Subgroups — Q₈×C₄⋊ΓL(1,𝔽₁₆) #14327224

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 340 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	#11752371	C₂	1	6	yes	maximal
4	#11752347	C₂	1	3	yes	maximal
5	C₄×C₄⋊ΓL(1,𝔽₁₆)	C₂	1	3	yes	maximal
6	Q₈×C₄⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
7	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
8	Q₈×ΓL(1,𝔽₁₆)	—	2	8	no	—
9	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	3	yes	—
10	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
11	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
12	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
13	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	6	yes	—
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	Q₈×C₄⋊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	#65712	—	3	6	no	—
25	#65688	—	3	3	no	—
26	C₄×C₄⋊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	D₄	1	4	yes	—
31	C₃×Q₈×D₅	Q₈	1	4	yes	—
32	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
33	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
34	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×Dic₁₀	C₂×C₄	1	3	yes	—
36	C₄⋊ΓL(1,𝔽₁₆)	—	2	12	no	—
37	C₄⋊ΓL(1,𝔽₁₆)	—	2	6	no	—
38	C₄⋊ΓL(1,𝔽₁₆)	—	4	6	no	—
39	C₄⋊ΓL(1,𝔽₁₆)	Q₈	1	4	yes	direct product factor
40	C₄×ΓL(1,𝔽₁₆)	—	2	12	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	3	yes	—
42	C₃×C₄²×C₅	C₂×C₄	1	3	yes	—
43	C₃×C₄⋊Dic₅	C₂×C₄	1	3	yes	—
44	C₃×#683	C₂×C₄	1	6	yes	—
45	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
46	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
47	C₃×C₄×Dic₅	C₂×C₄	1	3	yes	—
48	C₂×C₃×C₄×Q₈	—	5	1	no	—
49	C₂×Q₈×Dic₃	—	5	2	no	—
50	#4984	—	5	6	no	—
51	#4935	—	5	3	no	—
52	C₄×C₄⋊Dic₃	—	5	3	no	—
53	C₂×Q₈×D₅	C₂×D₃	1	1	yes	characteristic
54	Q₈×AGL(1,𝔽₅)	—	6	8	no	—
55	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
56	C₂×C₄⋊AGL(1,𝔽₅)	—	3	3	no	—
57	C₂×C₄⋊AGL(1,𝔽₅)	—	3	6	no	—
58	C₂×C₄⋊AGL(1,𝔽₅)	—	3	6	no	—
59	C₂×C₄×AGL(1,𝔽₅)	—	3	6	no	—
60	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
61	Q₈×Dic₅	Dic₃	1	1	yes	characteristic, complemented
62	D₅×C₄⋊C₄	C₂×D₃	1	3	yes	—
63	#4033	Dic₃	1	3	yes	complemented
64	C₄²×D₅	C₂×D₃	1	3	yes	—
65	C₄×Dic₁₀	Dic₃	1	3	yes	complemented
66	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	6	no	—
67	Q₈×C₄⋊C₄	—	15	1	no	Sylow
68	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
70	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
71	C₂×ΓL(1,𝔽₁₆)	—	2	6	no	—
72	C₂×ΓL(1,𝔽₁₆)	—	2	6	no	—
73	C₂×ΓL(1,𝔽₁₆)	—	2	6	no	—
74	C₂×ΓL(1,𝔽₁₆)	C₂×Q₈	1	4	yes	—
75	C₃×C₅×Q₈	C₄⋊C₄	1	4	yes	complemented
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃×Dic₅	C₂²×C₄	1	3	yes	—
80	C₂×C₃×Dic₅	C₂²×C₄	1	3	yes	—
81	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
82	C₃×C₄×D₅	—	2	3	no	—
83	C₃×C₄×D₅	—	2	3	no	—
84	C₃×C₄×D₅	C₂×D₄	1	6	yes	—
85	C₃×C₄×D₅	C₂×Q₈	1	6	yes	—
86	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
87	C₃×C₄×D₅	#41	1	2	yes	—
