Subgroups — #36523913

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029363	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668032	C₂	1	1	yes	maximal, characteristic
4	#26019073	C₂	1	2	yes	maximal, complemented
5	#26019068	C₂	1	2	yes	maximal, complemented
6	#26019055	C₂	1	2	yes	maximal, complemented
7	#26019049	C₂	1	2	yes	maximal, complemented
8	C₂×#19151348	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018640	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	Q₈×#10623494	C₂²	1	2	yes	—
15	#19151722	C₂²	1	2	yes	—
16	C₄×#13083564	C₄	1	1	yes	characteristic
17	C₄×#13083564	C₂²	1	1	yes	characteristic
18	C₄×#13083561	C₄	1	1	yes	characteristic
19	C₄×#13083561	C₂²	1	1	yes	characteristic
20	C₄×#13083562	C₄	1	1	yes	characteristic
21	C₄×#13083562	C₂²	1	1	yes	characteristic
22	C₄×#13083559	C₄	1	1	yes	characteristic
23	C₄×#13083559	C₂²	1	1	yes	characteristic
24	D₄×#10623494	—	2	2	no	—
25	D₄×#10623494	C₂²	1	2	yes	—
26	#19151663	C₂²	1	2	yes	—
27	C₈×C₂²⋊D₈₉	—	2	2	no	—
28	#19151651	—	2	1	no	—
29	#19151651	C₂²	1	1	yes	characteristic
30	#19151650	—	2	1	no	—
31	#19151634	C₄	1	1	yes	characteristic
32	C₂×C₄⋊#10623494	—	2	1	no	—
33	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
34	C₄⋊C₈×D₈₉	—	2	1	no	—
35	#19151594	C₄	1	1	yes	characteristic
36	#19151592	C₄	1	1	yes	characteristic
37	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
38	#19151348	C₂²	1	2	yes	—
39	#19151348	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#19151320	C₂²	1	2	yes	—
43	C₈×#10623494	C₂²	1	2	yes	—
44	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
45	#431×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
48	D₄⋊C₈×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	#15668032	C₈	1	8	yes	complemented
51	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
55	C₂²×#10623494	—	2	2	no	—
56	C₂²×#10623494	—	2	1	no	—
57	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
58	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
62	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₈₉	—	2	1	no	—
65	C₄×C₂²⋊D₈₉	—	2	1	no	—
66	#15667971	C₂×C₄	1	1	yes	characteristic
67	#15667969	—	2	1	no	—
68	C₄²×D₈₉	—	2	1	no	—
69	#15667945	C₂×C₄	1	1	yes	characteristic
70	#15667945	C₂×C₄	1	1	yes	characteristic
71	#15667943	C₂×C₄	1	1	yes	characteristic
72	#15667943	C₂×C₄	1	1	yes	characteristic
73	C₄⋊#10623494	—	2	2	no	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	D₄	1	1	yes	characteristic
76	C₄⋊#10623494	D₄	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	2	yes	—
78	#15667941	—	2	2	no	—
79	#15667936	C₂×C₄	1	1	yes	characteristic
80	#15667936	C₂×C₄	1	1	yes	characteristic
81	#15667935	C₂×C₄	1	1	yes	characteristic
82	#15667935	C₂×C₄	1	1	yes	characteristic
83	#15667933	C₂×C₄	1	1	yes	characteristic
84	#15667933	C₂×C₄	1	1	yes	characteristic
85	#15667932	C₂×C₄	1	1	yes	characteristic
86	#15667932	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#10623494	—	2	2	no	—
88	C₂²⋊#10623494	D₄	1	2	yes	—
89	#15667924	—	2	2	no	—
90	C₄×#10623494	—	2	2	no	—
91	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
92	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
93	C₄×#10623494	C₂³	1	1	yes	characteristic
94	C₄×#10623494	C₂³	1	1	yes	characteristic
95	C₄×#10623494	C₂³	1	2	yes	—
96	C₈×Dic₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	—	2	1	no	—
99	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₈₉	—	2	1	no	—
102	C₄×D₄×C₈₉	—	2	1	no	—
103	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
105	#117×C₈₉	—	2	1	no	—
