Subgroups — #36709166

Order 22784.

524 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	#26030761	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022427	C₂	1	2	yes	maximal, complemented
4	#26022426	C₂	1	2	yes	maximal, complemented
5	#26022424	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022423	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022420	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022023	C₂	1	2	yes	maximal, complemented
9	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021986	C₂	1	2	yes	maximal
11	C₈₉×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₂²	1	1	yes	characteristic
13	#131×D₈₉	—	2	1	no	—
14	#19152153	—	2	1	no	—
15	M₃₂×D₈₉	C₂²	1	2	yes	—
16	#19152001	—	2	1	no	—
17	#19151998	—	2	1	no	—
18	#19151998	C₂²	1	2	yes	complemented
19	#19151996	C₂²	1	1	yes	characteristic, complemented
20	#19151716	C₂²	1	1	yes	characteristic
21	#19151715	C₂²	1	1	yes	characteristic
22	#19151714	C₂²	1	1	yes	characteristic
23	#19151713	—	2	1	no	—
24	#19151712	—	2	1	no	—
25	#108×D₈₉	C₂²	1	1	yes	characteristic
26	#19151633	—	2	1	no	—
27	#19151633	C₂²	1	2	yes	—
28	#104×D₈₉	—	2	1	no	—
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	#19151422	C₂²	1	2	yes	complemented
31	#19151421	C₂²	1	2	yes	complemented
32	#19151420	C₂²	1	2	yes	complemented
33	#19151419	C₂²	1	1	yes	characteristic, complemented
34	#19151418	C₂²	1	2	yes	complemented
35	#19151409	C₂²	1	2	yes	—
36	#19151408	C₂²	1	2	yes	—
37	#19151407	C₂²	1	2	yes	—
38	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#443×C₈₉	C₂²	1	1	yes	characteristic
40	#365×C₈₉	C₂²	1	2	yes	complemented
41	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#360×C₈₉	C₂²	1	2	yes	—
43	#41×D₈₉	—	2	1	no	—
44	#15668035	Q₈	1	1	yes	characteristic, complemented
45	#15668034	C₂³	1	1	yes	characteristic
46	#15668033	—	2	1	no	—
47	#15668032	—	2	1	no	—
48	#15668031	Q₈	1	1	yes	characteristic, complemented
49	Q₁₆×D₈₉	Q₈	1	1	yes	characteristic, complemented
50	SD₁₆×D₈₉	—	2	1	no	—
51	D₈×D₈₉	Q₈	1	1	yes	characteristic, complemented
52	#15668020	—	2	1	no	—
53	#15668020	—	4	1	no	—
54	#15668019	—	2	1	no	—
55	#15668018	—	2	1	no	—
56	#15668018	—	4	1	no	—
57	M₁₆×D₈₉	—	2	1	no	—
58	M₁₆×D₈₉	—	4	1	no	—
59	C₂×C₈×D₈₉	—	4	1	no	—
60	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
61	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
62	#15668012	—	2	1	no	—
63	#15668003	—	2	2	no	—
64	#15667992	—	4	1	no	—
65	#15667988	—	4	1	no	—
66	Q₈×Dic₈₉	—	4	1	no	—
67	#15667977	—	4	1	no	—
68	#15667970	—	2	2	no	—
69	C₄²×D₈₉	D₄	1	1	yes	characteristic
70	#15667952	C₂³	1	2	yes	—
71	#15667951	—	2	2	no	—
72	C₁₆×D₈₉	—	2	2	no	—
73	#15667948	C₂³	1	1	yes	characteristic
74	#15667947	—	2	1	no	—
75	#15667945	—	2	2	no	—
76	#15667945	—	2	2	no	—
77	#15667944	—	2	1	no	—
78	#15667944	C₂³	1	2	yes	—
79	#15667940	—	2	1	no	—
80	#15667939	—	2	1	no	—
81	#15667938	—	2	1	no	—
82	C₄×#10623494	D₄	1	1	yes	characteristic
83	C₈×Dic₈₉	D₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
85	#135×C₈₉	C₂³	1	1	yes	characteristic
86	#131×C₈₉	—	2	1	no	—
87	C₄⋊Q₈×C₈₉	—	2	1	no	—
88	M₃₂×C₈₉	C₂³	1	2	yes	—
89	#108×C₈₉	C₂³	1	1	yes	characteristic
90	#106×C₈₉	—	2	1	no	—
91	#106×C₈₉	C₂³	1	2	yes	—
92	#104×C₈₉	—	2	1	no	—
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#13083575	—	2	1	no	—
