Subgroups — #36562622

Order 22784.

738 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	#26030595	C₂	1	1	yes	maximal, characteristic
2	#26029191	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028967	C₂	1	1	yes	maximal, characteristic
4	#26021227	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021078	C₂	1	1	yes	maximal, characteristic
6	#26020963	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020959	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020955	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020391	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020097	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020093	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020092	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020088	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1938	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668020	C₂²	1	1	yes	characteristic
17	C₂×#15668019	C₂²	1	1	yes	characteristic
18	#19152151	C₂²	1	1	yes	characteristic
19	#19152144	C₂²	1	1	yes	characteristic
20	#19151965	C₄	1	2	yes	complemented
21	#19151961	C₄	1	2	yes	complemented
22	#19151959	C₄	1	2	yes	complemented
23	#19151956	C₄	1	2	yes	complemented
24	#19151727	—	2	2	no	—
25	#19151725	—	2	2	no	—
26	#19151672	—	2	2	no	—
27	#19151666	—	2	2	no	—
28	#19151624	C₂²	1	1	yes	characteristic
29	#19151621	C₂²	1	1	yes	characteristic
30	#19151621	C₂²	1	1	yes	characteristic
31	C₂×#15667940	C₂²	1	1	yes	characteristic
32	C₂×#15667939	C₂²	1	1	yes	characteristic
33	C₂×#15667938	C₂²	1	1	yes	characteristic
34	#19151595	C₂²	1	1	yes	characteristic
35	#19151594	C₂²	1	1	yes	characteristic
36	#19151592	C₂²	1	1	yes	characteristic
37	#19151564	C₂²	1	1	yes	characteristic
38	#19151556	C₂²	1	1	yes	characteristic
39	#19151554	C₂²	1	1	yes	characteristic
40	C₂×#15667923	C₂²	1	1	yes	characteristic
41	C₂×#15667922	C₂²	1	1	yes	characteristic
42	C₂×#15667922	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
45	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
46	#19151363	C₂²	1	1	yes	characteristic
47	#19151362	C₂²	1	1	yes	characteristic
48	#19151362	C₂²	1	1	yes	characteristic
49	#19151359	C₂²	1	1	yes	characteristic
50	#19151358	C₂²	1	1	yes	characteristic
51	#19151357	C₂²	1	1	yes	characteristic
52	#424×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
54	#416×C₈₉	C₂²	1	1	yes	characteristic
55	#408×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
57	#341×C₈₉	C₂²	1	1	yes	characteristic
58	#339×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083574	C₂³	1	1	yes	characteristic
60	#15668020	—	2	2	no	—
61	#15668020	—	2	2	no	—
62	#15668019	—	2	2	no	—
63	#15668019	—	2	2	no	—
64	C₂×#13083558	—	2	1	no	—
65	C₂×#13083558	C₂³	1	1	yes	characteristic
66	C₂×#13083558	C₂³	1	1	yes	characteristic
67	C₂×#13083557	—	2	1	no	—
68	C₂²×#10623494	—	2	1	no	—
69	C₂²×#10623494	C₂³	1	1	yes	characteristic
70	C₂²×#10623494	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₈₉	—	2	1	no	—
72	#15668011	C₂×C₄	1	2	yes	—
73	#15668010	C₂×C₄	1	1	yes	characteristic
