Subgroups — #36573886

Order 22784.

752 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15668032	C₂	1	1	yes	maximal, characteristic
2	#26028917	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020955	C₂	1	2	yes	maximal, complemented
4	#26020848	C₂	1	2	yes	maximal, complemented
5	#26020579	C₂	1	2	yes	maximal
6	#26020389	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020272	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020269	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020117	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020087	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₂²	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
15	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
16	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
17	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
18	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
19	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
20	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
21	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
22	#19151658	—	2	2	no	—
23	#19151654	—	2	1	no	—
24	#19151650	—	2	1	no	—
25	#19151634	C₂²	1	1	yes	characteristic
26	#19151622	C₂²	1	1	yes	characteristic
27	C₂×#15667939	C₂²	1	2	yes	—
28	C₂×#15667938	C₂²	1	2	yes	—
29	#19151594	C₂²	1	1	yes	characteristic
30	#19151592	C₂²	1	1	yes	characteristic
31	#19151564	C₂²	1	2	yes	—
32	#19151553	C₂²	1	2	yes	—
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
36	#19151362	C₂²	1	2	yes	—
37	#19151362	C₂²	1	2	yes	—
38	#19151359	C₂²	1	2	yes	—
39	#19151357	C₂²	1	2	yes	—
40	#19151352	C₂²	1	2	yes	—
41	C₂×#131×C₈₉	C₂²	1	2	yes	—
42	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
43	#424×C₈₉	—	2	2	no	—
44	#424×C₈₉	C₂²	1	2	yes	—
45	#423×C₈₉	—	2	1	no	—
46	#423×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
48	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	C₂³	1	1	yes	characteristic
50	#15668032	—	2	2	no	—
51	#15668032	—	2	2	no	—
52	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083558	C₂³	1	2	yes	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
61	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
62	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₈₉	—	2	1	no	—
64	C₄×C₂²⋊D₈₉	—	2	1	no	—
65	#15667971	C₂³	1	1	yes	characteristic
66	#15667969	—	2	1	no	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
69	C₄²×D₈₉	—	2	1	no	—
70	#15667945	C₂×C₄	1	1	yes	characteristic
71	#15667945	C₂×C₄	1	1	yes	characteristic
72	#15667943	C₂×C₄	1	1	yes	characteristic
73	#15667943	C₂×C₄	1	1	yes	characteristic
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	#15667939	—	2	4	no	—
77	#15667938	—	4	2	no	—
78	#15667936	C₂×C₄	1	1	yes	characteristic
79	#15667936	C₂×C₄	1	1	yes	characteristic
80	#15667935	C₂×C₄	1	1	yes	characteristic
81	#15667935	C₂×C₄	1	1	yes	characteristic
82	#15667933	C₂×C₄	1	1	yes	characteristic
83	#15667933	C₂×C₄	1	1	yes	characteristic
84	#15667932	C₂×C₄	1	1	yes	characteristic
85	#15667932	C₂×C₄	1	1	yes	characteristic
86	#15667924	—	2	2	no	—
87	#15667924	—	2	2	no	—
88	#15667922	—	2	2	no	—
