Subgroups — D₄×#3944 #12252514

Order 1280.

734 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	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3944	C₂	1	2	yes	maximal, complemented
3	#10602756	C₂	1	2	yes	maximal, complemented
4	#10601651	C₂	1	2	yes	maximal, complemented
5	#10601650	C₂	1	4	yes	maximal, complemented
6	D₄×#672	C₂	1	2	yes	maximal, complemented
7	#10600536	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#3944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
11	C₅×C₈×D₄	C₄	1	2	yes	—
12	C₅×C₈×D₄	C₄	1	1	yes	characteristic
13	C₅×C₈×D₄	C₄	1	1	yes	characteristic
14	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
15	C₅×C₈×D₄	C₂²	1	2	yes	—
16	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×#3944	—	2	8	no	—
21	C₂×#3944	C₂²	1	1	yes	characteristic
22	C₂×#3944	C₂²	1	2	yes	—
23	C₂×#3944	C₂²	1	1	yes	characteristic
24	C₂×#3944	C₂²	1	4	yes	complemented
25	C₂²×#672	C₂²	1	4	yes	complemented
26	C₂²⋊#672	C₂²	1	4	yes	complemented
27	C₂²⋊#672	C₂²	1	4	yes	complemented
28	C₄⋊#672	C₂²	1	2	yes	complemented
29	C₄⋊#672	C₂²	1	2	yes	complemented
30	#64681	C₂²	1	2	yes	complemented
31	C₄×#672	C₂²	1	2	yes	complemented
32	D₄×M₃₂	—	5	1	no	maximal, Sylow
33	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₅×C₈	—	2	4	no	—
36	C₂²×C₅×C₈	—	2	4	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₄×C₅×D₄	C₈	1	2	yes	—
45	C₄×C₅×D₄	C₈	1	1	yes	characteristic
46	C₄×C₅×D₄	C₈	1	1	yes	characteristic
47	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
48	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₄	C₈	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
55	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
57	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
58	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
64	#3944	—	2	4	no	—
65	#3944	—	2	2	no	—
66	#3944	—	2	8	no	—
67	#3944	D₄	1	4	yes	direct product factor
68	C₂×#672	—	2	8	no	—
69	C₂×#672	C₂³	1	2	yes	—
70	C₂×#672	C₂³	1	4	yes	—
71	C₂×#672	C₂³	1	2	yes	—
72	C₂²×M₃₂	—	5	2	no	—
73	C₂×C₈×D₄	D₅	1	1	yes	characteristic
74	#2169	—	5	2	no	—
75	#2168	—	5	4	no	—
76	D₄×C₁₆	—	5	2	no	—
77	#2150	—	5	1	no	—
78	#2112	—	5	2	no	—
79	C₄×M₃₂	—	5	1	no	—
80	C₂⁴×C₅	C₂×C₈	1	2	yes	—
81	C₂×C₅×D₄	—	2	4	no	—
82	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
83	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
84	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	—	2	4	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
89	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
90	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
91	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₅×C₈	—	2	4	no	—
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
109	C₂×C₅×C₈	#41	1	2	yes	—
110	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
112	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
113	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
114	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
115	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
116	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
117	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
118	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
119	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	#672	—	2	4	no	—
123	#672	—	2	2	no	—
124	#672	C₂×D₄	1	4	yes	complemented
125	C₂³×C₈	C₂×D₅	1	2	yes	—
126	C₂×C₄×D₄	Dic₅	1	1	yes	characteristic
127	C₂×M₃₂	—	5	1	no	—
128	C₂×M₃₂	—	5	1	no	—
129	C₂×M₃₂	—	5	2	no	—
130	C₂×M₃₂	—	5	4	no	—
