Subgroups — #36572889

Order 22784.

870 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151712	C₂	1	2	yes	maximal
2	C₄×#15668032	C₂	1	1	yes	maximal, characteristic
3	#26028821	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028820	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020999	C₂	1	2	yes	maximal, complemented
6	#26020528	C₂	1	2	yes	maximal, complemented
7	#26020525	C₂	1	2	yes	maximal, complemented
8	#26020423	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020273	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	C₂×#15668019	C₂²	1	2	yes	—
15	C₄×#13083574	C₂²	1	1	yes	characteristic
16	#19151712	—	2	8	no	—
17	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
18	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
19	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
20	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
21	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
22	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
23	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
24	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
25	C₂×#15667947	C₂²	1	2	yes	—
26	C₂×#15667947	C₂²	1	2	yes	—
27	#19151634	C₂²	1	1	yes	characteristic
28	#19151626	C₂²	1	2	yes	—
29	#19151625	—	2	2	no	—
30	#19151625	C₂²	1	2	yes	—
31	#19151623	—	2	2	no	—
32	#19151622	—	2	1	no	—
33	#19151622	C₂²	1	1	yes	characteristic
34	#19151620	—	2	1	no	—
35	C₂×C₄⋊#10623494	—	2	1	no	—
36	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×D₈₉	—	2	1	no	—
38	C₂×#15667940	C₂²	1	2	yes	—
39	#19151594	C₂²	1	1	yes	characteristic
40	#19151592	C₂²	1	1	yes	characteristic
41	C₂×C₄×#10623494	C₂²	1	2	yes	—
42	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
43	#19151358	C₂²	1	2	yes	—
44	#19151353	C₂²	1	2	yes	—
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	#423×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#104×C₈₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
49	#339×C₈₉	C₂²	1	2	yes	—
50	C₂×#13083574	C₂³	1	1	yes	characteristic
51	#15668032	D₄	1	4	yes	—
52	#15668032	Q₈	1	4	yes	—
53	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
57	#15668020	—	2	4	no	—
58	#15668020	—	4	2	no	—
59	#15668019	—	2	4	no	—
60	#15668019	—	4	2	no	—
61	C₂×#13083558	—	2	2	no	—
62	C₂×#13083558	C₂³	1	2	yes	—
63	C₂×#13083557	—	2	2	no	—
64	C₂²×#10623494	—	2	2	no	—
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	2	yes	—
67	C₂²×#10623494	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₈₉	—	2	2	no	—
69	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
71	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
72	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₈₉	—	2	1	no	—
74	C₄×C₂²⋊D₈₉	—	2	1	no	—
75	#15667971	C₂³	1	1	yes	characteristic
76	#15667969	—	2	1	no	—
77	C₄²×D₈₉	—	2	1	no	—
78	#15667947	—	2	4	no	—
79	#15667947	—	4	2	no	—
80	#15667945	C₂×C₄	1	1	yes	characteristic
81	#15667945	C₂×C₄	1	1	yes	characteristic
82	#15667943	C₂×C₄	1	1	yes	characteristic
83	#15667943	C₂×C₄	1	1	yes	characteristic
84	C₄⋊#10623494	—	2	2	no	—
85	C₄⋊#10623494	—	2	2	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	1	yes	characteristic
90	C₄⋊#10623494	D₄	1	2	yes	—
91	#15667941	—	2	2	no	—
92	#15667941	—	2	2	no	—
93	#15667940	—	2	4	no	—
