Subgroups — #26029889

Order 11392.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668020	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152164	C₂	1	1	yes	maximal, characteristic
5	#19151845	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151841	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151830	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151829	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151826	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151825	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151635	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151605	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083574	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂×#13083563	C₂²	1	1	yes	characteristic
20	C₂×#13083562	C₂²	1	1	yes	characteristic
21	C₂×#13083561	C₂²	1	1	yes	characteristic
22	SD₁₆×D₈₉	—	2	4	no	—
23	#15668020	—	2	4	no	—
24	C₂×#13083557	C₂²	1	1	yes	characteristic
25	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#10623494	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
29	#15668011	—	2	1	no	—
30	#15668008	—	2	1	no	—
31	#15667998	—	2	1	no	—
32	#15667998	—	2	1	no	—
33	#15667997	—	2	1	no	—
34	#15667994	—	2	1	no	—
35	#15667992	C₂²	1	1	yes	characteristic, complemented
36	#15667991	C₂²	1	1	yes	characteristic, complemented
37	#15667988	C₂²	1	1	yes	characteristic, complemented
38	#15667987	C₂²	1	1	yes	characteristic
39	#15667986	C₂²	1	1	yes	characteristic
40	#15667983	C₂²	1	1	yes	characteristic
41	#15667982	—	2	1	no	—
42	#15667980	—	2	1	no	—
43	#15667970	C₂²	1	1	yes	characteristic
44	#15667970	C₂²	1	1	yes	characteristic
45	#15667946	C₂²	1	1	yes	characteristic, complemented
46	#15667943	C₂²	1	1	yes	characteristic, complemented
47	#15667943	C₂²	1	1	yes	characteristic, complemented
48	#15667937	C₂²	1	1	yes	characteristic, complemented
49	#15667936	C₂²	1	1	yes	characteristic, complemented
50	#15667935	C₂²	1	1	yes	characteristic, complemented
51	#15667934	C₂²	1	1	yes	characteristic
52	#15667933	C₂²	1	1	yes	characteristic
53	#15667932	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#121×C₈₉	C₂²	1	1	yes	characteristic
58	#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₉	C₂²	1	1	yes	characteristic
61	C₂³×D₈₉	—	2	1	no	—
62	#13083574	—	2	2	no	—
63	#13083574	—	2	2	no	—
64	C₂×Dic₁₇₈	—	2	1	no	—
65	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	Q₈×D₈₉	—	2	2	no	—
68	Q₈×D₈₉	—	2	2	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	D₄	1	1	yes	characteristic
71	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₈₉	—	2	1	no	—
73	C₂×C₂²⋊D₈₉	—	2	1	no	—
74	C₂×C₂²⋊D₈₉	—	2	1	no	—
75	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
77	D₄×D₈₉	—	2	2	no	—
78	D₄×D₈₉	—	2	2	no	—
79	C₂×C₄×D₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
82	#13083563	—	2	2	no	—
83	#13083562	—	2	2	no	—
84	#13083561	—	2	2	no	—
85	#13083557	—	2	2	no	—
86	#13083557	—	2	2	no	—
