Subgroups — #26031757

Order 11392.

494 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	C₂×#15668044	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152241	C₂	1	1	yes	maximal, characteristic
5	#19151993	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151843	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151838	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151804	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151763	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151752	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151750	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151735	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151696	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151668	C₂	1	1	yes	maximal, characteristic, complemented
15	#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	#15668044	—	2	4	no	—
21	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083563	C₂²	1	1	yes	characteristic
24	C₂×#13083563	C₂²	1	1	yes	characteristic
25	C₂×#13083562	C₂²	1	1	yes	characteristic
26	C₂×#13083562	C₂²	1	1	yes	characteristic
27	C₂×#13083561	C₂²	1	1	yes	characteristic
28	SD₁₆×D₈₉	—	2	4	no	—
29	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
31	#15668012	—	2	1	no	—
32	#15668012	C₂²	1	1	yes	characteristic, complemented
33	#15667994	—	2	1	no	—
34	#15667992	—	2	1	no	—
35	#15667992	—	2	1	no	—
36	#15667992	C₂²	1	1	yes	characteristic
37	#15667992	C₂²	1	1	yes	characteristic, complemented
38	#15667988	C₂²	1	1	yes	characteristic
39	#15667985	—	2	1	no	—
40	#15667983	C₂²	1	1	yes	characteristic
41	#15667982	—	2	1	no	—
42	C₄×D₃₅₆	—	2	1	no	—
43	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
44	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
45	C₂²⋊C₄×D₈₉	—	2	1	no	—
46	#15667945	C₂²	1	1	yes	characteristic, complemented
47	#15667937	C₂²	1	1	yes	characteristic, complemented
48	#15667937	C₂²	1	1	yes	characteristic, complemented
49	#15667936	C₂²	1	1	yes	characteristic, complemented
50	#15667932	C₂²	1	1	yes	characteristic
51	#15667924	C₂²	1	1	yes	characteristic
52	#15667924	C₂²	1	1	yes	characteristic, complemented
53	#15667923	C₂²	1	1	yes	characteristic, complemented
54	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	#124×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₉	C₂²	1	1	yes	characteristic
61	C₂³×D₈₉	—	2	1	no	—
62	#13083575	—	2	2	no	—
63	#13083575	—	4	1	no	—
64	C₂×Dic₁₇₈	—	2	1	no	—
65	C₂×Dic₁₇₈	—	2	1	no	—
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
68	Q₈×D₈₉	—	2	2	no	—
69	Q₈×D₈₉	—	2	2	no	—
70	Q₈×D₈₉	—	4	1	no	—
71	Q₈×D₈₉	—	4	1	no	—
72	C₂×D₃₅₆	—	2	1	no	—
73	C₂×D₃₅₆	D₄	1	1	yes	characteristic
74	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₈₉	—	2	1	no	—
76	C₂×C₂²⋊D₈₉	—	2	1	no	—
77	D₄×D₈₉	—	2	2	no	—
78	D₄×D₈₉	—	4	1	no	—
79	C₂×C₄×D₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	—	2	1	no	—
82	C₂×C₄×D₈₉	—	2	1	no	—
83	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
85	#13083564	—	2	2	no	—
86	#13083564	—	4	1	no	—
