Subgroups — #36523688

Order 22784.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029219	C₂	1	1	yes	maximal, characteristic
2	#26028918	C₂	1	1	yes	maximal, characteristic
3	#26019043	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019038	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019035	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019033	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019030	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019020	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019017	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019013	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018998	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2925	C₂	1	1	yes	maximal, characteristic
16	#19151729	C₄	1	1	yes	characteristic
17	#19151729	C₄	1	1	yes	characteristic
18	#19151676	C₄	1	1	yes	characteristic
19	#19151676	C₄	1	1	yes	characteristic
20	#19151670	C₄	1	1	yes	characteristic
21	#19151670	C₄	1	1	yes	characteristic
22	#19151670	C₄	1	1	yes	characteristic
23	#19151670	C₄	1	1	yes	characteristic
24	#19151659	—	2	1	no	—
25	#19151659	—	2	1	no	—
26	#19151655	C₂²	1	1	yes	characteristic
27	#19151655	C₂²	1	1	yes	characteristic
28	#19151651	C₂²	1	1	yes	characteristic
29	#19151651	C₂²	1	1	yes	characteristic
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151651	C₂²	1	1	yes	characteristic
32	#19151651	C₂²	1	1	yes	characteristic
33	#19151622	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
35	#19151565	—	2	1	no	—
36	#19151554	—	2	1	no	—
37	C₄×#13083558	C₂²	1	1	yes	characteristic
38	C₄×#13083558	C₂²	1	1	yes	characteristic
39	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	1	yes	characteristic
41	#19151350	C₂²	1	1	yes	characteristic
42	#19151350	C₂²	1	1	yes	characteristic
43	#19151350	C₂²	1	1	yes	characteristic
44	#19151350	C₂²	1	1	yes	characteristic
45	#19151350	C₂²	1	1	yes	characteristic
46	#19151350	C₂²	1	1	yes	characteristic
47	#19151350	C₂²	1	1	yes	characteristic
48	#19151348	C₂²	1	1	yes	characteristic
49	#19151348	C₂²	1	1	yes	characteristic
50	#19151348	C₂²	1	1	yes	characteristic
51	#19151348	C₂²	1	1	yes	characteristic
52	#19151348	C₂²	1	1	yes	characteristic
53	#19151348	C₂²	1	1	yes	characteristic
54	#19151348	C₂²	1	1	yes	characteristic
55	#19151348	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	#433×C₈₉	—	2	1	no	—
58	#433×C₈₉	—	2	1	no	—
59	#432×C₈₉	C₂²	1	1	yes	characteristic
60	#432×C₈₉	C₂²	1	1	yes	characteristic
61	#431×C₈₉	C₂²	1	1	yes	characteristic
62	#431×C₈₉	C₂²	1	1	yes	characteristic
63	#423×C₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	#408×C₈₉	—	2	1	no	—
66	#405×C₈₉	—	2	1	no	—
67	C₂×#13083558	—	2	1	no	—
68	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
72	C₂²×#10623494	—	2	1	no	—
73	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
74	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
78	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
79	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
80	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
81	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
83	C₄⋊#10623494	C₂³	1	1	yes	characteristic
84	C₄⋊#10623494	C₂³	1	1	yes	characteristic
85	C₄⋊#10623494	C₂³	1	1	yes	characteristic
86	C₄⋊#10623494	C₂³	1	1	yes	characteristic
87	C₂²⋊#10623494	—	2	1	no	—
88	C₂²⋊#10623494	—	2	1	no	—
89	C₂²⋊#10623494	—	2	1	no	—
90	C₂²⋊#10623494	—	2	1	no	—
91	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
97	#15667923	—	2	1	no	—
98	#15667923	—	2	1	no	—
99	#15667923	C₂×C₄	1	1	yes	characteristic
100	#15667923	C₂×C₄	1	1	yes	characteristic
101	#15667923	C₂×C₄	1	1	yes	characteristic
102	#15667923	C₂×C₄	1	1	yes	characteristic
103	C₄×#10623494	—	2	1	no	—
104	C₄×#10623494	—	2	1	no	—
105	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
106	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
