Subgroups — #26029870

Order 11392.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152108	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151849	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151842	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151833	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151831	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151828	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151826	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151637	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151596	C₂	1	1	yes	maximal, characteristic, complemented
15	#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083573	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₈₉	—	2	1	no	—
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
20	#15668036	—	2	4	no	—
21	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083558	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083557	C₂²	1	1	yes	characteristic
26	C₂×#13083557	C₂²	1	1	yes	characteristic
27	M₁₆×D₈₉	—	2	4	no	—
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
30	#15667994	—	2	1	no	—
31	#15667992	C₂²	1	1	yes	characteristic, complemented
32	#15667991	C₂²	1	1	yes	characteristic, complemented
33	#15667987	C₂²	1	1	yes	characteristic
34	#15667986	C₂²	1	1	yes	characteristic
35	#15667985	—	2	1	no	—
36	#15667984	—	2	1	no	—
37	#15667983	C₂²	1	1	yes	characteristic
38	#15667983	C₂²	1	1	yes	characteristic, complemented
39	#15667980	—	2	1	no	—
40	D₄×Dic₈₉	—	2	1	no	—
41	#15667972	—	2	1	no	—
42	#15667970	C₂²	1	1	yes	characteristic
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	#15667935	C₂²	1	1	yes	characteristic, complemented
50	#15667934	C₂²	1	1	yes	characteristic, complemented
51	#15667933	C₂²	1	1	yes	characteristic, complemented
52	#15667933	C₂²	1	1	yes	characteristic, complemented
53	#15667932	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#121×C₈₉	C₂²	1	1	yes	characteristic
57	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#102×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	D₄	1	1	yes	characteristic
63	#13083573	—	2	2	no	—
64	#13083573	—	2	2	no	—
65	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	2	1	no	—
73	D₄×D₈₉	—	2	2	no	—
74	D₄×D₈₉	—	2	2	no	—
75	D₄×D₈₉	—	4	4	no	—
76	C₂²×Dic₈₉	—	2	1	no	—
77	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₈₉	—	2	2	no	—
79	C₂×C₄×D₈₉	—	2	2	no	—
80	C₂×C₄×D₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
82	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
83	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
85	#13083563	—	2	2	no	—
86	#13083562	—	2	2	no	—
87	#13083559	—	2	2	no	—
88	#13083558	—	2	2	no	—
89	#13083557	—	2	2	no	—
90	#13083557	D₄	1	4	yes	complemented
91	C₂×#10623494	C₂³	1	1	yes	characteristic
92	C₂×#10623494	C₂³	1	1	yes	characteristic
93	C₈×D₈₉	—	2	2	no	—
94	C₈×D₈₉	—	2	2	no	—
95	C₄⋊Dic₈₉	—	2	1	no	—
96	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
98	#13083553	—	2	1	no	—
99	#13083553	—	2	1	no	—
100	C₂²⋊Dic₈₉	—	2	1	no	—
101	C₂²⋊Dic₈₉	—	2	1	no	—
102	C₂²⋊Dic₈₉	—	2	1	no	—
