Subgroups — #36525281

Order 22784.

584 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029347	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029328	C₂	1	1	yes	maximal, characteristic
3	#26019131	C₂	1	2	yes	maximal, complemented
4	#26019110	C₂	1	2	yes	maximal, complemented
5	#26019096	C₂	1	2	yes	maximal, complemented
6	#26019089	C₂	1	2	yes	maximal, complemented
7	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018725	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018721	C₂	1	1	yes	maximal, characteristic
10	#26018544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	2	no	—
13	#19151729	C₂²	1	2	yes	—
14	Q₈×#10623494	C₂²	1	2	yes	—
15	#19151676	C₂²	1	2	yes	—
16	#19151670	—	2	2	no	—
17	D₄×#10623494	C₂²	1	2	yes	—
18	#19151659	—	2	2	no	—
19	#19151655	C₂²	1	1	yes	characteristic
20	#19151655	C₂²	1	1	yes	characteristic
21	#19151651	C₂²	1	1	yes	characteristic
22	#19151651	C₂²	1	1	yes	characteristic
23	#19151565	—	2	2	no	—
24	#19151351	C₂²	1	2	yes	—
25	#19151349	C₂²	1	2	yes	—
26	Q₈⋊#10623494	C₂²	1	2	yes	—
27	Q₈⋊#10623494	C₂²	1	2	yes	—
28	D₄⋊#10623494	C₂²	1	2	yes	—
29	D₄⋊#10623494	C₂²	1	2	yes	—
30	#19151320	C₂²	1	1	yes	characteristic
31	#19151320	C₂²	1	1	yes	characteristic
32	#19151320	C₂²	1	1	yes	characteristic
33	#19151320	C₂²	1	1	yes	characteristic
34	#533×C₈₉	C₂²	1	1	yes	characteristic
35	#532×C₈₉	C₂²	1	1	yes	characteristic
36	#498×C₈₉	C₄	1	1	yes	characteristic
37	#492×C₈₉	C₄	1	1	yes	characteristic
38	#487×C₈₉	C₄	1	1	yes	characteristic
39	#486×C₈₉	C₄	1	1	yes	characteristic
40	#465×C₈₉	C₄	1	2	yes	—
41	#465×C₈₉	C₄	1	2	yes	—
42	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
43	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083558	—	2	2	no	—
46	C₂²×#10623494	—	2	2	no	—
47	C₄⋊#10623494	—	2	2	no	—
48	C₄⋊#10623494	—	2	2	no	—
49	C₄⋊#10623494	—	2	1	no	—
50	C₄⋊#10623494	D₄	1	2	yes	—
51	C₄⋊#10623494	C₂³	1	2	yes	—
52	C₄⋊#10623494	C₂³	1	2	yes	—
53	C₂²⋊#10623494	—	2	2	no	—
54	C₂²⋊#10623494	—	2	2	no	—
55	C₂²⋊#10623494	—	2	1	no	—
56	C₂²⋊#10623494	—	2	1	no	—
57	C₂²⋊#10623494	—	2	1	no	—
58	C₂²⋊#10623494	D₄	1	2	yes	—
59	#15667923	—	2	2	no	—
60	#15667923	—	2	1	no	—
61	#15667923	—	2	1	no	—
62	C₄×#10623494	—	2	2	no	—
63	C₄×#10623494	C₂³	1	1	yes	characteristic
64	C₄×#10623494	C₂³	1	1	yes	characteristic
65	C₄×#10623494	C₂³	1	1	yes	characteristic
66	C₄×#10623494	C₂³	1	1	yes	characteristic
67	C₂×#41×C₈₉	—	2	1	no	—
68	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
69	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
75	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
76	#125×C₈₉	—	2	1	no	—
77	#124×C₈₉	—	2	1	no	—
78	C₂²⋊Q₈×C₈₉	—	2	1	no	—
79	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
80	#121×C₈₉	—	2	1	no	—
81	#121×C₈₉	C₂×C₄	1	2	yes	—
82	C₄×Q₈×C₈₉	—	2	1	no	—
83	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
84	C₄×D₄×C₈₉	—	2	1	no	—
85	C₄×D₄×C₈₉	C₂³	1	2	yes	—
86	#117×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	#106×C₈₉	C₂×C₄	1	2	yes	—
89	#106×C₈₉	C₂×C₄	1	2	yes	—
90	#103×C₈₉	C₂×C₄	1	2	yes	—
91	#103×C₈₉	C₂×C₄	1	2	yes	—
92	#102×C₈₉	C₂×C₄	1	2	yes	—
93	#102×C₈₉	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#13083558	—	8	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	—	2	2	no	—