107	C₄×#10623494	C₂³	1	1	yes	characteristic
108	C₄×#10623494	C₂³	1	1	yes	characteristic
109	C₄×#10623494	C₂³	1	1	yes	characteristic
110	C₄×#10623494	C₂³	1	1	yes	characteristic
111	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
112	C₂×M₁₆×C₈₉	—	2	1	no	—
113	C₂²×C₈×C₈₉	—	2	1	no	—
114	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×Q₈×C₈₉	Q₈	1	1	yes	characteristic
116	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
118	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₈₉	Q₈	1	1	yes	characteristic
120	C₄×D₄×C₈₉	Q₈	1	1	yes	characteristic
121	C₄×D₄×C₈₉	Q₈	1	1	yes	characteristic
122	#117×C₈₉	D₄	1	1	yes	characteristic
123	#117×C₈₉	D₄	1	1	yes	characteristic
124	#117×C₈₉	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₈₉	—	2	1	no	—
129	C₄⋊C₈×C₈₉	—	2	1	no	—
130	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²⋊C₈×C₈₉	—	2	1	no	—
135	C₂²⋊C₈×C₈₉	—	2	1	no	—
136	C₂²⋊C₈×C₈₉	—	2	1	no	—
137	C₂²⋊C₈×C₈₉	—	2	1	no	—
138	#97×C₈₉	—	2	1	no	—
139	#97×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	#13083558	—	2	2	no	—
143	#13083558	—	2	2	no	—
144	#13083558	—	4	1	no	—
145	#13083558	—	4	1	no	—
146	#13083558	—	4	2	no	—
147	C₂×#10623494	—	2	2	no	—
148	C₂×#10623494	—	2	1	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	4	1	no	—
153	C₂×#10623494	—	4	2	no	—
154	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
155	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
156	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
157	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
158	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
159	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
160	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	#41×C₈₉	—	4	1	no	—
163	#41×C₈₉	—	4	1	no	—
164	C₂×Q₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
165	C₂×D₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
166	C₂×D₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
167	C₂×D₄×C₈₉	C₄⋊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	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
177	M₁₆×C₈₉	—	4	2	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	—	4	2	no	—
183	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
185	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
188	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
190	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
195	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
202	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
203	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
204	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
208	Q₈×C₈₉	—	4	1	no	—
209	D₄×C₈₉	—	4	1	no	—
210	D₄×C₈₉	—	4	1	no	—
211	D₄×C₈₉	—	4	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	1	no	—
218	C₂×C₄×C₈₉	—	2	1	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	—	2	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	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
239	C₈×C₈₉	—	4	1	no	—
240	C₈×C₈₉	—	4	1	no	—
241	C₈×C₈₉	—	4	1	no	—
242	C₈×C₈₉	—	4	1	no	—
243	#10623494	—	2	1	no	—
244	#10623494	—	2	1	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	2	1	no	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	4	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	#131	1	2	yes	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	1	no	—
257	C₂²×C₈₉	—	2	1	no	—
258	C₂²×C₈₉	—	2	1	no	—
259	C₂²×C₈₉	—	2	1	no	—
260	C₂²×C₈₉	—	2	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	2	1	no	—
263	C₂²×C₈₉	—	2	1	no	—
264	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	1	no	—
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	—	2	1	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	—	2	1	no	—
275	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
276	C₄×C₈₉	#568	1	1	yes	characteristic
277	C₄×C₈₉	#575	1	1	yes	characteristic
278	C₄×C₈₉	#575	1	1	yes	characteristic
