Subgroups — #36545696

Order 22784.

798 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26032600	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#26031853	C₂	1	2	yes	maximal, complemented
4	#26019844	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019718	C₂	1	2	yes	maximal, complemented
6	#26019641	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019433	C₂	1	2	yes	maximal, complemented
9	#26019343	C₂	1	2	yes	maximal, complemented
10	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668036	—	2	2	no	—
13	C₂²×D₇₁₂	—	2	1	no	—
14	#19152252	C₂²	1	2	yes	complemented
15	D₄×D₃₅₆	C₂²	1	2	yes	—
16	#19152003	C₂²	1	1	yes	characteristic, complemented
17	#19151975	C₂²	1	1	yes	characteristic
18	#19151971	C₂²	1	2	yes	complemented
19	#19151945	C₂²	1	2	yes	complemented
20	#19151912	—	2	2	no	—
21	#19151879	C₂²	1	2	yes	complemented
22	#19151845	—	2	2	no	—
23	#19151834	—	2	1	no	—
24	#19151834	—	2	1	no	—
25	#19151803	C₂²	1	2	yes	—
26	#19151794	C₂²	1	2	yes	—
27	#19151793	C₂²	1	2	yes	complemented
28	#19151750	—	2	2	no	—
29	#19151744	—	2	2	no	—
30	#19151734	—	2	2	no	—
31	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
32	#19151677	C₂²	1	2	yes	complemented
33	C₂×#15667946	—	2	1	no	—
34	#19151351	C₂²	1	1	yes	characteristic, complemented
35	#19151343	C₂²	1	2	yes	complemented
36	#19151341	C₂²	1	2	yes	complemented
37	#19151327	C₂²	1	2	yes	complemented
38	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#335×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13083573	—	2	2	no	—
46	C₂²×D₃₅₆	—	2	2	no	—
47	C₂×D₄×D₈₉	—	2	2	no	—
48	#15668036	—	4	8	no	—
49	C₂×#13083563	—	2	2	no	—
50	C₂×#13083563	—	2	2	no	—
51	C₂×#13083562	—	2	2	no	—
52	C₂×D₇₁₂	—	2	2	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	—	4	4	no	—
56	C₂×D₇₁₂	D₄	1	1	yes	characteristic
57	C₂×#13083559	—	2	2	no	—
58	C₂×#13083557	—	2	2	no	—
59	#15668012	C₂³	1	2	yes	—
60	#15668009	C₂³	1	2	yes	—
61	#15667996	—	4	2	no	—
62	#15667992	—	2	2	no	—
63	#15667987	—	2	2	no	—
64	#15667986	—	2	2	no	—
65	#15667986	—	2	2	no	—
66	#15667982	—	4	2	no	—
67	C₄×D₃₅₆	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₈₉	—	2	2	no	—
69	#15667946	—	2	2	no	—
70	#15667946	—	2	1	no	—
71	#15667946	—	2	1	no	—
72	#15667946	D₄	1	1	yes	characteristic
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667935	—	2	2	no	—
75	#15667934	—	2	2	no	—
76	#15667934	—	2	2	no	—
77	#15667934	—	4	2	no	—
78	#15667934	D₄	1	2	yes	—
79	#15667932	—	2	2	no	—
80	#15667924	—	2	2	no	—
81	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	—	2	1	no	—
83	C₂²×C₈×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	#107×C₈₉	D₄	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
89	#102×C₈₉	D₄	1	1	yes	characteristic
90	#102×C₈₉	D₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₈₉	—	2	1	no	—
92	C₂²⋊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	#13083573	—	4	4	no	—
98	#13083573	—	8	2	no	—
99	C₂×Dic₁₇₈	—	2	2	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	2	2	no	—
102	C₂×D₃₅₆	—	2	2	no	—
103	C₂×D₃₅₆	—	4	4	no	—
104	C₂×D₃₅₆	—	4	2	no	—
105	C₂×D₃₅₆	—	8	2	no	—
106	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
