Subgroups — #36613344

Order 22784.

690 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030099	C₂	1	2	yes	maximal
2	#26028849	C₂	1	1	yes	maximal, characteristic
3	#26021760	C₂	1	2	yes	maximal, complemented
4	#26021594	C₂	1	2	yes	maximal, complemented
5	#26021037	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021001	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020475	C₂	1	2	yes	maximal
8	#26020410	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020317	C₂	1	1	yes	maximal, characteristic
10	#26020091	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	1	yes	characteristic
13	#19152078	C₂²	1	2	yes	—
14	#19151902	—	2	2	no	—
15	#19151895	—	2	2	no	—
16	#19151890	—	2	2	no	—
17	#19151875	—	2	2	no	—
18	C₂×#15667948	C₂²	1	1	yes	characteristic
19	#19151641	C₂²	1	2	yes	—
20	#19151641	C₂²	1	2	yes	—
21	#19151637	—	2	2	no	—
22	#19151635	—	2	1	no	—
23	C₂×#15667946	C₂²	1	1	yes	characteristic
24	C₂×#15667945	C₂²	1	2	yes	—
25	#107×D₈₉	—	2	1	no	—
26	#19151625	C₂²	1	2	yes	—
27	C₂×#15667938	C₂²	1	1	yes	characteristic
28	#19151597	C₂²	1	2	yes	—
29	#19151592	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151467	C₂²	1	2	yes	—
32	#19151367	C₂²	1	2	yes	—
33	#19151366	C₂²	1	2	yes	—
34	#19151362	C₂²	1	1	yes	characteristic
35	#19151357	C₂²	1	2	yes	—
36	#19151357	C₂²	1	1	yes	characteristic
37	#544×C₈₉	C₂²	1	2	yes	—
38	#501×C₈₉	—	2	2	no	—
39	#500×C₈₉	—	2	1	no	—
40	#499×C₈₉	—	2	1	no	—
41	#428×C₈₉	C₂²	1	2	yes	—
42	#427×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
44	#405×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083574	C₂³	1	1	yes	characteristic
46	#15668018	—	2	2	no	—
47	#15668018	Q₈	1	4	yes	complemented
48	C₂×#13083558	C₂³	1	2	yes	—
49	C₂×#13083558	C₂³	1	1	yes	characteristic
50	C₂×#13083557	—	2	1	no	—
51	C₂²×#10623494	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₈₉	—	2	1	no	—
53	C₄×Dic₁₇₈	—	2	2	no	—
54	C₄×D₃₅₆	—	2	2	no	—
55	#15667972	—	4	2	no	—
56	#15667970	—	2	2	no	—
57	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
58	C₂×#13083553	—	4	2	no	—
59	C₄⋊C₄×D₈₉	—	2	2	no	—
60	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
61	#15667948	—	2	2	no	—
62	#15667946	—	2	1	no	—
63	#15667946	—	2	1	no	—
64	#15667945	—	2	2	no	—
65	#15667945	—	2	2	no	—
66	#15667945	—	2	2	no	—
67	#15667945	—	2	2	no	—
68	#15667943	—	2	2	no	—
69	#15667943	—	2	2	no	—
70	C₄⋊#10623494	—	2	2	no	—
71	C₄⋊#10623494	—	2	2	no	—
72	#15667938	Q₈	1	4	yes	complemented
73	#15667935	—	2	2	no	—
74	#15667935	D₄	1	1	yes	characteristic
75	#15667935	D₄	1	1	yes	characteristic
76	#15667932	—	2	2	no	—
77	#15667932	D₄	1	1	yes	characteristic
78	#15667932	D₄	1	1	yes	characteristic
79	C₈×Dic₈₉	—	2	2	no	—
80	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	—	2	2	no	—
83	C₄⋊Q₈×C₈₉	—	2	2	no	—
84	#125×C₈₉	—	2	2	no	—
85	#125×C₈₉	—	2	2	no	—
86	C₂²⋊Q₈×C₈₉	—	4	2	no	—
87	#117×C₈₉	C₂³	1	2	yes	—
88	#117×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	#107×C₈₉	—	2	1	no	—