94	#15667936	C₂×C₄	1	1	yes	characteristic
95	#15667936	C₂×C₄	1	1	yes	characteristic
96	#15667935	C₂×C₄	1	1	yes	characteristic
97	#15667935	C₂×C₄	1	1	yes	characteristic
98	#15667933	C₂×C₄	1	1	yes	characteristic
99	#15667933	C₂×C₄	1	1	yes	characteristic
100	#15667932	C₂×C₄	1	1	yes	characteristic
101	#15667932	C₂×C₄	1	1	yes	characteristic
102	C₄×#10623494	—	2	4	no	—
103	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
104	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
105	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
106	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
107	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
109	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
110	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₄×D₄×C₈₉	—	2	1	no	—
112	C₄×D₄×C₈₉	—	2	1	no	—
113	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
115	#117×C₈₉	—	2	1	no	—
116	#117×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₄²×C₈₉	—	2	1	no	—
119	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₈₉	—	2	1	no	—
122	C₄⋊C₈×C₈₉	—	2	1	no	—
123	#104×C₈₉	—	2	4	no	—
124	#95×C₈₉	—	2	1	no	—
125	#13083574	—	2	1	no	—
126	#13083574	—	2	1	no	—
127	#13083574	C₂×D₄	1	2	yes	—
128	#13083574	C₂×Q₈	1	2	yes	—
129	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊D₈₉	—	2	1	no	—
132	C₂×C₄×D₈₉	—	2	1	no	—
133	C₂×C₄×D₈₉	—	2	1	no	—
134	C₂×C₄×D₈₉	—	2	1	no	—
135	#13083564	C₄⋊C₄	1	4	yes	complemented
136	#13083562	C₄⋊C₄	1	4	yes	complemented
137	#13083561	C₄⋊C₄	1	4	yes	complemented
138	#13083559	C₄⋊C₄	1	4	yes	complemented
139	#13083558	—	2	2	no	—
140	#13083558	—	2	2	no	—
141	#13083558	—	4	4	no	—
142	#13083557	—	4	4	no	—
143	C₂×#10623494	—	2	2	no	—
144	C₂×#10623494	—	2	2	no	—
145	C₂×#10623494	—	2	1	no	—
146	C₂×#10623494	—	2	1	no	—
147	C₂×#10623494	—	2	2	no	—
148	C₂×#10623494	—	4	4	no	—
149	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
150	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
151	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
152	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
153	C₂×#10623494	C₂×D₄	1	2	yes	—
154	C₂×#10623494	C₂×D₄	1	2	yes	—
155	C₂×#10623494	C₂×D₄	1	2	yes	—
156	C₂×#10623494	C₂×Q₈	1	2	yes	—
157	C₈×D₈₉	—	4	4	no	—
158	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
160	#13083553	—	2	1	no	—
161	#13083553	—	2	1	no	—
162	C₂²⋊Dic₈₉	—	2	1	no	—
163	#13083551	—	2	1	no	—
164	#13083551	—	2	1	no	—
165	C₄×Dic₈₉	—	2	1	no	—
166	C₄×Dic₈₉	—	2	1	no	—
167	C₄×Dic₈₉	—	2	1	no	—
168	#41×C₈₉	—	2	1	no	—
169	#41×C₈₉	—	2	1	no	—
170	#41×C₈₉	C₂×D₄	1	2	yes	—
171	#41×C₈₉	C₂×Q₈	1	2	yes	—
172	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	2	no	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
182	M₁₆×C₈₉	—	2	2	no	—
183	M₁₆×C₈₉	—	2	2	no	—
184	C₂×C₈×C₈₉	—	2	2	no	—
185	C₄⋊C₄×C₈₉	—	2	4	no	—
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²⋊C₄×C₈₉	—	2	1	no	—
191	C₂²⋊C₄×C₈₉	—	2	1	no	—
192	C₂²⋊C₄×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	—	2	1	no	—
195	C₄²×C₈₉	—	2	1	no	—
196	C₄²×C₈₉	—	2	2	no	—
197	C₄²×C₈₉	—	2	2	no	—
198	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₂³×C₈₉	—	2	1	no	—
203	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₂²×D₈₉	—	2	1	no	—
205	Q₈×C₈₉	—	2	1	no	—
