Subgroups — C₄×Q₈×ΓL(1,𝔽₁₆) #14319620

Order 1920.

1368 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal
2	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×ΓL(1,𝔽₁₆)	C₂	1	6	yes	maximal
4	C₄×C₄⋊ΓL(1,𝔽₁₆)	C₂	1	3	yes	maximal
5	C₄²×ΓL(1,𝔽₁₆)	C₂	1	3	yes	maximal
6	C₄×Q₈×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
7	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
8	Q₈×ΓL(1,𝔽₁₆)	C₄	1	16	yes	direct product factor
9	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
10	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	3	yes	—
11	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
12	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
13	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
15	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic, complemented
16	C₃×D₅×C₄⋊C₄	C₂²	1	3	yes	—
17	C₃×#4033	C₄	1	3	yes	complemented
18	C₃×C₄²×D₅	C₂²	1	3	yes	—
19	C₃×C₄×Dic₁₀	C₄	1	3	yes	complemented
20	#91235	C₂²	1	6	yes	—
21	C₄×Q₈×Dic₃	—	5	1	no	maximal, Hall
22	C₂×Q₈×AGL(1,𝔽₅)	—	3	2	no	—
23	C₄×Q₈×D₅	D₃	1	1	yes	characteristic
24	C₄⋊C₄×AGL(1,𝔽₅)	—	3	6	no	—
25	C₄×C₄⋊AGL(1,𝔽₅)	—	3	3	no	—
26	C₄²×AGL(1,𝔽₅)	—	3	3	no	—
27	C₂²×ΓL(1,𝔽₁₆)	C₂³	1	6	yes	—
28	C₂²×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
30	C₃×Q₈×D₅	C₂×C₄	1	8	yes	—
31	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
32	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
33	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×Dic₁₀	C₂×C₄	1	3	yes	—
35	C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	1	24	yes	—
36	C₄×ΓL(1,𝔽₁₆)	—	2	12	no	—
37	C₄×ΓL(1,𝔽₁₆)	—	2	6	no	—
38	C₄×ΓL(1,𝔽₁₆)	C₂×C₄	1	24	yes	—
39	C₄×ΓL(1,𝔽₁₆)	Q₈	1	4	yes	direct product factor
40	C₃×C₅×C₄⋊C₄	C₂×C₄	1	3	yes	—
41	C₃×C₄²×C₅	C₂×C₄	1	3	yes	—
42	C₃×C₄⋊Dic₅	C₂×C₄	1	3	yes	—
43	C₃×#683	C₂×C₄	1	6	yes	—
44	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
45	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
46	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
47	C₂×C₃×C₄×Q₈	—	5	1	no	—
48	C₂×Q₈×Dic₃	—	5	2	no	—
49	Dic₃×C₄⋊C₄	—	5	6	no	—
50	C₄×C₄⋊Dic₃	—	5	3	no	—
51	C₄²×Dic₃	—	5	3	no	—
52	C₂×Q₈×D₅	C₂×D₃	1	1	yes	characteristic
53	Q₈×AGL(1,𝔽₅)	—	3	16	no	—
54	C₂×C₄⋊AGL(1,𝔽₅)	—	3	6	no	—
55	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
56	C₂×C₄×AGL(1,𝔽₅)	—	3	6	no	—
57	C₂×C₄×AGL(1,𝔽₅)	—	3	3	no	—
58	C₂×C₄×AGL(1,𝔽₅)	—	3	6	no	—
