Subgroups — #10948768

Order 768.

662 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₃)⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₆×#67	C₂	1	2	yes	maximal, complemented
5	D₄×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#69277	C₂	1	1	yes	maximal, characteristic, complemented
7	#69274	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₂²⋊C₁₆	C₂	1	2	yes	maximal, complemented
9	#67⋊C₁₆	C₂	1	2	yes	maximal, complemented
10	C₁₆×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	#69052	C₂	1	1	yes	maximal, characteristic, complemented
12	#33486	—	3	1	no	maximal, Sylow
13	C₂²×D₃×C₈	C₂²	1	2	yes	—
14	C₄×D₃×D₄	C₄	1	1	yes	characteristic
15	C₂²×C₃×C₁₆	C₂²	1	2	yes	complemented
16	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
17	C₈×#67	C₂²	1	2	yes	—
18	C₂²×C₃⋊C₁₆	C₂²	1	2	yes	complemented
19	D₄×C₃⋊C₈	C₄	1	1	yes	characteristic
20	C₂×D₃×C₁₆	C₂²	1	2	yes	complemented
21	C₂×D₃×C₁₆	C₂²	1	2	yes	complemented
22	#4834	C₄	1	1	yes	characteristic
23	D₃×C₄⋊C₈	C₄	1	1	yes	characteristic
24	#67⋊C₈	C₄	1	2	yes	—
25	D₃×C₂²⋊C₈	C₄	1	2	yes	—
26	C₈×D₁₂	C₂²	1	1	yes	characteristic
27	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
30	C₃×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	#4549	C₂²	1	2	yes	complemented
32	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	—
33	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
34	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
35	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	complemented
36	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	complemented
37	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	Dic₃×C₁₆	C₂²	1	2	yes	complemented
40	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₈×D₄	—	3	1	no	—
43	D₄×C₁₆	—	3	2	no	—
44	D₄×C₁₆	—	3	1	no	—
45	D₄×C₁₆	—	3	1	no	—
46	D₄×C₁₆	—	3	2	no	—
47	D₄×C₁₆	—	3	1	no	—
48	D₄×C₁₆	D₃	1	1	yes	characteristic, complemented
49	#2162	—	3	1	no	—
50	#2162	—	3	1	no	—
51	C₂×C₂²⋊C₁₆	—	3	2	no	—
52	C₂×C₂²⋊C₁₆	—	3	2	no	—
53	C₂×D₃×D₄	C₈	1	1	yes	characteristic
54	C₂²×C₄×D₃	C₂×C₄	1	2	yes	—
55	C₂²×C₃×C₈	C₂³	1	2	yes	—
56	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
57	D₄×Dic₃	C₈	1	1	yes	characteristic
58	C₄×#67	C₂×C₄	1	2	yes	—
59	C₂²×C₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×D₃×C₈	—	4	2	no	—
61	C₂×D₃×C₈	—	4	2	no	—
62	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂×D₃×C₈	C₂×C₄	1	2	yes	—
64	C₂×D₃×C₈	C₂×C₄	1	2	yes	—
65	C₂×D₃×C₈	C₂³	1	2	yes	—
66	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
