Subgroups — #26029881

Order 11392.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668044	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152111	C₂	1	1	yes	maximal, characteristic
4	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151854	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151846	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151838	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151836	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151830	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151828	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151637	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151605	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151598	C₂	1	1	yes	maximal, characteristic, complemented
15	#470×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668044	—	2	4	no	—
20	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083558	C₂²	1	1	yes	characteristic
24	C₂×#13083557	C₂²	1	1	yes	characteristic
25	C₂×#13083557	C₂²	1	1	yes	characteristic
26	M₁₆×D₈₉	—	2	4	no	—
27	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
29	#15667997	—	2	1	no	—
30	#15667992	C₂²	1	1	yes	characteristic
31	#15667991	C₂²	1	1	yes	characteristic
32	#15667990	—	2	1	no	—
33	#15667989	—	2	1	no	—
34	#15667988	C₂²	1	1	yes	characteristic
35	#15667988	C₂²	1	1	yes	characteristic
36	#15667987	C₂²	1	1	yes	characteristic
37	#15667986	C₂²	1	1	yes	characteristic
38	#15667982	—	2	1	no	—
39	#15667974	—	2	1	no	—
40	#15667972	—	2	1	no	—
41	#15667970	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₈₉	—	2	1	no	—
43	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×D₈₉	—	2	1	no	—
45	#15667946	C₂²	1	1	yes	characteristic, complemented
46	#15667945	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	#15667936	C₂²	1	1	yes	characteristic, complemented
51	#15667935	C₂²	1	1	yes	characteristic, complemented
52	#15667934	C₂²	1	1	yes	characteristic, complemented
53	#15667932	C₂²	1	1	yes	characteristic, complemented
54	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
58	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	D₄	1	1	yes	characteristic
62	#13083575	—	2	2	no	—
63	#13083575	—	2	2	no	—
64	C₂×Dic₁₇₈	—	2	1	no	—
65	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	Q₈×D₈₉	—	2	2	no	—
67	Q₈×D₈₉	—	2	2	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
73	C₂×C₄×D₈₉	—	2	2	no	—
74	C₂×C₄×D₈₉	—	2	2	no	—
75	C₂×C₄×D₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	2	1	no	—
77	C₂×C₄×D₈₉	—	2	1	no	—
78	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
80	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
82	#13083564	—	2	2	no	—
83	#13083563	—	2	2	no	—
84	#13083561	—	2	2	no	—
85	#13083558	—	2	2	no	—
86	#13083557	—	2	2	no	—
87	#13083557	D₄	1	4	yes	complemented
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	—	2	2	no	—
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	#13083553	—	2	1	no	—
98	#13083553	—	2	1	no	—
99	C₂²⋊Dic₈₉	—	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	#13083551	—	2	1	no	—
106	C₄×Dic₈₉	—	2	1	no	—
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	Q₁₆×C₈₉	—	2	2	no	—
111	M₁₆×C₈₉	—	2	2	no	—
112	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₈₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₈₉	—	2	2	no	—
122	C₂²×D₈₉	—	2	2	no	—
123	C₂²×D₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	4	1	no	—
125	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₈₉	—	2	1	no	—
128	Q₈×C₈₉	—	2	1	no	—
129	Q₈×C₈₉	—	2	1	no	—
130	Q₈×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	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	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂²⋊D₈₉	—	4	2	no	—
140	C₂×Dic₈₉	—	2	2	no	—
141	C₂×Dic₈₉	—	2	1	no	—
142	C₂×Dic₈₉	—	2	1	no	—