87	#13083563	—	2	2	no	—
88	#13083563	—	2	2	no	—
89	#13083562	—	2	2	no	—
90	#13083562	—	4	1	no	—
91	#13083561	D₄	1	4	yes	complemented
92	#13083557	—	2	2	no	—
93	C₂×#10623494	C₂³	1	1	yes	characteristic
94	C₂×#10623494	C₂³	1	1	yes	characteristic
95	C₈×D₈₉	—	2	2	no	—
96	C₄⋊Dic₈₉	—	2	1	no	—
97	C₄⋊Dic₈₉	—	2	1	no	—
98	C₄⋊Dic₈₉	—	2	1	no	—
99	C₄⋊Dic₈₉	—	2	1	no	—
100	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
101	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
102	#13083553	—	2	1	no	—
103	C₂²⋊Dic₈₉	—	2	1	no	—
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	#13083551	—	2	1	no	—
108	#13083551	D₄	1	1	yes	characteristic
109	#13083551	D₄	1	1	yes	characteristic
110	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	Q₁₆×C₈₉	—	2	2	no	—
114	SD₁₆×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₄²×C₈₉	—	2	1	no	—
122	C₄²×C₈₉	C₂³	1	1	yes	characteristic
123	C₂³×C₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	2	1	no	—
125	C₂²×D₈₉	—	4	2	no	—
126	C₂²×D₈₉	—	4	2	no	—
127	C₂²×D₈₉	—	8	1	no	—
128	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
130	Q₈×C₈₉	—	2	1	no	—
131	Q₈×C₈₉	—	2	1	no	—
132	Q₈×C₈₉	—	2	1	no	—
133	Q₈×C₈₉	C₂×D₄	1	2	yes	—
134	D₄×C₈₉	—	2	1	no	—
135	D₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₈₉	—	4	2	no	—
143	C₂²⋊D₈₉	—	8	1	no	—
144	C₂×Dic₈₉	—	2	1	no	—
145	C₂×Dic₈₉	—	2	1	no	—
146	C₂×Dic₈₉	—	2	1	no	—
147	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
149	D₃₅₆	—	2	2	no	—
150	D₃₅₆	—	2	1	no	—
151	D₃₅₆	—	4	2	no	—
152	D₃₅₆	C₂×D₄	1	2	yes	—
153	C₄×D₈₉	—	2	1	no	—
154	C₄×D₈₉	—	2	1	no	—
155	C₄×D₈₉	—	2	1	no	—
156	C₄×D₈₉	—	2	1	no	—
157	C₄×D₈₉	—	4	2	no	—
158	C₄×D₈₉	—	4	2	no	—
159	C₄×D₈₉	—	4	2	no	—
160	C₄×D₈₉	—	8	1	no	—
161	Dic₁₇₈	—	2	1	no	—
162	Dic₁₇₈	—	2	1	no	—
163	Dic₁₇₈	—	2	1	no	—
164	Dic₁₇₈	—	2	1	no	—
165	Dic₁₇₈	—	4	2	no	—
166	Dic₁₇₈	—	4	2	no	—
167	C₈×C₈₉	—	2	1	no	—
168	C₈×C₈₉	—	2	1	no	—
169	#10623494	—	2	1	no	—
170	#10623494	C₂×D₄	1	2	yes	—
171	C₂²×C₈₉	—	4	1	no	—
172	C₂²×C₈₉	—	4	1	no	—
173	C₂²×C₈₉	—	4	1	no	—
174	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×D₈₉	—	2	1	no	—
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	2	1	no	—
178	C₂×D₈₉	—	2	2	no	—
179	C₂×D₈₉	—	2	1	no	—
180	C₂×D₈₉	—	2	1	no	—
181	C₂×D₈₉	—	4	1	no	—
182	C₂×D₈₉	—	4	1	no	—
183	C₂×D₈₉	—	8	4	no	—
184	C₂×D₈₉	#137	1	2	yes	complemented
185	C₄×C₈₉	—	2	2	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	4	1	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
192	Dic₈₉	—	2	1	no	—
193	Dic₈₉	—	2	1	no	—
194	Dic₈₉	—	4	1	no	—
195	Dic₈₉	—	4	1	no	—
196	Dic₈₉	—	4	1	no	—
197	C₂×C₈₉	—	8	1	no	—
198	C₂×C₈₉	D₄²	1	1	yes	characteristic
199	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
200	C₂×C₈₉	#577	1	1	yes	characteristic
201	D₈₉	—	2	2	no	—
202	D₈₉	—	4	1	no	—
203	D₈₉	—	4	2	no	—
204	#3266	—	89	1	no	maximal, Sylow
205	C₈₉	#3266	1	1	yes	characteristic, complemented, Sylow
206	C₂×#137	—	89	1	no	—
207	C₂²×SD₁₆	—	89	1	no	—
208	D₄×Q₈	—	89	1	no	—
209	#546	—	89	1	no	—
210	#497	—	89	1	no	—
211	#468	—	89	1	no	—
