Subgroups — #36545913

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033241	C₂	1	1	yes	maximal, characteristic, complemented
2	#26032486	C₂	1	2	yes	maximal, complemented
3	#26031927	C₂	1	1	yes	maximal, characteristic
4	#26019857	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019812	C₂	1	2	yes	maximal, complemented
6	#26019618	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019432	C₂	1	2	yes	maximal, complemented
8	#26019361	C₂	1	2	yes	maximal, complemented
9	#26019136	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	—	2	1	no	—
13	#19152321	C₂²	1	2	yes	complemented
14	#19152233	C₂²	1	2	yes	—
15	#19151982	—	2	1	no	—
16	#19151978	C₂²	1	1	yes	characteristic, complemented
17	#19151944	C₂²	1	2	yes	complemented
18	#19151944	C₂²	1	2	yes	complemented
19	#19151920	—	2	2	no	—
20	#19151879	C₂²	1	2	yes	—
21	#19151841	—	2	2	no	—
22	#19151831	—	2	1	no	—
23	#19151821	—	2	2	no	—
24	#19151804	C₂²	1	2	yes	complemented
25	#19151790	C₂²	1	2	yes	—
26	#19151747	—	2	2	no	—
27	#19151730	—	2	2	no	—
28	C₄×Dic₃₅₆	—	2	1	no	—
29	C₄×#13083561	C₂²	1	1	yes	characteristic
30	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
31	#19151675	C₂²	1	2	yes	complemented
32	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
33	#19151601	—	2	2	no	—
34	#19151348	C₂²	1	1	yes	characteristic, complemented
35	#19151343	C₂²	1	2	yes	complemented
36	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
37	#19151325	C₂²	1	1	yes	characteristic
38	#19151325	C₂²	1	2	yes	complemented
39	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
40	#493×C₈₉	C₂²	1	1	yes	characteristic
41	#460×C₈₉	C₂²	1	2	yes	complemented
42	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#335×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#331×C₈₉	C₂²	1	2	yes	complemented
45	C₂×D₄×D₈₉	—	2	2	no	—
46	C₂×D₄×D₈₉	—	2	2	no	—
47	C₂×Dic₃₅₆	—	2	1	no	—
48	C₂×Dic₃₅₆	—	2	1	no	—
49	C₂×#13083563	—	2	2	no	—
50	C₂×#13083561	D₄	1	1	yes	characteristic
51	C₂×D₇₁₂	D₄	1	1	yes	characteristic
52	C₂×#13083559	—	2	2	no	—
53	D₈×D₈₉	—	4	4	no	—
54	C₂×#13083557	—	2	2	no	—
55	C₂×C₈×D₈₉	—	2	1	no	—
56	#15668012	C₂³	1	2	yes	—
57	#15668007	—	4	2	no	—
58	#15668000	—	2	2	no	—
59	#15667988	—	2	2	no	—
60	#15667983	—	2	2	no	—
61	#15667983	—	2	2	no	—
62	#15667980	—	4	2	no	—
63	C₄×Dic₁₇₈	—	2	2	no	—
64	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂³	1	2	yes	—
66	#15667970	—	2	2	no	—
67	#15667946	—	2	2	no	—
68	#15667946	D₄	1	1	yes	characteristic
69	#15667943	D₄	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667937	—	2	2	no	—
72	#15667936	D₄	1	1	yes	characteristic
73	#15667934	—	2	2	no	—
74	#15667934	D₄	1	2	yes	—
75	#15667933	—	2	2	no	—
76	#15667933	—	2	2	no	—
77	#15667933	—	2	2	no	—
78	#15667933	—	4	2	no	—
79	#15667932	D₄	1	1	yes	characteristic
80	#15667924	—	2	2	no	—
81	#15667924	—	2	1	no	—
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₄×#10623494	C₂³	1	1	yes	characteristic
84	C₂×SD₁₆×C₈₉	—	2	2	no	—
85	C₂×D₈×C₈₉	—	2	1	no	—
86	C₂×D₈×C₈₉	—	2	1	no	—
87	#127×C₈₉	C₂³	1	2	yes	—
88	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	#102×C₈₉	—	2	2	no	—
93	C₄×C₈×C₈₉	—	2	1	no	—
