Subgroups — #36561228

Order 22784.

958 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151720	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028947	C₂	1	2	yes	maximal, complemented
3	C₂²×#15667922	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021146	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021006	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020965	C₂	1	2	yes	maximal, complemented
7	#26020696	C₂	1	2	yes	maximal, complemented
8	#26020290	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020099	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	C₂³×#10623494	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
15	#19151720	—	2	4	no	—
16	#19151670	—	2	4	no	—
17	D₄×#10623494	—	2	4	no	—
18	C₂×#15667948	C₂²	1	1	yes	characteristic
19	C₂×#15667948	C₂²	1	1	yes	characteristic
20	#19151625	C₂²	1	2	yes	—
21	C₂×#15667939	C₂²	1	2	yes	—
22	C₂×#15667939	C₂²	1	2	yes	—
23	#19151565	C₂²	1	2	yes	—
24	#19151562	C₂²	1	2	yes	—
25	#19151554	C₂²	1	2	yes	—
26	C₂×#15667922	—	2	4	no	—
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×#15667922	C₂²	1	1	yes	characteristic
29	C₂×#15667922	C₂²	1	1	yes	characteristic
30	C₂×#15667922	C₂²	1	1	yes	characteristic
31	#19151363	C₂²	1	2	yes	—
32	#19151357	C₂²	1	2	yes	—
33	#19151357	C₂²	1	2	yes	—
34	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
36	#525×C₈₉	C₂²	1	2	yes	—
37	#467×C₈₉	C₄	1	2	yes	complemented
38	#466×C₈₉	C₄	1	2	yes	complemented
39	#465×C₈₉	C₄	1	4	yes	complemented
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#416×C₈₉	C₂²	1	2	yes	—
42	C₂³×Dic₈₉	—	2	1	no	—
43	#15668019	—	2	4	no	—
44	#15668019	—	2	4	no	—
45	C₂×#13083558	—	2	2	no	—
46	C₂×#13083558	C₂³	1	2	yes	—
47	C₂×#13083558	C₂³	1	2	yes	—
48	C₂²×#10623494	—	2	2	no	—
49	C₂²×#10623494	—	2	2	no	—
50	C₂²×#10623494	—	2	2	no	—
51	C₂²×#10623494	D₄	1	4	yes	—
52	C₂²×#10623494	C₂³	1	1	yes	characteristic
53	C₂²×#10623494	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₈₉	—	2	2	no	—
55	C₂×C₄×Dic₈₉	—	2	2	no	—
56	C₂×C₄×Dic₈₉	—	2	1	no	—
57	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
59	#15667948	—	2	2	no	—
60	#15667948	—	2	2	no	—
61	C₄⋊#10623494	—	2	4	no	—
62	#15667939	—	2	4	no	—
63	#15667939	—	2	4	no	—
64	C₂²⋊#10623494	—	2	4	no	—
65	C₂²⋊#10623494	—	2	4	no	—
66	#15667923	—	2	2	no	—
67	#15667922	—	2	2	no	—
68	#15667922	—	2	2	no	—
69	#15667922	—	2	2	no	—
70	#15667922	D₄	1	4	yes	complemented
71	C₄×#10623494	—	2	2	no	—
72	C₂×#41×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	#135×C₈₉	—	2	2	no	—
75	#135×C₈₉	—	2	2	no	—
76	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
78	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂²×C₈×C₈₉	—	2	2	no	—
80	C₂²×C₈×C₈₉	—	2	2	no	—
81	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	#123×C₈₉	—	2	2	no	—
86	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
87	#121×C₈₉	C₂×C₄	1	4	yes	—
88	#120×C₈₉	—	2	2	no	—
89	C₄×D₄×C₈₉	—	2	4	no	—
90	#117×C₈₉	C₂³	1	2	yes	—
91	#107×C₈₉	C₂×C₄	1	2	yes	complemented
92	#106×C₈₉	C₂×C₄	1	2	yes	complemented
93	#103×C₈₉	C₂×C₄	1	4	yes	complemented
94	#102×C₈₉	C₂×C₄	1	4	yes	complemented
