Subgroups — #26031883

Order 11392.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668041	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152255	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152242	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151981	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151856	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151848	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151818	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151811	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151760	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151749	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151740	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151735	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151674	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083573	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
18	#15668041	—	2	4	no	—
19	C₂×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083562	C₂²	1	1	yes	characteristic
22	C₂×#13083562	C₂²	1	1	yes	characteristic
23	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
25	#15667999	—	2	1	no	—
26	#15667999	C₂²	1	1	yes	characteristic
27	#15667999	C₂²	1	1	yes	characteristic, complemented
28	#15667993	—	2	1	no	—
29	#15667991	—	2	1	no	—
30	#15667991	C₂²	1	1	yes	characteristic
31	#15667991	C₂²	1	1	yes	characteristic
32	#15667984	—	2	1	no	—
33	#15667983	—	2	1	no	—
34	#15667983	C₂²	1	1	yes	characteristic
35	#15667983	C₂²	1	1	yes	characteristic, complemented
36	#15667981	—	2	1	no	—
37	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
38	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₈₉	—	2	1	no	—
40	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
42	#15667944	C₂²	1	1	yes	characteristic, complemented
43	#15667941	C₂²	1	1	yes	characteristic, complemented
44	#15667937	C₂²	1	1	yes	characteristic, complemented
45	#15667937	C₂²	1	1	yes	characteristic, complemented
46	#15667936	C₂²	1	1	yes	characteristic, complemented
47	#15667933	C₂²	1	1	yes	characteristic
48	#15667933	C₂²	1	1	yes	characteristic
49	#15667933	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#10623494	C₂²	1	1	yes	characteristic
51	#15667924	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
56	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
61	#13083573	—	2	2	no	—
62	#13083573	—	4	1	no	—
63	C₂×Dic₁₇₈	—	2	1	no	—
64	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	Q₈×D₈₉	—	2	2	no	—
67	Q₈×D₈₉	—	4	1	no	—
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	D₄	1	1	yes	characteristic
72	C₂²×Dic₈₉	—	2	1	no	—
73	C₂²×Dic₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	—	2	1	no	—
75	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
76	Dic₃₅₆	—	2	2	no	—
77	#13083564	—	2	2	no	—
78	#13083562	—	2	2	no	—
79	#13083562	—	4	1	no	—
80	#13083562	—	4	1	no	—
81	#13083557	—	2	2	no	—
82	C₂×#10623494	C₂³	1	1	yes	characteristic
83	C₂×#10623494	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₈₉	—	2	1	no	—
85	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
87	#13083553	—	2	1	no	—
88	#13083553	—	2	1	no	—
89	#13083553	D₄	1	1	yes	characteristic
90	C₂²⋊Dic₈₉	—	2	1	no	—
91	C₂²⋊Dic₈₉	—	2	1	no	—
92	C₂²⋊Dic₈₉	—	2	1	no	—
93	C₂²⋊Dic₈₉	—	2	1	no	—
94	C₂²⋊Dic₈₉	—	2	1	no	—
95	C₂²⋊Dic₈₉	—	2	1	no	—
96	C₂²⋊Dic₈₉	—	2	1	no	—
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	C₂²⋊Dic₈₉	—	2	1	no	—
99	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
100	#13083551	D₄	1	1	yes	characteristic
101	C₄×Dic₈₉	—	2	1	no	—
102	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
103	C₂⁴×C₈₉	—	2	1	no	—
104	#41×C₈₉	—	2	2	no	—
105	#41×C₈₉	—	4	1	no	—
106	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₈₉	—	2	2	no	—
108	C₂×D₄×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	—	2	1	no	—
110	C₂×D₄×C₈₉	—	4	1	no	—
