Subgroups — #36612715

Order 22784.

744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023223	C₂	1	1	yes	maximal, characteristic
2	#26021637	C₂	1	1	yes	maximal, characteristic
3	#26021623	C₂	1	1	yes	maximal, characteristic
4	#26021385	C₂	1	1	yes	maximal, characteristic
5	#26021385	C₂	1	1	yes	maximal, characteristic
6	#26021205	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021201	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021020	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020976	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020841	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020827	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020387	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020249	C₂	1	1	yes	maximal, characteristic
14	#26020080	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
17	C₂×#15667945	C₂²	1	1	yes	characteristic
18	C₂×#15667943	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
22	C₂×#15667932	C₂²	1	1	yes	characteristic
23	C₂×#15667932	C₂²	1	1	yes	characteristic
24	C₂×#15667932	C₂²	1	1	yes	characteristic
25	C₂×#15667932	C₂²	1	1	yes	characteristic
26	C₂×#15667923	C₂²	1	1	yes	characteristic
27	#19151500	C₂²	1	1	yes	characteristic
28	#19151500	C₂²	1	1	yes	characteristic
29	#19151488	—	2	1	no	—
30	#19151488	—	2	1	no	—
31	#19151464	C₂²	1	1	yes	characteristic
32	#19151460	—	2	1	no	—
33	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
35	#19151445	—	2	1	no	—
36	#19151360	C₂²	1	1	yes	characteristic
37	#19151360	C₂²	1	1	yes	characteristic
38	#19151360	C₂²	1	1	yes	characteristic
39	#19151360	C₂²	1	1	yes	characteristic
40	#19151360	C₂²	1	1	yes	characteristic
41	#19151360	C₂²	1	1	yes	characteristic
42	#19151360	C₂²	1	1	yes	characteristic
43	#19151360	C₂²	1	1	yes	characteristic
44	#19151360	C₂²	1	1	yes	characteristic
45	#19151360	C₂²	1	1	yes	characteristic
46	#19151353	C₂²	1	1	yes	characteristic
47	#19151353	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
49	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
51	#395×C₈₉	—	2	1	no	—
52	#395×C₈₉	—	2	1	no	—
53	#389×C₈₉	—	2	1	no	—
54	#389×C₈₉	C₂²	1	1	yes	characteristic
55	#389×C₈₉	C₂²	1	1	yes	characteristic
56	#384×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
60	C₂²×C₄×D₈₉	—	2	1	no	—
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
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	C₄×D₃₅₆	—	2	2	no	—
66	C₄×D₃₅₆	Q₈	1	4	yes	complemented
67	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
70	C₂×#13083551	—	2	1	no	—
71	C₂×#13083551	—	2	1	no	—
72	C₂×#13083551	—	2	1	no	—
73	C₂×#13083551	—	2	1	no	—
74	C₂×#13083551	—	2	1	no	—
75	C₂×C₄×Dic₈₉	—	2	1	no	—
76	C₂×C₄×Dic₈₉	—	2	1	no	—
77	#15667945	—	2	2	no	—
78	#15667943	—	2	2	no	—
79	C₄⋊#10623494	—	2	2	no	—
80	C₄⋊#10623494	—	4	1	no	—