95	#13083574	—	2	1	no	—
96	#13083574	—	4	1	no	—
97	#13083573	—	2	1	no	—
98	#13083573	—	4	1	no	—
99	C₂×Dic₁₇₈	—	4	1	no	—
100	Q₈×D₈₉	—	2	1	no	—
101	D₄×D₈₉	—	2	1	no	—
102	D₄×D₈₉	—	4	1	no	—
103	C₂×C₄×D₈₉	—	2	1	no	—
104	C₂×C₄×D₈₉	—	4	1	no	—
105	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
106	Dic₃₅₆	C₂×Q₈	1	1	yes	characteristic
107	#13083564	—	2	1	no	—
108	#13083563	—	2	1	no	—
109	#13083562	—	2	1	no	—
110	#13083561	—	2	1	no	—
111	D₇₁₂	C₂×Q₈	1	1	yes	characteristic
112	#13083559	—	2	1	no	—
113	#13083558	—	2	1	no	—
114	#13083558	—	4	1	no	—
115	#13083557	—	4	1	no	—
116	#13083557	—	4	1	no	—
117	#13083557	—	4	1	no	—
118	C₂×#10623494	—	4	1	no	—
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₈×D₈₉	—	4	1	no	—
122	C₈×D₈₉	—	4	1	no	—
123	C₈×D₈₉	—	4	1	no	—
124	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
125	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
126	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
127	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
128	C₈×D₈₉	C₂×Q₈	1	1	yes	characteristic
129	C₈×D₈₉	C₂×Q₈	1	1	yes	characteristic
130	C₈×D₈₉	#41	1	1	yes	characteristic
131	C₈×D₈₉	#41	1	1	yes	characteristic
132	C₄⋊Dic₈₉	—	2	2	no	—
133	C₄⋊Dic₈₉	—	4	2	no	—
134	C₄⋊Dic₈₉	—	4	1	no	—
135	#13083553	—	4	2	no	—
136	#13083551	—	4	2	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	4	2	no	—
139	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
140	#13083549	—	2	2	no	—
141	#41×C₈₉	—	2	1	no	—
142	C₂×Q₈×C₈₉	—	4	1	no	—
143	Q₁₆×C₈₉	C₂×Q₈	1	1	yes	characteristic
144	SD₁₆×C₈₉	—	2	1	no	—
145	D₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
146	M₁₆×C₈₉	—	2	1	no	—
147	M₁₆×C₈₉	—	4	1	no	—
148	C₂×C₈×C₈₉	—	4	1	no	—
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	4	1	no	—
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₈₉	—	2	2	no	—
155	C₂²×D₈₉	—	4	1	no	—
156	C₂²×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	Q₈×C₈₉	—	2	1	no	—
158	Q₈×C₈₉	—	8	2	no	—
159	D₄×C₈₉	—	2	1	no	—
160	D₄×C₈₉	—	4	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
165	C₂²⋊D₈₉	—	4	1	no	—
166	C₂²⋊D₈₉	—	4	1	no	—
167	C₂²⋊D₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	4	1	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	D₃₅₆	—	2	1	no	—
173	D₃₅₆	—	4	1	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	1	no	—
176	C₄×D₈₉	—	4	1	no	—
177	C₄×D₈₉	—	4	1	no	—
178	C₄×D₈₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₄×D₈₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₄×D₈₉	C₂×SD₁₆	1	1	yes	characteristic
181	C₄×D₈₉	C₂×SD₁₆	1	1	yes	characteristic
182	Dic₁₇₈	—	2	1	no	—
183	Dic₁₇₈	—	4	1	no	—
184	Dic₁₇₈	—	8	2	no	—
185	C₈×C₈₉	—	4	1	no	—
186	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
187	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
188	C₈×C₈₉	C₂²×Q₈	1	1	yes	characteristic
189	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
190	#10623494	—	4	1	no	—
191	#10623494	C₂²⋊Q₈	1	1	yes	characteristic
192	#10623494	C₂²⋊Q₈	1	1	yes	characteristic
193	#10623494	C₂×SD₁₆	1	1	yes	characteristic
194	#10623494	C₂×SD₁₆	1	1	yes	characteristic
195	C₂²×C₈₉	—	4	1	no	—
196	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	4	1	no	—
199	C₂×D₈₉	—	8	2	no	—
200	C₂×D₈₉	#476	1	1	yes	characteristic
201	C₂×D₈₉	#476	1	1	yes	characteristic
