Subgroups — #36524550

Order 22784.

678 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030253	C₂	1	1	yes	maximal, characteristic
2	#26029327	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029275	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019118	C₂	1	2	yes	maximal, complemented
5	#26019083	C₂	1	2	yes	maximal, complemented
6	#26019077	C₂	1	2	yes	maximal, complemented
7	C₈×D₇₁₂	C₂	1	2	yes	maximal, complemented
8	#26019032	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018696	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018670	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152148	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19151912	C₄	1	2	yes	—
15	#19151879	C₄	1	2	yes	—
16	#19151794	C₄	1	2	yes	—
17	#19151734	C₄	1	2	yes	—
18	C₄×D₇₁₂	C₂²	1	2	yes	—
19	C₄×D₇₁₂	C₂²	1	2	yes	—
20	#19151677	C₂²	1	2	yes	complemented
21	#19151668	—	2	2	no	—
22	C₈×D₃₅₆	C₂²	1	2	yes	—
23	C₈×D₃₅₆	C₂²	1	2	yes	—
24	C₈×D₃₅₆	C₂²	1	2	yes	complemented
25	#19151663	—	2	2	no	—
26	#19151655	C₂²	1	1	yes	characteristic
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151563	—	2	2	no	—
29	C₂²⋊C₈×D₈₉	—	2	2	no	—
30	#19151351	C₂²	1	2	yes	complemented
31	#19151349	C₂²	1	2	yes	complemented
32	#19151327	C₂²	1	2	yes	—
33	#19151327	C₂²	1	2	yes	—
34	#19151327	C₂²	1	2	yes	complemented
35	#19151327	C₂²	1	2	yes	complemented
36	#431×C₈₉	C₂²	1	1	yes	characteristic
37	#431×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13083574	—	2	1	no	—
44	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₈₉	—	2	1	no	—
46	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
47	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
48	C₂×#13083557	—	2	2	no	—
49	C₂×C₈×D₈₉	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	C₂×C₈×D₈₉	—	2	2	no	—
52	#15668012	C₂×C₄	1	1	yes	characteristic
53	#15668009	C₂×C₄	1	1	yes	characteristic
54	#15668000	—	2	1	no	—
55	#15667986	—	2	1	no	—
56	#15667986	C₂×C₄	1	2	yes	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	—	2	1	no	—
59	C₄×D₃₅₆	—	2	1	no	—
60	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
61	C₄×D₃₅₆	C₂³	1	2	yes	—
62	C₄×D₃₅₆	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂×#13083551	—	2	1	no	—
65	#15667946	C₂×C₄	1	2	yes	—
66	#15667946	C₂×C₄	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667934	C₂×C₄	1	2	yes	—
70	#15667934	C₂×C₄	1	2	yes	—
71	#15667934	C₂×C₄	1	2	yes	—
72	#15667934	C₂×C₄	1	2	yes	—
73	C₂²⋊#10623494	—	2	1	no	—
74	C₂²⋊#10623494	—	2	1	no	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	#15667924	—	2	2	no	—
79	#15667923	—	2	1	no	—
80	C₄×#10623494	—	2	1	no	—
81	C₂×M₁₆×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
84	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
85	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
87	#97×C₈₉	—	2	1	no	—
88	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×D₈₉	—	2	1	no	—
95	#13083574	—	8	2	no	—
