Subgroups — C₄×Q₁₆×#6923 #30614499

Order 15616.

1110 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×#6923	C₂	1	2	yes	maximal
2	C₄×Q₈×#6923	C₂	1	2	yes	maximal
3	#107×#6923	C₂	1	2	yes	maximal
4	C₄×#14519846	C₂	1	1	yes	maximal, characteristic
5	#103×#6923	C₂	1	4	yes	maximal
6	C₄×#14519840	C₂	1	2	yes	maximal
7	C₄×C₈×#6923	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×#6923	C₂²	1	4	yes	—
10	Q₁₆×#6923	C₄	1	16	yes	direct product factor
11	C₂×#14519846	C₂²	1	2	yes	—
12	C₂×#14519840	C₂²	1	4	yes	—
13	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×#6923	C₂²	1	2	yes	—
15	C₂×C₈×#6923	C₂²	1	2	yes	—
16	C₄⋊C₄×#6923	—	2	4	no	—
17	C₄⋊C₄×#6923	C₂²	1	4	yes	—
18	C₄×C₄⋊#6923	—	2	2	no	—
19	C₄×C₄⋊#6923	C₂²	1	2	yes	—
20	C₄²×#6923	—	2	2	no	—
21	C₄²×#6923	C₂²	1	1	yes	characteristic
22	#16840636	C₂²	1	2	yes	—
23	#16840635	C₂²	1	4	yes	—
24	C₂×Q₁₆×D₆₁	C₂²	1	1	yes	characteristic
25	C₄×Q₈×D₆₁	C₂²	1	2	yes	—
26	C₄×Dic₂₄₄	C₄	1	1	yes	characteristic, complemented
27	Q₁₆×Dic₆₁	C₄	1	1	yes	characteristic, complemented
28	#16839856	C₄	1	1	yes	characteristic, complemented
29	C₄×#11758202	C₄	1	2	yes	complemented
30	#16839854	C₄	1	2	yes	complemented
31	#107×D₆₁	C₂²	1	1	yes	characteristic
32	#103×D₆₁	C₂²	1	2	yes	—
33	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
35	C₂×D₆₁⋊C₈	C₂³	1	2	yes	—
36	Q₈×#6923	—	2	8	no	—
37	Q₈×#6923	C₂×C₄	1	16	yes	—
38	C₂×C₄⋊#6923	—	2	4	no	—
39	C₂×C₄⋊#6923	C₂³	1	4	yes	—
40	C₂×C₄×#6923	—	2	4	no	—
41	C₂×C₄×#6923	—	2	4	no	—
42	C₂×C₄×#6923	—	2	2	no	—
43	C₂×C₄×#6923	D₄	1	1	yes	characteristic
44	C₂×C₄×#6923	D₄	1	2	yes	—
45	C₂×C₄×#6923	D₄	1	1	yes	characteristic
46	C₂×C₄×#6923	C₂³	1	2	yes	—
47	#14519846	C₂×C₄	1	8	yes	—
48	#14519840	C₂×C₄	1	16	yes	—
49	C₄×#92420	—	2	1	no	—
50	C₄×#92420	—	2	1	no	—
51	C₈×#6923	—	2	4	no	—
52	C₈×#6923	C₂×C₄	1	8	yes	—
53	(C₂×#6923)⋊C₄	—	2	4	no	—
54	(C₂×#6923)⋊C₄	—	2	2	no	—
55	C₂×Q₈×D₆₁	C₂³	1	2	yes	—
56	C₂×Dic₂₄₄	C₂×C₄	1	1	yes	characteristic
57	C₂×#11758202	C₂×C₄	1	2	yes	—
58	Q₁₆×D₆₁	C₂×C₄	1	8	yes	—
59	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
61	Q₈×Dic₆₁	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₂₂	—	2	2	no	—
63	C₄×Dic₁₂₂	C₂×C₄	1	2	yes	—
64	#14519742	—	2	2	no	—
65	#14519742	C₂×C₄	1	2	yes	—
66	C₄⋊C₄×D₆₁	—	2	2	no	—
67	C₄⋊C₄×D₆₁	C₂³	1	2	yes	—
68	C₄²×D₆₁	—	2	2	no	—
69	C₄²×D₆₁	C₂³	1	1	yes	characteristic
70	#14519711	C₂×C₄	1	1	yes	characteristic
71	#14519710	C₂×C₄	1	2	yes	—
