Subgroups — #36711219

Order 22784.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033392	C₂	1	2	yes	maximal, complemented
2	#26032052	C₂	1	1	yes	maximal, characteristic, complemented
3	#26032051	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022501	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022371	C₂	1	2	yes	maximal, complemented
6	#26022329	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022212	C₂	1	2	yes	maximal, complemented
8	#26022206	C₂	1	2	yes	maximal, complemented
9	#26022131	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022088	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2213	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152403	—	2	1	no	—
13	#19152400	C₂²	1	2	yes	complemented
14	#19152399	—	2	1	no	—
15	#19152399	C₂²	1	2	yes	complemented
16	#19152036	C₂²	1	2	yes	complemented
17	#19152035	—	2	2	no	—
18	#19152032	—	2	2	no	—
19	#19152029	—	2	2	no	—
20	#19152028	C₂²	1	1	yes	characteristic
21	C₂×#15667953	C₂²	1	2	yes	complemented
22	C₂×#15667953	C₂²	1	2	yes	complemented
23	D₁₆×D₈₉	—	2	2	no	—
24	#19152016	C₂²	1	2	yes	complemented
25	#19151975	C₂²	1	1	yes	characteristic, complemented
26	#19151869	C₂²	1	2	yes	complemented
27	#19151868	—	2	1	no	—
28	#19151865	—	2	1	no	—
29	#19151865	C₂²	1	2	yes	complemented
30	#19151767	—	2	2	no	—
31	#19151765	—	2	2	no	—
32	#19151716	C₂²	1	1	yes	characteristic
33	#19151716	C₂²	1	1	yes	characteristic, complemented
34	#19151427	C₂²	1	1	yes	characteristic, complemented
35	#19151412	C₂²	1	2	yes	complemented
36	#19151405	C₂²	1	1	yes	characteristic, complemented
37	#19151404	C₂²	1	1	yes	characteristic, complemented
38	#19151383	C₂²	1	2	yes	complemented
39	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
40	#509×C₈₉	C₂²	1	2	yes	complemented
41	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#443×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#361×C₈₉	C₂²	1	2	yes	complemented
45	#15668058	—	2	2	no	—
46	#15668057	—	2	2	no	—
47	#15668040	—	2	2	no	—
48	#15668040	—	4	2	no	—
49	#15668039	—	4	2	no	—
50	#15668038	—	2	2	no	—
51	#15668038	—	2	2	no	—
52	#15668037	—	2	2	no	—
53	#15668036	—	4	2	no	—
54	#15668036	—	4	2	no	—
55	#15668035	—	2	2	no	—
56	#15668034	—	4	1	no	—
57	#15668034	D₄	1	1	yes	characteristic
58	#15668034	C₂³	1	1	yes	characteristic
59	#15668031	—	2	2	no	—
60	#15668031	—	4	1	no	—
61	C₂×D₇₁₂	—	2	1	no	—
62	C₂×D₇₁₂	—	4	1	no	—
63	C₂×D₇₁₂	C₂³	1	2	yes	—
64	D₈×D₈₉	—	2	2	no	—
65	D₈×D₈₉	—	2	2	no	—
66	D₈×D₈₉	—	4	1	no	—
67	#15668018	—	2	1	no	—
68	#15668018	C₂³	1	2	yes	—
69	#15668009	—	2	1	no	—
70	#15667958	D₄	1	1	yes	characteristic, complemented
71	#15667957	—	2	2	no	—
72	#15667956	D₄	1	1	yes	characteristic, complemented
73	#15667955	D₄	1	1	yes	characteristic, complemented
