Subgroups — #26031734

Order 11392.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152243	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151987	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151852	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151828	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151813	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151793	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151750	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151744	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151733	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151733	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151671	C₂	1	1	yes	maximal, characteristic, complemented
15	#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₃₅₆	—	2	1	no	—
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
21	#15668036	—	2	4	no	—
22	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13083559	C₂²	1	1	yes	characteristic
28	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
30	D₈×D₈₉	—	2	4	no	—
31	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
33	#15668009	C₂²	1	1	yes	characteristic, complemented
34	#15668000	C₂²	1	1	yes	characteristic, complemented
35	#15667996	—	2	1	no	—
36	#15667992	C₂²	1	1	yes	characteristic, complemented
37	#15667987	C₂²	1	1	yes	characteristic
38	#15667987	C₂²	1	1	yes	characteristic, complemented
39	#15667987	C₂²	1	1	yes	characteristic, complemented
40	#15667986	—	2	1	no	—
41	#15667986	—	2	1	no	—
42	#15667982	—	2	1	no	—
43	#15667982	—	2	1	no	—
44	#15667982	—	2	1	no	—
45	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
46	C₂×#13083551	—	2	1	no	—
47	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
48	#15667935	C₂²	1	1	yes	characteristic, complemented
49	#15667932	C₂²	1	1	yes	characteristic, complemented
50	#15667932	C₂²	1	1	yes	characteristic, complemented
51	#15667932	C₂²	1	1	yes	characteristic, complemented
52	#15667924	C₂²	1	1	yes	characteristic, complemented
53	#15667924	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	C₂³×D₈₉	—	2	1	no	—
64	#13083573	—	2	2	no	—
65	#13083573	—	4	1	no	—
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	—	2	1	no	—
71	C₂×D₃₅₆	—	2	1	no	—
72	C₂×D₃₅₆	—	4	4	no	—
73	C₂×D₃₅₆	D₄	1	1	yes	characteristic
74	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
75	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
76	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊D₈₉	—	2	1	no	—
78	C₂×C₂²⋊D₈₉	—	2	1	no	—
79	C₂×C₂²⋊D₈₉	—	2	1	no	—
80	C₂×C₂²⋊D₈₉	—	2	1	no	—
81	D₄×D₈₉	—	2	2	no	—
82	D₄×D₈₉	—	2	2	no	—
83	D₄×D₈₉	—	2	2	no	—
84	D₄×D₈₉	—	4	1	no	—
85	D₄×D₈₉	—	4	1	no	—
86	D₄×D₈₉	—	4	1	no	—
87	C₂²×Dic₈₉	—	2	1	no	—
88	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
90	#13083563	—	2	2	no	—
91	#13083563	—	4	1	no	—
92	#13083562	—	2	2	no	—
93	D₇₁₂	—	2	2	no	—
94	D₇₁₂	—	4	1	no	—
95	#13083559	—	2	2	no	—
96	#13083559	—	2	2	no	—
97	#13083559	—	2	2	no	—
98	#13083557	—	2	2	no	—
99	C₂×#10623494	C₂³	1	1	yes	characteristic
100	C₂×#10623494	C₂³	1	1	yes	characteristic
101	C₈×D₈₉	—	2	2	no	—
102	C₄⋊Dic₈₉	—	2	1	no	—
103	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	#13083551	—	2	1	no	—