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×D₈₉	—	4	2	no	—
96	C₂×Dic₁₇₈	—	2	2	no	—
97	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
98	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₈₉	—	4	2	no	—
100	C₂×C₂²⋊D₈₉	—	4	2	no	—
101	D₄×D₈₉	—	4	4	no	—
102	D₄×D₈₉	—	4	4	no	—
103	D₄×D₈₉	—	8	2	no	—
104	D₄×D₈₉	—	8	2	no	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	2	1	no	—
107	Dic₃₅₆	—	4	2	no	—
108	Dic₃₅₆	—	8	1	no	—
109	#13083563	—	8	2	no	—
110	#13083561	—	2	2	no	—
111	D₇₁₂	—	2	2	no	—
112	#13083559	—	4	4	no	—
113	#13083557	—	8	2	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
117	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
118	C₈×D₈₉	—	4	2	no	—
119	C₄⋊Dic₈₉	—	2	2	no	—
120	C₄⋊Dic₈₉	—	2	2	no	—
121	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
122	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
123	#13083553	—	4	2	no	—
124	C₂²⋊Dic₈₉	—	4	2	no	—
125	#13083551	—	2	1	no	—
126	#13083551	—	2	2	no	—
127	#13083551	—	4	2	no	—
128	#13083551	—	4	2	no	—
129	C₄×Dic₈₉	—	4	2	no	—
130	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₈₉	—	2	2	no	—
132	C₂×D₄×C₈₉	—	2	2	no	—
133	C₂×D₄×C₈₉	—	2	2	no	—
134	SD₁₆×C₈₉	—	8	2	no	—
135	D₈×C₈₉	—	4	2	no	—
136	D₈×C₈₉	—	8	1	no	—
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂³×C₈₉	—	4	2	no	—
146	C₂²×D₈₉	—	2	1	no	—
147	C₂²×D₈₉	—	2	2	no	—
148	C₂²×D₈₉	—	8	4	no	—
149	C₂²×D₈₉	—	8	4	no	—
150	C₂²×D₈₉	—	16	2	no	—
151	Q₈×C₈₉	—	2	1	no	—
152	Q₈×C₈₉	—	2	1	no	—
153	D₄×C₈₉	—	4	2	no	—
154	D₄×C₈₉	—	4	2	no	—
155	D₄×C₈₉	—	4	2	no	—
156	D₄×C₈₉	—	4	2	no	—
157	D₄×C₈₉	—	8	2	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	8	4	no	—
164	C₂²⋊D₈₉	—	8	4	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	4	2	no	—
168	D₃₅₆	—	2	2	no	—
169	D₃₅₆	—	2	1	no	—
170	D₃₅₆	—	2	2	no	—
171	D₃₅₆	#135	1	2	yes	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	—	4	1	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	1	no	—
176	Dic₁₇₈	—	4	2	no	—
177	Dic₁₇₈	—	4	2	no	—
178	C₈×C₈₉	—	2	1	no	—
179	C₈×C₈₉	—	4	2	no	—
180	C₈×C₈₉	—	4	1	no	—
181	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
182	#10623494	—	2	1	no	—
183	#10623494	—	2	1	no	—
184	#10623494	—	4	1	no	—
185	#10623494	—	4	1	no	—
186	C₂²×C₈₉	—	8	2	no	—
187	C₂²×C₈₉	—	8	2	no	—
188	C₂²×C₈₉	—	8	2	no	—
189	C₂²×C₈₉	D₄²	1	1	yes	characteristic
190	C₂×D₈₉	—	2	2	no	—
191	C₂×D₈₉	—	4	1	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	4	2	no	—
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	16	8	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
201	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₄×C₈₉	#576	1	1	yes	characteristic
203	C₄×C₈₉	#576	1	1	yes	characteristic
204	Dic₈₉	—	4	1	no	—
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	8	2	no	—
207	#19900	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	16	2	no	—
209	C₂×C₈₉	#3274	1	1	yes	characteristic
210	C₂×C₈₉	#3280	1	1	yes	characteristic
211	C₂×C₈₉	#3290	1	1	yes	characteristic
212	D₈₉	—	4	2	no	—
213	D₈₉	—	8	2	no	—
214	#3393	—	89	1	no	—
215	#3324	—	89	2	no	—
216	D₄×D₈	—	89	1	no	—
217	#1709	—	89	1	no	—
218	#1701	—	89	2	no	—