96	C₂×Dic₁₇₈	—	2	1	no	—
97	C₂×D₃₅₆	—	2	1	no	—
98	C₂×D₃₅₆	—	2	4	no	—
99	C₂×D₃₅₆	—	2	1	no	—
100	C₂×D₃₅₆	—	2	1	no	—
101	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
102	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
103	C₂×C₂²⋊D₈₉	—	2	2	no	—
104	C₂²×Dic₈₉	—	2	1	no	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	2	2	no	—
107	C₂×C₄×D₈₉	—	2	2	no	—
108	C₂×C₄×D₈₉	—	8	2	no	—
109	D₇₁₂	—	2	4	no	—
110	D₇₁₂	—	2	4	no	—
111	#13083557	—	8	2	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₈×D₈₉	—	8	2	no	—
115	C₈×D₈₉	—	8	2	no	—
116	C₈×D₈₉	—	8	2	no	—
117	C₄⋊Dic₈₉	—	2	1	no	—
118	C₄⋊Dic₈₉	—	2	1	no	—
119	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
120	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
121	#13083551	—	2	2	no	—
122	#13083551	—	2	2	no	—
123	#13083551	—	2	2	no	—
124	#13083551	—	2	2	no	—
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
128	M₁₆×C₈₉	—	4	2	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
135	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₈₉	#41	1	1	yes	characteristic
138	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
140	C₂²×D₈₉	—	2	2	no	—
141	C₂²×D₈₉	—	2	4	no	—
142	C₂²×D₈₉	—	2	2	no	—
143	C₂²×D₈₉	—	8	1	no	—
144	C₂²×D₈₉	—	8	1	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
154	C₂²⋊D₈₉	—	8	2	no	—
155	C₂×Dic₈₉	—	2	2	no	—
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	8	1	no	—
158	D₃₅₆	—	2	4	no	—
159	D₃₅₆	—	2	2	no	—
160	D₃₅₆	—	2	2	no	—
161	D₃₅₆	—	2	2	no	—
162	D₃₅₆	—	8	1	no	—
163	D₃₅₆	—	8	1	no	—
164	D₃₅₆	#131	1	4	yes	—
165	C₄×D₈₉	—	4	2	no	—
166	C₄×D₈₉	—	4	2	no	—
167	C₄×D₈₉	—	4	2	no	—
168	C₄×D₈₉	—	4	2	no	—
169	C₄×D₈₉	—	8	2	no	—
170	Dic₁₇₈	—	8	1	no	—
171	C₈×C₈₉	—	2	2	no	—
172	C₈×C₈₉	—	2	2	no	—
173	C₈×C₈₉	—	2	2	no	—
174	C₈×C₈₉	—	2	2	no	—
175	C₈×C₈₉	—	2	2	no	—
176	C₈×C₈₉	—	4	1	no	—
177	#10623494	—	4	2	no	—
178	#10623494	—	4	2	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×D₈₉	—	2	4	no	—
184	C₂×D₈₉	—	4	2	no	—
185	C₂×D₈₉	—	4	2	no	—
186	C₂×D₈₉	—	4	2	no	—
187	C₂×D₈₉	—	4	2	no	—
188	C₂×D₈₉	—	4	2	no	—
189	C₂×D₈₉	—	8	4	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	C₂×#131	1	2	yes	—
195	C₄×C₈₉	#576	1	2	yes	—
196	Dic₈₉	—	4	2	no	—
197	Dic₈₉	—	4	2	no	—
198	#17922	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	—	4	1	no	—
200	C₂×C₈₉	#2929	1	1	yes	characteristic
201	C₂×C₈₉	#2948	1	1	yes	characteristic
202	C₂×C₈₉	#2956	1	1	yes	characteristic
203	D₈₉	—	4	4	no	—
204	D₈₉	—	8	2	no	—
205	#3100	—	89	1	no	—
206	#2981	—	89	1	no	—
207	#2972	—	89	1	no	—
208	#1586	—	89	2	no	—
209	#1581	—	89	2	no	—
210	#1580	—	89	2	no	—
211	C₈×D₈	—	89	2	no	—
212	#1572	—	89	1	no	—
213	#1490	—	89	1	no	—
214	#1484	—	89	1	no	—
215	#1453	D₈₉	1	1	yes	characteristic, complemented
216	C₈₉	#17922	1	1	yes	characteristic, complemented, Sylow
217	#532	—	89	1	no	—
218	C₂×C₄×D₄	—	89	1	no	—
219	#480	—	89	2	no	—
220	#474	—	89	2	no	—
221	#459	—	89	2	no	—
222	#447	—	89	2	no	—