89	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
90	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
91	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
92	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₈₉	—	2	2	no	—
94	C₈×Dic₈₉	—	4	2	no	—
95	#15667919	—	2	1	no	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	#131×C₈₉	—	2	4	no	—
98	#131×C₈₉	—	4	2	no	—
99	C₂×M₁₆×C₈₉	—	2	2	no	—
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₈₉	—	2	2	no	—
102	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
103	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₉	—	2	1	no	—
106	C₄×D₄×C₈₉	—	2	1	no	—
107	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
109	#117×C₈₉	—	2	1	no	—
110	#117×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₈₉	—	2	1	no	—
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₈₉	—	2	2	no	—
114	C₄⋊C₈×C₈₉	—	2	2	no	—
115	C₄⋊C₈×C₈₉	—	2	1	no	—
116	C₄⋊C₈×C₈₉	—	2	1	no	—
117	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
118	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
119	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
120	#13083574	—	2	1	no	—
121	#13083574	—	2	1	no	—
122	#13083574	—	2	1	no	—
123	#13083574	—	2	1	no	—
124	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₈₉	—	2	1	no	—
127	C₂²×Dic₈₉	—	2	2	no	—
128	C₂×C₄×D₈₉	—	2	1	no	—
129	C₂×C₄×D₈₉	—	2	1	no	—
130	C₂×C₄×D₈₉	—	2	1	no	—
131	#13083564	—	2	2	no	—
132	#13083562	—	2	2	no	—
133	#13083561	—	2	2	no	—
134	#13083559	—	2	2	no	—
135	#13083558	—	2	2	no	—
136	#13083558	—	2	2	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	—	2	1	no	—
139	C₂×#10623494	—	2	1	no	—
140	C₂×#10623494	—	2	1	no	—
141	C₂×#10623494	—	2	2	no	—
142	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
143	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
144	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
145	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊Dic₈₉	—	2	4	no	—
147	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
149	#13083553	—	2	1	no	—
150	#13083553	—	2	1	no	—
151	C₂²⋊Dic₈₉	—	2	1	no	—
152	#13083551	—	2	1	no	—
153	#13083551	—	2	1	no	—
154	C₄×Dic₈₉	—	2	1	no	—
155	C₄×Dic₈₉	—	2	1	no	—
156	C₄×Dic₈₉	—	2	1	no	—
157	C₄×Dic₈₉	—	2	2	no	—
158	C₄×Dic₈₉	—	2	2	no	—
159	#41×C₈₉	—	2	1	no	—
160	#41×C₈₉	—	2	1	no	—
161	#41×C₈₉	#41	1	2	yes	—
162	#41×C₈₉	#41	1	2	yes	—
163	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×D₄×C₈₉	—	2	1	no	—
165	C₂×D₄×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	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₈₉	—	2	2	no	—
173	M₁₆×C₈₉	—	2	2	no	—
174	M₁₆×C₈₉	—	4	4	no	—
175	C₂×C₈×C₈₉	—	2	2	no	—
176	C₂×C₈×C₈₉	—	2	2	no	—
177	C₂×C₈×C₈₉	—	2	2	no	—
178	C₂×C₈×C₈₉	—	4	4	no	—
179	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²⋊C₄×C₈₉	—	2	1	no	—
186	C₂²⋊C₄×C₈₉	—	2	1	no	—
187	C₂²⋊C₄×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	1	no	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₈₉	—	2	1	no	—
196	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
197	C₂²×D₈₉	—	2	1	no	—
198	Q₈×C₈₉	—	2	1	no	—
199	Q₈×C₈₉	#117	1	2	yes	—
200	D₄×C₈₉	—	2	2	no	—
