Subgroups — #36581202

Order 22784.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023552	C₂	1	1	yes	maximal, characteristic
2	#26020975	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020974	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020967	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020862	C₂	1	1	yes	maximal, characteristic
6	#26020861	C₂	1	1	yes	maximal, characteristic
7	#26020819	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020816	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020810	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020437	C₂	1	1	yes	maximal, characteristic
11	#26020434	C₂	1	1	yes	maximal, characteristic
12	#26020434	C₂	1	1	yes	maximal, characteristic
13	#26020405	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1924	C₂	1	1	yes	maximal, characteristic
16	C₂²×#13083558	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
19	C₂×#15667941	C₂²	1	1	yes	characteristic
20	C₂×#15667941	C₂²	1	1	yes	characteristic
21	C₂×#15667941	C₂²	1	1	yes	characteristic
22	C₂×#15667941	C₂²	1	1	yes	characteristic
23	C₂×#15667941	C₂²	1	1	yes	characteristic
24	C₂×#15667941	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
26	C₂×#15667922	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
28	C₈₉⋊#401	C₄	1	1	yes	characteristic
29	#19151540	C₄	1	1	yes	characteristic
30	#19151539	C₄	1	1	yes	characteristic
31	#19151538	C₄	1	1	yes	characteristic
32	#19151526	C₄	1	1	yes	characteristic
33	#19151526	C₄	1	1	yes	characteristic
34	#19151523	C₄	1	1	yes	characteristic
35	#19151521	C₄	1	1	yes	characteristic
36	C₄×#13083553	C₂²	1	1	yes	characteristic
37	C₄×#13083553	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
41	#19151444	C₂²	1	1	yes	characteristic
42	#19151353	C₂²	1	1	yes	characteristic
43	#19151353	C₂²	1	1	yes	characteristic
44	#19151352	C₂²	1	1	yes	characteristic
45	#19151352	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	#19151352	C₂²	1	1	yes	characteristic
51	#19151352	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083558	—	4	1	no	—
60	C₂×#13083558	—	4	1	no	—
61	C₂×#13083558	—	4	1	no	—
62	C₂²×#10623494	C₂³	1	1	yes	characteristic
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	—	4	1	no	—
81	C₄⋊#10623494	—	4	1	no	—
82	#15667941	—	4	1	no	—
83	#15667941	—	4	1	no	—
84	#15667941	—	4	1	no	—
85	#15667941	—	4	1	no	—
86	#15667941	—	4	1	no	—
87	#15667941	—	4	1	no	—
88	C₂²⋊#10623494	—	4	1	no	—
89	#15667922	—	4	1	no	—
90	C₈×Dic₈₉	—	4	1	no	—
91	#15667919	C₂×C₄	1	1	yes	characteristic
92	#15667919	C₂×C₄	1	1	yes	characteristic
93	#15667919	C₂×C₄	1	1	yes	characteristic
94	#15667919	C₂×C₄	1	1	yes	characteristic
95	#15667919	C₂×C₄	1	1	yes	characteristic
96	#15667919	C₂×C₄	1	1	yes	characteristic
97	#15667919	C₂×C₄	1	1	yes	characteristic
98	#15667919	C₂×C₄	1	1	yes	characteristic
99	#15667919	C₂×C₄	1	1	yes	characteristic
100	#15667919	C₂×C₄	1	1	yes	characteristic
101	#15667919	C₂×C₄	1	1	yes	characteristic
102	#15667919	C₂×C₄	1	1	yes	characteristic
103	#15667919	C₂×C₄	1	1	yes	characteristic
104	#15667919	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₈₉	—	4	1	no	—
115	C₂²⋊C₈×C₈₉	—	4	1	no	—
116	C₂²⋊C₈×C₈₉	—	4	1	no	—
117	#97×C₈₉	—	4	1	no	—
118	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
