Subgroups — #26031787

Order 11392.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 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	#19152270	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151988	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151847	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151833	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151794	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151759	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151746	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151742	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151733	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151696	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151668	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×#13083575	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	#15668039	—	2	4	no	—
21	#15668035	—	2	4	no	—
22	C₂×#13083561	C₂²	1	1	yes	characteristic
23	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
26	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
27	C₂×#13083559	C₂²	1	1	yes	characteristic
28	C₂×#13083559	C₂²	1	1	yes	characteristic
29	C₂×#13083557	C₂²	1	1	yes	characteristic
30	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
31	#15668009	—	2	1	no	—
32	#15668009	C₂²	1	1	yes	characteristic, complemented
33	#15667994	—	2	1	no	—
34	#15667988	C₂²	1	1	yes	characteristic
35	#15667987	—	2	1	no	—
36	#15667987	—	2	1	no	—
37	#15667987	C₂²	1	1	yes	characteristic
38	#15667987	C₂²	1	1	yes	characteristic, complemented
39	#15667985	—	2	1	no	—
40	#15667983	C₂²	1	1	yes	characteristic
41	#15667982	—	2	1	no	—
42	C₄×D₃₅₆	—	2	1	no	—
43	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
44	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
45	C₂²⋊C₄×D₈₉	—	2	1	no	—
46	#15667945	C₂²	1	1	yes	characteristic, complemented
47	#15667936	C₂²	1	1	yes	characteristic, complemented
48	#15667934	C₂²	1	1	yes	characteristic, complemented
49	#15667934	C₂²	1	1	yes	characteristic, complemented
50	#15667932	C₂²	1	1	yes	characteristic
51	#15667924	C₂²	1	1	yes	characteristic
52	#15667924	C₂²	1	1	yes	characteristic, complemented
53	#15667923	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	—	4	1	no	—
66	#13083575	—	4	1	no	—
67	#13083575	—	4	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	—	2	1	no	—
71	C₂×D₃₅₆	—	2	1	no	—
72	C₂×D₃₅₆	—	2	1	no	—
73	C₂×D₃₅₆	—	2	1	no	—
74	C₂×D₃₅₆	—	2	1	no	—
75	C₂×D₃₅₆	D₄	1	1	yes	characteristic
76	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
77	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
78	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊D₈₉	—	2	1	no	—
80	C₂×C₂²⋊D₈₉	—	2	1	no	—
81	D₄×D₈₉	—	2	2	no	—
82	D₄×D₈₉	—	4	1	no	—
83	C₂×C₄×D₈₉	—	2	1	no	—
84	C₂×C₄×D₈₉	—	2	1	no	—
85	C₂×C₄×D₈₉	—	2	1	no	—
86	C₂×C₄×D₈₉	—	2	1	no	—
87	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
89	#13083561	—	2	2	no	—
90	#13083561	—	4	1	no	—
91	#13083561	D₄	1	4	yes	complemented
92	D₇₁₂	—	2	2	no	—