219	#1669	—	89	1	no	—
220	#1668	D₈₉	1	1	yes	characteristic, complemented
221	#1639	—	89	2	no	—
222	#1628	—	89	2	no	—
223	#1589	—	89	1	no	—
224	C₈×SD₁₆	—	89	1	no	—
225	C₈₉	#19900	1	1	yes	characteristic, complemented, Sylow
226	C₂²×D₈	—	178	1	no	—
227	#556	—	89	2	no	—
228	D₄²	—	89	2	no	—
229	#495	—	178	1	no	—
230	#494	—	89	1	no	—
231	#493	C₂×D₈₉	1	1	yes	characteristic
232	#486	—	89	2	no	—
233	#486	—	89	2	no	—
234	#482	—	178	2	no	—
235	#474	—	89	2	no	—
236	#468	—	178	2	no	—
237	#466	—	178	1	no	—
238	#464	—	178	2	no	—
239	#461	—	89	2	no	—
240	#460	C₂×D₈₉	1	2	yes	complemented
241	#459	—	89	2	no	—
242	#450	—	178	2	no	—
243	#447	—	178	2	no	—
244	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
245	C₄×Q₁₆	—	178	1	no	—
246	C₄×SD₁₆	—	89	1	no	—
247	C₄×D₈	—	89	1	no	—
248	#436	—	89	2	no	—
249	C₈×D₄	—	89	1	no	—
250	#418	—	178	2	no	—
251	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
252	#334	—	89	1	no	—
253	#332	—	89	2	no	—
254	#331	C₂×D₈₉	1	2	yes	complemented
255	Q₈⋊C₈	—	89	1	no	—
256	D₄⋊C₈	—	89	1	no	—
257	D₄⋊C₈	—	89	2	no	—
258	C₈²	—	89	1	no	—
259	C₂²×D₄	—	178	2	no	—
260	C₂²×D₄	—	178	2	no	—
261	C₂×Q₁₆	—	178	1	no	—
262	C₂×Q₁₆	—	178	1	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	89	1	no	—
265	C₂×SD₁₆	—	178	2	no	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	89	1	no	—
269	C₂×D₈	—	356	4	no	—
270	C₂×D₈	—	178	2	no	—
271	C₂×M₁₆	—	178	2	no	—
272	C₂²×C₈	—	178	1	no	—
273	C₄⋊Q₈	—	89	2	no	—
274	#127	C₂²×D₈₉	1	2	yes	—
275	#126	—	356	2	no	—
276	#124	—	178	2	no	—
277	C₂²⋊Q₈	—	178	2	no	—
278	#121	—	178	2	no	—
279	#121	—	178	2	no	—
280	#120	—	356	2	no	—
281	C₄×Q₈	—	178	2	no	—
282	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
283	C₄×D₄	—	89	1	no	—
284	C₄×D₄	—	89	2	no	—
285	#117	—	178	2	no	—
286	#107	—	89	1	no	—
287	#107	—	178	2	no	—
288	#106	—	89	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	89	1	no	—
291	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
293	#103	—	89	1	no	—
294	#103	—	178	2	no	—
295	#102	—	2	2	no	—
296	#102	—	89	2	no	—
297	#102	—	89	1	no	—
298	#102	—	356	2	no	—
299	#102	—	178	2	no	—
300	#102	—	178	2	no	—
301	#102	—	178	2	no	—
302	#102	—	178	2	no	—
303	C₂²⋊C₈	—	178	2	no	—
304	C₂²⋊C₈	—	178	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	89	1	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₂⁴	—	356	2	no	—
310	C₂×Q₈	—	178	2	no	—
311	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	89	1	no	—
316	C₂×D₄	—	89	2	no	—
317	C₂×D₄	—	356	4	no	—
318	C₂×D₄	—	356	4	no	—
319	C₂×D₄	—	356	2	no	—
320	C₂×D₄	—	356	2	no	—
321	C₂×D₄	—	712	2	no	—
322	C₂×D₄	—	712	2	no	—
323	C₂²×C₄	—	178	2	no	—
324	C₂²×C₄	—	178	1	no	—
325	Q₁₆	—	356	2	no	—
326	Q₁₆	—	712	1	no	—
327	SD₁₆	—	8	2	no	—
328	SD₁₆	—	178	2	no	—
329	SD₁₆	—	712	2	no	—
330	D₈	—	4	2	no	—
331	D₈	—	8	1	no	—
332	D₈	—	356	4	no	—
333	D₈	—	178	2	no	—
334	M₁₆	—	712	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	89	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	356	2	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	—	178	1	no	—
342	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	89	2	no	—
346	C₄⋊C₄	—	89	1	no	—
