Subgroups — #26032397

Order 11392.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152300	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151961	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151921	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151917	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151900	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151848	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151832	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151791	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151730	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151710	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151666	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15667933	C₂	1	1	yes	maximal, characteristic, complemented
15	#447×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₈₉	—	2	1	no	—
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#10623494	C₂²	1	1	yes	characteristic, complemented
21	#15668008	C₂²	1	1	yes	characteristic
22	#15668005	—	2	1	no	—
23	#15668003	C₂²	1	1	yes	characteristic, complemented
24	#15667996	—	2	1	no	—
25	#15667986	C₂²	1	1	yes	characteristic
26	#15667984	—	2	1	no	—
27	#15667984	—	2	1	no	—
28	#15667983	C₂²	1	1	yes	characteristic
29	#15667983	C₂²	1	1	yes	characteristic, complemented
30	#15667981	—	2	1	no	—
31	#15667980	—	2	1	no	—
32	D₄×Dic₈₉	—	2	1	no	—
33	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
34	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
36	#15667970	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
38	#15667945	C₂²	1	1	yes	characteristic, complemented
39	#15667944	C₂²	1	1	yes	characteristic, complemented
40	#15667944	C₂²	1	1	yes	characteristic, complemented
41	#15667941	C₂²	1	1	yes	characteristic, complemented
42	#15667934	C₂²	1	1	yes	characteristic, complemented
43	#15667934	C₂²	1	1	yes	characteristic, complemented
44	#15667933	C₂²	1	1	yes	characteristic
45	#15667933	C₂²	1	1	yes	characteristic
46	#15667933	C₂²	1	1	yes	characteristic, complemented
47	#15667933	C₂²	1	1	yes	characteristic, complemented
48	#15667933	C₂²	1	1	yes	characteristic, complemented
49	#15667932	C₂²	1	1	yes	characteristic, complemented
50	#15667924	C₂²	1	1	yes	characteristic, complemented
51	#15667922	C₂²	1	1	yes	characteristic, complemented
52	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#102×C₈₉	C₂²	1	1	yes	characteristic
57	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₈₉	—	2	1	no	—
60	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊D₈₉	—	2	1	no	—
62	C₂×C₂²⋊D₈₉	—	2	1	no	—
63	C₂×C₂²⋊D₈₉	—	2	1	no	—
64	C₂×C₂²⋊D₈₉	—	2	1	no	—
65	C₂×C₂²⋊D₈₉	—	2	1	no	—
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	C₂×C₂²⋊D₈₉	—	4	4	no	—
68	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
69	D₄×D₈₉	—	2	2	no	—
70	D₄×D₈₉	—	4	1	no	—
71	C₂²×Dic₈₉	—	2	1	no	—
72	C₂²×Dic₈₉	—	2	1	no	—
73	C₂²×Dic₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
75	#13083559	—	4	1	no	—
76	#13083557	—	4	1	no	—
77	C₂×#10623494	—	4	1	no	—
78	C₂×#10623494	C₂³	1	1	yes	characteristic