93	D₇₁₂	—	2	2	no	—
94	#13083559	—	2	2	no	—
95	#13083559	—	4	1	no	—
96	#13083557	—	2	2	no	—
97	C₂×#10623494	C₂³	1	1	yes	characteristic
98	C₂×#10623494	C₂³	1	1	yes	characteristic
99	C₈×D₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
101	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
102	#13083553	—	2	1	no	—
103	C₂²⋊Dic₈₉	—	2	1	no	—
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	#13083551	—	2	1	no	—
108	#13083551	D₄	1	1	yes	characteristic
109	#13083551	D₄	1	1	yes	characteristic
110	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	Q₁₆×C₈₉	—	2	2	no	—
114	SD₁₆×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	—	2	1	no	—
118	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₄²×C₈₉	—	2	1	no	—
122	C₄²×C₈₉	C₂³	1	1	yes	characteristic
123	C₂³×C₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	2	1	no	—
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	—	4	2	no	—
128	C₂²×D₈₉	—	4	2	no	—
129	C₂²×D₈₉	—	8	1	no	—
130	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₈₉	—	2	1	no	—
133	Q₈×C₈₉	—	2	1	no	—
134	Q₈×C₈₉	—	2	1	no	—
135	Q₈×C₈₉	C₂×D₄	1	2	yes	—
136	D₄×C₈₉	—	2	1	no	—
137	D₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₈₉	—	4	2	no	—
145	C₂²⋊D₈₉	—	8	1	no	—
146	C₂×Dic₈₉	—	2	1	no	—
147	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
149	D₃₅₆	—	2	1	no	—
150	D₃₅₆	—	2	1	no	—
151	D₃₅₆	—	2	1	no	—
152	D₃₅₆	—	2	1	no	—
153	D₃₅₆	—	2	1	no	—
154	D₃₅₆	—	4	1	no	—
155	D₃₅₆	—	4	2	no	—
156	D₃₅₆	—	4	2	no	—
157	D₃₅₆	—	4	2	no	—
158	D₃₅₆	—	4	2	no	—
159	D₃₅₆	—	8	1	no	—
160	D₃₅₆	—	8	1	no	—
161	D₃₅₆	—	8	1	no	—
162	D₃₅₆	C₂×D₄	1	2	yes	—
163	C₄×D₈₉	—	2	1	no	—
164	C₄×D₈₉	—	2	1	no	—
165	C₄×D₈₉	—	2	1	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	4	2	no	—
168	C₄×D₈₉	—	4	2	no	—
169	C₄×D₈₉	—	4	2	no	—
170	C₄×D₈₉	—	8	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	—	2	1	no	—
173	#10623494	—	2	1	no	—
174	#10623494	C₂×D₄	1	2	yes	—
175	C₂²×C₈₉	—	4	1	no	—
176	C₂²×C₈₉	—	4	1	no	—
177	C₂²×C₈₉	—	4	1	no	—
178	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×D₈₉	—	2	1	no	—
180	C₂×D₈₉	—	2	1	no	—
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	1	no	—
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	1	no	—
186	C₂×D₈₉	—	4	1	no	—
187	C₂×D₈₉	—	4	1	no	—
188	C₂×D₈₉	—	4	1	no	—
189	C₂×D₈₉	—	4	1	no	—
190	C₂×D₈₉	—	4	1	no	—
191	C₂×D₈₉	—	4	1	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	4	1	no	—
194	C₂×D₈₉	—	8	4	no	—
195	C₄×C₈₉	—	2	2	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
202	Dic₈₉	—	2	1	no	—
203	Dic₈₉	—	2	1	no	—
204	Dic₈₉	—	4	1	no	—
205	C₂×C₈₉	—	8	1	no	—
206	C₂×C₈₉	D₄²	1	1	yes	characteristic
207	C₂×C₈₉	#575	1	1	yes	characteristic
208	C₂×C₈₉	#576	1	1	yes	characteristic
209	D₈₉	—	4	1	no	—
210	D₈₉	—	4	1	no	—
211	D₈₉	—	4	2	no	—
212	D₈₉	—	8	1	no	—
213	D₈₉	—	8	1	no	—
214	#3268	—	89	1	no	maximal, Sylow
215	C₈₉	#3268	1	1	yes	characteristic, complemented, Sylow
216	C₂×AGL(1,ℤ/8)	—	89	1	no	—
217	C₂×#135	—	89	1	no	—
218	#550	—	89	1	no	—
219	#546	—	89	1	no	—
220	#496	—	89	1	no	—
