Subgroups — #36449216

Order 22784.

664 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×#19151879	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic
3	#26021213	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021175	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151327	C₂	1	1	yes	maximal, characteristic
6	#26018136	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668012	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₅₆	—	2	1	no	—
10	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×D₈₉	—	2	1	no	—
12	#19151879	—	2	2	no	—
13	#19151879	C₄	1	4	yes	complemented
14	C₂×#15667946	—	2	1	no	—
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×#15667935	—	2	1	no	—
17	C₂×#15667935	—	2	1	no	—
18	C₂×#15667934	—	2	1	no	—
19	#19151496	—	2	1	no	—
20	#19151472	—	2	2	no	—
21	#19151468	C₂²	1	1	yes	characteristic
22	#19151455	—	2	1	no	—
23	#19151361	—	2	2	no	—
24	#19151327	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₇₈	—	2	1	no	—
29	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₈₉	—	2	2	no	—
31	C₂²×C₄×D₈₉	—	2	1	no	—
32	C₂²×#10623494	—	2	1	no	—
33	#15668012	—	2	1	no	—
34	#15668012	—	2	1	no	—
35	#15668012	—	2	1	no	—
36	#15668012	C₂×C₄	1	2	yes	complemented
37	C₄×D₃₅₆	—	2	1	no	—
38	C₄×D₃₅₆	—	2	1	no	—
39	C₄×D₃₅₆	—	4	2	no	—
40	C₄×D₃₅₆	—	4	2	no	—
41	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
42	C₄×D₃₅₆	D₄	1	2	yes	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	—	2	1	no	—
45	C₂×C₄⋊Dic₈₉	—	2	1	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
49	C₂×#13083553	—	2	2	no	—
50	C₄⋊C₄×D₈₉	—	4	2	no	—
51	C₄⋊C₄×D₈₉	—	4	2	no	—
52	C₂×#13083551	—	2	2	no	—
53	C₂×#13083551	—	2	1	no	—
54	#15667946	—	2	4	no	—
55	C₄⋊#10623494	—	2	1	no	—
56	C₄⋊#10623494	—	2	1	no	—
57	#15667935	—	4	2	no	—
58	#15667935	—	4	2	no	—
59	#15667934	—	2	4	no	—
60	#15667919	—	2	2	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂²×C₈×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	—	2	1	no	—
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₈₉	—	2	1	no	—
68	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
69	C₄×C₈×C₈₉	—	2	1	no	—
70	C₄×C₈×C₈₉	—	2	1	no	—
71	#95×C₈₉	—	2	1	no	—
72	C₂³×D₈₉	—	2	1	no	—
73	C₂×Dic₁₇₈	—	2	2	no	—
74	C₂×Dic₁₇₈	—	4	1	no	—
75	C₂×Dic₁₇₈	—	4	1	no	—
76	C₂×Dic₁₇₈	—	4	1	no	—
77	C₂×Dic₁₇₈	—	4	1	no	—
78	C₂×Dic₁₇₈	—	4	1	no	—
79	C₂×D₃₅₆	—	2	1	no	—
80	C₂×D₃₅₆	—	2	1	no	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	C₂²⋊C₄	1	2	yes	—
83	C₂×D₃₅₆	SD₁₆	1	2	yes	—
84	C₂×D₃₅₆	Q₁₆	1	2	yes	—
85	C₂²×Dic₈₉	—	2	1	no	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	—	4	1	no	—
88	C₂×C₄×D₈₉	—	2	2	no	—
89	C₂×C₄×D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	4	1	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	4	no	—
95	C₂×C₄×D₈₉	—	4	4	no	—
96	C₂×C₄×D₈₉	—	8	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	2	no	—
102	C₄⋊Dic₈₉	—	2	2	no	—
103	C₄⋊Dic₈₉	—	4	1	no	—
104	C₄⋊Dic₈₉	—	4	1	no	—
105	C₄⋊Dic₈₉	—	4	1	no	—
