Subgroups — #36539678

Order 22784.

650 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	#26030339	C₂	1	1	yes	maximal, characteristic
2	#26030256	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029275	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019686	C₂	1	2	yes	maximal, complemented
5	#26019658	C₂	1	2	yes	maximal, complemented
6	#26019648	C₂	1	2	yes	maximal, complemented
7	#26019624	C₂	1	2	yes	maximal, complemented
8	#26019032	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018962	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018914	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
13	#19151926	—	2	1	no	—
14	#19151914	—	2	1	no	—
15	#19151885	C₂²	1	2	yes	—
16	#19151885	C₂²	1	2	yes	—
17	#19151800	C₂²	1	2	yes	—
18	#19151790	C₂²	1	2	yes	—
19	#19151748	—	2	1	no	—
20	#19151731	—	2	1	no	—
21	#19151708	—	2	2	no	—
22	C₄×#13083561	—	2	2	no	—
23	C₈×D₃₅₆	C₂²	1	2	yes	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151663	—	2	2	no	—
26	#19151655	C₂²	1	1	yes	characteristic
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151651	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₈₉	—	2	2	no	—
30	#19151351	C₂²	1	2	yes	complemented
31	#19151349	C₂²	1	2	yes	complemented
32	#19151347	C₂²	1	2	yes	complemented
33	#19151347	C₂²	1	2	yes	complemented
34	#19151344	C₂²	1	2	yes	complemented
35	#19151342	C₂²	1	2	yes	complemented
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	#532×C₈₉	C₂²	1	1	yes	characteristic
38	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#482×C₈₉	—	2	2	no	—
43	#478×C₈₉	—	2	2	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₈₉	—	2	1	no	—
47	C₂×#13083561	—	2	2	no	—
48	C₂×#13083559	—	2	2	no	—
49	C₂×C₈×D₈₉	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	C₄×D₃₅₆	—	2	1	no	—
52	C₄×D₃₅₆	—	2	1	no	—
53	C₄×D₃₅₆	D₄	1	2	yes	—
54	C₄×D₃₅₆	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
56	C₂×#13083551	—	2	1	no	—
57	#15667943	—	2	2	no	—
58	#15667943	—	2	2	no	—
59	C₄⋊#10623494	C₂³	1	2	yes	—
60	C₄⋊#10623494	C₂³	1	2	yes	—
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	#15667936	—	2	2	no	—
63	#15667933	—	2	2	no	—
64	#15667932	—	2	2	no	—
65	#15667932	—	2	2	no	—
66	C₂²⋊#10623494	—	2	1	no	—
67	C₂²⋊#10623494	—	2	1	no	—
68	C₂²⋊#10623494	—	2	1	no	—
69	#15667924	—	2	2	no	—
70	#15667924	—	2	2	no	—
71	#15667923	—	2	1	no	—
72	C₄×#10623494	—	2	1	no	—
73	C₄×#10623494	—	2	1	no	—
74	C₂×#41×C₈₉	—	2	1	no	—
75	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
78	#127×C₈₉	C₂³	1	1	yes	characteristic
79	#125×C₈₉	—	2	1	no	—
80	#124×C₈₉	—	2	1	no	—
81	C₂²⋊Q₈×C₈₉	—	2	1	no	—
82	C₂²⋊Q₈×C₈₉	—	2	1	no	—
83	#121×C₈₉	—	2	1	no	—
84	#121×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	—	2	1	no	—
87	C₄×D₄×C₈₉	—	2	1	no	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	#117×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	#107×C₈₉	—	2	2	no	—
92	#106×C₈₉	—	2	2	no	—
93	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
94	#102×C₈₉	—	2	2	no	—
95	#102×C₈₉	—	2	2	no	—
96	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×D₈₉	—	2	1	no	—
100	C₂×D₃₅₆	—	2	1	no	—
101	C₂×D₃₅₆	—	2	4	no	—
102	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
103	C₂²×Dic₈₉	—	2	1	no	—
104	C₂×C₄×D₈₉	—	2	2	no	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	8	2	no	—
107	#13083561	—	4	4	no	—
108	#13083559	—	4	4	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	2	2	no	—
112	C₈×D₈₉	—	8	2	no	—
113	C₈×D₈₉	—	8	2	no	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
116	#13083551	—	2	2	no	—
117	#13083551	—	2	2	no	—
118	#41×C₈₉	—	8	2	no	—
119	C₂×Q₈×C₈₉	—	2	1	no	—
120	C₂×Q₈×C₈₉	—	2	1	no	—
121	C₂×Q₈×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	—	2	1	no	—
125	C₂×D₄×C₈₉	—	4	1	no	—
126	C₂²×C₄×C₈₉	—	4	1	no	—
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
130	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	1	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	4	1	no	—
139	C₄⋊C₄×C₈₉	—	4	1	no	—
140	C₂²⋊C₄×C₈₉	—	4	1	no	—
141	C₂²⋊C₄×C₈₉	—	4	1	no	—
142	C₂²⋊C₄×C₈₉	—	4	1	no	—
143	C₄²×C₈₉	—	4	1	no	—
144	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₈₉	#41	1	1	yes	characteristic
147	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₈₉	—	4	1	no	—
149	C₂³×C₈₉	#121	1	1	yes	characteristic
150	C₂²×D₈₉	—	2	2	no	—
151	C₂²×D₈₉	—	2	4	no	—
152	C₂²×D₈₉	—	8	1	no	—
153	C₂²×D₈₉	—	8	1	no	—
154	Q₈×C₈₉	—	4	2	no	—
155	Q₈×C₈₉	—	8	1	no	—
156	Q₈×C₈₉	—	8	1	no	—
157	D₄×C₈₉	—	4	2	no	—
158	D₄×C₈₉	—	4	2	no	—
159	D₄×C₈₉	—	8	1	no	—
160	D₄×C₈₉	—	8	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	8	2	no	—
168	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	8	1	no	—
176	D₃₅₆	—	2	4	no	—
177	D₃₅₆	—	2	2	no	—
178	D₃₅₆	#135	1	4	yes	—
179	C₄×D₈₉	—	4	2	no	—
180	C₄×D₈₉	—	4	2	no	—
181	C₄×D₈₉	—	8	2	no	—
182	C₈×C₈₉	—	2	2	no	—
183	C₈×C₈₉	—	2	2	no	—
184	#10623494	—	4	2	no	—
185	#10623494	—	4	2	no	—
186	#10623494	—	4	2	no	—
187	C₂²×C₈₉	—	2	1	no	—
188	C₂²×C₈₉	—	2	1	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	8	1	no	—
191	C₂²×C₈₉	—	8	1	no	—
192	C₂²×C₈₉	—	8	1	no	—
