Subgroups — #36552608

Order 22784.

950 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151660	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151657	C₂	1	1	yes	maximal, characteristic
3	#26022591	C₂	1	1	yes	maximal, characteristic
4	#26020112	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020110	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#15667941	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020021	C₂	1	1	yes	maximal, characteristic
9	#26020019	C₂	1	1	yes	maximal, characteristic
10	#26020015	C₂	1	1	yes	maximal, characteristic
11	C₄×#15667924	C₂	1	1	yes	maximal, characteristic
12	#26020000	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019997	C₂	1	1	yes	maximal, characteristic, complemented
14	#26019939	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15667969	C₂²	1	1	yes	characteristic
17	C₂×#15667969	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
19	#19151660	C₄	1	8	yes	complemented
20	#19151657	C₄	1	8	yes	complemented
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×#15667924	C₂²	1	1	yes	characteristic
26	C₂×#15667924	C₂²	1	1	yes	characteristic
27	C₂×#15667924	C₂²	1	1	yes	characteristic
28	C₂×#15667924	C₂²	1	1	yes	characteristic
29	C₂×#15667923	C₂²	1	1	yes	characteristic
30	C₂×#15667923	C₂²	1	1	yes	characteristic
31	C₂×#15667923	C₂²	1	1	yes	characteristic
32	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
35	#19151449	C₄	1	2	yes	—
36	#19151449	C₄	1	2	yes	—
37	#19151445	C₄	1	2	yes	—
38	#19151445	C₄	1	2	yes	—
39	#19151444	C₂²	1	1	yes	characteristic
40	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
41	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
42	#19151352	C₂²	1	1	yes	characteristic
43	#19151352	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	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
56	#376×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₂²×#10623494	C₂³	1	1	yes	characteristic
63	#15667969	—	2	2	no	—
64	#15667969	—	2	2	no	—
65	#15667969	C₂×C₄	1	4	yes	—
66	#15667969	C₂×C₄	1	4	yes	—
67	C₂×#13083553	C₂×C₄	1	2	yes	—
68	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083551	C₂×C₄	1	2	yes	—
71	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
77	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
78	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
81	C₄²×D₈₉	—	2	2	no	—
82	C₄²×D₈₉	—	2	2	no	—
83	#15667941	C₂×C₄	1	4	yes	complemented
84	#15667941	C₂×C₄	1	4	yes	complemented
85	#15667941	C₂×C₄	1	4	yes	complemented
86	#15667941	C₂×C₄	1	4	yes	complemented
87	#15667924	C₂×C₄	1	4	yes	—
88	#15667924	C₂×C₄	1	4	yes	—
89	#15667924	C₂×C₄	1	4	yes	—
90	#15667924	C₂×C₄	1	4	yes	—
91	#15667923	—	2	2	no	—
92	#15667923	—	2	2	no	—
93	#15667923	C₂×C₄	1	4	yes	complemented
94	C₄×#10623494	—	2	2	no	—