88	C₃×Dic₁₀	C₄⋊C₄	1	12	yes	complemented
89	C₂²×C₃×Q₈	—	5	1	no	—
90	C₃×C₄×Q₈	—	5	1	no	—
91	C₃×C₄×Q₈	—	5	3	no	—
92	C₃×C₄×Q₈	—	5	3	no	—
93	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
94	C₂×C₃×C₄⋊C₄	—	5	3	no	—
95	C₂×C₃×C₄²	—	5	3	no	—
96	Q₈×Dic₃	—	10	8	no	—
97	C₂×C₄⋊Dic₃	—	5	1	no	—
98	C₂×C₄⋊Dic₃	—	5	3	no	—
99	C₂×C₄⋊Dic₃	—	5	6	no	—
100	C₂×C₄⋊Dic₃	—	5	6	no	—
101	C₂×C₄×Dic₃	—	5	6	no	—
102	C₃⋊#95	—	5	6	no	—
103	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
104	C₂²×AGL(1,𝔽₅)	—	3	6	no	—
105	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
106	Q₈×D₅	Dic₆	1	4	yes	—
107	Q₈×D₅	D₁₂	1	4	yes	—
108	C₂×C₄×D₅	C₂²×D₃	1	3	yes	—
109	C₂×C₄×D₅	C₂²×D₃	1	3	yes	—
110	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
111	C₂×Dic₁₀	C₂×Dic₃	1	3	yes	—
112	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
113	C₄⋊AGL(1,𝔽₅)	—	6	12	no	—
114	C₄⋊AGL(1,𝔽₅)	—	6	6	no	—
115	C₄⋊AGL(1,𝔽₅)	—	12	6	no	—
116	C₄×AGL(1,𝔽₅)	—	6	12	no	—
117	C₅×C₄⋊C₄	C₂×Dic₃	1	3	yes	—
118	C₄²×C₅	C₂×Dic₃	1	3	yes	—
119	C₄⋊Dic₅	C₂×Dic₃	1	3	yes	—
120	#683	C₂×Dic₃	1	6	yes	—
121	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
122	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
123	C₄×Dic₅	C₂×Dic₃	1	3	yes	—
124	C₂×C₄×Q₈	—	5	1	no	—
125	C₂×C₄×Q₈	—	15	2	no	—
126	#389	—	15	6	no	—
127	#384	—	15	3	no	—
128	C₄×C₄⋊C₄	—	15	3	no	—
129	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
134	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₃×D₅	2₋¹⁺⁴	1	1	yes	characteristic
136	ΓL(1,𝔽₁₆)	—	2	4	no	—
137	ΓL(1,𝔽₁₆)	—	4	6	no	—
138	C₃×C₄×C₅	—	2	3	no	—
139	C₃×C₄×C₅	C₂×C₄⋊C₄	1	6	yes	—
140	C₃×C₄×C₅	C₄×Q₈	1	2	yes	complemented
141	C₃×Dic₅	—	2	3	no	—
142	C₃×Dic₅	C₂×C₄⋊C₄	1	6	yes	—
143	C₃×Dic₅	C₄×Q₈	1	2	yes	complemented
144	C₂×C₃×Q₈	—	5	4	no	—
145	C₂×C₃×Q₈	—	5	4	no	—
146	C₂×C₃×Q₈	—	5	3	no	—
147	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
148	C₂²×C₃×C₄	—	5	3	no	—
149	C₂²×C₃×C₄	—	5	1	no	—
150	C₂²×C₃×C₄	—	5	3	no	—
151	C₂²×Dic₃	—	5	2	no	—
152	C₂²×Dic₃	—	5	6	no	—
153	C₃×C₄⋊C₄	—	5	6	no	—
154	C₃×C₄⋊C₄	—	5	3	no	—
155	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
156	C₃×C₄²	—	5	3	no	—
157	C₃×C₄²	—	5	3	no	—
158	C₃×C₄²	—	5	3	no	—
159	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	3	yes	—
160	C₄⋊Dic₃	—	5	4	no	—
161	C₄⋊Dic₃	—	10	6	no	—
162	C₄⋊Dic₃	—	10	12	no	—
163	C₄⋊Dic₃	—	20	6	no	—
164	C₄×Dic₃	—	10	12	no	—
165	C₂²×D₅	C₂³×D₃	1	1	yes	characteristic
166	C₂×AGL(1,𝔽₅)	—	3	4	no	—
167	C₂×AGL(1,𝔽₅)	—	6	2	no	—
168	C₂×AGL(1,𝔽₅)	—	6	2	no	—
169	C₂×AGL(1,𝔽₅)	—	6	6	no	—
170	C₂×AGL(1,𝔽₅)	—	6	6	no	—
171	C₂×AGL(1,𝔽₅)	—	6	6	no	—
172	C₅×Q₈	C₄⋊Dic₃	1	4	yes	complemented
173	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
174	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
175	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
176	C₂×Dic₅	C₂²×Dic₃	1	3	yes	—
177	C₂×Dic₅	C₂²×Dic₃	1	3	yes	—
178	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
179	C₄×D₅	—	2	3	no	—
180	C₄×D₅	—	2	3	no	—
