Subgroups — #26029929

Order 11392.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668020	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152177	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151850	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151843	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151832	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151831	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151828	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151825	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151637	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151591	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083574	C₂²	1	1	yes	characteristic
17	C₂×#13083573	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668036	—	2	4	no	—
20	C₂×#13083563	C₂²	1	1	yes	characteristic
21	C₂×#13083562	C₂²	1	1	yes	characteristic
22	C₂×#13083559	C₂²	1	1	yes	characteristic
23	#15668020	—	2	4	no	—
24	C₂×#13083557	C₂²	1	1	yes	characteristic
25	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#10623494	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
29	#15668008	—	2	1	no	—
30	#15667998	—	2	1	no	—
31	#15667992	C₂²	1	1	yes	characteristic, complemented
32	#15667991	C₂²	1	1	yes	characteristic, complemented
33	#15667989	—	2	1	no	—
34	#15667987	C₂²	1	1	yes	characteristic
35	#15667986	C₂²	1	1	yes	characteristic
36	#15667985	—	2	1	no	—
37	#15667984	—	2	1	no	—
38	#15667983	—	2	1	no	—
39	#15667983	C₂²	1	1	yes	characteristic
40	#15667983	C₂²	1	1	yes	characteristic, complemented
41	#15667982	—	2	1	no	—
42	#15667980	—	2	1	no	—
43	#15667970	C₂²	1	1	yes	characteristic
44	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
45	#15667946	C₂²	1	1	yes	characteristic, complemented
46	#15667945	C₂²	1	1	yes	characteristic, complemented
47	#15667943	C₂²	1	1	yes	characteristic, complemented
48	#15667937	C₂²	1	1	yes	characteristic, complemented
49	#15667935	C₂²	1	1	yes	characteristic, complemented
50	#15667934	C₂²	1	1	yes	characteristic
51	#15667933	C₂²	1	1	yes	characteristic
52	#15667933	C₂²	1	1	yes	characteristic, complemented
53	#15667932	C₂²	1	1	yes	characteristic
54	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#121×C₈₉	C₂²	1	1	yes	characteristic
57	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₈₉	C₂²	1	1	yes	characteristic
60	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	#13083574	—	2	2	no	—
63	#13083574	—	2	2	no	—
64	#13083573	—	2	2	no	—
65	#13083573	—	2	2	no	—
66	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
67	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	D₄	1	1	yes	characteristic
70	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	2	1	no	—
73	C₂×C₂²⋊D₈₉	—	2	1	no	—
74	C₂×C₂²⋊D₈₉	—	2	1	no	—
75	C₂×C₂²⋊D₈₉	—	2	1	no	—
76	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
78	D₄×D₈₉	—	2	2	no	—
79	D₄×D₈₉	—	2	2	no	—
80	C₂²×Dic₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	—	2	1	no	—
82	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
84	#13083563	—	2	2	no	—
85	#13083562	—	2	2	no	—
86	#13083559	—	2	2	no	—
