Subgroups — #36449016

Order 22784.

584 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13083563	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151677	C₂	1	1	yes	maximal, characteristic
3	#26021188	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151327	C₂	1	1	yes	maximal, characteristic
6	#26018087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083563	C₄	1	1	yes	characteristic
9	C₂²×#13083557	—	2	1	no	—
10	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
12	C₄×#13083563	—	2	2	no	—
13	C₄×#13083563	—	2	2	no	—
14	#19151677	—	2	2	no	—
15	#19151677	—	2	2	no	—
16	C₂×#15667944	C₄	1	1	yes	characteristic
17	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
19	C₂×#15667937	C₄	1	1	yes	characteristic
20	C₂×#15667934	C₄	1	1	yes	characteristic
21	C₂×#15667924	—	2	1	no	—
22	#19151352	—	2	1	no	—
23	#19151352	—	2	1	no	—
24	#19151330	—	2	2	no	—
25	#19151327	—	2	2	no	—
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₈₉	—	2	1	no	—
32	C₂×#13083563	—	2	2	no	—
33	C₂×#13083563	—	2	2	no	—
34	C₂×#13083563	—	2	2	no	—
35	C₂×#13083557	—	2	4	no	—
36	C₂×#13083557	—	4	2	no	—
37	C₂×#13083557	—	4	2	no	—
38	C₂²×#10623494	—	2	1	no	—
39	C₂²×#10623494	—	2	1	no	—
40	C₄×Dic₁₇₈	—	2	1	no	—
41	C₄×Dic₁₇₈	—	2	1	no	—
42	C₄×Dic₁₇₈	—	2	1	no	—
43	C₄×Dic₁₇₈	—	2	1	no	—
44	C₄×D₃₅₆	—	2	1	no	—
45	C₄×D₃₅₆	—	2	1	no	—
46	C₄×D₃₅₆	D₄	1	2	yes	—
47	C₄×D₃₅₆	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083553	—	2	1	no	—
51	C₂×#13083551	—	2	1	no	—
52	C₂×C₄×Dic₈₉	—	2	1	no	—
53	#15667944	—	2	2	no	—
54	C₄⋊#10623494	—	2	1	no	—
55	C₄⋊#10623494	—	2	1	no	—
56	C₄⋊#10623494	—	2	1	no	—
57	C₄⋊#10623494	D₄	1	2	yes	—
58	#15667937	—	2	2	no	—
59	#15667934	—	2	2	no	—
60	#15667924	—	2	4	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₈₉	—	2	1	no	—
68	C₄×C₈×C₈₉	—	2	1	no	—
69	C₄×C₈×C₈₉	—	2	1	no	—
70	C₄×C₈×C₈₉	—	2	1	no	—
71	C₄×C₈×C₈₉	—	2	1	no	—
72	C₄×C₈×C₈₉	—	2	1	no	—
73	C₂³×D₈₉	—	2	1	no	—
74	C₂×Dic₁₇₈	—	2	1	no	—
75	C₂×Dic₁₇₈	—	2	1	no	—
76	C₂×Dic₁₇₈	—	2	1	no	—
77	C₂×Dic₁₇₈	—	2	1	no	—
78	C₂×Dic₁₇₈	—	2	1	no	—
79	C₂×Dic₁₇₈	M₁₆	1	2	yes	complemented
80	C₂×D₃₅₆	—	2	1	no	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	—	2	1	no	—
83	C₂×D₃₅₆	—	2	1	no	—
84	C₂×D₃₅₆	—	2	1	no	—
85	C₂×D₃₅₆	C₂²⋊C₄	1	2	yes	—
86	C₂²×Dic₈₉	—	2	1	no	—
87	C₂²×Dic₈₉	—	2	1	no	—
88	C₂²×Dic₈₉	—	2	1	no	—
89	C₂×C₄×D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	2	2	no	—
91	C₂×C₄×D₈₉	—	4	1	no	—
92	C₂×C₄×D₈₉	—	4	1	no	—
93	C₂×C₄×D₈₉	—	4	1	no	—
94	C₂×C₄×D₈₉	—	4	1	no	—
95	#13083563	—	2	8	no	—
96	#13083557	—	4	8	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	4	1	no	—
99	C₂×#10623494	—	4	1	no	—
100	C₂×#10623494	—	4	1	no	—
101	C₂×#10623494	—	4	1	no	—
102	C₂×#10623494	—	4	1	no	—
103	C₄⋊Dic₈₉	—	2	1	no	—
104	C₄⋊Dic₈₉	—	2	1	no	—
105	C₄⋊Dic₈₉	—	2	1	no	—
106	C₄⋊Dic₈₉	C₂²⋊C₄	1	2	yes	—
107	#13083553	—	4	1	no	—
108	#13083553	—	4	1	no	—
109	#13083551	—	2	2	no	—
110	#13083551	—	2	2	no	—
111	C₄×Dic₈₉	—	4	1	no	—
112	C₄×Dic₈₉	—	4	1	no	—