74	#15668008	C₂×C₄	1	1	yes	characteristic
75	#15668003	C₂×C₄	1	2	yes	—
76	#15668001	C₂×C₄	1	1	yes	characteristic
77	#15667999	C₂×C₄	1	1	yes	characteristic
78	#15667989	—	2	2	no	—
79	#15667984	—	2	2	no	—
80	C₄×Dic₁₇₈	—	2	2	no	—
81	C₄×C₂²⋊D₈₉	—	2	2	no	—
82	#15667971	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₈₉	—	2	2	no	—
84	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
86	#15667941	—	2	2	no	—
87	#15667941	—	2	2	no	—
88	#15667941	—	2	2	no	—
89	#15667940	—	2	2	no	—
90	#15667939	—	2	2	no	—
91	#15667938	—	2	2	no	—
92	#15667937	C₂×C₄	1	2	yes	—
93	#15667936	C₂×C₄	1	2	yes	—
94	#15667935	C₂×C₄	1	2	yes	—
95	#15667934	C₂×C₄	1	2	yes	—
96	#15667933	C₂×C₄	1	2	yes	—
97	#15667932	C₂×C₄	1	2	yes	—
98	#15667924	—	2	2	no	—
99	#15667923	—	2	1	no	—
100	#15667923	—	2	2	no	—
101	#15667922	—	2	1	no	—
102	#15667922	C₂×C₄	1	2	yes	—
103	#15667922	C₂×C₄	1	2	yes	—
104	#15667922	D₄	1	2	yes	—
105	#15667922	D₄	1	2	yes	—
106	C₄×#10623494	—	2	1	no	—
107	C₈×Dic₈₉	—	2	1	no	—
108	C₈×Dic₈₉	—	2	2	no	—
109	C₈×Dic₈₉	—	2	2	no	—
110	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	#117×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₈₉	—	2	2	no	—
118	#104×C₈₉	—	2	2	no	—
119	#103×C₈₉	C₂×C₄	1	2	yes	—
120	#102×C₈₉	C₂×C₄	1	2	yes	—
121	C₂²⋊C₈×C₈₉	—	2	2	no	—
122	#97×C₈₉	—	2	2	no	—
123	#13083574	—	2	1	no	—
124	#13083574	—	2	1	no	—
125	#13083574	—	2	1	no	—
126	#13083574	—	2	1	no	—
127	C₂×Dic₁₇₈	—	2	2	no	—
128	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₈₉	—	2	1	no	—
131	C₂×C₂²⋊D₈₉	—	2	2	no	—
132	C₂²×Dic₈₉	—	2	1	no	—
133	C₂²×Dic₈₉	#41	1	2	yes	—
134	C₂×C₄×D₈₉	—	2	1	no	—
135	#13083558	—	2	1	no	—
136	#13083558	—	2	1	no	—
137	#13083558	—	2	1	no	—
138	#13083558	—	2	1	no	—
139	#13083558	—	4	2	no	—
140	#13083557	—	4	2	no	—
141	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	—	4	2	no	—
146	C₂×#10623494	C₂²×C₄	1	2	yes	—
147	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
148	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
149	C₂×#10623494	#41	1	2	yes	—
150	C₂×#10623494	#41	1	2	yes	—
151	C₈×D₈₉	—	4	2	no	—
152	C₄⋊Dic₈₉	—	2	2	no	—
153	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
154	#13083553	—	2	2	no	—
155	#13083553	—	2	2	no	—
156	#13083553	—	2	2	no	—
157	C₂²⋊Dic₈₉	—	2	1	no	—
158	C₂²⋊Dic₈₉	—	2	2	no	—
159	#13083551	—	2	2	no	—
160	C₄×Dic₈₉	—	2	1	no	—
161	C₄×Dic₈₉	—	2	1	no	—
162	C₄×Dic₈₉	—	4	4	no	—
163	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
166	C₄×Dic₈₉	#41	1	2	yes	—
167	#41×C₈₉	—	2	1	no	—
168	#41×C₈₉	—	2	1	no	—
169	#41×C₈₉	—	2	1	no	—
170	#41×C₈₉	—	2	1	no	—
171	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₈₉	—	2	1	no	—
178	M₁₆×C₈₉	—	2	1	no	—
179	M₁₆×C₈₉	—	2	1	no	—
180	M₁₆×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
190	C₂²⋊C₄×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₄²×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	#41	1	2	yes	—
194	C₂³×C₈₉	—	2	1	no	—
195	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
196	C₂²×D₈₉	—	2	1	no	—
197	Q₈×C₈₉	—	2	1	no	—
198	Q₈×C₈₉	—	2	1	no	—
199	D₄×C₈₉	—	2	1	no	—
