Subgroups — #36449719

Order 22784.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151972	C₂	1	1	yes	maximal, characteristic
2	#26023316	C₂	1	1	yes	maximal, characteristic
3	#26021201	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
5	#26018093	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018091	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083561	—	2	2	no	—
9	C₂×#15668009	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₅₆	—	2	1	no	—
11	C₂×#15667974	—	2	1	no	—
12	#19151972	—	2	2	no	—
13	#19151972	C₄	1	4	yes	complemented
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
16	#19151500	—	2	1	no	—
17	#19151499	—	2	1	no	—
18	#19151476	—	2	2	no	—
19	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
20	#19151360	—	2	1	no	—
21	#19151360	—	2	1	no	—
22	#19151341	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	#340×C₈₉	—	2	1	no	—
27	#340×C₈₉	—	2	1	no	—
28	C₂²×D₃₅₆	—	2	1	no	—
29	C₂²×D₃₅₆	—	2	1	no	—
30	C₂²×D₃₅₆	D₄	1	2	yes	—
31	C₂²×C₄×D₈₉	—	2	2	no	—
32	C₂×#13083561	—	2	8	no	—
33	C₂×#13083561	—	4	4	no	—
34	C₂×#13083561	—	4	4	no	—
35	C₂²×#10623494	—	2	1	no	—
36	C₂²×#10623494	—	2	1	no	—
37	#15668009	—	2	1	no	—
38	#15668009	—	2	1	no	—
39	#15668009	C₂×C₄	1	2	yes	—
40	#15668009	D₄	1	2	yes	—
41	C₄×D₃₅₆	—	4	2	no	—
42	C₄×D₃₅₆	—	4	2	no	—
43	#15667974	—	4	2	no	—
44	#15667974	—	4	2	no	—
45	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
47	C₂×#13083551	—	2	2	no	—
48	C₂×#13083551	—	2	2	no	—
49	C₂×#13083551	—	2	2	no	—
50	C₂×C₄×Dic₈₉	—	2	1	no	—
51	C₄⋊#10623494	—	2	1	no	—
52	C₄⋊#10623494	—	2	1	no	—
53	C₄×#10623494	—	2	1	no	—
54	C₄×#10623494	C₂×C₄	1	2	yes	complemented
55	#15667919	—	2	1	no	—
56	C₂²×Q₈×C₈₉	—	2	1	no	—
57	C₂²×C₈×C₈₉	—	2	1	no	—
58	C₄⋊Q₈×C₈₉	—	2	1	no	—
59	C₄⋊Q₈×C₈₉	—	2	1	no	—
60	C₄⋊Q₈×C₈₉	—	2	1	no	—
61	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	complemented
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	—	2	1	no	—
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₈₉	—	2	1	no	—
69	C₄⋊C₈×C₈₉	—	2	1	no	—
70	#95×C₈₉	—	2	1	no	—
71	C₂³×D₈₉	—	2	2	no	—
72	C₂×D₃₅₆	—	2	2	no	—
73	C₂×D₃₅₆	—	2	2	no	—
74	C₂×D₃₅₆	—	2	2	no	—
75	C₂×D₃₅₆	—	2	2	no	—
76	C₂×D₃₅₆	—	2	2	no	—
77	C₂×D₃₅₆	—	4	1	no	—
78	C₂×D₃₅₆	—	4	1	no	—
79	C₂×D₃₅₆	—	4	1	no	—
80	C₂×D₃₅₆	—	4	1	no	—
81	C₂×D₃₅₆	—	4	1	no	—
82	C₂×D₃₅₆	—	4	1	no	—
83	C₂×D₃₅₆	—	4	1	no	—
84	C₂×D₃₅₆	—	4	1	no	—
85	C₂×D₃₅₆	—	4	2	no	—
86	C₂×D₃₅₆	—	4	2	no	—
87	C₂×D₃₅₆	C₂²⋊C₄	1	4	yes	—
88	C₂²×Dic₈₉	—	2	1	no	—
89	C₂²×Dic₈₉	—	2	1	no	—
90	C₂×C₄×D₈₉	—	4	4	no	—
91	C₂×C₄×D₈₉	—	4	4	no	—
92	C₂×C₄×D₈₉	—	8	2	no	—
93	#13083561	—	4	16	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	4	1	no	—
98	C₂×#10623494	—	4	1	no	—
99	C₂×#10623494	—	4	1	no	—
100	C₄⋊Dic₈₉	—	2	1	no	—
101	C₄⋊Dic₈₉	—	2	1	no	—
102	C₄⋊Dic₈₉	—	2	1	no	—
103	C₄⋊Dic₈₉	SD₁₆	1	2	yes	complemented
104	#13083551	—	4	4	no	—
105	#13083551	—	4	4	no	—
106	#13083551	—	8	2	no	—
107	C₄×Dic₈₉	—	4	1	no	—
108	C₄×Dic₈₉	—	4	1	no	—
109	C₂×Q₈×C₈₉	—	2	2	no	—
110	C₂×Q₈×C₈₉	—	4	2	no	—
111	C₂×Q₈×C₈₉	—	4	2	no	—