279	#17831	—	89	1	no	maximal, Sylow
280	C₂×C₈₉	—	4	1	no	—
281	C₂×C₈₉	—	4	1	no	—
282	C₂×C₈₉	—	4	1	no	—
283	C₂×C₈₉	#2906	1	1	yes	characteristic
284	C₂×C₈₉	#2911	1	1	yes	characteristic
285	C₂×C₈₉	#2916	1	1	yes	characteristic
286	#2965	—	89	1	no	—
287	#2925	—	89	1	no	—
288	#2925	D₈₉	1	1	yes	characteristic
289	#1574	—	89	1	no	—
290	#1574	—	89	1	no	—
291	#1573	—	89	1	no	—
292	#1573	—	89	1	no	—
293	#1572	—	89	1	no	—
294	#1572	—	89	1	no	—
295	#1569	—	89	1	no	—
296	#1569	—	89	1	no	—
297	#1568	—	89	1	no	—
298	#1565	—	89	1	no	—
299	#1565	—	89	1	no	—
300	#1564	—	89	1	no	—
301	C₈₉	#17831	1	1	yes	characteristic, complemented, Sylow
302	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
303	#446	—	89	1	no	—
304	#446	—	89	1	no	—
305	#436	—	89	1	no	—
306	#436	—	89	1	no	—
307	#435	—	89	1	no	—
308	#435	—	89	1	no	—
309	#435	—	89	1	no	—
310	#435	—	89	1	no	—
311	#433	—	2	1	no	—
312	#433	—	2	1	no	—
313	#433	—	178	1	no	—
314	#433	—	178	1	no	—
315	#432	—	89	1	no	—
316	#432	—	89	1	no	—
317	#432	C₂×D₈₉	1	1	yes	characteristic
318	#432	C₂×D₈₉	1	1	yes	characteristic
319	#431	—	89	1	no	—
320	#431	—	89	1	no	—
321	#431	—	89	1	no	—
322	#431	—	89	1	no	—
323	#431	—	89	1	no	—
324	#431	C₂×D₈₉	1	1	yes	characteristic
325	#431	C₂×D₈₉	1	1	yes	characteristic
326	#423	—	89	1	no	—
327	#423	C₂×D₈₉	1	1	yes	characteristic
328	C₂×C₄⋊C₈	—	89	1	no	—
329	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
330	#408	—	2	1	no	—
331	#408	—	178	1	no	—
332	#405	—	2	1	no	—
333	#405	—	178	1	no	—
334	C₄×M₁₆	—	89	1	no	—
335	C₄×M₁₆	—	89	1	no	—
336	C₂×C₄×C₈	—	89	1	no	—
337	#335	—	89	1	no	—
338	#335	—	89	1	no	—
339	#335	—	89	1	no	—
340	#335	—	89	1	no	—
341	#335	—	89	1	no	—
342	#335	—	89	1	no	—
343	#335	—	89	1	no	—
344	#335	—	89	1	no	—
345	#334	—	89	1	no	—
346	#334	—	89	1	no	—
347	#334	—	89	1	no	—
348	#334	—	89	1	no	—
349	#334	—	89	1	no	—
350	#334	—	89	1	no	—
351	#334	—	89	1	no	—
352	#334	—	89	1	no	—
353	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	89	1	no	—
356	C₂×M₁₆	—	89	1	no	—
357	C₂×M₁₆	—	89	1	no	—
358	C₂×M₁₆	—	89	1	no	—
359	C₂×M₁₆	—	178	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₂²×C₈	—	89	1	no	—
363	C₂²×C₈	—	178	1	no	—
364	C₄×Q₈	Dic₁₇₈	1	1	yes	characteristic
365	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
366	C₄×D₄	Dic₁₇₈	1	1	yes	characteristic
367	C₄×D₄	Dic₁₇₈	1	1	yes	characteristic
368	C₄×D₄	Dic₁₇₈	1	1	yes	characteristic
369	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
370	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
371	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
372	#117	C₂²⋊D₈₉	1	1	yes	characteristic
373	#117	C₂²⋊D₈₉	1	1	yes	characteristic
374	#117	C₂²⋊D₈₉	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	89	1	no	—
381	C₄⋊C₈	—	89	1	no	—
382	C₄⋊C₈	—	89	1	no	—
383	C₄⋊C₈	—	89	1	no	—
384	C₄⋊C₈	—	89	1	no	—
385	C₄⋊C₈	—	89	1	no	—
386	C₄⋊C₈	—	89	1	no	—
387	C₄⋊C₈	—	89	1	no	—
388	C₄⋊C₈	—	89	1	no	—
389	C₄⋊C₈	—	89	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	89	1	no	—
401	C₂²⋊C₈	—	89	1	no	—
402	C₂²⋊C₈	—	89	1	no	—
403	C₂²⋊C₈	—	89	1	no	—
404	C₂²⋊C₈	—	89	1	no	—
405	C₂²⋊C₈	—	89	1	no	—
406	C₂²⋊C₈	—	178	1	no	—
407	C₂²⋊C₈	—	178	1	no	—
408	C₂²⋊C₈	—	178	1	no	—
409	C₂²⋊C₈	—	178	1	no	—
410	#97	—	2	1	no	—
411	#97	—	2	1	no	—
412	#97	—	89	1	no	—
413	#97	—	89	1	no	—
414	#97	—	89	1	no	—
415	#97	—	89	1	no	—
416	#97	—	178	1	no	—
417	#97	—	178	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	89	1	no	—
425	C₄×C₈	—	89	1	no	—
426	C₄×C₈	—	178	1	no	—
427	C₄×C₈	—	178	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	C₂×Q₈	#13083553	1	1	yes	characteristic
431	C₂×D₄	#13083553	1	1	yes	characteristic
432	C₂×D₄	#13083553	1	1	yes	characteristic
433	C₂×D₄	#13083553	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
441	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
442	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