95	C₄×#10623494	—	2	2	no	—
96	C₄×#10623494	C₂×C₄	1	4	yes	complemented
97	#15667919	C₂×C₄	1	2	yes	—
98	#15667919	C₂×C₄	1	2	yes	—
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	#97×C₈₉	—	2	2	no	—
107	#97×C₈₉	—	2	2	no	—
108	#97×C₈₉	C₂×C₄	1	4	yes	complemented
109	C₄×C₈×C₈₉	—	2	2	no	—
110	C₄×C₈×C₈₉	—	2	2	no	—
111	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
112	#95×C₈₉	C₂×C₄	1	2	yes	—
113	#95×C₈₉	C₂×C₄	1	2	yes	—
114	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	2	1	no	—
124	C₂×C₄×D₈₉	—	2	4	no	—
125	C₂×C₄×D₈₉	—	2	4	no	—
126	C₂×C₄×D₈₉	—	4	2	no	—
127	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
128	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
138	C₂×#10623494	C₂²×C₄	1	2	yes	—
139	C₂×#10623494	C₂²×C₄	1	2	yes	—
140	C₂×#10623494	C₂²×C₄	1	2	yes	—
141	#13083553	—	2	4	no	—
142	#13083553	C₄²	1	4	yes	—
143	#13083553	C₄²	1	4	yes	—
144	#13083551	—	2	4	no	—
145	#13083551	C₄²	1	4	yes	—
146	#13083551	C₄²	1	4	yes	—
147	C₄×Dic₈₉	—	2	4	no	—
148	C₄×Dic₈₉	—	2	1	no	—
149	C₄×Dic₈₉	—	2	1	no	—
150	C₄×Dic₈₉	—	2	1	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	4	no	—
153	C₄×Dic₈₉	—	2	4	no	—
154	C₄×Dic₈₉	—	4	2	no	—
155	C₄×Dic₈₉	—	4	2	no	—
156	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
157	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	—	2	1	no	—
167	C₂×C₈×C₈₉	—	2	1	no	—
168	C₂×C₈×C₈₉	—	2	1	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
175	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
176	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
177	C₄²×C₈₉	#41	1	2	yes	—
178	C₄²×C₈₉	#41	1	2	yes	—
179	C₄²×C₈₉	#41	1	2	yes	—
180	C₄²×C₈₉	#41	1	2	yes	—
181	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
182	C₂²×D₈₉	—	2	1	no	—
183	C₂²×D₈₉	—	2	1	no	—
184	C₂²×D₈₉	—	2	2	no	—
185	C₂²×D₈₉	—	2	2	no	—
186	C₂²×D₈₉	C₂×C₄²	1	2	yes	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
194	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
195	C₂×C₄×C₈₉	#117	1	4	yes	—
196	C₂×C₄×C₈₉	#117	1	4	yes	—
197	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₈₉	—	2	2	no	—
204	C₂×Dic₈₉	—	2	1	no	—
205	C₂×Dic₈₉	—	2	1	no	—
206	C₂×Dic₈₉	—	2	2	no	—
207	C₂×Dic₈₉	—	2	2	no	—
208	C₂×Dic₈₉	—	2	2	no	—
209	C₂×Dic₈₉	—	2	2	no	—
210	C₂×Dic₈₉	—	2	2	no	—
211	C₂×Dic₈₉	—	2	2	no	—
212	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
213	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
214	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
215	C₂×Dic₈₉	#131	1	4	yes	—
216	C₄×D₈₉	—	2	2	no	—
217	C₄×D₈₉	—	2	2	no	—
218	C₄×D₈₉	—	2	2	no	—
219	C₄×D₈₉	—	2	2	no	—
220	C₄×D₈₉	—	4	8	no	—
221	C₈×C₈₉	—	2	2	no	—
222	C₈×C₈₉	—	2	2	no	—
223	C₈×C₈₉	—	2	2	no	—
224	C₈×C₈₉	—	2	2	no	—
225	#10623494	—	2	2	no	—
226	#10623494	—	2	2	no	—
227	#10623494	—	2	2	no	—
228	#10623494	—	2	2	no	—