79	C₂×#10623494	C₂³	1	1	yes	characteristic
80	C₄⋊Dic₈₉	—	2	1	no	—
81	C₄⋊Dic₈₉	—	2	1	no	—
82	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
85	#13083553	—	2	1	no	—
86	#13083553	D₄	1	1	yes	characteristic
87	C₂²⋊Dic₈₉	—	2	1	no	—
88	C₂²⋊Dic₈₉	—	2	1	no	—
89	C₂²⋊Dic₈₉	—	2	1	no	—
90	C₂²⋊Dic₈₉	—	2	1	no	—
91	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
92	#13083551	—	2	1	no	—
93	#13083551	—	2	1	no	—
94	#13083551	D₄	1	1	yes	characteristic
95	C₄×Dic₈₉	—	2	1	no	—
96	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
97	C₂⁴×C₈₉	—	2	1	no	—
98	C₂×D₄×C₈₉	—	2	2	no	—
99	C₂×D₄×C₈₉	—	2	1	no	—
100	C₂×D₄×C₈₉	—	2	1	no	—
101	C₂×D₄×C₈₉	—	4	1	no	—
102	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	D₈×C₈₉	—	2	2	no	—
107	D₈×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂³×C₈₉	—	2	1	no	—
113	C₂³×C₈₉	—	2	1	no	—
114	C₂³×C₈₉	—	2	1	no	—
115	C₂³×C₈₉	—	4	2	no	—
116	C₂³×C₈₉	—	4	2	no	—
117	C₂³×C₈₉	—	8	1	no	—
118	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×D₈₉	—	2	1	no	—
120	C₂²×D₈₉	—	4	2	no	—
121	C₂²×D₈₉	—	4	2	no	—
122	C₂²×D₈₉	—	8	1	no	—
123	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
124	D₄×C₈₉	—	2	1	no	—
125	D₄×C₈₉	—	2	1	no	—
126	D₄×C₈₉	—	2	1	no	—
127	D₄×C₈₉	—	2	1	no	—
128	D₄×C₈₉	—	2	1	no	—
129	D₄×C₈₉	—	4	2	no	—
130	D₄×C₈₉	—	4	2	no	—
131	D₄×C₈₉	#41	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₂²⋊D₈₉	—	2	2	no	—
138	C₂²⋊D₈₉	—	4	2	no	—
139	C₂²⋊D₈₉	—	4	2	no	—
140	C₂²⋊D₈₉	—	4	2	no	—
141	C₂²⋊D₈₉	—	4	2	no	—
142	C₂²⋊D₈₉	—	8	1	no	—
143	C₂²⋊D₈₉	—	8	1	no	—
144	C₂×Dic₈₉	—	2	1	no	—
145	C₂×Dic₈₉	—	2	1	no	—
146	C₂×Dic₈₉	—	2	1	no	—
147	C₂×Dic₈₉	—	4	2	no	—
148	C₂×Dic₈₉	—	8	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	C₄×D₈₉	—	2	1	no	—
156	C₄×D₈₉	—	2	1	no	—
157	C₈×C₈₉	—	2	1	no	—
158	C₈×C₈₉	—	2	1	no	—
159	#10623494	—	2	1	no	—
160	#10623494	—	2	1	no	—
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	—	4	1	no	—
165	C₂²×C₈₉	—	4	1	no	—
166	C₂²×C₈₉	—	4	1	no	—
167	C₂²×C₈₉	—	4	1	no	—
168	C₂²×C₈₉	—	4	1	no	—
169	C₂²×C₈₉	—	4	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	—	4	1	no	—
172	C₂²×C₈₉	—	8	4	no	—
173	C₂²×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×D₈₉	—	2	1	no	—
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	2	1	no	—
178	C₂×D₈₉	—	4	1	no	—
179	C₂×D₈₉	—	4	1	no	—
180	C₂×D₈₉	—	4	1	no	—
181	C₂×D₈₉	—	8	4	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	4	1	no	—
184	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
185	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
186	Dic₈₉	—	2	1	no	—
187	Dic₈₉	—	2	1	no	—
188	Dic₈₉	—	2	1	no	—
189	Dic₈₉	—	4	1	no	—
190	Dic₈₉	—	4	1	no	—
191	Dic₈₉	—	4	1	no	—
192	C₂×C₈₉	—	2	2	no	—
193	C₂×C₈₉	—	4	2	no	—
194	C₂×C₈₉	—	8	1	no	—
195	C₂×C₈₉	—	8	1	no	—
196	C₂×C₈₉	#546	1	1	yes	characteristic
197	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×C₈₉	#576	1	1	yes	characteristic
199	D₈₉	—	4	1	no	—
200	D₈₉	—	8	1	no	—
201	#3318	—	89	1	no	maximal, Sylow
202	C₈₉	#3318	1	1	yes	characteristic, complemented, Sylow
203	#553	—	89	1	no	—
204	D₄²	—	89	1	no	—
205	#490	—	89	1	no	—
206	#482	—	89	1	no	—
207	#481	—	89	1	no	—