347	C₄⋊C₄	—	356	2	no	—
348	C₄⋊C₄	—	178	2	no	—
349	C₄⋊C₄	—	178	2	no	—
350	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
351	C₂²⋊C₄	—	356	2	no	—
352	C₂²⋊C₄	—	356	2	no	—
353	C₂²⋊C₄	—	356	2	no	—
354	C₂²⋊C₄	—	178	1	no	—
355	C₂²⋊C₄	—	178	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	356	2	no	—
358	C₄²	C₂³×D₈₉	1	1	yes	characteristic
359	C₂³	—	4	2	no	—
360	C₂³	—	1424	2	no	—
361	C₂³	—	178	2	no	—
362	C₂³	—	178	1	no	—
363	C₂³	—	712	4	no	—
364	C₂³	—	712	4	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	356	2	no	—
368	Q₈	—	356	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	89	2	no	—
375	D₄	—	178	2	no	—
376	D₄	—	178	1	no	—
377	D₄	—	178	2	no	—
378	D₄	—	712	4	no	—
379	D₄	—	712	4	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	356	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	#15668058	1	1	yes	characteristic
392	C₈	—	2	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	356	1	no	—
396	C₈	—	356	1	no	—
397	C₈	—	178	1	no	—
398	C₈	—	178	1	no	—
399	C₈	#15668039	1	2	yes	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	356	1	no	—
404	C₂²	—	356	1	no	—
405	C₂²	—	356	2	no	—
406	C₂²	—	356	2	no	—
407	C₂²	—	356	2	no	—
408	C₂²	—	1424	8	no	—
409	C₂²	—	178	2	no	—
410	C₂²	#19152232	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	356	2	no	—
415	C₄	—	356	1	no	—
416	C₄	—	712	2	no	—
417	C₄	#135×D₈₉	1	1	yes	characteristic
418	C₄	C₂×#15668039	1	1	yes	characteristic
419	C₄	#19152399	1	1	yes	characteristic
420	C₄	#19152402	1	1	yes	characteristic
421	C₂	—	16	2	no	—
422	C₂	—	356	2	no	—
423	C₂	—	712	2	no	—
424	C₂	#26031867	1	1	yes	characteristic
425	C₂	#26031940	1	1	yes	characteristic
426	C₂	#26032033	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19152232
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1668	C₂
socle	C₂²×C₈₉	D₄²
prime radical	#26031927	C₂
hypercenter	#1668	D₈₉
hypocenter	C₈₉	#19900
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1668

Complements

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

N	H ≅ G/N	type
1. #26033241	C₂	semidirect
2. #26032486	C₂	semidirect
4. #26019857	C₂	semidirect
5. #26019812	C₂	semidirect
6. #26019618	C₂	semidirect
7. #26019432	C₂	semidirect
8. #26019361	C₂	semidirect
9. #26019136	C₂	semidirect
10. C₈×#13083561	C₂	semidirect
11. C₈₉×#1668	C₂	semidirect
13. #19152321	C₂²	semidirect
16. #19151978	C₂²	semidirect
17. #19151944	C₂²	semidirect
18. #19151944	C₂²	semidirect
24. #19151804	C₂²	semidirect
31. #19151675	C₂²	semidirect
34. #19151348	C₂²	semidirect
35. #19151343	C₂²	semidirect
36. Q₈⋊#10623494	C₂²	semidirect
38. #19151325	C₂²	semidirect
39. C₈×#10623494	C₂²	semidirect
41. #460×C₈₉	C₂²	semidirect
42. C₈×Q₈×C₈₉	C₂²	semidirect
43. #335×C₈₉	C₂²	semidirect
44. #331×C₈₉	C₂²	semidirect
220. #1668	D₈₉	semidirect
225. C₈₉	#19900	semidirect
240. #460	C₂×D₈₉	semidirect
244. C₈×Q₈	C₂×D₈₉	semidirect
251. #335	C₂×D₈₉	semidirect
254. #331	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033241	2
#26032486	2
#26031927	2
#26019857	2
#26019812	2
#26019618	2
#26019432	2
#26019361	2
#26019136	2
C₈×#13083561	2
C₈₉×#1668	2
#19900	89