Subgroups — #36523587

Order 22784.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028884	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151654	C₂	1	1	yes	maximal, characteristic
3	#431×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019031	C₂	1	4	yes	maximal, complemented
5	#26019027	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019024	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019022	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019014	C₂	1	4	yes	maximal, complemented
9	C₈₉×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
11	#19151654	—	2	1	no	—
12	#19151654	—	2	1	no	—
13	#19151654	—	2	1	no	—
14	#19151654	C₂²	1	2	yes	—
15	#19151654	C₂²	1	2	yes	—
16	#19151654	C₂²	1	2	yes	—
17	#19151651	C₂²	1	1	yes	characteristic
18	#19151650	—	2	1	no	—
19	#19151650	C₄	1	2	yes	—
20	#19151650	C₂²	1	2	yes	—
21	#19151649	C₂²	1	2	yes	—
22	#19151648	C₄	1	2	yes	—
23	#19151622	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
25	C₄⋊C₈×D₈₉	C₄	1	2	yes	—
26	#19151561	—	2	1	no	—
27	C₂×#15667924	—	2	1	no	—
28	C₂²⋊C₈×D₈₉	C₄	1	2	yes	—
29	M₁₆×Dic₈₉	—	2	1	no	—
30	C₂×#15667922	—	2	1	no	—
31	C₄×C₈×D₈₉	C₂²	1	2	yes	—
32	#19151351	C₂²	1	4	yes	complemented
33	#19151348	C₂²	1	4	yes	complemented
34	#19151348	C₂²	1	4	yes	complemented
35	#431×C₈₉	C₂²	1	1	yes	characteristic
36	#423×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	#335×C₈₉	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
42	C₂×#13083558	—	2	1	no	—
43	C₂²×#10623494	—	2	1	no	—
44	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
48	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₈₉	D₄	1	1	yes	characteristic
51	C₄²×D₈₉	D₄	1	1	yes	characteristic
52	C₄²×D₈₉	Q₈	1	1	yes	characteristic
53	C₄²×D₈₉	Q₈	1	1	yes	characteristic
54	C₄²×D₈₉	C₂³	1	1	yes	characteristic
55	C₄²×D₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊#10623494	—	2	1	no	—
57	C₄⋊#10623494	—	2	1	no	—
58	C₄⋊#10623494	C₂×C₄	1	2	yes	—
59	C₄⋊#10623494	C₂³	1	2	yes	—
60	C₄⋊#10623494	C₂³	1	2	yes	—
61	#15667941	C₂×C₄	1	4	yes	—
62	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
63	#15667924	—	2	2	no	—
64	#15667924	—	2	2	no	—
65	#15667924	—	2	2	no	—
66	#15667924	—	2	2	no	—
67	#15667924	C₂×C₄	1	4	yes	—
68	#15667922	—	2	2	no	—
69	#15667922	—	2	2	no	—
70	#15667922	—	2	2	no	—
71	C₄×#10623494	C₂³	1	2	yes	—
72	C₈×Dic₈₉	—	2	2	no	—
73	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
74	C₂×M₁₆×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₈₉	—	2	1	no	—
78	C₄⋊C₈×C₈₉	—	2	1	no	—
79	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
81	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
82	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
83	C₄×C₈×C₈₉	C₂³	1	2	yes	—
84	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₈₉	—	2	2	no	—
89	C₂×C₄×D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	4	2	no	—
91	C₂×C₄×D₈₉	—	4	2	no	—
92	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
104	#13083558	—	4	2	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	4	2	no	—
108	C₂×#10623494	C₂²×C₄	1	4	yes	—
109	C₈×D₈₉	—	4	4	no	—
110	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
112	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
119	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
120	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
121	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
125	M₁₆×C₈₉	—	4	2	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	—	4	2	no	—
129	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
130	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
133	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₈₉	—	2	2	no	—
136	C₂²×D₈₉	—	2	2	no	—
