Subgroups — #36545919

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033241	C₂	1	1	yes	maximal, characteristic, complemented
2	#26032485	C₂	1	2	yes	maximal, complemented
3	D₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic
4	#26019858	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019814	C₂	1	2	yes	maximal, complemented
6	#26019617	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019434	C₂	1	2	yes	maximal, complemented
9	#26019365	C₂	1	2	yes	maximal, complemented
10	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₇₁₂	—	2	1	no	—
13	#19152321	C₂²	1	2	yes	complemented
14	D₄×D₃₅₆	C₂²	1	2	yes	—
15	#19151982	—	2	1	no	—
16	#19151978	C₂²	1	1	yes	characteristic, complemented
17	#19151975	C₂²	1	1	yes	characteristic
18	#19151945	C₂²	1	2	yes	complemented
19	#19151945	C₂²	1	2	yes	complemented
20	#19151924	—	2	2	no	—
21	#19151878	C₂²	1	2	yes	—
22	#19151847	—	2	2	no	—
23	#19151834	—	2	1	no	—
24	#19151821	—	2	2	no	—
25	#19151804	C₂²	1	2	yes	complemented
26	#19151798	C₂²	1	2	yes	complemented
27	#19151794	C₂²	1	2	yes	—
28	#19151747	—	2	2	no	—
29	#19151734	—	2	2	no	—
30	C₄×Dic₃₅₆	—	2	1	no	—
31	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
32	#19151677	C₂²	1	2	yes	complemented
33	#19151601	—	2	2	no	—
34	#19151351	C₂²	1	1	yes	characteristic, complemented
35	#19151345	C₂²	1	2	yes	complemented
36	#19151341	C₂²	1	2	yes	complemented
37	#19151327	C₂²	1	2	yes	complemented
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₃₅₆	—	2	2	no	—
46	C₂×D₄×D₈₉	—	2	2	no	—
47	C₂×Dic₃₅₆	—	2	1	no	—
48	C₂×Dic₃₅₆	—	2	1	no	—
49	C₂×#13083563	—	2	2	no	—
50	C₂×#13083561	—	2	2	no	—
51	C₂×D₇₁₂	—	2	2	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×D₇₁₂	—	4	4	no	—
55	C₂×D₇₁₂	D₄	1	1	yes	characteristic
56	C₂×#13083557	—	2	2	no	—
57	#15668012	C₂³	1	2	yes	—
58	#15668009	C₂³	1	2	yes	—
59	#15668007	—	4	2	no	—
60	#15668000	—	2	2	no	—
61	#15667988	—	2	2	no	—
62	#15667987	—	2	2	no	—
63	#15667986	—	2	2	no	—
64	#15667982	—	4	2	no	—
65	C₄×Dic₁₇₈	—	2	2	no	—
66	C₄×D₃₅₆	C₂³	1	2	yes	—
67	#15667970	—	2	2	no	—
68	#15667946	D₄	1	1	yes	characteristic
69	#15667945	—	2	2	no	—
70	C₄⋊#10623494	C₂³	1	2	yes	—
71	#15667937	—	2	2	no	—
72	#15667934	—	2	2	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667934	—	4	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×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	—	2	1	no	—
82	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	#106×C₈₉	D₄	1	1	yes	characteristic
85	C₄⋊C₈×C₈₉	—	2	1	no	—
86	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	#103×C₈₉	D₄	1	1	yes	characteristic
89	#102×C₈₉	D₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₈₉	—	2	1	no	—
91	C₄×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	D₄×D₈₉	—	4	4	no	—
106	D₄×D₈₉	—	8	2	no	—
107	C₂×C₄×D₈₉	—	2	2	no	—
108	Dic₃₅₆	—	4	2	no	—
109	Dic₃₅₆	—	8	1	no	—
110	#13083563	—	8	2	no	—
111	#13083561	—	8	2	no	—
112	D₇₁₂	—	2	2	no	—
113	D₇₁₂	—	4	4	no	—
114	D₇₁₂	—	4	2	no	—
115	D₇₁₂	—	8	1	no	—
116	#13083557	—	8	2	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	—	2	2	no	—
120	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
121	#13083553	—	4	2	no	—
122	#13083551	—	2	2	no	—
123	#13083551	—	4	2	no	—
124	#13083551	—	4	2	no	—
125	#13083551	—	4	2	no	—
126	C₄×Dic₈₉	—	4	2	no	—
127	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	SD₁₆×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	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	—	2	1	no	—
140	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
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	Q₈×C₈₉	—	2	1	no	—
152	Q₈×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	—	2	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	8	4	no	—
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	4	2	no	—
166	D₃₅₆	—	2	2	no	—
167	D₃₅₆	—	2	2	no	—