221	#468	—	89	1	no	—
222	#466	—	89	1	no	—
223	#464	D₈₉	1	1	yes	characteristic, complemented
224	#459	—	89	1	no	—
225	#452	—	89	1	no	—
226	#449	—	89	1	no	—
227	#449	—	89	1	no	—
228	#447	—	89	1	no	—
229	#440	—	89	1	no	—
230	#435	—	89	1	no	—
231	C₂×#41	—	89	1	no	—
232	C₂×#41	—	89	1	no	—
233	C₂×#41	—	89	1	no	—
234	C₂²×D₄	—	89	1	no	—
235	AGL(1,ℤ/8)	—	178	4	no	—
236	#135	—	178	4	no	—
237	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
238	C₂×SD₁₆	—	89	1	no	—
239	C₂×SD₁₆	—	89	1	no	—
240	C₂×SD₁₆	—	89	1	no	—
241	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
242	C₂×D₈	—	89	1	no	—
243	C₂×D₈	—	89	1	no	—
244	C₂×D₈	—	89	1	no	—
245	C₂×D₈	—	89	1	no	—
246	C₂×M₁₆	—	89	1	no	—
247	C₂²×C₈	—	89	1	no	—
248	#127	—	89	1	no	—
249	#127	—	178	1	no	—
250	#124	C₂×D₈₉	1	1	yes	characteristic
251	#123	—	178	1	no	—
252	C₂²⋊Q₈	—	89	1	no	—
253	#121	—	89	1	no	—
254	#121	—	89	1	no	—
255	#121	—	89	1	no	—
256	#121	—	178	1	no	—
257	#121	—	178	1	no	—
258	#121	—	178	1	no	—
259	#120	—	178	1	no	—
260	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
261	C₄×D₄	—	89	1	no	—
262	C₄×D₄	—	89	1	no	—
263	C₄×D₄	—	178	1	no	—
264	C₂×C₂²⋊C₄	—	178	1	no	—
265	#107	—	89	1	no	—
266	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
267	#103	—	89	1	no	—
268	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
269	#102	—	89	1	no	—
270	#102	—	89	1	no	—
271	#102	—	89	1	no	—
272	#102	C₂×D₈₉	1	1	yes	characteristic
273	C₂²⋊C₈	—	89	1	no	—
274	C₂²⋊C₈	—	89	1	no	—
275	#97	—	89	1	no	—
276	C₂⁴	—	178	1	no	—
277	#41	—	356	1	no	—
278	#41	—	356	1	no	—
279	#41	—	356	1	no	—
280	#41	—	178	2	no	—
281	#41	—	178	2	no	—
282	#41	—	178	2	no	—
283	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×D₄	—	89	1	no	—
286	C₂×D₄	—	89	1	no	—
287	C₂×D₄	—	89	1	no	—
288	C₂×D₄	—	89	1	no	—
289	C₂×D₄	—	356	1	no	—
290	C₂×D₄	—	178	1	no	—
291	C₂×D₄	—	178	1	no	—
292	C₂×D₄	—	178	1	no	—
293	C₂×D₄	—	178	1	no	—
294	C₂×D₄	—	178	1	no	—
295	C₂×D₄	—	178	1	no	—
296	C₂×D₄	—	178	2	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂×D₄	—	178	1	no	—
300	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
301	C₂²×C₄	—	89	1	no	—
302	C₂²×C₄	—	89	1	no	—
303	C₂²×C₄	—	178	1	no	—
304	C₂²×C₄	—	178	1	no	—
305	C₂²×C₄	—	178	1	no	—
306	C₂²×C₄	—	178	1	no	—
307	Q₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	89	4	no	—
310	SD₁₆	—	356	1	no	—
311	SD₁₆	—	178	2	no	—
312	D₈	—	356	1	no	—
313	D₈	—	178	2	no	—
314	D₈	—	178	2	no	—
315	D₈	—	178	2	no	—
316	M₁₆	—	178	2	no	—
317	C₂×C₈	—	89	1	no	—
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	178	2	no	—
320	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	89	1	no	—
324	C₄⋊C₄	—	89	1	no	—
325	C₄⋊C₄	—	178	1	no	—
326	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	89	1	no	—
330	C₂²⋊C₄	—	89	1	no	—
331	C₂²⋊C₄	—	178	1	no	—
332	C₂²⋊C₄	—	178	1	no	—
333	C₂²⋊C₄	—	178	1	no	—
334	C₂²⋊C₄	—	178	1	no	—
335	C₂²⋊C₄	—	178	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	C₂²×D₈₉	1	1	yes	characteristic
338	C₂³	—	2	1	no	—
339	C₂³	—	89	1	no	—
340	C₂³	—	89	1	no	—