87	C₂×#10623494	—	2	2	no	—
88	C₂×#10623494	C₂³	1	1	yes	characteristic
89	C₂×#10623494	C₂³	1	1	yes	characteristic
90	C₈×D₈₉	—	2	2	no	—
91	C₈×D₈₉	D₄	1	4	yes	complemented
92	C₄⋊Dic₈₉	—	2	1	no	—
93	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
95	#13083553	—	2	1	no	—
96	#13083553	—	2	1	no	—
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	C₂²⋊Dic₈₉	—	2	1	no	—
99	#13083551	—	2	1	no	—
100	#13083551	—	2	1	no	—
101	#13083551	—	2	1	no	—
102	#13083551	—	2	1	no	—
103	#13083551	—	2	1	no	—
104	#13083551	—	2	1	no	—
105	C₄×Dic₈₉	—	2	1	no	—
106	C₄×Dic₈₉	—	2	1	no	—
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	SD₁₆×C₈₉	—	2	2	no	—
112	M₁₆×C₈₉	—	2	2	no	—
113	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×D₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	4	2	no	—
124	C₂²×D₈₉	—	8	1	no	—
125	C₂²×D₈₉	—	8	1	no	—
126	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₈₉	—	2	1	no	—
129	Q₈×C₈₉	—	2	1	no	—
130	D₄×C₈₉	—	2	1	no	—
131	D₄×C₈₉	—	2	1	no	—
132	D₄×C₈₉	—	8	1	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂²⋊D₈₉	—	2	2	no	—
141	C₂²⋊D₈₉	—	2	2	no	—
142	C₂²⋊D₈₉	—	4	2	no	—
143	C₂²⋊D₈₉	—	8	1	no	—
144	C₂²⋊D₈₉	—	8	1	no	—
145	C₂×Dic₈₉	—	2	1	no	—
146	C₂×Dic₈₉	—	2	1	no	—
147	C₂×Dic₈₉	—	2	1	no	—
148	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
150	D₃₅₆	—	2	2	no	—
151	D₃₅₆	—	2	1	no	—
152	D₃₅₆	—	2	1	no	—
153	D₃₅₆	—	8	1	no	—
154	C₄×D₈₉	—	2	1	no	—
155	C₄×D₈₉	—	2	1	no	—
156	C₄×D₈₉	—	4	2	no	—
157	C₄×D₈₉	C₂×D₄	1	2	yes	—
158	C₄×D₈₉	#41	1	2	yes	—
159	Dic₁₇₈	—	2	2	no	—
160	Dic₁₇₈	—	2	1	no	—
161	Dic₁₇₈	—	2	1	no	—
162	Dic₁₇₈	—	4	2	no	—
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	C₂×D₄	1	2	yes	—
165	#10623494	—	2	1	no	—
166	#10623494	C₂×D₄	1	2	yes	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	—	4	1	no	—
172	C₂²×C₈₉	—	4	1	no	—
173	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×D₈₉	—	2	1	no	—
175	C₂×D₈₉	—	2	1	no	—
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	2	1	no	—
178	C₂×D₈₉	—	2	1	no	—
179	C₂×D₈₉	—	4	1	no	—
180	C₂×D₈₉	—	4	1	no	—
181	C₂×D₈₉	—	4	1	no	—
182	C₂×D₈₉	—	8	4	no	—
183	C₂×D₈₉	#121	1	2	yes	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	4	1	no	—
186	C₄×C₈₉	—	4	1	no	—
187	C₄×C₈₉	—	4	1	no	—
188	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	Dic₈₉	—	2	1	no	—
191	Dic₈₉	—	4	1	no	—
192	Dic₈₉	—	4	1	no	—
193	Dic₈₉	—	4	1	no	—
194	Dic₈₉	#121	1	2	yes	—
195	C₂×C₈₉	—	4	1	no	—
196	C₂×C₈₉	—	8	1	no	—
197	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
198	C₂×C₈₉	#577	1	1	yes	characteristic
199	C₂×C₈₉	#577	1	1	yes	characteristic
200	D₈₉	—	2	2	no	—
201	D₈₉	—	4	1	no	—
202	D₈₉	—	8	1	no	—
203	#3057	—	89	1	no	maximal, Sylow
204	C₈₉	#3057	1	1	yes	characteristic, complemented, Sylow
205	C₂²×SD₁₆	—	89	1	no	—
206	C₂×#131	—	89	1	no	—
207	#536	—	89	1	no	—
208	#535	—	89	1	no	—
209	#468	—	89	1	no	—
210	#468	—	89	1	no	—
211	#468	—	89	1	no	—
212	#468	D₈₉	1	1	yes	characteristic, complemented
213	#465	—	89	1	no	—