74	D₁₄₂₄	—	2	2	no	—
75	#15667953	—	2	2	no	—
76	#15667953	—	2	2	no	—
77	#15667953	—	4	2	no	—
78	#15667953	D₄	1	1	yes	characteristic, complemented
79	#15667951	—	2	2	no	—
80	C₂×#13083549	C₂³	1	1	yes	characteristic
81	C₂×#13083549	C₂³	1	1	yes	characteristic
82	C₁₆×D₈₉	—	2	2	no	—
83	#15667948	D₄	1	1	yes	characteristic
84	#15667948	C₂³	1	1	yes	characteristic
85	#15667940	—	2	1	no	—
86	#15667940	D₄	1	2	yes	—
87	#15667929	—	2	2	no	—
88	#15667928	—	2	2	no	—
89	#135×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×D₈×C₈₉	—	2	1	no	—
91	C₂×D₈×C₈₉	C₂³	1	2	yes	—
92	#131×C₈₉	—	2	1	no	—
93	#127×C₈₉	—	2	1	no	—
94	SD₃₂×C₈₉	—	2	2	no	—
95	D₁₆×C₈₉	—	2	2	no	—
96	M₃₂×C₈₉	C₂³	1	2	yes	—
97	#108×C₈₉	C₂³	1	1	yes	characteristic
98	#104×C₈₉	—	2	1	no	—
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#13083575	—	4	2	no	—
101	#13083574	—	2	1	no	—
102	#13083574	—	4	2	no	—
103	#13083574	C₂×D₄	1	2	yes	—
104	#13083573	—	4	2	no	—
105	#13083573	—	4	2	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×D₃₅₆	—	4	2	no	—
108	C₂×D₃₅₆	—	8	1	no	—
109	C₂×C₂²⋊D₈₉	—	8	2	no	—
110	D₄×D₈₉	—	4	2	no	—
111	D₄×D₈₉	—	4	2	no	—
112	D₄×D₈₉	—	4	2	no	—
113	D₄×D₈₉	—	8	2	no	—
114	Dic₃₅₆	D₈	1	1	yes	characteristic
115	Dic₃₅₆	C₂×D₄	1	1	yes	characteristic
116	#13083563	—	2	1	no	—
117	#13083563	—	4	2	no	—
118	#13083563	D₈	1	2	yes	—
119	#13083562	—	4	2	no	—
120	#13083562	—	4	2	no	—
121	#13083561	—	4	2	no	—
122	D₇₁₂	—	2	2	no	—
123	D₇₁₂	—	2	2	no	—
124	D₇₁₂	—	4	2	no	—
125	D₇₁₂	—	4	1	no	—
126	D₇₁₂	—	4	1	no	—
127	D₇₁₂	D₈	1	1	yes	characteristic
128	D₇₁₂	C₂×D₄	1	1	yes	characteristic
129	#13083559	—	4	2	no	—
130	#13083559	—	4	2	no	—
131	#13083559	—	4	2	no	—
132	#13083558	—	2	1	no	—
133	#13083558	C₂×D₄	1	2	yes	—
134	#13083557	—	2	2	no	—
135	#13083557	—	4	1	no	—
136	C₈×D₈₉	—	2	2	no	—
137	C₈×D₈₉	—	4	1	no	—
138	#13083549	—	2	1	no	—
139	#13083549	C₂×D₄	1	1	yes	characteristic
140	#13083549	C₂×D₄	1	1	yes	characteristic
141	#41×C₈₉	—	2	1	no	—
142	C₂×D₄×C₈₉	—	2	2	no	—
143	C₂×D₄×C₈₉	—	8	1	no	—
144	Q₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
145	SD₁₆×C₈₉	—	2	1	no	—
146	D₈×C₈₉	—	2	2	no	—
147	D₈×C₈₉	—	2	2	no	—
148	D₈×C₈₉	—	4	1	no	—
149	D₈×C₈₉	—	4	1	no	—
150	D₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	M₁₆×C₈₉	—	2	1	no	—
152	M₁₆×C₈₉	—	4	1	no	—
153	C₂×C₈×C₈₉	—	4	1	no	—
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₈₉	—	2	2	no	—
158	C₂³×C₈₉	—	4	2	no	—
159	C₂²×D₈₉	—	4	2	no	—
160	C₂²×D₈₉	—	8	2	no	—
161	C₂²×D₈₉	—	8	2	no	—
162	Q₈×C₈₉	—	2	1	no	—
163	D₄×C₈₉	—	2	1	no	—
164	D₄×C₈₉	—	4	1	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	—	16	2	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂²⋊D₈₉	—	2	2	no	—
172	C₂²⋊D₈₉	—	4	1	no	—
173	C₂²⋊D₈₉	—	8	2	no	—
174	C₂²⋊D₈₉	—	8	2	no	—
175	C₂²⋊D₈₉	—	8	2	no	—