200	D₄×C₈₉	—	2	1	no	—
201	D₄×C₈₉	—	4	1	no	—
202	D₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	2	2	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	4	2	no	—
207	C₂×C₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₈₉	—	4	1	no	—
216	C₂²⋊D₈₉	—	4	1	no	—
217	C₂²⋊D₈₉	—	8	2	no	—
218	C₂×Dic₈₉	—	2	4	no	—
219	C₂×Dic₈₉	—	2	2	no	—
220	C₂×Dic₈₉	—	2	2	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	4	2	no	—
223	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
224	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
225	D₃₅₆	—	2	1	no	—
226	D₃₅₆	—	2	1	no	—
227	C₄×D₈₉	—	4	1	no	—
228	C₄×D₈₉	—	4	1	no	—
229	Dic₁₇₈	—	2	1	no	—
230	Dic₁₇₈	—	2	1	no	—
231	Dic₁₇₈	—	8	2	no	—
232	C₈×C₈₉	—	2	2	no	—
233	C₈×C₈₉	—	2	2	no	—
234	C₈×C₈₉	—	4	1	no	—
235	C₈×C₈₉	—	4	1	no	—
236	#10623494	—	2	2	no	—
237	#10623494	—	4	1	no	—
238	#10623494	—	4	1	no	—
239	#10623494	#124	1	2	yes	—
240	#10623494	#124	1	2	yes	—
241	C₂²×C₈₉	—	2	2	no	—
242	C₂²×C₈₉	—	4	2	no	—
243	C₂²×C₈₉	—	4	1	no	—
244	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₈₉	#529	1	1	yes	characteristic
246	C₂²×C₈₉	#529	1	1	yes	characteristic
247	C₂×D₈₉	—	4	2	no	—
248	C₂×D₈₉	—	4	1	no	—
249	C₄×C₈₉	—	4	2	no	—
250	C₄×C₈₉	—	4	2	no	—
251	C₄×C₈₉	—	4	1	no	—
252	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
253	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
254	C₄×C₈₉	C₂×#124	1	1	yes	characteristic
255	C₄×C₈₉	#532	1	1	yes	characteristic
256	Dic₈₉	—	2	4	no	—
257	Dic₈₉	—	2	2	no	—
258	Dic₈₉	—	2	2	no	—
259	Dic₈₉	—	4	2	no	—
260	Dic₈₉	—	4	1	no	—
261	#21662	—	89	1	no	maximal, Sylow
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	2	1	no	—
264	C₂×C₈₉	—	8	1	no	—
265	C₂×C₈₉	C₄×#124	1	1	yes	characteristic
266	C₂×C₈₉	#2956	1	2	yes	—
267	D₈₉	—	8	1	no	—
268	#3135	—	89	1	no	—
269	#2961	—	89	1	no	—
270	#2932	—	89	1	no	—
271	#1994	—	89	1	no	—
272	#1962	—	89	1	no	—
273	#1938	—	89	1	no	—
274	#1938	D₈₉	1	1	yes	characteristic, complemented
275	#1937	—	89	1	no	—
276	#1937	—	89	1	no	—
277	#1838	—	89	1	no	—
278	#1765	—	89	1	no	—
279	#1765	—	89	1	no	—
280	#1764	—	89	1	no	—
281	#1764	—	89	1	no	—
282	C₄×#97	—	89	1	no	—
283	C₈₉	#21662	1	1	yes	characteristic, complemented, Sylow
284	C₂×#131	—	89	1	no	—
285	C₂×#131	—	89	1	no	—
286	#533	—	89	1	no	—
287	#532	—	89	1	no	—
288	#491	—	89	2	no	—
289	#490	—	89	2	no	—
290	#489	—	89	2	no	—
291	#489	—	89	2	no	—
292	#446	—	178	2	no	—
293	#446	—	178	2	no	—
294	#435	—	178	2	no	—
295	#435	—	178	2	no	—
296	#424	—	89	1	no	—
297	#424	C₂×D₈₉	1	1	yes	characteristic
298	#423	—	89	1	no	—
299	#423	—	89	1	no	—
300	C₂×#104	—	89	1	no	—
301	C₂×#104	—	89	1	no	—
302	C₂×#104	—	89	1	no	—
303	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
304	#416	—	89	1	no	—
305	#416	—	89	1	no	—
306	#416	—	89	1	no	—
307	#416	C₂×D₈₉	1	1	yes	characteristic
308	#408	—	89	1	no	—
309	#408	C₂×D₈₉	1	1	yes	characteristic
310	#405	—	89	1	no	—
311	#405	—	89	1	no	—
312	C₂×#97	—	89	1	no	—
313	C₂×#97	—	89	1	no	—
314	C₂×#97	—	89	1	no	—
315	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
316	C₂×C₄×C₈	—	89	1	no	—
