Subgroups — #26029714

Order 11392.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152147	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151814	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151813	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151810	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151802	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151801	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	#19151620	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151598	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151596	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×#13083573	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₈₉	—	2	1	no	—
20	#15668039	—	2	4	no	—
21	#15668036	—	2	4	no	—
22	C₂×#13083563	C₂²	1	1	yes	characteristic
23	C₂×#13083562	C₂²	1	1	yes	characteristic
24	C₂×#13083561	C₂²	1	1	yes	characteristic
25	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
26	C₂×#13083559	C₂²	1	1	yes	characteristic
27	C₂×#13083559	C₂²	1	1	yes	characteristic
28	C₂×#13083557	C₂²	1	1	yes	characteristic
29	C₂×#13083557	C₂²	1	1	yes	characteristic
30	#15668010	C₂²	1	1	yes	characteristic, complemented
31	#15668008	C₂²	1	1	yes	characteristic, complemented
32	#15668000	C₂²	1	1	yes	characteristic, complemented
33	#15667985	—	2	1	no	—
34	#15667985	—	2	1	no	—
35	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
36	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
37	#15667974	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₈₉	—	2	1	no	—
39	#15667972	—	2	1	no	—
40	#15667972	—	2	1	no	—
41	#15667972	—	2	1	no	—
42	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₈₉	—	2	1	no	—
44	C₄²×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	#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, complemented
52	#15667933	C₂²	1	1	yes	characteristic, complemented
53	#15667932	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
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
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	#13083575	—	2	2	no	—
63	#13083575	—	2	2	no	—
64	#13083573	—	2	2	no	—
65	#13083573	—	2	2	no	—
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	2	1	no	—
73	C₂×C₂²⋊D₈₉	—	2	1	no	—
74	D₄×D₈₉	—	2	2	no	—
75	D₄×D₈₉	D₄	1	4	yes	complemented
76	C₂²×Dic₈₉	—	2	1	no	—
77	C₂²×Dic₈₉	—	2	1	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	—	4	4	no	—
83	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
84	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
85	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
86	#13083563	—	2	2	no	—
87	#13083562	—	2	2	no	—
88	#13083561	—	2	2	no	—
89	D₇₁₂	—	2	2	no	—
90	#13083559	—	2	2	no	—
91	#13083559	—	2	2	no	—
92	#13083557	—	2	2	no	—
93	#13083557	—	2	2	no	—
94	C₂×#10623494	C₂³	1	1	yes	characteristic
95	C₂×#10623494	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
97	#13083553	—	2	1	no	—
98	#13083553	—	2	1	no	—
99	#13083553	—	2	1	no	—
100	C₂²⋊Dic₈₉	—	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	D₄	1	1	yes	characteristic
106	C₄×Dic₈₉	D₄	1	1	yes	characteristic
107	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	—	2	1	no	—
112	SD₁₆×C₈₉	—	2	2	no	—
113	D₈×C₈₉	—	2	2	no	—
114	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂³×C₈₉	—	2	1	no	—
122	C₂³×C₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	2	4	no	—
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	4	2	no	—
127	C₂²×D₈₉	—	4	2	no	—
128	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
129	Q₈×C₈₉	—	2	1	no	—
130	Q₈×C₈₉	—	2	1	no	—
131	D₄×C₈₉	—	2	1	no	—
132	D₄×C₈₉	—	2	1	no	—
133	D₄×C₈₉	—	2	1	no	—
134	D₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₈₉	—	2	4	no	—
142	C₂²⋊D₈₉	—	4	2	no	—