81	C₄⋊#10623494	—	4	1	no	—
82	#15667932	—	2	2	no	—
83	#15667932	—	2	2	no	—
84	#15667932	—	4	1	no	—
85	#15667932	—	4	1	no	—
86	#15667923	—	2	2	no	—
87	#15667919	—	2	1	no	—
88	#15667919	—	2	1	no	—
89	#15667919	—	2	1	no	—
90	#15667919	—	2	1	no	—
91	C₂²×Q₈×C₈₉	—	2	1	no	—
92	C₂²×Q₈×C₈₉	—	2	1	no	—
93	C₄⋊Q₈×C₈₉	—	2	2	no	—
94	C₄⋊Q₈×C₈₉	—	2	2	no	—
95	C₄⋊Q₈×C₈₉	—	4	1	no	—
96	C₄⋊Q₈×C₈₉	—	4	1	no	—
97	C₄⋊Q₈×C₈₉	—	4	4	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	—	2	1	no	—
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	#95×C₈₉	—	2	1	no	—
115	#95×C₈₉	—	2	1	no	—
116	#95×C₈₉	—	2	1	no	—
117	#95×C₈₉	D₄	1	1	yes	characteristic
118	#95×C₈₉	D₄	1	1	yes	characteristic
119	C₂³×D₈₉	—	2	1	no	—
120	C₂×D₃₅₆	—	2	1	no	—
121	C₂×D₃₅₆	—	2	1	no	—
122	C₂×D₃₅₆	—	2	1	no	—
123	C₂×D₃₅₆	—	2	1	no	—
124	C₂×D₃₅₆	—	2	1	no	—
125	C₂×D₃₅₆	C₂×Q₈	1	2	yes	—
126	C₂²×Dic₈₉	—	2	1	no	—
127	C₂²×Dic₈₉	—	2	1	no	—
128	C₂²×Dic₈₉	—	2	1	no	—
129	C₂×C₄×D₈₉	—	2	4	no	—
130	C₂×C₄×D₈₉	—	8	1	no	—
131	C₂×C₄×D₈₉	—	8	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	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₄⋊Dic₈₉	—	2	1	no	—
145	C₄⋊Dic₈₉	—	2	1	no	—
146	C₄⋊Dic₈₉	—	2	1	no	—
147	C₄⋊Dic₈₉	—	2	1	no	—
148	C₄⋊Dic₈₉	—	2	1	no	—
149	C₄⋊Dic₈₉	C₂×Q₈	1	2	yes	—
150	#13083551	—	2	4	no	—
151	#13083551	—	4	2	no	—
152	#13083551	—	4	2	no	—
153	#13083551	—	8	1	no	—
154	#13083551	—	8	1	no	—
155	C₄×Dic₈₉	—	8	1	no	—
156	C₄×Dic₈₉	—	8	1	no	—
157	C₂×Q₈×C₈₉	—	4	2	no	—
158	C₂×Q₈×C₈₉	—	4	2	no	—
159	C₂×Q₈×C₈₉	—	4	2	no	—
160	C₂×Q₈×C₈₉	—	4	2	no	—
161	C₂×Q₈×C₈₉	—	8	1	no	—
162	C₂×Q₈×C₈₉	—	8	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	—	2	1	no	—
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₈₉	—	2	2	no	—
175	C₄⋊C₄×C₈₉	—	2	2	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	4	2	no	—
183	C₄⋊C₄×C₈₉	—	4	2	no	—
184	C₄⋊C₄×C₈₉	—	4	2	no	—
185	C₄⋊C₄×C₈₉	—	4	2	no	—
186	C₄⋊C₄×C₈₉	—	4	2	no	—
187	C₄⋊C₄×C₈₉	—	8	1	no	—
188	C₄⋊C₄×C₈₉	#41	1	2	yes	—
189	C₄⋊C₄×C₈₉	#41	1	2	yes	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₄²×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	—	4	2	no	—
195	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
196	C₄²×C₈₉	#41	1	2	yes	—
197	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²×D₈₉	—	2	2	no	—
199	C₂²×D₈₉	—	4	1	no	—
200	C₂²×D₈₉	—	4	1	no	—
201	C₂²×D₈₉	—	4	1	no	—
202	C₂²×D₈₉	—	4	1	no	—
203	C₂²×D₈₉	—	4	1	no	—
204	C₂²×D₈₉	—	4	1	no	—
205	Q₈×C₈₉	—	8	4	no	—
206	Q₈×C₈₉	—	8	4	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	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	4	1	no	—
232	C₂×C₄×C₈₉	—	4	1	no	—
233	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
234	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
235	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₈₉	#137	1	2	yes	—