201	D₄×C₈₉	—	2	2	no	—
202	D₄×C₈₉	—	2	1	no	—
203	D₄×C₈₉	#117	1	2	yes	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	2	2	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	4	1	no	—
211	C₂×C₄×C₈₉	—	4	2	no	—
212	C₂×C₄×C₈₉	—	8	1	no	—
213	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂²⋊D₈₉	—	4	1	no	—
224	C₂²⋊D₈₉	—	4	1	no	—
225	C₂×Dic₈₉	—	2	4	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	—	4	2	no	—
230	C₂×Dic₈₉	—	4	2	no	—
231	D₃₅₆	—	2	1	no	—
232	D₃₅₆	—	2	1	no	—
233	C₄×D₈₉	—	4	1	no	—
234	C₄×D₈₉	—	4	1	no	—
235	C₄×D₈₉	—	4	2	no	—
236	C₄×D₈₉	—	8	1	no	—
237	Dic₁₇₈	—	2	1	no	—
238	Dic₁₇₈	—	2	1	no	—
239	C₈×C₈₉	—	2	2	no	—
240	C₈×C₈₉	—	2	2	no	—
241	C₈×C₈₉	—	4	2	no	—
242	#10623494	—	2	1	no	—
243	#10623494	—	2	1	no	—
244	#10623494	—	2	1	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	4	2	no	—
247	C₂²×C₈₉	—	2	1	no	—
248	C₂²×C₈₉	—	2	1	no	—
249	C₂²×C₈₉	—	2	2	no	—
250	C₂²×C₈₉	—	4	1	no	—
251	C₂²×C₈₉	—	4	1	no	—
252	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₈₉	#552	1	1	yes	characteristic
254	C₂²×C₈₉	#553	1	1	yes	characteristic
255	C₂×D₈₉	—	4	1	no	—
256	C₂×D₈₉	—	4	1	no	—
257	C₂×D₈₉	—	4	1	no	—
258	C₄×C₈₉	—	2	2	no	—
259	C₄×C₈₉	—	2	1	no	—
260	C₄×C₈₉	—	2	1	no	—
261	C₄×C₈₉	—	2	1	no	—
262	C₄×C₈₉	—	4	1	no	—
263	C₄×C₈₉	—	4	1	no	—
264	C₄×C₈₉	#443	1	2	yes	—
265	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
266	C₄×C₈₉	#520	1	1	yes	characteristic
267	C₄×C₈₉	#546	1	1	yes	characteristic
268	C₄×C₈₉	#548	1	1	yes	characteristic
269	Dic₈₉	—	4	4	no	—
270	Dic₈₉	—	4	1	no	—
271	Dic₈₉	—	4	1	no	—
272	Dic₈₉	—	4	1	no	—
273	#22783	—	89	1	no	maximal, Sylow
274	C₂×C₈₉	—	2	1	no	—
275	C₂×C₈₉	—	2	1	no	—
276	C₂×C₈₉	—	4	2	no	—
277	C₂×C₈₉	#2352	1	1	yes	characteristic
278	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
279	C₂×C₈₉	#2957	1	1	yes	characteristic
280	D₈₉	—	8	1	no	—
281	C₄×#135	—	89	1	no	—
282	#2925	—	89	1	no	—
283	#2906	D₈₉	1	1	yes	characteristic, complemented
284	#1937	—	89	2	no	—
285	#1922	—	89	2	no	—
286	#1876	—	89	2	no	—
287	#1837	—	89	1	no	—
288	#1806	—	89	1	no	—
289	#1806	—	89	1	no	—
290	C₈×C₄⋊C₄	—	89	1	no	—
291	#1764	—	89	2	no	—
292	C₈₉	#22783	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	—	89	1	no	—
294	C₂×#131	C₂×D₈₉	1	2	yes	—
295	C₄×#41	—	89	1	no	—
296	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
297	C₄×Q₁₆	—	89	1	no	—
298	C₄×Q₁₆	—	89	1	no	—
299	C₄×SD₁₆	—	89	1	no	—
300	C₄×SD₁₆	—	89	1	no	—
301	C₄×SD₁₆	—	89	1	no	—
302	C₄×SD₁₆	—	89	1	no	—
303	C₄×D₈	—	89	1	no	—
304	C₄×D₈	—	89	1	no	—
305	#433	—	178	2	no	—
306	#432	—	178	1	no	—
307	#431	—	178	1	no	—
308	#427	—	89	1	no	—
309	#424	—	2	2	no	—
310	#424	C₂×D₈₉	1	2	yes	—
311	#423	—	2	1	no	—
312	#423	—	89	1	no	—
313	#423	C₂×D₈₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	—	2	1	no	—
315	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
316	C₂×#104	—	89	2	no	—
317	C₂×#104	—	89	2	no	—
318	#416	—	89	1	no	—
319	#416	—	89	1	no	—
320	#408	—	89	2	no	—
321	#405	—	89	2	no	—
322	C₂×C₄×C₈	—	89	1	no	—
323	C₂×C₄×C₈	—	89	2	no	—
324	C₄×C₄⋊C₄	—	89	1	no	—
325	#341	—	89	2	no	—
326	#341	—	89	2	no	—
327	#339	—	89	2	no	—
328	#339	—	89	2	no	—
329	#336	—	89	2	no	—