143	C₂²⋊D₈₉	—	4	2	no	—
144	C₂²⋊D₈₉	—	4	2	no	—
145	C₂×Dic₈₉	—	2	1	no	—
146	C₂×Dic₈₉	—	2	1	no	—
147	C₂×Dic₈₉	—	4	2	no	—
148	C₂×Dic₈₉	—	4	2	no	—
149	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	D₃₅₆	—	2	1	no	—
153	D₃₅₆	—	2	1	no	—
154	D₃₅₆	—	2	1	no	—
155	D₃₅₆	—	4	2	no	—
156	D₃₅₆	C₂×D₄	1	2	yes	—
157	C₄×D₈₉	—	2	2	no	—
158	C₄×D₈₉	—	4	1	no	—
159	C₄×D₈₉	—	4	2	no	—
160	C₄×D₈₉	—	4	2	no	—
161	C₄×D₈₉	—	4	2	no	—
162	C₄×D₈₉	—	4	2	no	—
163	C₄×D₈₉	C₂×D₄	1	2	yes	—
164	C₄×D₈₉	#41	1	2	yes	—
165	Dic₁₇₈	—	2	1	no	—
166	Dic₁₇₈	—	2	1	no	—
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	8	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	#121	1	2	yes	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	4	1	no	—
191	C₄×C₈₉	—	4	1	no	—
192	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
194	Dic₈₉	—	2	1	no	—
195	Dic₈₉	—	4	1	no	—
196	Dic₈₉	—	4	1	no	—
197	Dic₈₉	#121	1	2	yes	—
198	Dic₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂×C₈₉	—	4	2	no	—
200	C₂×C₈₉	—	8	1	no	—
201	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
202	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₈₉	#575	1	1	yes	characteristic
204	D₈₉	—	2	2	no	—
205	D₈₉	—	4	2	no	—
206	D₈₉	—	8	1	no	—
207	#3036	—	89	1	no	maximal, Sylow
208	C₈₉	#3036	1	1	yes	characteristic, complemented, Sylow
209	C₂×AGL(1,ℤ/8)	—	89	1	no	—
210	C₂×AGL(1,ℤ/8)	—	89	1	no	—
211	#532	—	89	1	no	—
212	C₂×C₄×D₄	—	89	1	no	—
213	#463	—	89	1	no	—
214	#463	—	89	1	no	—
215	#463	—	89	1	no	—
216	#463	D₈₉	1	1	yes	characteristic, complemented
217	#461	—	89	1	no	—
218	#461	—	89	1	no	—
219	#459	—	89	1	no	—
220	#459	—	89	1	no	—
221	#423	—	89	1	no	—
222	#417	—	89	1	no	—
223	#417	—	89	1	no	—
224	C₂×#41	—	89	1	no	—
225	C₂×#41	—	89	1	no	—
226	C₂²×D₄	—	89	1	no	—
227	C₂³×C₄	—	178	1	no	—
228	AGL(1,ℤ/8)	—	178	4	no	—
229	AGL(1,ℤ/8)	—	178	4	no	—
230	C₂×SD₁₆	—	89	1	no	—
231	C₂×SD₁₆	—	89	1	no	—
232	C₂×SD₁₆	—	89	1	no	—
233	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
234	C₂×D₈	—	89	1	no	—
235	C₂×D₈	—	89	1	no	—
236	C₂×D₈	—	89	1	no	—
237	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
238	C₂×M₁₆	—	89	1	no	—
239	C₂×M₁₆	—	89	1	no	—
240	C₄⋊Q₈	—	89	1	no	—
241	#127	—	89	1	no	—
242	#124	—	89	1	no	—
243	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
244	#121	—	178	1	no	—
245	#121	—	178	1	no	—
246	C₄×D₄	—	89	1	no	—
247	C₄×D₄	—	89	1	no	—
248	C₄×D₄	—	89	1	no	—
249	C₄×D₄	—	178	1	no	—
250	C₄×D₄	—	178	1	no	—
251	C₄×D₄	—	178	1	no	—
252	C₄×D₄	—	178	1	no	—
253	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	89	1	no	—
255	C₂×C₂²⋊C₄	—	178	1	no	—
256	C₂×C₄²	—	89	1	no	—
257	C₄⋊C₈	—	89	1	no	—
258	C₄⋊C₈	—	89	1	no	—
259	C₄⋊C₈	—	89	1	no	—
260	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
261	#103	—	89	1	no	—
262	#103	—	89	1	no	—
263	#103	—	89	1	no	—
264	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
265	#102	—	89	1	no	—
266	#102	—	89	1	no	—
267	#102	—	89	1	no	—
268	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
269	C₂⁴	—	178	1	no	—
270	#41	—	178	2	no	—
271	#41	—	178	2	no	—
272	#41	—	178	2	no	—
273	#41	—	178	2	no	—
274	C₂×Q₈	—	89	1	no	—
275	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
276	C₂×D₄	—	89	4	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	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	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	89	1	no	—
289	C₂²×C₄	—	89	1	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	356	4	no	—
292	C₂²×C₄	—	178	1	no	—
293	C₂²×C₄	—	178	1	no	—
294	C₂²×C₄	—	178	1	no	—
295	C₂²×C₄	—	178	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	—	178	1	no	—
298	SD₁₆	—	2	2	no	—
299	SD₁₆	—	178	2	no	—
300	SD₁₆	—	178	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	M₁₆	—	178	2	no	—