108	#13083551	—	2	1	no	—
109	#13083551	—	2	1	no	—
110	#13083551	D₄	1	1	yes	characteristic
111	#13083551	D₄	1	1	yes	characteristic
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	D₈×C₈₉	D₄	1	4	yes	complemented
117	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	—	2	1	no	—
128	C₂²×D₈₉	—	2	1	no	—
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	4	2	no	—
135	C₂²×D₈₉	—	8	1	no	—
136	C₂²×D₈₉	—	8	1	no	—
137	C₂²×D₈₉	—	8	1	no	—
138	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
140	D₄×C₈₉	—	2	1	no	—
141	D₄×C₈₉	—	2	1	no	—
142	D₄×C₈₉	C₂×D₄	1	2	yes	—
143	D₄×C₈₉	C₂×D₄	1	2	yes	complemented
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	4	2	no	—
147	C₂×C₄×C₈₉	—	8	1	no	—
148	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²⋊D₈₉	—	4	2	no	—
152	C₂²⋊D₈₉	—	4	2	no	—
153	C₂²⋊D₈₉	—	4	2	no	—
154	C₂²⋊D₈₉	—	4	2	no	—
155	C₂×Dic₈₉	—	2	1	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
159	D₃₅₆	—	2	2	no	—
160	D₃₅₆	—	2	1	no	—
161	D₃₅₆	—	2	1	no	—
162	D₃₅₆	—	2	1	no	—
163	D₃₅₆	—	2	1	no	—
164	D₃₅₆	—	2	1	no	—
165	D₃₅₆	—	2	1	no	—
166	D₃₅₆	—	4	2	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	4	2	no	—
169	D₃₅₆	—	8	1	no	—
170	D₃₅₆	—	8	1	no	—
171	C₄×D₈₉	—	2	1	no	—
172	C₄×D₈₉	—	2	1	no	—
173	C₄×D₈₉	—	2	1	no	—
174	C₄×D₈₉	—	2	1	no	—
175	Dic₁₇₈	—	2	1	no	—
176	Dic₁₇₈	—	2	1	no	—
177	C₈×C₈₉	—	2	1	no	—
178	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
179	#10623494	—	2	1	no	—
180	#10623494	—	2	1	no	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×D₈₉	—	2	1	no	—
189	C₂×D₈₉	—	2	1	no	—
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	2	1	no	—
193	C₂×D₈₉	—	4	1	no	—
194	C₂×D₈₉	—	4	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	4	1	no	—
199	C₂×D₈₉	—	4	1	no	—
200	C₂×D₈₉	—	4	1	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	8	4	no	—
203	C₂×D₈₉	—	8	4	no	—
204	C₂×D₈₉	—	8	4	no	—
205	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	4	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	—	2	1	no	—
214	Dic₈₉	—	4	1	no	—
215	C₂×C₈₉	—	4	2	no	—
216	C₂×C₈₉	—	4	2	no	—
217	C₂×C₈₉	D₄²	1	1	yes	characteristic
218	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×C₈₉	#576	1	1	yes	characteristic
220	D₈₉	—	2	2	no	—
221	D₈₉	—	4	1	no	—
222	D₈₉	—	8	1	no	—
223	D₈₉	—	8	1	no	—
224	D₈₉	—	8	1	no	—
225	#3264	—	89	1	no	maximal, Sylow
226	C₈₉	#3264	1	1	yes	characteristic, complemented, Sylow
227	C₂×AGL(1,ℤ/8)	—	89	1	no	—
228	C₂²×D₈	—	89	1	no	—
229	#546	—	89	1	no	—
230	D₄²	—	89	1	no	—
231	#496	—	89	1	no	—
232	#469	—	89	1	no	—
233	#465	—	89	1	no	—
234	#463	—	89	1	no	—
235	#459	—	89	1	no	—
236	#450	—	89	1	no	—
237	#449	—	89	1	no	—
238	#447	—	89	1	no	—
239	#447	—	89	1	no	—
240	#442	D₈₉	1	1	yes	characteristic, complemented
241	#435	—	89	1	no	—
242	C₂×#41	—	89	1	no	—
243	C₂²×D₄	—	89	1	no	—
244	C₂²×D₄	—	89	1	no	—
245	C₂²×D₄	—	89	1	no	—
246	C₂²×D₄	—	178	1	no	—
247	AGL(1,ℤ/8)	—	178	4	no	—
248	C₂×SD₁₆	—	89	1	no	—
249	C₂×SD₁₆	—	89	1	no	—
250	C₂×SD₁₆	—	89	1	no	—
251	C₂×D₈	—	89	1	no	—
252	C₂×D₈	—	89	1	no	—
253	C₂×D₈	—	89	1	no	—
254	C₂×D₈	—	89	1	no	—
255	C₂×D₈	—	89	1	no	—
256	C₂×D₈	—	178	4	no	—
257	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