229	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
230	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
231	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
232	C₂²×C₈₉	C₂×#131	1	2	yes	—
233	C₂²×C₈₉	#568	1	2	yes	—
234	C₂×D₈₉	—	2	2	no	—
235	C₂×D₈₉	—	2	2	no	—
236	C₂×D₈₉	—	2	2	no	—
237	C₂×D₈₉	—	4	2	no	—
238	C₂×D₈₉	—	4	2	no	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	2	2	no	—
241	C₄×C₈₉	—	2	4	no	—
242	C₄×C₈₉	—	2	4	no	—
243	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
244	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
245	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
246	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
247	Dic₈₉	—	2	2	no	—
248	Dic₈₉	—	2	2	no	—
249	Dic₈₉	—	2	4	no	—
250	Dic₈₉	—	2	2	no	—
251	Dic₈₉	—	4	2	no	—
252	#20468	—	89	1	no	maximal, Sylow
253	C₂×C₈₉	C₄×#117	1	1	yes	characteristic
254	C₂×C₈₉	C₄×#131	1	1	yes	characteristic
255	C₂×C₈₉	#2875	1	1	yes	characteristic
256	C₂×C₈₉	#2924	1	2	yes	—
257	C₂×C₈₉	#2925	1	2	yes	—
258	D₈₉	—	4	2	no	—
259	C₂×#433	—	89	1	no	—
260	C₂×#433	—	89	1	no	—
261	C₄×#117	—	89	1	no	—
262	#1768	—	89	1	no	—
263	#1768	—	89	1	no	—
264	#1767	—	89	1	no	—
265	C₄×C₄⋊C₈	—	89	1	no	—
266	#1750	—	89	1	no	—
267	#1750	—	89	1	no	—
268	#1749	—	89	1	no	—
269	C₄×C₂²⋊C₈	—	89	1	no	—
270	#1745	—	89	1	no	—
271	#1744	—	89	1	no	—
272	#1726	—	89	1	no	—
273	#1726	D₈₉	1	1	yes	characteristic, complemented
274	C₈₉	#20468	1	1	yes	characteristic, complemented, Sylow
275	C₂×#117	—	89	1	no	—
276	C₂×#117	—	89	1	no	—
277	C₂²×C₄²	—	89	1	no	—
278	#433	—	89	8	no	—
279	#433	—	89	8	no	—
280	C₂×C₄⋊C₈	—	89	1	no	—
281	C₂×C₄⋊C₈	—	89	1	no	—
282	C₂×C₄⋊C₈	—	89	1	no	—
283	C₂×C₄⋊C₈	—	89	1	no	—
284	C₂×C₂²⋊C₈	—	89	1	no	—
285	C₂×C₂²⋊C₈	—	89	1	no	—
286	C₂×C₂²⋊C₈	—	89	1	no	—
287	C₂×C₂²⋊C₈	—	89	1	no	—
288	C₂×#97	—	89	1	no	—
289	C₂×#97	—	89	1	no	—
290	C₂×#97	—	89	1	no	—
291	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
292	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
293	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
294	C₂×C₄×C₈	—	89	1	no	—
295	C₂×C₄×C₈	—	89	1	no	—
296	C₂×C₄×C₈	—	89	1	no	—
297	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
300	C₄×C₄⋊C₄	—	89	2	no	—
301	C₄×C₄⋊C₄	—	89	2	no	—
302	C₄×C₂²⋊C₄	—	89	2	no	—
303	C₄×C₂²⋊C₄	—	89	2	no	—
304	#376	—	89	1	no	—
305	#376	C₂×D₈₉	1	1	yes	characteristic
306	C₄³	—	89	1	no	—
307	C₄³	—	89	1	no	—
308	#336	—	89	1	no	—
309	#336	—	89	1	no	—
310	#336	—	89	1	no	—
311	#336	—	89	1	no	—
312	#336	—	89	1	no	—
313	#336	—	89	1	no	—
314	#336	—	89	1	no	—
315	#336	—	89	1	no	—
316	C₂³×C₄	—	89	1	no	—
317	C₂³×C₄	—	89	2	no	—
318	C₂²×C₈	—	89	1	no	—
319	C₂²×C₈	—	89	1	no	—
320	C₂²×C₈	—	89	1	no	—
321	C₂²×C₈	—	89	1	no	—
322	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	#117	—	89	4	no	—
327	#117	—	89	4	no	—
328	#117	—	178	2	no	—
