Subgroups — #26031726

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×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151984	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151851	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151824	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151815	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151791	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151747	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151743	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151732	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151730	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151710	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151667	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₈₉	—	2	1	no	—
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083559	C₂²	1	1	yes	characteristic
22	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
24	D₈×D₈₉	—	2	4	no	—
25	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
26	#15668008	C₂²	1	1	yes	characteristic, complemented
27	#15668001	C₂²	1	1	yes	characteristic, complemented
28	#15667995	—	2	1	no	—
29	#15667988	C₂²	1	1	yes	characteristic, complemented
30	#15667986	C₂²	1	1	yes	characteristic, complemented
31	#15667986	C₂²	1	1	yes	characteristic, complemented
32	#15667984	—	2	1	no	—
33	#15667984	—	2	1	no	—
34	#15667983	C₂²	1	1	yes	characteristic
35	#15667981	—	2	1	no	—
36	#15667980	—	2	1	no	—
37	#15667980	—	2	1	no	—
38	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
41	C₂×#13083551	—	2	1	no	—
42	#15667944	C₂²	1	1	yes	characteristic, complemented
43	#15667941	C₂²	1	1	yes	characteristic, complemented
44	#15667936	C₂²	1	1	yes	characteristic, complemented
45	#15667934	C₂²	1	1	yes	characteristic, complemented
46	#15667934	C₂²	1	1	yes	characteristic, complemented
47	#15667933	C₂²	1	1	yes	characteristic, complemented
48	#15667933	C₂²	1	1	yes	characteristic, complemented
49	#15667933	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
51	#15667924	C₂²	1	1	yes	characteristic, complemented
52	#15667922	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
56	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
64	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₈₉	—	2	1	no	—
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	C₂×C₂²⋊D₈₉	—	2	1	no	—
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	4	4	no	—
73	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
74	D₄×D₈₉	—	2	2	no	—
75	D₄×D₈₉	—	2	2	no	—
76	D₄×D₈₉	—	4	1	no	—
77	D₄×D₈₉	—	4	1	no	—
78	C₂²×Dic₈₉	—	2	1	no	—
79	C₂²×Dic₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
81	#13083561	—	4	1	no	—
82	D₇₁₂	—	2	2	no	—
83	#13083559	—	2	2	no	—
84	#13083559	—	2	2	no	—
85	#13083559	—	4	1	no	—
86	C₂×#10623494	C₂³	1	1	yes	characteristic
87	C₂×#10623494	C₂³	1	1	yes	characteristic
88	C₈×D₈₉	—	2	2	no	—
89	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
91	#13083553	—	2	1	no	—
92	#13083553	D₄	1	1	yes	characteristic
93	C₂²⋊Dic₈₉	—	2	1	no	—
94	C₂²⋊Dic₈₉	—	2	1	no	—
95	C₂²⋊Dic₈₉	—	2	1	no	—
96	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
97	#13083551	—	2	1	no	—
98	#13083551	—	2	1	no	—
99	#13083551	—	2	1	no	—
100	#13083551	—	2	1	no	—
101	#13083551	—	2	1	no	—
102	#13083551	D₄	1	1	yes	characteristic
103	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₈₉	—	2	1	no	—
105	#41×C₈₉	—	2	2	no	—
106	#41×C₈₉	—	4	1	no	—
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	—	2	2	no	—
109	C₂×D₄×C₈₉	—	2	1	no	—
110	C₂×D₄×C₈₉	—	2	1	no	—
111	C₂×D₄×C₈₉	—	4	1	no	—
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₈₉	—	2	2	no	—
118	SD₁₆×C₈₉	—	2	2	no	—
119	D₈×C₈₉	—	2	2	no	—
120	D₈×C₈₉	D₄	1	4	yes	complemented