206	Q₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
207	D₄×C₈₉	—	2	2	no	—
208	D₄×C₈₉	—	2	2	no	—
209	D₄×C₈₉	—	2	1	no	—
210	D₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	2	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	4	1	no	—
219	C₂×C₄×C₈₉	—	4	2	no	—
220	C₂×C₄×C₈₉	—	4	2	no	—
221	C₂×C₄×C₈₉	—	4	2	no	—
222	C₂×C₄×C₈₉	—	8	1	no	—
223	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
233	C₂²⋊D₈₉	—	2	2	no	—
234	C₂²⋊D₈₉	—	2	2	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	D₃₅₆	—	2	1	no	—
239	D₃₅₆	C₂×C₄⋊C₄	1	2	yes	—
240	C₄×D₈₉	—	2	2	no	—
241	C₄×D₈₉	—	2	2	no	—
242	C₄×D₈₉	—	4	2	no	—
243	C₄×D₈₉	—	8	1	no	—
244	Dic₁₇₈	—	2	1	no	—
245	Dic₁₇₈	C₂×C₄⋊C₄	1	2	yes	—
246	C₈×C₈₉	—	4	2	no	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	2	no	—
250	#10623494	—	2	2	no	—
251	#10623494	—	4	2	no	—
252	#10623494	C₂×C₄⋊C₄	1	2	yes	—
253	#10623494	C₂×C₄⋊C₄	1	2	yes	—
254	C₂²×C₈₉	—	2	1	no	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	2	no	—
257	C₂²×C₈₉	—	4	1	no	—
258	C₂²×C₈₉	—	4	1	no	—
259	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂²×C₈₉	#547	1	1	yes	characteristic
261	C₂²×C₈₉	#554	1	1	yes	characteristic
262	C₂×D₈₉	—	2	2	no	—
263	C₂×D₈₉	—	4	1	no	—
264	C₂×D₈₉	—	4	1	no	—
265	C₄×C₈₉	—	2	2	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	1	no	—
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	—	4	4	no	—
270	C₄×C₈₉	—	4	1	no	—
271	C₄×C₈₉	—	4	1	no	—
272	C₄×C₈₉	#443	1	2	yes	complemented
273	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
274	C₄×C₈₉	#520	1	1	yes	characteristic
275	C₄×C₈₉	D₄²	1	1	yes	characteristic
276	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
277	Dic₈₉	—	2	2	no	—
278	Dic₈₉	—	4	1	no	—
279	Dic₈₉	—	4	1	no	—
280	#22688	—	89	1	no	maximal, Sylow
281	C₂×C₈₉	—	2	1	no	—
282	C₂×C₈₉	—	2	1	no	—
283	C₂×C₈₉	—	4	2	no	—
284	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
285	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
286	C₂×C₈₉	#2957	1	1	yes	characteristic
287	D₈₉	—	4	2	no	—
288	C₂×#443	—	89	2	no	—
289	C₄×#135	—	89	1	no	—
290	#2906	—	89	1	no	—
291	#2906	—	89	1	no	—
292	#1945	—	89	2	no	—
293	#1866	—	89	2	no	—
294	#1866	—	89	2	no	—
295	#1848	—	89	1	no	—
296	#1806	—	89	1	no	—
297	#1806	D₈₉	1	1	yes	characteristic, complemented
298	C₈×C₄⋊C₄	—	89	1	no	—
299	C₈₉	#22688	1	1	yes	characteristic, complemented, Sylow
300	C₂×#135	—	89	1	no	—
301	C₂×#131	—	89	2	no	—
302	C₂×#131	—	89	2	no	—
303	C₄×#41	—	89	1	no	—
304	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
305	#443	—	178	8	no	—
306	C₄×Q₁₆	—	89	1	no	—
307	C₄×Q₁₆	—	89	1	no	—
308	C₄×SD₁₆	—	89	1	no	—
309	C₄×SD₁₆	—	89	1	no	—
310	C₄×SD₁₆	—	89	1	no	—
311	C₄×SD₁₆	—	89	1	no	—
312	C₄×D₈	—	89	1	no	—
313	C₄×D₈	—	89	1	no	—
314	C₂×#108	—	89	2	no	—
315	C₂×#108	—	89	2	no	—
316	#427	—	89	1	no	—
317	#424	—	89	2	no	—
318	#424	—	89	2	no	—
319	#424	—	178	2	no	—
320	#424	—	178	2	no	—
321	#423	—	89	1	no	—
322	#423	—	178	1	no	—
323	#423	—	178	1	no	—
324	#423	C₂×D₈₉	1	1	yes	characteristic
325	C₂×C₄⋊C₈	—	89	1	no	—
326	C₂×C₄⋊C₈	—	178	1	no	—
327	C₂×C₄⋊C₈	—	178	1	no	—
328	C₂×#104	—	89	2	no	—
329	C₂×#104	C₂×D₈₉	1	2	yes	—
330	#416	—	89	1	no	—
331	#416	—	89	1	no	—
332	C₂×C₄×C₈	—	89	1	no	—
333	C₂×C₄×C₈	—	89	2	no	—
334	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