193	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂×D₈₉	—	2	4	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	8	4	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	8	1	no	—
203	C₄×C₈₉	—	8	1	no	—
204	C₄×C₈₉	—	8	1	no	—
205	C₄×C₈₉	C₂×#135	1	2	yes	—
206	C₄×C₈₉	#577	1	2	yes	—
207	Dic₈₉	—	4	2	no	—
208	#19394	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	—	4	1	no	—
210	C₂×C₈₉	—	16	1	no	—
211	C₂×C₈₉	#3042	1	1	yes	characteristic
212	C₂×C₈₉	#3050	1	1	yes	characteristic
213	C₂×C₈₉	#3068	1	1	yes	characteristic
214	D₈₉	—	4	4	no	—
215	#3228	D₈₉	1	1	yes	characteristic, complemented
216	#3109	—	89	1	no	—
217	#3101	—	89	1	no	—
218	#2972	—	89	1	no	—
219	#1681	—	89	2	no	—
220	#1677	—	89	2	no	—
221	#1675	—	89	2	no	—
222	#1671	—	89	2	no	—
223	#1572	—	89	1	no	—
224	#1554	—	89	1	no	—
225	#1543	—	89	1	no	—
226	C₈₉	#19394	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₈₉	1	1	yes	characteristic
228	#532	C₂×D₈₉	1	1	yes	characteristic
229	C₂×C₄×D₄	—	89	1	no	—
230	#500	C₂×D₈₉	1	1	yes	characteristic, complemented
231	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
232	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
233	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
234	#483	—	178	1	no	—
235	#482	—	2	2	no	—
236	#481	—	178	1	no	—
237	#478	—	2	2	no	—
238	#476	—	89	2	no	—
239	#476	—	89	2	no	—
240	#461	—	89	2	no	—
241	#459	—	89	2	no	—
242	#450	—	178	1	no	—
243	#447	—	178	1	no	—
244	#442	—	178	2	no	—
245	C₄×SD₁₆	—	178	2	no	—
246	C₈×D₄	—	89	2	no	—
247	C₈×D₄	—	89	2	no	—
248	C₈×D₄	—	178	2	no	—
249	#432	—	89	1	no	—
250	#431	—	89	1	no	—
251	#431	—	89	1	no	—
252	#431	C₂×D₈₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	—	178	2	no	—
254	#335	—	89	2	no	—
255	#334	—	89	2	no	—
256	#333	—	89	2	no	—
257	#333	—	89	2	no	—
258	#332	—	89	2	no	—
259	#331	—	89	2	no	—
260	C₂×#41	—	2	1	no	—
261	C₂²×D₄	—	89	1	no	—
262	C₂³×C₄	—	178	1	no	—
263	C₂×SD₁₆	—	178	2	no	—
264	C₂×D₈	—	178	2	no	—
265	C₂²×C₈	—	178	2	no	—
266	C₂²×C₈	—	178	2	no	—
267	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
268	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
270	#127	C₂²×D₈₉	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	#124	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	89	2	no	—
282	C₄×D₄	—	89	2	no	—
283	C₄×D₄	—	178	1	no	—
284	C₄×D₄	—	178	1	no	—
285	#117	—	2	1	no	—
286	C₂×C₄⋊C₄	—	89	1	no	—
287	C₂×C₂²⋊C₄	—	178	1	no	—
288	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	178	2	no	—
292	#106	—	178	2	no	—
293	C₄⋊C₈	—	89	2	no	—
294	C₄⋊C₈	—	89	2	no	—
295	C₄⋊C₈	—	89	2	no	—
296	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
297	#103	—	178	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	178	2	no	—
301	#102	—	178	2	no	—
302	#102	—	178	2	no	—
303	C₂²⋊C₈	—	178	1	no	—
304	C₂²⋊C₈	—	178	1	no	—
305	C₂²⋊C₈	—	178	1	no	—
306	C₂²⋊C₈	—	178	2	no	—
307	C₂²⋊C₈	—	178	2	no	—
308	C₂²⋊C₈	C₂²⋊D₈₉	1	2	yes	—
309	#97	—	178	1	no	—
310	C₄×C₈	—	178	1	no	—
311	C₄×C₈	—	178	1	no	—
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₂⁴	—	178	1	no	—
315	#41	—	8	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	89	2	no	—
324	C₂×D₄	—	178	4	no	—
325	C₂×D₄	—	178	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	178	2	no	—
328	C₂²×C₄	—	178	1	no	—
329	C₂²×C₄	—	178	2	no	—
330	C₂²×C₄	—	712	2	no	—
331	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
333	C₂²×C₄	#13083573	1	1	yes	characteristic
334	SD₁₆	—	356	4	no	—
335	D₈	—	356	4	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	—	712	2	no	—
340	C₂×C₈	—	712	2	no	—
341	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	89	2	no	—
352	C₄⋊C₄	—	178	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	178	2	no	—
357	C₂²⋊C₄	—	178	2	no	—
358	C₄²	—	4	1	no	—
359	C₄²	D₄×D₈₉	1	1	yes	characteristic
360	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
361	C₄²	#13083573	1	1	yes	characteristic
362	C₄²	C₂³×D₈₉	1	1	yes	characteristic
363	C₂³	—	4	1	no	—
364	C₂³	—	178	4	no	—
365	C₂³	—	178	2	no	—
366	C₂³	—	712	1	no	—
367	C₂³	—	712	1	no	—
368	C₂³	#15667983	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	89	4	no	—
377	D₄	—	178	4	no	—
378	D₄	—	178	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	712	2	no	—
390	C₂×C₄	—	712	1	no	—
391	C₂×C₄	#15667983	1	1	yes	characteristic
392	C₂×C₄	#15667983	1	1	yes	characteristic
393	C₂×C₄	#15667983	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	356	2	no	—
400	C₈	—	356	2	no	—
401	C₈	—	356	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	356	2	no	—
409	C₂²	—	356	2	no	—
410	C₂²	—	178	4	no	—
411	C₂²	—	712	4	no	—
412	C₂²	C₂×#15667983	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	356	2	no	—
421	C₄	#135×D₈₉	1	2	yes	—
422	C₄	#19152406	1	2	yes	—
423	C₂	—	4	1	no	—
424	C₂	—	16	1	no	—
425	C₂	—	356	4	no	—
426	C₂	#26029760	1	1	yes	characteristic
427	C₂	#26029829	1	1	yes	characteristic
428	C₂	#26029976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3228	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26030339	C₂
hypercenter	#3228	D₈₉
hypocenter	C₈₉	#19394
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3228