212	#467	—	89	1	no	—
213	#464	D₈₉	1	1	yes	characteristic, complemented
214	#461	—	89	1	no	—
215	#452	—	89	1	no	—
216	#451	—	89	1	no	—
217	#450	—	89	1	no	—
218	#448	—	89	1	no	—
219	#440	—	89	1	no	—
220	#435	—	89	1	no	—
221	C₂×#41	—	89	1	no	—
222	C₂²×Q₈	—	89	1	no	—
223	C₂²×Q₈	—	89	1	no	—
224	C₂²×D₄	—	89	1	no	—
225	#137	—	178	4	no	—
226	C₂×Q₁₆	—	89	1	no	—
227	C₂×Q₁₆	—	89	1	no	—
228	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	89	1	no	—
230	C₂×SD₁₆	—	89	1	no	—
231	C₂×SD₁₆	—	89	1	no	—
232	C₂×SD₁₆	—	89	1	no	—
233	C₂×SD₁₆	—	89	1	no	—
234	C₂×SD₁₆	—	178	4	no	—
235	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
236	C₂×M₁₆	—	89	1	no	—
237	C₂²×C₈	—	89	1	no	—
238	C₄⋊Q₈	—	89	1	no	—
239	C₄⋊Q₈	—	178	1	no	—
240	#124	C₂×D₈₉	1	1	yes	characteristic
241	#123	—	178	1	no	—
242	C₂²⋊Q₈	—	89	1	no	—
243	C₂²⋊Q₈	—	89	1	no	—
244	C₂²⋊Q₈	—	89	1	no	—
245	C₂²⋊Q₈	—	178	1	no	—
246	C₂²⋊Q₈	—	178	1	no	—
247	#121	—	89	1	no	—
248	#121	—	178	1	no	—
249	#120	—	178	1	no	—
250	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
251	C₄×D₄	—	89	1	no	—
252	C₄×D₄	—	89	1	no	—
253	C₄×D₄	—	178	1	no	—
254	C₂×C₂²⋊C₄	—	178	1	no	—
255	#107	—	89	1	no	—
256	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#103	—	89	1	no	—
258	#103	—	89	1	no	—
259	#103	—	89	1	no	—
260	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
261	#102	—	89	1	no	—
262	#102	C₂×D₈₉	1	1	yes	characteristic
263	C₂²⋊C₈	—	89	1	no	—
264	C₂²⋊C₈	—	89	1	no	—
265	#97	—	89	1	no	—
266	C₂⁴	—	178	1	no	—
267	#41	—	356	1	no	—
268	#41	—	178	2	no	—
269	C₂×Q₈	—	89	1	no	—
270	C₂×Q₈	—	89	1	no	—
271	C₂×Q₈	—	356	1	no	—
272	C₂×Q₈	—	356	1	no	—
273	C₂×Q₈	—	178	1	no	—
274	C₂×Q₈	—	178	1	no	—
275	C₂×Q₈	—	178	2	no	—
276	C₂×Q₈	—	178	2	no	—
277	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
279	C₂×D₄	—	89	1	no	—
280	C₂×D₄	—	89	1	no	—
281	C₂×D₄	—	356	1	no	—
282	C₂×D₄	—	178	1	no	—
283	C₂×D₄	—	178	1	no	—
284	C₂×D₄	—	178	2	no	—
285	C₂×D₄	—	178	1	no	—
286	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
287	C₂²×C₄	—	89	1	no	—
288	C₂²×C₄	—	89	1	no	—
289	C₂²×C₄	—	178	1	no	—
290	C₂²×C₄	—	178	1	no	—
291	C₂²×C₄	—	178	1	no	—
292	C₂²×C₄	—	178	1	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	356	1	no	—
295	Q₁₆	—	178	2	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	89	4	no	—
298	SD₁₆	—	356	1	no	—
299	SD₁₆	—	178	2	no	—
300	SD₁₆	—	178	2	no	—
301	SD₁₆	—	178	2	no	—
302	M₁₆	—	178	2	no	—
303	C₂×C₈	—	89	1	no	—
304	C₂×C₈	—	89	1	no	—
305	C₂×C₈	—	178	2	no	—
306	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	89	1	no	—
310	C₄⋊C₄	—	89	1	no	—
311	C₄⋊C₄	—	178	1	no	—
312	C₄⋊C₄	—	178	1	no	—
313	C₄⋊C₄	—	178	1	no	—
314	C₄⋊C₄	—	178	1	no	—
315	C₄⋊C₄	—	178	1	no	—
316	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	89	1	no	—
320	C₂²⋊C₄	—	89	1	no	—
321	C₂²⋊C₄	—	178	1	no	—
322	C₂²⋊C₄	—	178	1	no	—
323	C₂²⋊C₄	—	178	1	no	—
324	C₂²⋊C₄	—	178	1	no	—
325	C₂²⋊C₄	—	178	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	C₂³	—	2	1	no	—
329	C₂³	—	89	1	no	—
330	C₂³	—	89	1	no	—
331	C₂³	—	356	2	no	—
332	C₂³	—	356	2	no	—
