Subgroups — #36545893

Order 22784.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26032675	C₂	1	1	yes	maximal, characteristic, complemented
2	#26032496	C₂	1	2	yes	maximal, complemented
3	D₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019844	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019786	C₂	1	2	yes	maximal, complemented
6	#26019651	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019370	C₂	1	2	yes	maximal, complemented
9	#26019337	C₂	1	2	yes	maximal, complemented
10	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₇₁₂	—	2	1	no	—
13	#19152313	C₂²	1	2	yes	complemented
14	D₄×D₃₅₆	C₂²	1	2	yes	—
15	#19152003	C₂²	1	1	yes	characteristic, complemented
16	#19151975	C₂²	1	1	yes	characteristic
17	#19151971	C₂²	1	2	yes	complemented
18	#19151945	C₂²	1	2	yes	complemented
19	#19151925	—	2	2	no	—
20	#19151923	—	2	2	no	—
21	#19151889	C₂²	1	2	yes	complemented
22	#19151888	C₂²	1	2	yes	—
23	#19151850	—	2	2	no	—
24	#19151834	—	2	1	no	—
25	#19151834	—	2	1	no	—
26	#19151794	C₂²	1	2	yes	—
27	#19151793	C₂²	1	2	yes	complemented
28	#19151734	—	2	2	no	—
29	#19151730	—	2	2	no	—
30	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	2	yes	complemented
32	#19151636	—	2	1	no	—
33	#19151601	—	2	2	no	—
34	#19151351	C₂²	1	1	yes	characteristic, complemented
35	#19151346	C₂²	1	2	yes	complemented
36	#19151341	C₂²	1	2	yes	complemented
37	#19151327	C₂²	1	2	yes	complemented
38	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#335×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₃₅₆	—	2	2	no	—
46	C₂×D₄×D₈₉	—	2	2	no	—
47	C₂×#13083563	—	4	2	no	—
48	C₂×D₇₁₂	—	2	2	no	—
49	C₂×D₇₁₂	—	2	1	no	—
50	C₂×D₇₁₂	—	2	1	no	—
51	C₂×D₇₁₂	—	4	4	no	—
52	C₂×D₇₁₂	D₄	1	1	yes	characteristic
53	C₂×#13083559	—	2	2	no	—
54	C₂×#13083557	—	2	2	no	—
55	#15668012	C₂³	1	2	yes	—
56	#15668009	C₂³	1	2	yes	—
57	#15667998	—	4	2	no	—
58	#15667987	—	2	2	no	—
59	#15667986	—	2	2	no	—
60	#15667986	—	2	2	no	—
61	#15667983	—	2	2	no	—
62	#15667982	—	4	2	no	—
63	C₄×D₃₅₆	C₂³	1	2	yes	—
64	#15667971	—	2	2	no	—
65	#15667970	—	2	2	no	—
66	#15667946	—	2	1	no	—
67	#15667946	—	2	1	no	—
68	#15667946	D₄	1	1	yes	characteristic
69	#15667944	—	2	2	no	—
70	#15667943	—	2	2	no	—
71	C₄⋊#10623494	C₂³	1	2	yes	—
72	#15667934	—	2	2	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667934	—	2	2	no	—
76	#15667934	D₄	1	2	yes	—
77	#15667933	—	2	2	no	—
78	#15667932	—	2	2	no	—
79	#15667924	—	2	2	no	—
80	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	—	2	1	no	—
82	C₂²×C₈×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	#107×C₈₉	D₄	1	1	yes	characteristic
86	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	#102×C₈₉	D₄	1	1	yes	characteristic
89	#102×C₈₉	D₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₈₉	—	2	1	no	—
91	C₂²⋊C₈×C₈₉	—	2	1	no	—
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×D₈₉	—	4	2	no	—
96	C₂×Dic₁₇₈	—	2	2	no	—
97	C₂×D₃₅₆	—	2	2	no	—
98	C₂×D₃₅₆	—	2	2	no	—
99	C₂×D₃₅₆	—	2	2	no	—
100	C₂×D₃₅₆	—	4	4	no	—
101	C₂×D₃₅₆	—	4	2	no	—