330	C₂×#41	—	89	1	no	—
331	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
332	#135	—	178	2	no	—
333	#135	—	178	2	no	—
334	C₂×Q₁₆	—	89	1	no	—
335	C₂×SD₁₆	—	89	1	no	—
336	C₂×SD₁₆	—	89	1	no	—
337	C₂×D₈	—	89	1	no	—
338	#131	—	2	4	no	—
339	#131	—	4	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	89	2	no	—
342	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	89	1	no	—
345	C₂²×C₈	—	89	1	no	—
346	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
347	C₄×Q₈	—	89	1	no	—
348	C₄×Q₈	—	89	1	no	—
349	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
350	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	89	1	no	—
354	C₄×D₄	—	89	1	no	—
355	C₄×D₄	—	178	1	no	—
356	C₄×D₄	—	178	1	no	—
357	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
358	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
359	#117	—	2	1	no	—
360	#117	—	89	1	no	—
361	#117	—	178	1	no	—
362	#117	C₂²×D₈₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	178	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	89	2	no	—
366	C₂×C₄²	—	178	1	no	—
367	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
368	#107	—	89	1	no	—
369	#107	—	89	1	no	—
370	#106	—	89	1	no	—
371	#106	—	89	1	no	—
372	C₄⋊C₈	—	2	2	no	—
373	C₄⋊C₈	—	2	2	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	178	1	no	—
377	C₄⋊C₈	—	178	1	no	—
378	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
379	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
381	#104	—	356	2	no	—
382	#104	—	178	4	no	—
383	#103	—	89	1	no	—
384	#103	—	89	1	no	—
385	#103	—	89	1	no	—
386	#103	—	89	1	no	—
387	#102	—	89	1	no	—
388	#102	—	89	1	no	—
389	#102	—	89	1	no	—
390	#102	—	89	1	no	—
391	C₂²⋊C₈	—	178	2	no	—
392	C₂²⋊C₈	—	178	2	no	—
393	#97	—	178	2	no	—
394	C₄×C₈	—	89	1	no	—
395	C₄×C₈	—	89	1	no	—
396	C₄×C₈	—	89	1	no	—
397	C₄×C₈	—	89	1	no	—
398	C₄×C₈	—	356	2	no	—
399	C₄×C₈	—	178	2	no	—
400	#95	—	178	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	178	1	no	—
404	#41	—	178	1	no	—
405	#41	—	178	1	no	—
406	#41	—	178	1	no	—
407	#41	#13083573	1	2	yes	—
408	#41	#13083575	1	2	yes	—
409	C₂×Q₈	—	89	1	no	—
410	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	89	1	no	—
413	C₂×D₄	—	178	1	no	—
414	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	178	2	no	—
419	C₂²×C₄	—	178	1	no	—
420	C₂²×C₄	—	178	1	no	—
421	C₂²×C₄	—	178	1	no	—
422	C₂²×C₄	#13083574	1	1	yes	characteristic
423	C₂²×C₄	#13083574	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
425	Q₁₆	—	178	2	no	—
426	SD₁₆	—	178	2	no	—
427	SD₁₆	—	178	2	no	—
428	D₈	—	178	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	4	4	no	—
432	M₁₆	—	178	2	no	—
433	M₁₆	—	178	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	4	no	—
438	C₂×C₈	—	89	1	no	—
439	C₂×C₈	—	89	1	no	—
440	C₂×C₈	—	89	1	no	—
441	C₂×C₈	—	89	1	no	—
442	C₂×C₈	—	178	2	no	—
443	C₂×C₈	—	178	1	no	—
444	C₂×C₈	—	178	1	no	—
445	C₂×C₈	—	178	1	no	—
446	C₂×C₈	—	178	1	no	—
447	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
448	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	89	1	no	—
452	C₄⋊C₄	—	89	1	no	—
453	C₄⋊C₄	—	178	4	no	—
454	C₄⋊C₄	—	178	1	no	—
455	C₄⋊C₄	—	178	1	no	—