67	#893	C₈	1	1	yes	characteristic
68	D₃×C₄⋊C₄	C₈	1	1	yes	characteristic
69	#67⋊C₄	C₈	1	2	yes	—
70	D₃×C₂²⋊C₄	C₈	1	2	yes	—
71	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₁₆	—	4	2	no	—
74	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₁₆	C₂³	1	2	yes	—
76	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
79	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
80	#830	C₂×C₄	1	2	yes	—
81	(C₂×D₃)⋊C₈	C₂×C₄	1	2	yes	—
82	(C₂×D₃)⋊C₈	C₂×C₄	1	2	yes	—
83	Dic₃⋊C₈	C₂×C₄	1	2	yes	—
84	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₃⋊C₁₆	—	4	2	no	—
87	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
89	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
90	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
91	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
92	D₃×C₁₆	—	4	2	no	—
93	D₃×C₁₆	—	4	2	no	—
94	C₂³×C₈	—	3	2	no	—
95	C₂×C₄×D₄	—	3	1	no	—
96	C₂²×C₁₆	—	3	2	no	—
97	C₂²×C₁₆	—	3	2	no	—
98	C₂²×C₁₆	—	3	2	no	—
99	C₂²×C₁₆	C₂×D₃	1	2	yes	complemented
100	C₈×D₄	—	3	2	no	—
101	C₈×D₄	—	3	1	no	—
102	C₈×D₄	—	3	1	no	—
103	C₈×D₄	—	3	2	no	—
104	C₈×D₄	—	3	1	no	—
105	C₈×D₄	C₂×D₃	1	1	yes	characteristic
106	C₂×C₄⋊C₈	—	3	1	no	—
107	C₂×C₂²⋊C₈	—	3	2	no	—
108	C₂×C₄×C₈	—	3	1	no	—
109	C₄⋊C₁₆	—	3	1	no	—
110	C₄⋊C₁₆	—	3	1	no	—
111	C₄⋊C₁₆	—	3	1	no	—
112	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂²⋊C₁₆	—	3	2	no	—
114	C₂²⋊C₁₆	—	3	2	no	—
115	C₂²⋊C₁₆	—	3	1	no	—
116	C₂²⋊C₁₆	—	3	1	no	—
117	C₂²⋊C₁₆	—	3	2	no	—
118	C₂²⋊C₁₆	—	3	2	no	—
119	C₂²⋊C₁₆	C₂×D₃	1	2	yes	complemented
120	C₄×C₁₆	—	3	2	no	—
121	C₄×C₁₆	—	3	1	no	—
122	C₄×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
123	C₂³×D₃	C₂×C₈	1	2	yes	—
124	C₂×C₃×D₄	C₂×C₈	1	1	yes	characteristic
125	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
126	C₂×#67	C₂×C₈	1	2	yes	—
127	C₂²×Dic₃	C₂×C₈	1	2	yes	—
128	D₃×D₄	C₁₆	1	8	yes	complemented
129	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
130	C₂×C₄×D₃	—	4	2	no	—
131	C₂×C₄×D₃	—	4	2	no	—
132	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
133	C₂×C₄×D₃	C₂×C₈	1	2	yes	—
134	C₂×C₄×D₃	C₂×C₈	1	2	yes	—
135	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
137	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₈	—	2	2	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
143	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
144	C₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
145	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
146	#217	C₂×C₈	1	2	yes	—
147	(C₂×D₃)⋊C₄	C₂×C₈	1	2	yes	—
148	(C₂×D₃)⋊C₄	C₂×C₈	1	2	yes	—