101	C₂×#10623494	—	2	1	no	—
102	C₂×#10623494	—	2	1	no	—
103	C₂×#10623494	—	8	2	no	—
104	C₂×#10623494	C₂×D₄	1	2	yes	—
105	C₂×#10623494	C₂×D₄	1	2	yes	—
106	#41×C₈₉	—	8	2	no	—
107	C₂×Q₈×C₈₉	—	2	1	no	—
108	C₂×Q₈×C₈₉	—	2	1	no	—
109	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₈₉	—	2	2	no	—
111	C₂×D₄×C₈₉	—	2	1	no	—
112	C₂×D₄×C₈₉	—	2	1	no	—
113	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
118	SD₁₆×C₈₉	—	4	2	no	—
119	SD₁₆×C₈₉	—	4	2	no	—
120	C₂×C₈×C₈₉	—	4	1	no	—
121	C₂×C₈×C₈₉	—	4	1	no	—
122	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	2	2	no	—
132	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₂²⋊C₄×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₈₉	#41	1	1	yes	characteristic
141	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂³×C₈₉	—	2	2	no	—
143	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₈₉	—	2	2	no	—
145	Q₈×C₈₉	—	2	2	no	—
146	Q₈×C₈₉	—	8	1	no	—
147	Q₈×C₈₉	—	8	1	no	—
148	D₄×C₈₉	—	2	2	no	—
149	D₄×C₈₉	—	2	2	no	—
150	D₄×C₈₉	—	8	1	no	—
151	D₄×C₈₉	—	8	1	no	—
152	D₄×C₈₉	—	8	2	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₈×C₈₉	—	2	1	no	—
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	#10623494	—	2	2	no	—
173	#10623494	—	2	2	no	—
174	#10623494	—	4	1	no	—
175	#10623494	—	4	1	no	—
176	#10623494	—	4	2	no	—
177	#10623494	—	4	2	no	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	4	2	no	—
182	C₂²×C₈₉	—	4	2	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	4	2	no	—
190	C₄×C₈₉	—	4	2	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	#568	1	1	yes	characteristic
193	C₄×C₈₉	#568	1	1	yes	characteristic
194	C₄×C₈₉	#577	1	2	yes	—
195	#17990	—	89	1	no	maximal, Sylow
196	C₂×C₈₉	—	4	1	no	—
197	C₂×C₈₉	—	8	2	no	—
198	C₂×C₈₉	#2932	1	1	yes	characteristic
199	C₂×C₈₉	#2949	1	1	yes	characteristic
200	C₂×C₈₉	#2957	1	1	yes	characteristic
201	#3167	D₈₉	1	1	yes	characteristic
202	#2985	—	89	1	no	—
203	#2981	—	89	1	no	—
204	#1588	—	89	2	no	—
205	#1585	—	89	2	no	—
206	#1583	—	89	2	no	—
207	#1582	—	89	2	no	—
208	#1568	—	89	1	no	—
209	#1497	—	89	1	no	—
210	#1496	—	89	1	no	—
211	#1452	—	89	1	no	—
212	C₈₉	#17990	1	1	yes	characteristic, complemented, Sylow
213	#533	C₂×D₈₉	1	1	yes	characteristic
214	#532	C₂×D₈₉	1	1	yes	characteristic
215	#498	Dic₈₉	1	1	yes	characteristic
216	#492	Dic₈₉	1	1	yes	characteristic
217	#487	Dic₈₉	1	1	yes	characteristic
218	#486	Dic₈₉	1	1	yes	characteristic
219	#465	Dic₈₉	1	2	yes	—
220	#465	Dic₈₉	1	2	yes	—
221	#446	—	89	2	no	—
222	#446	—	178	2	no	—
223	C₈×Q₈	—	89	2	no	—
224	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
225	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
226	#436	—	89	2	no	—
227	#435	—	178	2	no	—
228	C₈×D₄	—	89	2	no	—
229	#433	—	178	2	no	—
230	#432	—	89	1	no	—
231	#432	—	89	1	no	—
232	#431	—	89	1	no	—
233	#431	—	89	1	no	—
234	#408	—	178	2	no	—
235	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
236	#335	—	89	2	no	—
237	#334	—	89	2	no	—
238	Q₈⋊C₈	—	89	2	no	—
239	Q₈⋊C₈	—	89	2	no	—
240	D₄⋊C₈	—	89	2	no	—
241	D₄⋊C₈	—	89	2	no	—
242	#322	—	89	1	no	—
243	#322	—	89	1	no	—
244	#322	—	89	1	no	—
245	#322	—	89	1	no	—
246	C₂×#41	—	2	1	no	—
247	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