317	C₂×C₄×C₈	—	89	1	no	—
318	C₄³	—	89	1	no	—
319	#341	—	89	1	no	—
320	#341	—	89	1	no	—
321	#341	—	89	1	no	—
322	#341	C₂×D₈₉	1	1	yes	characteristic
323	#339	—	89	1	no	—
324	#339	—	89	1	no	—
325	#339	—	89	1	no	—
326	#339	C₂×D₈₉	1	1	yes	characteristic
327	C₂×#41	—	89	1	no	—
328	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
329	#131	—	178	2	no	—
330	#131	—	178	2	no	—
331	#131	—	178	2	no	—
332	#131	—	178	2	no	—
333	C₂×M₁₆	—	89	1	no	—
334	C₂×M₁₆	—	89	1	no	—
335	C₂×M₁₆	—	178	1	no	—
336	C₂×M₁₆	—	178	1	no	—
337	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
339	C₂²×C₈	—	89	1	no	—
340	C₂²×C₈	—	89	1	no	—
341	C₂²×C₈	—	178	1	no	—
342	C₂²×C₈	—	178	1	no	—
343	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
345	C₄⋊Q₈	—	89	2	no	—
346	C₄⋊Q₈	—	89	1	no	—
347	#127	—	89	1	no	—
348	#125	—	89	2	no	—
349	#124	—	89	1	no	—
350	#124	—	89	1	no	—
351	C₂²⋊Q₈	—	178	2	no	—
352	#121	—	178	2	no	—
353	C₄×Q₈	—	178	2	no	—
354	C₄×D₄	—	178	2	no	—
355	#117	—	89	1	no	—
356	#117	C₂²×D₈₉	1	1	yes	characteristic
357	C₂×C₄²	—	89	1	no	—
358	C₂×C₄²	—	89	1	no	—
359	C₂×C₄²	—	178	2	no	—
360	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	—	178	2	no	—
363	C₄⋊C₈	—	178	2	no	—
364	C₄⋊C₈	—	178	2	no	—
365	#104	—	2	2	no	—
366	#104	—	178	2	no	—
367	#104	—	178	2	no	—
368	#104	—	178	2	no	—
369	#103	—	89	2	no	—
370	#103	—	89	2	no	—
371	#103	—	89	2	no	—
372	#103	C₄×D₈₉	1	2	yes	—
373	#102	—	89	2	no	—
374	#102	—	89	2	no	—
375	#102	—	89	2	no	—
376	#102	C₄×D₈₉	1	2	yes	—
377	C₂²⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	—	178	2	no	—
379	#97	—	2	2	no	—
380	#97	—	89	2	no	—
381	#97	—	89	2	no	—
382	#97	—	89	2	no	—
383	#97	—	89	2	no	—
384	#97	—	178	2	no	—
385	#97	—	178	1	no	—
386	#97	—	178	1	no	—
387	C₄×C₈	—	178	1	no	—
388	C₄×C₈	—	178	2	no	—
389	C₄×C₈	—	178	2	no	—
390	C₄×C₈	—	178	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	178	1	no	—
396	#41	—	178	1	no	—
397	#41	—	178	1	no	—
398	#41	—	178	1	no	—
399	C₂×Q₈	—	89	1	no	—
400	C₂×Q₈	—	178	2	no	—
401	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	89	1	no	—
404	C₂×D₄	—	178	2	no	—
405	C₂×D₄	—	178	1	no	—
406	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	89	2	no	—
410	C₂²×C₄	—	178	1	no	—
411	C₂²×C₄	—	178	1	no	—
412	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
413	M₁₆	—	2	1	no	—
414	M₁₆	—	2	1	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	356	2	no	—
418	M₁₆	—	356	2	no	—
419	M₁₆	—	178	1	no	—
420	M₁₆	—	178	1	no	—
421	M₁₆	—	178	1	no	—
422	M₁₆	—	178	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	89	1	no	—
430	C₂×C₈	—	89	1	no	—
431	C₂×C₈	—	89	2	no	—
432	C₂×C₈	—	89	2	no	—
433	C₂×C₈	—	89	2	no	—
434	C₂×C₈	—	356	2	no	—
435	C₂×C₈	—	356	2	no	—
436	C₂×C₈	—	178	1	no	—
437	C₂×C₈	—	178	1	no	—
438	C₂×C₈	—	178	1	no	—
439	C₂×C₈	—	178	1	no	—
440	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
441	C₂×C₈	D₄×D₈₉	1	2	yes	—
442	C₄⋊C₄	—	89	2	no	—
443	C₄⋊C₄	—	178	2	no	—
444	C₄⋊C₄	—	178	2	no	—
445	C₄⋊C₄	—	178	2	no	—
446	C₄⋊C₄	—	178	2	no	—
447	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	178	2	no	—