106	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	—	2	1	no	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₈₉	—	2	1	no	—
110	C₄⋊C₈×C₈₉	—	2	1	no	—
111	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
112	C₂²⋊C₈×C₈₉	—	2	1	no	—
113	C₄×C₈×C₈₉	C₂³	1	2	yes	—
114	#13083574	—	2	2	no	—
115	#13083574	C₂×C₈	1	4	yes	complemented
116	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₉	—	2	1	no	—
119	C₂×C₄×D₈₉	—	2	1	no	—
120	C₂×C₄×D₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	#13083564	C₂×C₈	1	4	yes	complemented
123	#13083562	C₂×C₈	1	4	yes	complemented
124	#13083561	C₂×C₈	1	4	yes	complemented
125	#13083559	C₂×C₈	1	4	yes	complemented
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	8	2	no	—
129	C₂×#10623494	—	8	1	no	—
130	C₂×#10623494	C₂×C₈	1	4	yes	complemented
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
133	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
134	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
135	C₂×#10623494	C₂×D₄	1	2	yes	—
136	C₂×#10623494	C₂×D₄	1	2	yes	—
137	C₈×D₈₉	—	8	2	no	—
138	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	#13083553	—	2	1	no	—
141	#13083553	—	2	1	no	—
142	C₂²⋊Dic₈₉	—	2	1	no	—
143	#13083551	—	2	1	no	—
144	#13083551	—	2	1	no	—
145	C₄×Dic₈₉	—	2	1	no	—
146	C₄×Dic₈₉	—	2	1	no	—
147	C₄×Dic₈₉	—	2	1	no	—
148	#41×C₈₉	—	2	2	no	—
149	#41×C₈₉	C₂×C₈	1	4	yes	complemented
150	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₈₉	—	2	1	no	—
152	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	8	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₈₉	—	2	1	no	—
167	C₂²⋊C₄×C₈₉	—	2	1	no	—
168	C₂²⋊C₄×C₈₉	—	2	1	no	—
169	C₄²×C₈₉	—	2	1	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	—	2	1	no	—
172	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₈₉	#41	1	1	yes	characteristic
175	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂³×C₈₉	—	2	1	no	—
177	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₈₉	—	2	1	no	—
179	Q₈×C₈₉	—	2	1	no	—
180	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
181	D₄×C₈₉	—	2	4	no	—
182	D₄×C₈₉	—	2	1	no	—
183	D₄×C₈₉	C₂²×C₈	1	2	yes	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	8	1	no	—
194	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
198	C₂×C₄×C₈₉	#131	1	2	yes	—
199	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₈₉	—	2	4	no	—
203	C₂×Dic₈₉	—	2	1	no	—
204	C₂×Dic₈₉	—	2	1	no	—
205	C₂×Dic₈₉	—	2	1	no	—
206	D₃₅₆	—	2	1	no	—
207	D₃₅₆	C₂²×C₈	1	2	yes	—
208	C₄×D₈₉	—	2	4	no	—
209	C₄×D₈₉	—	4	1	no	—
210	C₄×D₈₉	—	4	1	no	—
211	C₄×D₈₉	—	8	1	no	—
212	Dic₁₇₈	—	2	1	no	—
213	Dic₁₇₈	C₂²×C₈	1	2	yes	—
214	C₈×C₈₉	—	4	2	no	—
215	C₈×C₈₉	—	4	2	no	—
216	#10623494	—	2	1	no	—
217	#10623494	—	2	1	no	—
218	#10623494	—	2	2	no	—
219	#10623494	—	2	2	no	—
220	#10623494	—	4	2	no	—
221	#10623494	C₂²×C₈	1	2	yes	—
222	#10623494	C₂²×C₈	1	2	yes	—
223	C₂²×C₈₉	—	2	1	no	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	2	no	—
226	C₂²×C₈₉	—	4	1	no	—
227	C₂²×C₈₉	—	4	1	no	—
228	C₂²×C₈₉	C₈×D₄	1	2	yes	—
229	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂×D₈₉	—	2	2	no	—
231	C₂×D₈₉	—	4	1	no	—
232	C₂×D₈₉	—	4	1	no	—
233	C₄×C₈₉	—	2	2	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	—	4	1	no	—
238	C₄×C₈₉	—	4	1	no	—
239	C₄×C₈₉	C₈×D₄	1	2	yes	—
240	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
241	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
242	C₄×C₈₉	#577	1	1	yes	characteristic
243	C₄×C₈₉	#577	1	1	yes	characteristic
244	Dic₈₉	—	2	2	no	—
245	Dic₈₉	—	4	1	no	—
246	Dic₈₉	—	4	1	no	—
247	#17858	—	89	1	no	maximal, Sylow
248	C₂×C₈₉	—	2	2	no	—
249	C₂×C₈₉	—	4	2	no	—
250	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
