Subgroups — #36552427

Order 22784.

1138 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151556	C₂	1	2	yes	maximal
3	#26022659	C₂	1	1	yes	maximal, characteristic
4	#26020124	C₂	1	4	yes	maximal, complemented
5	#26020119	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊Dic₈₉	C₂	1	2	yes	maximal, complemented
7	#26019950	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×#10623494	C₂²	1	2	yes	—
10	C₂×#15667971	C₂²	1	2	yes	—
11	C₂×C₄⋊#10623494	C₄	1	8	yes	complemented
12	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
15	#19151556	—	2	8	no	—
16	C₂×#15667922	C₂²	1	4	yes	—
17	C₂×C₈×Dic₈₉	C₂²	1	4	yes	—
18	#19151468	C₄	1	2	yes	—
19	#19151464	C₄	1	2	yes	—
20	#19151458	C₄	1	2	yes	—
21	#19151458	C₄	1	2	yes	—
22	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
24	#19151352	C₂²	1	4	yes	—
25	#19151352	C₂²	1	4	yes	—
26	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₈₉	C₄	1	8	yes	complemented
30	C₂×#97×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
32	C₂²×#10623494	—	2	4	no	—
33	C₂²×#10623494	—	2	4	no	—
34	C₂²×#10623494	C₂×C₄	1	8	yes	—
35	C₂²×#10623494	C₂³	1	2	yes	—
36	C₂²×#10623494	C₂³	1	2	yes	—
37	#15667971	—	2	4	no	—
38	#15667971	—	2	4	no	—
39	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
42	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	4	yes	—
43	C₂×C₄×Dic₈₉	C₂³	1	4	yes	—
44	C₄⋊#10623494	C₂×C₄	1	4	yes	—
45	C₄⋊#10623494	C₂×C₄	1	4	yes	—
46	C₄⋊#10623494	C₂×C₄	1	8	yes	—
47	#15667922	—	2	8	no	—
48	C₈×Dic₈₉	—	2	8	no	—
49	#15667919	C₂×C₄	1	4	yes	—
50	#15667919	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₈₉	—	2	2	no	—
55	C₂×M₁₆×C₈₉	—	2	2	no	—
56	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
57	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
58	C₂×M₁₆×C₈₉	D₄	1	4	yes	—
59	C₂×M₁₆×C₈₉	Q₈	1	4	yes	—
60	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
62	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	#97×C₈₉	C₂×C₄	1	8	yes	—
69	C₄×C₈×C₈₉	C₂×C₄	1	8	yes	—
70	C₂²×Dic₈₉	C₂²×C₄	1	8	yes	—
71	C₂×#10623494	—	2	16	no	—
72	C₂×#10623494	—	2	2	no	—
73	C₂×#10623494	—	2	2	no	—
74	C₂×#10623494	—	2	2	no	—
75	C₂×#10623494	—	2	2	no	—
76	C₂×#10623494	C₂²×C₄	1	4	yes	—
77	C₂×#10623494	C₂²×C₄	1	4	yes	—
78	C₄⋊Dic₈₉	—	2	8	no	—
79	C₄⋊Dic₈₉	—	2	8	no	—
80	C₄⋊Dic₈₉	—	4	4	no	—
81	C₂²⋊Dic₈₉	—	2	8	no	—
82	C₄×Dic₈₉	—	2	4	no	—
83	C₄×Dic₈₉	—	2	4	no	—
84	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	—	2	4	no	—
86	C₂²×C₄×C₈₉	—	4	2	no	—
87	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
88	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
89	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₈₉	#41	1	2	yes	—
99	C₂²×C₄×C₈₉	#41	1	2	yes	—
100	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₈₉	—	2	8	no	—
102	M₁₆×C₈₉	C₄⋊C₄	1	16	yes	complemented
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
106	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
108	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
109	C₄²×C₈₉	C₄²	1	4	yes	—
110	C₄²×C₈₉	C₄²	1	4	yes	—
111	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
112	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
113	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
114	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
115	C₂³×C₈₉	—	2	2	no	—
116	C₂³×C₈₉	—	2	2	no	—
117	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
118	C₂³×C₈₉	C₄×D₄	1	2	yes	—
119	C₂³×C₈₉	C₄×Q₈	1	2	yes	—
120	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₈₉	—	2	2	no	—
122	C₂×C₄×C₈₉	—	2	2	no	—
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	8	no	—
125	C₂×C₄×C₈₉	—	4	4	no	—
126	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
132	C₂×C₄×C₈₉	#117	1	4	yes	—
133	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