168	D₃₅₆	—	4	2	no	—
169	D₃₅₆	—	4	2	no	—
170	D₃₅₆	—	4	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	8	2	no	—
173	D₃₅₆	—	8	4	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	2	no	—
176	Dic₁₇₈	—	4	2	no	—
177	Dic₁₇₈	—	4	2	no	—
178	C₈×C₈₉	—	2	1	no	—
179	C₈×C₈₉	—	2	1	no	—
180	C₈×C₈₉	—	2	1	no	—
181	C₈×C₈₉	—	4	1	no	—
182	C₈×C₈₉	—	4	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
185	#10623494	—	4	2	no	—
186	C₂²×C₈₉	—	2	2	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	D₄²	1	1	yes	characteristic
190	C₂×D₈₉	—	4	2	no	—
191	C₂×D₈₉	—	4	2	no	—
192	C₂×D₈₉	—	4	2	no	—
193	C₂×D₈₉	—	8	2	no	—
194	C₂×D₈₉	—	8	2	no	—
195	C₂×D₈₉	—	8	2	no	—
196	C₂×D₈₉	—	16	8	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
202	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₄×C₈₉	#576	1	1	yes	characteristic
204	C₄×C₈₉	#576	1	1	yes	characteristic
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	8	2	no	—
207	#19900	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	4	2	no	—
209	C₂×C₈₉	#3274	1	1	yes	characteristic
210	C₂×C₈₉	#3280	1	1	yes	characteristic
211	C₂×C₈₉	#3290	1	1	yes	characteristic
212	D₈₉	—	8	2	no	—
213	D₈₉	—	16	2	no	—
214	#3393	—	89	1	no	—
215	#3324	—	89	2	no	—
216	D₄×D₈	—	89	1	no	—
217	#1709	—	89	1	no	—
218	#1701	—	89	2	no	—
219	#1669	—	89	1	no	—
220	#1668	—	89	1	no	—
221	#1639	—	89	2	no	—
222	#1628	—	89	2	no	—
223	#1589	—	89	1	no	—
224	C₈×SD₁₆	D₈₉	1	1	yes	characteristic, complemented
225	C₈₉	#19900	1	1	yes	characteristic, complemented, Sylow
226	C₂²×D₈	—	178	1	no	—
227	#556	—	89	2	no	—
228	D₄²	—	89	2	no	—
229	#495	—	178	1	no	—
230	#494	—	89	1	no	—
231	#493	—	89	1	no	—
232	#486	—	89	2	no	—
233	#486	—	89	2	no	—
234	#482	—	178	2	no	—
235	#474	—	89	2	no	—
236	#468	—	178	2	no	—
237	#466	—	178	1	no	—
238	#464	—	178	2	no	—
239	#461	—	89	2	no	—
240	#460	—	89	2	no	—
241	#459	—	89	2	no	—
242	#450	—	178	2	no	—
243	#447	—	178	2	no	—
244	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
245	C₄×Q₁₆	—	178	1	no	—
246	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
247	C₄×D₈	—	89	1	no	—
248	#436	—	89	2	no	—
249	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
250	#418	—	178	2	no	—
251	#335	—	89	1	no	—
252	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
253	#332	—	89	2	no	—
254	#331	—	89	2	no	—
255	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
256	D₄⋊C₈	—	89	2	no	—
257	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
258	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
259	C₂²×D₄	—	178	2	no	—
260	C₂²×D₄	—	178	2	no	—
261	C₂×Q₁₆	—	178	1	no	—
262	C₂×Q₁₆	—	178	1	no	—
263	C₂×SD₁₆	—	178	2	no	—
264	C₂×SD₁₆	—	178	2	no	—
265	C₂×SD₁₆	D₃₅₆	1	1	yes	characteristic
266	C₂×D₈	—	89	1	no	—
267	C₂×D₈	—	356	4	no	—
268	C₂×D₈	—	178	2	no	—
269	C₂×D₈	—	178	1	no	—
270	C₂×D₈	—	178	1	no	—
271	C₂×M₁₆	—	178	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₄⋊Q₈	—	89	2	no	—
274	#127	—	89	2	no	—
275	#126	—	356	2	no	—
276	#124	—	178	2	no	—
277	C₂²⋊Q₈	—	178	2	no	—
278	#121	—	178	2	no	—
279	#121	—	178	2	no	—
280	#120	—	356	2	no	—
281	C₄×Q₈	—	178	2	no	—
282	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
283	C₄×D₄	—	89	2	no	—
284	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
285	#117	—	178	2	no	—
286	#107	—	89	1	no	—
287	#107	—	178	2	no	—
288	#106	D₃₅₆	1	1	yes	characteristic
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	89	2	no	—
291	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
293	#103	—	178	2	no	—
294	#103	D₃₅₆	1	1	yes	characteristic
295	#102	—	89	2	no	—
296	#102	—	356	2	no	—
297	#102	—	178	2	no	—
298	#102	—	178	2	no	—
299	#102	—	178	2	no	—
300	#102	—	178	2	no	—
301	#102	—	178	2	no	—
302	#102	D₃₅₆	1	1	yes	characteristic
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	178	2	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₂⁴	—	356	2	no	—