251	C₂×C₈₉	#2952	1	1	yes	characteristic
252	C₂×C₈₉	#2957	1	1	yes	characteristic
253	D₈₉	—	4	2	no	—
254	#2988	—	89	1	no	—
255	#2988	—	89	1	no	—
256	C₄×#135	—	89	1	no	—
257	#1580	—	89	2	no	—
258	#1579	—	89	2	no	—
259	C₈×SD₁₆	—	89	2	no	—
260	C₈×SD₁₆	—	89	2	no	—
261	C₂×#334	—	89	1	no	—
262	#1477	—	89	1	no	—
263	#1477	D₈₉	1	1	yes	characteristic, complemented
264	#1450	—	89	1	no	—
265	C₈₉	#17858	1	1	yes	characteristic, complemented, Sylow
266	C₂×#135	—	89	1	no	—
267	C₄×#41	—	89	1	no	—
268	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
269	C₈×Q₈	—	89	2	no	—
270	C₈×Q₈	—	89	2	no	—
271	C₄×Q₁₆	—	89	1	no	—
272	C₄×Q₁₆	—	89	1	no	—
273	C₄×SD₁₆	—	89	1	no	—
274	C₄×SD₁₆	—	89	1	no	—
275	C₄×SD₁₆	—	89	1	no	—
276	C₄×SD₁₆	—	89	1	no	—
277	C₄×D₈	—	89	1	no	—
278	C₄×D₈	—	89	1	no	—
279	C₈×D₄	—	89	2	no	—
280	C₈×D₄	—	89	2	no	—
281	C₈×D₄	—	178	2	no	—
282	C₈×D₄	—	178	2	no	—
283	#431	—	89	1	no	—
284	#431	—	178	1	no	—
285	#431	—	178	1	no	—
286	#431	C₂×D₈₉	1	1	yes	characteristic
287	#427	—	89	1	no	—
288	C₂×C₄⋊C₈	—	89	1	no	—
289	C₂×C₄⋊C₈	—	178	1	no	—
290	C₂×C₄⋊C₈	—	178	1	no	—
291	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
292	#416	—	89	1	no	—
293	#416	—	89	1	no	—
294	C₂×C₄×C₈	—	89	1	no	—
295	#334	—	89	2	no	—
296	#334	—	89	2	no	—
297	Q₈⋊C₈	—	89	2	no	—
298	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
299	D₄⋊C₈	—	89	2	no	—
300	D₄⋊C₈	C₂×D₈₉	1	2	yes	—
301	#322	—	89	2	no	—
302	C₈²	—	89	2	no	—
303	C₂×#41	—	89	1	no	—
304	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
305	#135	—	89	8	no	—
306	C₂×Q₁₆	—	89	1	no	—
307	C₂×SD₁₆	—	89	1	no	—
308	C₂×SD₁₆	—	89	1	no	—
309	C₂×D₈	—	89	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	89	1	no	—
312	C₂²×C₈	—	89	1	no	—
313	C₂²×C₈	—	178	2	no	—
314	C₂²×C₈	—	178	2	no	—
315	C₂²×C₈	—	178	1	no	—
316	C₄×Q₈	—	89	1	no	—
317	C₄×Q₈	—	89	1	no	—
318	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
319	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	89	1	no	—
323	C₄×D₄	—	89	1	no	—
324	C₄×D₄	—	178	1	no	—
325	C₄×D₄	—	178	1	no	—
326	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
327	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
328	#117	—	2	1	no	—
329	#117	—	89	1	no	—
330	#117	—	178	1	no	—
331	#117	C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	178	1	no	—
334	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
335	#107	—	89	1	no	—
336	#107	—	89	1	no	—
337	#106	—	89	1	no	—
338	#106	—	89	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	89	1	no	—
342	C₄⋊C₈	—	89	1	no	—
343	C₄⋊C₈	—	89	2	no	—
344	C₄⋊C₈	—	178	2	no	—
345	C₄⋊C₈	—	178	2	no	—
346	C₄⋊C₈	—	178	1	no	—
347	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
348	#103	—	89	1	no	—
349	#103	—	89	1	no	—
350	#103	—	89	1	no	—
351	#103	—	89	1	no	—
352	#102	—	89	1	no	—
353	#102	—	89	1	no	—
354	#102	—	89	1	no	—
355	#102	—	89	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	89	2	no	—
358	C₂²⋊C₈	—	178	2	no	—
359	C₂²⋊C₈	—	178	2	no	—
360	C₄×C₈	—	89	1	no	—
361	C₄×C₈	—	89	1	no	—
362	C₄×C₈	—	89	1	no	—
363	C₄×C₈	—	89	2	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	178	2	no	—
366	C₄×C₈	—	178	2	no	—
367	C₄×C₈	C₂²×D₈₉	1	2	yes	—
368	#41	—	2	2	no	—
369	#41	—	89	4	no	—
370	#41	—	178	2	no	—
371	#41	C₈×D₈₉	1	4	yes	complemented
372	C₂×Q₈	—	89	1	no	—
373	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	89	1	no	—
376	C₂×D₄	—	178	1	no	—
377	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	178	1	no	—
382	C₂²×C₄	—	178	1	no	—
383	C₂²×C₄	—	178	1	no	—
384	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
385	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
