C₂×#137	—	89	2	no	—
282	C₂×#137	—	89	2	no	—
283	C₂²×Q₁₆	—	89	2	no	—
284	C₂×#131	—	89	2	no	—
285	#532	—	89	1	no	—
286	C₂×C₄⋊Q₈	—	89	1	no	—
287	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
288	#497	—	178	2	no	—
289	#494	—	178	1	no	—
290	#492	—	178	1	no	—
291	#473	—	178	8	no	—
292	#464	—	178	2	no	—
293	#462	—	178	1	no	—
294	#462	—	178	2	no	—
295	#462	—	178	1	no	—
296	#462	—	178	1	no	—
297	#460	—	178	1	no	—
298	#436	—	178	1	no	—
299	#435	—	178	2	no	—
300	C₈×D₄	—	178	1	no	—
301	C₂×#108	—	89	2	no	—
302	#423	—	89	1	no	—
303	C₂×C₄⋊C₈	—	89	1	no	—
304	#417	—	89	2	no	—
305	C₂×#103	—	89	2	no	—
306	C₂×#101	—	89	2	no	—
307	C₂×#101	—	89	2	no	—
308	C₂×#101	C₂×D₈₉	1	1	yes	characteristic
309	C₂×#101	C₂×D₈₉	1	1	yes	characteristic
310	#408	—	89	2	no	—
311	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
312	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
313	#343	C₂×D₈₉	1	1	yes	characteristic
314	#343	C₂×D₈₉	1	1	yes	characteristic
315	#341	—	89	2	no	—
316	C₂×#41	—	89	2	no	—
317	C₂²×Q₈	—	89	2	no	—
318	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
319	#137	—	356	2	no	—
320	#137	—	356	2	no	—
321	#137	—	356	2	no	—
322	#137	—	178	4	no	—
323	#137	—	178	4	no	—
324	#137	—	178	4	no	—
325	C₂×Q₁₆	—	356	2	no	—
326	C₂×Q₁₆	—	178	2	no	—
327	C₂×Q₁₆	—	178	2	no	—
328	C₂×Q₁₆	—	178	2	no	—
329	C₂×Q₁₆	—	178	2	no	—
330	C₂×Q₁₆	—	178	2	no	—
331	C₂×Q₁₆	—	178	4	no	—
332	C₂×SD₁₆	—	178	2	no	—
333	C₂×SD₁₆	—	178	2	no	—
334	C₂×SD₁₆	—	178	2	no	—
335	#131	—	356	2	no	—
336	#131	—	178	4	no	—
337	C₂×M₁₆	—	89	2	no	—
338	C₂×M₁₆	—	178	2	no	—
339	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
340	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
341	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
342	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
343	C₂²×C₈	—	89	2	no	—
344	C₂²×C₈	—	178	2	no	—
345	C₄⋊Q₈	—	89	1	no	—
346	C₄⋊Q₈	—	178	1	no	—
347	C₄⋊Q₈	—	178	1	no	—
348	C₄⋊Q₈	—	178	1	no	—
349	C₄⋊Q₈	—	178	1	no	—
350	#127	—	89	1	no	—
351	#124	—	89	2	no	—
352	#121	—	178	1	no	—
353	#121	—	178	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	178	1	no	—
359	C₄×D₄	—	178	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	178	1	no	—
362	C₂×C₄⋊C₄	—	178	1	no	—
363	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
366	#108	—	178	4	no	—
367	C₄⋊C₈	—	89	1	no	—
368	C₄⋊C₈	—	89	2	no	—
369	C₄⋊C₈	—	89	1	no	—
370	C₄⋊C₈	—	178	1	no	—
371	C₄⋊C₈	—	178	1	no	—
372	#103	—	178	2	no	—
373	#103	—	178	2	no	—
374	#103	—	178	2	no	—
375	#102	—	178	2	no	—
376	#101	—	2	2	no	—
377	#101	—	356	2	no	—
378	#101	—	178	4	no	—
379	#101	D₃₅₆	1	4	yes	complemented
380	C₂²⋊C₈	—	178	2	no	—
381	C₂²⋊C₈	—	178	2	no	—
382	#97	—	2	1	no	—
383	#97	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	#41	—	178	2	no	—
387	#41	—	178	2	no	—
388	#41	—	178	2	no	—
389	#41	—	178	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	89	2	no	—
396	C₂×Q₈	—	178	2	no	—
397	C₂×Q₈	—	178	2	no	—
398	C₂×Q₈	—	178	2	no	—
399	C₂×Q₈	—	178	2	no	—
400	C₂×Q₈	—	178	2	no	—
401	C₂×Q₈	—	178	2	no	—
402	C₂×Q₈	C₂×D₃₅₆	1	2	yes	—
403	C₂×D₄	—	89	2	no	—
404	C₂×D₄	—	178	2	no	—
405	C₂×D₄	—	178	1	no	—
406	C₂×D₄	—	178	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	178	2	no	—
410	C₂²×C₄	—	178	2	no	—
411	C₂²×C₄	#13083574	1	1	yes	characteristic
412	C₂²×C₄	#13083574	1	1	yes	characteristic
413	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
414	Q₁₆	—	356	4	no	—
415	Q₁₆	—	356	4	no	—
416	Q₁₆	—	356	4	no	—
417	Q₁₆	—	356	4	no	—
418	Q₁₆	—	356	4	no	—