95	C₂²×Dic₈₉	—	2	4	no	—
96	C₂²×Dic₈₉	—	2	1	no	—
97	C₂²×Dic₈₉	—	2	1	no	—
98	C₂²×Dic₈₉	—	4	4	no	—
99	#13083558	—	2	2	no	—
100	#13083558	—	2	2	no	—
101	#13083558	—	2	2	no	—
102	#13083558	—	2	2	no	—
103	#13083558	—	4	4	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	1	no	—
106	C₂×#10623494	—	2	8	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	—	4	4	no	—
110	C₂×#10623494	C₂×D₄	1	2	yes	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₂×#10623494	#41	1	2	yes	—
114	C₄×Dic₈₉	—	2	4	no	—
115	C₄×Dic₈₉	—	2	1	no	—
116	C₄×Dic₈₉	—	2	1	no	—
117	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
118	C₄×Dic₈₉	#41	1	2	yes	—
119	C₂⁴×C₈₉	#41	1	1	yes	characteristic
120	#41×C₈₉	—	2	2	no	—
121	#41×C₈₉	—	2	2	no	—
122	#41×C₈₉	—	2	2	no	—
123	#41×C₈₉	—	2	2	no	—
124	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
125	C₂×D₄×C₈₉	—	2	4	no	—
126	C₂×D₄×C₈₉	—	2	2	no	—
127	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₈₉	—	2	2	no	—
138	SD₁₆×C₈₉	—	2	4	no	—
139	D₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	4	no	—
143	C₂×C₈×C₈₉	—	2	4	no	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₈₉	#41	1	2	yes	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
151	C₂²⋊C₄×C₈₉	—	2	4	no	—
152	C₂²⋊C₄×C₈₉	—	2	2	no	—
153	C₂²⋊C₄×C₈₉	—	2	4	no	—
154	C₄²×C₈₉	—	2	2	no	—
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	—	2	1	no	—
157	C₂³×C₈₉	—	2	4	no	—
158	C₂³×C₈₉	—	2	2	no	—
159	C₂³×C₈₉	C₄×D₄	1	2	yes	—
160	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
161	Q₈×C₈₉	—	2	2	no	—
162	Q₈×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	2	no	—
164	D₄×C₈₉	—	2	2	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	—	4	8	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	—	4	2	no	—
178	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₈₉	—	2	2	no	—
186	C₂×Dic₈₉	—	2	2	no	—
187	C₂×Dic₈₉	—	4	8	no	—
188	C₂×Dic₈₉	—	4	2	no	—
189	C₂×Dic₈₉	—	4	2	no	—
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	C₄×D₄	1	2	yes	—
192	C₈×C₈₉	C₄×D₄	1	2	yes	—
193	#10623494	—	2	2	no	—
194	#10623494	—	4	2	no	—
195	#10623494	—	4	2	no	—
196	#10623494	#121	1	4	yes	—
197	C₂²×C₈₉	—	2	4	no	—
198	C₂²×C₈₉	—	2	4	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	2	2	no	—
201	C₂²×C₈₉	—	2	2	no	—
202	C₂²×C₈₉	—	4	4	no	—
203	C₂²×C₈₉	—	4	2	no	—
204	C₂²×C₈₉	#444	1	4	yes	complemented
205	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₈₉	#525	1	1	yes	characteristic
207	C₂²×C₈₉	#529	1	1	yes	characteristic
208	C₄×C₈₉	—	2	2	no	—
209	C₄×C₈₉	—	4	4	no	—
210	C₄×C₈₉	—	4	2	no	—
211	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
213	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
214	C₄×C₈₉	#532	1	1	yes	characteristic
215	Dic₈₉	—	4	2	no	—
216	Dic₈₉	—	4	2	no	—
217	#21546	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	—	2	1	no	—
219	C₂×C₈₉	—	2	1	no	—
220	C₂×C₈₉	—	2	4	no	—
221	C₂×C₈₉	—	8	2	no	—
222	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
223	C₂×C₈₉	C₂×#444	1	2	yes	—
224	#3050	D₈₉	1	1	yes	characteristic
225	C₂×#444	—	89	1	no	—
226	#2929	—	89	2	no	—
227	C₂²×#97	—	89	1	no	—
228	#1975	—	89	1	no	—
229	#1946	—	89	1	no	—
