Subgroups — #26029753

Order 11392.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668039	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152166	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152070	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151816	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151815	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151810	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151794	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151793	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151792	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151791	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151623	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151593	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668039	—	2	4	no	—
20	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
22	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083559	C₂²	1	1	yes	characteristic
24	C₂×#13083559	C₂²	1	1	yes	characteristic
25	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
26	D₈×D₈₉	—	2	4	no	—
27	C₂×#13083557	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
29	#15668009	C₂²	1	1	yes	characteristic, complemented
30	#15668008	C₂²	1	1	yes	characteristic, complemented
31	#15668001	C₂²	1	1	yes	characteristic, complemented
32	#15667985	—	2	1	no	—
33	#15667985	—	2	1	no	—
34	#15667982	—	2	1	no	—
35	#15667982	—	2	1	no	—
36	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
37	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
38	#15667974	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊D₈₉	—	2	1	no	—
40	#15667972	—	2	1	no	—
41	#15667970	C₂²	1	1	yes	characteristic
42	#15667969	C₂²	1	1	yes	characteristic
43	C₂×#13083551	—	2	1	no	—
44	C₂²⋊C₄×D₈₉	—	2	1	no	—
45	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
46	#15667941	C₂²	1	1	yes	characteristic, complemented
47	#15667941	C₂²	1	1	yes	characteristic, complemented
48	#15667936	C₂²	1	1	yes	characteristic, complemented
49	#15667934	C₂²	1	1	yes	characteristic, complemented
50	#15667934	C₂²	1	1	yes	characteristic, complemented
51	#15667933	C₂²	1	1	yes	characteristic, complemented
52	#15667932	C₂²	1	1	yes	characteristic, complemented
53	#15667932	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
56	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	#13083575	—	2	2	no	—
64	#13083575	—	2	2	no	—
65	C₂×D₃₅₆	—	2	1	no	—
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
70	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	2	1	no	—
73	C₂×C₂²⋊D₈₉	—	2	1	no	—
74	C₂×C₂²⋊D₈₉	—	2	1	no	—
75	D₄×D₈₉	—	2	2	no	—
76	D₄×D₈₉	—	2	2	no	—
77	D₄×D₈₉	—	2	2	no	—
78	D₄×D₈₉	D₄	1	4	yes	complemented
79	C₂²×Dic₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	—	2	1	no	—
82	C₂×C₄×D₈₉	—	2	1	no	—
83	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
84	#13083561	—	2	2	no	—
85	D₇₁₂	—	2	2	no	—
86	D₇₁₂	—	2	2	no	—
87	#13083559	—	2	2	no	—
88	#13083559	—	2	2	no	—
89	#13083559	—	2	2	no	—
90	#13083557	—	2	2	no	—
91	C₂×#10623494	C₂³	1	1	yes	characteristic
92	C₂×#10623494	C₂³	1	1	yes	characteristic
93	C₈×D₈₉	—	2	2	no	—