102	C₂×D₃₅₆	—	8	2	no	—
103	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
104	C₂×C₂²⋊D₈₉	—	4	2	no	—
105	C₂×C₂²⋊D₈₉	—	4	2	no	—
106	D₄×D₈₉	—	4	4	no	—
107	D₄×D₈₉	—	8	2	no	—
108	C₂×C₄×D₈₉	—	2	2	no	—
109	#13083563	—	8	4	no	—
110	D₇₁₂	—	2	2	no	—
111	D₇₁₂	—	4	4	no	—
112	D₇₁₂	—	4	2	no	—
113	D₇₁₂	—	8	1	no	—
114	#13083559	—	8	2	no	—
115	#13083557	—	8	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
120	C₂²⋊Dic₈₉	—	4	2	no	—
121	#13083551	—	2	2	no	—
122	#13083551	—	4	2	no	—
123	#13083551	—	4	2	no	—
124	C₄×Dic₈₉	—	4	2	no	—
125	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	D₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	4	2	no	—
134	C₂×C₈×C₈₉	—	4	2	no	—
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂³×C₈₉	—	2	1	no	—
145	C₂³×C₈₉	—	2	1	no	—
146	C₂²×D₈₉	—	2	2	no	—
147	C₂²×D₈₉	—	4	2	no	—
148	C₂²×D₈₉	—	8	4	no	—
149	C₂²×D₈₉	—	8	4	no	—
150	C₂²×D₈₉	—	16	2	no	—
151	D₄×C₈₉	—	2	1	no	—
152	D₄×C₈₉	—	2	1	no	—
153	D₄×C₈₉	—	2	1	no	—
154	D₄×C₈₉	#135	1	2	yes	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	1	no	—
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂²⋊D₈₉	—	8	4	no	—
165	C₂²⋊D₈₉	—	16	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	4	2	no	—
168	D₃₅₆	—	2	2	no	—
169	D₃₅₆	—	2	2	no	—
170	D₃₅₆	—	4	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	4	2	no	—
173	D₃₅₆	—	4	2	no	—
174	D₃₅₆	—	8	2	no	—
175	D₃₅₆	—	8	4	no	—
176	C₄×D₈₉	—	4	2	no	—
177	C₄×D₈₉	—	4	2	no	—
178	Dic₁₇₈	—	8	2	no	—
179	C₈×C₈₉	—	2	2	no	—
180	C₈×C₈₉	—	2	1	no	—
181	C₈×C₈₉	—	2	1	no	—
182	C₈×C₈₉	—	2	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	—	4	1	no	—
185	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
186	#10623494	—	4	2	no	—
187	C₂²×C₈₉	—	2	2	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	1	no	—
190	C₂²×C₈₉	—	4	1	no	—
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	—	4	1	no	—
193	C₂²×C₈₉	D₄²	1	1	yes	characteristic
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	8	2	no	—
198	C₂×D₈₉	—	8	2	no	—
199	C₂×D₈₉	—	8	2	no	—
200	C₂×D₈₉	—	16	8	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	4	1	no	—
203	C₄×C₈₉	—	4	1	no	—
204	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
205	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₄×C₈₉	#576	1	1	yes	characteristic
207	C₄×C₈₉	#577	1	1	yes	characteristic
208	Dic₈₉	—	4	2	no	—
209	Dic₈₉	—	8	2	no	—
210	#19898	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	—	4	2	no	—
212	C₂×C₈₉	—	8	1	no	—
213	C₂×C₈₉	#3272	1	1	yes	characteristic
214	C₂×C₈₉	#3280	1	1	yes	characteristic
215	C₂×C₈₉	#3292	1	1	yes	characteristic
216	D₈₉	—	8	2	no	—
217	D₈₉	—	16	2	no	—
218	#3341	—	89	1	no	—
219	#3325	—	89	2	no	—
220	D₄×D₈	—	89	1	no	—
221	#1706	—	89	1	no	—
222	#1697	—	89	2	no	—
223	#1675	—	89	1	no	—
224	#1667	—	89	1	no	—
225	#1629	—	89	2	no	—
226	#1624	—	89	2	no	—
227	#1589	—	89	1	no	—
228	C₈×D₈	D₈₉	1	1	yes	characteristic, complemented
229	C₈₉	#19898	1	1	yes	characteristic, complemented, Sylow
230	C₂²×D₈	—	178	1	no	—