237	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
243	C₂×Dic₈₉	—	2	2	no	—
244	C₂×Dic₈₉	—	4	1	no	—
245	C₂×Dic₈₉	—	4	1	no	—
246	C₂×Dic₈₉	—	4	1	no	—
247	C₂×Dic₈₉	—	4	1	no	—
248	C₂×Dic₈₉	—	4	1	no	—
249	C₂×Dic₈₉	—	4	1	no	—
250	C₂×Dic₈₉	—	4	1	no	—
251	C₂×Dic₈₉	—	4	1	no	—
252	D₃₅₆	—	2	2	no	—
253	D₃₅₆	—	2	2	no	—
254	D₃₅₆	—	4	1	no	—
255	D₃₅₆	—	4	1	no	—
256	C₄×D₈₉	—	8	4	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	—	4	1	no	—
261	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₈₉	#546	1	1	yes	characteristic
263	C₂²×C₈₉	#548	1	1	yes	characteristic
264	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
266	C₂²×C₈₉	#576	1	1	yes	characteristic
267	C₂²×C₈₉	#577	1	1	yes	characteristic
268	C₂×D₈₉	—	4	2	no	—
269	C₂×D₈₉	—	4	2	no	—
270	C₂×D₈₉	—	4	2	no	—
271	C₂×D₈₉	—	8	1	no	—
272	C₂×D₈₉	—	8	1	no	—
273	C₂×D₈₉	—	8	1	no	—
274	C₂×D₈₉	—	8	1	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	2	2	no	—
278	C₄×C₈₉	—	2	2	no	—
279	C₄×C₈₉	—	4	2	no	—
280	C₄×C₈₉	—	4	1	no	—
281	C₄×C₈₉	—	4	2	no	—
282	C₄×C₈₉	—	4	1	no	—
283	C₄×C₈₉	—	8	1	no	—
284	C₄×C₈₉	—	8	1	no	—
285	C₄×C₈₉	#533	1	1	yes	characteristic
286	C₄×C₈₉	#544	1	1	yes	characteristic
287	C₄×C₈₉	#555	1	1	yes	characteristic
288	C₄×C₈₉	#556	1	1	yes	characteristic
289	Dic₈₉	—	4	2	no	—
290	Dic₈₉	—	8	1	no	—
291	Dic₈₉	—	8	1	no	—
292	#26036	—	89	1	no	maximal, Sylow
293	C₂×C₈₉	#2439	1	1	yes	characteristic
294	C₂×C₈₉	#3079	1	1	yes	characteristic
295	C₂×C₈₉	#3081	1	1	yes	characteristic
296	C₂×C₈₉	#3318	1	1	yes	characteristic
297	C₂×C₈₉	#3320	1	1	yes	characteristic
298	C₂×C₈₉	#3373	1	1	yes	characteristic
299	C₂×C₈₉	#3375	1	1	yes	characteristic
300	D₈₉	—	8	2	no	—
301	#2551	D₈₉	1	1	yes	characteristic, complemented
302	#2357	—	89	1	no	—
303	#2067	—	89	1	no	—
304	#2065	—	89	1	no	—
305	#2023	—	89	1	no	—
306	#2023	—	89	1	no	—
307	#1988	—	89	1	no	—
308	#1987	—	89	1	no	—
309	#1949	—	89	1	no	—
310	#1940	—	89	1	no	—
311	#1921	—	89	1	no	—
312	#1919	—	89	1	no	—
313	#1836	—	89	1	no	—
314	#1802	—	89	1	no	—
315	#1762	—	89	1	no	—
316	C₈₉	#26036	1	1	yes	characteristic, complemented, Sylow
317	C₂×C₄⋊Q₈	—	2	1	no	—
318	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
319	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
320	C₂×C₄×D₄	—	89	1	no	—
321	C₂×#107	—	89	1	no	—
322	C₂×#106	—	89	1	no	—
323	C₂×C₄⋊C₈	—	89	1	no	—
324	C₂×C₄⋊C₈	—	89	1	no	—
325	C₂×C₄⋊C₈	—	89	1	no	—
326	C₂×#102	—	89	1	no	—
327	C₂×#102	—	89	1	no	—
328	C₂×#102	—	89	1	no	—
329	C₂×#102	—	89	1	no	—
330	C₂×#97	—	89	1	no	—
331	#395	—	2	1	no	—
332	#395	—	2	1	no	—
333	#390	—	89	1	no	—
334	#390	—	89	1	no	—
335	#389	—	2	1	no	—
336	#389	C₂×D₈₉	1	1	yes	characteristic
337	#389	C₂×D₈₉	1	1	yes	characteristic
338	#388	—	178	1	no	—
339	#388	—	178	1	no	—
340	#384	C₂×D₈₉	1	1	yes	characteristic
341	#382	—	89	1	no	—
342	#381	—	178	1	no	—
343	C₄×C₄⋊C₄	—	89	1	no	—