119	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	#13083558	—	4	4	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	2	1	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	1	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	C₄⋊Dic₈₉	—	2	2	no	—
142	C₄⋊Dic₈₉	—	4	1	no	—
143	#13083553	—	2	2	no	—
144	#13083553	—	4	1	no	—
145	#13083553	—	4	1	no	—
146	#13083553	—	4	1	no	—
147	C₂²⋊Dic₈₉	—	2	2	no	—
148	C₂²⋊Dic₈₉	—	4	1	no	—
149	C₂²⋊Dic₈₉	—	4	1	no	—
150	C₂²⋊Dic₈₉	—	4	1	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₄×Dic₈₉	—	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	1	no	—
158	C₄×Dic₈₉	—	2	1	no	—
159	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	2	1	no	—
164	C₂²×C₄×C₈₉	—	2	1	no	—
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₈₉	—	2	1	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
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	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂²⋊C₄×C₈₉	—	4	1	no	—
185	C₂²⋊C₄×C₈₉	—	4	1	no	—
186	C₄²×C₈₉	—	2	1	no	—
187	C₄²×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	1	no	—
190	C₂³×C₈₉	—	2	1	no	—
191	C₂³×C₈₉	—	2	1	no	—
192	C₂³×C₈₉	—	2	1	no	—
193	C₂³×C₈₉	—	2	1	no	—
194	C₂³×C₈₉	—	2	1	no	—
195	C₂³×C₈₉	—	2	1	no	—
196	C₂³×C₈₉	—	2	1	no	—
197	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	2	1	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	4	1	no	—
214	C₂×C₄×C₈₉	—	4	1	no	—
215	C₂×C₄×C₈₉	—	4	1	no	—
216	C₂×C₄×C₈₉	—	4	1	no	—
217	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
222	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×Dic₈₉	—	2	1	no	—
224	C₂×Dic₈₉	—	2	1	no	—
225	C₂×Dic₈₉	—	2	1	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	—	2	1	no	—
230	C₂×Dic₈₉	—	2	1	no	—
231	C₂×Dic₈₉	—	2	1	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	2	1	no	—
242	C₂×Dic₈₉	—	2	1	no	—
243	C₂×Dic₈₉	—	2	1	no	—
244	C₂×Dic₈₉	—	2	1	no	—
245	C₂×Dic₈₉	—	2	1	no	—
246	C₂×Dic₈₉	#131	1	2	yes	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	C₂²×C₈₉	—	4	1	no	—
256	C₂²×C₈₉	—	4	1	no	—
257	C₂²×C₈₉	—	4	1	no	—
258	C₂²×C₈₉	—	4	1	no	—
259	C₂²×C₈₉	—	4	1	no	—
260	C₂²×C₈₉	—	4	1	no	—
261	C₂²×C₈₉	—	4	1	no	—
262	C₂²×C₈₉	#520	1	1	yes	characteristic
263	C₂²×C₈₉	#520	1	1	yes	characteristic
264	C₂²×C₈₉	#520	1	1	yes	characteristic
265	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
266	C₂²×C₈₉	#568	1	1	yes	characteristic
267	C₂²×C₈₉	#568	1	1	yes	characteristic
268	C₂²×C₈₉	#568	1	1	yes	characteristic
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	—	4	1	no	—
271	C₄×C₈₉	—	4	1	no	—
272	C₄×C₈₉	—	4	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	#560	1	1	yes	characteristic
275	C₄×C₈₉	#563	1	1	yes	characteristic
276	C₄×C₈₉	#563	1	1	yes	characteristic
277	C₄×C₈₉	#563	1	1	yes	characteristic
278	Dic₈₉	—	2	2	no	—
279	Dic₈₉	—	4	1	no	—
280	Dic₈₉	—	4	1	no	—
281	Dic₈₉	—	4	1	no	—
282	Dic₈₉	—	4	1	no	—
283	Dic₈₉	—	4	1	no	—
284	Dic₈₉	—	4	1	no	—
285	Dic₈₉	—	4	1	no	—
286	#23382	—	89	1	no	maximal, Sylow
287	C₂×C₈₉	—	8	1	no	—
288	C₂×C₈₉	#2383	1	1	yes	characteristic
289	C₂×C₈₉	#2992	1	1	yes	characteristic
290	C₂×C₈₉	#2993	1	1	yes	characteristic
291	C₂×C₈₉	#2993	1	1	yes	characteristic
292	C₂×C₈₉	#2995	1	1	yes	characteristic
293	C₂×C₈₉	#2995	1	1	yes	characteristic
294	C₂×C₈₉	#2995	1	1	yes	characteristic
295	#2401	—	89	1	no	—
296	#1940	—	89	1	no	—
297	#1940	—	89	1	no	—
