Subgroups — #36537970

Order 22784.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031564	C₂	1	1	yes	maximal, characteristic
2	#26031375	C₂	1	1	yes	maximal, characteristic
3	#26030634	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028995	C₂	1	1	yes	maximal, characteristic
5	#26019830	C₂	1	2	yes	maximal, complemented
6	#26019802	C₂	1	2	yes	maximal, complemented
7	#26019706	C₂	1	2	yes	maximal, complemented
8	#26019678	C₂	1	2	yes	maximal, complemented
9	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	C₂×#15668012	C₂²	1	1	yes	characteristic
15	#19152003	—	2	1	no	—
16	#19151968	—	2	2	no	—
17	#19151950	C₂²	1	2	yes	—
18	#19151950	C₂²	1	2	yes	—
19	#19151945	—	2	1	no	—
20	#19151912	—	2	2	no	—
21	#19151885	C₂²	1	2	yes	—
22	#19151883	—	2	1	no	—
23	#19151879	C₂²	1	2	yes	—
24	#19151879	C₂²	1	2	yes	—
25	#19151829	—	2	2	no	—
26	#19151800	C₂²	1	2	yes	—
27	#19151798	—	2	1	no	—
28	#19151675	C₂²	1	2	yes	—
29	#19151668	—	2	2	no	—
30	#19151663	C₂²	1	2	yes	—
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151606	—	2	1	no	—
33	#19151606	—	2	1	no	—
34	#19151564	—	2	1	no	—
35	C₄×#13083558	C₂²	1	1	yes	characteristic
36	#19151350	C₂²	1	2	yes	—
37	#19151348	C₂²	1	2	yes	—
38	#19151345	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#533×C₈₉	C₂²	1	1	yes	characteristic
41	#431×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#333×C₈₉	C₂²	1	1	yes	characteristic
44	#333×C₈₉	C₂²	1	1	yes	characteristic
45	#332×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂²×Dic₁₇₈	—	2	1	no	—
49	C₂×#13083561	—	2	2	no	—
50	#15668018	—	4	4	no	—
51	C₂×#13083558	D₄	1	1	yes	characteristic
52	C₂×#13083558	D₄	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	—	2	1	no	—
57	#15668012	—	2	1	no	—
58	#15668012	—	2	1	no	—
59	#15668012	D₄	1	1	yes	characteristic
60	#15668012	C₂³	1	2	yes	—
61	#15668009	D₄	1	1	yes	characteristic
62	#15668000	—	2	1	no	—
63	#15667986	—	2	1	no	—
64	#15667986	D₄	1	2	yes	—
65	C₄×D₃₅₆	—	2	1	no	—
66	C₄×D₃₅₆	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄⋊Dic₈₉	—	2	1	no	—
69	#15667946	—	2	2	no	—
70	#15667946	—	2	2	no	—
71	#15667943	—	2	2	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667936	—	2	2	no	—
75	#15667935	—	2	2	no	—
76	#15667935	—	2	2	no	—
77	#15667935	—	2	2	no	—
78	#15667935	—	2	2	no	—
79	#15667934	—	2	2	no	—
80	#15667934	—	2	2	no	—
81	#15667932	—	2	2	no	—
82	#15667924	—	2	2	no	—
83	#15667924	—	2	2	no	—
84	#15667923	D₄	1	2	yes	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₂²×C₈×C₈₉	—	2	1	no	—
87	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	#125×C₈₉	—	2	1	no	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	#117×C₈₉	—	2	1	no	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×Dic₁₇₈	—	4	2	no	—
108	C₂×Dic₁₇₈	—	4	2	no	—
109	C₂×Dic₁₇₈	—	4	1	no	—
110	C₂×D₃₅₆	—	2	1	no	—
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
113	C₂×C₂²⋊D₈₉	—	2	2	no	—
114	C₂²×Dic₈₉	—	4	1	no	—
115	C₂×C₄×D₈₉	—	2	2	no	—
116	#13083561	—	8	2	no	—
117	#13083558	—	2	2	no	—
118	#13083558	—	2	2	no	—
119	#13083557	—	4	4	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	8	1	no	—
122	C₂×#10623494	C₂×D₄	1	2	yes	—
123	C₂×#10623494	C₂×D₄	1	2	yes	—
124	C₈×D₈₉	—	4	4	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	2	2	no	—
128	C₄⋊Dic₈₉	—	4	1	no	—
129	C₄⋊Dic₈₉	—	4	1	no	—
130	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
131	#13083551	—	2	2	no	—
132	#13083551	—	2	2	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	4	2	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	4	1	no	—
148	C₄⋊C₄×C₈₉	—	4	1	no	—
149	C₂²⋊C₄×C₈₉	—	4	1	no	—
150	C₄²×C₈₉	—	4	1	no	—
151	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	#41	1	1	yes	characteristic
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	#121	1	1	yes	characteristic