107	C₂×C₂²⋊D₈₉	—	4	2	no	—
108	C₂×C₂²⋊D₈₉	—	4	2	no	—
109	D₄×D₈₉	—	4	4	no	—
110	D₄×D₈₉	—	8	2	no	—
111	C₂²×Dic₈₉	—	4	2	no	—
112	C₂×C₄×D₈₉	—	2	2	no	—
113	#13083563	—	4	4	no	—
114	#13083563	—	8	2	no	—
115	#13083562	—	4	4	no	—
116	D₇₁₂	—	2	2	no	—
117	D₇₁₂	—	4	4	no	—
118	D₇₁₂	—	4	2	no	—
119	D₇₁₂	—	8	1	no	—
120	#13083559	—	4	4	no	—
121	#13083557	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₄⋊Dic₈₉	—	2	2	no	—
124	C₄⋊Dic₈₉	—	2	2	no	—
125	C₄⋊Dic₈₉	—	4	2	no	—
126	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
127	#13083551	—	2	2	no	—
128	#13083551	—	4	2	no	—
129	#13083551	—	4	2	no	—
130	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	D₈×C₈₉	D₈	1	4	yes	complemented
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	4	2	no	—
139	C₂×C₈×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₂³×C₈₉	—	2	1	no	—
150	C₂³×C₈₉	—	2	1	no	—
151	C₂²×D₈₉	—	2	2	no	—
152	C₂²×D₈₉	—	4	2	no	—
153	C₂²×D₈₉	—	8	4	no	—
154	C₂²×D₈₉	—	8	4	no	—
155	C₂²×D₈₉	—	16	2	no	—
156	D₄×C₈₉	—	2	1	no	—
157	D₄×C₈₉	—	2	1	no	—
158	D₄×C₈₉	C₂×D₈	1	2	yes	—
159	D₄×C₈₉	C₂×D₈	1	2	yes	complemented
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²⋊D₈₉	—	8	4	no	—
170	C₂²⋊D₈₉	—	8	4	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	8	4	no	—
174	D₃₅₆	—	2	2	no	—
175	D₃₅₆	—	2	2	no	—
176	D₃₅₆	—	4	2	no	—
177	D₃₅₆	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	8	2	no	—
181	D₃₅₆	—	8	4	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	Dic₁₇₈	—	4	2	no	—
185	Dic₁₇₈	—	4	2	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	1	no	—
190	C₈×C₈₉	—	4	1	no	—
191	C₈×C₈₉	C₂×D₈	1	2	yes	complemented
192	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
193	#10623494	—	4	2	no	—
194	C₂²×C₈₉	—	2	2	no	—
195	C₂²×C₈₉	—	2	2	no	—
196	C₂²×C₈₉	—	4	1	no	—
197	C₂²×C₈₉	—	4	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	D₄²	1	1	yes	characteristic
201	C₂×D₈₉	—	4	2	no	—
202	C₂×D₈₉	—	4	2	no	—
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	8	2	no	—
205	C₂×D₈₉	—	8	2	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₂×D₈₉	—	16	8	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
212	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₄×C₈₉	#576	1	1	yes	characteristic
214	C₄×C₈₉	#577	1	1	yes	characteristic
215	Dic₈₉	—	4	2	no	—
216	Dic₈₉	—	8	2	no	—
217	#19883	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	—	4	2	no	—
219	C₂×C₈₉	—	4	2	no	—
220	C₂×C₈₉	#3272	1	1	yes	characteristic
221	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
222	C₂×C₈₉	#3290	1	1	yes	characteristic
223	D₈₉	—	8	2	no	—
224	D₈₉	—	16	2	no	—
225	#3334	—	89	1	no	—
226	D₄×D₈	—	89	1	no	—
227	#3272	—	89	2	no	—
228	#1706	—	89	1	no	—
229	#1685	—	89	2	no	—
230	#1673	—	89	1	no	—
231	#1667	—	89	1	no	—
232	#1639	—	89	2	no	—
233	#1625	—	89	2	no	—
234	#1589	—	89	1	no	—
235	C₈×D₈	D₈₉	1	1	yes	characteristic, complemented
236	C₈₉	#19883	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	178	2	no	—
238	C₂²×D₈	—	178	1	no	—
239	#547	—	89	2	no	—
240	D₄²	—	89	2	no	—
241	#500	—	89	1	no	—
242	#493	—	89	1	no	—
243	#492	—	89	2	no	—
244	#486	—	89	2	no	—
245	#480	—	178	2	no	—
246	#474	—	89	2	no	—
247	#468	—	178	2	no	—
248	#466	—	178	1	no	—