176	C₂×Dic₈₉	—	8	2	no	—
177	D₃₅₆	—	2	1	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	8	2	no	—
181	D₃₅₆	—	16	2	no	—
182	D₃₅₆	C₂×D₈	1	2	yes	—
183	C₄×D₈₉	—	2	2	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₄×D₈₉	—	8	2	no	—
186	Dic₁₇₈	—	2	1	no	—
187	Dic₁₇₈	C₂×D₈	1	2	yes	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
190	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
191	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
193	#10623494	—	2	2	no	—
194	#10623494	—	4	1	no	—
195	C₂²×C₈₉	—	4	1	no	—
196	C₂²×C₈₉	—	8	2	no	—
197	C₂²×C₈₉	—	16	2	no	—
198	C₂²×C₈₉	#576	1	1	yes	characteristic
199	C₂×D₈₉	—	2	2	no	—
200	C₂×D₈₉	—	4	1	no	—
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	16	2	no	—
203	C₂×D₈₉	—	32	2	no	—
204	C₂×D₈₉	—	32	2	no	—
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	D₄²	1	1	yes	characteristic
208	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
209	Dic₈₉	—	2	2	no	—
210	Dic₈₉	—	4	1	no	—
211	#33858	—	89	1	no	maximal, Sylow
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	—	8	1	no	—
214	C₂×C₈₉	—	16	2	no	—
215	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
216	D₈₉	—	4	2	no	—
217	D₈₉	—	8	1	no	—
218	D₈₉	—	16	2	no	—
219	#3415	—	89	2	no	—
220	#3292	—	89	1	no	—
221	#3292	—	89	1	no	—
222	#2246	—	89	1	no	—
223	#2221	—	89	2	no	—
224	#2213	—	89	1	no	—
225	#2213	D₈₉	1	1	yes	characteristic, complemented
226	#2192	—	89	2	no	—
227	#2192	—	89	2	no	—
228	#2178	—	89	1	no	—
229	#2170	—	89	1	no	—
230	C₈₉	#33858	1	1	yes	characteristic, complemented, Sylow
231	#576	—	89	2	no	—
232	#576	—	89	2	no	—
233	#576	—	178	1	no	—
234	#576	—	178	1	no	—
235	#509	—	89	2	no	—
236	#509	—	178	2	no	—
237	#509	—	178	2	no	—
238	#509	C₂×D₈₉	1	2	yes	complemented
239	#508	—	89	1	no	—
240	#508	—	178	2	no	—
241	C₂×D₁₆	—	89	2	no	—
242	C₂×D₁₆	—	89	2	no	—
243	C₂×D₁₆	—	178	2	no	—
244	#504	—	89	2	no	—
245	#493	—	89	1	no	—
246	#493	C₂×D₈₉	1	1	yes	characteristic, complemented
247	#472	—	89	2	no	—
248	#472	—	89	2	no	—
249	#472	—	178	1	no	—
250	#472	—	178	1	no	—
251	#453	—	178	2	no	—
252	#453	—	178	2	no	—
253	#443	—	89	1	no	—
254	#443	—	89	1	no	—
255	#443	C₂×D₈₉	1	1	yes	characteristic, complemented
256	#368	—	89	1	no	—
257	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
258	#361	—	89	2	no	—
259	#361	C₂×D₈₉	1	2	yes	complemented
260	#359	—	89	1	no	—
261	#359	—	89	1	no	—
262	#350	—	89	2	no	—
263	C₄×C₁₆	—	89	1	no	—
264	H(5,𝔽₂)	—	178	2	no	—
265	H(5,𝔽₂)	—	178	2	no	—
266	AGL(1,ℤ/8)	—	356	2	no	—
267	AGL(1,ℤ/8)	—	356	2	no	—
268	AGL(1,ℤ/8)	—	356	2	no	—
269	AGL(1,ℤ/8)	—	356	2	no	—
270	AGL(1,ℤ/8)	—	178	2	no	—
271	AGL(1,ℤ/8)	—	178	2	no	—
272	AGL(1,ℤ/8)	—	178	2	no	—
273	AGL(1,ℤ/8)	—	178	2	no	—
274	#135	—	89	1	no	—
275	#135	—	89	1	no	—
276	#135	—	356	1	no	—