419	SD₁₆	—	356	4	no	—
420	SD₁₆	—	356	4	no	—
421	SD₁₆	—	356	4	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	356	4	no	—
428	M₁₆	—	178	2	no	—
429	M₁₆	—	178	2	no	—
430	M₁₆	C₂×D₃₅₆	1	2	yes	—
431	M₁₆	C₂×D₃₅₆	1	2	yes	—
432	M₁₆	#13083574	1	2	yes	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	89	2	no	—
438	C₂×C₈	—	89	2	no	—
439	C₂×C₈	—	356	4	no	—
440	C₂×C₈	—	178	2	no	—
441	C₂×C₈	—	178	2	no	—
442	C₂×C₈	—	178	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	356	1	no	—
448	C₄⋊C₄	—	356	1	no	—
449	C₄⋊C₄	—	356	1	no	—
450	C₄⋊C₄	—	356	1	no	—
451	C₄⋊C₄	—	178	1	no	—
452	C₄⋊C₄	—	178	1	no	—
453	C₂²⋊C₄	—	178	2	no	—
454	C₂²⋊C₄	—	178	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	D₄×D₈₉	1	1	yes	characteristic
458	C₄²	D₄×D₈₉	1	1	yes	characteristic
459	C₄²	D₄×D₈₉	1	1	yes	characteristic
460	C₄²	D₄×D₈₉	1	1	yes	characteristic
461	C₂³	—	178	2	no	—
462	C₂³	C₂×#13083574	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	356	2	no	—
468	Q₈	—	356	2	no	—
469	Q₈	—	356	2	no	—
470	Q₈	—	356	2	no	—
471	Q₈	—	178	2	no	—
472	Q₈	—	178	2	no	—
473	D₄	—	356	2	no	—
474	D₄	—	356	2	no	—
475	D₄	—	356	2	no	—
476	D₄	—	178	2	no	—
477	D₄	—	178	2	no	—
478	D₄	—	712	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	356	2	no	—
487	C₂×C₄	—	356	2	no	—
488	C₂×C₄	—	356	2	no	—
489	C₂×C₄	—	356	2	no	—
490	C₂×C₄	—	356	2	no	—
491	C₂×C₄	—	178	2	no	—
492	C₂×C₄	#15667985	1	1	yes	characteristic
493	C₂×C₄	#15667985	1	1	yes	characteristic
494	C₂×C₄	#15667985	1	1	yes	characteristic
495	C₂×C₄	#15667985	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
499	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
500	C₂×C₄	#15668058	1	1	yes	characteristic
501	C₂×C₄	#15668058	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	2	2	no	—
505	C₈	—	4	1	no	—
506	C₈	—	356	2	no	—
507	C₈	—	178	2	no	—
508	C₈	—	178	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	356	2	no	—
512	C₂²	—	356	2	no	—
513	C₂²	—	356	2	no	—
514	C₂²	C₂×#15667985	1	1	yes	characteristic
515	C₂²	#19152148	1	1	yes	characteristic
516	C₂²	#19152203	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	356	2	no	—
523	C₄	—	712	2	no	—
524	C₄	#19151872	1	2	yes	complemented
525	C₄	D₄×D₃₅₆	1	1	yes	characteristic
526	C₄	D₄×D₃₅₆	1	1	yes	characteristic
527	C₄	#19152244	1	1	yes	characteristic
528	C₄	#19152269	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	712	2	no	—
532	C₂	#26023840	1	1	yes	characteristic
533	C₂	C₂×#19151872	1	1	yes	characteristic
534	C₂	#26029992	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667985
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#101×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	C₄×#101	D₈₉
hypocenter	C₈₉	#25406
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#101

Complements

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

N	H ≅ G/N	type
2. C₂×#19151872	C₂	semidirect
4. C₂×#19151808	C₂	semidirect
6. #26021554	C₂	semidirect
7. #26021372	C₂	semidirect
8. #26021096	C₂	semidirect
9. #26021027	C₂	semidirect
10. #26020768	C₂	semidirect
11. C₄×#101×C₈₉	C₂	semidirect
113. #101×C₈₉	D₄	semidirect
254. C₄×C₈₉	#473	semidirect
278. C₄×#101	D₈₉	semidirect
279. C₈₉	#25406	semidirect
379. #101	D₃₅₆	semidirect
524. C₄	#19151872	semidirect

Maximal subgroups

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

subgroup	index
#26030711	2
C₂×#19151872	2
#26029724	2
C₂×#19151808	2
#26028998	2
#26021554	2
#26021372	2
#26021096	2
#26021027	2
#26020768	2
C₄×#101×C₈₉	2
#25406	89