386	C₂²×C₄	#13083573	1	1	yes	characteristic
387	Q₁₆	—	89	4	no	—
388	SD₁₆	—	89	4	no	—
389	SD₁₆	—	89	4	no	—
390	D₈	—	89	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	8	1	no	—
394	C₂×C₈	—	89	4	no	—
395	C₂×C₈	—	89	1	no	—
396	C₂×C₈	—	89	1	no	—
397	C₂×C₈	—	89	1	no	—
398	C₂×C₈	—	89	1	no	—
399	C₂×C₈	—	89	2	no	—
400	C₂×C₈	—	89	2	no	—
401	C₂×C₈	—	178	2	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	712	2	no	—
404	C₂×C₈	—	712	1	no	—
405	C₂×C₈	—	712	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	89	1	no	—
409	C₄⋊C₄	—	89	1	no	—
410	C₄⋊C₄	—	178	1	no	—
411	C₄⋊C₄	—	178	1	no	—
412	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
413	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	178	1	no	—
418	C₂²⋊C₄	—	178	1	no	—
419	C₂²⋊C₄	—	178	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	178	1	no	—
424	C₄²	—	178	1	no	—
425	C₄²	—	178	1	no	—
426	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₄²	D₄×D₈₉	1	1	yes	characteristic
428	C₄²	#13083573	1	1	yes	characteristic
429	C₄²	C₂³×D₈₉	1	1	yes	characteristic
430	C₂³	—	2	1	no	—
431	C₂³	—	178	1	no	—
432	C₂³	#15667972	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	89	2	no	—
435	Q₈	—	178	1	no	—
436	Q₈	C₂×C₈×D₈₉	1	2	yes	—
437	D₄	—	2	4	no	—
438	D₄	—	2	1	no	—
439	D₄	—	89	2	no	—
440	D₄	—	178	4	no	—
441	D₄	—	178	1	no	—
442	D₄	C₂×C₈×D₈₉	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	356	1	no	—
454	C₂×C₄	—	356	1	no	—
455	C₂×C₄	—	178	1	no	—
456	C₂×C₄	—	178	1	no	—
457	C₂×C₄	—	178	1	no	—
458	C₂×C₄	—	178	4	no	—
459	C₂×C₄	—	712	1	no	—
460	C₂×C₄	#15667972	1	1	yes	characteristic
461	C₂×C₄	#15667972	1	1	yes	characteristic
462	C₂×C₄	#15667972	1	1	yes	characteristic
463	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
464	C₂×C₄	#15668020	1	2	yes	—
465	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	89	2	no	—
471	C₈	—	89	2	no	—
472	C₈	—	356	2	no	—
473	C₈	—	178	2	no	—
474	C₈	—	178	2	no	—
475	C₈	—	178	1	no	—
476	C₈	—	178	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	356	1	no	—
483	C₂²	—	356	1	no	—
484	C₂²	—	178	2	no	—
485	C₂²	#19151661	1	2	yes	—
486	C₂²	C₂×#15667972	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	356	1	no	—
494	C₄	—	356	1	no	—
495	C₄	—	178	2	no	—
496	C₄	#19151661	1	2	yes	—
497	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
498	C₄	C₂×#15668020	1	1	yes	characteristic
499	C₄	#19152407	1	1	yes	characteristic
500	C₄	#19152408	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	356	2	no	—
504	C₂	C₂×#19151661	1	1	yes	characteristic
505	C₂	#26029131	1	1	yes	characteristic
506	C₂	#26029165	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1477	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1477	D₈₉
hypocenter	C₈₉	#17858
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
1. #26029363	C₂	semidirect
2. #26029361	C₂	semidirect
4. #26019073	C₂	semidirect
5. #26019068	C₂	semidirect
6. #26019055	C₂	semidirect
7. #26019049	C₂	semidirect
8. C₂×#19151348	C₂	semidirect
9. #26018640	C₂	semidirect
10. #26018536	C₂	semidirect
11. C₈₉×#1477	C₂	semidirect
50. #15668032	C₈	semidirect
115. #13083574	C₂×C₈	semidirect
122. #13083564	C₂×C₈	semidirect
123. #13083562	C₂×C₈	semidirect
124. #13083561	C₂×C₈	semidirect
125. #13083559	C₂×C₈	semidirect
130. C₂×#10623494	C₂×C₈	semidirect
149. #41×C₈₉	C₂×C₈	semidirect
263. #1477	D₈₉	semidirect
265. C₈₉	#17858	semidirect
371. #41	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029363	2
#26029361	2
C₄×#15668032	2
#26019073	2
#26019068	2
#26019055	2
#26019049	2
C₂×#19151348	2
#26018640	2
#26018536	2
C₈₉×#1477	2
#17858	89