258	C₂×M₁₆	—	89	1	no	—
259	C₂²×C₈	—	89	1	no	—
260	#127	—	89	1	no	—
261	#124	—	89	1	no	—
262	#123	—	178	1	no	—
263	C₂²⋊Q₈	—	89	1	no	—
264	#121	—	89	1	no	—
265	#121	—	89	1	no	—
266	#121	—	89	1	no	—
267	#121	—	178	1	no	—
268	#121	—	178	1	no	—
269	#120	—	178	1	no	—
270	#120	—	178	1	no	—
271	#120	—	178	1	no	—
272	C₄×D₄	—	89	1	no	—
273	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
274	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	178	1	no	—
276	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
277	C₄⋊C₈	—	89	1	no	—
278	#103	—	89	1	no	—
279	#102	—	89	1	no	—
280	#102	—	89	1	no	—
281	#102	—	89	1	no	—
282	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
283	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
284	C₂²⋊C₈	—	89	1	no	—
285	C₂²⋊C₈	—	89	1	no	—
286	#97	C₂×D₈₉	1	1	yes	characteristic, complemented
287	C₂⁴	—	178	1	no	—
288	C₂⁴	—	178	1	no	—
289	C₂⁴	—	178	1	no	—
290	#41	—	356	1	no	—
291	#41	—	178	2	no	—
292	C₂×Q₈	—	89	1	no	—
293	C₂×D₄	—	89	1	no	—
294	C₂×D₄	—	89	1	no	—
295	C₂×D₄	—	89	1	no	—
296	C₂×D₄	—	89	1	no	—
297	C₂×D₄	—	356	4	no	—
298	C₂×D₄	—	356	1	no	—
299	C₂×D₄	—	356	1	no	—
300	C₂×D₄	—	356	1	no	—
301	C₂×D₄	—	178	1	no	—
302	C₂×D₄	—	178	1	no	—
303	C₂×D₄	—	178	1	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	2	no	—
309	C₂×D₄	—	178	2	no	—
310	C₂×D₄	—	178	2	no	—
311	C₂×D₄	—	178	1	no	—
312	C₂×D₄	—	178	1	no	—
313	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	89	1	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	178	1	no	—
320	SD₁₆	—	356	1	no	—
321	SD₁₆	—	178	2	no	—
322	SD₁₆	—	178	2	no	—
323	D₈	—	356	1	no	—
324	D₈	—	178	2	no	—
325	D₈	—	178	2	no	—
326	D₈	—	178	2	no	—
327	D₈	—	178	2	no	—
328	D₈	D₃₅₆	1	4	yes	complemented
329	M₁₆	—	178	2	no	—
330	C₂×C₈	—	89	1	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	178	2	no	—
333	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
335	C₄⋊C₄	—	89	1	no	—
336	C₄⋊C₄	—	178	1	no	—
337	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	89	1	no	—
342	C₂²⋊C₄	—	89	1	no	—
343	C₂²⋊C₄	—	178	1	no	—
344	C₂²⋊C₄	—	178	1	no	—
345	C₂²⋊C₄	—	178	1	no	—
346	C₂²⋊C₄	—	178	1	no	—
347	C₂²⋊C₄	—	178	1	no	—
348	C₂²⋊C₄	—	178	1	no	—
349	C₄²	C₂²×D₈₉	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	89	1	no	—
353	C₂³	—	89	1	no	—
354	C₂³	—	356	2	no	—
355	C₂³	—	356	2	no	—
356	C₂³	—	356	2	no	—
357	C₂³	—	356	2	no	—
358	C₂³	—	356	2	no	—
359	C₂³	—	356	2	no	—
360	C₂³	—	178	1	no	—
361	C₂³	—	178	1	no	—
362	C₂³	—	178	1	no	—
363	C₂³	—	712	1	no	—
364	C₂³	—	712	1	no	—
365	C₂³	—	712	1	no	—
366	Q₈	—	178	1	no	—
367	Q₈	—	178	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	356	2	no	—
371	D₄	—	356	2	no	—
372	D₄	—	356	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	356	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	178	2	no	—
378	D₄	—	178	1	no	—
379	D₄	—	178	1	no	—
380	D₄	—	178	1	no	—
381	D₄	—	178	1	no	—
382	D₄	—	178	1	no	—
383	D₄	—	178	1	no	—
384	D₄	—	712	1	no	—
385	D₄	—	712	1	no	—
386	D₄	C₂×D₃₅₆	1	2	yes	—
387	D₄	C₂×D₃₅₆	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	89	1	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	178	1	no	—
396	C₂×C₄	—	178	1	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