91	#107×C₈₉	—	2	1	no	—
92	#107×C₈₉	—	2	2	no	—
93	#107×C₈₉	D₄	1	1	yes	characteristic
94	#107×C₈₉	D₄	1	1	yes	characteristic
95	#106×C₈₉	—	2	2	no	—
96	#106×C₈₉	D₄	1	2	yes	—
97	#97×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	—	2	1	no	—
99	#13083574	—	2	1	no	—
100	#13083574	—	2	1	no	—
101	#13083574	C₂×Q₈	1	2	yes	—
102	#13083574	C₂×Q₈	1	2	yes	—
103	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
104	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₈₉	—	2	1	no	—
106	C₂²×Dic₈₉	—	2	1	no	—
107	C₂²×Dic₈₉	—	2	2	no	—
108	C₂×C₄×D₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	4	2	no	—
110	#13083558	—	2	1	no	—
111	#13083558	—	2	2	no	—
112	#13083558	—	2	2	no	—
113	#13083558	C₂×Q₈	1	2	yes	—
114	#13083557	—	2	4	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₈×D₈₉	—	2	4	no	—
122	C₄⋊Dic₈₉	—	2	2	no	—
123	C₄⋊Dic₈₉	—	2	2	no	—
124	#13083553	—	4	2	no	—
125	#13083553	—	8	4	no	—
126	#13083551	—	4	2	no	—
127	C₄×Dic₈₉	—	2	1	no	—
128	C₄×Dic₈₉	—	4	2	no	—
129	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
130	C₂×Q₈×C₈₉	—	4	2	no	—
131	C₂²×C₄×C₈₉	—	2	2	no	—
132	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₈₉	—	2	1	no	—
134	M₁₆×C₈₉	C₂×Q₈	1	2	yes	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
139	C₂×C₈×C₈₉	#41	1	2	yes	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	—	4	2	no	—
143	C₄⋊C₄×C₈₉	—	4	2	no	—
144	C₄⋊C₄×C₈₉	—	4	2	no	—
145	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₈₉	—	2	2	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂²×D₈₉	—	2	1	no	—
155	Q₈×C₈₉	—	16	2	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	8	2	no	—
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂²⋊D₈₉	—	2	2	no	—
169	C₂²⋊D₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	—	2	1	no	—
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	—	4	2	no	—
175	C₂×Dic₈₉	—	8	2	no	—
176	D₃₅₆	—	2	1	no	—
177	D₃₅₆	C₄⋊Q₈	1	2	yes	—
178	C₄×D₈₉	—	2	2	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	—	16	2	no	—
181	Dic₁₇₈	—	2	1	no	—
182	Dic₁₇₈	C₄⋊Q₈	1	2	yes	—
183	C₈×C₈₉	—	2	2	no	—
184	C₈×C₈₉	C₂²⋊Q₈	1	2	yes	—
185	C₈×C₈₉	C₂²⋊Q₈	1	2	yes	—
186	#10623494	—	2	2	no	—
187	#10623494	—	2	1	no	—
188	#10623494	—	2	1	no	—
189	#10623494	—	4	2	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	#544	1	1	yes	characteristic
193	C₂²×C₈₉	D₄²	1	1	yes	characteristic
194	C₂²×C₈₉	#554	1	1	yes	characteristic
195	C₂×D₈₉	—	2	2	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	—	8	2	no	—
203	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₄×C₈₉	#547	1	1	yes	characteristic
206	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
207	Dic₈₉	—	2	4	no	—
208	Dic₈₉	—	2	2	no	—
209	Dic₈₉	—	8	2	no	—
210	#26083	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	#2440	1	1	yes	characteristic
214	C₂×C₈₉	#3292	1	1	yes	characteristic
215	C₂×C₈₉	#3293	1	1	yes	characteristic
216	D₈₉	—	4	2	no	—
217	#3164	D₈₉	1	1	yes	characteristic, complemented
218	#3083	—	89	2	no	—
219	#2913	—	89	1	no	—