335	#339	—	89	2	no	—
336	#339	C₂×D₈₉	1	2	yes	—
337	#336	—	89	2	no	—
338	C₂×#41	—	89	1	no	—
339	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
340	#135	—	89	4	no	—
341	#135	—	89	4	no	—
342	C₂×Q₁₆	—	89	1	no	—
343	C₂×SD₁₆	—	89	1	no	—
344	C₂×SD₁₆	—	89	1	no	—
345	C₂×D₈	—	89	1	no	—
346	#131	—	356	2	no	—
347	#131	—	356	2	no	—
348	#131	—	178	4	no	—
349	#131	—	178	4	no	—
350	C₂×M₁₆	—	89	2	no	—
351	C₂×M₁₆	—	178	2	no	—
352	C₂×M₁₆	—	178	2	no	—
353	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
354	C₂²×C₈	—	89	1	no	—
355	C₂²×C₈	—	89	2	no	—
356	C₂²×C₈	—	89	1	no	—
357	C₂²×C₈	—	178	2	no	—
358	C₂²×C₈	—	178	2	no	—
359	C₄×Q₈	—	89	1	no	—
360	C₄×Q₈	—	89	1	no	—
361	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
362	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	89	1	no	—
366	C₄×D₄	—	89	1	no	—
367	C₄×D₄	—	178	1	no	—
368	C₄×D₄	—	178	1	no	—
369	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
370	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	—	89	1	no	—
373	#117	—	178	1	no	—
374	#117	C₂²×D₈₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	178	1	no	—
378	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
379	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
380	#108	—	356	2	no	—
381	#108	—	178	4	no	—
382	#107	—	89	1	no	—
383	#107	—	89	1	no	—
384	#106	—	89	1	no	—
385	#106	—	89	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	89	1	no	—
389	C₄⋊C₈	—	89	1	no	—
390	C₄⋊C₈	—	89	2	no	—
391	C₄⋊C₈	—	178	2	no	—
392	C₄⋊C₈	—	178	2	no	—
393	C₄⋊C₈	—	178	2	no	—
394	C₄⋊C₈	—	178	2	no	—
395	C₄⋊C₈	—	178	1	no	—
396	C₄⋊C₈	—	178	1	no	—
397	#104	—	2	4	no	—
398	#104	—	178	4	no	—
399	#103	—	89	1	no	—
400	#103	—	89	1	no	—
401	#103	—	89	1	no	—
402	#103	—	89	1	no	—
403	#102	—	89	1	no	—
404	#102	—	89	1	no	—
405	#102	—	89	1	no	—
406	#102	—	89	1	no	—
407	C₄×C₈	—	89	1	no	—
408	C₄×C₈	—	89	1	no	—
409	C₄×C₈	—	89	1	no	—
410	C₄×C₈	—	89	1	no	—
411	C₄×C₈	—	178	4	no	—
412	#95	—	2	1	no	—
413	#41	—	2	1	no	—
414	#41	—	2	1	no	—
415	#41	—	89	2	no	—
416	#41	—	89	2	no	—
417	#41	—	178	1	no	—
418	#41	—	178	1	no	—
419	#41	D₄×D₈₉	1	2	yes	—
420	#41	Q₈×D₈₉	1	2	yes	—
421	C₂×Q₈	—	89	1	no	—
422	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	89	1	no	—
425	C₂×D₄	—	178	1	no	—
426	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	178	1	no	—
432	C₂²×C₄	—	178	1	no	—
433	C₂²×C₄	—	178	1	no	—
434	C₂²×C₄	#13083573	1	1	yes	characteristic
435	C₂²×C₄	#13083573	1	1	yes	characteristic
436	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
437	Q₁₆	—	89	4	no	—
438	SD₁₆	—	89	4	no	—
439	SD₁₆	—	89	4	no	—
440	D₈	—	89	4	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	356	4	no	—
444	M₁₆	—	356	4	no	—
445	M₁₆	—	178	2	no	—
446	M₁₆	—	178	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	89	1	no	—
449	C₂×C₈	—	89	1	no	—
450	C₂×C₈	—	89	2	no	—
451	C₂×C₈	—	89	2	no	—
452	C₂×C₈	—	89	1	no	—
453	C₂×C₈	—	89	1	no	—
454	C₂×C₈	—	89	2	no	—
455	C₂×C₈	—	89	2	no	—
456	C₂×C₈	—	356	4	no	—
457	C₂×C₈	—	356	4	no	—
458	C₂×C₈	—	178	2	no	—
459	C₂×C₈	—	178	2	no	—
460	C₂×C₈	—	178	1	no	—
461	C₂×C₈	—	178	2	no	—
462	C₂×C₈	—	178	1	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	89	1	no	—
467	C₄⋊C₄	—	89	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	178	1	no	—