137	C₂²×D₈₉	—	4	1	no	—
138	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#135	1	2	yes	—
146	C₂×C₄×C₈₉	#135	1	2	yes	—
147	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
150	C₂×Dic₈₉	—	2	2	no	—
151	C₂×Dic₈₉	—	4	1	no	—
152	C₂×Dic₈₉	—	4	1	no	—
153	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₄×D₈₉	—	2	2	no	—
160	C₄×D₈₉	—	2	2	no	—
161	C₄×D₈₉	—	2	2	no	—
162	C₄×D₈₉	—	2	2	no	—
163	C₄×D₈₉	—	2	1	no	—
164	C₄×D₈₉	—	2	1	no	—
165	C₄×D₈₉	—	2	1	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	2	2	no	—
168	C₄×D₈₉	—	2	2	no	—
169	C₄×D₈₉	—	4	1	no	—
170	C₄×D₈₉	—	4	1	no	—
171	C₄×D₈₉	—	4	1	no	—
172	C₄×D₈₉	—	4	1	no	—
173	C₈×C₈₉	—	2	4	no	—
174	C₈×C₈₉	—	4	2	no	—
175	C₈×C₈₉	—	4	2	no	—
176	#10623494	—	2	4	no	—
177	#10623494	—	4	2	no	—
178	#10623494	—	4	2	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	#427	1	2	yes	—
182	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	1	no	—
186	C₂×D₈₉	—	2	1	no	—
187	C₂×D₈₉	—	2	1	no	—
188	C₂×D₈₉	—	4	4	no	—
189	C₂×D₈₉	#430	1	2	yes	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	#427	1	2	yes	—
194	C₄×C₈₉	#568	1	2	yes	—
195	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
196	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
197	Dic₈₉	—	2	1	no	—
198	Dic₈₉	—	2	1	no	—
199	Dic₈₉	—	2	1	no	—
200	Dic₈₉	—	2	1	no	—
201	Dic₈₉	—	2	1	no	—
202	Dic₈₉	—	2	1	no	—
203	#17816	—	89	1	no	maximal, Sylow
204	C₂×C₈₉	—	2	2	no	—
205	C₂×C₈₉	#2905	1	1	yes	characteristic
206	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
208	D₈₉	—	2	2	no	—
209	D₈₉	—	4	1	no	—
210	#2920	—	89	1	no	—
211	C₂×#432	—	89	1	no	—
212	C₂×#431	—	89	1	no	—
213	#1572	—	89	4	no	—
214	#1571	—	89	1	no	—
215	#1571	D₈₉	1	1	yes	characteristic, complemented
216	#1570	—	89	1	no	—
217	#1570	—	89	1	no	—
218	#1568	—	89	4	no	—
219	C₈₉	#17816	1	1	yes	characteristic, complemented, Sylow
220	C₂²×C₄²	—	89	1	no	—
221	#432	—	89	2	no	—
222	#432	—	89	2	no	—
223	#432	—	89	2	no	—
224	#432	—	178	1	no	—
225	#432	—	178	1	no	—
226	#432	—	178	1	no	—
227	#431	—	89	1	no	—
228	#431	—	89	2	no	—
229	#431	—	89	2	no	—
230	#431	—	89	2	no	—
231	#431	—	89	2	no	—
232	#431	—	178	1	no	—
233	#431	C₂×D₈₉	1	1	yes	characteristic
234	#423	—	89	1	no	—
235	#423	C₂×D₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	89	2	no	—
237	C₂×C₄⋊C₈	—	89	1	no	—
238	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
239	#407	—	178	1	no	—
240	C₂×C₂²⋊C₈	—	89	2	no	—
241	C₂×C₂²⋊C₈	—	178	1	no	—
242	C₄×M₁₆	—	178	1	no	—
243	C₂×#97	—	178	1	no	—
244	C₂×C₄×C₈	—	89	2	no	—
245	#335	—	89	4	no	—
246	#335	C₂×D₈₉	1	4	yes	complemented
247	#334	—	89	4	no	—
248	#334	—	89	4	no	—
249	C₂³×C₄	—	89	1	no	—
250	C₂³×C₄	—	89	1	no	—
251	C₂³×C₄	—	89	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	178	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	89	4	no	—
256	C₂²×C₈	—	178	1	no	—
257	C₂×C₄²	—	89	1	no	—
258	C₂×C₄²	—	89	1	no	—
259	C₂×C₄²	—	89	1	no	—
260	C₂×C₄²	—	89	1	no	—
261	C₂×C₄²	—	89	1	no	—
262	C₂×C₄²	—	89	1	no	—
263	C₂×C₄²	—	89	1	no	—
264	C₂×C₄²	—	89	1	no	—
265	C₂×C₄²	—	89	1	no	—
266	C₂×C₄²	—	89	1	no	—
267	C₂×C₄²	—	89	1	no	—
268	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	89	4	no	—
272	C₄⋊C₈	—	89	2	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	178	1	no	—
276	C₄⋊C₈	—	178	1	no	—
277	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
278	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
279	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
280	C₂²⋊C₈	—	89	2	no	—
281	C₂²⋊C₈	—	89	4	no	—
282	C₂²⋊C₈	—	178	2	no	—
283	C₂²⋊C₈	—	178	2	no	—
284	C₂²⋊C₈	—	178	2	no	—
285	C₂²⋊C₈	—	178	2	no	—
286	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
287	#97	—	178	2	no	—