220	#2089	—	89	2	no	—
221	#2060	—	89	2	no	—
222	#1952	—	89	1	no	—
223	#1945	—	89	1	no	—
224	#1859	—	89	2	no	—
225	#1845	—	89	1	no	—
226	#1816	—	89	1	no	—
227	#1764	—	89	1	no	—
228	C₈₉	#26083	1	1	yes	characteristic, complemented, Sylow
229	C₂×#131	—	89	1	no	—
230	#544	C₂×D₈₉	1	2	yes	—
231	#520	—	89	2	no	—
232	#501	—	2	2	no	—
233	#500	—	2	1	no	—
234	#499	—	2	1	no	—
235	#479	—	178	2	no	—
236	#478	—	178	2	no	—
237	#477	—	178	2	no	—
238	#474	—	178	2	no	—
239	C₂×#108	—	89	1	no	—
240	#428	—	89	2	no	—
241	#428	—	89	2	no	—
242	#428	—	178	2	no	—
243	#428	C₂×D₈₉	1	2	yes	—
244	#427	—	178	1	no	—
245	#427	C₂×D₈₉	1	1	yes	characteristic
246	C₂×#107	—	89	1	no	—
247	C₂×#107	—	89	2	no	—
248	C₂×#107	—	178	1	no	—
249	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
250	#424	—	89	2	no	—
251	C₂×#104	—	89	1	no	—
252	#417	—	89	2	no	—
253	#416	—	89	1	no	—
254	#405	C₂×D₈₉	1	1	yes	characteristic
255	C₂×C₄×C₈	—	89	1	no	—
256	#384	—	89	2	no	—
257	#343	—	89	2	no	—
258	#343	—	89	2	no	—
259	#341	—	89	1	no	—
260	#339	—	89	1	no	—
261	#339	—	89	2	no	—
262	C₂×#41	—	89	1	no	—
263	#131	—	89	4	no	—
264	#131	—	178	2	no	—
265	C₂×M₁₆	—	89	1	no	—
266	C₂×M₁₆	—	89	2	no	—
267	C₂×M₁₆	—	178	1	no	—
268	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
269	C₂²×C₈	—	89	1	no	—
270	C₂²×C₈	—	178	1	no	—
271	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	#125	—	2	2	no	—
275	#125	—	2	2	no	—
276	C₂²⋊Q₈	—	4	2	no	—
277	C₄×Q₈	—	178	2	no	—
278	C₄×D₄	—	356	2	no	—
279	C₄×D₄	—	178	2	no	—
280	#117	—	178	2	no	—
281	#117	C₂²×D₈₉	1	1	yes	characteristic
282	#117	C₂²×D₈₉	1	2	yes	—
283	C₂×C₄⋊C₄	—	89	2	no	—
284	C₂×C₄⋊C₄	—	356	2	no	—
285	C₂×C₄⋊C₄	—	178	2	no	—
286	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
287	C₂×C₄²	—	89	1	no	—
288	#108	—	178	2	no	—
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	2	2	no	—
292	#107	—	178	2	no	—
293	#107	—	178	2	no	—
294	#107	—	178	1	no	—
295	#107	—	178	1	no	—
296	#107	—	178	2	no	—
297	#107	—	178	2	no	—
298	#107	C₂²⋊D₈₉	1	1	yes	characteristic
299	#107	C₂²⋊D₈₉	1	1	yes	characteristic
300	#106	—	2	2	no	—
301	#106	—	178	2	no	—
302	#106	—	178	2	no	—
303	#106	C₂²⋊D₈₉	1	2	yes	—
304	C₄⋊C₈	—	178	2	no	—
305	C₄⋊C₈	—	178	2	no	—
306	#104	—	89	4	no	—
307	#103	—	89	1	no	—
308	#103	—	89	1	no	—
309	#103	—	178	2	no	—
310	#102	—	89	1	no	—
311	#102	—	89	1	no	—
312	#102	—	178	2	no	—
313	#97	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	178	2	no	—
316	#41	—	89	2	no	—
317	#41	—	89	2	no	—
318	#41	—	178	1	no	—
319	#41	—	178	1	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	89	1	no	—
322	C₂×D₄	—	89	1	no	—
323	C₂×D₄	—	178	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	356	2	no	—
326	C₂²×C₄	—	178	2	no	—
327	C₂²×C₄	—	178	1	no	—
328	C₂²×C₄	—	178	1	no	—
329	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
330	M₁₆	—	2	1	no	—
331	M₁₆	—	89	2	no	—
332	M₁₆	—	178	2	no	—
333	M₁₆	—	178	2	no	—
334	M₁₆	—	178	1	no	—
335	M₁₆	—	178	4	no	—
336	M₁₆	Q₈×D₈₉	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	178	2	no	—