223	C₄×D₈	—	89	2	no	—
224	C₄×D₈	—	89	2	no	—
225	#436	—	89	2	no	—
226	#435	—	178	2	no	—
227	C₈×D₄	—	89	2	no	—
228	C₈×D₄	—	89	2	no	—
229	C₈×D₄	—	89	2	no	—
230	C₈×D₄	—	178	2	no	—
231	#432	—	89	1	no	—
232	#431	—	89	1	no	—
233	#431	C₂×D₈₉	1	1	yes	characteristic
234	#431	C₂×D₈₉	1	1	yes	characteristic
235	#408	—	178	2	no	—
236	C₂×C₂²⋊C₈	—	178	2	no	—
237	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
238	#335	—	89	2	no	—
239	#334	—	89	2	no	—
240	D₄⋊C₈	—	89	2	no	—
241	D₄⋊C₈	—	89	2	no	—
242	D₄⋊C₈	—	89	2	no	—
243	D₄⋊C₈	—	89	2	no	—
244	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
245	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
246	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
247	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
248	C₂×#41	—	178	1	no	—
249	C₂²×D₄	—	89	1	no	—
250	C₂³×C₄	—	178	1	no	—
251	C₂×D₈	—	89	2	no	—
252	C₂×D₈	—	89	2	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	178	2	no	—
255	C₂²×C₈	—	178	2	no	—
256	C₂²×C₈	—	178	2	no	—
257	C₂²×C₈	—	178	2	no	—
258	C₄⋊Q₈	—	89	1	no	—
259	#127	—	89	1	no	—
260	#124	—	178	1	no	—
261	#121	—	89	2	no	—
262	#121	—	178	1	no	—
263	C₄×D₄	—	89	2	no	—
264	C₄×D₄	—	89	2	no	—
265	C₄×D₄	—	89	2	no	—
266	C₄×D₄	—	178	1	no	—
267	C₄×D₄	—	178	1	no	—
268	C₄×D₄	—	178	1	no	—
269	C₂×C₄⋊C₄	—	89	1	no	—
270	C₂×C₂²⋊C₄	—	178	1	no	—
271	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
272	#107	—	89	2	no	—
273	#107	—	89	2	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	89	2	no	—
276	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
277	C₄⋊C₈	D₃₅₆	1	2	yes	—
278	#102	—	89	2	no	—
279	#102	—	89	2	no	—
280	#102	—	89	2	no	—
281	#102	—	89	2	no	—
282	C₂²⋊C₈	—	178	1	no	—
283	C₂²⋊C₈	—	178	1	no	—
284	C₂²⋊C₈	—	178	2	no	—
285	C₂²⋊C₈	—	178	2	no	—
286	C₂²⋊C₈	—	178	2	no	—
287	C₂²⋊C₈	—	178	2	no	—
288	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
289	C₂²⋊C₈	D₃₅₆	1	2	yes	—
290	#97	—	2	1	no	—
291	#97	—	178	1	no	—
292	C₄×C₈	—	178	1	no	—
293	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₂⁴	—	178	1	no	—
300	#41	—	712	2	no	—
301	C₂×Q₈	—	178	1	no	—
302	C₂×D₄	—	89	2	no	—
303	C₂×D₄	—	89	2	no	—
304	C₂×D₄	—	178	4	no	—
305	C₂×D₄	—	178	2	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	—	178	1	no	—
309	C₂²×C₄	—	178	2	no	—
310	C₂²×C₄	—	178	2	no	—
311	C₂²×C₄	—	178	1	no	—
312	C₂²×C₄	—	178	2	no	—
313	C₂²×C₄	—	712	2	no	—
314	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
316	C₂²×C₄	#13083574	1	1	yes	characteristic
317	D₈	—	178	4	no	—
318	D₈	—	178	4	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	712	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	178	2	no	—
324	C₂×C₈	—	178	2	no	—
325	C₂×C₈	—	712	2	no	—
326	C₂×C₈	—	712	2	no	—
327	C₂×C₈	—	712	2	no	—
328	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
329	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
330	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