208	#478	—	89	1	no	—
209	#469	—	89	1	no	—
210	#466	—	89	1	no	—
211	#459	—	89	1	no	—
212	#447	—	89	1	no	—
213	#447	D₈₉	1	1	yes	characteristic, complemented
214	#442	—	89	1	no	—
215	#435	—	89	1	no	—
216	#418	—	89	1	no	—
217	C₂×#102	—	89	1	no	—
218	C₂²×D₄	—	89	1	no	—
219	C₂²×D₄	—	178	1	no	—
220	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
221	C₂×D₈	—	89	1	no	—
222	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
223	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
224	C₂×M₁₆	—	89	1	no	—
225	C₂²×C₈	—	89	1	no	—
226	#127	—	89	1	no	—
227	#126	—	178	1	no	—
228	#125	—	89	1	no	—
229	#123	—	178	1	no	—
230	#121	—	89	1	no	—
231	#121	—	89	1	no	—
232	#121	—	89	1	no	—
233	#121	—	178	1	no	—
234	#121	—	178	1	no	—
235	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
236	#120	—	178	1	no	—
237	#120	—	178	1	no	—
238	C₄×D₄	—	89	1	no	—
239	C₄×D₄	—	89	1	no	—
240	C₄×D₄	—	89	1	no	—
241	C₄×D₄	—	178	1	no	—
242	#117	—	89	1	no	—
243	C₂×C₄⋊C₄	—	89	1	no	—
244	#107	—	89	1	no	—
245	#106	—	89	1	no	—
246	#106	—	89	1	no	—
247	C₄⋊C₈	—	89	1	no	—
248	#102	—	89	1	no	—
249	#102	—	89	1	no	—
250	#102	—	89	1	no	—
251	#102	—	89	1	no	—
252	#102	—	89	1	no	—
253	#102	—	89	1	no	—
254	#102	—	89	1	no	—
255	#102	—	89	1	no	—
256	#102	C₂×D₈₉	1	1	yes	characteristic
257	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	—	89	1	no	—
259	C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
260	#97	—	89	1	no	—
261	C₂⁴	—	2	1	no	—
262	C₂⁴	—	178	1	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	89	1	no	—
268	C₂×D₄	—	89	1	no	—
269	C₂×D₄	—	356	4	no	—
270	C₂×D₄	—	356	1	no	—
271	C₂×D₄	—	178	1	no	—
272	C₂×D₄	—	178	1	no	—
273	C₂×D₄	—	178	1	no	—
274	C₂×D₄	—	178	1	no	—
275	C₂×D₄	—	178	1	no	—
276	C₂×D₄	—	178	2	no	—
277	C₂×D₄	—	178	1	no	—
278	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
279	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
280	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
281	C₂²×C₄	—	89	1	no	—
282	C₂²×C₄	—	178	1	no	—
283	C₂²×C₄	—	178	1	no	—
284	C₂²×C₄	—	178	1	no	—
285	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
286	D₈	—	2	2	no	—
287	D₈	—	4	1	no	—
288	D₈	—	356	1	no	—
289	M₁₆	—	356	1	no	—
290	C₂×C₈	—	89	1	no	—
291	C₂×C₈	—	89	1	no	—
292	C₂×C₈	—	356	1	no	—
293	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
295	C₄⋊C₄	—	89	1	no	—
296	C₄⋊C₄	—	89	1	no	—
297	C₄⋊C₄	—	89	1	no	—
298	C₄⋊C₄	—	89	1	no	—
299	C₄⋊C₄	—	178	1	no	—
300	C₄⋊C₄	—	178	1	no	—
301	C₄⋊C₄	—	178	1	no	—
302	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	89	1	no	—
305	C₂²⋊C₄	—	89	1	no	—
306	C₂²⋊C₄	—	178	1	no	—
307	C₂²⋊C₄	—	178	1	no	—
308	C₂²⋊C₄	—	178	1	no	—
309	C₂²⋊C₄	—	178	1	no	—
310	C₂²⋊C₄	—	178	1	no	—
311	C₂²⋊C₄	—	178	1	no	—
312	C₄²	—	89	1	no	—
313	C₄²	—	178	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	89	1	no	—
321	C₂³	—	356	2	no	—
322	C₂³	—	356	2	no	—
323	C₂³	—	178	1	no	—
324	C₂³	—	712	1	no	—
325	C₂³	D₄×D₈₉	1	1	yes	characteristic
326	D₄	—	2	1	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	2	1	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	356	2	no	—
334	D₄	—	356	2	no	—