121	M₁₆×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	2	1	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	4	2	no	—
129	C₂³×C₈₉	—	8	1	no	—
130	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₈₉	—	2	1	no	—
132	C₂²×D₈₉	—	2	1	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	4	2	no	—
135	C₂²×D₈₉	—	4	2	no	—
136	C₂²×D₈₉	—	4	2	no	—
137	C₂²×D₈₉	—	8	1	no	—
138	C₂²×D₈₉	—	8	1	no	—
139	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
140	Q₈×C₈₉	—	2	1	no	—
141	Q₈×C₈₉	—	2	1	no	—
142	D₄×C₈₉	—	2	1	no	—
143	D₄×C₈₉	—	2	1	no	—
144	D₄×C₈₉	—	2	1	no	—
145	D₄×C₈₉	—	2	1	no	—
146	D₄×C₈₉	—	4	2	no	—
147	D₄×C₈₉	—	4	2	no	—
148	D₄×C₈₉	C₂×D₄	1	2	yes	—
149	D₄×C₈₉	C₂×D₄	1	2	yes	complemented
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂²⋊D₈₉	—	2	2	no	—
157	C₂²⋊D₈₉	—	4	2	no	—
158	C₂²⋊D₈₉	—	4	2	no	—
159	C₂²⋊D₈₉	—	4	2	no	—
160	C₂²⋊D₈₉	—	4	2	no	—
161	C₂²⋊D₈₉	—	4	2	no	—
162	C₂²⋊D₈₉	—	8	1	no	—
163	C₂²⋊D₈₉	—	8	1	no	—
164	C₂×Dic₈₉	—	2	1	no	—
165	C₂×Dic₈₉	—	2	1	no	—
166	C₂×Dic₈₉	—	4	2	no	—
167	C₂×Dic₈₉	—	8	1	no	—
168	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
171	D₃₅₆	—	2	1	no	—
172	D₃₅₆	—	2	1	no	—
173	D₃₅₆	—	2	1	no	—
174	D₃₅₆	—	2	1	no	—
175	C₄×D₈₉	—	2	1	no	—
176	C₄×D₈₉	—	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	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	1	no	—
190	C₂²×C₈₉	—	4	1	no	—
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	—	4	1	no	—
193	C₂²×C₈₉	—	8	4	no	—
194	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×D₈₉	—	2	1	no	—
196	C₂×D₈₉	—	2	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	—	4	1	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	—	4	1	no	—
208	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
210	Dic₈₉	—	2	1	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	1	no	—
215	C₂×C₈₉	—	4	2	no	—
216	C₂×C₈₉	—	4	2	no	—
217	C₂×C₈₉	—	4	1	no	—
218	C₂×C₈₉	—	8	1	no	—
219	C₂×C₈₉	D₄²	1	1	yes	characteristic
220	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂×C₈₉	#576	1	1	yes	characteristic
222	D₈₉	—	2	2	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)	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
241	#435	—	89	1	no	—
242	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	89	1	no	—
244	C₂²×D₄	—	89	1	no	—
245	C₂²×D₄	—	178	1	no	—
246	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
247	AGL(1,ℤ/8)	—	2	4	no	—
248	C₂×SD₁₆	—	89	1	no	—
249	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
250	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
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	—	178	4	no	—
256	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
257	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
258	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
274	C₄×D₄	—	89	1	no	—
275	C₂×C₂²⋊C₄	—	178	1	no	—
276	#106	—	89	1	no	—
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	—	89	1	no	—
283	#102	—	89	1	no	—
284	C₂²⋊C₈	—	89	1	no	—
285	C₂²⋊C₈	—	89	1	no	—
286	#97	—	89	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂⁴	—	178	1	no	—
289	C₂⁴	—	178	1	no	—
290	#41	—	2	2	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	89	1	no	—
298	C₂×D₄	—	89	1	no	—
299	C₂×D₄	—	89	1	no	—
300	C₂×D₄	—	356	4	no	—
301	C₂×D₄	—	356	1	no	—
302	C₂×D₄	—	356	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	1	no	—
309	C₂×D₄	—	178	2	no	—
310	C₂×D₄	—	178	2	no	—
311	C₂×D₄	—	178	1	no	—
312	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
317	C₂²×C₄	—	178	1	no	—
318	C₂²×C₄	—	178	1	no	—
319	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	356	1	no	—
323	D₈	—	2	2	no	—
324	D₈	—	356	1	no	—
325	D₈	—	178	2	no	—
326	D₈	—	178	2	no	—
327	D₈	—	178	2	no	—
328	D₈	C₂²⋊D₈₉	1	4	yes	complemented
329	M₁₆	—	2	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	—	89	1	no	—
337	C₄⋊C₄	—	89	1	no	—
338	C₄⋊C₄	—	178	1	no	—