333	C₂³	—	178	1	no	—
334	C₂³	—	712	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	356	2	no	—
339	Q₈	—	356	2	no	—
340	Q₈	—	178	1	no	—
341	Q₈	—	178	1	no	—
342	Q₈	—	178	1	no	—
343	Q₈	—	178	1	no	—
344	Q₈	D₄×D₈₉	1	2	yes	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	89	2	no	—
348	D₄	—	356	2	no	—
349	D₄	—	356	2	no	—
350	D₄	—	178	2	no	—
351	D₄	—	178	1	no	—
352	D₄	—	712	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	89	1	no	—
357	C₂×C₄	—	89	1	no	—
358	C₂×C₄	—	356	2	no	—
359	C₂×C₄	—	356	2	no	—
360	C₂×C₄	—	356	2	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	—	178	1	no	—
366	C₂×C₄	—	178	1	no	—
367	C₂×C₄	—	178	1	no	—
368	C₂×C₄	—	712	1	no	—
369	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	89	2	no	—
375	C₈	—	178	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	89	2	no	—
380	C₂²	—	356	1	no	—
381	C₂²	—	356	1	no	—
382	C₂²	—	178	1	no	—
383	C₂²	—	178	1	no	—
384	C₂²	—	178	1	no	—
385	C₂²	—	178	2	no	—
386	C₂²	—	178	1	no	—
387	C₂²	—	178	1	no	—
388	C₂²	—	712	4	no	—
389	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	356	1	no	—
396	C₄	—	356	1	no	—
397	C₄	—	356	1	no	—
398	C₄	—	178	1	no	—
399	C₄	—	178	1	no	—
400	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
401	C₄	#15668058	1	1	yes	characteristic
402	C₂	—	8	1	no	—
403	C₂	—	356	2	no	—
404	C₂	—	356	1	no	—
405	C₂	—	178	2	no	—
406	C₂	#19152232	1	1	yes	characteristic
407	C₂	#137×D₈₉	1	1	yes	characteristic
408	C₂	#19152405	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#464×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#19152241	C₂
hypercenter	#464	D₈₉
hypocenter	C₈₉	#3266
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
1. C₂×#15668044	C₂	semidirect
2. C₂×SD₁₆×D₈₉	C₂	semidirect
3. Q₈×D₃₅₆	C₂	semidirect
5. #19151993	C₂	semidirect
6. #19151843	C₂	semidirect
7. #19151838	C₂	semidirect
8. #19151804	C₂	semidirect
9. #19151763	C₂	semidirect
10. #19151752	C₂	semidirect
11. #19151750	C₂	semidirect
12. #19151735	C₂	semidirect
13. #19151696	C₂	semidirect
14. #19151668	C₂	semidirect
15. #464×C₈₉	C₂	semidirect
18. C₂×Q₈×D₈₉	C₂²	semidirect
21. C₂×#13083564	C₂²	semidirect
22. C₂×#13083564	C₂²	semidirect
29. C₂×#13083557	C₂²	semidirect
32. #15668012	C₂²	semidirect
37. #15667992	C₂²	semidirect
46. #15667945	C₂²	semidirect
47. #15667937	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667936	C₂²	semidirect
52. #15667924	C₂²	semidirect
53. #15667923	C₂²	semidirect
54. C₂×Q₁₆×C₈₉	C₂²	semidirect
57. C₄×Q₈×C₈₉	C₂²	semidirect
58. C₄⋊C₈×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
91. #13083561	D₄	semidirect
184. C₂×D₈₉	#137	semidirect
205. C₈₉	#3266	semidirect
213. #464	D₈₉	semidirect
228. C₂×Q₁₆	C₂×D₈₉	semidirect
250. C₄×Q₈	C₂×D₈₉	semidirect
256. C₄⋊C₈	C₂×D₈₉	semidirect
260. #103	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668044	2
C₂×SD₁₆×D₈₉	2
Q₈×D₃₅₆	2
#19152241	2
#19151993	2
#19151843	2
#19151838	2
#19151804	2
#19151763	2
#19151752	2
#19151750	2
#19151735	2
#19151696	2
#19151668	2
#464×C₈₉	2
#3266	89