298	#1939	—	89	1	no	—
299	#1924	—	89	1	no	—
300	#1924	D₈₉	1	1	yes	characteristic
301	#1923	—	89	1	no	—
302	#1917	—	89	1	no	—
303	#1917	—	89	1	no	—
304	#1916	—	89	1	no	—
305	#1851	—	89	1	no	—
306	#1851	—	89	1	no	—
307	#1851	—	89	1	no	—
308	#1843	—	89	1	no	—
309	#1840	—	89	1	no	—
310	C₈₉	#23382	1	1	yes	characteristic, complemented, Sylow
311	C₂²×M₁₆	—	89	1	no	—
312	C₂×C₄⋊C₈	—	89	1	no	—
313	C₂×C₄⋊C₈	—	89	1	no	—
314	C₂×C₄⋊C₈	—	89	1	no	—
315	C₂×C₄⋊C₈	—	89	1	no	—
316	C₂×C₄⋊C₈	—	89	1	no	—
317	C₂×C₄⋊C₈	—	89	1	no	—
318	C₂×C₄⋊C₈	—	89	1	no	—
319	C₂×C₄⋊C₈	—	89	1	no	—
320	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	—	89	1	no	—
322	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
324	C₂×#97	—	89	1	no	—
325	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
326	C₂×C₄×C₈	—	89	1	no	—
327	#401	—	89	1	no	—
328	#400	—	89	1	no	—
329	#400	—	89	1	no	—
330	#400	—	89	1	no	—
331	#397	—	89	1	no	—
332	#397	—	89	1	no	—
333	#397	—	89	1	no	—
334	#396	—	89	1	no	—
335	C₄×C₄⋊C₄	—	89	1	no	—
336	C₄×C₄⋊C₄	—	89	1	no	—
337	C₄×C₄⋊C₄	—	89	1	no	—
338	C₄×C₂²⋊C₄	—	89	1	no	—
339	C₄×C₂²⋊C₄	—	89	1	no	—
340	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
341	#376	—	89	1	no	—
342	#336	—	89	1	no	—
343	#336	—	89	1	no	—
344	#336	—	89	1	no	—
345	#336	—	89	1	no	—
346	#336	—	89	1	no	—
347	#336	—	89	1	no	—
348	#336	—	89	1	no	—
349	#336	—	89	1	no	—
350	#336	—	89	1	no	—
351	#336	—	89	1	no	—
352	#336	C₂×D₈₉	1	1	yes	characteristic
353	#336	C₂×D₈₉	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
355	C₂×M₁₆	—	356	1	no	—
356	C₂×M₁₆	—	356	1	no	—
357	C₂×M₁₆	—	356	1	no	—
358	C₂²×C₈	—	89	1	no	—
359	C₂²×C₈	—	89	1	no	—
360	C₂²×C₈	—	89	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	89	1	no	—
367	C₂×C₄⋊C₄	—	89	1	no	—
368	C₂×C₄⋊C₄	—	89	1	no	—
369	C₂×C₄⋊C₄	—	89	1	no	—
370	C₂×C₄⋊C₄	—	89	1	no	—
371	C₂×C₄⋊C₄	—	89	1	no	—
372	C₂×C₂²⋊C₄	—	89	1	no	—
373	C₂×C₂²⋊C₄	—	89	1	no	—
374	C₂×C₂²⋊C₄	—	89	1	no	—
375	C₂×C₂²⋊C₄	—	89	1	no	—
376	C₂×C₂²⋊C₄	C₄×D₈₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₄×D₈₉	1	1	yes	characteristic
378	C₂×C₄²	—	89	1	no	—
379	C₂×C₄²	—	89	1	no	—
380	C₂×C₄²	—	89	1	no	—
381	C₂×C₄²	—	89	1	no	—
382	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
384	C₄⋊C₈	—	4	1	no	—
385	C₄⋊C₈	—	356	1	no	—
386	C₄⋊C₈	—	356	1	no	—
387	C₄⋊C₈	—	356	1	no	—
388	C₄⋊C₈	—	356	1	no	—
389	C₄⋊C₈	—	356	1	no	—
390	C₄⋊C₈	—	356	1	no	—
391	C₄⋊C₈	—	356	1	no	—
392	C₄⋊C₈	—	356	1	no	—
393	C₂²⋊C₈	—	4	1	no	—
394	C₂²⋊C₈	—	4	1	no	—
395	C₂²⋊C₈	—	356	1	no	—
396	#97	—	4	1	no	—
397	#97	—	356	1	no	—
398	C₄×C₈	—	356	1	no	—
399	#95	—	89	1	no	—
400	#95	—	89	1	no	—
401	#95	—	89	1	no	—
402	#95	—	89	1	no	—
403	#95	—	89	1	no	—
404	#95	—	89	1	no	—
405	#95	—	89	1	no	—
406	#95	—	89	1	no	—
407	#95	—	89	1	no	—
408	#95	—	89	1	no	—
409	#95	—	89	1	no	—
410	#95	—	89	1	no	—
411	#95	—	89	1	no	—
412	#95	—	89	1	no	—
413	#95	C₄×D₈₉	1	1	yes	characteristic
414	#95	C₄×D₈₉	1	1	yes	characteristic
415	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	89	1	no	—
423	C₂²×C₄	—	89	1	no	—
424	C₂²×C₄	—	89	1	no	—
425	C₂²×C₄	—	89	1	no	—
426	C₂²×C₄	—	89	1	no	—
427	C₂²×C₄	—	89	1	no	—
428	C₂²×C₄	—	89	1	no	—
429	C₂²×C₄	—	89	1	no	—
430	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
436	M₁₆	—	356	4	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	178	1	no	—