230	#1938	—	89	2	no	—
231	#1896	—	89	2	no	—
232	#1810	—	89	1	no	—
233	#1773	—	89	1	no	—
234	#1765	—	89	2	no	—
235	C₈₉	#21546	1	1	yes	characteristic, complemented, Sylow
236	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
237	C₂×#131	—	89	2	no	—
238	C₂³×C₈	—	89	1	no	—
239	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
240	#525	C₂×D₈₉	1	2	yes	—
241	C₂²×C₄²	—	89	1	no	—
242	#467	Dic₈₉	1	2	yes	complemented
243	#466	Dic₈₉	1	2	yes	complemented
244	#465	Dic₈₉	1	4	yes	complemented
245	#444	—	178	4	no	—
246	#435	—	178	4	no	—
247	C₈×D₄	—	178	4	no	—
248	C₂×#108	—	89	1	no	—
249	C₂×#108	—	89	1	no	—
250	#427	C₂×D₈₉	1	1	yes	characteristic
251	#424	—	89	2	no	—
252	C₂×#104	—	89	2	no	—
253	C₂×#104	—	89	2	no	—
254	#416	C₂×D₈₉	1	2	yes	—
255	#408	—	89	2	no	—
256	#407	—	89	2	no	—
257	#405	—	89	2	no	—
258	C₂×#97	—	89	1	no	—
259	C₂×#97	—	89	1	no	—
260	C₂×#97	—	89	1	no	—
261	C₂×#97	—	89	1	no	—
262	C₂×#97	—	178	4	no	—
263	#341	—	89	2	no	—
264	#339	—	89	2	no	—
265	#339	—	89	2	no	—
266	C₂×#41	C₂²×D₈₉	1	2	yes	—
267	C₂³×C₄	—	178	1	no	—
268	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	complemented
273	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic, complemented
274	#131	—	178	4	no	—
275	#131	—	178	4	no	—
276	C₂×M₁₆	—	89	2	no	—
277	C₂×M₁₆	—	89	2	no	—
278	C₂×M₁₆	—	178	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	89	1	no	—
282	C₂²×C₈	—	89	4	no	—
283	C₂²×C₈	—	89	1	no	—
284	C₂²×C₈	—	178	2	no	—
285	C₂²×C₈	—	178	2	no	—
286	C₂²×C₈	—	178	2	no	—
287	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
288	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
289	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
291	#123	—	2	2	no	—
292	C₂²⋊Q₈	C₂×Dic₈₉	1	4	yes	—
293	#121	C₂×Dic₈₉	1	4	yes	—
294	#120	—	2	2	no	—
295	C₄×D₄	—	2	4	no	—
296	#117	C₂²×D₈₉	1	2	yes	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	89	1	no	—
299	C₂×C₄²	—	178	2	no	—
300	C₂×C₄²	—	178	2	no	—
301	C₂×C₄²	—	178	1	no	—
302	#108	—	178	2	no	—
303	#108	—	178	2	no	—
304	#107	C₂×Dic₈₉	1	2	yes	complemented
305	#106	C₂×Dic₈₉	1	2	yes	complemented
306	C₄⋊C₈	—	178	4	no	—
307	#104	—	178	4	no	—
308	#104	—	178	4	no	—
309	#103	C₂×Dic₈₉	1	4	yes	complemented
310	#102	C₂×Dic₈₉	1	4	yes	complemented
311	C₂²⋊C₈	—	178	4	no	—
312	C₂²⋊C₈	—	178	4	no	—
313	#97	—	89	4	no	—
314	#97	—	178	2	no	—
315	#97	—	178	2	no	—
316	#97	—	178	2	no	—
317	#97	—	178	2	no	—
318	C₄×C₈	—	178	2	no	—
319	C₂⁴	#13083573	1	1	yes	characteristic
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	356	4	no	—
334	C₂²×C₄	—	178	4	no	—
335	C₂²×C₄	—	178	1	no	—
336	C₂²×C₄	—	178	1	no	—
337	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
338	C₂²×C₄	D₄×D₈₉	1	2	yes	—
339	C₂²×C₄	#13083573	1	1	yes	characteristic
340	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	D₈	—	2	2	no	—
344	M₁₆	—	356	4	no	—
345	M₁₆	—	178	2	no	—
346	M₁₆	—	178	2	no	—
347	M₁₆	—	178	2	no	—
348	M₁₆	—	178	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	89	2	no	—
355	C₂×C₈	—	89	2	no	—
356	C₂×C₈	—	89	2	no	—
357	C₂×C₈	—	356	4	no	—
358	C₂×C₈	—	178	8	no	—
359	C₂×C₈	—	178	2	no	—
360	C₂×C₈	—	178	2	no	—