202	C₄×C₈₉	—	2	2	no	—
203	C₄×C₈₉	—	4	1	no	—
204	C₄×C₈₉	—	8	2	no	—
205	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
207	Dic₈₉	—	4	1	no	—
208	Dic₈₉	—	4	1	no	—
209	Dic₈₉	—	8	2	no	—
210	Dic₈₉	#476	1	1	yes	characteristic
211	Dic₈₉	#476	1	1	yes	characteristic
212	#33637	—	89	1	no	maximal, Sylow
213	C₂×C₈₉	—	2	1	no	—
214	C₂×C₈₉	—	8	1	no	—
215	C₂×C₈₉	C₂×#476	1	1	yes	characteristic
216	D₈₉	—	2	1	no	—
217	D₈₉	—	2	1	no	—
218	D₈₉	—	8	1	no	—
219	#3160	—	89	1	no	—
220	C₂×#443	—	89	1	no	—
221	#2231	—	89	2	no	—
222	#2231	—	89	2	no	—
223	#2230	—	89	1	no	—
224	#2230	—	89	1	no	—
225	#2230	—	89	1	no	—
226	#2230	D₈₉	1	1	yes	characteristic, complemented
227	#2155	—	89	2	no	—
228	C₂×#364	—	89	1	no	—
229	#2145	—	89	2	no	—
230	C₈₉	#33637	1	1	yes	characteristic, complemented, Sylow
231	C₂×#135	—	89	1	no	—
232	C₂×#131	—	178	1	no	—
233	#533	—	178	1	no	—
234	C₂×M₃₂	—	89	2	no	—
235	#500	—	178	1	no	—
236	#499	—	89	2	no	—
237	#499	—	178	1	no	—
238	#498	—	89	1	no	—
239	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
240	#443	—	89	1	no	—
241	#443	—	89	1	no	—
242	#443	—	89	1	no	—
243	#443	—	178	1	no	—
244	#443	—	178	1	no	—
245	#443	C₂×D₈₉	1	1	yes	characteristic
246	C₂×#108	—	89	1	no	—
247	#427	—	89	2	no	—
248	#427	—	178	1	no	—
249	C₂×#104	—	178	1	no	—
250	C₂×C₄×C₈	—	89	1	no	—
251	#365	—	89	2	no	—
252	#365	—	89	2	no	—
253	#365	—	89	2	no	—
254	#365	C₂×D₈₉	1	2	yes	complemented
255	#364	—	89	2	no	—
256	#364	—	89	1	no	—
257	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
258	#360	—	89	2	no	—
259	#360	—	89	2	no	—
260	#360	—	89	2	no	—
261	#360	C₂×D₈₉	1	2	yes	—
262	C₂×#41	—	178	1	no	—
263	#135	—	89	1	no	—
264	#135	—	89	1	no	—
265	#135	—	89	1	no	—
266	#135	—	178	1	no	—
267	#135	—	178	1	no	—
268	#135	C₂²×D₈₉	1	1	yes	characteristic
269	C₂×Q₁₆	—	89	1	no	—
270	C₂×SD₁₆	—	178	1	no	—
271	C₂×D₈	—	89	1	no	—
272	#131	—	2	1	no	—
273	#131	—	356	1	no	—
274	#131	—	356	1	no	—
275	#131	—	178	1	no	—
276	#131	—	178	1	no	—
277	#131	—	178	1	no	—
278	C₂×M₁₆	—	356	1	no	—
279	C₂×M₁₆	—	178	1	no	—
280	C₂²×C₈	—	89	1	no	—
281	C₂²×C₈	—	89	1	no	—
282	C₂²×C₈	—	356	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	178	1	no	—
285	#125	—	178	2	no	—
286	C₂²⋊Q₈	—	356	1	no	—
287	C₂²⋊Q₈	—	356	1	no	—
288	C₄×Q₈	—	356	1	no	—
289	C₄×Q₈	—	356	1	no	—
290	#117	—	178	2	no	—
291	C₂×C₄²	—	89	1	no	—
292	M₃₂	—	89	2	no	—
293	M₃₂	—	178	2	no	—
294	M₃₂	C₂²×D₈₉	1	2	yes	—
295	C₂×C₁₆	—	178	2	no	—
296	#108	—	89	1	no	—
297	#108	—	178	1	no	—
298	#108	C₂²×D₈₉	1	1	yes	characteristic
299	#107	—	178	2	no	—
300	#107	—	178	2	no	—
301	#106	—	2	1	no	—
302	#106	—	89	2	no	—
303	#106	—	178	1	no	—
304	#106	C₂²×D₈₉	1	2	yes	—
305	#104	—	2	1	no	—
306	#104	—	178	1	no	—
307	#104	—	178	1	no	—
308	#104	—	178	1	no	—
309	C₄×C₈	—	89	1	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	#41	—	2	1	no	—
314	#41	—	356	1	no	—
315	#41	—	356	1	no	—
316	#41	—	178	1	no	—
317	#41	—	178	1	no	—
318	#41	—	178	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	356	1	no	—
321	C₂×Q₈	—	178	1	no	—
322	C₂×D₄	—	356	1	no	—
323	C₂×D₄	—	178	1	no	—
324	C₂²×C₄	—	89	1	no	—
325	C₂²×C₄	—	356	1	no	—
326	C₂²×C₄	—	178	1	no	—
327	Q₁₆	—	89	1	no	—
328	Q₁₆	—	178	1	no	—
329	Q₁₆	Q₈×D₈₉	1	1	yes	characteristic
330	SD₁₆	—	2	1	no	—
331	SD₁₆	—	178	1	no	—
332	SD₁₆	—	178	1	no	—