344	C₄×C₄⋊C₄	—	89	1	no	—
345	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	—	178	1	no	—
348	#340	—	89	1	no	—
349	#340	—	89	1	no	—
350	#340	—	89	1	no	—
351	#340	—	89	1	no	—
352	#340	—	89	1	no	—
353	#340	—	89	1	no	—
354	#340	—	89	1	no	—
355	#340	—	89	1	no	—
356	#340	—	89	1	no	—
357	#340	—	89	1	no	—
358	#336	—	89	1	no	—
359	#336	—	89	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×D₄	—	89	1	no	—
363	C₂³×C₄	—	178	1	no	—
364	C₂²×C₈	—	89	1	no	—
365	C₂²×C₈	—	89	1	no	—
366	C₂²×C₈	—	89	1	no	—
367	C₂²×C₈	—	89	1	no	—
368	C₄⋊Q₈	—	2	2	no	—
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	—	4	1	no	—
371	C₄⋊Q₈	—	4	1	no	—
372	C₄⋊Q₈	—	4	4	no	—
373	C₄×D₄	—	89	4	no	—
374	C₄×D₄	—	178	2	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	89	1	no	—
382	C₂×C₄⋊C₄	—	89	1	no	—
383	C₂×C₄⋊C₄	—	89	1	no	—
384	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	178	1	no	—
391	C₂×C₂²⋊C₄	—	178	1	no	—
392	C₂×C₂²⋊C₄	—	178	1	no	—
393	C₂×C₂²⋊C₄	—	178	1	no	—
394	C₂×C₂²⋊C₄	—	178	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	178	1	no	—
397	C₂×C₄²	—	178	1	no	—
398	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
399	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
401	#107	—	178	2	no	—
402	#106	—	178	2	no	—
403	C₄⋊C₈	—	356	1	no	—
404	C₄⋊C₈	—	356	1	no	—
405	C₄⋊C₈	—	178	2	no	—
406	#102	—	356	1	no	—
407	#102	—	356	1	no	—
408	#102	—	178	2	no	—
409	#102	—	178	2	no	—
410	#97	—	178	2	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	178	1	no	—
415	#95	—	178	1	no	—
416	#95	—	178	1	no	—
417	#95	—	178	1	no	—
418	#95	C₂²⋊D₈₉	1	1	yes	characteristic
419	#95	C₂²⋊D₈₉	1	1	yes	characteristic
420	C₂⁴	—	178	1	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×Q₈	—	8	1	no	—
426	C₂×Q₈	—	8	1	no	—
427	C₂×D₄	—	89	2	no	—
428	C₂×D₄	—	178	1	no	—
429	C₂×D₄	—	178	1	no	—
430	C₂×D₄	—	178	1	no	—
431	C₂×D₄	—	178	1	no	—
432	C₂×D₄	—	178	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	178	1	no	—
438	C₂²×C₄	—	178	1	no	—
439	C₂²×C₄	—	178	1	no	—
440	C₂²×C₄	—	178	4	no	—
441	C₂²×C₄	—	712	1	no	—
442	C₂²×C₄	—	712	1	no	—
443	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
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	C₂×C₈	—	178	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	8	1	no	—
476	C₄⋊C₄	—	89	2	no	—
477	C₄⋊C₄	—	178	1	no	—
478	C₄⋊C₄	—	178	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	#13083573	1	2	yes	—
483	C₄⋊C₄	#13083575	1	2	yes	—
484	C₂²⋊C₄	—	356	2	no	—
485	C₂²⋊C₄	—	356	2	no	—
486	C₂²⋊C₄	—	178	4	no	—
487	C₂²⋊C₄	—	712	1	no	—
488	C₂²⋊C₄	—	712	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	712	1	no	—
495	C₄²	—	712	1	no	—
496	C₄²	Q₈×D₈₉	1	2	yes	—
497	C₄²	#13083575	1	2	yes	—
498	C₂³	—	356	1	no	—
499	C₂³	—	356	1	no	—
500	C₂³	—	356	1	no	—
501	C₂³	—	356	1	no	—
502	C₂³	—	356	1	no	—
503	C₂³	—	356	1	no	—
