Subgroups — #36525647

Order 22784.

598 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029384	C₂	1	1	yes	maximal, characteristic
2	#26029354	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019143	C₂	1	2	yes	maximal, complemented
4	#26019131	C₂	1	2	yes	maximal, complemented
5	#26019124	C₂	1	2	yes	maximal, complemented
6	Q₁₆×#10623494	C₂	1	2	yes	maximal, complemented
7	#26019041	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018707	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018634	C₂	1	1	yes	maximal, characteristic
10	#26018536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	1	no	—
13	#19151729	C₂²	1	2	yes	—
14	Q₈×#10623494	—	2	1	no	—
15	Q₈×#10623494	C₂²	1	2	yes	—
16	Q₈×#10623494	C₂²	1	2	yes	—
17	#19151676	—	2	2	no	—
18	#19151676	C₂²	1	2	yes	—
19	#19151659	—	2	2	no	—
20	#19151651	—	2	1	no	—
21	#19151651	C₂²	1	1	yes	characteristic
22	#19151651	C₂²	1	1	yes	characteristic
23	#19151622	—	2	1	no	—
24	#19151622	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151351	C₂²	1	2	yes	—
27	#19151349	C₂²	1	2	yes	—
28	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
29	Q₈⋊#10623494	C₂²	1	2	yes	—
30	Q₈⋊#10623494	C₂²	1	2	yes	—
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
32	D₄⋊#10623494	C₂²	1	1	yes	characteristic
33	D₄⋊#10623494	C₂²	1	1	yes	characteristic
34	#19151320	C₂²	1	2	yes	—
35	C₈×#10623494	C₂²	1	2	yes	—
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
38	#485×C₈₉	C₄	1	2	yes	—
39	#475×C₈₉	C₄	1	1	yes	characteristic
40	#474×C₈₉	C₄	1	1	yes	characteristic
41	#462×C₈₉	C₄	1	1	yes	characteristic
42	#461×C₈₉	C₄	1	1	yes	characteristic
43	#452×C₈₉	C₄	1	2	yes	—
44	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083558	—	2	2	no	—
48	C₂×#13083558	—	2	1	no	—
49	C₂²×#10623494	—	2	1	no	—
50	C₄⋊#10623494	—	2	2	no	—
51	C₄⋊#10623494	—	2	2	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	D₄	1	1	yes	characteristic
55	C₄⋊#10623494	D₄	1	1	yes	characteristic
56	C₄⋊#10623494	C₂³	1	2	yes	—
57	C₄⋊#10623494	C₂³	1	1	yes	characteristic
58	C₄⋊#10623494	C₂³	1	1	yes	characteristic
59	C₂²⋊#10623494	—	2	2	no	—
60	C₂²⋊#10623494	—	2	1	no	—
61	C₂²⋊#10623494	D₄	1	2	yes	—
62	#15667923	—	2	2	no	—
63	C₄×#10623494	—	2	2	no	—
64	C₄×#10623494	—	2	2	no	—
65	C₄×#10623494	—	2	1	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₄×#10623494	C₂³	1	1	yes	characteristic
68	C₄×#10623494	C₂³	1	1	yes	characteristic
69	C₄×#10623494	C₂³	1	2	yes	—
70	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
73	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
75	#125×C₈₉	—	2	1	no	—
76	C₂²⋊Q₈×C₈₉	—	2	1	no	—
77	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₈₉	—	2	1	no	—
79	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
81	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	#117×C₈₉	—	2	1	no	—
87	#117×C₈₉	—	2	1	no	—
88	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	#107×C₈₉	C₂×C₄	1	2	yes	—
92	#106×C₈₉	C₂×C₄	1	2	yes	—
93	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	#103×C₈₉	C₂×C₄	1	2	yes	—
96	#103×C₈₉	C₂×C₄	1	2	yes	—
97	#103×C₈₉	C₂×C₄	1	2	yes	—
98	#102×C₈₉	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₈₉	C₂³	1	2	yes	—
101	#13083558	—	8	2	no	—
102	#13083558	—	8	1	no	—
103	C₂×#10623494	—	2	4	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	1	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	2	1	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	C₂×D₄	1	2	yes	—