131	C₂×M₃₂	—	10	8	no	—
132	C₂²×C₁₆	—	5	4	no	—
133	C₈×D₄	Dic₅	1	2	yes	—
134	C₈×D₄	Dic₅	1	1	yes	characteristic
135	C₈×D₄	Dic₅	1	1	yes	characteristic
136	C₈×D₄	C₂×D₅	1	1	yes	characteristic
137	C₈×D₄	C₂×D₅	1	2	yes	—
138	C₈×D₄	C₂×D₅	1	1	yes	characteristic
139	C₂×C₄⋊C₈	Dic₅	1	1	yes	characteristic
140	C₂×C₂²⋊C₈	Dic₅	1	2	yes	—
141	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
142	C₄⋊C₁₆	—	5	2	no	—
143	C₄⋊C₁₆	—	5	2	no	—
144	C₂²⋊C₁₆	—	5	4	no	—
145	C₂²⋊C₁₆	—	5	4	no	—
146	#346	—	5	2	no	—
147	C₄×C₁₆	—	5	2	no	—
148	C₂³×C₅	—	2	4	no	—
149	C₂³×C₅	—	2	4	no	—
150	C₂³×C₅	—	4	2	no	—
151	C₂³×C₅	C₂²×C₈	1	2	yes	—
152	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
153	C₂³×C₅	C₂²×C₈	1	2	yes	—
154	C₅×D₄	—	2	4	no	—
155	C₅×D₄	—	2	2	no	—
156	C₅×D₄	M₃₂	1	4	yes	complemented
157	C₂×C₄×C₅	—	2	4	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	2	4	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	4	1	no	—
166	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
172	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₅	#131	1	2	yes	—
175	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₅×C₈	—	2	2	no	—
177	C₅×C₈	—	2	2	no	—
178	C₅×C₈	—	2	1	no	—
179	C₅×C₈	—	2	1	no	—
180	C₅×C₈	C₄×D₄	1	2	yes	—
181	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
182	C₅×C₈	C₂×#41	1	1	yes	characteristic
183	C₂²×D₄	#168	1	1	yes	characteristic
184	C₂³×C₄	C₂×Dic₅	1	2	yes	—
185	C₂²×C₈	—	2	4	no	—
186	C₂²×C₈	—	2	4	no	—
187	C₂²×C₈	C₂×Dic₅	1	2	yes	—
188	C₂²×C₈	C₂×Dic₅	1	2	yes	—
189	C₂²×C₈	C₂×Dic₅	1	2	yes	—
190	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
191	C₂²×C₈	C₂²×D₅	1	2	yes	—
192	C₂²×C₈	C₂²×D₅	1	2	yes	—
193	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
194	C₄×D₄	#168	1	2	yes	—
195	C₄×D₄	#168	1	1	yes	characteristic
196	C₄×D₄	#168	1	1	yes	characteristic
197	C₄×D₄	C₂×Dic₅	1	2	yes	—
198	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
199	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
200	C₂×C₄⋊C₄	#168	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	#168	1	2	yes	—
202	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
203	M₃₂	—	5	4	no	—
204	M₃₂	—	10	8	no	—
205	M₃₂	—	10	4	no	—
206	M₃₂	—	10	2	no	—
207	C₂×C₁₆	—	5	2	no	—
208	C₂×C₁₆	—	5	2	no	—
209	C₂×C₁₆	—	5	4	no	—
210	C₂×C₁₆	—	10	8	no	—
211	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
212	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
213	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
214	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
215	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
216	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
217	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
218	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
219	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
220	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
221	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	2	no	—
229	C₂²×C₅	—	4	8	no	—
230	C₂²×C₅	C₈×D₄	1	2	yes	—
231	C₂²×C₅	C₂×M₃₂	1	4	yes	complemented
232	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
233	C₄×C₅	—	2	1	no	—
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	2	no	—
238	C₄×C₅	C₈×D₄	1	2	yes	—
239	C₄×C₅	C₂×M₃₂	1	2	yes	complemented
240	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₅	C₂×#131	1	1	yes	characteristic
242	C₂⁴	C₂×#168	1	2	yes	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	C₂×#168	1	2	yes	—
245	C₂×D₄	C₂×#168	1	1	yes	characteristic