277	#135	—	356	1	no	—
278	#135	—	178	2	no	—
279	#135	—	178	2	no	—
280	#135	C₂²×D₈₉	1	1	yes	characteristic
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	89	2	no	—
283	C₂×D₈	—	356	1	no	—
284	C₂×D₈	—	356	1	no	—
285	C₂×D₈	—	178	2	no	—
286	C₂×D₈	—	178	2	no	—
287	C₂×D₈	—	178	1	no	—
288	C₂×D₈	C₂²×D₈₉	1	2	yes	—
289	#131	—	2	1	no	—
290	#131	—	89	2	no	—
291	#131	—	178	1	no	—
292	#127	—	2	1	no	—
293	#127	—	178	1	no	—
294	Q₃₂	—	89	1	no	—
295	SD₃₂	—	2	2	no	—
296	SD₃₂	—	89	1	no	—
297	SD₃₂	—	89	1	no	—
298	SD₃₂	—	178	2	no	—
299	D₁₆	—	2	2	no	—
300	D₁₆	—	89	1	no	—
301	D₁₆	—	356	2	no	—
302	D₁₆	—	178	2	no	—
303	D₁₆	—	178	2	no	—
304	D₁₆	—	178	2	no	—
305	M₃₂	—	178	2	no	—
306	M₃₂	C₂²×D₈₉	1	2	yes	—
307	C₂×C₁₆	—	89	1	no	—
308	C₂×C₁₆	—	89	1	no	—
309	C₂×C₁₆	—	178	2	no	—
310	#108	—	89	1	no	—
311	#108	—	89	1	no	—
312	#108	C₂²×D₈₉	1	1	yes	characteristic
313	#104	—	2	1	no	—
314	#104	—	89	2	no	—
315	#104	—	178	1	no	—
316	#100	—	178	2	no	—
317	#100	—	178	2	no	—
318	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
319	#41	—	2	1	no	—
320	#41	—	89	2	no	—
321	#41	—	356	2	no	—
322	#41	—	356	2	no	—
323	#41	—	356	2	no	—
324	#41	—	356	2	no	—
325	#41	—	178	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	8	1	no	—
328	C₂×D₄	—	356	2	no	—
329	C₂×D₄	—	356	2	no	—
330	C₂×D₄	—	356	2	no	—
331	C₂×D₄	—	356	2	no	—
332	C₂×D₄	—	178	2	no	—
333	C₂×D₄	—	712	1	no	—
334	C₂×D₄	—	712	2	no	—
335	C₂×D₄	—	712	2	no	—
336	Q₁₆	—	89	1	no	—
337	Q₁₆	—	89	1	no	—
338	Q₁₆	D₄×D₈₉	1	1	yes	characteristic
339	SD₁₆	—	2	1	no	—
340	SD₁₆	—	89	2	no	—
341	SD₁₆	—	356	2	no	—
342	SD₁₆	—	356	2	no	—
343	SD₁₆	—	356	2	no	—
344	SD₁₆	—	356	2	no	—
345	SD₁₆	—	178	1	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	4	1	no	—
349	D₈	—	4	1	no	—
350	D₈	—	89	1	no	—
351	D₈	—	89	1	no	—
352	D₈	—	356	2	no	—
353	D₈	—	356	2	no	—
354	D₈	—	356	2	no	—
355	D₈	—	356	2	no	—
356	D₈	—	356	1	no	—
357	D₈	—	356	1	no	—
358	D₈	—	178	2	no	—
359	D₈	—	178	2	no	—
360	D₈	D₄×D₈₉	1	1	yes	characteristic
361	M₁₆	—	2	1	no	—
362	M₁₆	—	4	1	no	—
363	M₁₆	—	89	2	no	—
364	M₁₆	—	356	1	no	—
365	M₁₆	—	178	1	no	—
366	M₁₆	—	178	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	356	1	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
371	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
372	C₄²	D₄×D₈₉	1	1	yes	characteristic
373	C₁₆	—	2	2	no	—
374	C₁₆	—	89	1	no	—
375	C₁₆	—	89	1	no	—
376	C₁₆	—	178	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	356	2	no	—
379	C₂³	—	712	2	no	—
380	C₂³	—	712	2	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	89	2	no	—
383	Q₈	—	178	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	16	2	no	—
389	D₄	—	89	2	no	—
390	D₄	—	356	1	no	—
391	D₄	—	356	2	no	—
392	D₄	—	356	2	no	—
393	D₄	—	1424	2	no	—
394	D₄	—	178	2	no	—