112	C₂×Q₈×C₈₉	—	4	1	no	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	4	1	no	—
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₈₉	—	4	1	no	—
120	C₂×C₈×C₈₉	—	4	1	no	—
121	C₂×C₈×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	1	no	—
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	4	1	no	—
128	C₄⋊C₄×C₈₉	—	4	1	no	—
129	C₄⋊C₄×C₈₉	SD₁₆	1	2	yes	complemented
130	C₄²×C₈₉	—	4	1	no	—
131	C₄²×C₈₉	—	4	1	no	—
132	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₈₉	#41	1	1	yes	characteristic
135	C₄²×C₈₉	#41	1	1	yes	characteristic
136	C₂³×C₈₉	#120	1	1	yes	characteristic
137	C₂²×D₈₉	—	2	4	no	—
138	C₂²×D₈₉	—	4	2	no	—
139	C₂²×D₈₉	—	4	2	no	—
140	C₂²×D₈₉	—	4	2	no	—
141	C₂²×D₈₉	—	4	2	no	—
142	C₂²×D₈₉	—	4	2	no	—
143	C₂²×D₈₉	—	4	2	no	—
144	Q₈×C₈₉	—	4	4	no	—
145	Q₈×C₈₉	—	8	2	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	—	4	1	no	—
155	C₂×C₄×C₈₉	—	8	1	no	—
156	C₂×C₄×C₈₉	—	8	1	no	—
157	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	—	4	1	no	—
173	C₂×Dic₈₉	—	4	1	no	—
174	C₂×Dic₈₉	—	4	1	no	—
175	C₂×Dic₈₉	—	4	1	no	—
176	C₂×Dic₈₉	—	4	1	no	—
177	D₃₅₆	—	4	4	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	4	2	no	—
186	D₃₅₆	—	8	2	no	—
187	C₄×D₈₉	—	8	8	no	—
188	C₈×C₈₉	—	8	1	no	—
189	#10623494	—	2	4	no	—
190	#10623494	—	8	1	no	—
191	C₂²×C₈₉	#386	1	1	yes	characteristic
192	C₂²×C₈₉	#450	1	1	yes	characteristic
193	C₂²×C₈₉	#450	1	1	yes	characteristic
194	C₂²×C₈₉	#452	1	1	yes	characteristic
195	C₂²×C₈₉	#452	1	1	yes	characteristic
196	C₂²×C₈₉	#453	1	1	yes	characteristic
197	C₂²×C₈₉	#453	1	1	yes	characteristic
198	C₂×D₈₉	—	4	4	no	—
199	C₂×D₈₉	—	4	4	no	—
200	C₂×D₈₉	—	4	4	no	—
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	—	8	2	no	—
204	C₂×D₈₉	—	8	2	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	—	8	1	no	—
209	C₄×C₈₉	—	8	2	no	—
210	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
211	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
212	C₄×C₈₉	#440	1	1	yes	characteristic
213	C₄×C₈₉	#440	1	1	yes	characteristic
214	C₄×C₈₉	#461	1	1	yes	characteristic
215	C₄×C₈₉	#461	1	1	yes	characteristic
216	C₄×C₈₉	#463	1	1	yes	characteristic
217	C₄×C₈₉	#463	1	1	yes	characteristic
218	Dic₈₉	—	4	2	no	—
219	Dic₈₉	—	8	1	no	—
220	#9064	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	#1629	1	1	yes	characteristic
222	C₂×C₈₉	#1630	1	1	yes	characteristic
223	C₂×C₈₉	#1631	1	1	yes	characteristic
224	C₂×C₈₉	#1631	1	1	yes	characteristic
225	C₂×C₈₉	#1877	1	1	yes	characteristic
226	C₂×C₈₉	#1877	1	1	yes	characteristic
227	C₂×C₈₉	#1887	1	1	yes	characteristic
228	D₈₉	—	8	4	no	—
229	C₂×#492	—	89	1	no	—
230	#2366	—	89	1	no	—
231	#1987	—	89	1	no	—
232	#1987	D₈₉	1	1	yes	characteristic, complemented
233	C₂×#331	—	89	1	no	—
234	#1279	—	89	1	no	—
235	#1279	—	89	1	no	—
236	C₈₉	#9064	1	1	yes	characteristic, complemented, Sylow
237	C₂²×SD₁₆	—	178	2	no	—
238	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
239	C₂×#127	—	89	1	no	—
240	C₂×C₄×D₄	—	178	1	no	—
241	C₂×C₄×D₄	—	178	1	no	—