103	#13083551	—	2	1	no	—
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	C₄×Dic₈₉	—	2	1	no	—
108	C₂×D₄×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	—	2	1	no	—
110	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	D₈×C₈₉	—	2	2	no	—
114	M₁₆×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂³×C₈₉	—	2	1	no	—
123	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×D₈₉	—	2	2	no	—
125	C₂²×D₈₉	—	2	2	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	—	4	1	no	—
128	C₂²×D₈₉	—	4	2	no	—
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
133	D₄×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	—	4	2	no	—
138	D₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂²⋊D₈₉	—	4	2	no	—
146	C₂²⋊D₈₉	—	4	2	no	—
147	C₂²⋊D₈₉	—	4	2	no	—
148	C₂²⋊D₈₉	—	4	2	no	—
149	C₂²⋊D₈₉	—	4	2	no	—
150	C₂×Dic₈₉	—	2	2	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	4	2	no	—
155	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
157	D₃₅₆	—	2	1	no	—
158	D₃₅₆	—	2	1	no	—
159	D₃₅₆	—	4	2	no	—
160	C₄×D₈₉	—	2	2	no	—
161	C₄×D₈₉	—	2	1	no	—
162	C₄×D₈₉	—	2	1	no	—
163	C₄×D₈₉	—	2	2	no	—
164	C₄×D₈₉	—	4	2	no	—
165	C₄×D₈₉	C₂×D₄	1	2	yes	—
166	C₄×D₈₉	#41	1	2	yes	—
167	Dic₁₇₈	—	2	1	no	—
168	Dic₁₇₈	—	2	1	no	—
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
171	#10623494	—	2	1	no	—
172	#10623494	C₂×D₄	1	2	yes	complemented
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	—	2	1	no	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	4	1	no	—
177	C₂²×C₈₉	—	4	1	no	—
178	C₂²×C₈₉	—	4	1	no	—
179	C₂²×C₈₉	—	4	1	no	—
180	C₂²×C₈₉	—	4	1	no	—
181	C₂²×C₈₉	—	4	1	no	—
182	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	1	no	—
186	C₂×D₈₉	—	2	1	no	—
187	C₂×D₈₉	—	4	4	no	—
188	C₂×D₈₉	—	4	1	no	—
189	C₂×D₈₉	—	4	1	no	—
190	C₂×D₈₉	—	4	1	no	—
191	C₂×D₈₉	—	8	4	no	—
192	C₂×D₈₉	#121	1	2	yes	—
193	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	—	4	1	no	—
197	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	Dic₈₉	—	2	1	no	—
200	Dic₈₉	—	4	1	no	—
201	Dic₈₉	—	4	1	no	—
202	Dic₈₉	—	4	1	no	—
203	Dic₈₉	#121	1	2	yes	—
204	C₂×C₈₉	—	4	1	no	—
205	C₂×C₈₉	—	8	1	no	—
206	C₂×C₈₉	—	8	1	no	—
207	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
208	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂×C₈₉	#575	1	1	yes	characteristic
210	D₈₉	—	2	2	no	—
211	D₈₉	—	2	2	no	—
212	D₈₉	—	8	1	no	—
213	#3055	—	89	1	no	maximal, Sylow
214	C₈₉	#3055	1	1	yes	characteristic, complemented, Sylow
215	C₂×AGL(1,ℤ/8)	—	89	1	no	—
216	C₂²×M₁₆	—	89	1	no	—
217	#525	—	89	1	no	—
218	C₂×#121	—	89	1	no	—
219	#469	—	89	1	no	—
220	#469	D₈₉	1	1	yes	characteristic, complemented
221	#468	—	89	1	no	—
222	#468	—	89	1	no	—
223	#466	—	89	1	no	—
224	#466	—	89	1	no	—
225	#465	—	89	1	no	—
226	#465	—	89	1	no	—
227	#428	—	89	1	no	—
228	#418	—	89	1	no	—
229	#417	—	89	1	no	—
230	C₂×#41	—	89	1	no	—
231	C₂²×D₄	—	89	1	no	—
232	C₂²×D₄	—	178	1	no	—
233	C₂³×C₄	—	89	1	no	—
234	AGL(1,ℤ/8)	—	178	4	no	—
235	C₂×SD₁₆	—	89	1	no	—
236	C₂×SD₁₆	—	89	1	no	—
237	C₂×D₈	—	89	1	no	—
238	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
239	C₂×M₁₆	—	89	1	no	—
240	C₂×M₁₆	—	89	1	no	—
