Subgroups — #36545716

Order 22784.

830 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033227	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#26031873	C₂	1	2	yes	maximal, complemented
4	#26019867	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019732	C₂	1	2	yes	maximal, complemented
6	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019319	C₂	1	2	yes	maximal, complemented
9	#26019308	C₂	1	2	yes	maximal, complemented
10	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668039	—	2	2	no	—
13	C₂²×D₇₁₂	—	2	1	no	—
14	#19152270	C₂²	1	2	yes	complemented
15	D₄×D₃₅₆	C₂²	1	2	yes	—
16	#19151975	—	2	1	no	—
17	#19151975	C₂²	1	1	yes	characteristic
18	#19151975	C₂²	1	2	yes	complemented
19	#19151975	C₂²	1	1	yes	characteristic, complemented
20	#19151975	C₂²	1	2	yes	complemented
21	#19151852	—	2	2	no	—
22	#19151834	—	2	1	no	—
23	#19151798	C₂²	1	2	yes	complemented
24	#19151794	—	2	2	no	—
25	#19151794	C₂²	1	2	yes	—
26	#19151794	C₂²	1	2	yes	complemented
27	#19151793	C₂²	1	2	yes	—
28	#19151746	—	2	2	no	—
29	#19151734	—	2	2	no	—
30	#19151733	—	2	2	no	—
31	C₄×D₇₁₂	—	2	1	no	—
32	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
33	#19151677	C₂²	1	2	yes	complemented
34	#19151351	C₂²	1	1	yes	characteristic, complemented
35	#19151341	C₂²	1	2	yes	complemented
36	#19151341	C₂²	1	2	yes	complemented
37	#19151327	C₂²	1	2	yes	complemented
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13083575	—	2	2	no	—
46	C₂²×D₃₅₆	—	2	2	no	—
47	C₂×D₄×D₈₉	—	2	2	no	—
48	#15668039	—	4	8	no	—
49	C₂×#13083561	—	2	2	no	—
50	C₂×D₇₁₂	—	2	2	no	—
51	C₂×D₇₁₂	—	2	2	no	—
52	C₂×D₇₁₂	—	2	2	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	—	2	1	no	—
56	C₂×D₇₁₂	—	2	2	no	—
57	C₂×D₇₁₂	—	2	1	no	—
58	C₂×D₇₁₂	—	4	2	no	—
59	C₂×D₇₁₂	—	4	4	no	—
60	C₂×D₇₁₂	D₄	1	1	yes	characteristic
61	C₂×#13083559	—	2	2	no	—
62	C₂×#13083557	—	2	2	no	—
63	#15668009	—	2	2	no	—
64	#15668009	C₂³	1	2	yes	—
65	#15668009	C₂³	1	2	yes	—
66	#15667987	—	2	2	no	—
67	#15667987	—	2	2	no	—
68	#15667987	—	4	2	no	—
69	#15667986	—	2	2	no	—
70	#15667982	—	4	2	no	—
71	C₄×D₃₅₆	—	2	2	no	—
72	C₄×D₃₅₆	C₂³	1	2	yes	—
73	#15667946	D₄	1	1	yes	characteristic
74	C₄⋊#10623494	C₂³	1	2	yes	—
75	#15667934	—	2	2	no	—
76	#15667934	—	2	2	no	—
77	#15667934	D₄	1	2	yes	—
78	#15667932	—	2	2	no	—
79	#15667932	—	2	2	no	—
80	#15667924	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	—	2	1	no	—
83	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	#106×C₈₉	D₄	1	1	yes	characteristic
86	C₄⋊C₈×C₈₉	—	2	1	no	—
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
89	#103×C₈₉	D₄	1	1	yes	characteristic
90	#102×C₈₉	D₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₈₉	—	2	1	no	—
92	C₄×C₈×C₈₉	—	2	1	no	—
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×D₈₉	—	4	2	no	—
97	#13083575	—	4	4	no	—
98	#13083575	—	8	2	no	—
99	C₂×D₃₅₆	—	2	2	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	2	2	no	—
102	C₂×D₃₅₆	—	2	2	no	—
103	C₂×D₃₅₆	—	2	2	no	—
104	C₂×D₃₅₆	—	2	2	no	—
105	C₂×D₃₅₆	—	4	4	no	—
106	C₂×D₃₅₆	—	4	2	no	—
107	C₂×D₃₅₆	—	4	2	no	—
108	C₂×D₃₅₆	—	4	2	no	—
109	C₂×D₃₅₆	—	8	2	no	—
110	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
111	C₂×C₂²⋊D₈₉	—	4	2	no	—
112	D₄×D₈₉	—	4	4	no	—