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	4	1	no	—
128	C₂×C₈×C₈₉	—	4	1	no	—
129	C₂×C₈×C₈₉	M₁₆	1	2	yes	complemented
130	C₂×C₈×C₈₉	SD₁₆	1	2	yes	complemented
131	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₈₉	#41	1	1	yes	characteristic
135	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₈₉	—	2	2	no	—
137	C₂²×D₈₉	—	4	1	no	—
138	C₂²×D₈₉	—	4	1	no	—
139	C₂²×D₈₉	—	4	1	no	—
140	C₂²×D₈₉	—	4	1	no	—
141	C₂²×D₈₉	—	4	1	no	—
142	C₂²×D₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
148	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
159	C₂×Dic₈₉	—	2	2	no	—
160	C₂×Dic₈₉	—	2	2	no	—
161	C₂×Dic₈₉	—	4	1	no	—
162	C₂×Dic₈₉	—	4	1	no	—
163	C₂×Dic₈₉	—	4	1	no	—
164	C₂×Dic₈₉	—	4	1	no	—
165	C₂×Dic₈₉	—	4	1	no	—
166	C₂×Dic₈₉	—	4	1	no	—
167	C₂×Dic₈₉	—	4	1	no	—
168	D₃₅₆	—	2	2	no	—
169	D₃₅₆	—	2	2	no	—
170	D₃₅₆	—	4	1	no	—
171	D₃₅₆	—	4	1	no	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	2	no	—
176	Dic₁₇₈	—	2	2	no	—
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	—	4	1	no	—
179	Dic₁₇₈	—	4	1	no	—
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	2	2	no	—
182	C₈×C₈₉	—	4	2	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	—	4	1	no	—
185	#10623494	—	4	2	no	—
186	#10623494	—	8	1	no	—
187	C₂²×C₈₉	#386	1	1	yes	characteristic
188	C₂²×C₈₉	#435	1	1	yes	characteristic
189	C₂²×C₈₉	#436	1	1	yes	characteristic
190	C₂²×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
191	C₂²×C₈₉	#440	1	1	yes	characteristic
192	C₂²×C₈₉	#443	1	1	yes	characteristic
193	C₂²×C₈₉	#444	1	1	yes	characteristic
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	8	1	no	—
198	C₂×D₈₉	—	8	1	no	—
199	C₂×D₈₉	—	8	1	no	—
200	C₂×D₈₉	—	8	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	#407	1	1	yes	characteristic
204	C₄×C₈₉	#408	1	1	yes	characteristic
205	C₄×C₈₉	#435	1	1	yes	characteristic
206	C₄×C₈₉	#436	1	1	yes	characteristic
207	C₄×C₈₉	#450	1	1	yes	characteristic
208	C₄×C₈₉	#452	1	1	yes	characteristic
209	C₄×C₈₉	#461	1	1	yes	characteristic
210	C₄×C₈₉	#463	1	1	yes	characteristic
211	Dic₈₉	—	4	2	no	—
212	Dic₈₉	—	4	2	no	—
213	Dic₈₉	—	8	1	no	—
214	#8949	—	89	1	no	maximal, Sylow
215	C₂×C₈₉	#1583	1	1	yes	characteristic
216	C₂×C₈₉	#1588	1	1	yes	characteristic
217	C₂×C₈₉	#1590	1	1	yes	characteristic
218	C₂×C₈₉	#1592	1	1	yes	characteristic
219	C₂×C₈₉	#1870	1	1	yes	characteristic
220	C₂×C₈₉	#1876	1	1	yes	characteristic
221	C₂×C₈₉	#1877	1	1	yes	characteristic
222	D₈₉	—	8	2	no	—
223	C₂×C₄×SD₁₆	—	89	1	no	—
224	C₂×#436	—	89	1	no	—
225	#1984	—	89	1	no	—
226	C₂×Q₈⋊C₈	—	89	1	no	—
227	C₂×D₄⋊C₈	—	89	1	no	—
228	#1277	—	89	1	no	—
229	#1273	D₈₉	1	1	yes	characteristic, complemented
230	C₈₉	#8949	1	1	yes	characteristic, complemented, Sylow
231	C₂²×SD₁₆	—	89	1	no	—
232	C₂²×M₁₆	—	178	1	no	—
233	C₂×C₄×Q₈	—	89	1	no	—
234	C₂×C₄×D₄	—	89	1	no	—
235	C₄×SD₁₆	—	178	2	no	—
236	C₄×SD₁₆	—	178	2	no	—
237	#436	—	178	2	no	—
238	#436	—	178	2	no	—
239	C₂×#106	—	89	1	no	—
240	C₂×C₄⋊C₈	—	89	1	no	—
241	C₂×C₄⋊C₈	—	89	1	no	—