307	M₁₆	—	178	2	no	—
308	C₂×C₈	—	89	1	no	—
309	C₂×C₈	—	89	1	no	—
310	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
311	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄⋊C₄	—	89	1	no	—
313	C₄⋊C₄	—	178	1	no	—
314	C₄⋊C₄	—	178	1	no	—
315	C₄⋊C₄	—	178	1	no	—
316	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	178	1	no	—
321	C₂²⋊C₄	—	178	1	no	—
322	C₂²⋊C₄	—	178	1	no	—
323	C₂²⋊C₄	—	178	1	no	—
324	C₂²⋊C₄	—	178	1	no	—
325	C₄²	—	89	1	no	—
326	C₄²	—	89	1	no	—
327	C₄²	—	89	1	no	—
328	C₄²	C₂²×D₈₉	1	1	yes	characteristic
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	89	1	no	—
332	C₂³	—	356	2	no	—
333	C₂³	—	356	2	no	—
334	C₂³	—	178	4	no	—
335	C₂³	—	178	1	no	—
336	C₂³	—	178	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	178	1	no	—
340	Q₈	—	178	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	89	2	no	—
345	D₄	—	356	2	no	—
346	D₄	—	356	2	no	—
347	D₄	—	356	2	no	—
348	D₄	—	356	2	no	—
349	D₄	—	178	4	no	—
350	D₄	—	178	1	no	—
351	D₄	—	178	1	no	—
352	D₄	—	178	1	no	—
353	D₄	D₄×D₈₉	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	89	1	no	—
358	C₂×C₄	—	89	1	no	—
359	C₂×C₄	—	89	2	no	—
360	C₂×C₄	—	89	2	no	—
361	C₂×C₄	—	89	1	no	—
362	C₂×C₄	—	356	2	no	—
363	C₂×C₄	—	356	1	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	356	2	no	—
367	C₂×C₄	—	356	2	no	—
368	C₂×C₄	—	356	2	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	1	no	—
371	C₂×C₄	—	178	1	no	—
372	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
373	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	178	1	no	—
378	C₈	—	178	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	89	2	no	—
386	C₂²	—	356	8	no	—
387	C₂²	—	356	1	no	—
388	C₂²	—	356	1	no	—
389	C₂²	—	356	1	no	—
390	C₂²	—	356	1	no	—
391	C₂²	—	356	1	no	—
392	C₂²	—	178	2	no	—
393	C₂²	—	178	1	no	—
394	C₂²	—	178	1	no	—
395	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	89	2	no	—
401	C₄	—	89	2	no	—
402	C₄	—	356	1	no	—
403	C₄	—	356	1	no	—
404	C₄	—	178	1	no	—
405	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
406	C₄	#41×D₈₉	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	—	8	1	no	—
409	C₂	—	356	2	no	—
410	C₂	—	178	2	no	—
411	C₂	—	712	1	no	—
412	C₂	#121×D₈₉	1	1	yes	characteristic
413	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
414	C₂	#19152395	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	#3036
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×#15668036	C₂	semidirect
3. #19152147	C₂	semidirect
4. C₄×D₄×D₈₉	C₂	semidirect
5. #19151814	C₂	semidirect
6. #19151813	C₂	semidirect
7. #19151810	C₂	semidirect
8. #19151802	C₂	semidirect
9. #19151801	C₂	semidirect
10. #19151792	C₂	semidirect
11. #19151791	C₂	semidirect
12. #19151620	C₂	semidirect
13. #19151598	C₂	semidirect
14. #19151596	C₂	semidirect
15. #463×C₈₉	C₂	semidirect
30. #15668010	C₂²	semidirect
31. #15668008	C₂²	semidirect
32. #15668000	C₂²	semidirect
45. C₄⋊#10623494	C₂²	semidirect
46. #15667941	C₂²	semidirect
47. #15667941	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667936	C₂²	semidirect
50. #15667935	C₂²	semidirect
51. #15667934	C₂²	semidirect
52. #15667933	C₂²	semidirect
53. #15667932	C₂²	semidirect
56. #124×C₈₉	C₂²	semidirect
58. C₄⋊C₈×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
60. #102×C₈₉	C₂²	semidirect
75. D₄×D₈₉	D₄	semidirect
198. Dic₈₉	AGL(1,ℤ/8)	semidirect
208. C₈₉	#3036	semidirect
216. #463	D₈₉	semidirect
243. #124	C₂×D₈₉	semidirect
260. C₄⋊C₈	C₂×D₈₉	semidirect
264. #103	C₂×D₈₉	semidirect
268. #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×#15668036	2
#19152147	2
C₄×D₄×D₈₉	2
#19151814	2
#19151813	2
#19151810	2
#19151802	2
#19151801	2
#19151792	2
#19151791	2
#19151620	2
#19151598	2
#19151596	2
#463×C₈₉	2
#3036	89