214	#465	—	89	1	no	—
215	#465	—	89	1	no	—
216	#465	—	89	1	no	—
217	#427	—	89	1	no	—
218	#419	—	89	1	no	—
219	#418	—	89	1	no	—
220	C₂×#41	—	89	1	no	—
221	C₂²×Q₈	—	89	1	no	—
222	C₂²×D₄	—	89	1	no	—
223	C₂×SD₁₆	—	89	1	no	—
224	C₂×SD₁₆	—	89	1	no	—
225	C₂×SD₁₆	—	89	1	no	—
226	C₂×SD₁₆	—	178	4	no	—
227	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
228	#131	—	178	4	no	—
229	C₂×M₁₆	—	89	1	no	—
230	C₂×M₁₆	—	89	1	no	—
231	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
232	C₂²×C₈	—	89	1	no	—
233	C₂²×C₈	—	89	1	no	—
234	C₂²×C₈	—	89	1	no	—
235	C₄⋊Q₈	—	178	1	no	—
236	#127	—	178	1	no	—
237	#124	—	178	1	no	—
238	#124	—	178	1	no	—
239	#123	—	178	1	no	—
240	#123	—	178	1	no	—
241	C₂²⋊Q₈	—	89	1	no	—
242	C₂²⋊Q₈	—	89	1	no	—
243	C₂²⋊Q₈	—	89	1	no	—
244	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
245	#121	—	89	1	no	—
246	#121	—	89	1	no	—
247	#121	—	89	1	no	—
248	#121	C₂×D₈₉	1	1	yes	characteristic
249	#120	—	178	1	no	—
250	#120	—	178	1	no	—
251	#117	—	89	1	no	—
252	#117	—	89	1	no	—
253	#107	—	89	1	no	—
254	#107	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#106	—	89	1	no	—
256	#106	—	89	1	no	—
257	#103	—	89	1	no	—
258	#103	—	89	1	no	—
259	#103	—	89	1	no	—
260	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
261	#102	—	89	1	no	—
262	#102	—	89	1	no	—
263	#102	—	89	1	no	—
264	#102	C₂×D₈₉	1	1	yes	characteristic
265	C₂⁴	—	178	1	no	—
266	#41	—	178	2	no	—
267	#41	—	178	2	no	—
268	C₂×Q₈	—	89	1	no	—
269	C₂×Q₈	—	89	1	no	—
270	C₂×Q₈	—	178	1	no	—
271	C₂×Q₈	—	178	2	no	—
272	C₂×Q₈	—	178	2	no	—
273	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	89	1	no	—
276	C₂×D₄	—	89	1	no	—
277	C₂×D₄	—	89	1	no	—
278	C₂×D₄	—	89	1	no	—
279	C₂×D₄	—	178	1	no	—
280	C₂×D₄	—	178	2	no	—
281	C₂×D₄	—	178	2	no	—
282	C₂×D₄	—	178	1	no	—
283	C₂×D₄	—	178	1	no	—
284	C₂×D₄	—	178	1	no	—
285	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
286	C₂²×C₄	—	89	1	no	—
287	C₂²×C₄	—	89	1	no	—
288	C₂²×C₄	—	178	1	no	—
289	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
290	SD₁₆	—	2	2	no	—
291	SD₁₆	—	178	2	no	—
292	SD₁₆	—	178	2	no	—
293	SD₁₆	—	178	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	178	2	no	—
296	M₁₆	—	178	2	no	—
297	C₂×C₈	—	89	1	no	—
298	C₂×C₈	—	89	4	no	—
299	C₂×C₈	—	89	1	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	—	178	2	no	—
302	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	89	1	no	—
306	C₄⋊C₄	—	89	1	no	—
307	C₄⋊C₄	—	178	1	no	—
308	C₄⋊C₄	—	178	1	no	—
309	C₄⋊C₄	—	178	1	no	—
310	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
311	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	178	1	no	—
315	C₂²⋊C₄	—	178	1	no	—
316	C₂²⋊C₄	—	178	1	no	—
317	C₂²⋊C₄	—	178	1	no	—
318	C₂²⋊C₄	—	178	1	no	—
319	C₂²⋊C₄	—	178	1	no	—
320	C₂²⋊C₄	—	178	1	no	—
321	C₂²⋊C₄	—	178	1	no	—
322	C₄²	—	178	1	no	—
323	C₄²	—	178	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	89	1	no	—
326	C₂³	—	89	1	no	—
327	C₂³	—	356	2	no	—
328	C₂³	—	178	1	no	—
