Subgroups — #26029794

Order 11392.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 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×#15668035	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152166	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152080	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151822	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151816	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151810	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151798	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151796	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151794	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151792	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151623	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151598	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×#13083575	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668039	—	2	4	no	—
20	#15668035	—	2	4	no	—
21	C₂×#13083561	C₂²	1	1	yes	characteristic
22	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
25	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13083559	C₂²	1	1	yes	characteristic
27	C₂×#13083557	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
29	#15668009	C₂²	1	1	yes	characteristic
30	#15668008	C₂²	1	1	yes	characteristic
31	#15668001	C₂²	1	1	yes	characteristic
32	#15667985	—	2	1	no	—
33	#15667985	—	2	1	no	—
34	#15667982	—	2	1	no	—
35	#15667982	—	2	1	no	—
36	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₃₅₆	—	2	1	no	—
38	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
39	#15667974	—	2	1	no	—
40	#15667974	C₂²	1	1	yes	characteristic, complemented
41	#15667969	—	2	1	no	—
42	#15667969	C₂²	1	1	yes	characteristic
43	C₄⋊C₄×D₈₉	—	2	1	no	—
44	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
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
50	#15667934	C₂²	1	1	yes	characteristic, complemented
51	#15667933	C₂²	1	1	yes	characteristic
52	#15667932	C₂²	1	1	yes	characteristic
53	#15667932	C₂²	1	1	yes	characteristic, complemented
54	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	#124×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×Q₈×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
61	C₂³×D₈₉	—	2	1	no	—
62	#13083575	—	2	2	no	—
63	#13083575	—	2	2	no	—
64	#13083575	—	2	2	no	—
65	#13083575	D₄	1	4	yes	complemented
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
71	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
72	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊D₈₉	—	2	1	no	—
74	C₂×C₂²⋊D₈₉	—	2	1	no	—
75	C₂×C₂²⋊D₈₉	—	2	1	no	—
76	D₄×D₈₉	—	2	2	no	—
77	D₄×D₈₉	—	2	2	no	—
78	C₂×C₄×D₈₉	—	2	1	no	—
79	C₂×C₄×D₈₉	—	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	#13083561	—	2	2	no	—
86	#13083561	—	2	2	no	—
87	D₇₁₂	—	2	2	no	—
88	D₇₁₂	—	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	—	2	1	no	—
95	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
96	#13083553	—	2	1	no	—
97	#13083553	D₄	1	1	yes	characteristic
98	#13083553	D₄	1	1	yes	characteristic
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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	Q₁₆×C₈₉	—	2	2	no	—
111	SD₁₆×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	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₄²×C₈₉	—	2	1	no	—
119	C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	1	no	—
121	C₂²×D₈₉	—	2	1	no	—
122	C₂²×D₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	4	2	no	—
125	C₂²×D₈₉	—	8	1	no	—
126	C₂²×D₈₉	—	8	1	no	—
127	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₈₉	—	2	1	no	—
129	Q₈×C₈₉	—	2	1	no	—
130	Q₈×C₈₉	—	2	1	no	—
131	Q₈×C₈₉	C₂×D₄	1	2	yes	—
132	D₄×C₈₉	—	2	1	no	—
133	D₄×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	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂²⋊D₈₉	—	4	2	no	—