401	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	178	1	no	—
405	C₈	—	178	1	no	—
406	C₈	C₂×D₃₅₆	1	2	yes	complemented
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	89	2	no	—
414	C₂²	—	356	1	no	—
415	C₂²	—	356	1	no	—
416	C₂²	—	356	1	no	—
417	C₂²	—	356	1	no	—
418	C₂²	—	356	1	no	—
419	C₂²	—	356	1	no	—
420	C₂²	—	356	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	178	1	no	—
424	C₂²	—	178	1	no	—
425	C₂²	—	178	1	no	—
426	C₂²	—	178	1	no	—
427	C₂²	—	178	1	no	—
428	C₂²	—	712	4	no	—
429	C₂²	—	712	4	no	—
430	C₂²	—	712	4	no	—
431	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	356	1	no	—
437	C₄	—	178	1	no	—
438	C₄	—	178	1	no	—
439	C₄	C₂²×D₃₅₆	1	1	yes	characteristic
440	C₄	#15668058	1	1	yes	characteristic
441	C₂	—	4	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	356	1	no	—
444	C₂	—	178	2	no	—
445	C₂	—	712	1	no	—
446	C₂	—	712	1	no	—
447	C₂	—	712	1	no	—
448	C₂	D₄×D₃₅₆	1	1	yes	characteristic
449	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
450	C₂	#19152402	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#442×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#442	D₈₉
hypocenter	C₈₉	#3264
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
1. C₂×#15668036	C₂	semidirect
2. C₂×D₈×D₈₉	C₂	semidirect
3. #19152243	C₂	semidirect
4. D₄×D₃₅₆	C₂	semidirect
5. #19151987	C₂	semidirect
6. #19151852	C₂	semidirect
7. #19151828	C₂	semidirect
8. #19151813	C₂	semidirect
9. #19151793	C₂	semidirect
10. #19151750	C₂	semidirect
11. #19151744	C₂	semidirect
12. #19151733	C₂	semidirect
13. #19151733	C₂	semidirect
14. #19151671	C₂	semidirect
15. #442×C₈₉	C₂	semidirect
16. C₂×#13083573	C₂²	semidirect
19. C₂×D₄×D₈₉	C₂²	semidirect
20. C₂×D₄×D₈₉	C₂²	semidirect
22. C₂×#13083563	C₂²	semidirect
23. C₂×#13083563	C₂²	semidirect
24. C₂×#13083562	C₂²	semidirect
25. C₂×D₇₁₂	C₂²	semidirect
26. C₂×D₇₁₂	C₂²	semidirect
28. C₂×#13083559	C₂²	semidirect
29. C₂×#13083559	C₂²	semidirect
31. C₂×#13083557	C₂²	semidirect
32. C₂×C₈×D₈₉	C₂²	semidirect
33. #15668009	C₂²	semidirect
34. #15668000	C₂²	semidirect
36. #15667992	C₂²	semidirect
38. #15667987	C₂²	semidirect
39. #15667987	C₂²	semidirect
47. C₄⋊#10623494	C₂²	semidirect
48. #15667935	C₂²	semidirect
49. #15667932	C₂²	semidirect
50. #15667932	C₂²	semidirect
51. #15667932	C₂²	semidirect
52. #15667924	C₂²	semidirect
53. #15667924	C₂²	semidirect
55. C₄×D₄×C₈₉	C₂²	semidirect
56. C₄×D₄×C₈₉	C₂²	semidirect
57. #106×C₈₉	C₂²	semidirect
58. #102×C₈₉	C₂²	semidirect
59. #102×C₈₉	C₂²	semidirect
60. #97×C₈₉	C₂²	semidirect
116. D₈×C₈₉	D₄	semidirect
143. D₄×C₈₉	C₂×D₄	semidirect
178. C₈×C₈₉	C₂×D₄	semidirect
205. C₂×D₈₉	AGL(1,ℤ/8)	semidirect
226. C₈₉	#3264	semidirect
240. #442	D₈₉	semidirect
273. C₄×D₄	C₂×D₈₉	semidirect
274. C₄×D₄	C₂×D₈₉	semidirect
276. #106	C₂×D₈₉	semidirect
282. #102	C₂×D₈₉	semidirect
283. #102	C₂×D₈₉	semidirect
286. #97	C₂×D₈₉	semidirect
328. D₈	D₃₅₆	semidirect
387. D₄	C₂×D₃₅₆	semidirect
406. C₈	C₂×D₃₅₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668036	2
C₂×D₈×D₈₉	2
#19152243	2
D₄×D₃₅₆	2
#19151987	2
#19151852	2
#19151828	2
#19151813	2
#19151793	2
#19151750	2
#19151744	2
#19151733	2
#19151671	2
#442×C₈₉	2
#3264	89