134	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₈₉	C₄×Q₈	1	4	yes	—
136	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
137	C₂×C₄×C₈₉	#131	1	4	yes	—
138	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
144	C₂×Dic₈₉	—	2	8	no	—
145	C₂×Dic₈₉	—	2	8	no	—
146	C₂×Dic₈₉	—	2	8	no	—
147	C₈×C₈₉	—	2	4	no	—
148	C₈×C₈₉	C₂×C₄⋊C₄	1	8	yes	—
149	#10623494	—	2	4	no	—
150	#10623494	—	2	4	no	—
151	C₂²×C₈₉	—	2	2	no	—
152	C₂²×C₈₉	—	2	2	no	—
153	C₂²×C₈₉	—	2	4	no	—
154	C₂²×C₈₉	—	2	4	no	—
155	C₂²×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
156	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
157	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
158	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
159	C₂²×C₈₉	C₂×#131	1	2	yes	—
160	C₂²×C₈₉	#568	1	2	yes	—
161	C₄×C₈₉	—	2	2	no	—
162	C₄×C₈₉	—	2	2	no	—
163	C₄×C₈₉	—	2	2	no	—
164	C₄×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
165	C₄×C₈₉	#405	1	4	yes	complemented
166	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
168	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
170	Dic₈₉	—	4	8	no	—
171	#20441	—	89	1	no	maximal, Sylow
172	C₂×C₈₉	—	2	4	no	—
173	C₂×C₈₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
175	C₂×C₈₉	#2873	1	1	yes	characteristic
176	C₂×C₈₉	#2935	1	2	yes	—
177	C₂×C₈₉	#2962	1	2	yes	—
178	C₂²×C₄⋊C₈	—	89	1	no	—
179	C₂×#405	—	89	2	no	—
180	C₂×C₄×M₁₆	D₈₉	1	1	yes	characteristic
181	#2285	—	89	1	no	—
182	#1771	—	89	4	no	—
183	#1770	—	89	2	no	—
184	C₈×C₄⋊C₄	—	89	2	no	—
185	#1729	—	89	2	no	—
186	C₈₉	#20441	1	1	yes	characteristic, complemented, Sylow
187	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
188	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
189	C₂³×C₈	—	89	2	no	—
190	C₂×#117	—	89	2	no	—
191	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
192	C₂×C₄⋊C₈	—	89	8	no	—
193	C₂×C₄⋊C₈	—	89	1	no	—
194	C₂×C₄⋊C₈	—	89	1	no	—
195	C₂×C₄⋊C₈	—	89	2	no	—
196	#405	—	178	8	no	—
197	C₄×M₁₆	Dic₈₉	1	8	yes	complemented
198	C₂×#97	—	89	4	no	—
199	C₂×#97	C₂×D₈₉	1	2	yes	—
200	C₂×C₄×C₈	—	89	4	no	—
201	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
202	#384	—	89	2	no	—
203	#382	—	89	2	no	—
204	#380	—	89	2	no	—
205	#380	—	89	2	no	—
206	C₄×C₄⋊C₄	—	89	2	no	—
207	C₄×C₄⋊C₄	—	89	2	no	—
208	#336	—	89	4	no	—
209	#336	—	89	4	no	—
210	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
211	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
212	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	Dic₁₇₈	1	4	yes	—
216	C₂×M₁₆	D₃₅₆	1	4	yes	—
217	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
218	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
219	C₂²×C₈	—	89	8	no	—
220	C₂²×C₈	—	89	2	no	—
221	C₂²×C₈	—	89	2	no	—
222	C₂²×C₈	—	178	4	no	—
223	C₂²×C₈	—	178	4	no	—
224	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
225	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
226	#117	—	178	4	no	—
227	#117	—	178	4	no	—
228	C₂×C₄⋊C₄	—	89	4	no	—
229	C₂×C₄⋊C₄	—	89	4	no	—
230	C₂×C₄⋊C₄	—	89	4	no	—
231	C₂×C₂²⋊C₄	—	89	4	no	—
232	C₂×C₄²	—	89	4	no	—
233	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₈₉	1	4	yes	—
236	C₂×C₄²	C₂×Dic₈₉	1	4	yes	—
237	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
239	C₄⋊C₈	—	89	4	no	—
240	C₄⋊C₈	—	89	4	no	—
241	C₄⋊C₈	—	89	8	no	—
242	#97	—	178	8	no	—
243	#97	C₂×Dic₈₉	1	8	yes	—
244	C₄×C₈	—	178	8	no	—
245	C₄×C₈	C₂×Dic₈₉	1	8	yes	—
246	#95	—	89	4	no	—
247	#95	—	89	4	no	—
248	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	89	8	no	—
252	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
253	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
254	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
258	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