310	C₂×Q₈	—	178	2	no	—
311	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
312	C₂×D₄	—	89	2	no	—
313	C₂×D₄	—	356	2	no	—
314	C₂×D₄	—	356	4	no	—
315	C₂×D₄	—	356	4	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂×D₄	—	178	2	no	—
319	C₂×D₄	—	178	2	no	—
320	C₂×D₄	—	712	2	no	—
321	C₂×D₄	—	712	2	no	—
322	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	178	2	no	—
325	Q₁₆	—	356	2	no	—
326	Q₁₆	—	712	1	no	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	712	2	no	—
329	SD₁₆	—	712	2	no	—
330	D₈	—	356	4	no	—
331	D₈	—	356	2	no	—
332	D₈	—	178	2	no	—
333	D₈	—	712	1	no	—
334	M₁₆	—	712	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	178	2	no	—
340	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
341	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
342	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
343	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	89	2	no	—
346	C₄⋊C₄	—	356	2	no	—
347	C₄⋊C₄	—	178	2	no	—
348	C₄⋊C₄	—	178	2	no	—
349	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	356	2	no	—
353	C₂²⋊C₄	—	356	2	no	—
354	C₂²⋊C₄	—	356	2	no	—
355	C₂²⋊C₄	—	178	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	356	2	no	—
358	C₄²	C₂³×D₈₉	1	1	yes	characteristic
359	C₂³	—	2	1	no	—
360	C₂³	—	356	2	no	—
361	C₂³	—	1424	2	no	—
362	C₂³	—	178	2	no	—
363	C₂³	—	712	4	no	—
364	C₂³	—	712	4	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	356	2	no	—
368	Q₈	—	356	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	356	2	no	—
371	D₄	—	356	2	no	—
372	D₄	—	356	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	178	2	no	—
375	D₄	—	178	2	no	—
376	D₄	—	712	2	no	—
377	D₄	—	712	4	no	—
378	D₄	—	712	4	no	—
379	D₄	#15668034	1	2	yes	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
391	C₂×C₄	#15668058	1	1	yes	characteristic
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	356	2	no	—
399	C₈	#15668039	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	356	2	no	—
404	C₂²	—	356	2	no	—
405	C₂²	—	356	2	no	—
406	C₂²	—	1424	8	no	—
407	C₂²	—	712	2	no	—
408	C₂²	—	712	2	no	—
409	C₂²	—	712	2	no	—
410	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	356	2	no	—
416	C₄	—	712	2	no	—
417	C₄	C₂×#15668034	1	1	yes	characteristic
418	C₄	C₂×#15668039	1	1	yes	characteristic
419	C₄	#19152400	1	1	yes	characteristic
420	C₄	#19152403	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	—	1424	2	no	—
423	C₂	—	712	2	no	—
424	C₂	#26031873	1	1	yes	characteristic
425	C₂	#26031939	1	1	yes	characteristic
426	C₂	#26032039	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₆
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	D₄²
prime radical	D₄×D₇₁₂	C₂
hypercenter	C₈×SD₁₆	D₈₉
hypocenter	C₈₉	#19900
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #26033241	C₂	semidirect
2. #26032485	C₂	semidirect
4. #26019858	C₂	semidirect
5. #26019814	C₂	semidirect
6. #26019617	C₂	semidirect
7. #26019612	C₂	semidirect
8. #26019434	C₂	semidirect
9. #26019365	C₂	semidirect
10. #26019138	C₂	semidirect
11. C₈×SD₁₆×C₈₉	C₂	semidirect
13. #19152321	C₂²	semidirect
16. #19151978	C₂²	semidirect
18. #19151945	C₂²	semidirect
19. #19151945	C₂²	semidirect
25. #19151804	C₂²	semidirect
26. #19151798	C₂²	semidirect
32. #19151677	C₂²	semidirect
34. #19151351	C₂²	semidirect
35. #19151345	C₂²	semidirect
36. #19151341	C₂²	semidirect
37. #19151327	C₂²	semidirect
38. C₈×Q₈×C₈₉	C₂²	semidirect
41. #334×C₈₉	C₂²	semidirect
42. Q₈⋊C₈×C₈₉	C₂²	semidirect
44. C₈²×C₈₉	C₂²	semidirect
224. C₈×SD₁₆	D₈₉	semidirect
225. C₈₉	#19900	semidirect
244. C₈×Q₈	C₂×D₈₉	semidirect
252. #334	C₂×D₈₉	semidirect
255. Q₈⋊C₈	C₂×D₈₉	semidirect
258. 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
#26033241	2
#26032485	2
D₄×D₇₁₂	2
#26019858	2
#26019814	2
#26019617	2
#26019612	2
#26019434	2
#26019365	2
#26019138	2
C₈×SD₁₆×C₈₉	2
#19900	89