231	#555	—	89	2	no	—
232	D₄²	—	89	2	no	—
233	#500	—	89	1	no	—
234	#493	—	89	1	no	—
235	#492	—	89	2	no	—
236	#486	—	89	2	no	—
237	#482	—	178	2	no	—
238	#482	—	178	2	no	—
239	#476	—	89	2	no	—
240	#476	—	89	2	no	—
241	#469	—	178	2	no	—
242	#466	—	178	1	no	—
243	#466	—	178	1	no	—
244	#459	—	89	2	no	—
245	#459	—	89	2	no	—
246	#447	—	178	2	no	—
247	#447	—	178	2	no	—
248	C₄×D₈	—	89	1	no	—
249	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
250	#436	—	89	2	no	—
251	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
252	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
253	#427	—	178	1	no	—
254	#418	—	178	2	no	—
255	#335	—	89	1	no	—
256	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#333	—	89	2	no	—
258	#331	—	89	2	no	—
259	D₄⋊C₈	—	89	2	no	—
260	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
261	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
262	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
263	C₂²×D₄	—	178	2	no	—
264	C₂²×D₄	—	178	2	no	—
265	C₂×SD₁₆	—	356	2	no	—
266	C₂×D₈	—	89	1	no	—
267	C₂×D₈	—	356	4	no	—
268	C₂×D₈	—	178	2	no	—
269	C₂×D₈	—	178	2	no	—
270	C₂×D₈	—	178	1	no	—
271	C₂×D₈	—	178	1	no	—
272	C₂×D₈	D₃₅₆	1	1	yes	characteristic
273	C₂×M₁₆	—	178	2	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₄⋊Q₈	—	89	2	no	—
277	#127	—	89	2	no	—
278	#124	—	356	2	no	—
279	#121	—	178	2	no	—
280	#121	—	178	2	no	—
281	#121	—	178	2	no	—
282	#121	—	178	2	no	—
283	#120	—	356	2	no	—
284	C₄×D₄	—	89	2	no	—
285	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
286	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
287	#117	—	178	2	no	—
288	#117	—	178	2	no	—
289	#107	—	89	1	no	—
290	#107	—	178	1	no	—
291	#107	—	178	1	no	—
292	#107	D₃₅₆	1	1	yes	characteristic
293	#106	—	178	2	no	—
294	#106	—	178	2	no	—
295	C₄⋊C₈	—	89	2	no	—
296	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
298	#102	—	89	2	no	—
299	#102	—	178	2	no	—
300	#102	—	178	2	no	—
301	#102	—	178	2	no	—
302	#102	—	178	2	no	—
303	#102	—	178	2	no	—
304	#102	—	178	2	no	—
305	#102	D₃₅₆	1	1	yes	characteristic
306	#102	D₃₅₆	1	1	yes	characteristic
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	178	2	no	—
310	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₂⁴	—	356	2	no	—
314	C₂×Q₈	—	178	2	no	—
315	C₂×D₄	—	89	2	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	356	4	no	—
318	C₂×D₄	—	356	4	no	—
319	C₂×D₄	—	356	2	no	—
320	C₂×D₄	—	356	2	no	—
321	C₂×D₄	—	178	2	no	—
322	C₂×D₄	—	178	2	no	—
323	C₂×D₄	—	178	2	no	—
324	C₂×D₄	—	712	2	no	—
325	C₂×D₄	—	712	2	no	—
326	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
327	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	178	2	no	—
331	SD₁₆	—	712	4	no	—
332	D₈	—	2	2	no	—
333	D₈	—	356	4	no	—
334	D₈	—	356	2	no	—
335	D₈	—	178	2	no	—
336	D₈	—	712	1	no	—
337	D₈	—	712	2	no	—
338	M₁₆	—	712	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	178	2	no	—
345	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
348	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