341	C₂³	—	356	2	no	—
342	C₂³	—	356	2	no	—
343	C₂³	—	178	1	no	—
344	C₂³	—	178	1	no	—
345	C₂³	—	178	1	no	—
346	C₂³	—	712	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	2	1	no	—
349	Q₈	—	2	1	no	—
350	Q₈	D₄×D₈₉	1	2	yes	—
351	D₄	—	2	1	no	—
352	D₄	—	2	1	no	—
353	D₄	—	89	2	no	—
354	D₄	—	356	2	no	—
355	D₄	—	356	2	no	—
356	D₄	—	356	2	no	—
357	D₄	—	356	1	no	—
358	D₄	—	356	2	no	—
359	D₄	—	356	2	no	—
360	D₄	—	178	1	no	—
361	D₄	—	178	1	no	—
362	D₄	—	178	1	no	—
363	D₄	—	178	1	no	—
364	D₄	—	178	1	no	—
365	D₄	—	712	1	no	—
366	D₄	—	712	1	no	—
367	D₄	—	712	1	no	—
368	D₄	—	712	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	89	1	no	—
373	C₂×C₄	—	89	1	no	—
374	C₂×C₄	—	356	2	no	—
375	C₂×C₄	—	356	2	no	—
376	C₂×C₄	—	356	2	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	—	178	1	no	—
382	C₂×C₄	—	712	1	no	—
383	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	89	2	no	—
389	C₈	—	178	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	356	1	no	—
394	C₂²	—	356	1	no	—
395	C₂²	—	356	1	no	—
396	C₂²	—	356	1	no	—
397	C₂²	—	356	1	no	—
398	C₂²	—	356	1	no	—
399	C₂²	—	356	1	no	—
400	C₂²	—	356	1	no	—
401	C₂²	—	178	1	no	—
402	C₂²	—	178	1	no	—
403	C₂²	—	178	1	no	—
404	C₂²	—	178	1	no	—
405	C₂²	—	178	2	no	—
406	C₂²	—	178	1	no	—
407	C₂²	—	178	1	no	—
408	C₂²	—	712	4	no	—
409	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	356	1	no	—
416	C₄	—	178	1	no	—
417	C₄	—	178	1	no	—
418	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
419	C₄	#15668058	1	1	yes	characteristic
420	C₂	—	8	1	no	—
421	C₂	—	356	2	no	—
422	C₂	—	356	1	no	—
423	C₂	—	356	1	no	—
424	C₂	—	712	1	no	—
425	C₂	—	712	1	no	—
426	C₂	#19152232	1	1	yes	characteristic
427	C₂	#19152397	1	1	yes	characteristic
428	C₂	#19152400	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	#3268
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. #19152270	C₂	semidirect
4. #19152241	C₂	semidirect
5. #19151988	C₂	semidirect
6. #19151847	C₂	semidirect
7. #19151833	C₂	semidirect
8. #19151794	C₂	semidirect
9. #19151759	C₂	semidirect
10. #19151746	C₂	semidirect
11. #19151742	C₂	semidirect
12. #19151733	C₂	semidirect
13. #19151696	C₂	semidirect
14. #19151668	C₂	semidirect
15. #464×C₈₉	C₂	semidirect
18. C₂×#13083575	C₂²	semidirect
23. C₂×#13083561	C₂²	semidirect
24. C₂×#13083561	C₂²	semidirect
30. C₂×C₈×D₈₉	C₂²	semidirect
32. #15668009	C₂²	semidirect
38. #15667987	C₂²	semidirect
46. #15667945	C₂²	semidirect
47. #15667936	C₂²	semidirect
48. #15667934	C₂²	semidirect
49. #15667934	C₂²	semidirect
52. #15667924	C₂²	semidirect
53. #15667923	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
91. #13083561	D₄	semidirect
215. C₈₉	#3268	semidirect
223. #464	D₈₉	semidirect
237. C₂×Q₁₆	C₂×D₈₉	semidirect
260. C₄×Q₈	C₂×D₈₉	semidirect
266. C₄⋊C₈	C₂×D₈₉	semidirect
268. #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
#19152270	2
#19152241	2
#19151988	2
#19151847	2
#19151833	2
#19151794	2
#19151759	2
#19151746	2
#19151742	2
#19151733	2
#19151696	2
#19151668	2
#464×C₈₉	2
#3268	89