341	C₂×C₈	—	178	1	no	—
342	C₂×C₈	—	178	1	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	—	178	4	no	—
345	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
347	C₂×C₈	Q₈×D₈₉	1	2	yes	—
348	C₂×C₈	#13083575	1	2	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	356	2	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	—	178	2	no	—
357	C₄⋊C₄	—	712	4	no	—
358	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
359	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
361	C₄⋊C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	356	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	89	2	no	—
368	C₄²	—	356	2	no	—
369	C₄²	—	178	1	no	—
370	C₂³	—	178	1	no	—
371	C₂³	#15668057	1	1	yes	characteristic
372	Q₈	—	16	2	no	—
373	Q₈	—	89	2	no	—
374	Q₈	—	178	1	no	—
375	D₄	—	89	2	no	—
376	D₄	—	178	2	no	—
377	D₄	—	178	2	no	—
378	D₄	—	178	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	1424	2	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	1	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	—	178	2	no	—
393	C₂×C₄	—	712	2	no	—
394	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
398	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
399	C₂×C₄	#15668060	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	356	2	no	—
402	C₈	—	178	1	no	—
403	C₈	—	178	1	no	—
404	C₈	—	178	2	no	—
405	C₈	#15667988	1	2	yes	—
406	C₈	#15667988	1	2	yes	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	356	1	no	—
410	C₂²	—	356	1	no	—
411	C₂²	—	178	2	no	—
412	C₂²	#19152225	1	1	yes	characteristic
413	C₂²	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
414	C₂²	#19152309	1	1	yes	characteristic
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	178	4	no	—
421	C₄	—	178	2	no	—
422	C₄	—	712	2	no	—
423	C₄	C₂×#15667988	1	1	yes	characteristic
424	C₄	C₄⋊Q₈×D₈₉	1	1	yes	characteristic
425	C₄	#19152251	1	1	yes	characteristic
426	C₄	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	356	2	no	—
430	C₂	#26023950	1	1	yes	characteristic
431	C₂	#26032049	1	1	yes	characteristic
432	C₂	#26032054	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₈₉
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#3164	C₂
socle	C₂²×C₈₉	D₄²
prime radical	C₂×#13083574	C₂³
hypercenter	#3164	D₈₉
hypocenter	C₈₉	#26083
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #3164

Complements

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

N	H ≅ G/N	type
3. #26021760	C₂	semidirect
4. #26021594	C₂	semidirect
5. #26021037	C₂	semidirect
6. #26021001	C₂	semidirect
8. #26020410	C₂	semidirect
11. C₈₉×#3164	C₂	semidirect
47. #15668018	Q₈	semidirect
72. #15667938	Q₈	semidirect
217. #3164	D₈₉	semidirect
228. C₈₉	#26083	semidirect

Maximal subgroups

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

subgroup	index
#26030099	2
#26028849	2
#26021760	2
#26021594	2
#26021037	2
#26021001	2
#26020475	2
#26020410	2
#26020317	2
#26020091	2
C₈₉×#3164	2
#26083	89