476	C₂²⋊C₄	—	178	1	no	—
477	C₂²⋊C₄	—	178	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	178	1	no	—
484	C₄²	—	178	1	no	—
485	C₄²	—	178	1	no	—
486	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
487	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
488	C₄²	D₄×D₈₉	1	1	yes	characteristic
489	C₄²	D₄×D₈₉	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	178	1	no	—
492	C₂³	C₂×#13083573	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	89	2	no	—
495	Q₈	—	178	1	no	—
496	Q₈	C₄⋊C₄×D₈₉	1	2	yes	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	1	no	—
500	D₄	—	89	2	no	—
501	D₄	—	178	2	no	—
502	D₄	—	178	2	no	—
503	D₄	—	178	1	no	—
504	D₄	C₄⋊C₄×D₈₉	1	2	yes	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	356	2	no	—
518	C₂×C₄	—	178	1	no	—
519	C₂×C₄	—	178	1	no	—
520	C₂×C₄	—	178	1	no	—
521	C₂×C₄	—	178	2	no	—
522	C₂×C₄	—	178	2	no	—
523	C₂×C₄	—	712	1	no	—
524	C₂×C₄	#15667972	1	1	yes	characteristic
525	C₂×C₄	#15667972	1	1	yes	characteristic
526	C₂×C₄	#15667972	1	1	yes	characteristic
527	C₂×C₄	#15667972	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
530	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
532	C₂×C₄	#15668058	1	1	yes	characteristic
533	C₂×C₄	#15668059	1	1	yes	characteristic
534	C₈	—	4	2	no	—
535	C₈	—	89	2	no	—
536	C₈	—	89	2	no	—
537	C₈	—	356	2	no	—
538	C₈	—	178	2	no	—
539	C₈	—	178	2	no	—
540	C₈	—	178	1	no	—
541	C₈	—	178	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	356	1	no	—
548	C₂²	—	356	1	no	—
549	C₂²	—	178	2	no	—
550	C₂²	C₂×#15667972	1	1	yes	characteristic
551	C₂²	#19152248	1	1	yes	characteristic
552	C₂²	#19152306	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	356	1	no	—
561	C₄	—	356	1	no	—
562	C₄	—	178	2	no	—
563	C₄	#19151712	1	2	yes	complemented
564	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
565	C₄	#19152078	1	1	yes	characteristic
566	C₄	#19152232	1	1	yes	characteristic
567	C₄	#19152261	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	356	2	no	—
572	C₂	#26023148	1	1	yes	characteristic
573	C₂	C₂×#19151712	1	1	yes	characteristic
574	C₂	#26029165	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1806	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1806	D₈₉
hypocenter	C₈₉	#22688
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
3. #26028821	C₂	semidirect
4. #26028820	C₂	semidirect
5. #26020999	C₂	semidirect
6. #26020528	C₂	semidirect
7. #26020525	C₂	semidirect
8. #26020423	C₂	semidirect
9. #26020273	C₂	semidirect
10. C₄⋊C₄×#10623494	C₂	semidirect
11. C₈₉×#1806	C₂	semidirect
17. C₄×#13083564	C₄	semidirect
18. C₄×#13083564	C₄	semidirect
19. C₄×#13083561	C₄	semidirect
20. C₄×#13083561	C₄	semidirect
21. C₄×#13083562	C₄	semidirect
22. C₄×#13083562	C₄	semidirect
23. C₄×#13083559	C₄	semidirect
24. C₄×#13083559	C₄	semidirect
135. #13083564	C₄⋊C₄	semidirect
136. #13083562	C₄⋊C₄	semidirect
137. #13083561	C₄⋊C₄	semidirect
138. #13083559	C₄⋊C₄	semidirect
272. C₄×C₈₉	#443	semidirect
297. #1806	D₈₉	semidirect
299. C₈₉	#22688	semidirect
563. C₄	#19151712	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151712	2
C₄×#15668032	2
#26028821	2
#26028820	2
#26020999	2
#26020528	2
#26020525	2
#26020423	2
#26020273	2
C₄⋊C₄×#10623494	2
C₈₉×#1806	2
#22688	89