87	#13083557	—	2	2	no	—
88	#13083557	D₄	1	4	yes	complemented
89	C₂×#10623494	—	2	2	no	—
90	C₂×#10623494	C₂³	1	1	yes	characteristic
91	C₂×#10623494	C₂³	1	1	yes	characteristic
92	C₈×D₈₉	—	2	2	no	—
93	C₈×D₈₉	—	2	2	no	—
94	C₄⋊Dic₈₉	—	2	1	no	—
95	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
97	#13083553	—	2	1	no	—
98	#13083553	—	2	1	no	—
99	C₂²⋊Dic₈₉	—	2	1	no	—
100	C₂²⋊Dic₈₉	—	2	1	no	—
101	C₂²⋊Dic₈₉	—	2	1	no	—
102	#13083551	—	2	1	no	—
103	#13083551	—	2	1	no	—
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	C₄×Dic₈₉	—	2	1	no	—
107	C₂×D₄×C₈₉	—	2	1	no	—
108	C₂×D₄×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	D₈×C₈₉	—	2	2	no	—
113	M₁₆×C₈₉	—	2	2	no	—
114	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	4	2	no	—
125	C₂²×D₈₉	—	8	1	no	—
126	C₂²×D₈₉	—	8	1	no	—
127	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
129	D₄×C₈₉	—	2	1	no	—
130	D₄×C₈₉	—	2	1	no	—
131	D₄×C₈₉	—	2	1	no	—
132	D₄×C₈₉	—	2	1	no	—
133	D₄×C₈₉	—	8	1	no	—
134	D₄×C₈₉	—	8	1	no	—
135	C₂×C₄×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	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₈₉	—	2	2	no	—
142	C₂²⋊D₈₉	—	2	2	no	—
143	C₂²⋊D₈₉	—	4	2	no	—
144	C₂²⋊D₈₉	—	4	2	no	—
145	C₂²⋊D₈₉	—	8	1	no	—
146	C₂²⋊D₈₉	—	8	1	no	—
147	C₂²⋊D₈₉	—	8	1	no	—
148	C₂×Dic₈₉	—	2	1	no	—
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	—	2	1	no	—
151	C₂×Dic₈₉	—	4	2	no	—
152	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
154	D₃₅₆	—	2	2	no	—
155	D₃₅₆	—	2	1	no	—
156	D₃₅₆	—	2	1	no	—
157	D₃₅₆	—	8	1	no	—
158	C₄×D₈₉	—	2	1	no	—
159	C₄×D₈₉	—	2	1	no	—
160	C₄×D₈₉	—	8	1	no	—
161	C₄×D₈₉	C₂×D₄	1	2	yes	—
162	C₄×D₈₉	#41	1	2	yes	—
163	Dic₁₇₈	—	2	2	no	—
164	Dic₁₇₈	—	2	1	no	—
165	Dic₁₇₈	—	2	1	no	—
166	C₈×C₈₉	—	2	1	no	—
167	C₈×C₈₉	C₂×D₄	1	2	yes	—
168	#10623494	—	2	1	no	—
169	#10623494	C₂×D₄	1	2	yes	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	—	2	1	no	—
173	C₂²×C₈₉	—	4	1	no	—
174	C₂²×C₈₉	—	4	1	no	—
175	C₂²×C₈₉	—	4	1	no	—
176	C₂²×C₈₉	—	4	1	no	—
177	C₂²×C₈₉	—	4	1	no	—
178	C₂²×C₈₉	—	4	1	no	—
179	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×D₈₉	—	2	1	no	—
181	C₂×D₈₉	—	2	1	no	—
182	C₂×D₈₉	—	2	1	no	—
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	4	1	no	—
186	C₂×D₈₉	—	4	1	no	—
187	C₂×D₈₉	—	4	1	no	—
188	C₂×D₈₉	—	8	4	no	—
189	C₂×D₈₉	#121	1	2	yes	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	4	1	no	—
192	C₄×C₈₉	—	4	1	no	—
193	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
194	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
195	Dic₈₉	—	2	1	no	—
196	Dic₈₉	—	4	1	no	—
197	Dic₈₉	—	4	1	no	—
198	Dic₈₉	—	4	1	no	—
199	Dic₈₉	#121	1	2	yes	—
200	C₂×C₈₉	—	4	1	no	—
201	C₂×C₈₉	—	8	1	no	—
202	C₂×C₈₉	—	8	1	no	—
203	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
204	C₂×C₈₉	#576	1	1	yes	characteristic
205	C₂×C₈₉	#577	1	1	yes	characteristic
206	D₈₉	—	2	2	no	—
207	D₈₉	—	4	1	no	—
208	D₈₉	—	8	1	no	—
209	#3062	—	89	1	no	maximal, Sylow
210	C₈₉	#3062	1	1	yes	characteristic, complemented, Sylow
211	C₂×AGL(1,ℤ/8)	—	89	1	no	—
212	C₂×#131	—	89	1	no	—
213	#537	—	89	1	no	—
214	#535	—	89	1	no	—
215	#469	—	89	1	no	—
216	#469	D₈₉	1	1	yes	characteristic, complemented