72	#14519702	C₂×C₄	1	2	yes	—
73	#14519701	C₂×C₄	1	2	yes	—
74	#14519700	C₂×C₄	1	2	yes	—
75	C₄×#92418	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
80	#107×C₆₁	C₂×C₄	1	1	yes	characteristic
81	#103×C₆₁	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂²×#6923	—	2	4	no	—
84	C₂²×#6923	C₂×D₄	1	2	yes	—
85	C₂²×#6923	C₂×D₄	1	2	yes	—
86	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
87	Q₈×D₆₁	—	2	4	no	—
88	Q₈×D₆₁	C₂²×C₄	1	8	yes	—
89	C₂×C₄×D₆₁	—	2	2	no	—
90	C₂×C₄×D₆₁	—	2	2	no	—
91	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
94	C₂×Dic₁₂₂	—	2	2	no	—
95	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
96	C₂×#92420	—	2	2	no	—
97	C₄⋊#6923	—	2	16	no	—
98	C₄⋊#6923	—	2	4	no	—
99	C₄⋊#6923	C₂²×C₄	1	8	yes	—
100	C₄×#6923	—	2	16	no	—
101	C₄×#6923	—	2	4	no	—
102	C₄×#6923	—	2	2	no	—
103	C₄×#6923	—	4	8	no	—
104	C₄×#6923	—	4	4	no	—
105	C₄×#6923	Q₁₆	1	4	yes	direct product factor
106	C₄×#6923	C₂²×C₄	1	4	yes	—
107	C₄×#6923	#41	1	4	yes	—
108	D₆₁⋊C₈	—	2	2	no	—
109	D₆₁⋊C₈	C₂²×C₄	1	4	yes	—
110	Q₁₆×C₆₁	C₄²	1	4	yes	complemented
111	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₆₁	—	2	2	no	—
116	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	#11758202	C₄²	1	8	yes	complemented
118	C₄⋊Dic₆₁	—	2	2	no	—
119	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
120	#11758196	—	2	2	no	—
121	#11758196	—	2	2	no	—
122	#11758196	—	2	2	no	—
123	C₄×Dic₆₁	—	2	2	no	—
124	C₄×Dic₆₁	—	2	2	no	—
125	C₄×Dic₆₁	—	2	2	no	—
126	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₆₁	#41	1	1	yes	characteristic
128	C₄×Dic₆₁	#41	1	1	yes	characteristic
129	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
130	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
131	Dic₂₄₄	C₄²	1	4	yes	complemented
132	C₈×D₆₁	—	2	2	no	—
133	C₈×D₆₁	C₂²×C₄	1	4	yes	—
134	C₂²×D₆₁	C₂²×D₄	1	1	yes	characteristic
135	C₂×#6923	—	2	2	no	—
136	C₂×#6923	—	2	2	no	—
137	C₂×#6923	—	2	8	no	—
138	C₂×#6923	—	4	4	no	—
139	C₂×#6923	—	4	4	no	—
140	C₂×#6923	C₄×D₄	1	4	yes	—
141	C₂×#6923	C₄×D₄	1	4	yes	—
142	C₂×#6923	C₂×Q₁₆	1	4	yes	—
143	C₂×#6923	#135	1	4	yes	—
144	Q₈×C₆₁	—	2	2	no	—
145	Q₈×C₆₁	C₂×C₄²	1	4	yes	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×Dic₆₁	—	2	2	no	—
152	C₂×Dic₆₁	—	2	2	no	—
153	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
154	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
155	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
156	C₄×D₆₁	—	2	8	no	—