113	D₄×D₈₉	—	8	2	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	C₂×C₄×D₈₉	—	4	2	no	—
116	#13083561	—	4	4	no	—
117	D₇₁₂	—	2	2	no	—
118	D₇₁₂	—	4	4	no	—
119	D₇₁₂	—	4	4	no	—
120	D₇₁₂	—	4	2	no	—
121	D₇₁₂	—	4	2	no	—
122	D₇₁₂	—	8	1	no	—
123	D₇₁₂	—	8	2	no	—
124	D₇₁₂	—	8	1	no	—
125	D₇₁₂	—	8	4	no	—
126	D₇₁₂	—	8	2	no	—
127	#13083559	—	4	4	no	—
128	#13083557	—	4	4	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
131	#13083551	—	2	2	no	—
132	#13083551	—	4	2	no	—
133	#13083551	—	4	2	no	—
134	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	SD₁₆×C₈₉	D₈	1	4	yes	complemented
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	4	2	no	—
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	—	2	1	no	—
153	C₂²×D₈₉	—	2	2	no	—
154	C₂²×D₈₉	—	4	2	no	—
155	C₂²×D₈₉	—	4	2	no	—
156	C₂²×D₈₉	—	8	4	no	—
157	C₂²×D₈₉	—	8	4	no	—
158	C₂²×D₈₉	—	16	2	no	—
159	Q₈×C₈₉	—	2	1	no	—
160	Q₈×C₈₉	C₂×D₈	1	2	yes	complemented
161	D₄×C₈₉	—	2	1	no	—
162	D₄×C₈₉	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₈₉	—	8	4	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	D₃₅₆	—	2	2	no	—
174	D₃₅₆	—	2	2	no	—
175	D₃₅₆	—	4	2	no	—
176	D₃₅₆	—	4	2	no	—
177	D₃₅₆	—	4	2	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	—	8	4	no	—
184	D₃₅₆	—	8	2	no	—
185	D₃₅₆	—	8	2	no	—
186	D₃₅₆	—	8	4	no	—
187	D₃₅₆	—	16	2	no	—
188	C₄×D₈₉	—	4	2	no	—
189	C₄×D₈₉	—	4	2	no	—
190	C₄×D₈₉	—	8	4	no	—
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	2	1	no	—
193	C₈×C₈₉	—	2	1	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	C₂×D₈	1	2	yes	complemented
197	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
198	#10623494	—	4	2	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	D₄²	1	1	yes	characteristic
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	2	no	—
205	C₂×D₈₉	—	4	2	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₂×D₈₉	—	8	2	no	—
208	C₂×D₈₉	—	8	2	no	—
209	C₂×D₈₉	—	8	2	no	—
210	C₂×D₈₉	—	8	2	no	—
211	C₂×D₈₉	—	8	2	no	—
212	C₂×D₈₉	—	16	8	no	—
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	4	1	no	—
216	C₄×C₈₉	—	4	1	no	—
217	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₄×C₈₉	#576	1	1	yes	characteristic
220	C₄×C₈₉	#576	1	1	yes	characteristic
221	Dic₈₉	—	4	2	no	—
222	#19885	—	89	1	no	maximal, Sylow
223	C₂×C₈₉	—	4	2	no	—
224	C₂×C₈₉	#3274	1	1	yes	characteristic
225	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
226	C₂×C₈₉	#3292	1	1	yes	characteristic
227	D₈₉	—	8	2	no	—
228	D₈₉	—	16	2	no	—
229	D₈₉	—	16	2	no	—
230	#3391	—	89	1	no	—
231	D₄×D₈	—	89	1	no	—
232	#3274	—	89	2	no	—
233	#1712	—	89	1	no	—
234	#1687	—	89	2	no	—
235	#1668	—	89	1	no	—
236	#1667	—	89	1	no	—
237	#1621	—	89	2	no	—
238	#1619	—	89	2	no	—
239	#1589	—	89	1	no	—
240	C₈×SD₁₆	D₈₉	1	1	yes	characteristic, complemented
241	C₈₉	#19885	1	1	yes	characteristic, complemented, Sylow
242	C₂×AGL(1,ℤ/8)	—	178	2	no	—
243	C₂²×D₈	—	178	1	no	—
244	#550	—	89	2	no	—
245	D₄²	—	89	2	no	—
246	#493	—	89	2	no	—
247	#493	—	89	1	no	—
248	#493	—	89	1	no	—
249	#493	—	89	2	no	—
250	#493	—	178	1	no	—
251	#469	—	178	2	no	—
252	#466	—	178	1	no	—
253	#460	—	89	2	no	—
254	#459	—	89	2	no	—
255	#459	—	89	2	no	—
256	#459	—	89	2	no	—
257	#459	—	178	2	no	—
258	#449	—	178	2	no	—
259	#447	—	178	2	no	—