143	C₂×Dic₈₉	—	2	1	no	—
144	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
146	D₃₅₆	—	2	1	no	—
147	D₃₅₆	—	2	1	no	—
148	D₃₅₆	—	4	2	no	—
149	D₃₅₆	—	4	2	no	—
150	C₄×D₈₉	—	2	2	no	—
151	C₄×D₈₉	—	2	1	no	—
152	C₄×D₈₉	—	2	1	no	—
153	C₄×D₈₉	—	2	2	no	—
154	C₄×D₈₉	—	4	2	no	—
155	C₄×D₈₉	—	4	2	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	1	no	—
160	Dic₁₇₈	—	2	1	no	—
161	Dic₁₇₈	—	4	2	no	—
162	C₈×C₈₉	—	2	1	no	—
163	C₈×C₈₉	C₂×D₄	1	2	yes	—
164	#10623494	—	2	1	no	—
165	#10623494	C₂×D₄	1	2	yes	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×D₈₉	—	2	1	no	—
171	C₂×D₈₉	—	2	1	no	—
172	C₂×D₈₉	—	2	1	no	—
173	C₂×D₈₉	—	2	1	no	—
174	C₂×D₈₉	—	4	4	no	—
175	C₂×D₈₉	—	4	1	no	—
176	C₂×D₈₉	—	4	1	no	—
177	C₂×D₈₉	—	4	1	no	—
178	C₂×D₈₉	#121	1	2	yes	—
179	C₂×D₈₉	#137	1	2	yes	complemented
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	4	1	no	—
182	C₄×C₈₉	—	4	1	no	—
183	C₄×C₈₉	—	4	1	no	—
184	C₄×C₈₉	—	4	1	no	—
185	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	Dic₈₉	—	2	1	no	—
188	Dic₈₉	—	4	1	no	—
189	Dic₈₉	—	4	1	no	—
190	Dic₈₉	—	4	1	no	—
191	Dic₈₉	#121	1	2	yes	—
192	C₂×C₈₉	—	4	1	no	—
193	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
195	C₂×C₈₉	#575	1	1	yes	characteristic
196	D₈₉	—	2	2	no	—
197	D₈₉	—	2	2	no	—
198	D₈₉	—	8	1	no	—
199	#3056	—	89	1	no	maximal, Sylow
200	C₈₉	#3056	1	1	yes	characteristic, complemented, Sylow
201	C₂×#137	—	89	1	no	—
202	C₂²×M₁₆	—	89	1	no	—
203	#525	—	89	1	no	—
204	C₂×C₂²⋊Q₈	—	89	1	no	—
205	#470	—	89	1	no	—
206	#470	D₈₉	1	1	yes	characteristic, complemented
207	#468	—	89	1	no	—
208	#468	—	89	1	no	—
209	#467	—	89	1	no	—
210	#467	—	89	1	no	—
211	#465	—	89	1	no	—
212	#465	—	89	1	no	—
213	#428	—	89	1	no	—
214	#419	—	89	1	no	—
215	#417	—	89	1	no	—
216	C₂×#41	—	89	1	no	—
217	C₂²×Q₈	—	89	1	no	—
218	C₂³×C₄	—	89	1	no	—
219	#137	—	178	4	no	—
220	C₂×Q₁₆	—	89	1	no	—
221	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	—	89	1	no	—
223	C₂×SD₁₆	—	89	1	no	—
224	C₂×M₁₆	—	89	1	no	—
225	C₂×M₁₆	—	89	1	no	—
226	C₂×M₁₆	—	89	1	no	—
227	C₂×M₁₆	—	178	4	no	—
228	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic
229	C₂²×C₈	—	89	1	no	—
230	C₂²×C₈	—	89	1	no	—
231	#123	—	178	1	no	—
232	C₂²⋊Q₈	—	89	1	no	—
233	C₂²⋊Q₈	—	89	1	no	—
234	C₂²⋊Q₈	—	89	1	no	—
235	C₂²⋊Q₈	—	89	1	no	—
236	C₂²⋊Q₈	—	178	1	no	—
237	C₂²⋊Q₈	—	178	1	no	—
238	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
239	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
240	#121	—	89	1	no	—
241	#121	—	89	1	no	—
242	#120	—	178	1	no	—
243	C₄×D₄	—	178	1	no	—
244	C₄×D₄	—	178	1	no	—
245	#117	—	89	1	no	—
246	C₂×C₄⋊C₄	—	89	1	no	—
247	C₂×C₄⋊C₄	—	178	1	no	—
248	C₂×C₂²⋊C₄	—	178	1	no	—
249	#107	—	89	1	no	—
250	#107	—	89	1	no	—
251	#106	—	89	1	no	—
252	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
253	#103	—	89	1	no	—
254	#103	—	89	1	no	—
255	#103	—	89	1	no	—
256	#103	—	89	1	no	—
257	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
258	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
259	#102	—	89	1	no	—
260	#102	—	89	1	no	—
261	C₂⁴	—	89	1	no	—
262	#41	—	178	2	no	—
263	#41	—	178	2	no	—
264	C₂×Q₈	—	89	1	no	—
265	C₂×Q₈	—	178	1	no	—
266	C₂×Q₈	—	178	2	no	—
267	C₂×Q₈	—	178	2	no	—
268	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
269	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×D₄	—	89	1	no	—
271	C₂×D₄	—	178	1	no	—
272	C₂×D₄	—	178	1	no	—
273	C₂×D₄	—	178	1	no	—
274	C₂²×C₄	—	89	1	no	—
275	C₂²×C₄	—	89	1	no	—
276	C₂²×C₄	—	89	1	no	—
277	C₂²×C₄	—	89	1	no	—
278	C₂²×C₄	—	89	1	no	—
279	C₂²×C₄	—	178	1	no	—
280	C₂²×C₄	—	178	2	no	—
281	C₂²×C₄	—	178	2	no	—
282	C₂²×C₄	—	178	1	no	—
283	C₂²×C₄	—	178	1	no	—
284	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	178	2	no	—
287	SD₁₆	—	178	2	no	—
288	SD₁₆	—	178	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	89	4	no	—
291	M₁₆	—	178	2	no	—