157	C₄×D₆₁	—	2	2	no	—
158	C₄×D₆₁	—	4	4	no	—
159	C₄×D₆₁	C₂×Q₁₆	1	2	yes	—
160	C₄×D₆₁	#135	1	2	yes	—
161	C₄×D₆₁	C₂³×C₄	1	2	yes	—
162	C₄×D₆₁	C₂×#41	1	2	yes	—
163	Dic₁₂₂	—	2	2	no	—
164	Dic₁₂₂	—	2	8	no	—
165	Dic₁₂₂	C₂×C₄²	1	4	yes	—
166	#92420	—	2	4	no	—
167	C₈×C₆₁	—	2	1	no	—
168	C₈×C₆₁	C₂×C₄²	1	2	yes	—
169	#92418	—	2	1	no	—
170	#92418	C₂×C₄²	1	2	yes	—
171	C₄²×Q₁₆	—	61	1	no	maximal, Sylow
172	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
173	C₂×D₆₁	C₂×C₄×D₄	1	2	yes	—
174	C₂×D₆₁	C₂²×Q₁₆	1	1	yes	characteristic
175	C₂×D₆₁	C₂×#135	1	2	yes	—
176	C₂×D₆₁	C₂×#135	1	1	yes	characteristic
177	#6923	—	2	4	no	—
178	#6923	—	4	8	no	—
179	#6923	C₄×Q₁₆	1	8	yes	direct product factor
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	4	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	C₄×Q₁₆	1	2	yes	complemented
184	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
185	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
186	Dic₆₁	—	2	1	no	—
187	Dic₆₁	—	2	4	no	—
188	Dic₆₁	—	4	2	no	—
189	Dic₆₁	C₄×Q₁₆	1	2	yes	complemented
190	Dic₆₁	C₄×#41	1	2	yes	—
191	C₂×C₄×Q₁₆	—	61	2	no	—
192	C₂×C₄×Q₁₆	—	61	1	no	—
193	C₄²×Q₈	—	61	2	no	—
194	C₄×#107	—	61	1	no	—
195	C₄×#107	—	61	2	no	—
196	C₄×#103	—	61	2	no	—
197	C₄×#103	—	61	4	no	—
198	C₄²×C₈	—	61	1	no	—
199	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
200	C₂×C₆₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
201	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
202	D₆₁	C₂×C₄×Q₁₆	1	2	yes	—
203	D₆₁	C₄×#135	1	2	yes	—
204	C₂²×Q₁₆	—	61	1	no	—
205	C₂×C₄×Q₈	—	61	4	no	—
206	C₂×C₄×Q₈	—	61	2	no	—
207	C₄×Q₁₆	—	61	16	no	—
208	C₄×Q₁₆	—	61	1	no	—
209	C₄×Q₁₆	—	61	2	no	—
210	C₄×Q₁₆	—	61	1	no	—
211	C₄×Q₁₆	—	61	2	no	—
212	C₄×Q₁₆	—	61	1	no	—
213	C₄×Q₁₆	#6923	1	1	yes	characteristic, direct product factor
214	C₂×#107	—	61	2	no	—
215	C₂×#107	—	61	1	no	—
216	C₂×#103	—	61	4	no	—
217	C₂×#103	—	61	2	no	—
218	C₂×C₄×C₈	—	61	2	no	—
219	C₂×C₄×C₈	—	61	1	no	—
220	C₂×C₄×C₈	—	61	2	no	—
221	C₂×C₄×C₈	—	61	1	no	—
222	C₄×C₄⋊C₄	—	61	2	no	—
223	C₄×C₄⋊C₄	—	61	4	no	—
224	C₄×C₄⋊C₄	—	122	2	no	—
225	C₄×C₄⋊C₄	—	122	4	no	—
226	C₄³	—	61	1	no	—
227	C₄³	—	122	2	no	—
228	#340	—	61	4	no	—
229	#340	—	61	2	no	—
230	C₆₁	C₄²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
231	C₂²×Q₈	—	61	2	no	—
232	C₂×Q₁₆	—	61	2	no	—
233	C₂×Q₁₆	—	61	8	no	—
234	C₂×Q₁₆	—	61	1	no	—
235	C₂×Q₁₆	C₂×#6923	1	1	yes	characteristic
236	C₂²×C₈	—	61	1	no	—