242	#492	—	89	4	no	—
243	#492	—	178	2	no	—
244	C₂×C₄⋊C₈	—	89	1	no	—
245	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
246	C₂×C₄×C₈	—	89	1	no	—
247	#390	—	178	1	no	—
248	#390	—	178	1	no	—
249	#386	—	178	2	no	—
250	C₄×C₄⋊C₄	—	89	1	no	—
251	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
252	#340	—	2	1	no	—
253	#340	—	2	1	no	—
254	#340	—	178	1	no	—
255	#340	—	178	1	no	—
256	#331	—	178	2	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	89	2	no	—
259	C₂²×D₄	—	178	1	no	—
260	C₂²×D₄	—	178	1	no	—
261	C₂³×C₄	—	178	2	no	—
262	C₂×SD₁₆	—	356	4	no	—
263	C₂×SD₁₆	—	356	4	no	—
264	C₂×SD₁₆	—	178	8	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	178	1	no	—
267	C₂²×C₈	—	178	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₄×D₈₉	1	2	yes	complemented
272	#127	—	89	2	no	—
273	#127	—	89	2	no	—
274	#127	—	178	1	no	—
275	#127	—	178	1	no	—
276	C₄×D₄	—	356	2	no	—
277	C₄×D₄	—	356	2	no	—
278	C₄×D₄	—	356	2	no	—
279	C₄×D₄	—	356	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	89	1	no	—
283	C₂×C₄⋊C₄	—	89	1	no	—
284	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	178	2	no	—
287	C₂×C₂²⋊C₄	—	178	2	no	—
288	C₂×C₂²⋊C₄	—	178	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	178	1	no	—
291	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	178	1	no	—
295	C₄⋊C₈	—	178	1	no	—
296	C₄×C₈	—	89	2	no	—
297	C₄×C₈	—	178	1	no	—
298	#95	—	2	1	no	—
299	#95	—	178	1	no	—
300	C₂⁴	—	178	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×D₄	—	89	4	no	—
306	C₂×D₄	—	356	2	no	—
307	C₂×D₄	—	356	2	no	—
308	C₂×D₄	—	356	1	no	—
309	C₂×D₄	—	356	1	no	—
310	C₂×D₄	—	356	1	no	—
311	C₂×D₄	—	356	1	no	—
312	C₂×D₄	—	356	1	no	—
313	C₂×D₄	—	356	1	no	—
314	C₂×D₄	—	356	1	no	—
315	C₂×D₄	—	356	1	no	—
316	C₂×D₄	—	178	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂×D₄	—	178	2	no	—
319	C₂×D₄	—	178	2	no	—
320	C₂×D₄	—	178	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	356	4	no	—
325	C₂²×C₄	—	356	4	no	—
326	C₂²×C₄	—	178	1	no	—
327	C₂²×C₄	—	178	1	no	—
328	C₂²×C₄	—	712	2	no	—
329	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
332	SD₁₆	—	356	16	no	—
333	C₂×C₈	—	4	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	—	178	2	no	—
340	C₂×C₈	—	178	2	no	—
341	C₂×C₈	—	178	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	89	2	no	—
350	C₄⋊C₄	—	178	1	no	—
351	C₄⋊C₄	—	178	1	no	—
352	C₄⋊C₄	—	178	1	no	—
353	C₄⋊C₄	#13083561	1	2	yes	complemented
354	C₂²⋊C₄	—	356	4	no	—
355	C₂²⋊C₄	—	356	4	no	—
356	C₂²⋊C₄	—	712	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	356	1	no	—
360	C₄²	—	356	1	no	—
361	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
362	C₄²	D₄×D₈₉	1	1	yes	characteristic
363	C₄²	#13083573	1	1	yes	characteristic
364	C₄²	#13083574	1	1	yes	characteristic
365	C₂³	—	356	2	no	—
366	C₂³	—	356	2	no	—
367	C₂³	—	356	2	no	—
368	C₂³	—	356	2	no	—
369	C₂³	—	356	2	no	—
370	C₂³	—	356	2	no	—
371	C₂³	—	178	4	no	—
372	C₂³	#15667980	1	1	yes	characteristic
373	Q₈	—	4	4	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	356	4	no	—