395	D₄	—	178	1	no	—
396	D₄	—	712	2	no	—
397	D₄	—	712	2	no	—
398	D₄	—	712	2	no	—
399	D₄	—	712	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	356	1	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	712	2	no	—
405	C₂×C₄	—	712	2	no	—
406	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
407	C₈	—	4	1	no	—
408	C₈	—	356	1	no	—
409	C₈	—	178	2	no	—
410	C₈	D₈×D₈₉	1	1	yes	characteristic
411	C₈	D₈×D₈₉	1	1	yes	characteristic
412	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
413	C₈	#15668058	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	2848	2	no	—
418	C₂²	—	2848	2	no	—
419	C₂²	—	356	1	no	—
420	C₂²	—	1424	2	no	—
421	C₂²	—	178	2	no	—
422	C₂²	—	712	2	no	—
423	C₂²	#19152402	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	356	1	no	—
427	C₄	—	178	2	no	—
428	C₄	#19152232	1	1	yes	characteristic
429	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	8	1	no	—
432	C₂	—	16	2	no	—
433	C₂	—	356	2	no	—
434	C₂	—	1424	2	no	—
435	C₂	—	712	1	no	—
436	C₂	#26031924	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26031924
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2213	C₂
socle	C₂×C₈₉	D₄×D₈
hypercenter	#2213	D₈₉
hypocenter	C₈₉	#33858
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2213

Complements

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

N	H ≅ G/N	type
1. #26033392	C₂	semidirect
2. #26032052	C₂	semidirect
3. #26032051	C₂	semidirect
4. #26022501	C₂	semidirect
5. #26022371	C₂	semidirect
6. #26022329	C₂	semidirect
7. #26022212	C₂	semidirect
8. #26022206	C₂	semidirect
9. #26022131	C₂	semidirect
10. #26022088	C₂	semidirect
11. C₈₉×#2213	C₂	semidirect
13. #19152400	C₂²	semidirect
15. #19152399	C₂²	semidirect
16. #19152036	C₂²	semidirect
21. C₂×#15667953	C₂²	semidirect
22. C₂×#15667953	C₂²	semidirect
24. #19152016	C₂²	semidirect
25. #19151975	C₂²	semidirect
26. #19151869	C₂²	semidirect
29. #19151865	C₂²	semidirect
33. #19151716	C₂²	semidirect
34. #19151427	C₂²	semidirect
35. #19151412	C₂²	semidirect
36. #19151405	C₂²	semidirect
37. #19151404	C₂²	semidirect
38. #19151383	C₂²	semidirect
39. C₄×#13083549	C₂²	semidirect
40. #509×C₈₉	C₂²	semidirect
41. #493×C₈₉	C₂²	semidirect
42. #443×C₈₉	C₂²	semidirect
43. #364×C₈₉	C₂²	semidirect
44. #361×C₈₉	C₂²	semidirect
70. #15667958	D₄	semidirect
72. #15667956	D₄	semidirect
73. #15667955	D₄	semidirect
78. #15667953	D₄	semidirect
225. #2213	D₈₉	semidirect
230. C₈₉	#33858	semidirect
238. #509	C₂×D₈₉	semidirect
246. #493	C₂×D₈₉	semidirect
255. #443	C₂×D₈₉	semidirect
257. #364	C₂×D₈₉	semidirect
259. #361	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033392	2
#26032052	2
#26032051	2
#26022501	2
#26022371	2
#26022329	2
#26022212	2
#26022206	2
#26022131	2
#26022088	2
C₈₉×#2213	2
#33858	89