329	#117	—	178	2	no	—
330	C₂×C₄⋊C₄	—	89	1	no	—
331	C₂×C₄⋊C₄	—	89	1	no	—
332	C₂×C₄⋊C₄	—	89	2	no	—
333	C₂×C₂²⋊C₄	—	89	1	no	—
334	C₂×C₂²⋊C₄	—	89	1	no	—
335	C₂×C₂²⋊C₄	—	89	2	no	—
336	C₂×C₄²	—	89	1	no	—
337	C₂×C₄²	—	89	2	no	—
338	C₂×C₄²	—	89	2	no	—
339	C₂×C₄²	—	89	2	no	—
340	C₂×C₄²	—	89	2	no	—
341	C₂×C₄²	—	89	2	no	—
342	C₂×C₄²	—	89	1	no	—
343	C₂×C₄²	—	89	1	no	—
344	C₂×C₄²	—	178	2	no	—
345	C₂×C₄²	—	178	2	no	—
346	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
347	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
349	C₄⋊C₈	—	89	4	no	—
350	C₄⋊C₈	—	89	4	no	—
351	C₄⋊C₈	—	89	4	no	—
352	C₄⋊C₈	—	89	4	no	—
353	C₂²⋊C₈	—	89	4	no	—
354	C₂²⋊C₈	—	89	4	no	—
355	C₂²⋊C₈	—	89	4	no	—
356	C₂²⋊C₈	—	89	4	no	—
357	#97	—	2	2	no	—
358	#97	—	2	2	no	—
359	#97	—	89	4	no	—
360	#97	—	178	2	no	—
361	#97	—	178	2	no	—
362	#97	C₄×D₈₉	1	4	yes	complemented
363	C₄×C₈	—	2	2	no	—
364	C₄×C₈	—	2	2	no	—
365	C₄×C₈	—	89	4	no	—
366	C₄×C₈	—	178	2	no	—
367	C₄×C₈	—	178	2	no	—
368	C₄×C₈	C₄×D₈₉	1	4	yes	complemented
369	#95	—	89	2	no	—
370	#95	—	89	2	no	—
371	#95	C₄×D₈₉	1	2	yes	—
372	#95	C₄×D₈₉	1	2	yes	—
373	C₂⁴	—	89	1	no	—
374	C₂²×C₄	—	89	1	no	—
375	C₂²×C₄	—	89	1	no	—
376	C₂²×C₄	—	89	2	no	—
377	C₂²×C₄	—	89	1	no	—
378	C₂²×C₄	—	89	2	no	—
379	C₂²×C₄	—	89	2	no	—
380	C₂²×C₄	—	89	2	no	—
381	C₂²×C₄	—	356	2	no	—
382	C₂²×C₄	—	178	4	no	—
383	C₂²×C₄	—	178	4	no	—
384	C₂²×C₄	—	178	1	no	—
385	C₂²×C₄	—	178	1	no	—
386	C₂²×C₄	—	178	1	no	—
387	C₂²×C₄	—	178	1	no	—
388	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
389	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
390	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	89	2	no	—
402	C₂×C₈	—	89	2	no	—
403	C₂×C₈	—	89	2	no	—
404	C₂×C₈	—	89	2	no	—
405	C₂×C₈	—	178	1	no	—
406	C₂×C₈	—	178	1	no	—
407	C₂×C₈	—	178	1	no	—
408	C₂×C₈	—	178	1	no	—
409	C₂×C₈	—	178	1	no	—
410	C₂×C₈	—	178	1	no	—
411	C₂×C₈	—	178	1	no	—
412	C₂×C₈	—	178	1	no	—
413	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
415	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
417	C₄⋊C₄	—	89	4	no	—
418	C₄⋊C₄	—	89	4	no	—
419	C₄⋊C₄	—	178	4	no	—
420	C₂²⋊C₄	—	89	4	no	—
421	C₂²⋊C₄	—	89	4	no	—
422	C₂²⋊C₄	—	178	4	no	—
423	C₄²	—	89	2	no	—
424	C₄²	—	89	2	no	—
425	C₄²	—	356	2	no	—
426	C₄²	—	356	2	no	—
427	C₄²	—	178	4	no	—
428	C₄²	—	178	4	no	—
429	C₄²	—	178	4	no	—
430	C₄²	—	178	1	no	—
431	C₄²	—	178	1	no	—
432	C₄²	—	178	1	no	—
433	C₄²	—	178	1	no	—
434	C₄²	C₂×C₄×D₈₉	1	2	yes	—
435	C₄²	C₂×C₄×D₈₉	1	2	yes	—
436	C₄²	#13083574	1	2	yes	—
437	C₄²	#13083574	1	2	yes	—
438	C₄²	#13083574	1	2	yes	—
439	C₄²	#13083574	1	2	yes	—
440	C₂³	—	89	2	no	—
441	C₂³	—	178	1	no	—
442	C₂³	—	178	1	no	—
443	C₂³	—	178	2	no	—
444	C₂³	—	178	2	no	—
445	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	89	2	no	—
453	C₂×C₄	—	89	2	no	—
454	C₂×C₄	—	89	2	no	—
455	C₂×C₄	—	89	4	no	—