249	#466	—	178	1	no	—
250	#461	—	89	2	no	—
251	#459	—	89	2	no	—
252	#459	—	89	2	no	—
253	#450	—	178	2	no	—
254	#449	—	178	2	no	—
255	#447	—	178	2	no	—
256	C₄×D₈	—	89	1	no	—
257	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
258	#436	—	89	2	no	—
259	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
260	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
261	C₂×#107	—	178	1	no	—
262	#335	—	89	1	no	—
263	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
264	#332	—	89	2	no	—
265	#331	—	89	2	no	—
266	D₄⋊C₈	—	89	2	no	—
267	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
268	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
269	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
270	C₂×#41	—	178	2	no	—
271	C₂²×D₄	—	178	2	no	—
272	C₂²×D₄	—	178	2	no	—
273	AGL(1,ℤ/8)	—	356	8	no	—
274	C₂×SD₁₆	—	178	2	no	—
275	C₂×SD₁₆	—	178	2	no	—
276	C₂×SD₁₆	—	178	2	no	—
277	C₂×D₈	—	89	1	no	—
278	C₂×D₈	—	356	4	no	—
279	C₂×D₈	—	178	2	no	—
280	C₂×D₈	—	178	2	no	—
281	C₂×D₈	—	178	1	no	—
282	C₂×D₈	—	178	1	no	—
283	C₂×D₈	D₃₅₆	1	1	yes	characteristic
284	C₂×M₁₆	—	178	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₄⋊Q₈	—	89	2	no	—
288	#127	—	89	2	no	—
289	#123	—	356	2	no	—
290	C₂²⋊Q₈	—	178	2	no	—
291	#121	—	178	2	no	—
292	#121	—	178	2	no	—
293	#121	—	178	2	no	—
294	#120	—	356	2	no	—
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	178	2	no	—
299	#107	—	89	1	no	—
300	#107	—	178	2	no	—
301	#107	—	178	1	no	—
302	#107	—	178	1	no	—
303	#107	D₃₅₆	1	1	yes	characteristic
304	C₄⋊C₈	—	89	2	no	—
305	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
307	#103	—	178	2	no	—
308	#102	—	89	2	no	—
309	#102	—	356	2	no	—
310	#102	—	178	2	no	—
311	#102	—	178	2	no	—
312	#102	—	178	2	no	—
313	#102	D₃₅₆	1	1	yes	characteristic
314	#102	D₃₅₆	1	1	yes	characteristic
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	178	2	no	—
318	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₂⁴	—	356	2	no	—
322	#41	—	356	4	no	—
323	#41	—	712	2	no	—
324	C₂×Q₈	—	178	2	no	—
325	C₂×D₄	—	89	2	no	—
326	C₂×D₄	—	356	2	no	—
327	C₂×D₄	—	356	4	no	—
328	C₂×D₄	—	356	4	no	—
329	C₂×D₄	—	356	2	no	—
330	C₂×D₄	—	356	2	no	—
331	C₂×D₄	—	178	2	no	—
332	C₂×D₄	—	178	2	no	—
333	C₂×D₄	—	178	2	no	—
334	C₂×D₄	—	712	2	no	—
335	C₂×D₄	—	712	2	no	—
336	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
337	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	356	2	no	—
341	C₂²×C₄	—	178	2	no	—
342	SD₁₆	—	356	4	no	—
343	SD₁₆	—	356	4	no	—
344	SD₁₆	—	712	2	no	—
345	D₈	—	356	4	no	—
346	D₈	—	356	4	no	—
347	D₈	—	356	2	no	—
348	D₈	—	178	2	no	—
349	D₈	—	712	1	no	—
350	D₈	D₇₁₂	1	4	yes	complemented
351	M₁₆	—	356	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	178	2	no	—
358	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
359	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
360	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
361	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
362	C₄⋊C₄	—	89	2	no	—
363	C₄⋊C₄	—	356	2	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	2	no	—
366	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	356	2	no	—
371	C₂²⋊C₄	—	356	2	no	—