361	C₂×C₈	—	178	1	no	—
362	C₂×C₈	—	178	1	no	—
363	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
364	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
365	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
366	C₂×C₈	D₄×D₈₉	1	2	yes	—
367	C₂×C₈	#13083573	1	2	yes	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	89	2	no	—
375	C₄²	—	89	2	no	—
376	C₄²	—	178	4	no	—
377	C₄²	—	178	1	no	—
378	C₄²	—	178	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	D₄×Dic₈₉	1	2	yes	—
384	C₂³	C₂×#13083573	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	8	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	356	8	no	—
403	C₂×C₄	—	356	2	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	178	2	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
408	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
411	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
412	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	89	4	no	—
416	C₈	—	356	2	no	—
417	C₈	—	356	2	no	—
418	C₈	—	178	2	no	—
419	C₈	D₄×Dic₈₉	1	2	yes	—
420	C₈	D₄×Dic₈₉	1	2	yes	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	#19151720	1	4	yes	complemented
429	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
430	C₂²	#19152108	1	1	yes	characteristic
431	C₂²	#19152129	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	2	no	—
435	C₄	—	356	2	no	—
436	C₄	—	356	2	no	—
437	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
438	C₄	#41×Dic₈₉	1	1	yes	characteristic
439	C₄	#121×D₈₉	1	1	yes	characteristic
440	C₄	#19152143	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	4	no	—
444	C₂	—	8	2	no	—
445	C₂	#121×Dic₈₉	1	1	yes	characteristic
446	C₂	C₂×#19151720	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3050	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3050	D₈₉
hypocenter	C₈₉	#21546
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#19151720	C₂	semidirect
2. #26028947	C₂	semidirect
3. C₂²×#15667922	C₂	semidirect
4. #26021146	C₂	semidirect
5. #26021006	C₂	semidirect
6. #26020965	C₂	semidirect
7. #26020696	C₂	semidirect
8. #26020290	C₂	semidirect
9. #26020138	C₂	semidirect
10. #26020099	C₂	semidirect
37. #467×C₈₉	C₄	semidirect
38. #466×C₈₉	C₄	semidirect
39. #465×C₈₉	C₄	semidirect
70. #15667922	D₄	semidirect
76. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
77. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
78. C₂×D₈×C₈₉	C₂×C₄	semidirect
91. #107×C₈₉	C₂×C₄	semidirect
92. #106×C₈₉	C₂×C₄	semidirect
93. #103×C₈₉	C₂×C₄	semidirect
94. #102×C₈₉	C₂×C₄	semidirect
204. C₂²×C₈₉	#444	semidirect
235. C₈₉	#21546	semidirect
242. #467	Dic₈₉	semidirect
243. #466	Dic₈₉	semidirect
244. #465	Dic₈₉	semidirect
271. C₂×Q₁₆	C₂×Dic₈₉	semidirect
272. C₂×SD₁₆	C₂×Dic₈₉	semidirect
273. C₂×D₈	C₂×Dic₈₉	semidirect
304. #107	C₂×Dic₈₉	semidirect
305. #106	C₂×Dic₈₉	semidirect
309. #103	C₂×Dic₈₉	semidirect
310. #102	C₂×Dic₈₉	semidirect
428. C₂²	#19151720	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151720	2
#26028947	2
C₂²×#15667922	2
#26021146	2
#26021006	2
#26020965	2
#26020696	2
#26020290	2
#26020138	2
#26020099	2
C₈₉×#3050	2
#21546	89