260	#447	—	178	2	no	—
261	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
262	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
263	C₄×D₈	—	89	1	no	—
264	C₄×D₈	—	178	1	no	—
265	#436	—	89	2	no	—
266	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
267	#335	—	89	1	no	—
268	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
269	#331	—	89	2	no	—
270	#331	—	89	2	no	—
271	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
272	D₄⋊C₈	—	89	2	no	—
273	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
274	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
275	C₂×#41	—	178	2	no	—
276	C₂²×D₄	—	178	2	no	—
277	C₂²×D₄	—	178	2	no	—
278	AGL(1,ℤ/8)	—	356	8	no	—
279	C₂×SD₁₆	—	178	2	no	—
280	C₂×SD₁₆	D₃₅₆	1	1	yes	characteristic
281	C₂×D₈	—	89	1	no	—
282	C₂×D₈	—	356	2	no	—
283	C₂×D₈	—	356	4	no	—
284	C₂×D₈	—	178	2	no	—
285	C₂×D₈	—	178	2	no	—
286	C₂×D₈	—	178	2	no	—
287	C₂×D₈	—	178	1	no	—
288	C₂×D₈	—	178	1	no	—
289	C₂×D₈	—	178	1	no	—
290	C₂×D₈	—	178	1	no	—
291	C₂×D₈	—	178	2	no	—
292	C₂×D₈	—	178	2	no	—
293	C₂×M₁₆	—	178	2	no	—
294	C₂²×C₈	—	2	1	no	—
295	#127	—	89	2	no	—
296	#127	—	89	2	no	—
297	#127	—	178	2	no	—
298	#121	—	356	2	no	—
299	#121	—	178	2	no	—
300	#121	—	178	2	no	—
301	#121	—	178	2	no	—
302	#120	—	356	2	no	—
303	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄×D₄	—	89	2	no	—
305	C₄×D₄	—	178	2	no	—
306	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
307	#107	—	89	1	no	—
308	#106	D₃₅₆	1	1	yes	characteristic
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	89	2	no	—
311	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
313	#103	D₃₅₆	1	1	yes	characteristic
314	#102	—	89	2	no	—
315	#102	—	178	2	no	—
316	#102	—	178	2	no	—
317	#102	—	178	2	no	—
318	#102	—	178	2	no	—
319	#102	D₃₅₆	1	1	yes	characteristic
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	178	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₂⁴	—	356	2	no	—
327	#41	—	356	4	no	—
328	#41	—	712	2	no	—
329	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
330	C₂×D₄	—	89	2	no	—
331	C₂×D₄	—	356	2	no	—
332	C₂×D₄	—	356	2	no	—
333	C₂×D₄	—	356	2	no	—
334	C₂×D₄	—	356	4	no	—
335	C₂×D₄	—	356	4	no	—
336	C₂×D₄	—	356	2	no	—
337	C₂×D₄	—	178	2	no	—
338	C₂×D₄	—	178	2	no	—
339	C₂×D₄	—	178	2	no	—
340	C₂×D₄	—	178	2	no	—
341	C₂×D₄	—	178	2	no	—
342	C₂×D₄	—	178	2	no	—
343	C₂×D₄	—	712	2	no	—
344	C₂×D₄	—	712	2	no	—
345	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	356	2	no	—
348	C₂²×C₄	—	178	2	no	—
349	SD₁₆	—	356	4	no	—
350	SD₁₆	D₇₁₂	1	4	yes	complemented
351	D₈	—	356	4	no	—
352	D₈	—	356	4	no	—
353	D₈	—	356	4	no	—
354	D₈	—	356	2	no	—
355	D₈	—	356	2	no	—
356	D₈	—	178	2	no	—
357	D₈	—	712	1	no	—
358	D₈	—	712	1	no	—
359	D₈	—	712	2	no	—
360	D₈	—	712	4	no	—
361	D₈	—	712	2	no	—
362	M₁₆	—	356	4	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
369	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
371	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	89	2	no	—
374	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
375	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	356	2	no	—
378	C₂²⋊C₄	—	356	2	no	—
379	C₂²⋊C₄	—	178	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	—	356	2	no	—