59	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
60	Q₈×Dic₅	Dic₃	1	1	yes	characteristic, complemented
61	D₅×C₄⋊C₄	C₂×D₃	1	3	yes	—
62	#4033	Dic₃	1	3	yes	complemented
63	C₄²×D₅	C₂×D₃	1	3	yes	—
64	C₄×Dic₁₀	Dic₃	1	3	yes	complemented
65	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	6	no	—
66	C₄²×Q₈	—	15	1	no	Sylow
67	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
68	C₂×ΓL(1,𝔽₁₆)	—	2	6	no	—
69	C₂×ΓL(1,𝔽₁₆)	—	2	6	no	—
70	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	12	yes	—
71	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	4	yes	—
72	C₂×ΓL(1,𝔽₁₆)	C₂×Q₈	1	4	yes	—
73	C₂×ΓL(1,𝔽₁₆)	#41	1	4	yes	—
74	C₃×C₅×Q₈	C₄²	1	4	yes	complemented
75	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×Dic₅	C₂²×C₄	1	3	yes	—
79	C₂×C₃×Dic₅	C₂²×C₄	1	3	yes	—
80	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
81	C₃×C₄×D₅	—	2	6	no	—
82	C₃×C₄×D₅	C₂²×C₄	1	12	yes	—
83	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
84	C₃×C₄×D₅	#41	1	2	yes	—
85	C₃×Dic₁₀	C₄²	1	12	yes	complemented
86	C₂²×C₃×Q₈	—	5	1	no	—
87	C₃×C₄×Q₈	—	5	1	no	—
88	C₃×C₄×Q₈	—	5	3	no	—
89	C₃×C₄×Q₈	—	5	3	no	—
90	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
91	C₂×C₃×C₄⋊C₄	—	5	3	no	—
92	C₂×C₃×C₄²	—	5	3	no	—
93	Q₈×Dic₃	—	5	16	no	—
94	C₂×C₄⋊Dic₃	—	5	6	no	—
95	C₂×C₄×Dic₃	—	5	1	no	—
96	C₂×C₄×Dic₃	—	5	6	no	—
97	C₂×C₄×Dic₃	—	5	3	no	—
98	C₂×C₄×Dic₃	—	5	6	no	—
99	C₃⋊#95	—	5	6	no	—
100	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
101	C₂²×AGL(1,𝔽₅)	—	3	6	no	—
102	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
103	Q₈×D₅	C₄×D₃	1	8	yes	—
104	C₂×C₄×D₅	C₂²×D₃	1	3	yes	—
105	C₂×C₄×D₅	C₂²×D₃	1	3	yes	—
106	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
107	C₂×Dic₁₀	C₂×Dic₃	1	3	yes	—
108	C₄⋊AGL(1,𝔽₅)	—	3	24	no	—
109	C₄×AGL(1,𝔽₅)	—	3	24	no	—
110	C₄×AGL(1,𝔽₅)	—	3	4	no	—
111	C₄×AGL(1,𝔽₅)	—	6	12	no	—
112	C₄×AGL(1,𝔽₅)	—	6	6	no	—
113	C₅×C₄⋊C₄	C₂×Dic₃	1	3	yes	—
114	C₄²×C₅	C₂×Dic₃	1	3	yes	—
115	C₄⋊Dic₅	C₂×Dic₃	1	3	yes	—
116	#683	C₂×Dic₃	1	6	yes	—
117	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
118	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
119	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
120	C₂×C₄×Q₈	—	5	1	no	—
121	C₂×C₄×Q₈	—	15	2	no	—
122	C₄×C₄⋊C₄	—	15	3	no	—
123	C₄×C₄⋊C₄	—	15	6	no	—
124	C₄³	—	15	3	no	—
125	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₃×D₅	C₂³×C₄	1	2	yes	—
127	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