106	C₄⋊Dic₈₉	—	4	1	no	—
107	C₄⋊Dic₈₉	—	4	1	no	—
108	C₄⋊Dic₈₉	—	4	1	no	—
109	C₄⋊Dic₈₉	—	4	2	no	—
110	C₄⋊Dic₈₉	C₂²⋊C₄	1	2	yes	—
111	#13083553	—	4	4	no	—
112	#13083551	—	2	2	no	—
113	#13083551	—	2	2	no	—
114	#13083551	—	4	4	no	—
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	—	4	1	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₂×C₈×C₈₉	—	4	1	no	—
125	C₂×C₈×C₈₉	—	4	1	no	—
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₄⋊C₄×C₈₉	D₈	1	2	yes	—
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	2	no	—
138	C₂²×D₈₉	—	2	2	no	—
139	C₂²×D₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	4	1	no	—
141	C₂²×D₈₉	—	4	1	no	—
142	C₂²×D₈₉	—	4	1	no	—
143	C₂²×D₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	4	2	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	8	1	no	—
174	C₂×Dic₈₉	—	8	1	no	—
175	D₃₅₆	—	2	2	no	—
176	D₃₅₆	—	2	2	no	—
177	D₃₅₆	—	2	2	no	—
178	D₃₅₆	#103	1	4	yes	complemented
179	C₄×D₈₉	—	4	2	no	—
180	C₄×D₈₉	—	4	2	no	—
181	C₄×D₈₉	—	4	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	8	8	no	—
184	Dic₁₇₈	—	4	2	no	—
185	Dic₁₇₈	—	4	2	no	—
186	Dic₁₇₈	—	8	1	no	—
187	Dic₁₇₈	—	8	1	no	—
188	C₈×C₈₉	—	4	2	no	—
189	C₈×C₈₉	—	4	2	no	—
190	#10623494	—	8	1	no	—
191	C₂²×C₈₉	#386	1	1	yes	characteristic
192	C₂²×C₈₉	#447	1	1	yes	characteristic
193	C₂²×C₈₉	#449	1	1	yes	characteristic
194	C₂²×C₈₉	#450	1	1	yes	characteristic
195	C₂²×C₈₉	#451	1	1	yes	characteristic
196	C₂²×C₈₉	#455	1	1	yes	characteristic
197	C₂²×C₈₉	#456	1	1	yes	characteristic
198	C₂×D₈₉	—	2	4	no	—
199	C₂×D₈₉	—	4	2	no	—
200	C₂×D₈₉	—	4	2	no	—
201	C₂×D₈₉	—	4	2	no	—
202	C₂×D₈₉	—	4	2	no	—
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	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	C₂×#103	1	1	yes	characteristic
210	C₄×C₈₉	#417	1	1	yes	characteristic
211	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
212	C₄×C₈₉	#442	1	1	yes	characteristic
213	C₄×C₈₉	#459	1	1	yes	characteristic
214	C₄×C₈₉	#463	1	1	yes	characteristic
215	C₄×C₈₉	#483	1	1	yes	characteristic
216	C₄×C₈₉	#484	1	1	yes	characteristic
217	Dic₈₉	—	4	2	no	—
218	Dic₈₉	—	8	2	no	—
219	Dic₈₉	—	8	2	no	—
220	#8981	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	#1639	1	1	yes	characteristic
222	C₂×C₈₉	#1644	1	1	yes	characteristic
223	C₂×C₈₉	#1649	1	1	yes	characteristic
224	C₂×C₈₉	#1654	1	1	yes	characteristic
225	C₂×C₈₉	#1872	1	1	yes	characteristic
226	C₂×C₈₉	#1879	1	1	yes	characteristic
227	C₂×C₈₉	#1882	1	1	yes	characteristic
228	D₈₉	—	4	4	no	—
229	C₂×#474	—	89	1	no	—
230	D₄×C₄⋊C₄	—	89	1	no	—
231	#1990	—	89	1	no	—
232	#1981	—	89	1	no	—
233	C₂×D₄⋊C₈	—	89	1	no	—
234	#1296	—	89	1	no	—
235	#1279	D₈₉	1	1	yes	characteristic, complemented
236	C₈₉	#8981	1	1	yes	characteristic, complemented, Sylow
237	C₂×C₄⋊Q₈	—	89	1	no	—
238	C₂×C₄×D₄	—	89	1	no	—
239	C₂×C₄×D₄	—	178	1	no	—
240	C₂²×C₄⋊C₄	—	178	1	no	—
241	#474	—	89	4	no	—
242	#474	—	178	2	no	—
243	C₂×#107	—	178	1	no	—
244	C₂×C₄⋊C₈	—	89	1	no	—
245	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