288	#97	—	178	2	no	—
289	#97	—	178	2	no	—
290	C₄×C₈	—	89	4	no	—
291	C₄×C₈	—	89	2	no	—
292	C₄×C₈	—	178	2	no	—
293	C₄×C₈	C₂²×D₈₉	1	2	yes	—
294	C₂⁴	—	89	1	no	—
295	C₂²×C₄	—	89	1	no	—
296	C₂²×C₄	—	89	1	no	—
297	C₂²×C₄	—	89	1	no	—
298	C₂²×C₄	—	89	1	no	—
299	C₂²×C₄	—	89	1	no	—
300	C₂²×C₄	—	89	1	no	—
301	C₂²×C₄	—	89	1	no	—
302	C₂²×C₄	—	89	1	no	—
303	C₂²×C₄	—	89	1	no	—
304	C₂²×C₄	—	89	1	no	—
305	C₂²×C₄	—	89	1	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	356	2	no	—
311	C₂²×C₄	—	356	2	no	—
312	C₂²×C₄	—	178	2	no	—
313	C₂²×C₄	—	178	2	no	—
314	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
316	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
317	M₁₆	—	4	2	no	—
318	M₁₆	—	356	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	89	4	no	—
323	C₂×C₈	—	356	4	no	—
324	C₂×C₈	—	356	2	no	—
325	C₂×C₈	—	178	2	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
328	C₄²	—	89	1	no	—
329	C₄²	—	89	1	no	—
330	C₄²	—	89	1	no	—
331	C₄²	—	89	1	no	—
332	C₄²	—	89	1	no	—
333	C₄²	—	89	1	no	—
334	C₄²	—	89	1	no	—
335	C₄²	—	89	1	no	—
336	C₄²	—	89	1	no	—
337	C₄²	—	89	1	no	—
338	C₄²	—	89	1	no	—
339	C₄²	—	89	1	no	—
340	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₄²	D₄×D₈₉	1	1	yes	characteristic
342	C₄²	Q₈×D₈₉	1	1	yes	characteristic
343	C₄²	C₂³×D₈₉	1	1	yes	characteristic
344	C₂³	—	89	1	no	—
345	C₂³	—	89	1	no	—
346	C₂³	—	356	1	no	—
347	C₂³	—	178	2	no	—
348	C₂³	—	178	2	no	—
349	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	89	1	no	—
353	C₂×C₄	—	89	1	no	—
354	C₂×C₄	—	89	1	no	—
355	C₂×C₄	—	89	1	no	—
356	C₂×C₄	—	89	1	no	—
357	C₂×C₄	—	89	1	no	—
358	C₂×C₄	—	356	1	no	—
359	C₂×C₄	—	356	1	no	—
360	C₂×C₄	—	356	1	no	—
361	C₂×C₄	—	356	1	no	—
362	C₂×C₄	—	356	1	no	—
363	C₂×C₄	—	356	1	no	—
364	C₂×C₄	—	178	2	no	—
365	C₂×C₄	—	178	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	178	2	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	1	no	—
372	C₂×C₄	—	178	1	no	—
373	C₂×C₄	—	178	1	no	—
374	C₂×C₄	—	178	1	no	—
375	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
378	C₂×C₄	#15668031	1	2	yes	—
379	C₂×C₄	#15668035	1	2	yes	—
380	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	356	2	no	—
387	C₈	—	356	2	no	—
388	C₈	—	178	4	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	89	2	no	—
392	C₂²	—	356	4	no	—
393	C₂²	—	178	1	no	—
394	C₂²	—	178	1	no	—
395	C₂²	—	178	1	no	—
396	C₂²	—	178	1	no	—
397	C₂²	—	178	1	no	—
398	C₂²	#19151635	1	2	yes	—
399	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	178	1	no	—
404	C₄	—	178	1	no	—
405	C₄	—	178	1	no	—
406	C₄	—	178	1	no	—
407	C₄	—	178	1	no	—
408	C₄	—	178	1	no	—
409	C₄	#19151635	1	2	yes	—
410	C₄	#19152363	1	2	yes	—
411	C₄	C₂×#15668031	1	1	yes	characteristic
412	C₄	C₂×#15668035	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	356	1	no	—
415	C₂	—	178	2	no	—
416	C₂	#26028813	1	1	yes	characteristic
417	C₂	C₂×#19151635	1	1	yes	characteristic
418	C₂	#430×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1571	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1571	D₈₉
hypocenter	C₈₉	#17816
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

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

N	H ≅ G/N	type
4. #26019031	C₂	semidirect
5. #26019027	C₂	semidirect
6. #26019024	C₂	semidirect
7. #26019022	C₂	semidirect
8. #26019014	C₂	semidirect
9. C₈₉×#1571	C₂	semidirect
32. #19151351	C₂²	semidirect
33. #19151348	C₂²	semidirect
34. #19151348	C₂²	semidirect
38. #335×C₈₉	C₂²	semidirect
215. #1571	D₈₉	semidirect
219. C₈₉	#17816	semidirect
246. #335	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028884	2
C₂×#19151654	2
#431×D₈₉	2
#26019031	2
#26019027	2
#26019024	2
#26019022	2
#26019014	2
C₈₉×#1571	2
#17816	89