129	C₂×C₃×D₅	C₂×#41	1	2	yes	—
130	ΓL(1,𝔽₁₆)	—	2	12	no	—
131	ΓL(1,𝔽₁₆)	C₄×Q₈	1	8	yes	direct product factor
132	C₃×C₄×C₅	—	2	3	no	—
133	C₃×C₄×C₅	C₂×C₄²	1	6	yes	—
134	C₃×C₄×C₅	C₄×Q₈	1	2	yes	complemented
135	C₃×Dic₅	—	2	3	no	—
136	C₃×Dic₅	C₂×C₄²	1	6	yes	—
137	C₃×Dic₅	C₄×Q₈	1	2	yes	complemented
138	C₂×C₃×Q₈	—	5	8	no	—
139	C₂×C₃×Q₈	—	5	3	no	—
140	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	5	1	no	—
142	C₂²×C₃×C₄	—	5	3	no	—
143	C₂²×C₃×C₄	—	5	3	no	—
144	C₂²×Dic₃	—	5	2	no	—
145	C₂²×Dic₃	—	5	6	no	—
146	C₃×C₄⋊C₄	—	5	6	no	—
147	C₃×C₄⋊C₄	—	5	3	no	—
148	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
149	C₃×C₄²	—	5	3	no	—
150	C₃×C₄²	—	5	3	no	—
151	C₃×C₄²	—	5	3	no	—
152	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	3	yes	—
153	C₄⋊Dic₃	—	5	24	no	—
154	C₄×Dic₃	—	5	24	no	—
155	C₄×Dic₃	—	5	4	no	—
156	C₄×Dic₃	—	10	12	no	—
157	C₄×Dic₃	—	10	6	no	—
158	C₂²×D₅	C₂³×D₃	1	1	yes	characteristic
159	C₂×AGL(1,𝔽₅)	—	3	4	no	—
160	C₂×AGL(1,𝔽₅)	—	3	4	no	—
161	C₂×AGL(1,𝔽₅)	—	3	4	no	—
162	C₂×AGL(1,𝔽₅)	—	3	12	no	—
163	C₂×AGL(1,𝔽₅)	—	6	6	no	—
164	C₂×AGL(1,𝔽₅)	—	6	6	no	—
165	C₅×Q₈	C₄×Dic₃	1	4	yes	complemented
166	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
167	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
168	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
169	C₂×Dic₅	C₂²×Dic₃	1	3	yes	—
170	C₂×Dic₅	C₂²×Dic₃	1	3	yes	—
171	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
172	C₄×D₅	—	2	6	no	—
173	C₄×D₅	C₂×C₄×D₃	1	12	yes	—
174	C₄×D₅	D₃×Q₈	1	2	yes	—
175	C₄×D₅	#239	1	2	yes	—
176	Dic₁₀	C₄×Dic₃	1	12	yes	complemented
177	C₂²×Q₈	—	5	1	no	—
178	C₄×Q₈	—	5	1	no	—
179	C₄×Q₈	—	5	3	no	—
180	C₄×Q₈	—	5	3	no	—
181	C₄×Q₈	—	15	16	no	—
182	C₄×Q₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
183	C₂×C₄⋊C₄	—	5	3	no	—
184	C₂×C₄⋊C₄	—	15	6	no	—
185	C₂×C₄²	—	5	3	no	—
186	C₂×C₄²	—	15	6	no	—
187	C₂×C₄²	—	15	1	no	—
188	C₂×C₄²	—	15	3	no	—
189	C₂×C₄²	—	15	6	no	—
190	#95	—	15	6	no	—
191	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
192	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
194	C₃×D₅	C₂×C₄×Q₈	1	2	yes	—
195	C₃×D₅	C₄×#41	1	2	yes	—
196	C₂³×C₃	—	5	1	no	—
197	C₃×Q₈	—	5	12	no	—
198	C₃×Q₈	C₄×AGL(1,𝔽₅)	1	4	yes	complemented
199	C₂×C₃×C₄	—	5	1	no	—
200	C₂×C₃×C₄	—	5	3	no	—
201	C₂×C₃×C₄	—	5	12	no	—
202	C₂×C₃×C₄	—	5	2	no	—
203	C₂×C₃×C₄	—	5	2	no	—
204	C₂×C₃×C₄	—	5	3	no	—
205	C₂×C₃×C₄	—	10	6	no	—