246	C₂×#103	—	178	1	no	—
247	C₂×#103	—	178	1	no	—
248	C₂×#102	—	178	1	no	—
249	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
250	#389	—	178	1	no	—
251	#385	—	178	2	no	—
252	#384	—	89	1	no	—
253	#380	—	178	1	no	—
254	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
255	#340	—	178	2	no	—
256	D₄⋊C₈	—	178	2	no	—
257	C₂²×Q₈	—	178	1	no	—
258	C₂²×D₄	—	89	1	no	—
259	C₂³×C₄	—	178	2	no	—
260	C₂³×C₄	—	178	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	178	1	no	—
264	C₄⋊Q₈	—	89	2	no	—
265	C₄⋊Q₈	—	178	1	no	—
266	C₄⋊Q₈	—	178	1	no	—
267	C₄⋊Q₈	—	178	1	no	—
268	C₄×D₄	—	89	2	no	—
269	C₄×D₄	—	89	2	no	—
270	C₄×D₄	—	356	2	no	—
271	C₄×D₄	—	356	2	no	—
272	C₄×D₄	—	178	1	no	—
273	C₄×D₄	—	178	1	no	—
274	C₂×C₄⋊C₄	—	89	1	no	—
275	C₂×C₄⋊C₄	—	89	2	no	—
276	C₂×C₄⋊C₄	—	356	2	no	—
277	C₂×C₄⋊C₄	—	356	2	no	—
278	C₂×C₄⋊C₄	—	178	2	no	—
279	C₂×C₄⋊C₄	—	178	1	no	—
280	C₂×C₄⋊C₄	—	178	1	no	—
281	C₂×C₄⋊C₄	—	178	1	no	—
282	C₂×C₄⋊C₄	—	178	1	no	—
283	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	178	2	no	—
286	C₂×C₂²⋊C₄	—	178	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
289	#107	—	178	4	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	178	1	no	—
292	C₄⋊C₈	—	178	1	no	—
293	C₄⋊C₈	C₄×D₈₉	1	2	yes	complemented
294	#103	—	356	2	no	—
295	#103	—	356	2	no	—
296	#102	—	178	4	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	178	2	no	—
301	C₂⁴	—	178	1	no	—
302	C₂×Q₈	—	356	1	no	—
303	C₂×Q₈	—	356	1	no	—
304	C₂×Q₈	—	356	1	no	—
305	C₂×Q₈	—	356	1	no	—
306	C₂×Q₈	—	356	1	no	—
307	C₂×Q₈	—	178	2	no	—
308	C₂×D₄	—	89	2	no	—
309	C₂×D₄	—	89	2	no	—
310	C₂×D₄	—	89	2	no	—
311	C₂×D₄	—	178	1	no	—
312	C₂×D₄	—	178	1	no	—
313	C₂×D₄	—	178	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	356	4	no	—
317	C₂²×C₄	—	356	4	no	—
318	C₂²×C₄	—	356	1	no	—
319	C₂²×C₄	—	356	1	no	—
320	C₂²×C₄	—	356	1	no	—
321	C₂²×C₄	—	356	1	no	—
322	C₂²×C₄	—	356	1	no	—
323	C₂²×C₄	—	178	2	no	—
324	C₂²×C₄	—	178	1	no	—
325	C₂²×C₄	—	178	2	no	—
326	C₂²×C₄	—	178	2	no	—
327	C₂²×C₄	—	712	2	no	—
328	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	356	1	no	—
338	C₂×C₈	—	356	1	no	—
339	C₂×C₈	—	356	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	89	2	no	—
344	C₄⋊C₄	—	356	2	no	—
345	C₄⋊C₄	—	356	4	no	—
346	C₄⋊C₄	—	356	1	no	—
347	C₄⋊C₄	—	356	1	no	—
348	C₄⋊C₄	—	356	1	no	—
349	C₄⋊C₄	—	356	1	no	—
350	C₄⋊C₄	—	356	1	no	—
351	C₄⋊C₄	—	356	1	no	—
352	C₄⋊C₄	—	178	2	no	—
353	C₄⋊C₄	—	178	2	no	—
354	C₄⋊C₄	—	178	1	no	—
355	C₄⋊C₄	D₇₁₂	1	2	yes	—
356	C₂²⋊C₄	—	356	4	no	—
357	C₂²⋊C₄	—	178	2	no	—
358	C₂²⋊C₄	—	178	2	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
362	C₄²	D₄×D₈₉	1	1	yes	characteristic
363	C₄²	#13083574	1	1	yes	characteristic
364	C₄²	#13083575	1	1	yes	characteristic
365	C₂³	—	356	1	no	—
366	C₂³	—	356	1	no	—
367	C₂³	—	356	1	no	—
368	C₂³	—	356	1	no	—
369	C₂³	—	178	2	no	—
370	C₂³	—	178	2	no	—
371	C₂³	—	178	2	no	—
372	C₂³	#15667982	1	1	yes	characteristic
373	Q₈	—	356	2	no	—
374	Q₈	—	356	2	no	—
375	Q₈	—	712	1	no	—