242	C₂×#103	—	89	1	no	—
243	C₂×#102	—	89	1	no	—
244	C₂×C₂²⋊C₈	—	178	1	no	—
245	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
248	#336	—	178	1	no	—
249	#336	—	178	1	no	—
250	Q₈⋊C₈	—	178	2	no	—
251	D₄⋊C₈	—	178	2	no	—
252	C₂²×Q₈	—	89	1	no	—
253	C₂²×D₄	—	89	1	no	—
254	C₂³×C₄	—	178	1	no	—
255	C₂×SD₁₆	—	178	2	no	—
256	C₂×SD₁₆	—	178	2	no	—
257	C₂×SD₁₆	—	178	2	no	—
258	C₂×M₁₆	—	356	2	no	—
259	C₂×M₁₆	—	356	2	no	—
260	C₂×M₁₆	—	178	4	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	178	1	no	—
263	C₂²×C₈	—	178	1	no	—
264	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
266	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
267	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
268	C₄×Q₈	—	178	1	no	—
269	C₄×Q₈	—	178	1	no	—
270	C₄×Q₈	—	178	1	no	—
271	C₄×Q₈	—	178	1	no	—
272	C₄×D₄	—	89	2	no	—
273	C₄×D₄	—	89	2	no	—
274	C₄×D₄	—	178	1	no	—
275	C₄×D₄	—	178	1	no	—
276	C₂×C₄⋊C₄	—	89	1	no	—
277	C₂×C₄⋊C₄	—	89	1	no	—
278	C₂×C₄⋊C₄	—	178	1	no	—
279	C₂×C₂²⋊C₄	—	178	1	no	—
280	C₂×C₄²	—	178	1	no	—
281	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
282	#106	—	178	2	no	—
283	C₄⋊C₈	—	89	2	no	—
284	C₄⋊C₈	—	178	1	no	—
285	C₄⋊C₈	—	178	1	no	—
286	C₄⋊C₈	—	178	1	no	—
287	#103	—	178	2	no	—
288	#102	—	178	2	no	—
289	C₂²⋊C₈	—	178	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₂⁴	—	178	1	no	—
297	C₂×Q₈	—	89	2	no	—
298	C₂×Q₈	—	178	1	no	—
299	C₂×Q₈	—	178	1	no	—
300	C₂×Q₈	—	178	1	no	—
301	C₂×Q₈	—	178	1	no	—
302	C₂×Q₈	—	178	1	no	—
303	C₂×D₄	—	89	2	no	—
304	C₂×D₄	—	178	1	no	—
305	C₂×D₄	—	178	1	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	—	178	1	no	—
309	C₂²×C₄	—	356	1	no	—
310	C₂²×C₄	—	356	1	no	—
311	C₂²×C₄	—	356	1	no	—
312	C₂²×C₄	—	356	1	no	—
313	C₂²×C₄	—	178	1	no	—
314	C₂²×C₄	—	178	1	no	—
315	C₂²×C₄	—	178	1	no	—
316	C₂²×C₄	—	178	2	no	—
317	C₂²×C₄	—	178	2	no	—
318	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
320	C₂²×C₄	#13083574	1	1	yes	characteristic
321	SD₁₆	—	178	8	no	—
322	M₁₆	—	356	8	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	356	1	no	—
337	C₂×C₈	—	356	1	no	—
338	C₂×C₈	—	356	1	no	—
339	C₂×C₈	—	356	1	no	—
340	C₂×C₈	—	356	1	no	—
341	C₂×C₈	—	178	2	no	—
342	C₂×C₈	#13083557	1	2	yes	complemented
343	C₂×C₈	#13083563	1	2	yes	complemented
344	C₄⋊C₄	—	89	2	no	—
345	C₄⋊C₄	—	356	1	no	—
346	C₄⋊C₄	—	356	1	no	—
347	C₄⋊C₄	—	178	1	no	—
348	C₄⋊C₄	—	178	1	no	—
349	C₄⋊C₄	—	178	1	no	—
350	C₂²⋊C₄	—	178	2	no	—
351	C₂²⋊C₄	—	178	2	no	—
352	C₄²	—	356	1	no	—
353	C₄²	—	356	1	no	—
354	C₄²	D₄×D₈₉	1	1	yes	characteristic
355	C₄²	D₄×D₈₉	1	1	yes	characteristic
356	C₄²	D₄×D₈₉	1	1	yes	characteristic
357	C₄²	#13083575	1	1	yes	characteristic
358	C₂³	—	356	1	no	—
359	C₂³	—	356	1	no	—
360	C₂³	—	356	1	no	—
361	C₂³	—	356	1	no	—
362	C₂³	—	356	1	no	—
363	C₂³	—	356	1	no	—
364	C₂³	—	178	2	no	—
365	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
366	Q₈	—	356	1	no	—
367	Q₈	—	356	1	no	—
368	Q₈	—	178	2	no	—
369	Q₈	—	178	2	no	—
370	D₄	—	356	1	no	—
371	D₄	—	356	1	no	—
372	D₄	—	178	2	no	—