372	C₂²⋊C₄	—	178	2	no	—
373	C₄²	C₂³×D₈₉	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	356	2	no	—
377	C₂³	—	1424	2	no	—
378	C₂³	—	178	2	no	—
379	C₂³	—	712	4	no	—
380	C₂³	—	712	4	no	—
381	Q₈	—	356	2	no	—
382	Q₈	—	356	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	356	2	no	—
386	D₄	—	356	2	no	—
387	D₄	—	356	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	178	2	no	—
390	D₄	—	178	2	no	—
391	D₄	—	712	2	no	—
392	D₄	—	712	4	no	—
393	D₄	—	712	4	no	—
394	D₄	—	712	4	no	—
395	D₄	C₂×D₇₁₂	1	2	yes	—
396	D₄	C₂×D₇₁₂	1	2	yes	complemented
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	356	2	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	—	712	4	no	—
408	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
410	C₂×C₄	#15668058	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	356	2	no	—
417	C₈	C₂×D₇₁₂	1	2	yes	complemented
418	C₈	#15668036	1	2	yes	complemented
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	356	2	no	—
426	C₂²	—	356	2	no	—
427	C₂²	—	356	2	no	—
428	C₂²	—	1424	8	no	—
429	C₂²	—	712	2	no	—
430	C₂²	—	712	2	no	—
431	C₂²	—	712	2	no	—
432	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	356	2	no	—
437	C₄	—	712	2	no	—
438	C₄	C₂²×D₇₁₂	1	1	yes	characteristic
439	C₄	C₂×#15668036	1	1	yes	characteristic
440	C₄	#19152403	1	1	yes	characteristic
441	C₄	#19152405	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	1424	2	no	—
445	C₂	—	712	2	no	—
446	C₂	#26031853	1	1	yes	characteristic
447	C₂	D₄×D₇₁₂	1	1	yes	characteristic
448	C₂	#26032039	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₆
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×D₈×C₈₉	C₂
socle	C₂²×C₈₉	D₄²
hypercenter	C₈×D₈	D₈₉
hypocenter	C₈₉	#19883
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #26032600	C₂	semidirect
2. D₄×D₇₁₂	C₂	semidirect
3. #26031853	C₂	semidirect
4. #26019844	C₂	semidirect
5. #26019718	C₂	semidirect
6. #26019641	C₂	semidirect
7. #26019607	C₂	semidirect
8. #26019433	C₂	semidirect
9. #26019343	C₂	semidirect
10. #26019138	C₂	semidirect
11. C₈×D₈×C₈₉	C₂	semidirect
14. #19152252	C₂²	semidirect
16. #19152003	C₂²	semidirect
18. #19151971	C₂²	semidirect
19. #19151945	C₂²	semidirect
21. #19151879	C₂²	semidirect
27. #19151793	C₂²	semidirect
32. #19151677	C₂²	semidirect
34. #19151351	C₂²	semidirect
35. #19151343	C₂²	semidirect
36. #19151341	C₂²	semidirect
37. #19151327	C₂²	semidirect
40. C₈×D₄×C₈₉	C₂²	semidirect
41. #335×C₈₉	C₂²	semidirect
43. D₄⋊C₈×C₈₉	C₂²	semidirect
44. C₈²×C₈₉	C₂²	semidirect
134. D₈×C₈₉	D₈	semidirect
159. D₄×C₈₉	C₂×D₈	semidirect
191. C₈×C₈₉	C₂×D₈	semidirect
192. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
235. C₈×D₈	D₈₉	semidirect
236. C₈₉	#19883	semidirect
260. C₈×D₄	C₂×D₈₉	semidirect
263. #335	C₂×D₈₉	semidirect
268. D₄⋊C₈	C₂×D₈₉	semidirect
269. C₈²	C₂×D₈₉	semidirect
350. D₈	D₇₁₂	semidirect
396. D₄	C₂×D₇₁₂	semidirect
417. C₈	C₂×D₇₁₂	semidirect
418. C₈	#15668036	semidirect

Maximal subgroups

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

subgroup	index
#26032600	2
D₄×D₇₁₂	2
#26031853	2
#26019844	2
#26019718	2
#26019641	2
#26019607	2
#26019433	2
#26019343	2
#26019138	2
C₈×D₈×C₈₉	2
#19883	89