376	Q₈	—	712	1	no	—
377	D₄	—	89	4	no	—
378	D₄	—	178	2	no	—
379	D₄	—	178	2	no	—
380	D₄	—	178	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	356	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	356	2	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	356	2	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	356	2	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	356	2	no	—
398	C₂×C₄	—	356	2	no	—
399	C₂×C₄	—	178	2	no	—
400	C₂×C₄	—	712	8	no	—
401	C₂×C₄	—	712	1	no	—
402	C₂×C₄	—	712	1	no	—
403	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄	#15667974	1	1	yes	characteristic
405	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
406	C₂×C₄	#15667985	1	1	yes	characteristic
407	C₂×C₄	#15667987	1	1	yes	characteristic
408	C₂×C₄	#15667997	1	1	yes	characteristic
409	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
411	C₂×C₄	Q₁₆×D₈₉	1	1	yes	characteristic
412	C₂×C₄	#15668034	1	1	yes	characteristic
413	C₂×C₄	#15668036	1	1	yes	characteristic
414	C₂×C₄	#15668040	1	1	yes	characteristic
415	C₂×C₄	#15668040	1	1	yes	characteristic
416	C₂×C₄	#15668041	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	712	1	no	—
420	C₂²	—	356	2	no	—
421	C₂²	—	356	2	no	—
422	C₂²	—	356	2	no	—
423	C₂²	—	356	2	no	—
424	C₂²	—	356	2	no	—
425	C₂²	—	356	2	no	—
426	C₂²	—	178	4	no	—
427	C₂²	#19151476	1	1	yes	characteristic
428	C₂²	#19151734	1	1	yes	characteristic
429	C₂²	#19151745	1	1	yes	characteristic
430	C₂²	#19151750	1	1	yes	characteristic
431	C₂²	#19151755	1	1	yes	characteristic
432	C₂²	#19151777	1	1	yes	characteristic
433	C₂²	#19151782	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	356	2	no	—
439	C₄	—	712	2	no	—
440	C₄	—	712	2	no	—
441	C₄	#103×D₈₉	1	1	yes	characteristic
442	C₄	#19151596	1	1	yes	characteristic
443	C₄	C₄×D₇₁₂	1	1	yes	characteristic
444	C₄	#19151711	1	1	yes	characteristic
445	C₄	#19151794	1	1	yes	characteristic
446	C₄	#19151814	1	1	yes	characteristic
447	C₄	#19151930	1	1	yes	characteristic
448	C₄	#19151935	1	1	yes	characteristic
449	C₂	—	356	4	no	—
450	C₂	#26019433	1	1	yes	characteristic
451	C₂	#26019468	1	1	yes	characteristic
452	C₂	#26019503	1	1	yes	characteristic
453	C₂	#26019538	1	1	yes	characteristic
454	C₂	#26020558	1	1	yes	characteristic
455	C₂	#26020599	1	1	yes	characteristic
456	C₂	#26020622	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1279	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1279	D₈₉
hypocenter	C₈₉	#8981
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
3. #26021213	C₂	semidirect
4. #26021175	C₂	semidirect
6. #26018136	C₂	semidirect
7. C₈₉×#1279	C₂	semidirect
13. #19151879	C₄	semidirect
36. #15668012	C₂×C₄	semidirect
68. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
178. D₃₅₆	#103	semidirect
235. #1279	D₈₉	semidirect
236. C₈₉	#8981	semidirect
293. C₄⋊C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151879	2
C₄⋊C₄×D₃₅₆	2
#26021213	2
#26021175	2
C₂×#19151327	2
#26018136	2
C₈₉×#1279	2
#8981	89