111	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	SD₁₆×C₈₉	—	2	2	no	—
117	SD₁₆×C₈₉	D₄	1	4	yes	complemented
118	D₈×C₈₉	—	2	2	no	—
119	D₈×C₈₉	—	2	2	no	—
120	M₁₆×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂³×C₈₉	—	2	1	no	—
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	4	2	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	8	1	no	—
129	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₈₉	—	2	1	no	—
132	Q₈×C₈₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	C₂×D₄	1	2	yes	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₂²⋊D₈₉	—	4	1	no	—
148	C₂²⋊D₈₉	—	4	2	no	—
149	C₂²⋊D₈₉	—	4	2	no	—
150	C₂²⋊D₈₉	—	8	1	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	8	1	no	—
157	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
160	C₄×D₈₉	—	2	1	no	—
161	C₄×D₈₉	—	2	1	no	—
162	C₄×D₈₉	—	4	2	no	—
163	Dic₁₇₈	—	2	1	no	—
164	Dic₁₇₈	—	2	1	no	—
165	Dic₁₇₈	—	2	1	no	—
166	Dic₁₇₈	—	2	1	no	—
167	Dic₁₇₈	—	4	2	no	—
168	C₈×C₈₉	—	2	1	no	—
169	C₈×C₈₉	C₂×D₄	1	2	yes	—
170	#10623494	—	2	1	no	—
171	#10623494	—	2	1	no	—
172	C₂²×C₈₉	—	2	2	no	—
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	—	4	1	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	8	4	no	—
185	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×D₈₉	—	2	1	no	—
187	C₂×D₈₉	—	2	1	no	—
188	C₂×D₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
193	Dic₈₉	—	2	1	no	—
194	Dic₈₉	—	2	1	no	—
195	Dic₈₉	—	2	1	no	—
196	Dic₈₉	—	4	1	no	—
197	Dic₈₉	—	4	1	no	—
198	Dic₈₉	—	4	1	no	—
199	Dic₈₉	—	4	1	no	—
200	C₂×C₈₉	—	4	1	no	—
201	C₂×C₈₉	—	4	2	no	—
202	C₂×C₈₉	—	8	1	no	—
203	C₂×C₈₉	—	8	1	no	—
204	C₂×C₈₉	D₄²	1	1	yes	characteristic
205	C₂×C₈₉	#575	1	1	yes	characteristic
206	C₂×C₈₉	#577	1	1	yes	characteristic
207	D₈₉	—	4	1	no	—
208	#3275	—	89	1	no	maximal, Sylow
209	C₈₉	#3275	1	1	yes	characteristic, complemented, Sylow
210	C₂×#137	—	89	1	no	—
211	C₂×AGL(1,ℤ/8)	D₈₉	1	1	yes	characteristic, complemented
212	#548	—	89	1	no	—
213	#546	—	89	1	no	—
214	#495	—	89	1	no	—
215	#470	—	89	1	no	—
216	#469	—	89	1	no	—
217	#464	—	89	1	no	—
218	#463	—	89	1	no	—
219	#452	—	89	1	no	—
220	#450	—	89	1	no	—
221	#449	—	89	1	no	—
222	#448	—	89	1	no	—
223	C₄×SD₁₆	—	89	1	no	—
224	#436	—	89	1	no	—
225	C₂×#41	—	89	1	no	—
226	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
227	C₂²×Q₈	—	89	1	no	—
228	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
229	#137	—	178	4	no	—
230	AGL(1,ℤ/8)	—	2	4	no	—
231	C₂×Q₁₆	—	89	1	no	—
232	C₂×Q₁₆	—	89	1	no	—
233	C₂×SD₁₆	—	89	1	no	—
234	C₂×SD₁₆	—	89	1	no	—
235	C₂×SD₁₆	—	89	1	no	—
236	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
237	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
238	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
239	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
240	C₂×M₁₆	—	89	1	no	—
241	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic
242	#124	—	89	1	no	—
243	#124	—	89	1	no	—
244	#124	—	178	1	no	—
245	#123	—	178	1	no	—
246	C₂²⋊Q₈	—	89	1	no	—
247	C₂²⋊Q₈	—	89	1	no	—
248	C₂²⋊Q₈	—	178	1	no	—
249	#121	—	89	1	no	—
250	#121	—	89	1	no	—
251	#121	—	178	1	no	—
252	#121	—	178	1	no	—
253	#120	—	178	1	no	—
254	C₄×Q₈	—	89	1	no	—
255	C₄×D₄	—	89	1	no	—
256	C₄×D₄	—	89	1	no	—
257	C₄×D₄	—	178	1	no	—
258	C₂×C₂²⋊C₄	—	178	1	no	—
259	#106	—	89	1	no	—
260	C₄⋊C₈	—	89	1	no	—
261	#103	—	89	1	no	—
262	#103	—	89	1	no	—
263	#103	—	89	1	no	—
264	#102	—	89	1	no	—
265	#102	—	89	1	no	—
266	#102	—	89	1	no	—
267	C₂²⋊C₈	—	89	1	no	—
268	C₂²⋊C₈	—	89	1	no	—
269	C₄×C₈	—	89	1	no	—
270	C₂⁴	—	2	1	no	—
271	#41	—	2	2	no	—
272	#41	—	4	1	no	—
273	#41	—	356	1	no	—
274	#41	—	178	2	no	—
275	C₂×Q₈	—	89	1	no	—
276	C₂×Q₈	—	89	1	no	—
277	C₂×Q₈	—	356	1	no	—
278	C₂×Q₈	—	178	1	no	—
279	C₂×Q₈	—	178	2	no	—
280	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	89	1	no	—
286	C₂×D₄	—	178	1	no	—
287	C₂×D₄	—	178	1	no	—
288	C₂×D₄	—	178	1	no	—
289	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