141	C₂²⋊D₈₉	—	8	1	no	—
142	C₂²⋊D₈₉	—	8	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	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
147	D₃₅₆	—	2	4	no	—
148	D₃₅₆	—	2	1	no	—
149	D₃₅₆	—	2	1	no	—
150	D₃₅₆	—	2	1	no	—
151	D₃₅₆	—	2	1	no	—
152	D₃₅₆	—	2	1	no	—
153	D₃₅₆	—	4	2	no	—
154	D₃₅₆	—	8	1	no	—
155	D₃₅₆	—	8	1	no	—
156	D₃₅₆	C₂×D₄	1	2	yes	—
157	C₄×D₈₉	—	2	4	no	—
158	C₄×D₈₉	—	4	2	no	—
159	C₄×D₈₉	—	8	1	no	—
160	C₄×D₈₉	—	8	1	no	—
161	C₄×D₈₉	—	8	1	no	—
162	C₄×D₈₉	C₂×D₄	1	2	yes	—
163	C₄×D₈₉	#41	1	2	yes	—
164	C₈×C₈₉	—	2	1	no	—
165	C₈×C₈₉	—	2	1	no	—
166	#10623494	—	2	1	no	—
167	#10623494	—	2	1	no	—
168	C₂²×C₈₉	—	4	1	no	—
169	C₂²×C₈₉	—	4	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₈₉	—	2	1	no	—
173	C₂×D₈₉	—	2	1	no	—
174	C₂×D₈₉	—	2	2	no	—
175	C₂×D₈₉	—	4	1	no	—
176	C₂×D₈₉	—	4	1	no	—
177	C₂×D₈₉	—	4	1	no	—
178	C₂×D₈₉	—	4	1	no	—
179	C₂×D₈₉	—	4	1	no	—
180	C₂×D₈₉	—	4	1	no	—
181	C₂×D₈₉	—	4	1	no	—
182	C₂×D₈₉	—	4	1	no	—
183	C₂×D₈₉	—	8	4	no	—
184	C₂×D₈₉	#121	1	2	yes	—
185	C₄×C₈₉	—	2	2	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	4	1	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	Dic₈₉	—	2	1	no	—
193	Dic₈₉	—	2	1	no	—
194	Dic₈₉	—	4	1	no	—
195	Dic₈₉	#121	1	2	yes	—
196	C₂×C₈₉	—	8	1	no	—
197	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
198	C₂×C₈₉	#576	1	1	yes	characteristic
199	C₂×C₈₉	#577	1	1	yes	characteristic
200	D₈₉	—	2	2	no	—
201	D₈₉	—	4	2	no	—
202	D₈₉	—	8	1	no	—
203	D₈₉	—	8	1	no	—
204	#3045	—	89	1	no	maximal, Sylow
205	C₈₉	#3045	1	1	yes	characteristic, complemented, Sylow
206	C₂×AGL(1,ℤ/8)	—	89	1	no	—
207	C₂×#135	—	89	1	no	—
208	#535	—	89	1	no	—
209	#520	—	89	1	no	—
210	#464	—	89	1	no	—
211	#464	D₈₉	1	1	yes	characteristic, complemented
212	#463	—	89	1	no	—
213	#463	—	89	1	no	—
214	#460	—	89	1	no	—
215	#460	—	89	1	no	—
216	#459	—	89	1	no	—
217	#459	—	89	1	no	—
218	#424	—	89	1	no	—
219	#417	—	89	1	no	—
220	C₂×#102	—	89	1	no	—
221	C₂×#41	—	89	1	no	—
222	C₂×#41	—	89	1	no	—
223	C₂²×D₄	—	89	1	no	—
224	AGL(1,ℤ/8)	—	178	4	no	—
225	#135	—	178	4	no	—
226	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
227	C₂×SD₁₆	—	89	1	no	—
228	C₂×SD₁₆	—	89	1	no	—
229	C₂×SD₁₆	—	89	1	no	—
230	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
231	C₂×D₈	—	89	1	no	—
232	C₂×D₈	—	89	1	no	—
233	C₂×D₈	—	89	1	no	—
234	C₂×M₁₆	—	89	1	no	—
235	C₂²×C₈	—	89	1	no	—
236	#127	—	89	1	no	—
237	#127	—	89	1	no	—
238	#124	—	89	1	no	—
239	#124	C₂×D₈₉	1	1	yes	characteristic
240	#121	—	178	1	no	—
241	#121	—	178	1	no	—
242	#120	—	178	1	no	—
243	#120	—	178	1	no	—
244	C₄×Q₈	—	89	1	no	—
245	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
246	C₄×D₄	—	89	1	no	—
247	C₄×D₄	—	89	1	no	—
248	C₄×D₄	—	178	1	no	—
249	C₄×D₄	—	178	1	no	—
250	#117	—	89	1	no	—
251	#117	—	178	1	no	—
252	C₂×C₄⋊C₄	—	89	1	no	—
253	C₂×C₄⋊C₄	—	178	1	no	—
254	C₄⋊C₈	—	89	1	no	—
255	C₄⋊C₈	—	89	1	no	—
256	C₄⋊C₈	—	89	1	no	—
257	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
258	#103	—	89	1	no	—
259	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
260	#102	—	89	1	no	—
261	#102	—	89	1	no	—
262	#102	—	89	1	no	—
263	#102	—	89	1	no	—
264	#102	—	89	1	no	—
265	#102	C₂×D₈₉	1	1	yes	characteristic
266	C₂⁴	—	178	1	no	—
267	#41	—	89	4	no	—
268	#41	—	178	2	no	—
269	#41	—	178	2	no	—
270	#41	—	178	2	no	—
271	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
273	C₂×D₄	—	89	1	no	—
274	C₂×D₄	—	89	1	no	—
275	C₂×D₄	—	89	1	no	—
276	C₂×D₄	—	178	1	no	—
277	C₂×D₄	—	178	1	no	—
278	C₂×D₄	—	178	2	no	—
279	C₂×D₄	—	178	2	no	—
280	C₂×D₄	—	178	1	no	—
281	C₂×D₄	—	178	1	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	—	178	1	no	—
288	C₂²×C₄	—	178	1	no	—
289	C₂²×C₄	—	178	1	no	—
290	C₂²×C₄	—	178	1	no	—
291	C₂²×C₄	—	178	1	no	—
292	Q₁₆	—	2	2	no	—
293	SD₁₆	—	2	2	no	—
294	SD₁₆	—	178	2	no	—
295	SD₁₆	—	178	2	no	—