181	C₄×D₅	C₂×Dic₆	1	6	yes	—
182	C₄×D₅	C₂×D₁₂	1	6	yes	—
183	C₄×D₅	D₃×Q₈	1	2	yes	—
184	C₄×D₅	#239	1	2	yes	—
185	Dic₁₀	C₄⋊Dic₃	1	12	yes	complemented
186	C₂²×Q₈	—	5	1	no	—
187	C₄×Q₈	—	5	1	no	—
188	C₄×Q₈	—	5	3	no	—
189	C₄×Q₈	—	5	3	no	—
190	C₄×Q₈	—	30	8	no	—
191	C₄×Q₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
192	C₂×C₄⋊C₄	—	5	3	no	—
193	C₂×C₄⋊C₄	—	15	1	no	—
194	C₂×C₄⋊C₄	—	15	6	no	—
195	C₂×C₄⋊C₄	—	15	3	no	—
196	C₂×C₄⋊C₄	—	15	6	no	—
197	C₂×C₄²	—	5	3	no	—
198	C₂×C₄²	—	15	6	no	—
199	#95	—	15	6	no	—
200	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₂×C₃×C₅	#520	1	1	yes	characteristic
203	C₃×D₅	D₄×Q₈	1	1	yes	characteristic
204	C₃×D₅	#550	1	1	yes	characteristic
205	C₃×D₅	#557	1	1	yes	characteristic
206	C₃×D₅	Q₈²	1	1	yes	characteristic
207	C₂³×C₃	—	5	1	no	—
208	C₃×Q₈	—	5	12	no	—
209	C₃×Q₈	C₄⋊AGL(1,𝔽₅)	1	4	yes	complemented
210	C₂×C₃×C₄	—	5	1	no	—
211	C₂×C₃×C₄	—	5	3	no	—
212	C₂×C₃×C₄	—	5	6	no	—
213	C₂×C₃×C₄	—	5	6	no	—
214	C₂×C₃×C₄	—	5	2	no	—
215	C₂×C₃×C₄	—	5	2	no	—
216	C₂×C₃×C₄	—	5	3	no	—
217	C₂×C₃×C₄	—	10	3	no	—
218	C₂×C₃×C₄	—	10	3	no	—
219	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	3	yes	—
220	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	3	yes	—
221	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₂×Dic₃	—	5	4	no	—
223	C₂×Dic₃	—	10	2	no	—
224	C₂×Dic₃	—	10	2	no	—
225	C₂×Dic₃	—	10	6	no	—
226	C₂×Dic₃	—	10	6	no	—
227	C₂×Dic₃	—	10	6	no	—
228	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
229	C₂×D₅	C₂²×Dic₆	1	1	yes	characteristic
230	C₂×D₅	C₂²×D₁₂	1	1	yes	characteristic
231	C₂×D₅	C₂×D₃×Q₈	1	1	yes	characteristic
232	C₂×D₅	C₂×#239	1	1	yes	characteristic
233	C₂×D₅	#1009	1	1	yes	characteristic
234	C₂×D₅	#1010	1	1	yes	characteristic
235	AGL(1,𝔽₅)	—	6	4	no	—
236	AGL(1,𝔽₅)	—	12	6	no	—
237	C₄×C₅	—	2	3	no	—
238	C₄×C₅	C₂×C₄⋊Dic₃	1	6	yes	—
239	C₄×C₅	Q₈×Dic₃	1	2	yes	complemented
240	Dic₅	—	2	3	no	—
241	Dic₅	C₂×C₄⋊Dic₃	1	6	yes	—
242	Dic₅	Q₈×Dic₃	1	2	yes	complemented
243	C₂×Q₈	—	5	4	no	—
244	C₂×Q₈	—	5	4	no	—
245	C₂×Q₈	—	5	3	no	—
246	C₂×Q₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
247	C₂²×C₄	—	5	1	no	—
248	C₂²×C₄	—	5	3	no	—
249	C₂²×C₄	—	5	3	no	—
250	C₂²×C₄	—	15	2	no	—
251	C₂²×C₄	—	15	6	no	—
252	C₄⋊C₄	—	5	6	no	—
253	C₄⋊C₄	—	5	3	no	—
254	C₄⋊C₄	—	15	4	no	—
255	C₄⋊C₄	—	30	12	no	—
256	C₄⋊C₄	—	30	6	no	—
257	C₄⋊C₄	—	60	6	no	—
258	C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	3	yes	—
259	C₄²	—	5	3	no	—
260	C₄²	—	5	3	no	—
261	C₄²	—	5	3	no	—
262	C₄²	—	30	12	no	—
263	C₄²	C₂×ΓL(1,𝔽₁₆)	1	3	yes	—
264	C₃×C₅	Q₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
265	C₂²×C₃	—	5	1	no	—
266	C₂²×C₃	—	5	1	no	—
267	C₂²×C₃	—	5	1	no	—
268	C₂²×C₃	—	5	1	no	—
269	C₂²×C₃	—	5	1	no	—
270	C₂²×C₃	—	5	1	no	—
271	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
272	C₃×C₄	—	2	3	no	—
273	C₃×C₄	—	5	6	no	—
274	C₃×C₄	—	5	2	no	—
275	C₃×C₄	—	10	3	no	—
276	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	6	yes	—