217	#468	—	89	1	no	—
218	#468	—	89	1	no	—
219	#466	—	89	1	no	—
220	#466	—	89	1	no	—
221	#465	—	89	1	no	—
222	#465	—	89	1	no	—
223	#428	—	89	1	no	—
224	#416	—	89	1	no	—
225	C₂×#102	—	89	1	no	—
226	C₂×#41	—	89	1	no	—
227	C₂×#41	—	89	1	no	—
228	C₂²×D₄	—	89	1	no	—
229	AGL(1,ℤ/8)	—	178	4	no	—
230	C₂×SD₁₆	—	89	1	no	—
231	C₂×SD₁₆	—	89	1	no	—
232	C₂×D₈	—	89	1	no	—
233	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
234	#131	—	178	4	no	—
235	C₂×M₁₆	—	89	1	no	—
236	C₂×M₁₆	—	89	1	no	—
237	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
238	C₂²×C₈	—	89	1	no	—
239	C₂²×C₈	—	89	1	no	—
240	C₂²×C₈	—	89	1	no	—
241	#127	—	178	1	no	—
242	#124	—	178	1	no	—
243	C₂²⋊Q₈	—	89	1	no	—
244	C₂²⋊Q₈	—	89	1	no	—
245	C₂²⋊Q₈	—	178	1	no	—
246	#121	—	89	1	no	—
247	#121	—	89	1	no	—
248	#121	—	89	1	no	—
249	#121	—	89	1	no	—
250	#121	—	178	1	no	—
251	#121	—	178	1	no	—
252	#121	—	178	1	no	—
253	#121	C₂×D₈₉	1	1	yes	characteristic
254	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#120	—	178	1	no	—
256	#120	—	178	1	no	—
257	#117	—	89	1	no	—
258	C₂×C₄⋊C₄	—	89	1	no	—
259	#107	—	89	1	no	—
260	#107	—	89	1	no	—
261	#106	—	89	1	no	—
262	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
263	#103	—	89	1	no	—
264	#103	—	89	1	no	—
265	#102	—	89	1	no	—
266	#102	—	89	1	no	—
267	#102	—	89	1	no	—
268	#102	—	89	1	no	—
269	#102	C₂×D₈₉	1	1	yes	characteristic
270	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
271	C₂⁴	—	178	1	no	—
272	#41	—	178	2	no	—
273	#41	—	178	2	no	—
274	#41	—	178	2	no	—
275	#41	—	178	2	no	—
276	C₂×Q₈	—	89	1	no	—
277	C₂×Q₈	—	89	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	89	1	no	—
281	C₂×D₄	—	89	1	no	—
282	C₂×D₄	—	89	1	no	—
283	C₂×D₄	—	89	1	no	—
284	C₂×D₄	—	178	1	no	—
285	C₂×D₄	—	178	2	no	—
286	C₂×D₄	—	178	2	no	—
287	C₂×D₄	—	178	1	no	—
288	C₂×D₄	—	178	1	no	—
289	C₂×D₄	—	178	1	no	—
290	C₂×D₄	—	178	1	no	—
291	C₂×D₄	—	178	1	no	—
292	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
293	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
294	C₂²×C₄	—	89	1	no	—
295	C₂²×C₄	—	89	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	—	178	1	no	—
298	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
299	SD₁₆	—	178	2	no	—
300	SD₁₆	—	178	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	178	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	89	4	no	—
305	M₁₆	—	178	2	no	—
306	C₂×C₈	—	89	1	no	—
307	C₂×C₈	—	89	1	no	—
308	C₂×C₈	—	178	2	no	—
309	C₂×C₈	—	178	2	no	—
310	C₂×C₈	—	178	2	no	—
311	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄⋊C₄	—	89	1	no	—
314	C₄⋊C₄	—	89	1	no	—
315	C₄⋊C₄	—	178	1	no	—
316	C₄⋊C₄	—	178	1	no	—
317	C₄⋊C₄	—	178	1	no	—
318	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
319	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	178	1	no	—
327	C₂²⋊C₄	—	178	1	no	—
328	C₂²⋊C₄	—	178	1	no	—
329	C₄²	—	178	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	89	1	no	—
333	C₂³	—	89	1	no	—
334	C₂³	—	356	2	no	—
335	C₂³	—	178	1	no	—
336	C₂³	—	712	1	no	—
337	C₂³	—	712	1	no	—
338	C₂³	D₄×D₈₉	1	1	yes	characteristic
339	Q₈	—	178	2	no	—
340	Q₈	—	178	1	no	—