149	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
150	Dic₃⋊C₄	C₂×C₈	1	2	yes	—
151	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃⋊C₈	—	4	2	no	—
155	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃⋊C₈	C₂²×C₄	1	2	yes	—
158	D₃×C₈	—	2	2	no	—
159	D₃×C₈	—	2	2	no	—
160	D₃×C₈	—	2	1	no	—
161	D₃×C₈	—	2	1	no	—
162	D₃×C₈	—	4	2	no	—
163	D₃×C₈	—	4	2	no	—
164	D₃×C₈	—	4	1	no	—
165	C₃×C₁₆	—	2	1	no	—
166	C₃×C₁₆	—	2	2	no	—
167	C₃×C₁₆	—	2	1	no	—
168	C₃⋊C₁₆	—	2	1	no	—
169	C₃⋊C₁₆	—	2	2	no	—
170	C₃⋊C₁₆	—	2	1	no	—
171	C₂²×D₄	—	3	1	no	—
172	C₂³×C₄	—	3	2	no	—
173	C₂²×C₈	—	3	2	no	—
174	C₂²×C₈	—	3	1	no	—
175	C₂²×C₈	—	3	2	no	—
176	C₂²×C₈	—	3	2	no	—
177	C₂²×C₈	—	3	2	no	—
178	C₂²×C₈	—	3	1	no	—
179	C₂²×C₈	—	12	2	no	—
180	C₂²×C₈	—	12	2	no	—
181	C₂²×C₈	C₂²×D₃	1	2	yes	—
182	C₄×D₄	—	3	1	no	—
183	C₄×D₄	—	3	2	no	—
184	C₄×D₄	—	3	1	no	—
185	C₄×D₄	—	3	2	no	—
186	C₄×D₄	—	3	1	no	—
187	C₄×D₄	C₄×D₃	1	1	yes	characteristic
188	C₂×C₄⋊C₄	—	3	1	no	—
189	C₂×C₂²⋊C₄	—	3	2	no	—
190	C₂×C₄²	—	3	1	no	—
191	C₂×C₁₆	—	3	1	no	—
192	C₂×C₁₆	—	3	2	no	—
193	C₂×C₁₆	—	3	1	no	—
194	C₂×C₁₆	—	4	2	no	—
195	C₂×C₁₆	—	12	2	no	—
196	C₂×C₁₆	—	12	2	no	—
197	C₂×C₁₆	—	12	2	no	—
198	C₂×C₁₆	C₂²×D₃	1	2	yes	—
199	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
201	C₄⋊C₈	—	3	2	no	—
202	C₄⋊C₈	—	3	1	no	—
203	C₄⋊C₈	C₄×D₃	1	1	yes	characteristic
204	C₂²⋊C₈	—	3	2	no	—
205	C₂²⋊C₈	—	3	2	no	—
206	C₂²⋊C₈	—	3	2	no	—
207	C₂²⋊C₈	C₄×D₃	1	2	yes	—
208	C₄×C₈	—	3	1	no	—
209	C₄×C₈	—	3	1	no	—
210	C₄×C₈	—	3	1	no	—
211	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
212	C₂³×C₃	C₂²×C₈	1	2	yes	—
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	—	4	2	no	—
215	C₂²×D₃	C₂×C₁₆	1	8	yes	complemented
216	C₂²×D₃	C₂²×C₈	1	2	yes	—
217	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
218	C₃×D₄	C₂×C₁₆	1	4	yes	complemented
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
223	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
225	#67	C₂×C₁₆	1	8	yes	complemented
226	C₂×Dic₃	—	4	2	no	—
227	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
228	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
229	C₂×Dic₃	C₂²×C₈	1	2	yes	—
230	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
231	D₁₂	C₂×C₁₆	1	4	yes	complemented
232	C₄×D₃	—	2	1	no	—
233	C₄×D₃	—	2	2	no	—
234	C₄×D₃	—	2	1	no	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	—	4	2	no	—
237	C₄×D₃	—	4	2	no	—
238	C₄×D₃	—	4	1	no	—
239	C₄×D₃	C₂×C₁₆	1	4	yes	complemented
240	C₃×C₈	—	2	2	no	—
241	C₃×C₈	—	2	1	no	—
242	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