450	C₂²⋊C₄	—	178	2	no	—
451	C₂²⋊C₄	—	178	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	89	1	no	—
455	C₄²	—	89	1	no	—
456	C₄²	—	89	2	no	—
457	C₄²	—	89	2	no	—
458	C₄²	—	356	4	no	—
459	C₄²	—	178	1	no	—
460	C₄²	—	178	1	no	—
461	C₄²	#13083573	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	178	1	no	—
464	C₂³	#41×D₈₉	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	178	1	no	—
468	Q₈	—	178	1	no	—
469	Q₈	—	712	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	356	1	no	—
475	D₄	—	356	1	no	—
476	D₄	—	178	1	no	—
477	D₄	—	178	1	no	—
478	D₄	—	712	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	89	2	no	—
486	C₂×C₄	—	89	2	no	—
487	C₂×C₄	—	356	1	no	—
488	C₂×C₄	—	356	1	no	—
489	C₂×C₄	—	356	2	no	—
490	C₂×C₄	—	178	2	no	—
491	C₂×C₄	—	178	1	no	—
492	C₂×C₄	—	178	4	no	—
493	C₂×C₄	—	178	2	no	—
494	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
496	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
497	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
498	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
499	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	2	2	no	—
502	C₈	—	4	1	no	—
503	C₈	—	4	1	no	—
504	C₈	—	89	2	no	—
505	C₈	—	89	2	no	—
506	C₈	—	356	1	no	—
507	C₈	—	356	1	no	—
508	C₈	—	178	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	356	2	no	—
513	C₂²	—	356	1	no	—
514	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
515	C₂²	#19152125	1	1	yes	characteristic
516	C₂²	#19152131	1	1	yes	characteristic
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	356	2	no	—
521	C₄	—	356	1	no	—
522	C₄	—	178	4	no	—
523	C₄	—	178	2	no	—
524	C₄	—	178	2	no	—
525	C₄	C₄×#13083573	1	1	yes	characteristic
526	C₄	#19152066	1	1	yes	characteristic
527	C₄	#124×D₈₉	1	1	yes	characteristic
528	C₄	#19152143	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	712	1	no	—
533	C₂	#26022793	1	1	yes	characteristic
534	C₂	#26029160	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1938	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152144	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1938	D₈₉
hypocenter	C₈₉	#21662
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1938

Complements

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

N	H ≅ G/N	type
2. #26029191	C₂	semidirect
4. #26021227	C₂	semidirect
6. #26020963	C₂	semidirect
7. #26020959	C₂	semidirect
8. #26020955	C₂	semidirect
9. #26020391	C₂	semidirect
10. #26020097	C₂	semidirect
11. #26020093	C₂	semidirect
12. #26020092	C₂	semidirect
13. #26020088	C₂	semidirect
14. #97×Dic₈₉	C₂	semidirect
15. C₈₉×#1938	C₂	semidirect
20. #19151965	C₄	semidirect
21. #19151961	C₄	semidirect
22. #19151959	C₄	semidirect
23. #19151956	C₄	semidirect
274. #1938	D₈₉	semidirect
283. C₈₉	#21662	semidirect

Maximal subgroups

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

subgroup	index
#26030595	2
#26029191	2
#26028967	2
#26021227	2
#26021078	2
#26020963	2
#26020959	2
#26020955	2
#26020391	2
#26020097	2
#26020093	2
#26020092	2
#26020088	2
#97×Dic₈₉	2
C₈₉×#1938	2
#21662	89