292	M₁₆	—	178	2	no	—
293	C₂×C₈	—	89	1	no	—
294	C₂×C₈	—	89	1	no	—
295	C₂×C₈	—	178	2	no	—
296	C₂×C₈	—	178	2	no	—
297	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	89	1	no	—
302	C₄⋊C₄	—	89	1	no	—
303	C₄⋊C₄	—	178	1	no	—
304	C₄⋊C₄	—	178	1	no	—
305	C₄⋊C₄	—	178	1	no	—
306	C₄⋊C₄	—	178	1	no	—
307	C₄⋊C₄	—	178	1	no	—
308	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
309	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
310	C₂²⋊C₄	—	2	1	no	—
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	178	1	no	—
313	C₂²⋊C₄	—	178	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	C₄²	—	178	1	no	—
320	C₂³	—	89	1	no	—
321	C₂³	—	89	1	no	—
322	C₂³	—	356	1	no	—
323	C₂³	—	178	2	no	—
324	C₂³	—	178	2	no	—
325	C₂³	—	178	1	no	—
326	C₂³	D₄×D₈₉	1	1	yes	characteristic
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	356	2	no	—
332	Q₈	—	178	1	no	—
333	Q₈	—	178	1	no	—
334	D₄	—	356	2	no	—
335	D₄	—	356	2	no	—
336	D₄	—	356	2	no	—
337	D₄	—	178	1	no	—
338	D₄	—	178	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	89	1	no	—
346	C₂×C₄	—	89	2	no	—
347	C₂×C₄	—	89	2	no	—
348	C₂×C₄	—	89	1	no	—
349	C₂×C₄	—	356	2	no	—
350	C₂×C₄	—	356	2	no	—
351	C₂×C₄	—	356	2	no	—
352	C₂×C₄	—	178	2	no	—
353	C₂×C₄	—	178	2	no	—
354	C₂×C₄	—	178	2	no	—
355	C₂×C₄	—	178	1	no	—
356	C₂×C₄	—	178	1	no	—
357	C₂×C₄	—	178	1	no	—
358	C₂×C₄	—	178	1	no	—
359	C₂×C₄	—	178	1	no	—
360	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	89	2	no	—
364	C₈	—	178	1	no	—
365	C₈	D₄×D₈₉	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	89	2	no	—
370	C₂²	—	89	2	no	—
371	C₂²	—	356	4	no	—
372	C₂²	—	356	1	no	—
373	C₂²	—	356	1	no	—
374	C₂²	—	356	1	no	—
375	C₂²	—	178	1	no	—
376	C₂²	—	178	1	no	—
377	C₂²	—	178	1	no	—
378	C₂²	—	178	1	no	—
379	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	89	2	no	—
386	C₄	—	356	1	no	—
387	C₄	—	356	1	no	—
388	C₄	—	356	1	no	—
389	C₄	—	178	1	no	—
390	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
391	C₄	#41×D₈₉	1	1	yes	characteristic
392	C₂	—	4	1	no	—
393	C₂	—	178	2	no	—
394	C₂	—	178	2	no	—
395	C₂	—	712	1	no	—
396	C₂	#121×D₈₉	1	1	yes	characteristic
397	C₂	#137×D₈₉	1	1	yes	characteristic
398	C₂	#19152397	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#470×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#19152111	C₂
hypercenter	#470	D₈₉
hypocenter	C₈₉	#3056
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #470

Complements

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

N	H ≅ G/N	type
1. C₂×#15668044	C₂	semidirect
2. C₂×M₁₆×D₈₉	C₂	semidirect
4. C₂²⋊Q₈×D₈₉	C₂	semidirect
5. #19151854	C₂	semidirect
6. #19151846	C₂	semidirect
7. #19151844	C₂	semidirect
8. #19151838	C₂	semidirect
9. #19151836	C₂	semidirect
10. #19151830	C₂	semidirect
11. #19151828	C₂	semidirect
12. #19151637	C₂	semidirect
13. #19151605	C₂	semidirect
14. #19151598	C₂	semidirect
15. #470×C₈₉	C₂	semidirect
20. C₂×#13083564	C₂²	semidirect
21. C₂×#13083563	C₂²	semidirect
22. C₂×#13083561	C₂²	semidirect
45. #15667946	C₂²	semidirect
46. #15667945	C₂²	semidirect
47. #15667943	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667936	C₂²	semidirect
50. #15667936	C₂²	semidirect
51. #15667935	C₂²	semidirect
52. #15667934	C₂²	semidirect
53. #15667932	C₂²	semidirect
54. C₂×Q₁₆×C₈₉	C₂²	semidirect
58. #106×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
60. #103×C₈₉	C₂²	semidirect
87. #13083557	D₄	semidirect
179. C₂×D₈₉	#137	semidirect
200. C₈₉	#3056	semidirect
206. #470	D₈₉	semidirect
221. C₂×Q₁₆	C₂×D₈₉	semidirect
252. #106	C₂×D₈₉	semidirect
257. #103	C₂×D₈₉	semidirect
258. #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×#15668044	2
C₂×M₁₆×D₈₉	2
#19152111	2
C₂²⋊Q₈×D₈₉	2
#19151854	2
#19151846	2
#19151844	2
#19151838	2
#19151836	2
#19151830	2
#19151828	2
#19151637	2
#19151605	2
#19151598	2
#470×C₈₉	2
#3056	89