156	C₂²×D₈₉	—	2	2	no	—
157	Q₈×C₈₉	—	4	1	no	—
158	Q₈×C₈₉	—	4	1	no	—
159	Q₈×C₈₉	—	8	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#135	1	2	yes	—
169	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₈₉	—	4	4	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	4	2	no	—
176	C₂×Dic₈₉	—	8	2	no	—
177	D₃₅₆	—	2	2	no	—
178	D₃₅₆	—	2	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	8	1	no	—
181	C₄×D₈₉	—	4	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	Dic₁₇₈	—	4	2	no	—
184	Dic₁₇₈	—	4	2	no	—
185	Dic₁₇₈	—	4	2	no	—
186	Dic₁₇₈	—	8	2	no	—
187	C₈×C₈₉	—	4	1	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	1	no	—
190	C₈×C₈₉	—	4	1	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	2	2	no	—
193	#10623494	—	4	2	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	#463	1	2	yes	—
197	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
198	C₂×D₈₉	—	4	2	no	—
199	C₂×D₈₉	—	4	2	no	—
200	C₂×D₈₉	—	4	2	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	8	1	no	—
205	C₄×C₈₉	—	8	1	no	—
206	C₄×C₈₉	#463	1	2	yes	—
207	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
208	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₄×C₈₉	#577	1	1	yes	characteristic
210	C₄×C₈₉	#578	1	1	yes	characteristic
211	Dic₈₉	—	4	2	no	—
212	Dic₈₉	—	8	2	no	—
213	#19235	—	89	1	no	maximal, Sylow
214	C₂×C₈₉	—	2	2	no	—
215	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
216	C₂×C₈₉	#3063	1	1	yes	characteristic
217	C₂×C₈₉	#3069	1	1	yes	characteristic
218	D₈₉	—	8	2	no	—
219	#3246	—	89	1	no	—
220	#3226	—	89	1	no	—
221	#3139	—	89	1	no	—
222	#2935	—	89	1	no	—
223	#1703	—	89	2	no	—
224	#1699	—	89	2	no	—
225	#1683	—	89	2	no	—
226	#1679	—	89	2	no	—
227	#1565	—	89	1	no	—
228	#1542	D₈₉	1	1	yes	characteristic, complemented
229	C₂×#332	—	89	1	no	—
230	C₈₉	#19235	1	1	yes	characteristic, complemented, Sylow
231	C₂×#131	—	178	1	no	—
232	#533	C₂×D₈₉	1	1	yes	characteristic
233	#532	—	89	1	no	—
234	C₂×C₄⋊Q₈	—	89	1	no	—
235	#500	—	178	1	no	—
236	#491	—	178	2	no	—
237	#487	—	89	2	no	—
238	#487	—	89	2	no	—
239	#486	—	178	1	no	—
240	#480	—	178	2	no	—
241	#476	—	89	2	no	—
242	#475	—	178	1	no	—
243	#474	—	89	2	no	—
244	#474	—	89	2	no	—
245	#465	—	178	2	no	—
246	#461	—	89	2	no	—
247	#460	—	178	1	no	—
248	#436	—	89	2	no	—
249	#435	—	178	2	no	—
250	C₈×D₄	—	89	2	no	—
251	#431	C₂×D₈₉	1	1	yes	characteristic
252	C₂×C₄⋊C₈	—	89	1	no	—
253	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
254	#419	—	178	1	no	—
255	#419	—	178	1	no	—
256	#408	—	178	1	no	—
257	C₄×M₁₆	—	89	1	no	—
258	#335	—	89	2	no	—
259	#334	—	89	2	no	—
260	#333	C₂×D₈₉	1	1	yes	characteristic
261	#333	C₂×D₈₉	1	1	yes	characteristic
262	#332	—	89	2	no	—
263	#332	—	89	2	no	—
264	#332	C₂×D₈₉	1	1	yes	characteristic
265	#332	C₂×D₈₉	1	1	yes	characteristic
266	C₂×#41	—	178	1	no	—
267	C₂²×Q₈	—	178	1	no	—
268	C₂×SD₁₆	—	178	2	no	—
269	#131	—	356	4	no	—
270	C₂×M₁₆	—	89	1	no	—
271	C₂×M₁₆	—	89	1	no	—
272	C₂×M₁₆	—	178	2	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	178	2	no	—
275	C₂²×C₈	—	178	1	no	—
276	C₄⋊Q₈	—	89	1	no	—
277	C₄⋊Q₈	—	89	2	no	—
278	C₄⋊Q₈	—	178	1	no	—
279	C₄⋊Q₈	—	178	1	no	—
280	C₄⋊Q₈	—	178	1	no	—
281	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
283	#127	—	89	1	no	—
284	#125	—	2	1	no	—
285	#124	—	178	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	#121	—	89	2	no	—
289	#121	—	178	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×D₄	—	89	2	no	—
293	C₄×D₄	—	178	1	no	—
294	#117	—	2	1	no	—
295	C₂×C₄⋊C₄	—	178	1	no	—
296	C₂×C₄⋊C₄	—	178	1	no	—
297	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
298	#107	—	178	2	no	—
299	#107	—	178	2	no	—
300	#106	—	178	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	89	2	no	—