376	D₄	—	356	2	no	—
377	D₄	—	356	2	no	—
378	D₄	—	356	2	no	—
379	D₄	—	356	2	no	—
380	D₄	—	356	2	no	—
381	D₄	—	356	2	no	—
382	D₄	—	356	2	no	—
383	D₄	—	356	2	no	—
384	D₄	—	712	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	—	356	1	no	—
397	C₂×C₄	—	356	1	no	—
398	C₂×C₄	—	356	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	178	2	no	—
402	C₂×C₄	—	712	8	no	—
403	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄	#15667972	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
406	C₂×C₄	#15667983	1	1	yes	characteristic
407	C₂×C₄	#15667985	1	1	yes	characteristic
408	C₂×C₄	#15667994	1	1	yes	characteristic
409	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
411	C₂×C₄	#15668032	1	1	yes	characteristic
412	C₂×C₄	#15668035	1	1	yes	characteristic
413	C₂×C₄	#15668037	1	1	yes	characteristic
414	C₂×C₄	#15668039	1	1	yes	characteristic
415	C₂×C₄	#15668043	1	1	yes	characteristic
416	C₂×C₄	#15668044	1	1	yes	characteristic
417	C₈	—	8	1	no	—
418	C₈	—	178	4	no	—
419	C₈	—	712	1	no	—
420	C₂²	—	356	4	no	—
421	C₂²	—	356	4	no	—
422	C₂²	—	356	4	no	—
423	C₂²	—	712	2	no	—
424	C₂²	—	712	2	no	—
425	C₂²	—	712	2	no	—
426	C₂²	—	712	2	no	—
427	C₂²	#19151474	1	1	yes	characteristic
428	C₂²	#19151747	1	1	yes	characteristic
429	C₂²	#19151748	1	1	yes	characteristic
430	C₂²	#19151758	1	1	yes	characteristic
431	C₂²	#19151759	1	1	yes	characteristic
432	C₂²	#19151764	1	1	yes	characteristic
433	C₂²	#19151764	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	356	2	no	—
440	C₄	—	712	1	no	—
441	C₄	#19151683	1	1	yes	characteristic
442	C₄	C₄×#13083561	1	1	yes	characteristic
443	C₄	#19151696	1	1	yes	characteristic
444	C₄	#19151701	1	1	yes	characteristic
445	C₄	#19151800	1	1	yes	characteristic
446	C₄	#19151802	1	1	yes	characteristic
447	C₄	#19151810	1	1	yes	characteristic
448	C₄	#19151816	1	1	yes	characteristic
449	C₂	—	712	4	no	—
450	C₂	#26019367	1	1	yes	characteristic
451	C₂	#26019372	1	1	yes	characteristic
452	C₂	#26019377	1	1	yes	characteristic
453	C₂	#26019378	1	1	yes	characteristic
454	C₂	#26020583	1	1	yes	characteristic
455	C₂	#26020589	1	1	yes	characteristic
456	C₂	#26020647	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667980
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1987	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1987	D₈₉
hypocenter	C₈₉	#9064
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1987

Complements

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

N	H ≅ G/N	type
3. #26021201	C₂	semidirect
5. #26018093	C₂	semidirect
6. #26018091	C₂	semidirect
7. C₈₉×#1987	C₂	semidirect
13. #19151972	C₄	semidirect
54. C₄×#10623494	C₂×C₄	semidirect
61. C₄⋊Q₈×C₈₉	C₂×C₄	semidirect
103. C₄⋊Dic₈₉	SD₁₆	semidirect
129. C₄⋊C₄×C₈₉	SD₁₆	semidirect
232. #1987	D₈₉	semidirect
236. C₈₉	#9064	semidirect
271. C₄⋊Q₈	C₄×D₈₉	semidirect
353. C₄⋊C₄	#13083561	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151972	2
#26023316	2
#26021201	2
C₂×#19151341	2
#26018093	2
#26018091	2
C₈₉×#1987	2
#9064	89