333	SD₁₆	—	178	1	no	—
334	D₈	—	89	1	no	—
335	D₈	—	178	1	no	—
336	D₈	Q₈×D₈₉	1	1	yes	characteristic
337	M₁₆	—	2	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	356	1	no	—
340	M₁₆	—	356	1	no	—
341	M₁₆	—	356	1	no	—
342	M₁₆	—	356	1	no	—
343	M₁₆	—	178	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	1	no	—
347	C₂×C₈	—	89	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	89	1	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	356	1	no	—
356	C₂×C₈	—	356	1	no	—
357	C₂×C₈	—	356	1	no	—
358	C₂×C₈	—	356	1	no	—
359	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	356	1	no	—
364	C₄⋊C₄	—	356	2	no	—
365	C₄⋊C₄	—	356	2	no	—
366	C₄⋊C₄	—	178	2	no	—
367	C₂²⋊C₄	—	356	2	no	—
368	C₄²	—	89	1	no	—
369	C₄²	—	356	2	no	—
370	C₄²	—	178	1	no	—
371	C₄²	D₄×D₈₉	1	1	yes	characteristic
372	C₁₆	—	2	2	no	—
373	C₁₆	—	178	2	no	—
374	C₂³	—	89	1	no	—
375	C₂³	—	356	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	356	1	no	—
379	Q₈	—	178	1	no	—
380	Q₈	—	712	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	356	1	no	—
384	D₄	—	356	1	no	—
385	D₄	—	356	1	no	—
386	D₄	—	356	1	no	—
387	D₄	—	178	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	89	1	no	—
392	C₂×C₄	—	89	1	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	356	1	no	—
398	C₂×C₄	—	356	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	2	no	—
402	C₂×C₄	—	178	1	no	—
403	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	89	1	no	—
406	C₈	—	89	1	no	—
407	C₈	—	89	1	no	—
408	C₈	—	89	1	no	—
409	C₈	—	356	1	no	—
410	C₈	SD₁₆×D₈₉	1	1	yes	characteristic
411	C₈	SD₁₆×D₈₉	1	1	yes	characteristic
412	C₈	C₂×Q₈×D₈₉	1	1	yes	characteristic
413	C₈	#41×D₈₉	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	89	1	no	—
416	C₂²	—	89	1	no	—
417	C₂²	—	356	1	no	—
418	C₂²	—	356	1	no	—
419	C₂²	—	712	2	no	—
420	C₂²	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	89	1	no	—
425	C₄	—	89	1	no	—
426	C₄	—	356	1	no	—
427	C₄	—	356	1	no	—
428	C₄	—	712	2	no	—
429	C₄	C₂²⋊Q₈×D₈₉	1	1	yes	characteristic
430	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	178	1	no	—
434	C₂	—	178	1	no	—
435	C₂	—	712	1	no	—
436	C₂	#476×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2230	C₂
socle	C₂×C₈₉	C₂×#476
prime radical	#135×D₈₉	C₂²
hypercenter	#2230	D₈₉
hypocenter	C₈₉	#33637
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #26030761	C₂	semidirect
3. #26022427	C₂	semidirect
4. #26022426	C₂	semidirect
5. #26022424	C₂	semidirect
6. #26022423	C₂	semidirect
7. #26022420	C₂	semidirect
8. #26022023	C₂	semidirect
9. #364×D₈₉	C₂	semidirect
11. C₈₉×#2230	C₂	semidirect
18. #19151998	C₂²	semidirect
19. #19151996	C₂²	semidirect
30. #19151422	C₂²	semidirect
31. #19151421	C₂²	semidirect
32. #19151420	C₂²	semidirect
33. #19151419	C₂²	semidirect
34. #19151418	C₂²	semidirect
38. #498×C₈₉	C₂²	semidirect
40. #365×C₈₉	C₂²	semidirect
41. #364×C₈₉	C₂²	semidirect
44. #15668035	Q₈	semidirect
48. #15668031	Q₈	semidirect
49. Q₁₆×D₈₉	Q₈	semidirect
51. D₈×D₈₉	Q₈	semidirect
226. #2230	D₈₉	semidirect
230. C₈₉	#33637	semidirect
239. #498	C₂×D₈₉	semidirect
254. #365	C₂×D₈₉	semidirect
257. #364	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030761	2
#443×D₈₉	2
#26022427	2
#26022426	2
#26022424	2
#26022423	2
#26022420	2
#26022023	2
#364×D₈₉	2
#26021986	2
C₈₉×#2230	2
#33637	89