384	C₂³	—	356	2	no	—
385	C₂³	—	1424	2	no	—
386	C₂³	—	178	2	no	—
387	C₂³	—	712	4	no	—
388	C₂³	—	712	4	no	—
389	Q₈	—	2	1	no	—
390	Q₈	C₂×D₇₁₂	1	2	yes	complemented
391	D₄	—	2	1	no	—
392	D₄	—	356	2	no	—
393	D₄	—	356	2	no	—
394	D₄	—	356	2	no	—
395	D₄	—	356	2	no	—
396	D₄	—	356	2	no	—
397	D₄	—	356	2	no	—
398	D₄	—	356	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	1424	2	no	—
401	D₄	—	178	2	no	—
402	D₄	—	178	2	no	—
403	D₄	—	712	4	no	—
404	D₄	—	712	2	no	—
405	D₄	—	712	2	no	—
406	D₄	—	712	4	no	—
407	D₄	—	712	4	no	—
408	D₄	C₂×D₇₁₂	1	2	yes	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	356	2	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	178	2	no	—
417	C₂×C₄	—	712	4	no	—
418	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
420	C₂×C₄	#15668058	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	356	2	no	—
427	C₈	C₂×D₇₁₂	1	2	yes	complemented
428	C₈	#15668039	1	2	yes	complemented
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	356	2	no	—
433	C₂²	—	356	2	no	—
434	C₂²	—	356	2	no	—
435	C₂²	—	1424	8	no	—
436	C₂²	—	712	2	no	—
437	C₂²	—	712	2	no	—
438	C₂²	—	712	2	no	—
439	C₂²	—	712	2	no	—
440	C₂²	—	712	2	no	—
441	C₂²	—	712	2	no	—
442	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	356	2	no	—
448	C₄	C₂²×D₇₁₂	1	1	yes	characteristic
449	C₄	C₂×#15668039	1	1	yes	characteristic
450	C₄	#19152400	1	1	yes	characteristic
451	C₄	#19152403	1	1	yes	characteristic
452	C₂	—	4	2	no	—
453	C₂	—	1424	2	no	—
454	C₂	—	1424	2	no	—
455	C₂	—	712	2	no	—
456	C₂	#26031873	1	1	yes	characteristic
457	C₂	D₄×D₇₁₂	1	1	yes	characteristic
458	C₂	#26032052	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₆
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	D₄²
hypercenter	C₈×SD₁₆	D₈₉
hypocenter	C₈₉	#19885
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #26033227	C₂	semidirect
2. D₄×D₇₁₂	C₂	semidirect
3. #26031873	C₂	semidirect
4. #26019867	C₂	semidirect
5. #26019732	C₂	semidirect
6. #26019612	C₂	semidirect
7. #26019607	C₂	semidirect
8. #26019319	C₂	semidirect
9. #26019308	C₂	semidirect
10. #26019138	C₂	semidirect
11. C₈×SD₁₆×C₈₉	C₂	semidirect
14. #19152270	C₂²	semidirect
18. #19151975	C₂²	semidirect
19. #19151975	C₂²	semidirect
20. #19151975	C₂²	semidirect
23. #19151798	C₂²	semidirect
26. #19151794	C₂²	semidirect
33. #19151677	C₂²	semidirect
34. #19151351	C₂²	semidirect
35. #19151341	C₂²	semidirect
36. #19151341	C₂²	semidirect
37. #19151327	C₂²	semidirect
38. C₈×Q₈×C₈₉	C₂²	semidirect
41. #334×C₈₉	C₂²	semidirect
42. Q₈⋊C₈×C₈₉	C₂²	semidirect
44. C₈²×C₈₉	C₂²	semidirect
137. SD₁₆×C₈₉	D₈	semidirect
160. Q₈×C₈₉	C₂×D₈	semidirect
196. C₈×C₈₉	C₂×D₈	semidirect
197. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
240. C₈×SD₁₆	D₈₉	semidirect
241. C₈₉	#19885	semidirect
261. C₈×Q₈	C₂×D₈₉	semidirect
268. #334	C₂×D₈₉	semidirect
271. Q₈⋊C₈	C₂×D₈₉	semidirect
274. C₈²	C₂×D₈₉	semidirect
350. SD₁₆	D₇₁₂	semidirect
390. Q₈	C₂×D₇₁₂	semidirect
427. C₈	C₂×D₇₁₂	semidirect
428. C₈	#15668039	semidirect

Maximal subgroups

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

subgroup	index
#26033227	2
D₄×D₇₁₂	2
#26031873	2
#26019867	2
#26019732	2
#26019612	2
#26019607	2
#26019319	2
#26019308	2
#26019138	2
C₈×SD₁₆×C₈₉	2
#19885	89