243	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
244	C₃⋊C₈	—	2	1	no	—
245	C₃⋊C₈	—	2	2	no	—
246	C₃⋊C₈	—	2	1	no	—
247	C₂⁴	—	3	2	no	—
248	C₂×D₄	—	3	2	no	—
249	C₂×D₄	—	3	8	no	—
250	C₂×D₄	—	3	1	no	—
251	C₂×D₄	D₃×C₈	1	1	yes	characteristic
252	C₂²×C₄	—	3	1	no	—
253	C₂²×C₄	—	3	2	no	—
254	C₂²×C₄	—	3	2	no	—
255	C₂²×C₄	—	3	1	no	—
256	C₂²×C₄	—	3	1	no	—
257	C₂²×C₄	—	3	2	no	—
258	C₂²×C₄	—	3	2	no	—
259	C₂²×C₄	—	12	2	no	—
260	C₂²×C₄	—	12	2	no	—
261	C₂²×C₄	C₂×C₄×D₃	1	2	yes	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	3	1	no	—
265	C₂×C₈	—	3	1	no	—
266	C₂×C₈	—	3	2	no	—
267	C₂×C₈	—	6	2	no	—
268	C₂×C₈	—	6	1	no	—
269	C₂×C₈	—	6	2	no	—
270	C₂×C₈	—	6	1	no	—
271	C₂×C₈	—	12	2	no	—
272	C₂×C₈	—	12	2	no	—
273	C₂×C₈	—	12	1	no	—
274	C₂×C₈	—	12	2	no	—
275	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₈	C₂×C₄×D₃	1	2	yes	—
277	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
278	C₄⋊C₄	—	3	2	no	—
279	C₄⋊C₄	—	3	1	no	—
280	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
281	C₂²⋊C₄	—	3	2	no	—
282	C₂²⋊C₄	—	3	2	no	—
283	C₂²⋊C₄	—	3	2	no	—
284	C₂²⋊C₄	D₃×C₈	1	2	yes	—
285	C₄²	—	3	1	no	—
286	C₄²	—	3	1	no	—
287	C₄²	—	3	1	no	—
288	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
289	C₁₆	—	2	1	no	—
290	C₁₆	—	2	2	no	—
291	C₁₆	—	2	1	no	—
292	C₁₆	—	6	1	no	—
293	C₁₆	—	6	2	no	—
294	C₁₆	—	6	1	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	C₂²×C₁₆	1	4	yes	—
298	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
299	C₂×D₃	—	2	1	no	—
300	C₂×D₃	—	2	2	no	—
301	C₂×D₃	—	2	1	no	—
302	C₂×D₃	—	2	2	no	—
303	C₂×D₃	—	4	8	no	—
304	C₂×D₃	C₂²×C₁₆	1	2	yes	—
305	C₂×D₃	C₂²×C₁₆	1	4	yes	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	C₂²×C₁₆	1	2	yes	—
309	C₃×C₄	#518	1	1	yes	characteristic
310	C₃×C₄	#568	1	1	yes	characteristic
311	Dic₃	—	2	1	no	—
312	Dic₃	—	2	1	no	—
313	Dic₃	—	2	2	no	—
314	Dic₃	C₂²×C₁₆	1	2	yes	—
315	C₂³	—	3	2	no	—
316	C₂³	—	3	1	no	—
317	C₂³	—	3	8	no	—
318	C₂³	—	12	2	no	—
319	C₂³	—	12	2	no	—
320	C₂³	C₂×D₃×C₈	1	2	yes	—
321	D₄	—	3	8	no	—
322	D₄	—	3	4	no	—
323	D₄	D₃×C₁₆	1	4	yes	complemented
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	3	1	no	—
327	C₂×C₄	—	3	4	no	—
328	C₂×C₄	—	3	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	6	1	no	—
332	C₂×C₄	—	6	2	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	12	2	no	—
336	C₂×C₄	—	12	2	no	—
337	C₂×C₄	—	12	1	no	—
338	C₂×C₄	—	12	2	no	—
339	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
340	C₂×C₄	C₂×D₃×C₈	1	2	yes	—