110	C₂×#10623494	C₂×D₄	1	2	yes	—
111	#41×C₈₉	—	2	2	no	—
112	#41×C₈₉	—	4	1	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
115	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₈₉	—	2	1	no	—
117	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	—	2	1	no	—
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
124	Q₁₆×C₈₉	—	2	4	no	—
125	SD₁₆×C₈₉	—	4	2	no	—
126	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₄⋊C₄×C₈₉	—	2	2	no	—
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₈₉	—	2	2	no	—
139	C₂²⋊C₄×C₈₉	—	2	1	no	—
140	C₂²⋊C₄×C₈₉	—	2	1	no	—
141	C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₄²×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₈₉	#41	1	1	yes	characteristic
149	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₈₉	—	2	1	no	—
151	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
152	Q₈×C₈₉	—	2	1	no	—
153	Q₈×C₈₉	—	2	2	no	—
154	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	4	2	no	—
156	Q₈×C₈₉	#131	1	2	yes	—
157	D₄×C₈₉	—	2	1	no	—
158	D₄×C₈₉	—	2	1	no	—
159	D₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	4	1	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	2	2	no	—
182	#10623494	—	2	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	2	2	no	—
186	#10623494	—	4	1	no	—
187	#10623494	—	4	2	no	—
188	#10623494	—	4	1	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	4	1	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	1	no	—
195	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	1	no	—
202	C₄×C₈₉	—	4	1	no	—
203	C₄×C₈₉	—	4	2	no	—
204	C₄×C₈₉	#443	1	2	yes	—
205	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
206	C₄×C₈₉	#568	1	1	yes	characteristic
207	C₄×C₈₉	#577	1	1	yes	characteristic
208	C₄×C₈₉	#578	1	1	yes	characteristic
209	#18019	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	4	1	no	—
211	C₂×C₈₉	—	8	1	no	—
212	C₂×C₈₉	#2933	1	1	yes	characteristic
213	C₂×C₈₉	#2947	1	1	yes	characteristic
214	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
215	#3107	D₈₉	1	1	yes	characteristic
216	#2991	—	89	1	no	—
217	#2986	—	89	1	no	—
218	#1590	—	89	2	no	—
219	#1588	—	89	2	no	—
220	#1587	—	89	2	no	—
221	C₈×Q₁₆	—	89	2	no	—
222	#1574	—	89	1	no	—
223	#1493	—	89	1	no	—
224	#1476	—	89	1	no	—
225	#1450	—	89	1	no	—
226	C₈₉	#18019	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₈₉	1	1	yes	characteristic
228	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
229	#485	Dic₈₉	1	2	yes	—
230	#475	Dic₈₉	1	1	yes	characteristic
231	#474	Dic₈₉	1	1	yes	characteristic
232	#462	Dic₈₉	1	1	yes	characteristic
233	#461	Dic₈₉	1	1	yes	characteristic
234	#452	Dic₈₉	1	2	yes	—
235	#446	—	89	2	no	—
236	#446	—	178	1	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₈×Q₈	—	89	2	no	—
239	C₈×Q₈	—	178	1	no	—
240	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
241	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
242	#436	—	89	2	no	—
243	#436	—	178	2	no	—
244	#433	—	178	2	no	—
245	#431	—	89	1	no	—
246	#431	—	89	1	no	—
247	#431	—	178	1	no	—
248	#431	C₂×D₈₉	1	1	yes	characteristic
249	#423	—	89	1	no	—
250	#423	—	178	1	no	—
251	C₂×C₄×C₈	—	89	1	no	—
252	#335	—	89	2	no	—
253	#334	—	89	2	no	—
254	Q₈⋊C₈	—	89	1	no	—
255	Q₈⋊C₈	—	89	2	no	—
256	Q₈⋊C₈	—	89	1	no	—
257	Q₈⋊C₈	—	89	2	no	—
258	D₄⋊C₈	—	89	1	no	—
259	D₄⋊C₈	—	89	1	no	—
260	#322	—	89	2	no	—
261	C₈²	—	89	2	no	—
262	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