335	D₄	—	356	2	no	—
336	D₄	—	356	2	no	—
337	D₄	—	178	2	no	—
338	D₄	—	178	1	no	—
339	D₄	—	178	1	no	—
340	D₄	—	712	1	no	—
341	D₄	—	712	1	no	—
342	D₄	#13083573	1	2	yes	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	89	1	no	—
347	C₂×C₄	—	89	1	no	—
348	C₂×C₄	—	89	1	no	—
349	C₂×C₄	—	356	2	no	—
350	C₂×C₄	—	178	1	no	—
351	C₂×C₄	—	178	1	no	—
352	C₂×C₄	—	178	1	no	—
353	C₂×C₄	—	178	1	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	—	712	1	no	—
356	C₂×C₄	—	712	1	no	—
357	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	178	1	no	—
362	C₈	—	178	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	356	1	no	—
376	C₂²	—	356	1	no	—
377	C₂²	—	356	1	no	—
378	C₂²	—	178	1	no	—
379	C₂²	—	178	1	no	—
380	C₂²	—	178	1	no	—
381	C₂²	—	712	4	no	—
382	C₂²	#15668036	1	2	yes	—
383	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	356	1	no	—
387	C₄	—	356	1	no	—
388	C₄	—	356	1	no	—
389	C₄	—	178	1	no	—
390	C₄	—	178	1	no	—
391	C₄	—	178	1	no	—
392	C₄	C₂×#13083573	1	1	yes	characteristic
393	C₄	#15668057	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	4	2	no	—
396	C₂	—	8	1	no	—
397	C₂	—	8	1	no	—
398	C₂	—	356	1	no	—
399	C₂	—	712	1	no	—
400	C₂	#19152235	1	1	yes	characteristic
401	C₂	C₂×#15668036	1	1	yes	characteristic
402	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	#447×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#447	D₈₉
hypocenter	C₈₉	#3318
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #447

Complements

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

N	H ≅ G/N	type
1. #19152300	C₂	semidirect
2. D₄×C₂²⋊D₈₉	C₂	semidirect
3. #19151961	C₂	semidirect
4. #19151921	C₂	semidirect
5. #19151917	C₂	semidirect
6. #19151900	C₂	semidirect
7. #19151848	C₂	semidirect
8. #19151832	C₂	semidirect
9. #19151791	C₂	semidirect
10. #19151730	C₂	semidirect
11. #19151710	C₂	semidirect
12. #19151666	C₂	semidirect
13. #19151601	C₂	semidirect
14. C₂×#15667933	C₂	semidirect
15. #447×C₈₉	C₂	semidirect
18. C₂×#13083559	C₂²	semidirect
19. C₂×#13083557	C₂²	semidirect
20. C₂²×#10623494	C₂²	semidirect
23. #15668003	C₂²	semidirect
29. #15667983	C₂²	semidirect
34. D₄×Dic₈₉	C₂²	semidirect
36. #15667970	C₂²	semidirect
37. C₂×C₄⋊Dic₈₉	C₂²	semidirect
38. #15667945	C₂²	semidirect
39. #15667944	C₂²	semidirect
40. #15667944	C₂²	semidirect
41. #15667941	C₂²	semidirect
42. #15667934	C₂²	semidirect
43. #15667934	C₂²	semidirect
46. #15667933	C₂²	semidirect
47. #15667933	C₂²	semidirect
48. #15667933	C₂²	semidirect
49. #15667932	C₂²	semidirect
50. #15667924	C₂²	semidirect
51. #15667922	C₂²	semidirect
54. C₂×D₈×C₈₉	C₂²	semidirect
55. #121×C₈₉	C₂²	semidirect
57. #102×C₈₉	C₂²	semidirect
58. C₂²⋊C₈×C₈₉	C₂²	semidirect
202. C₈₉	#3318	semidirect
213. #447	D₈₉	semidirect
223. C₂×D₈	C₂×D₈₉	semidirect
235. #121	C₂×D₈₉	semidirect
257. #102	C₂×D₈₉	semidirect
259. C₂²⋊C₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152300	2
D₄×C₂²⋊D₈₉	2
#19151961	2
#19151921	2
#19151917	2
#19151900	2
#19151848	2
#19151832	2
#19151791	2
#19151730	2
#19151710	2
#19151666	2
#19151601	2
C₂×#15667933	2
#447×C₈₉	2
#3318	89