443	M₁₆	—	4	2	no	—
444	M₁₆	—	356	2	no	—
445	M₁₆	—	356	1	no	—
446	M₁₆	—	356	1	no	—
447	M₁₆	—	178	2	no	—
448	M₁₆	—	178	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	4	2	no	—
454	C₂×C₈	—	89	1	no	—
455	C₂×C₈	—	89	1	no	—
456	C₂×C₈	—	89	1	no	—
457	C₂×C₈	—	89	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	89	1	no	—
462	C₂×C₈	—	356	2	no	—
463	C₂×C₈	—	356	1	no	—
464	C₂×C₈	—	178	2	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₄⋊C₄	#13083553	1	1	yes	characteristic
470	C₄⋊C₄	#13083553	1	1	yes	characteristic
471	C₄⋊C₄	#13083553	1	1	yes	characteristic
472	C₄⋊C₄	#13083553	1	1	yes	characteristic
473	C₄⋊C₄	#13083553	1	1	yes	characteristic
474	C₄⋊C₄	#13083553	1	1	yes	characteristic
475	C₂²⋊C₄	#13083553	1	1	yes	characteristic
476	C₂²⋊C₄	#13083553	1	1	yes	characteristic
477	C₂²⋊C₄	#13083553	1	1	yes	characteristic
478	C₂²⋊C₄	#13083553	1	1	yes	characteristic
479	C₂²⋊C₄	#13083553	1	1	yes	characteristic
480	C₂²⋊C₄	#13083553	1	1	yes	characteristic
481	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
482	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
483	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
484	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
485	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
486	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
487	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
488	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
489	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
490	C₄²	C₂³×D₈₉	1	1	yes	characteristic
491	C₂³	C₂×#13083553	1	1	yes	characteristic
492	C₂³	C₂×#13083553	1	1	yes	characteristic
493	C₂³	C₂×#13083553	1	1	yes	characteristic
494	Q₈	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	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	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
514	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
515	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
516	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
517	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
518	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
519	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
520	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
521	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	89	2	no	—
530	C₈	—	356	1	no	—
531	C₈	—	356	1	no	—
532	C₈	—	356	1	no	—
533	C₈	—	356	1	no	—
534	C₈	—	178	1	no	—
535	C₈	—	178	1	no	—
536	C₈	—	178	1	no	—
537	C₈	—	178	1	no	—
538	C₈	—	178	1	no	—
539	C₈	—	178	1	no	—
540	C₈	—	178	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	C₂²×#13083553	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	#131×D₈₉	1	1	yes	characteristic
562	C₄	#19152363	1	1	yes	characteristic
563	C₄	#19152396	1	1	yes	characteristic
564	C₄	#19152396	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	4	1	no	—
567	C₂	—	4	1	no	—
568	C₂	#26028818	1	1	yes	characteristic
569	C₂	#26028841	1	1	yes	characteristic
570	C₂	#26028861	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2925	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₈₉	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2925	D₈₉
hypocenter	C₈₉	#17831
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #26019043	C₂	semidirect
4. #26019040	C₂	semidirect
5. #26019038	C₂	semidirect
6. #26019035	C₂	semidirect
7. #26019033	C₂	semidirect
8. #26019030	C₂	semidirect
9. #26019020	C₂	semidirect
10. #26019017	C₂	semidirect
11. #26019013	C₂	semidirect
12. #26019005	C₂	semidirect
13. #26019002	C₂	semidirect
14. #26018998	C₂	semidirect
301. C₈₉	#17831	semidirect

Maximal subgroups

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

subgroup	index
#26029219	2
#26028918	2
#26019043	2
#26019040	2
#26019038	2
#26019035	2
#26019033	2
#26019030	2
#26019020	2
#26019017	2
#26019013	2
#26019005	2
#26019002	2
#26018998	2
C₈₉×#2925	2
#17831	89