206	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	3	yes	—
207	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	3	yes	—
208	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₂×Dic₃	—	5	4	no	—
210	C₂×Dic₃	—	5	4	no	—
211	C₂×Dic₃	—	5	4	no	—
212	C₂×Dic₃	—	5	12	no	—
213	C₂×Dic₃	—	10	6	no	—
214	C₂×Dic₃	—	10	6	no	—
215	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
216	C₂×D₅	C₂²×C₄×D₃	1	2	yes	—
217	C₂×D₅	C₂×D₃×Q₈	1	1	yes	characteristic
218	C₂×D₅	C₂×#239	1	1	yes	characteristic
219	C₂×D₅	D₃×#41	1	2	yes	—
220	AGL(1,𝔽₅)	—	3	8	no	—
221	AGL(1,𝔽₅)	—	6	12	no	—
222	C₄×C₅	—	2	3	no	—
223	C₄×C₅	C₂×C₄×Dic₃	1	6	yes	—
224	C₄×C₅	Q₈×Dic₃	1	2	yes	complemented
225	Dic₅	—	2	3	no	—
226	Dic₅	C₂×C₄×Dic₃	1	6	yes	—
227	Dic₅	Q₈×Dic₃	1	2	yes	complemented
228	C₂×Q₈	—	5	8	no	—
229	C₂×Q₈	—	5	3	no	—
230	C₂×Q₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
231	C₂²×C₄	—	5	3	no	—
232	C₂²×C₄	—	5	1	no	—
233	C₂²×C₄	—	5	3	no	—
234	C₂²×C₄	—	15	2	no	—
235	C₂²×C₄	—	15	6	no	—
236	C₄⋊C₄	—	5	6	no	—
237	C₄⋊C₄	—	5	3	no	—
238	C₄⋊C₄	—	15	24	no	—
239	C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	3	yes	—
240	C₄²	—	5	3	no	—
241	C₄²	—	5	3	no	—
242	C₄²	—	5	3	no	—
243	C₄²	—	15	24	no	—
244	C₄²	—	15	4	no	—
245	C₄²	—	30	6	no	—
246	C₄²	—	30	12	no	—
247	C₄²	C₂×ΓL(1,𝔽₁₆)	1	3	yes	—
248	C₃×C₅	C₄²×Q₈	1	1	yes	characteristic, complemented, Hall
249	C₂²×C₃	—	5	2	no	—
250	C₂²×C₃	—	5	1	no	—
251	C₂²×C₃	—	5	1	no	—
252	C₂²×C₃	—	5	2	no	—
253	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
254	C₃×C₄	—	2	3	no	—
255	C₃×C₄	—	5	6	no	—
256	C₃×C₄	—	5	2	no	—
257	C₃×C₄	—	10	3	no	—
258	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	6	yes	—
259	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	2	yes	complemented
260	Dic₃	—	5	8	no	—
261	Dic₃	—	10	12	no	—
262	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
263	C₂×C₅	C₂×Q₈×Dic₃	1	1	yes	characteristic
264	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
265	D₅	C₄×D₃×Q₈	1	2	yes	—
266	D₅	C₄×#239	1	2	yes	—
267	C₂³	—	5	1	no	—
268	Q₈	—	5	12	no	—
269	Q₈	C₄×ΓL(1,𝔽₁₆)	1	4	yes	direct product factor
270	C₂×C₄	—	5	1	no	—
271	C₂×C₄	—	5	3	no	—
272	C₂×C₄	—	5	12	no	—
273	C₂×C₄	—	5	2	no	—
274	C₂×C₄	—	5	2	no	—
275	C₂×C₄	—	5	3	no	—
276	C₂×C₄	—	10	6	no	—
277	C₂×C₄	—	15	4	no	—
278	C₂×C₄	—	15	4	no	—
279	C₂×C₄	—	15	4	no	—
280	C₂×C₄	—	15	12	no	—
281	C₂×C₄	—	30	6	no	—
282	C₂×C₄	—	30	6	no	—