277	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	2	yes	complemented
278	Dic₃	—	10	4	no	—
279	Dic₃	—	20	6	no	—
280	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
281	C₂×C₅	C₂×Q₈×Dic₃	1	1	yes	characteristic
282	C₂×C₅	#5827	1	1	yes	characteristic
283	D₅	Q₈×Dic₆	1	1	yes	characteristic
284	D₅	#5570	1	1	yes	characteristic
285	D₅	Q₈×D₁₂	1	1	yes	characteristic
286	D₅	#5577	1	1	yes	characteristic
287	C₂³	—	5	1	no	—
288	Q₈	—	5	12	no	—
289	Q₈	C₄⋊ΓL(1,𝔽₁₆)	1	4	yes	direct product factor
290	C₂×C₄	—	5	1	no	—
291	C₂×C₄	—	5	3	no	—
292	C₂×C₄	—	5	6	no	—
293	C₂×C₄	—	5	6	no	—
294	C₂×C₄	—	5	2	no	—
295	C₂×C₄	—	5	2	no	—
296	C₂×C₄	—	5	3	no	—
297	C₂×C₄	—	10	3	no	—
298	C₂×C₄	—	10	3	no	—
299	C₂×C₄	—	15	4	no	—
300	C₂×C₄	—	30	2	no	—
301	C₂×C₄	—	30	2	no	—
302	C₂×C₄	—	30	6	no	—
303	C₂×C₄	—	30	6	no	—
304	C₂×C₄	—	30	6	no	—
305	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	3	yes	—
306	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	3	yes	—
307	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
308	C₂×C₃	—	5	1	no	—
309	C₂×C₃	—	5	1	no	—
310	C₂×C₃	—	5	1	no	—
311	C₂×C₃	—	5	1	no	—
312	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₂×C₃	#66266	1	1	yes	characteristic
315	C₅	Q₈×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
316	C₂²	—	5	1	no	—
317	C₂²	—	5	1	no	—
318	C₂²	—	5	1	no	—
319	C₂²	—	5	1	no	—
320	C₂²	—	5	1	no	—
321	C₂²	—	5	1	no	—
322	C₂²	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
323	C₄	—	2	3	no	—
324	C₄	—	5	6	no	—
325	C₄	—	5	2	no	—
326	C₄	—	10	3	no	—
327	C₄	—	30	4	no	—
328	C₄	—	60	6	no	—
329	C₄	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	6	yes	—
330	C₄	Q₈×ΓL(1,𝔽₁₆)	1	2	yes	complemented
331	C₃	Q₈×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
332	C₂	—	5	1	no	—
333	C₂	—	5	1	no	—
334	C₂	—	5	1	no	—
335	C₂	—	5	1	no	—
336	C₂	C₂²×C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
337	C₂	C₂×Q₈×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
338	C₂	#11756995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
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)
60. C₄×C₅×Q₈	Dic₃	semidirect
61. Q₈×Dic₅	Dic₃	semidirect
63. #4033	Dic₃	semidirect
65. C₄×Dic₁₀	Dic₃	semidirect
75. C₃×C₅×Q₈	C₄⋊C₄	semidirect
88. C₃×Dic₁₀	C₄⋊C₄	semidirect
93. C₃×C₄×Q₈	AGL(1,𝔽₅)	semidirect
140. C₃×C₄×C₅	C₄×Q₈	semidirect
143. C₃×Dic₅	C₄×Q₈	semidirect
172. C₅×Q₈	C₄⋊Dic₃	semidirect
185. Dic₁₀	C₄⋊Dic₃	semidirect
191. C₄×Q₈	ΓL(1,𝔽₁₆)	semidirect
209. C₃×Q₈	C₄⋊AGL(1,𝔽₅)	semidirect
239. C₄×C₅	Q₈×Dic₃	semidirect
242. Dic₅	Q₈×Dic₃	semidirect
264. C₃×C₅	Q₈×C₄⋊C₄	semidirect
277. C₃×C₄	Q₈×AGL(1,𝔽₅)	semidirect
289. Q₈	C₄⋊ΓL(1,𝔽₁₆)	direct (N × H)
315. C₅	Q₈×C₄⋊Dic₃	semidirect
330. C₄	Q₈×ΓL(1,𝔽₁₆)	semidirect
331. C₃	Q₈×C₄⋊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
#11752371	2
#11752347	2
C₄×C₄⋊ΓL(1,𝔽₁₆)	2
Q₈×C₄⋊AGL(1,𝔽₅)	3
Q₈×C₄⋊Dic₃	5

Subgroups — Q8×C4⋊ΓL(1,𝔽16) #14327224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₄⋊ΓL(1,𝔽₁₆) #14327224