263	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
264	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂×M₁₆	—	178	1	no	—
267	C₂²×C₈	—	178	1	no	—
268	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
275	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
276	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
280	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	C₂×Dic₈₉	1	1	yes	characteristic
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	#107	C₂×Dic₈₉	1	2	yes	—
287	#106	C₂×Dic₈₉	1	2	yes	—
288	C₄⋊C₈	—	89	1	no	—
289	C₄⋊C₈	—	89	1	no	—
290	C₄⋊C₈	—	89	1	no	—
291	C₄⋊C₈	—	89	1	no	—
292	C₄⋊C₈	—	89	2	no	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	2	no	—
295	C₄⋊C₈	—	178	2	no	—
296	C₄⋊C₈	—	178	1	no	—
297	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
299	#103	C₂×Dic₈₉	1	2	yes	—
300	#103	C₂×Dic₈₉	1	2	yes	—
301	#103	C₂×Dic₈₉	1	2	yes	—
302	#102	C₂×Dic₈₉	1	2	yes	—
303	C₂²⋊C₈	—	89	2	no	—
304	C₂²⋊C₈	—	178	2	no	—
305	C₂²⋊C₈	—	178	1	no	—
306	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
307	#97	—	178	2	no	—
308	C₄×C₈	—	89	2	no	—
309	C₄×C₈	—	89	1	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	—	178	2	no	—
312	C₄×C₈	—	178	2	no	—
313	C₄×C₈	—	178	1	no	—
314	C₄×C₈	—	178	1	no	—
315	C₄×C₈	C₂²×D₈₉	1	2	yes	—
316	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
320	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
328	C₂²×C₄	#13083573	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	SD₁₆	—	4	2	no	—
331	M₁₆	—	712	1	no	—
332	M₁₆	—	712	2	no	—
333	C₂×C₈	—	89	2	no	—
334	C₂×C₈	—	89	2	no	—
335	C₂×C₈	—	178	1	no	—
336	C₂×C₈	—	178	1	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	4	no	—
339	C₂×C₈	—	178	1	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
342	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
351	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
362	C₄²	D₄×D₈₉	1	1	yes	characteristic
363	C₄²	#13083573	1	1	yes	characteristic
364	C₄²	C₂³×D₈₉	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	#15668019	1	2	yes	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
390	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
391	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	356	1	no	—
398	C₈	—	356	2	no	—
399	C₈	—	356	1	no	—
400	C₈	—	178	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₈	—	178	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	#19151715	1	2	yes	—
420	C₄	C₂×#15668019	1	1	yes	characteristic
421	C₄	#19152365	1	1	yes	characteristic
422	C₄	#19152407	1	1	yes	characteristic
423	C₄	#19152414	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	8	1	no	—
426	C₂	#26028979	1	1	yes	characteristic
427	C₂	#26029096	1	1	yes	characteristic
428	C₂	C₂×#19151715	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×#3107	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3107	D₈₉
hypocenter	C₈₉	#18019
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #26029354	C₂	semidirect
3. #26019143	C₂	semidirect
4. #26019131	C₂	semidirect
5. #26019124	C₂	semidirect
6. Q₁₆×#10623494	C₂	semidirect
7. #26019041	C₂	semidirect
8. #26018707	C₂	semidirect
10. #26018536	C₂	semidirect
226. C₈₉	#18019	semidirect

Maximal subgroups

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

subgroup	index
#26029384	2
#26029354	2
#26019143	2
#26019131	2
#26019124	2
Q₁₆×#10623494	2
#26019041	2
#26018707	2
#26018634	2
#26018536	2
C₈₉×#3107	2
#18019	89