241	C₂×M₁₆	—	89	1	no	—
242	C₂×M₁₆	—	178	4	no	—
243	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
244	C₂²×C₈	—	89	1	no	—
245	C₂²×C₈	—	89	1	no	—
246	#123	—	178	1	no	—
247	C₂²⋊Q₈	—	89	1	no	—
248	C₂²⋊Q₈	—	89	1	no	—
249	#121	—	89	1	no	—
250	#121	—	89	1	no	—
251	#121	—	89	1	no	—
252	#121	—	89	1	no	—
253	#121	—	178	1	no	—
254	#121	—	178	1	no	—
255	#121	C₂×D₈₉	1	1	yes	characteristic
256	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#120	—	178	1	no	—
258	C₄×D₄	—	178	1	no	—
259	C₄×D₄	—	178	1	no	—
260	#117	—	89	1	no	—
261	C₂×C₄⋊C₄	—	89	1	no	—
262	C₂×C₂²⋊C₄	—	178	1	no	—
263	#107	—	89	1	no	—
264	#107	—	89	1	no	—
265	#106	—	89	1	no	—
266	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
267	#103	—	89	1	no	—
268	#103	—	89	1	no	—
269	#102	—	89	1	no	—
270	#102	—	89	1	no	—
271	#102	—	89	1	no	—
272	#102	—	89	1	no	—
273	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
274	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
275	C₂⁴	—	89	1	no	—
276	C₂⁴	—	178	1	no	—
277	#41	—	178	2	no	—
278	#41	—	178	2	no	—
279	C₂×Q₈	—	89	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	89	1	no	—
283	C₂×D₄	—	356	4	no	—
284	C₂×D₄	—	178	1	no	—
285	C₂×D₄	—	178	2	no	—
286	C₂×D₄	—	178	2	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	—	89	1	no	—
295	C₂²×C₄	—	89	1	no	—
296	C₂²×C₄	—	89	1	no	—
297	C₂²×C₄	—	89	1	no	—
298	C₂²×C₄	—	89	1	no	—
299	C₂²×C₄	—	178	2	no	—
300	C₂²×C₄	—	178	2	no	—
301	C₂²×C₄	—	178	1	no	—
302	C₂²×C₄	—	178	1	no	—
303	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
304	SD₁₆	—	178	2	no	—
305	SD₁₆	—	178	2	no	—
306	D₈	—	2	2	no	—
307	D₈	—	178	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	89	4	no	—
310	M₁₆	—	178	2	no	—
311	M₁₆	—	178	2	no	—
312	C₂×C₈	—	89	1	no	—
313	C₂×C₈	—	89	1	no	—
314	C₂×C₈	—	178	2	no	—
315	C₂×C₈	—	178	2	no	—
316	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
317	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₄⋊C₄	—	89	1	no	—
319	C₄⋊C₄	—	89	1	no	—
320	C₄⋊C₄	—	178	1	no	—
321	C₄⋊C₄	—	178	1	no	—
322	C₄⋊C₄	—	178	1	no	—
323	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
324	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	178	1	no	—
328	C₂²⋊C₄	—	178	1	no	—
329	C₂²⋊C₄	—	178	1	no	—
330	C₂²⋊C₄	—	178	1	no	—
331	C₂²⋊C₄	—	178	1	no	—
332	C₂²⋊C₄	—	178	1	no	—
333	C₂²⋊C₄	—	178	1	no	—
334	C₄²	—	178	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	89	1	no	—
338	C₂³	—	89	1	no	—
339	C₂³	—	356	1	no	—
340	C₂³	—	356	2	no	—
341	C₂³	—	356	2	no	—
342	C₂³	—	356	2	no	—
343	C₂³	—	178	2	no	—
344	C₂³	—	178	2	no	—
345	C₂³	—	178	1	no	—
346	C₂³	D₄×D₈₉	1	1	yes	characteristic
347	Q₈	—	178	1	no	—
348	Q₈	—	178	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	2	1	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	356	2	no	—
356	D₄	—	356	2	no	—
357	D₄	—	356	2	no	—
358	D₄	—	356	2	no	—
359	D₄	—	356	2	no	—
360	D₄	—	356	2	no	—
361	D₄	—	178	1	no	—
362	D₄	—	178	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	89	1	no	—
368	C₂×C₄	—	89	2	no	—
369	C₂×C₄	—	89	2	no	—
370	C₂×C₄	—	89	1	no	—
371	C₂×C₄	—	356	2	no	—
372	C₂×C₄	—	356	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	178	2	no	—