349	C₄⋊C₄	—	89	2	no	—
350	C₄⋊C₄	—	178	2	no	—
351	C₄⋊C₄	—	178	2	no	—
352	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	356	2	no	—
357	C₂²⋊C₄	—	356	2	no	—
358	C₂²⋊C₄	—	356	2	no	—
359	C₂²⋊C₄	—	178	2	no	—
360	C₄²	—	356	2	no	—
361	C₄²	C₂³×D₈₉	1	1	yes	characteristic
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	356	2	no	—
365	C₂³	—	1424	2	no	—
366	C₂³	—	178	2	no	—
367	C₂³	—	712	4	no	—
368	C₂³	—	712	4	no	—
369	Q₈	—	712	2	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	356	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	1424	2	no	—
378	D₄	—	178	2	no	—
379	D₄	—	178	2	no	—
380	D₄	—	712	2	no	—
381	D₄	—	712	4	no	—
382	D₄	—	712	4	no	—
383	D₄	#15668034	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	356	2	no	—
391	C₂×C₄	—	356	2	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	178	2	no	—
394	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
396	C₂×C₄	#15668058	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₈	—	356	2	no	—
404	C₈	#15668036	1	2	yes	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	356	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	356	2	no	—
414	C₂²	—	1424	8	no	—
415	C₂²	—	712	2	no	—
416	C₂²	—	712	2	no	—
417	C₂²	—	712	2	no	—
418	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	356	2	no	—
423	C₄	—	712	2	no	—
424	C₄	C₂×#15668034	1	1	yes	characteristic
425	C₄	C₂×#15668036	1	1	yes	characteristic
426	C₄	#19152403	1	1	yes	characteristic
427	C₄	#19152405	1	1	yes	characteristic
428	C₂	—	4	2	no	—
429	C₂	—	8	1	no	—
430	C₂	—	1424	2	no	—
431	C₂	—	712	2	no	—
432	C₂	#26031853	1	1	yes	characteristic
433	C₂	#26031939	1	1	yes	characteristic
434	C₂	#26032052	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₆
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×D₈×C₈₉	C₂
socle	C₂²×C₈₉	D₄²
hypercenter	C₈×D₈	D₈₉
hypocenter	C₈₉	#19898
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #26032675	C₂	semidirect
2. #26032496	C₂	semidirect
3. D₄×D₇₁₂	C₂	semidirect
4. #26019844	C₂	semidirect
5. #26019786	C₂	semidirect
6. #26019651	C₂	semidirect
7. #26019607	C₂	semidirect
8. #26019370	C₂	semidirect
9. #26019337	C₂	semidirect
10. #26019138	C₂	semidirect
11. C₈×D₈×C₈₉	C₂	semidirect
13. #19152313	C₂²	semidirect
15. #19152003	C₂²	semidirect
17. #19151971	C₂²	semidirect
18. #19151945	C₂²	semidirect
21. #19151889	C₂²	semidirect
27. #19151793	C₂²	semidirect
31. #19151677	C₂²	semidirect
34. #19151351	C₂²	semidirect
35. #19151346	C₂²	semidirect
36. #19151341	C₂²	semidirect
37. #19151327	C₂²	semidirect
40. C₈×D₄×C₈₉	C₂²	semidirect
41. #335×C₈₉	C₂²	semidirect
43. D₄⋊C₈×C₈₉	C₂²	semidirect
44. C₈²×C₈₉	C₂²	semidirect
228. C₈×D₈	D₈₉	semidirect
229. C₈₉	#19898	semidirect
252. C₈×D₄	C₂×D₈₉	semidirect
256. #335	C₂×D₈₉	semidirect
261. D₄⋊C₈	C₂×D₈₉	semidirect
262. 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
#26032675	2
#26032496	2
D₄×D₇₁₂	2
#26019844	2
#26019786	2
#26019651	2
#26019607	2
#26019370	2
#26019337	2
#26019138	2
C₈×D₈×C₈₉	2
#19898	89