94	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
95	#13083553	D₄	1	1	yes	characteristic
96	#13083553	D₄	1	1	yes	characteristic
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	#13083551	—	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	D₄	1	1	yes	characteristic
104	#13083551	D₄	1	1	yes	characteristic
105	C₄×Dic₈₉	—	2	1	no	—
106	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	SD₁₆×C₈₉	—	2	2	no	—
112	D₈×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	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂²×D₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	2	4	no	—
124	C₂²×D₈₉	—	2	1	no	—
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	4	2	no	—
127	C₂²×D₈₉	—	8	1	no	—
128	C₂²×D₈₉	—	8	1	no	—
129	C₂²×D₈₉	—	8	1	no	—
130	C₂²×D₈₉	—	8	1	no	—
131	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₈₉	—	2	1	no	—
133	Q₈×C₈₉	—	2	1	no	—
134	D₄×C₈₉	—	2	1	no	—
135	D₄×C₈₉	—	2	1	no	—
136	D₄×C₈₉	—	2	1	no	—
137	D₄×C₈₉	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	8	1	no	—
141	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₈₉	—	2	4	no	—
145	C₂²⋊D₈₉	—	4	2	no	—
146	C₂²⋊D₈₉	—	8	1	no	—
147	C₂²⋊D₈₉	—	8	1	no	—
148	C₂×Dic₈₉	—	2	1	no	—
149	C₂×Dic₈₉	—	8	1	no	—
150	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
153	D₃₅₆	—	2	1	no	—
154	D₃₅₆	—	2	1	no	—
155	D₃₅₆	—	2	1	no	—
156	D₃₅₆	—	2	1	no	—
157	D₃₅₆	—	2	1	no	—
158	D₃₅₆	—	4	2	no	—
159	D₃₅₆	—	8	1	no	—
160	D₃₅₆	—	8	1	no	—
161	D₃₅₆	C₂×D₄	1	2	yes	—
162	C₄×D₈₉	—	4	2	no	—
163	C₄×D₈₉	—	8	1	no	—
164	C₄×D₈₉	—	8	1	no	—
165	C₄×D₈₉	C₂×D₄	1	2	yes	—
166	C₄×D₈₉	#41	1	2	yes	—
167	C₈×C₈₉	—	2	1	no	—
168	C₈×C₈₉	—	2	1	no	—
169	#10623494	—	2	1	no	—
170	#10623494	—	2	1	no	—
171	C₂²×C₈₉	—	2	2	no	—
172	C₂²×C₈₉	—	4	1	no	—
173	C₂²×C₈₉	—	4	1	no	—
174	C₂²×C₈₉	—	4	1	no	—
175	C₂²×C₈₉	—	4	1	no	—
176	C₂²×C₈₉	—	4	1	no	—
177	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₈₉	—	2	1	no	—
179	C₂×D₈₉	—	2	1	no	—
180	C₂×D₈₉	—	2	2	no	—
181	C₂×D₈₉	—	4	1	no	—
182	C₂×D₈₉	—	4	1	no	—
183	C₂×D₈₉	—	4	1	no	—
184	C₂×D₈₉	—	4	1	no	—
185	C₂×D₈₉	—	4	1	no	—
186	C₂×D₈₉	—	4	1	no	—
187	C₂×D₈₉	—	4	1	no	—
188	C₂×D₈₉	—	4	1	no	—
189	C₂×D₈₉	—	8	4	no	—
190	C₂×D₈₉	—	8	4	no	—
191	C₂×D₈₉	#121	1	2	yes	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	4	1	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
198	Dic₈₉	—	2	1	no	—
199	Dic₈₉	—	2	1	no	—
200	Dic₈₉	—	4	1	no	—
201	Dic₈₉	#121	1	2	yes	—
202	C₂×C₈₉	—	4	2	no	—
203	C₂×C₈₉	—	8	1	no	—
204	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
205	C₂×C₈₉	#576	1	1	yes	characteristic
206	C₂×C₈₉	#576	1	1	yes	characteristic
207	D₈₉	—	2	2	no	—
208	D₈₉	—	4	2	no	—
209	D₈₉	—	8	1	no	—
210	D₈₉	—	8	1	no	—
211	#3041	—	89	1	no	maximal, Sylow
212	C₈₉	#3041	1	1	yes	characteristic, complemented, Sylow
213	C₂×AGL(1,ℤ/8)	—	89	1	no	—
214	C₂²×D₈	—	89	1	no	—
215	#535	—	89	1	no	—
216	#518	—	89	1	no	—
217	#463	—	89	1	no	—
218	#463	—	89	1	no	—
219	#463	—	89	1	no	—
220	#463	D₈₉	1	1	yes	characteristic, complemented
221	#459	—	89	1	no	—
222	#459	—	89	1	no	—
223	#459	—	89	1	no	—
224	#459	—	89	1	no	—
225	#424	—	89	1	no	—
226	#418	—	89	1	no	—
227	#416	—	89	1	no	—
228	C₂×#41	—	89	1	no	—