339	C₂²⋊C₄	—	89	1	no	—
340	C₂²⋊C₄	—	89	1	no	—
341	C₂²⋊C₄	—	178	1	no	—
342	C₂²⋊C₄	—	178	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	—	89	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	89	1	no	—
357	C₂³	—	356	2	no	—
358	C₂³	—	356	2	no	—
359	C₂³	—	356	2	no	—
360	C₂³	—	356	2	no	—
361	C₂³	—	178	1	no	—
362	C₂³	—	178	1	no	—
363	C₂³	—	712	1	no	—
364	C₂³	—	712	1	no	—
365	C₂³	D₄×D₈₉	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	356	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	356	2	no	—
378	D₄	—	356	2	no	—
379	D₄	—	178	2	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×C₂²⋊D₈₉	1	2	yes	—
387	D₄	C₂×C₂²⋊D₈₉	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	89	1	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	356	2	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	—	712	1	no	—
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×C₂²⋊D₈₉	1	2	yes	complemented
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	8	4	no	—
420	C₂²	—	89	2	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	—	356	1	no	—
425	C₂²	—	356	1	no	—
426	C₂²	—	356	1	no	—
427	C₂²	—	178	1	no	—
428	C₂²	—	178	1	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	—	4	1	no	—
434	C₄	—	356	1	no	—
435	C₄	—	356	1	no	—
436	C₄	—	178	1	no	—
437	C₄	—	178	1	no	—
438	C₄	—	178	1	no	—
439	C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₄	#15668057	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	4	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	8	1	no	—
445	C₂	—	178	2	no	—
446	C₂	—	712	1	no	—
447	C₂	—	712	1	no	—
448	C₂	D₄×C₂²⋊D₈₉	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	C₂×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#3264
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×D₈₉	C₂	semidirect
2. #19152236	C₂	semidirect
3. D₄×C₂²⋊D₈₉	C₂	semidirect
4. #19151984	C₂	semidirect
5. #19151851	C₂	semidirect
6. #19151824	C₂	semidirect
7. #19151815	C₂	semidirect
8. #19151791	C₂	semidirect
9. #19151747	C₂	semidirect
10. #19151743	C₂	semidirect
11. #19151732	C₂	semidirect
12. #19151730	C₂	semidirect
13. #19151710	C₂	semidirect
14. #19151667	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
18. C₂×D₄×D₈₉	C₂²	semidirect
19. C₂×#13083561	C₂²	semidirect
20. C₂×D₇₁₂	C₂²	semidirect
22. C₂×#13083559	C₂²	semidirect
23. C₂×#13083559	C₂²	semidirect
25. C₂×C₈×D₈₉	C₂²	semidirect
26. #15668008	C₂²	semidirect
27. #15668001	C₂²	semidirect
29. #15667988	C₂²	semidirect
30. #15667986	C₂²	semidirect
31. #15667986	C₂²	semidirect
38. D₄×Dic₈₉	C₂²	semidirect
39. D₄×Dic₈₉	C₂²	semidirect
42. #15667944	C₂²	semidirect
43. #15667941	C₂²	semidirect
44. #15667936	C₂²	semidirect
45. #15667934	C₂²	semidirect
46. #15667934	C₂²	semidirect
47. #15667933	C₂²	semidirect
48. #15667933	C₂²	semidirect
49. #15667933	C₂²	semidirect
50. C₂²⋊#10623494	C₂²	semidirect
51. #15667924	C₂²	semidirect
52. #15667922	C₂²	semidirect
53. C₂×#41×C₈₉	C₂²	semidirect
54. C₂²×D₄×C₈₉	C₂²	semidirect
56. C₂×SD₁₆×C₈₉	C₂²	semidirect
57. C₂×SD₁₆×C₈₉	C₂²	semidirect
59. C₂×D₈×C₈₉	C₂²	semidirect
60. C₂×M₁₆×C₈₉	C₂²	semidirect
120. D₈×C₈₉	D₄	semidirect
149. D₄×C₈₉	C₂×D₄	semidirect
178. C₈×C₈₉	C₂×D₄	semidirect
205. C₂×D₈₉	AGL(1,ℤ/8)	semidirect
226. C₈₉	#3264	semidirect
227. C₂×AGL(1,ℤ/8)	D₈₉	semidirect
242. C₂×#41	C₂×D₈₉	semidirect
246. C₂²×D₄	C₂×D₈₉	semidirect
249. C₂×SD₁₆	C₂×D₈₉	semidirect
250. C₂×SD₁₆	C₂×D₈₉	semidirect
257. C₂×D₈	C₂×D₈₉	semidirect
258. C₂×M₁₆	C₂×D₈₉	semidirect
328. D₈	C₂²⋊D₈₉	semidirect
387. D₄	C₂×C₂²⋊D₈₉	semidirect
406. C₈	C₂×C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×D₈₉	2
#19152236	2
D₄×C₂²⋊D₈₉	2
#19151984	2
#19151851	2
#19151824	2
#19151815	2
#19151791	2
#19151747	2
#19151743	2
#19151732	2
#19151730	2
#19151710	2
#19151667	2
C₂×AGL(1,ℤ/8)×C₈₉	2
#3264	89