450	C₂×C₈	—	178	1	no	—
451	C₂×C₈	—	178	1	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	178	1	no	—
455	C₂×C₈	—	178	1	no	—
456	C₂×C₈	—	178	1	no	—
457	C₂×C₈	—	178	1	no	—
458	C₂×C₈	—	178	1	no	—
459	C₂×C₈	—	178	1	no	—
460	C₂×C₈	—	178	1	no	—
461	C₄⋊C₄	—	356	1	no	—
462	C₄⋊C₄	—	356	1	no	—
463	C₄⋊C₄	—	356	1	no	—
464	C₄⋊C₄	—	356	1	no	—
465	C₄⋊C₄	—	178	2	no	—
466	C₄⋊C₄	—	178	2	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	356	1	no	—
470	C₂²⋊C₄	—	356	1	no	—
471	C₂²⋊C₄	—	356	1	no	—
472	C₂²⋊C₄	—	178	2	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	178	1	no	—
478	C₄²	—	178	1	no	—
479	C₄²	—	178	1	no	—
480	C₄²	—	178	1	no	—
481	C₄²	—	178	1	no	—
482	C₄²	—	178	1	no	—
483	C₄²	—	178	1	no	—
484	C₄²	—	178	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	89	2	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	—	178	1	no	—
519	C₂×C₄	—	178	1	no	—
520	C₂×C₄	—	178	1	no	—
521	C₂×C₄	—	178	1	no	—
522	C₂×C₄	—	178	1	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	—	178	1	no	—
531	C₂×C₄	—	178	1	no	—
532	C₂×C₄	—	178	1	no	—
533	C₂×C₄	—	178	1	no	—
534	C₂×C₄	—	178	1	no	—
535	C₂×C₄	—	178	1	no	—
536	C₂×C₄	#15668057	1	1	yes	characteristic
537	C₂×C₄	#15668057	1	1	yes	characteristic
538	C₂×C₄	#15668058	1	1	yes	characteristic
539	C₂×C₄	#15668059	1	1	yes	characteristic
540	C₂×C₄	#15668059	1	1	yes	characteristic
541	C₂×C₄	#15668059	1	1	yes	characteristic
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	356	1	no	—
547	C₈	—	356	1	no	—
548	C₈	—	356	1	no	—
549	C₈	—	356	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	#19152077	1	1	yes	characteristic
558	C₂²	#19152077	1	1	yes	characteristic
559	C₂²	#19152078	1	1	yes	characteristic
560	C₂²	#131×D₈₉	1	1	yes	characteristic
561	C₂²	#19152363	1	1	yes	characteristic
562	C₂²	#19152364	1	1	yes	characteristic
563	C₂²	#19152364	1	1	yes	characteristic
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	356	1	no	—
570	C₄	—	356	1	no	—
571	C₄	—	356	1	no	—
572	C₄	—	356	1	no	—
573	C₄	—	356	1	no	—
574	C₄	—	356	1	no	—
575	C₄	—	356	1	no	—
576	C₄	—	178	2	no	—
577	C₄	#19152336	1	1	yes	characteristic
578	C₄	#19152348	1	1	yes	characteristic
579	C₄	#19152350	1	1	yes	characteristic
580	C₄	#19152351	1	1	yes	characteristic
581	C₂	—	8	1	no	—
582	C₂	#26023439	1	1	yes	characteristic
583	C₂	#26029386	1	1	yes	characteristic
584	C₂	#26029394	1	1	yes	characteristic
585	C₂	#26029394	1	1	yes	characteristic
586	C₂	#26029416	1	1	yes	characteristic
587	C₂	#26029418	1	1	yes	characteristic
588	C₂	#26029424	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1924	C₂
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1924	D₈₉
hypocenter	C₈₉	#23382
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1924

Complements

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

N	H ≅ G/N	type
2. #26020975	C₂	semidirect
3. #26020974	C₂	semidirect
4. #26020967	C₂	semidirect
7. #26020819	C₂	semidirect
8. #26020816	C₂	semidirect
9. #26020810	C₂	semidirect
13. #26020405	C₂	semidirect
14. #26020396	C₂	semidirect
310. C₈₉	#23382	semidirect

Maximal subgroups

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

subgroup	index
#26023552	2
#26020975	2
#26020974	2
#26020967	2
#26020862	2
#26020861	2
#26020819	2
#26020816	2
#26020810	2
#26020437	2
#26020434	2
#26020405	2
#26020396	2
C₈₉×#1924	2
#23382	89