341	Q₈	—	178	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	1	no	—
346	D₄	—	8	1	no	—
347	D₄	—	8	1	no	—
348	D₄	—	356	2	no	—
349	D₄	—	356	2	no	—
350	D₄	—	178	2	no	—
351	D₄	—	178	2	no	—
352	D₄	—	178	2	no	—
353	D₄	—	178	1	no	—
354	D₄	—	178	1	no	—
355	D₄	—	712	1	no	—
356	D₄	—	712	1	no	—
357	D₄	—	712	1	no	—
358	D₄	—	712	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	89	1	no	—
364	C₂×C₄	—	89	2	no	—
365	C₂×C₄	—	89	2	no	—
366	C₂×C₄	—	89	1	no	—
367	C₂×C₄	—	356	2	no	—
368	C₂×C₄	—	178	1	no	—
369	C₂×C₄	—	178	1	no	—
370	C₂×C₄	—	178	1	no	—
371	C₂×C₄	—	178	1	no	—
372	C₂×C₄	—	178	1	no	—
373	C₂×C₄	—	712	1	no	—
374	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
375	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	89	2	no	—
378	C₈	—	178	1	no	—
379	C₈	D₄×D₈₉	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	89	2	no	—
390	C₂²	—	356	1	no	—
391	C₂²	—	356	1	no	—
392	C₂²	—	356	1	no	—
393	C₂²	—	178	1	no	—
394	C₂²	—	178	1	no	—
395	C₂²	—	178	1	no	—
396	C₂²	—	178	1	no	—
397	C₂²	—	178	1	no	—
398	C₂²	—	712	4	no	—
399	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	89	2	no	—
404	C₄	—	356	1	no	—
405	C₄	—	356	1	no	—
406	C₄	—	356	1	no	—
407	C₄	—	178	1	no	—
408	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
409	C₄	#41×D₈₉	1	1	yes	characteristic
410	C₂	—	4	1	no	—
411	C₂	—	8	1	no	—
412	C₂	—	8	1	no	—
413	C₂	—	356	1	no	—
414	C₂	—	178	2	no	—
415	C₂	—	712	1	no	—
416	C₂	#121×D₈₉	1	1	yes	characteristic
417	C₂	#19152402	1	1	yes	characteristic
418	C₂	#19152408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#469×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#469	D₈₉
hypocenter	C₈₉	#3062
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #469

Complements

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

N	H ≅ G/N	type
1. C₂×#15668036	C₂	semidirect
2. C₂×#15668020	C₂	semidirect
3. #19152177	C₂	semidirect
4. #19152164	C₂	semidirect
5. #19151850	C₂	semidirect
6. #19151844	C₂	semidirect
7. #19151843	C₂	semidirect
8. #19151832	C₂	semidirect
9. #19151831	C₂	semidirect
10. #19151828	C₂	semidirect
11. #19151825	C₂	semidirect
12. #19151637	C₂	semidirect
13. #19151591	C₂	semidirect
14. #102×D₈₉	C₂	semidirect
15. #469×C₈₉	C₂	semidirect
25. C₂×#13083557	C₂²	semidirect
26. C₂²×#10623494	C₂²	semidirect
28. C₂×C₈×D₈₉	C₂²	semidirect
31. #15667992	C₂²	semidirect
32. #15667991	C₂²	semidirect
40. #15667983	C₂²	semidirect
45. #15667946	C₂²	semidirect
46. #15667945	C₂²	semidirect
47. #15667943	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667935	C₂²	semidirect
52. #15667933	C₂²	semidirect
55. C₂×M₁₆×C₈₉	C₂²	semidirect
57. #121×C₈₉	C₂²	semidirect
58. #106×C₈₉	C₂²	semidirect
60. #102×C₈₉	C₂²	semidirect
88. #13083557	D₄	semidirect
210. C₈₉	#3062	semidirect
216. #469	D₈₉	semidirect
237. C₂×M₁₆	C₂×D₈₉	semidirect
254. #121	C₂×D₈₉	semidirect
262. #106	C₂×D₈₉	semidirect
270. #102	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×#15668036	2
C₂×#15668020	2
#19152177	2
#19152164	2
#19151850	2
#19151844	2
#19151843	2
#19151832	2
#19151831	2
#19151828	2
#19151825	2
#19151637	2
#19151591	2
#102×D₈₉	2
#469×C₈₉	2
#3062	89