329	C₂³	—	712	1	no	—
330	C₂³	—	712	1	no	—
331	C₂³	D₄×D₈₉	1	1	yes	characteristic
332	Q₈	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	356	2	no	—
335	Q₈	—	178	2	no	—
336	Q₈	—	178	1	no	—
337	Q₈	—	178	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	8	1	no	—
341	D₄	—	356	2	no	—
342	D₄	—	178	2	no	—
343	D₄	—	178	2	no	—
344	D₄	—	178	2	no	—
345	D₄	—	178	1	no	—
346	D₄	—	178	1	no	—
347	D₄	—	712	1	no	—
348	D₄	—	712	1	no	—
349	D₄	—	712	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	89	1	no	—
356	C₂×C₄	—	89	2	no	—
357	C₂×C₄	—	89	2	no	—
358	C₂×C₄	—	89	1	no	—
359	C₂×C₄	—	356	2	no	—
360	C₂×C₄	—	178	1	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	89	2	no	—
369	C₈	—	178	1	no	—
370	C₈	D₄×D₈₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	89	2	no	—
378	C₂²	—	356	1	no	—
379	C₂²	—	356	1	no	—
380	C₂²	—	356	1	no	—
381	C₂²	—	178	1	no	—
382	C₂²	—	178	1	no	—
383	C₂²	—	178	1	no	—
384	C₂²	—	178	1	no	—
385	C₂²	—	178	1	no	—
386	C₂²	—	712	4	no	—
387	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	89	2	no	—
393	C₄	—	356	1	no	—
394	C₄	—	356	1	no	—
395	C₄	—	356	1	no	—
396	C₄	—	178	1	no	—
397	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
398	C₄	#41×D₈₉	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	8	1	no	—
401	C₂	—	356	1	no	—
402	C₂	—	178	2	no	—
403	C₂	—	712	1	no	—
404	C₂	#121×D₈₉	1	1	yes	characteristic
405	C₂	#19152407	1	1	yes	characteristic
406	C₂	#19152408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#468×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#19152164	C₂
hypercenter	#468	D₈₉
hypocenter	C₈₉	#3057
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₈₉	C₂	semidirect
2. C₂×#15668020	C₂	semidirect
3. #19152171	C₂	semidirect
5. #19151845	C₂	semidirect
6. #19151844	C₂	semidirect
7. #19151841	C₂	semidirect
8. #19151830	C₂	semidirect
9. #19151829	C₂	semidirect
10. #19151826	C₂	semidirect
11. #19151825	C₂	semidirect
12. #19151635	C₂	semidirect
13. #19151605	C₂	semidirect
14. #19151601	C₂	semidirect
15. #468×C₈₉	C₂	semidirect
25. C₂×#13083557	C₂²	semidirect
26. C₂²×#10623494	C₂²	semidirect
28. C₂×C₈×D₈₉	C₂²	semidirect
35. #15667992	C₂²	semidirect
36. #15667991	C₂²	semidirect
37. #15667988	C₂²	semidirect
45. #15667946	C₂²	semidirect
46. #15667943	C₂²	semidirect
47. #15667943	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667936	C₂²	semidirect
50. #15667935	C₂²	semidirect
55. C₂×M₁₆×C₈₉	C₂²	semidirect
56. C₂²⋊Q₈×C₈₉	C₂²	semidirect
58. #107×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
91. C₈×D₈₉	D₄	semidirect
204. C₈₉	#3057	semidirect
212. #468	D₈₉	semidirect
231. C₂×M₁₆	C₂×D₈₉	semidirect
244. C₂²⋊Q₈	C₂×D₈₉	semidirect
254. #107	C₂×D₈₉	semidirect
260. #103	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₈₉	2
C₂×#15668020	2
#19152171	2
#19152164	2
#19151845	2
#19151844	2
#19151841	2
#19151830	2
#19151829	2
#19151826	2
#19151825	2
#19151635	2
#19151605	2
#19151601	2
#468×C₈₉	2
#3057	89