283	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	3	yes	—
284	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	3	yes	—
285	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
286	C₂×C₃	—	5	2	no	—
287	C₂×C₃	—	5	2	no	—
288	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
291	C₅	C₄×Q₈×Dic₃	1	1	yes	characteristic, complemented, Sylow
292	C₂²	—	5	2	no	—
293	C₂²	—	5	1	no	—
294	C₂²	—	5	1	no	—
295	C₂²	—	5	2	no	—
296	C₂²	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
297	C₄	—	2	3	no	—
298	C₄	—	5	6	no	—
299	C₄	—	5	2	no	—
300	C₄	—	10	3	no	—
301	C₄	—	15	8	no	—
302	C₄	—	30	12	no	—
303	C₄	C₂×C₄×ΓL(1,𝔽₁₆)	1	6	yes	—
304	C₄	Q₈×ΓL(1,𝔽₁₆)	1	2	yes	direct product factor
305	C₃	C₄×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
306	C₂	—	5	2	no	—
307	C₂	—	5	2	no	—
308	C₂	C₂²×C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
309	C₂	C₂×Q₈×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
310	C₂	#41×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂²	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₃×C₄×C₅×Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical, cosocle	C₂²×C₃×D₅	C₂⁴
hypercenter	C₄×Q₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₄²×Q₈
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
8. Q₈×ΓL(1,𝔽₁₆)	C₄	direct (N × H)
14. C₃×C₄×C₅×Q₈	C₄	semidirect
15. C₃×Q₈×Dic₅	C₄	semidirect
17. C₃×#4033	C₄	semidirect
19. C₃×C₄×Dic₁₀	C₄	semidirect
39. C₄×ΓL(1,𝔽₁₆)	Q₈	direct (N × H)
59. C₄×C₅×Q₈	Dic₃	semidirect
60. Q₈×Dic₅	Dic₃	semidirect
62. #4033	Dic₃	semidirect
64. C₄×Dic₁₀	Dic₃	semidirect
74. C₃×C₅×Q₈	C₄²	semidirect
85. C₃×Dic₁₀	C₄²	semidirect
90. C₃×C₄×Q₈	AGL(1,𝔽₅)	semidirect
131. ΓL(1,𝔽₁₆)	C₄×Q₈	direct (N × H)
134. C₃×C₄×C₅	C₄×Q₈	semidirect
137. C₃×Dic₅	C₄×Q₈	semidirect
165. C₅×Q₈	C₄×Dic₃	semidirect
176. Dic₁₀	C₄×Dic₃	semidirect
182. C₄×Q₈	ΓL(1,𝔽₁₆)	direct (N × H)
198. C₃×Q₈	C₄×AGL(1,𝔽₅)	semidirect
224. C₄×C₅	Q₈×Dic₃	semidirect
227. Dic₅	Q₈×Dic₃	semidirect
248. C₃×C₅	C₄²×Q₈	semidirect
259. C₃×C₄	Q₈×AGL(1,𝔽₅)	semidirect
269. Q₈	C₄×ΓL(1,𝔽₁₆)	direct (N × H)
291. C₅	C₄×Q₈×Dic₃	semidirect
304. C₄	Q₈×ΓL(1,𝔽₁₆)	direct (N × H)
305. C₃	C₄×Q₈×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×ΓL(1,𝔽₁₆)	2
C₃×C₄×Q₈×D₅	2
C₄⋊C₄×ΓL(1,𝔽₁₆)	2
C₄×C₄⋊ΓL(1,𝔽₁₆)	2
C₄²×ΓL(1,𝔽₁₆)	2
C₄×Q₈×AGL(1,𝔽₅)	3
C₄×Q₈×Dic₃	5

Subgroups — C4×Q8×ΓL(1,𝔽16) #14319620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×ΓL(1,𝔽₁₆) #14319620