Complements

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

N	H ≅ G/N	type
2. #26030256	C₂	semidirect
3. #26029275	C₂	semidirect
4. #26019686	C₂	semidirect
5. #26019658	C₂	semidirect
6. #26019648	C₂	semidirect
7. #26019624	C₂	semidirect
8. #26019032	C₂	semidirect
9. #26018962	C₂	semidirect
10. #26018914	C₂	semidirect
11. C₈₉×#3228	C₂	semidirect
30. #19151351	C₂²	semidirect
31. #19151349	C₂²	semidirect
32. #19151347	C₂²	semidirect
33. #19151347	C₂²	semidirect
34. #19151344	C₂²	semidirect
35. #19151342	C₂²	semidirect
38. #500×C₈₉	C₂²	semidirect
39. #498×C₈₉	C₂²	semidirect
40. #486×C₈₉	C₂²	semidirect
41. #486×C₈₉	C₂²	semidirect
215. #3228	D₈₉	semidirect
226. C₈₉	#19394	semidirect
230. #500	C₂×D₈₉	semidirect
231. #498	C₂×D₈₉	semidirect
232. #486	C₂×D₈₉	semidirect
233. #486	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030339	2
#26030256	2
#26029275	2
#26019686	2
#26019658	2
#26019648	2
#26019624	2
#26019032	2
#26018962	2
#26018914	2
C₈₉×#3228	2
#19394	89