229	C₂²×D₄	—	89	1	no	—
230	C₂²×D₄	—	89	1	no	—
231	AGL(1,ℤ/8)	—	178	4	no	—
232	C₂×SD₁₆	—	89	1	no	—
233	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
234	C₂×D₈	—	89	1	no	—
235	C₂×D₈	—	89	1	no	—
236	C₂×D₈	—	89	1	no	—
237	C₂×D₈	—	89	1	no	—
238	C₂×D₈	—	89	1	no	—
239	C₂×D₈	—	178	4	no	—
240	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
241	C₂×M₁₆	—	89	1	no	—
242	C₂²×C₈	—	89	1	no	—
243	#127	—	89	1	no	—
244	#127	—	89	1	no	—
245	#124	—	89	1	no	—
246	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
247	#121	—	178	1	no	—
248	#121	—	178	1	no	—
249	#120	—	178	1	no	—
250	#120	—	178	1	no	—
251	C₄×D₄	—	89	1	no	—
252	C₄×D₄	—	89	1	no	—
253	C₄×D₄	—	89	1	no	—
254	C₄×D₄	—	178	1	no	—
255	C₄×D₄	—	178	1	no	—
256	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#117	—	89	1	no	—
258	#117	—	89	1	no	—
259	C₂×C₂²⋊C₄	—	178	1	no	—
260	C₂×C₂²⋊C₄	—	178	1	no	—
261	C₄⋊C₈	—	89	1	no	—
262	C₄⋊C₈	—	89	1	no	—
263	C₄⋊C₈	—	89	1	no	—
264	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
265	#103	—	89	1	no	—
266	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
267	#102	—	89	1	no	—
268	#102	—	89	1	no	—
269	#102	—	89	1	no	—
270	#102	—	89	1	no	—
271	#102	—	89	1	no	—
272	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
273	C₂⁴	—	178	1	no	—
274	C₂⁴	—	178	1	no	—
275	#41	—	178	2	no	—
276	#41	—	178	2	no	—
277	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×D₄	—	89	4	no	—
279	C₂×D₄	—	89	1	no	—
280	C₂×D₄	—	89	1	no	—
281	C₂×D₄	—	89	1	no	—
282	C₂×D₄	—	178	1	no	—
283	C₂×D₄	—	178	2	no	—
284	C₂×D₄	—	178	2	no	—
285	C₂×D₄	—	178	2	no	—
286	C₂×D₄	—	178	1	no	—
287	C₂×D₄	—	178	1	no	—
288	C₂×D₄	—	178	1	no	—
289	C₂×D₄	—	178	1	no	—
290	C₂×D₄	—	178	1	no	—
291	C₂×D₄	—	178	1	no	—
292	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
293	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	89	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	—	178	1	no	—
298	C₂²×C₄	—	178	1	no	—
299	C₂²×C₄	—	178	1	no	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	178	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	178	2	no	—
304	D₈	—	178	2	no	—
305	D₈	—	178	2	no	—
306	D₈	—	178	2	no	—
307	D₈	—	178	2	no	—
308	M₁₆	—	178	2	no	—
309	C₂×C₈	—	89	1	no	—
310	C₂×C₈	—	89	1	no	—
311	C₂×C₈	—	178	2	no	—
312	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄⋊C₄	—	89	1	no	—
315	C₄⋊C₄	—	89	1	no	—
316	C₄⋊C₄	—	89	1	no	—
317	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	89	1	no	—
322	C₂²⋊C₄	—	89	1	no	—
323	C₂²⋊C₄	—	178	1	no	—
324	C₂²⋊C₄	—	178	1	no	—
325	C₂²⋊C₄	—	178	1	no	—
326	C₂²⋊C₄	—	178	1	no	—
327	C₂²⋊C₄	—	178	1	no	—
328	C₂²⋊C₄	—	178	1	no	—
329	C₄²	—	89	1	no	—
330	C₄²	—	178	1	no	—
331	C₄²	C₂²×D₈₉	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	89	1	no	—
335	C₂³	—	356	2	no	—
336	C₂³	—	178	4	no	—
337	C₂³	—	178	1	no	—
338	C₂³	—	178	1	no	—
339	C₂³	—	178	1	no	—
340	C₂³	—	712	1	no	—
341	C₂³	—	712	1	no	—
342	C₂³	—	712	1	no	—
343	C₂³	—	712	1	no	—
344	Q₈	—	2	1	no	—
345	Q₈	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	89	2	no	—
350	D₄	—	356	2	no	—
351	D₄	—	356	2	no	—
352	D₄	—	178	4	no	—
353	D₄	—	178	1	no	—
354	D₄	—	178	1	no	—
355	D₄	—	178	1	no	—
356	D₄	—	178	1	no	—