296	SD₁₆	—	178	2	no	—
297	D₈	—	178	2	no	—
298	D₈	—	178	2	no	—
299	D₈	—	178	2	no	—
300	M₁₆	—	178	2	no	—
301	C₂×C₈	—	89	1	no	—
302	C₂×C₈	—	89	1	no	—
303	C₂×C₈	—	178	2	no	—
304	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	89	1	no	—
308	C₄⋊C₄	—	89	1	no	—
309	C₄⋊C₄	—	89	1	no	—
310	C₄⋊C₄	—	178	1	no	—
311	C₄⋊C₄	—	178	1	no	—
312	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	89	1	no	—
316	C₂²⋊C₄	—	89	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	C₄²	—	2	1	no	—
322	C₄²	—	89	1	no	—
323	C₄²	—	178	1	no	—
324	C₄²	C₂²×D₈₉	1	1	yes	characteristic
325	C₂³	—	2	1	no	—
326	C₂³	—	89	1	no	—
327	C₂³	—	356	2	no	—
328	C₂³	—	178	1	no	—
329	C₂³	—	178	1	no	—
330	C₂³	—	178	1	no	—
331	C₂³	—	712	1	no	—
332	C₂³	—	712	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	D₄×D₈₉	1	2	yes	—
337	D₄	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	89	2	no	—
340	D₄	—	356	2	no	—
341	D₄	—	356	2	no	—
342	D₄	—	178	4	no	—
343	D₄	—	178	1	no	—
344	D₄	—	178	1	no	—
345	D₄	—	178	1	no	—
346	D₄	—	178	1	no	—
347	D₄	—	178	1	no	—
348	D₄	—	712	1	no	—
349	D₄	—	712	1	no	—
350	D₄	—	712	1	no	—
351	D₄	—	712	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	—	89	1	no	—
360	C₂×C₄	—	356	2	no	—
361	C₂×C₄	—	178	4	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	712	1	no	—
364	C₂×C₄	—	712	1	no	—
365	C₂×C₄	—	712	1	no	—
366	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
367	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
368	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	178	1	no	—
372	C₈	—	178	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	89	2	no	—
377	C₂²	—	356	1	no	—
378	C₂²	—	356	1	no	—
379	C₂²	—	356	1	no	—
380	C₂²	—	356	1	no	—
381	C₂²	—	356	1	no	—
382	C₂²	—	356	1	no	—
383	C₂²	—	356	1	no	—
384	C₂²	—	356	1	no	—
385	C₂²	—	178	2	no	—
386	C₂²	—	178	1	no	—
387	C₂²	—	178	1	no	—
388	C₂²	—	712	4	no	—
389	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	89	2	no	—
396	C₄	—	356	1	no	—
397	C₄	—	178	1	no	—
398	C₄	—	178	1	no	—
399	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
400	C₄	#41×D₈₉	1	1	yes	characteristic
401	C₂	—	8	1	no	—
402	C₂	—	356	2	no	—
403	C₂	—	178	2	no	—
404	C₂	—	712	1	no	—
405	C₂	—	712	1	no	—
406	C₂	#121×D₈₉	1	1	yes	characteristic
407	C₂	#19152400	1	1	yes	characteristic
408	C₂	#19152407	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#464×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#464	D₈₉
hypocenter	C₈₉	#3045
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
1. C₂×#15668039	C₂	semidirect
2. C₂×#15668035	C₂	semidirect
3. #19152166	C₂	semidirect
4. #19152080	C₂	semidirect
5. #19151822	C₂	semidirect
6. #19151816	C₂	semidirect
7. #19151810	C₂	semidirect
8. #19151798	C₂	semidirect
9. #19151796	C₂	semidirect
10. #19151794	C₂	semidirect
11. #19151792	C₂	semidirect
12. #19151623	C₂	semidirect
13. #19151598	C₂	semidirect
14. #102×D₈₉	C₂	semidirect
15. #464×C₈₉	C₂	semidirect
22. C₂×#13083561	C₂²	semidirect
23. C₂×#13083561	C₂²	semidirect
25. C₂×D₇₁₂	C₂²	semidirect
36. Q₈×Dic₈₉	C₂²	semidirect
38. C₄×D₃₅₆	C₂²	semidirect
40. #15667974	C₂²	semidirect
45. C₄⋊#10623494	C₂²	semidirect
46. #15667941	C₂²	semidirect
47. #15667941	C₂²	semidirect
48. #15667936	C₂²	semidirect
50. #15667934	C₂²	semidirect
53. #15667932	C₂²	semidirect
54. C₂×Q₁₆×C₈₉	C₂²	semidirect
57. C₄×Q₈×C₈₉	C₂²	semidirect
58. C₄⋊C₈×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
65. #13083575	D₄	semidirect
205. C₈₉	#3045	semidirect
211. #464	D₈₉	semidirect
226. C₂×Q₁₆	C₂×D₈₉	semidirect
245. C₄×Q₈	C₂×D₈₉	semidirect
257. C₄⋊C₈	C₂×D₈₉	semidirect
259. #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×#15668039	2
C₂×#15668035	2
#19152166	2
#19152080	2
#19151822	2
#19151816	2
#19151810	2
#19151798	2
#19151796	2
#19151794	2
#19151792	2
#19151623	2
#19151598	2
#102×D₈₉	2
#464×C₈₉	2
#3045	89