341	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	2	no	—
345	C₈	—	6	1	no	—
346	C₈	—	6	1	no	—
347	C₈	—	6	2	no	—
348	C₈	#1004	1	1	yes	characteristic
349	C₈	#1009	1	1	yes	characteristic
350	C₂×C₃	—	2	4	no	—
351	C₂×C₃	#2972	1	1	yes	characteristic
352	C₂×C₃	C₂³×C₁₆	1	1	yes	characteristic
353	C₂×C₃	#3407	1	1	yes	characteristic
354	D₃	—	2	2	no	—
355	D₃	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	3	2	no	—
359	C₂²	—	3	4	no	—
360	C₂²	—	6	1	no	—
361	C₂²	—	6	2	no	—
362	C₂²	—	6	1	no	—
363	C₂²	—	6	2	no	—
364	C₂²	—	12	8	no	—
365	C₂²	C₂×D₃×C₁₆	1	4	yes	—
366	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	1	no	—
369	C₄	—	3	2	no	—
370	C₄	—	6	1	no	—
371	C₄	—	6	2	no	—
372	C₄	—	6	1	no	—
373	C₄	C₂×D₃×C₁₆	1	2	yes	—
374	C₄	#5545	1	1	yes	characteristic
375	C₄	#5750	1	1	yes	characteristic
376	C₃	#33486	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	6	2	no	—
379	C₂	—	6	4	no	—
380	C₂	#79426	1	1	yes	characteristic
381	C₂	C₂²×D₃×C₁₆	1	1	yes	characteristic
382	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator	C₂×C₃	C₂³×C₁₆
Fitting	C₃×D₄×C₁₆	C₂
socle	C₂²×C₃	C₂³×C₈
prime radical	C₂×D₃×D₄	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	D₄×C₁₆	D₃
hypocenter	C₃	#33486
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×D₄×C₁₆	C₂	semidirect
3. C₂×(C₂×D₃)⋊C₁₆	C₂	semidirect
4. C₁₆×#67	C₂	semidirect
5. D₄×C₃⋊C₁₆	C₂	semidirect
6. #69277	C₂	semidirect
7. #69274	C₂	semidirect
8. D₃×C₂²⋊C₁₆	C₂	semidirect
9. #67⋊C₁₆	C₂	semidirect
10. C₁₆×D₁₂	C₂	semidirect
11. #69052	C₂	semidirect
15. C₂²×C₃×C₁₆	C₂²	semidirect
18. C₂²×C₃⋊C₁₆	C₂²	semidirect
20. C₂×D₃×C₁₆	C₂²	semidirect
21. C₂×D₃×C₁₆	C₂²	semidirect
28. C₃×C₄⋊C₁₆	C₂²	semidirect
29. C₃×C₂²⋊C₁₆	C₂²	semidirect
30. C₃×C₄×C₁₆	C₂²	semidirect
31. #4549	C₂²	semidirect
35. (C₂×D₃)⋊C₁₆	C₂²	semidirect
36. (C₂×D₃)⋊C₁₆	C₂²	semidirect
37. Dic₃⋊C₁₆	C₂²	semidirect
38. Dic₃⋊C₁₆	C₂²	semidirect
39. Dic₃×C₁₆	C₂²	semidirect
40. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
41. C₄×C₃⋊C₁₆	C₂²	semidirect
48. D₄×C₁₆	D₃	semidirect
99. C₂²×C₁₆	C₂×D₃	semidirect
112. C₄⋊C₁₆	C₂×D₃	semidirect
119. C₂²⋊C₁₆	C₂×D₃	semidirect
122. C₄×C₁₆	C₂×D₃	semidirect
128. D₃×D₄	C₁₆	semidirect
215. C₂²×D₃	C₂×C₁₆	semidirect
218. C₃×D₄	C₂×C₁₆	semidirect
225. #67	C₂×C₁₆	semidirect
231. D₁₂	C₂×C₁₆	semidirect
239. C₄×D₃	C₂×C₁₆	semidirect
323. D₄	D₃×C₁₆	semidirect
376. C₃	#33486	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₈×D₄	2
C₃×D₄×C₁₆	2
C₂×(C₂×D₃)⋊C₁₆	2
C₁₆×#67	2
D₄×C₃⋊C₁₆	2
#69277	2
#69274	2
D₃×C₂²⋊C₁₆	2
#67⋊C₁₆	2
C₁₆×D₁₂	2
#69052	2
#33486	3