331	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
332	C₄⋊C₄	—	89	2	no	—
333	C₄⋊C₄	—	89	2	no	—
334	C₄⋊C₄	—	178	1	no	—
335	C₄⋊C₄	—	178	1	no	—
336	C₂²⋊C₄	—	178	2	no	—
337	C₂²⋊C₄	—	178	2	no	—
338	C₂²⋊C₄	—	178	2	no	—
339	C₂²⋊C₄	—	178	2	no	—
340	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
342	C₄²	#13083574	1	1	yes	characteristic
343	C₄²	C₂³×D₈₉	1	1	yes	characteristic
344	C₂³	—	178	4	no	—
345	C₂³	—	178	2	no	—
346	C₂³	—	178	2	no	—
347	C₂³	—	712	1	no	—
348	C₂³	—	712	1	no	—
349	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
350	Q₈	—	712	1	no	—
351	D₄	—	89	4	no	—
352	D₄	—	178	4	no	—
353	D₄	—	178	2	no	—
354	D₄	—	178	2	no	—
355	D₄	—	178	2	no	—
356	D₄	—	712	1	no	—
357	D₄	—	712	1	no	—
358	D₄	—	712	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	356	2	no	—
363	C₂×C₄	—	356	2	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	712	2	no	—
369	C₂×C₄	—	712	1	no	—
370	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
371	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
372	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
375	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	356	2	no	—
383	C₈	—	356	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	356	2	no	—
388	C₂²	—	356	2	no	—
389	C₂²	—	356	2	no	—
390	C₂²	—	356	2	no	—
391	C₂²	—	356	2	no	—
392	C₂²	—	178	4	no	—
393	C₂²	—	712	4	no	—
394	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	356	2	no	—
400	C₄	—	356	2	no	—
401	C₄	#131×D₈₉	1	2	yes	—
402	C₄	#19152403	1	2	yes	—
403	C₂	—	4	1	no	—
404	C₂	—	356	4	no	—
405	C₂	—	712	2	no	—
406	C₂	#26028948	1	1	yes	characteristic
407	C₂	#26029105	1	1	yes	characteristic
408	C₂	#26029163	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1453	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030253	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1453	D₈₉
hypocenter	C₈₉	#17922
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1453

Complements

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

N	H ≅ G/N	type
2. #26029327	C₂	semidirect
3. #26029275	C₂	semidirect
4. #26019118	C₂	semidirect
5. #26019083	C₂	semidirect
6. #26019077	C₂	semidirect
7. C₈×D₇₁₂	C₂	semidirect
8. #26019032	C₂	semidirect
9. #26018696	C₂	semidirect
10. #26018670	C₂	semidirect
11. C₈₉×#1453	C₂	semidirect
20. #19151677	C₂²	semidirect
24. C₈×D₃₅₆	C₂²	semidirect
30. #19151351	C₂²	semidirect
31. #19151349	C₂²	semidirect
34. #19151327	C₂²	semidirect
35. #19151327	C₂²	semidirect
39. #322×C₈₉	C₂²	semidirect
40. #322×C₈₉	C₂²	semidirect
41. #322×C₈₉	C₂²	semidirect
42. C₈²×C₈₉	C₂²	semidirect
215. #1453	D₈₉	semidirect
216. C₈₉	#17922	semidirect
244. #322	C₂×D₈₉	semidirect
245. #322	C₂×D₈₉	semidirect
246. #322	C₂×D₈₉	semidirect
247. C₈²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030253	2
#26029327	2
#26029275	2
#26019118	2
#26019083	2
#26019077	2
C₈×D₇₁₂	2
#26019032	2
#26018696	2
#26018670	2
C₈₉×#1453	2
#17922	89