373	D₄	—	178	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	356	1	no	—
377	C₂×C₄	—	356	1	no	—
378	C₂×C₄	—	356	1	no	—
379	C₂×C₄	—	356	1	no	—
380	C₂×C₄	—	356	2	no	—
381	C₂×C₄	—	356	2	no	—
382	C₂×C₄	—	356	2	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	1	no	—
386	C₂×C₄	—	356	1	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	#15667974	1	1	yes	characteristic
391	C₂×C₄	#15667982	1	1	yes	characteristic
392	C₂×C₄	#15667985	1	1	yes	characteristic
393	C₂×C₄	#15667987	1	1	yes	characteristic
394	C₂×C₄	#15667997	1	1	yes	characteristic
395	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
397	C₂×C₄	#15668018	1	1	yes	characteristic
398	C₂×C₄	#15668020	1	1	yes	characteristic
399	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
400	C₂×C₄	#15668034	1	1	yes	characteristic
401	C₂×C₄	#15668040	1	1	yes	characteristic
402	C₂×C₄	#15668045	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	356	2	no	—
409	C₈	—	712	1	no	—
410	C₂²	—	356	2	no	—
411	C₂²	—	356	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	712	1	no	—
414	C₂²	—	712	1	no	—
415	C₂²	—	712	1	no	—
416	C₂²	—	712	1	no	—
417	C₂²	#19151476	1	1	yes	characteristic
418	C₂²	#19151671	1	1	yes	characteristic
419	C₂²	#19151677	1	1	yes	characteristic
420	C₂²	C₄×#13083563	1	1	yes	characteristic
421	C₂²	#19151700	1	1	yes	characteristic
422	C₂²	#19151716	1	1	yes	characteristic
423	C₂²	#19151721	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	356	2	no	—
427	C₄	—	356	2	no	—
428	C₄	—	712	1	no	—
429	C₄	#19151560	1	1	yes	characteristic
430	C₄	#19151563	1	1	yes	characteristic
431	C₄	#19151668	1	1	yes	characteristic
432	C₄	#19151675	1	1	yes	characteristic
433	C₄	#19151751	1	1	yes	characteristic
434	C₄	#19151762	1	1	yes	characteristic
435	C₄	#19151804	1	1	yes	characteristic
436	C₄	#19151814	1	1	yes	characteristic
437	C₂	—	712	2	no	—
438	C₂	#26019097	1	1	yes	characteristic
439	C₂	#26019132	1	1	yes	characteristic
440	C₂	#26019144	1	1	yes	characteristic
441	C₂	#26019156	1	1	yes	characteristic
442	C₂	#26020548	1	1	yes	characteristic
443	C₂	#26020578	1	1	yes	characteristic
444	C₂	#26020585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₅₆
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1273	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂²×D₃₅₆	C₂×C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#8949
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1273

Complements

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

N	H ≅ G/N	type
3. #26021188	C₂	semidirect
4. C₂×#19151330	C₂	semidirect
6. #26018087	C₂	semidirect
7. C₈₉×#1273	C₂	semidirect
79. C₂×Dic₁₇₈	M₁₆	semidirect
129. C₂×C₈×C₈₉	M₁₆	semidirect
130. C₂×C₈×C₈₉	SD₁₆	semidirect
229. #1273	D₈₉	semidirect
230. C₈₉	#8949	semidirect
342. C₂×C₈	#13083557	semidirect
343. C₂×C₈	#13083563	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#13083563	2
C₂×#19151677	2
#26021188	2
C₂×#19151330	2
C₂×#19151327	2
#26018087	2
C₈₉×#1273	2
#8949	89