375	C₂×C₄	—	178	2	no	—
376	C₂×C₄	—	178	1	no	—
377	C₂×C₄	—	178	1	no	—
378	C₂×C₄	—	178	1	no	—
379	C₂×C₄	—	178	1	no	—
380	C₂×C₄	—	178	1	no	—
381	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	89	2	no	—
385	C₈	—	178	1	no	—
386	C₈	D₄×D₈₉	1	2	yes	complemented
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	89	2	no	—
397	C₂²	—	89	2	no	—
398	C₂²	—	356	4	no	—
399	C₂²	—	356	1	no	—
400	C₂²	—	356	1	no	—
401	C₂²	—	356	1	no	—
402	C₂²	—	178	1	no	—
403	C₂²	—	178	1	no	—
404	C₂²	—	178	1	no	—
405	C₂²	—	178	1	no	—
406	C₂²	—	712	4	no	—
407	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	89	2	no	—
412	C₄	—	356	1	no	—
413	C₄	—	356	1	no	—
414	C₄	—	356	1	no	—
415	C₄	—	178	1	no	—
416	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
417	C₄	#41×D₈₉	1	1	yes	characteristic
418	C₂	—	4	1	no	—
419	C₂	—	8	1	no	—
420	C₂	—	8	1	no	—
421	C₂	—	178	2	no	—
422	C₂	—	178	2	no	—
423	C₂	—	712	1	no	—
424	C₂	#121×D₈₉	1	1	yes	characteristic
425	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
426	C₂	#19152394	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#469×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#469	D₈₉
hypocenter	C₈₉	#3055
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #469

Complements

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

N	H ≅ G/N	type
1. C₂×#15668036	C₂	semidirect
2. C₂×M₁₆×D₈₉	C₂	semidirect
3. #19152108	C₂	semidirect
4. #121×D₈₉	C₂	semidirect
5. #19151849	C₂	semidirect
6. #19151844	C₂	semidirect
7. #19151842	C₂	semidirect
8. #19151833	C₂	semidirect
9. #19151831	C₂	semidirect
10. #19151828	C₂	semidirect
11. #19151826	C₂	semidirect
12. #19151637	C₂	semidirect
13. #19151601	C₂	semidirect
14. #19151596	C₂	semidirect
15. #469×C₈₉	C₂	semidirect
21. C₂×#13083563	C₂²	semidirect
22. C₂×#13083562	C₂²	semidirect
23. C₂×#13083559	C₂²	semidirect
24. C₂×#13083558	C₂²	semidirect
28. C₂×C₈×D₈₉	C₂²	semidirect
29. C₂×C₈×D₈₉	C₂²	semidirect
31. #15667992	C₂²	semidirect
32. #15667991	C₂²	semidirect
38. #15667983	C₂²	semidirect
45. #15667946	C₂²	semidirect
46. #15667945	C₂²	semidirect
47. #15667943	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667935	C₂²	semidirect
50. #15667934	C₂²	semidirect
51. #15667933	C₂²	semidirect
52. #15667933	C₂²	semidirect
53. #15667932	C₂²	semidirect
54. C₂×D₈×C₈₉	C₂²	semidirect
55. C₂×M₁₆×C₈₉	C₂²	semidirect
57. #121×C₈₉	C₂²	semidirect
58. #106×C₈₉	C₂²	semidirect
59. #102×C₈₉	C₂²	semidirect
60. #102×C₈₉	C₂²	semidirect
90. #13083557	D₄	semidirect
170. C₈×C₈₉	C₂×D₄	semidirect
172. #10623494	C₂×D₄	semidirect
193. C₂×D₈₉	AGL(1,ℤ/8)	semidirect
214. C₈₉	#3055	semidirect
220. #469	D₈₉	semidirect
238. C₂×D₈	C₂×D₈₉	semidirect
243. C₂×M₁₆	C₂×D₈₉	semidirect
256. #121	C₂×D₈₉	semidirect
266. #106	C₂×D₈₉	semidirect
273. #102	C₂×D₈₉	semidirect
274. #102	C₂×D₈₉	semidirect
386. C₈	D₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668036	2
C₂×M₁₆×D₈₉	2
#19152108	2
#121×D₈₉	2
#19151849	2
#19151844	2
#19151842	2
#19151833	2
#19151831	2
#19151828	2
#19151826	2
#19151637	2
#19151601	2
#19151596	2
#469×C₈₉	2
#3055	89