237	C₂²×C₈	—	61	2	no	—
238	C₂²×C₈	—	61	1	no	—
239	C₄×Q₈	—	61	16	no	—
240	C₄×Q₈	—	61	2	no	—
241	C₄×Q₈	—	61	2	no	—
242	C₄×Q₈	—	61	2	no	—
243	C₄×Q₈	—	122	2	no	—
244	C₄×Q₈	—	122	2	no	—
245	C₄×Q₈	—	122	8	no	—
246	C₄×Q₈	C₂×#6923	1	2	yes	—
247	C₂×C₄⋊C₄	—	61	4	no	—
248	C₂×C₄⋊C₄	—	61	2	no	—
249	C₂×C₄⋊C₄	—	122	2	no	—
250	C₂×C₄⋊C₄	—	122	4	no	—
251	C₂×C₄²	—	61	2	no	—
252	C₂×C₄²	—	61	1	no	—
253	C₂×C₄²	—	61	1	no	—
254	C₂×C₄²	—	61	2	no	—
255	C₂×C₄²	—	61	1	no	—
256	C₂×C₄²	—	122	2	no	—
257	C₂×C₄²	—	122	4	no	—
258	C₂×C₄²	—	122	4	no	—
259	C₂×C₄²	—	122	2	no	—
260	#107	—	61	8	no	—
261	#107	—	61	1	no	—
262	#107	—	61	2	no	—
263	#107	C₂×#6923	1	1	yes	characteristic
264	#103	—	61	16	no	—
265	#103	—	61	2	no	—
266	#103	—	61	2	no	—
267	#103	—	61	2	no	—
268	#103	C₂×#6923	1	2	yes	—
269	C₄×C₈	—	61	8	no	—
270	C₄×C₈	—	61	1	no	—
271	C₄×C₈	—	61	1	no	—
272	C₄×C₈	—	61	1	no	—
273	C₄×C₈	—	122	4	no	—
274	C₄×C₈	—	122	1	no	—
275	C₄×C₈	—	122	1	no	—
276	C₄×C₈	C₂×#6923	1	1	yes	characteristic
277	#95	—	122	4	no	—
278	#95	—	122	2	no	—
279	C₂×Q₈	—	61	8	no	—
280	C₂×Q₈	—	61	2	no	—
281	C₂×Q₈	—	122	2	no	—
282	C₂×Q₈	—	122	4	no	—
283	C₂×Q₈	C₂²×#6923	1	2	yes	—
284	C₂²×C₄	—	61	2	no	—
285	C₂²×C₄	—	61	1	no	—
286	C₂²×C₄	—	61	1	no	—
287	C₂²×C₄	—	61	2	no	—
288	C₂²×C₄	—	61	1	no	—
289	C₂²×C₄	—	122	2	no	—
290	C₂²×C₄	—	122	2	no	—
291	C₂²×C₄	—	122	4	no	—
292	Q₁₆	—	61	8	no	—
293	Q₁₆	—	61	4	no	—
294	Q₁₆	C₄×#6923	1	4	yes	direct product factor
295	C₂×C₈	—	61	1	no	—
296	C₂×C₈	—	61	4	no	—
297	C₂×C₈	—	61	4	no	—
298	C₂×C₈	—	61	1	no	—
299	C₂×C₈	—	122	2	no	—
300	C₂×C₈	—	122	2	no	—
301	C₂×C₈	—	122	2	no	—
302	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
303	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	61	8	no	—
306	C₄⋊C₄	—	61	2	no	—
307	C₄⋊C₄	—	122	2	no	—
308	C₄⋊C₄	—	122	2	no	—
309	C₄⋊C₄	—	122	2	no	—
310	C₄⋊C₄	—	122	4	no	—
311	C₄⋊C₄	—	122	16	no	—
312	C₄⋊C₄	—	122	2	no	—
313	C₄⋊C₄	C₂²×#6923	1	2	yes	—
314	C₄²	—	2	2	no	—
315	C₄²	—	61	4	no	—
316	C₄²	—	61	4	no	—
317	C₄²	—	61	4	no	—
318	C₄²	—	61	1	no	—
319	C₄²	—	61	1	no	—
320	C₄²	—	61	1	no	—
321	C₄²	—	122	2	no	—
322	C₄²	—	122	2	no	—
323	C₄²	—	122	4	no	—
324	C₄²	—	122	2	no	—
325	C₄²	—	122	16	no	—
326	C₄²	—	122	2	no	—
327	C₄²	—	244	8	no	—
328	C₄²	—	244	4	no	—
329	C₄²	C₂²×#6923	1	1	yes	characteristic
330	C₂³	—	61	1	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	61	4	no	—
333	Q₈	—	122	8	no	—
334	Q₈	—	122	2	no	—