290	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
291	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	89	1	no	—
294	C₂²×C₄	—	178	1	no	—
295	C₂²×C₄	—	178	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
298	Q₁₆	—	178	2	no	—
299	Q₁₆	—	178	2	no	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	356	1	no	—
302	SD₁₆	—	356	1	no	—
303	SD₁₆	—	178	2	no	—
304	SD₁₆	C₂²⋊D₈₉	1	4	yes	complemented
305	D₈	—	2	2	no	—
306	D₈	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	178	2	no	—
309	C₂×C₈	—	89	1	no	—
310	C₂×C₈	—	89	1	no	—
311	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄⋊C₄	—	89	1	no	—
314	C₄⋊C₄	—	89	1	no	—
315	C₄⋊C₄	—	89	1	no	—
316	C₄⋊C₄	—	178	1	no	—
317	C₄⋊C₄	—	178	1	no	—
318	C₄⋊C₄	—	178	1	no	—
319	C₂²⋊C₄	—	89	1	no	—
320	C₂²⋊C₄	—	89	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	C₂²⋊C₄	—	178	1	no	—
326	C₂²⋊C₄	—	178	1	no	—
327	C₂²⋊C₄	—	178	1	no	—
328	C₂²⋊C₄	—	178	1	no	—
329	C₂²⋊C₄	—	178	1	no	—
330	C₄²	—	89	1	no	—
331	C₄²	—	178	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	89	1	no	—
339	C₂³	D₄×D₈₉	1	1	yes	characteristic
340	Q₈	—	2	1	no	—
341	Q₈	—	356	2	no	—
342	Q₈	—	178	1	no	—
343	Q₈	—	178	1	no	—
344	Q₈	—	178	1	no	—
345	Q₈	—	178	1	no	—
346	Q₈	C₂×C₂²⋊D₈₉	1	2	yes	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	356	2	no	—
355	D₄	—	356	2	no	—
356	D₄	—	356	1	no	—
357	D₄	—	712	1	no	—
358	D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	89	1	no	—
364	C₂×C₄	—	89	1	no	—
365	C₂×C₄	—	89	1	no	—
366	C₂×C₄	—	356	2	no	—
367	C₂×C₄	—	356	2	no	—
368	C₂×C₄	—	178	1	no	—
369	C₂×C₄	—	178	1	no	—
370	C₂×C₄	—	178	1	no	—
371	C₂×C₄	—	178	1	no	—
372	C₂×C₄	—	178	1	no	—
373	C₂×C₄	—	178	1	no	—
374	C₂×C₄	—	712	1	no	—
375	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
377	C₈	—	2	1	no	—
378	C₈	—	178	1	no	—
379	C₈	—	178	1	no	—
380	C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	178	1	no	—
395	C₂²	—	178	1	no	—
396	C₂²	—	178	1	no	—
397	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	356	1	no	—
401	C₄	—	356	1	no	—
402	C₄	—	356	1	no	—
403	C₄	—	356	1	no	—
404	C₄	—	178	1	no	—
405	C₄	—	178	1	no	—
406	C₄	—	178	1	no	—
407	C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
408	C₄	#15668057	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	4	2	no	—
411	C₂	—	8	1	no	—
412	C₂	—	8	1	no	—
413	C₂	—	356	1	no	—
414	C₂	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
415	C₂	#19152394	1	1	yes	characteristic
416	C₂	#19152408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₂×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#3275
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#15668041	C₂	semidirect
2. #19152255	C₂	semidirect
3. #19152242	C₂	semidirect
4. #19151981	C₂	semidirect
5. #19151856	C₂	semidirect
6. #19151848	C₂	semidirect
7. #19151818	C₂	semidirect
8. #19151811	C₂	semidirect
9. #19151760	C₂	semidirect
10. #19151749	C₂	semidirect
11. #19151740	C₂	semidirect
12. #19151735	C₂	semidirect
13. SD₁₆×Dic₈₉	C₂	semidirect
14. #19151674	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
17. C₂×Q₈×D₈₉	C₂²	semidirect
19. C₂×Dic₃₅₆	C₂²	semidirect
20. C₂×#13083564	C₂²	semidirect
23. C₂×#13083562	C₂²	semidirect
24. C₂×#13083557	C₂²	semidirect
27. #15667999	C₂²	semidirect
35. #15667983	C₂²	semidirect
37. Q₈×Dic₈₉	C₂²	semidirect
42. #15667944	C₂²	semidirect
43. #15667941	C₂²	semidirect
44. #15667937	C₂²	semidirect
45. #15667937	C₂²	semidirect
46. #15667936	C₂²	semidirect
49. #15667933	C₂²	semidirect
51. #15667924	C₂²	semidirect
52. C₈×Dic₈₉	C₂²	semidirect
117. SD₁₆×C₈₉	D₄	semidirect
209. C₈₉	#3275	semidirect
211. C₂×AGL(1,ℤ/8)	D₈₉	semidirect
304. SD₁₆	C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668041	2
#19152255	2
#19152242	2
#19151981	2
#19151856	2
#19151848	2
#19151818	2
#19151811	2
#19151760	2
#19151749	2
#19151740	2
#19151735	2
SD₁₆×Dic₈₉	2
#19151674	2
C₂×AGL(1,ℤ/8)×C₈₉	2
#3275	89