248	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
249	C₂×M₁₆	—	178	2	no	—
250	C₂²×C₈	—	178	2	no	—
251	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
252	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
253	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
254	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
255	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
256	#127	C₂×Dic₈₉	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#124	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
261	#121	—	2	1	no	—
262	#121	C₂×Dic₈₉	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂²×D₈₉	1	2	yes	—
267	#117	—	2	1	no	—
268	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
269	#106	C₂×Dic₈₉	1	2	yes	—
270	#106	C₂×Dic₈₉	1	2	yes	—
271	C₄⋊C₈	—	89	2	no	—
272	C₄⋊C₈	—	89	2	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	178	2	no	—
275	C₄⋊C₈	—	178	2	no	—
276	C₄⋊C₈	—	178	1	no	—
277	#103	C₂×Dic₈₉	1	2	yes	—
278	#103	C₂×Dic₈₉	1	2	yes	—
279	#102	C₂×Dic₈₉	1	2	yes	—
280	#102	C₂×Dic₈₉	1	2	yes	—
281	C₂²⋊C₈	—	89	2	no	—
282	C₂²⋊C₈	—	178	2	no	—
283	C₂²⋊C₈	—	178	2	no	—
284	C₂²⋊C₈	—	178	1	no	—
285	C₂²⋊C₈	—	178	1	no	—
286	C₂²⋊C₈	—	178	1	no	—
287	#97	—	178	2	no	—
288	#97	—	178	1	no	—
289	#97	—	178	1	no	—
290	C₄×C₈	—	89	1	no	—
291	C₄×C₈	—	89	1	no	—
292	C₄×C₈	—	89	1	no	—
293	C₄×C₈	—	89	1	no	—
294	C₄×C₈	—	178	2	no	—
295	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	#13083573	1	1	yes	characteristic
311	SD₁₆	—	4	2	no	—
312	SD₁₆	—	4	2	no	—
313	M₁₆	—	712	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	89	2	no	—
317	C₂×C₈	—	89	2	no	—
318	C₂×C₈	—	178	2	no	—
319	C₂×C₈	—	178	2	no	—
320	C₂×C₈	—	178	1	no	—
321	C₂×C₈	—	178	1	no	—
322	C₂×C₈	—	712	2	no	—
323	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
324	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
334	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
340	C₄²	D₄×D₈₉	1	1	yes	characteristic
341	C₄²	#13083573	1	1	yes	characteristic
342	C₄²	C₂³×D₈₉	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	356	1	no	—
374	C₈	—	356	1	no	—
375	C₈	—	356	2	no	—
376	C₈	—	356	2	no	—
377	C₈	—	178	2	no	—
378	C₈	—	178	2	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	#19152365	1	1	yes	characteristic
394	C₄	#19152365	1	1	yes	characteristic
395	C₄	#19152404	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	#26028970	1	1	yes	characteristic
399	C₂	#26029112	1	1	yes	characteristic
400	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3167	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#532×C₈₉	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3167	D₈₉
hypocenter	C₈₉	#17990
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #26029347	C₂	semidirect
3. #26019131	C₂	semidirect
4. #26019110	C₂	semidirect
5. #26019096	C₂	semidirect
6. #26019089	C₂	semidirect
7. #26019015	C₂	semidirect
8. #26018725	C₂	semidirect
10. #26018544	C₂	semidirect
212. C₈₉	#17990	semidirect

Maximal subgroups

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

subgroup	index
#26029347	2
#26029328	2
#26019131	2
#26019110	2
#26019096	2
#26019089	2
#26019015	2
#26018725	2
#26018721	2
#26018544	2
C₈₉×#3167	2
#17990	89