357	D₄	—	178	1	no	—
358	D₄	—	712	1	no	—
359	D₄	—	712	1	no	—
360	D₄	—	712	1	no	—
361	D₄	—	712	1	no	—
362	D₄	D₄×D₈₉	1	2	yes	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	—	89	1	no	—
367	C₂×C₄	—	89	2	no	—
368	C₂×C₄	—	89	2	no	—
369	C₂×C₄	—	89	1	no	—
370	C₂×C₄	—	89	1	no	—
371	C₂×C₄	—	356	2	no	—
372	C₂×C₄	—	178	1	no	—
373	C₂×C₄	—	712	1	no	—
374	C₂×C₄	—	712	1	no	—
375	C₂×C₄	—	712	1	no	—
376	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
377	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	178	1	no	—
382	C₈	—	178	1	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	89	2	no	—
390	C₂²	—	356	1	no	—
391	C₂²	—	356	1	no	—
392	C₂²	—	356	1	no	—
393	C₂²	—	356	1	no	—
394	C₂²	—	356	1	no	—
395	C₂²	—	356	1	no	—
396	C₂²	—	356	1	no	—
397	C₂²	—	356	1	no	—
398	C₂²	—	178	2	no	—
399	C₂²	—	178	1	no	—
400	C₂²	—	178	1	no	—
401	C₂²	—	712	4	no	—
402	C₂²	—	712	4	no	—
403	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	89	2	no	—
409	C₄	—	356	1	no	—
410	C₄	—	178	1	no	—
411	C₄	—	178	1	no	—
412	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
413	C₄	#41×D₈₉	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	8	1	no	—
416	C₂	—	356	2	no	—
417	C₂	—	178	2	no	—
418	C₂	—	712	1	no	—
419	C₂	—	712	1	no	—
420	C₂	#121×D₈₉	1	1	yes	characteristic
421	C₂	#19152400	1	1	yes	characteristic
422	C₂	#19152402	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#463×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#463	D₈₉
hypocenter	C₈₉	#3041
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×#15668039	C₂	semidirect
2. C₂×D₈×D₈₉	C₂	semidirect
3. #19152166	C₂	semidirect
4. #19152070	C₂	semidirect
5. #19151816	C₂	semidirect
6. #19151815	C₂	semidirect
7. #19151810	C₂	semidirect
8. #19151794	C₂	semidirect
9. #19151793	C₂	semidirect
10. #19151792	C₂	semidirect
11. #19151791	C₂	semidirect
12. #19151623	C₂	semidirect
13. #19151601	C₂	semidirect
14. #19151593	C₂	semidirect
15. #463×C₈₉	C₂	semidirect
20. C₂×#13083561	C₂²	semidirect
22. C₂×D₇₁₂	C₂²	semidirect
25. C₂×#13083559	C₂²	semidirect
29. #15668009	C₂²	semidirect
30. #15668008	C₂²	semidirect
31. #15668001	C₂²	semidirect
36. C₄×D₃₅₆	C₂²	semidirect
37. D₄×Dic₈₉	C₂²	semidirect
38. #15667974	C₂²	semidirect
45. C₄⋊#10623494	C₂²	semidirect
46. #15667941	C₂²	semidirect
47. #15667941	C₂²	semidirect
48. #15667936	C₂²	semidirect
49. #15667934	C₂²	semidirect
50. #15667934	C₂²	semidirect
51. #15667933	C₂²	semidirect
52. #15667932	C₂²	semidirect
53. #15667932	C₂²	semidirect
54. C₂×SD₁₆×C₈₉	C₂²	semidirect
56. #124×C₈₉	C₂²	semidirect
57. C₄×D₄×C₈₉	C₂²	semidirect
58. C₄⋊C₈×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
60. #102×C₈₉	C₂²	semidirect
78. D₄×D₈₉	D₄	semidirect
212. C₈₉	#3041	semidirect
220. #463	D₈₉	semidirect
233. C₂×SD₁₆	C₂×D₈₉	semidirect
246. #124	C₂×D₈₉	semidirect
256. C₄×D₄	C₂×D₈₉	semidirect
264. C₄⋊C₈	C₂×D₈₉	semidirect
266. #103	C₂×D₈₉	semidirect
272. #102	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×#15668039	2
C₂×D₈×D₈₉	2
#19152166	2
#19152070	2
#19151816	2
#19151815	2
#19151810	2
#19151794	2
#19151793	2
#19151792	2
#19151791	2
#19151623	2
#19151601	2
#19151593	2
#463×C₈₉	2
#3041	89