303	C₄⋊C₈	—	178	1	no	—
304	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
308	#103	—	178	2	no	—
309	#103	—	178	2	no	—
310	#103	—	178	2	no	—
311	#103	—	178	2	no	—
312	#103	—	178	2	no	—
313	#102	—	178	2	no	—
314	#102	—	178	2	no	—
315	#102	—	178	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	178	2	no	—
318	C₂²⋊C₈	—	178	2	no	—
319	#97	—	89	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	89	2	no	—
322	#41	—	356	2	no	—
323	#41	—	356	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	356	1	no	—
327	C₂×Q₈	—	356	2	no	—
328	C₂×Q₈	—	356	2	no	—
329	C₂×Q₈	—	178	2	no	—
330	C₂×Q₈	—	178	1	no	—
331	C₂×D₄	—	89	2	no	—
332	C₂×D₄	—	178	2	no	—
333	C₂×D₄	—	178	1	no	—
334	C₂×D₄	—	178	1	no	—
335	C₂²×C₄	—	356	1	no	—
336	C₂²×C₄	—	178	2	no	—
337	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	#13083574	1	1	yes	characteristic
340	SD₁₆	—	712	2	no	—
341	M₁₆	—	356	4	no	—
342	M₁₆	—	178	2	no	—
343	M₁₆	—	178	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	89	2	no	—
350	C₂×C₈	—	89	2	no	—
351	C₂×C₈	—	356	4	no	—
352	C₂×C₈	—	178	2	no	—
353	C₂×C₈	—	712	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	89	2	no	—
361	C₄⋊C₄	—	356	1	no	—
362	C₄⋊C₄	—	356	1	no	—
363	C₄⋊C₄	—	178	2	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	178	2	no	—
368	C₂²⋊C₄	—	178	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	D₄×D₈₉	1	1	yes	characteristic
371	C₄²	D₄×D₈₉	1	1	yes	characteristic
372	C₄²	#13083574	1	1	yes	characteristic
373	C₄²	C₂³×D₈₉	1	1	yes	characteristic
374	C₂³	—	178	2	no	—
375	C₂³	#15667985	1	1	yes	characteristic
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	8	1	no	—
379	Q₈	—	356	2	no	—
380	Q₈	—	356	2	no	—
381	Q₈	—	356	2	no	—
382	Q₈	—	712	2	no	—
383	D₄	—	356	4	no	—
384	D₄	—	356	2	no	—
385	D₄	—	178	2	no	—
386	D₄	—	178	2	no	—
387	D₄	—	712	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	356	2	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	356	2	no	—
396	C₂×C₄	—	178	2	no	—
397	C₂×C₄	—	712	2	no	—
398	C₂×C₄	#15667985	1	1	yes	characteristic
399	C₂×C₄	#15667985	1	1	yes	characteristic
400	C₂×C₄	#15667985	1	1	yes	characteristic
401	C₂×C₄	#15668035	1	2	yes	—
402	C₂×C₄	#15668039	1	2	yes	—
403	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	356	2	no	—
411	C₈	—	178	2	no	—
412	C₈	—	178	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	356	2	no	—
416	C₂²	—	356	2	no	—
417	C₂²	—	356	2	no	—
418	C₂²	#19151816	1	2	yes	—
419	C₂²	C₂×#15667985	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	—	356	2	no	—
426	C₄	—	712	2	no	—
427	C₄	#19151816	1	2	yes	—
428	C₄	C₂×#15668035	1	1	yes	characteristic
429	C₄	C₂×#15668039	1	1	yes	characteristic
430	C₄	#19152405	1	1	yes	characteristic
431	C₄	#19152412	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	712	2	no	—
434	C₂	C₂×#19151816	1	1	yes	characteristic
435	C₂	#26029946	1	1	yes	characteristic
436	C₂	#26029992	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667985
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1542	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#1542	D₈₉
hypocenter	C₈₉	#19235
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1542

Complements

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

N	H ≅ G/N	type
3. #26030634	C₂	semidirect
5. #26019830	C₂	semidirect
6. #26019802	C₂	semidirect
7. #26019706	C₂	semidirect
8. #26019678	C₂	semidirect
9. #26019005	C₂	semidirect
10. C₂×#19151345	C₂	semidirect
11. C₈₉×#1542	C₂	semidirect
228. #1542	D₈₉	semidirect
230. C₈₉	#19235	semidirect

Maximal subgroups

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

subgroup	index
#26031564	2
#26031375	2
#26030634	2
#26028995	2
#26019830	2
#26019802	2
#26019706	2
#26019678	2
#26019005	2
C₂×#19151345	2
C₈₉×#1542	2
#19235	89