504	C₂³	—	178	2	no	—
505	C₂³	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
506	Q₈	—	8	4	no	—
507	Q₈	—	8	4	no	—
508	D₄	—	356	1	no	—
509	D₄	—	356	1	no	—
510	D₄	—	178	2	no	—
511	D₄	—	178	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	356	1	no	—
539	C₂×C₄	—	356	1	no	—
540	C₂×C₄	—	356	1	no	—
541	C₂×C₄	—	356	1	no	—
542	C₂×C₄	—	356	1	no	—
543	C₂×C₄	—	356	1	no	—
544	C₂×C₄	—	356	1	no	—
545	C₂×C₄	—	356	1	no	—
546	C₂×C₄	—	178	2	no	—
547	C₂×C₄	—	712	4	no	—
548	C₂×C₄	#15667988	1	2	yes	—
549	C₂×C₄	#15667988	1	2	yes	—
550	C₂×C₄	#15668038	1	2	yes	—
551	C₂×C₄	#15668043	1	2	yes	—
552	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
554	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
555	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
556	C₂×C₄	#15668057	1	1	yes	characteristic
557	C₂×C₄	#15668060	1	1	yes	characteristic
558	C₈	—	356	1	no	—
559	C₈	—	356	1	no	—
560	C₈	—	356	1	no	—
561	C₈	—	356	1	no	—
562	C₂²	—	356	2	no	—
563	C₂²	—	356	2	no	—
564	C₂²	—	356	2	no	—
565	C₂²	—	712	1	no	—
566	C₂²	—	712	1	no	—
567	C₂²	—	712	1	no	—
568	C₂²	—	712	1	no	—
569	C₂²	C₂×#15667988	1	1	yes	characteristic
570	C₂²	#19152242	1	1	yes	characteristic
571	C₂²	#19152259	1	1	yes	characteristic
572	C₂²	C₂×#15668038	1	1	yes	characteristic
573	C₂²	C₂×#15668043	1	1	yes	characteristic
574	C₂²	#19152401	1	1	yes	characteristic
575	C₂²	#19152406	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	356	2	no	—
587	C₄	—	712	1	no	—
588	C₄	—	712	1	no	—
589	C₄	#19152153	1	1	yes	characteristic
590	C₄	#19152225	1	1	yes	characteristic
591	C₄	#19152314	1	1	yes	characteristic
592	C₄	#19152322	1	1	yes	characteristic
593	C₂	—	712	2	no	—
594	C₂	#26023939	1	1	yes	characteristic
595	C₂	#26030061	1	1	yes	characteristic
596	C₂	#26030077	1	1	yes	characteristic
597	C₂	#26032393	1	1	yes	characteristic
598	C₂	#26032423	1	1	yes	characteristic
599	C₂	#26033044	1	1	yes	characteristic
600	C₂	#26033066	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2551	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×D₃₅₆	C₂³
hypercenter	#2551	D₈₉
hypocenter	C₈₉	#26036
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2551

Complements

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

N	H ≅ G/N	type
6. #26021205	C₂	semidirect
7. #26021201	C₂	semidirect
8. #26021020	C₂	semidirect
9. #26020976	C₂	semidirect
10. #26020841	C₂	semidirect
11. #26020827	C₂	semidirect
12. #26020387	C₂	semidirect
15. C₈₉×#2551	C₂	semidirect
66. C₄×D₃₅₆	Q₈	semidirect
301. #2551	D₈₉	semidirect
316. C₈₉	#26036	semidirect

Maximal subgroups

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

subgroup	index
#26023223	2
#26021637	2
#26021623	2
#26021385	2
#26021205	2
#26021201	2
#26021020	2
#26020976	2
#26020841	2
#26020827	2
#26020387	2
#26020249	2
#26020080	2
C₈₉×#2551	2
#26036	89