456	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
457	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	178	1	no	—
462	C₂²⋊C₄	—	178	1	no	—
463	C₂²⋊C₄	—	178	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	178	2	no	—
468	C₄²	—	178	2	no	—
469	C₄²	—	178	1	no	—
470	C₄²	—	178	1	no	—
471	C₄²	—	178	1	no	—
472	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	178	1	no	—
478	C₂³	C₂×#13083574	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	178	1	no	—
481	Q₈	—	178	1	no	—
482	Q₈	#15667970	1	2	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	356	1	no	—
487	D₄	—	356	1	no	—
488	D₄	—	178	1	no	—
489	D₄	—	178	1	no	—
490	D₄	#15667970	1	2	yes	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	356	2	no	—
501	C₂×C₄	—	356	2	no	—
502	C₂×C₄	—	356	2	no	—
503	C₂×C₄	—	356	1	no	—
504	C₂×C₄	—	356	1	no	—
505	C₂×C₄	—	178	4	no	—
506	C₂×C₄	—	178	1	no	—
507	C₂×C₄	—	178	1	no	—
508	C₂×C₄	—	178	1	no	—
509	C₂×C₄	—	712	1	no	—
510	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
511	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
512	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
517	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
518	C₂×C₄	#15668057	1	1	yes	characteristic
519	C₂×C₄	#15668060	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	356	2	no	—
524	C₈	—	178	1	no	—
525	C₈	—	178	1	no	—
526	C₈	—	178	1	no	—
527	C₈	—	178	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	356	1	no	—
534	C₂²	—	356	1	no	—
535	C₂²	—	356	1	no	—
536	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
537	C₂²	#19152283	1	1	yes	characteristic
538	C₂²	#19152296	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	356	4	no	—
546	C₄	—	356	1	no	—
547	C₄	—	356	1	no	—
548	C₄	—	356	1	no	—
549	C₄	#19151713	1	2	yes	—
550	C₄	C₂×#15667970	1	1	yes	characteristic
551	C₄	#19152079	1	1	yes	characteristic
552	C₄	#19152242	1	1	yes	characteristic
553	C₄	#19152259	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	712	1	no	—
558	C₂	#26023177	1	1	yes	characteristic
559	C₂	C₂×#19151713	1	1	yes	characteristic
560	C₂	#26029167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2906	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2906	D₈₉
hypocenter	C₈₉	#22783
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2906

Complements

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

N	H ≅ G/N	type
2. #26028917	C₂	semidirect
3. #26020955	C₂	semidirect
4. #26020848	C₂	semidirect
6. #26020389	C₂	semidirect
7. #26020272	C₂	semidirect
8. #26020269	C₂	semidirect
9. #26020117	C₂	semidirect
10. #26020087	C₂	semidirect
11. C₈₉×#2906	C₂	semidirect
14. C₄×#13083564	C₄	semidirect
15. C₄×#13083564	C₄	semidirect
16. C₄×#13083561	C₄	semidirect
17. C₄×#13083561	C₄	semidirect
18. C₄×#13083562	C₄	semidirect
19. C₄×#13083562	C₄	semidirect
20. C₄×#13083559	C₄	semidirect
21. C₄×#13083559	C₄	semidirect
283. #2906	D₈₉	semidirect
292. C₈₉	#22783	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668032	2
#26028917	2
#26020955	2
#26020848	2
#26020579	2
#26020389	2
#26020272	2
#26020269	2
#26020117	2
#26020087	2
C₈₉×#2906	2
#22783	89