335	Q₈	C₂×C₄×#6923	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	61	4	no	—
339	C₂×C₄	—	61	4	no	—
340	C₂×C₄	—	61	4	no	—
341	C₂×C₄	—	61	1	no	—
342	C₂×C₄	—	61	1	no	—
343	C₂×C₄	—	61	2	no	—
344	C₂×C₄	—	61	2	no	—
345	C₂×C₄	—	61	2	no	—
346	C₂×C₄	—	61	2	no	—
347	C₂×C₄	—	61	4	no	—
348	C₂×C₄	—	61	1	no	—
349	C₂×C₄	—	122	8	no	—
350	C₂×C₄	—	122	2	no	—
351	C₂×C₄	—	122	2	no	—
352	C₂×C₄	—	122	2	no	—
353	C₂×C₄	—	122	2	no	—
354	C₂×C₄	—	122	8	no	—
355	C₂×C₄	—	122	2	no	—
356	C₂×C₄	—	244	4	no	—
357	C₂×C₄	—	244	4	no	—
358	C₂×C₄	—	244	4	no	—
359	C₂×C₄	D₄×#6923	1	1	yes	characteristic
360	C₂×C₄	D₄×#6923	1	1	yes	characteristic
361	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	61	2	no	—
364	C₈	—	122	4	no	—
365	C₈	—	122	1	no	—
366	C₈	C₂×C₄×#6923	1	2	yes	—
367	C₂²	—	61	1	no	—
368	C₂²	—	61	1	no	—
369	C₂²	—	61	2	no	—
370	C₂²	—	61	2	no	—
371	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	4	no	—
374	C₄	—	4	2	no	—
375	C₄	—	61	8	no	—
376	C₄	—	61	2	no	—
377	C₄	—	61	2	no	—
378	C₄	—	122	4	no	—
379	C₄	—	122	1	no	—
380	C₄	—	122	4	no	—
381	C₄	—	244	8	no	—
382	C₄	—	244	2	no	—
383	C₄	Q₁₆×#6923	1	2	yes	direct product factor
384	C₄	C₂²×C₄×#6923	1	1	yes	characteristic
385	C₄	#41×#6923	1	1	yes	characteristic
386	C₂	—	61	2	no	—
387	C₂	—	61	2	no	—
388	C₂	C₄×D₄×#6923	1	1	yes	characteristic
389	C₂	C₂×Q₁₆×#6923	1	1	yes	characteristic
390	C₂	#135×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₄×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂²×D₆₁	C₂²×D₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	C₄×Q₁₆	#6923
hypocenter	C₆₁	C₄²×Q₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
10. Q₁₆×#6923	C₄	direct (N × H)
26. C₄×Dic₂₄₄	C₄	semidirect
27. Q₁₆×Dic₆₁	C₄	semidirect
28. #16839856	C₄	semidirect
29. C₄×#11758202	C₄	semidirect
30. #16839854	C₄	semidirect
34. C₄×Q₁₆×C₆₁	C₄	semidirect
105. C₄×#6923	Q₁₆	direct (N × H)
110. Q₁₆×C₆₁	C₄²	semidirect
117. #11758202	C₄²	semidirect
131. Dic₂₄₄	C₄²	semidirect
179. #6923	C₄×Q₁₆	direct (N × H)
183. C₄×C₆₁	C₄×Q₁₆	semidirect
189. Dic₆₁	C₄×Q₁₆	semidirect
213. C₄×Q₁₆	#6923	direct (N × H)
230. C₆₁	C₄²×Q₁₆	semidirect
294. Q₁₆	C₄×#6923	direct (N × H)
383. C₄	Q₁₆×#6923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×#6923	2
C₄×Q₈×#6923	2
#107×#6923	2
C₄×#14519846	2
#103×#6923	2
C₄×#14519840	2
C₄×C₈×#6923	2
C₄×Q₁₆×D₆₁	2
C₄²×Q₁₆	61

Subgroups — C4×Q16×#6923 #30614499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₁₆×#6923 #30614499