261	C₂²×C₄	C₂×D₃₅₆	1	2	yes	—
262	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
263	C₂²×C₄	#13083574	1	2	yes	—
264	C₂²×C₄	#13083574	1	2	yes	—
265	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
266	M₁₆	—	2	8	no	—
267	M₁₆	C₄⋊Dic₈₉	1	16	yes	complemented
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	89	4	no	—
271	C₂×C₈	—	89	4	no	—
272	C₂×C₈	—	178	16	no	—
273	C₂×C₈	—	178	2	no	—
274	C₂×C₈	—	178	2	no	—
275	C₂×C₈	—	178	2	no	—
276	C₂×C₈	—	178	2	no	—
277	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
278	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
279	C₂×C₈	C₂×D₃₅₆	1	4	yes	—
280	C₂×C₈	C₂×Dic₁₇₈	1	4	yes	—
281	C₄⋊C₄	—	356	4	no	—
282	C₄⋊C₄	—	178	8	no	—
283	C₄⋊C₄	—	178	8	no	—
284	C₂²⋊C₄	—	178	8	no	—
285	C₄²	—	178	4	no	—
286	C₄²	—	178	4	no	—
287	C₄²	C₄×Dic₈₉	1	4	yes	—
288	C₄²	C₄×Dic₈₉	1	4	yes	—
289	C₄²	C₂×C₄×D₈₉	1	2	yes	—
290	C₄²	C₂×C₄×D₈₉	1	2	yes	—
291	C₄²	C₂²×Dic₈₉	1	2	yes	—
292	C₄²	C₂²×Dic₈₉	1	2	yes	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	C₂×C₄×Dic₈₉	1	2	yes	—
296	C₂³	C₄×D₃₅₆	1	2	yes	—
297	C₂³	C₄×Dic₁₇₈	1	2	yes	—
298	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	178	8	no	—
305	C₂×C₄	—	178	8	no	—
306	C₂×C₄	—	178	8	no	—
307	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
308	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
309	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
310	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
311	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
312	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
313	C₂×C₄	#15667971	1	4	yes	—
314	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
315	C₂×C₄	C₄×D₃₅₆	1	4	yes	—
316	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
317	C₂×C₄	C₄×Dic₁₇₈	1	4	yes	—
318	C₂×C₄	#15668020	1	4	yes	—
319	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
320	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
322	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
323	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
324	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
325	C₈	—	2	4	no	—
326	C₈	—	178	4	no	—
327	C₈	—	178	4	no	—
328	C₈	C₂×C₄⋊Dic₈₉	1	8	yes	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	C₄×C₄⋊Dic₈₉	1	4	yes	—
334	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
335	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
336	C₂²	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
337	C₂²	C₂×#15668020	1	2	yes	—
338	C₂²	#19152364	1	2	yes	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	356	8	no	—
343	C₄	C₄×C₄⋊Dic₈₉	1	4	yes	—
344	C₄	#19151556	1	4	yes	complemented
345	C₄	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
346	C₄	C₂×#15667971	1	1	yes	characteristic
347	C₄	C₂×C₄×D₃₅₆	1	1	yes	characteristic
348	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	C₂×C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
351	C₂	C₂×#19151556	1	1	yes	characteristic
352	C₂	#26028670	1	1	yes	characteristic
353	C₂	#26028998	1	2	yes	—
354	C₂	#26029199	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₂×C₄×M₁₆×C₈₉	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₈₉
hypocenter	C₈₉	#20441
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #26020124	C₂	semidirect
5. #26020119	C₂	semidirect
6. C₈×C₄⋊Dic₈₉	C₂	semidirect
11. C₂×C₄⋊#10623494	C₄	semidirect
29. C₄×M₁₆×C₈₉	C₄	semidirect
102. M₁₆×C₈₉	C₄⋊C₄	semidirect
165. C₄×C₈₉	#405	semidirect
186. C₈₉	#20441	semidirect
197. C₄×M₁₆	Dic₈₉	semidirect
267. M₁₆	C₄⋊Dic₈₉	semidirect
344. C₄	#19151556	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#10623494	2
C₂×#19151556	2
#26022659	2
#26020124	2
#26020119	2
C₈×C₄⋊Dic₈₉	2
#26019950	2
C₂×C₄×M₁₆×C₈₉	2
#20441	89