456	C₂×C₄	—	356	8	no	—
457	C₂×C₄	—	178	2	no	—
458	C₂×C₄	—	178	2	no	—
459	C₂×C₄	—	178	2	no	—
460	C₂×C₄	—	178	2	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	178	2	no	—
464	C₂×C₄	—	178	2	no	—
465	C₂×C₄	—	178	2	no	—
466	C₂×C₄	—	178	2	no	—
467	C₂×C₄	—	178	2	no	—
468	C₂×C₄	—	178	2	no	—
469	C₂×C₄	—	178	2	no	—
470	C₂×C₄	C₄²×D₈₉	1	2	yes	—
471	C₂×C₄	C₄²×D₈₉	1	2	yes	—
472	C₂×C₄	#15667969	1	4	yes	—
473	C₂×C₄	#15667969	1	4	yes	—
474	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
476	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
477	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
478	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
479	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	178	2	no	—
485	C₈	—	178	2	no	—
486	C₈	—	178	2	no	—
487	C₈	—	178	2	no	—
488	C₂²	—	356	2	no	—
489	C₂²	—	356	2	no	—
490	C₂²	—	178	2	no	—
491	C₂²	—	178	2	no	—
492	C₂²	—	178	2	no	—
493	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
494	C₂²	C₂×#15667969	1	1	yes	characteristic
495	C₂²	C₂×#15667969	1	1	yes	characteristic
496	C₂²	#131×D₈₉	1	2	yes	—
497	C₂²	#19152363	1	2	yes	—
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	356	2	no	—
503	C₄	—	178	4	no	—
504	C₄	—	178	2	no	—
505	C₄	—	178	2	no	—
506	C₄	—	178	2	no	—
507	C₄	C₄×#13083574	1	1	yes	characteristic
508	C₄	C₄×#13083574	1	1	yes	characteristic
509	C₄	C₄×#13083574	1	1	yes	characteristic
510	C₄	C₄×#13083574	1	1	yes	characteristic
511	C₂	—	356	2	no	—
512	C₂	C₄×#15667969	1	1	yes	characteristic
513	C₂	#26028674	1	1	yes	characteristic
514	C₂	#26028679	1	1	yes	characteristic
515	C₂	#26028907	1	2	yes	—
516	C₂	#26028916	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#1726	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1726	D₈₉
hypocenter	C₈₉	#20468
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1726

Complements

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

N	H ≅ G/N	type
4. #26020112	C₂	semidirect
5. #26020110	C₂	semidirect
6. #26020106	C₂	semidirect
7. C₄×#15667941	C₂	semidirect
12. #26020000	C₂	semidirect
13. #26019997	C₂	semidirect
14. #26019939	C₂	semidirect
15. C₈₉×#1726	C₂	semidirect
19. #19151660	C₄	semidirect
20. #19151657	C₄	semidirect
83. #15667941	C₂×C₄	semidirect
84. #15667941	C₂×C₄	semidirect
85. #15667941	C₂×C₄	semidirect
86. #15667941	C₂×C₄	semidirect
93. #15667923	C₂×C₄	semidirect
96. C₄×#10623494	C₂×C₄	semidirect
108. #97×C₈₉	C₂×C₄	semidirect
111. C₄×C₈×C₈₉	C₂×C₄	semidirect
273. #1726	D₈₉	semidirect
274. C₈₉	#20468	semidirect
362. #97	C₄×D₈₉	semidirect
368. C₄×C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151660	2
C₂×#19151657	2
#26022591	2
#26020112	2
#26020110	2
#26020106	2
C₄×#15667941	2
#26020021	2
#26020019	2
#26020015	2
C₄×#15667924	2
#26020000	2
#26019997	2
#26019939	2
C₈₉×#1726	2
#20468	89