246	C₂×D₄	C₂×#168	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	C₂×#168	1	1	yes	characteristic
250	C₂²×C₄	C₂×#168	1	2	yes	—
251	C₂²×C₄	C₂×#168	1	2	yes	—
252	C₂²×C₄	C₂×#168	1	2	yes	—
253	C₂²×C₄	C₂×#168	1	1	yes	characteristic
254	C₂²×C₄	C₂²×Dic₅	1	2	yes	—
255	C₂²×C₄	C₂²×Dic₅	1	2	yes	—
256	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	D₄×D₅	1	2	yes	—
266	C₂×C₈	#711	1	2	yes	—
267	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
268	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
269	C₂×C₈	C₂²×Dic₅	1	2	yes	—
270	C₂×C₈	C₂²×Dic₅	1	2	yes	—
271	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
272	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
273	C₄⋊C₄	C₂×#168	1	2	yes	—
274	C₄⋊C₄	C₂×#168	1	1	yes	characteristic
275	C₄⋊C₄	C₂×#168	1	1	yes	characteristic
276	C₂²⋊C₄	C₂×#168	1	2	yes	—
277	C₂²⋊C₄	C₂×#168	1	2	yes	—
278	C₂²⋊C₄	C₂×#168	1	2	yes	—
279	C₂²⋊C₄	C₂×#168	1	2	yes	—
280	C₄²	C₂×#168	1	1	yes	characteristic
281	C₄²	C₂×#168	1	1	yes	characteristic
282	C₄²	C₂²×Dic₅	1	1	yes	characteristic
283	C₄²	C₂²×Dic₅	1	1	yes	characteristic
284	C₁₆	—	5	4	no	—
285	C₁₆	—	10	4	no	—
286	C₁₆	—	10	2	no	—
287	C₂×C₅	—	2	2	no	—
288	C₂×C₅	—	2	4	no	—
289	C₂×C₅	—	4	2	no	—
290	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
291	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
292	C₂×C₅	#3407	1	1	yes	characteristic
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	4	2	no	—
296	C₂³	C₂²×#168	1	2	yes	—
297	C₂³	C₂²×#168	1	1	yes	characteristic
298	C₂³	C₂²×#168	1	2	yes	—
299	D₄	—	2	4	no	—
300	D₄	—	2	2	no	—
301	D₄	#3944	1	4	yes	direct product factor
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	C₂²×#168	1	1	yes	characteristic
312	C₂×C₄	C₂²×#168	1	1	yes	characteristic
313	C₂×C₄	C₂²×#168	1	1	yes	characteristic
314	C₂×C₄	C₂²×#168	1	2	yes	—
315	C₂×C₄	C₂²×#168	1	2	yes	—
316	C₂×C₄	C₂²×#168	1	1	yes	characteristic
317	C₂×C₄	C₂²×#168	1	1	yes	characteristic
318	C₂×C₄	D₄×Dic₅	1	2	yes	—
319	C₂×C₄	#4094	1	2	yes	—
320	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
321	C₈	—	2	2	no	—
322	C₈	—	2	2	no	—
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	D₄×Dic₅	1	2	yes	—
326	C₈	C₂×D₄×D₅	1	1	yes	characteristic
327	C₈	C₂×#711	1	1	yes	characteristic
328	C₅	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	D₄×#168	1	2	yes	—
338	C₂²	C₂×#3944	1	4	yes	complemented
339	C₂²	C₂³×#168	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	D₄×#168	1	2	yes	—
346	C₄	C₂×#3944	1	2	yes	complemented
347	C₄	C₂×D₄×Dic₅	1	1	yes	characteristic
348	C₄	C₂×#4094	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×D₄×#168	1	1	yes	characteristic
353	C₂	C₂²×#3944	1	1	yes	characteristic
354	C₂	#10615511	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₂×C₅×C₈×D₄	C₂
prime radical	C₂²×C₅×D₄	C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	C₂×C₈×D₄	D₅
hypocenter	C₅	D₄×M₃₂
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#3944	C₂	semidirect
3. #10602756	C₂	semidirect
4. #10601651	C₂	semidirect
5. #10601650	C₂	semidirect
6. D₄×#672	C₂	semidirect
7. #10600536	C₂	semidirect
8. C₄×#3944	C₂	semidirect
24. C₂×#3944	C₂²	semidirect
25. C₂²×#672	C₂²	semidirect
26. C₂²⋊#672	C₂²	semidirect
27. C₂²⋊#672	C₂²	semidirect
28. C₄⋊#672	C₂²	semidirect
29. C₄⋊#672	C₂²	semidirect
30. #64681	C₂²	semidirect
31. C₄×#672	C₂²	semidirect
67. #3944	D₄	direct (N × H)
124. #672	C₂×D₄	semidirect
156. C₅×D₄	M₃₂	semidirect
231. C₂²×C₅	C₂×M₃₂	semidirect
239. C₄×C₅	C₂×M₃₂	semidirect
301. D₄	#3944	direct (N × H)
328. C₅	D₄×M₃₂	semidirect
338. C₂²	C₂×#3944	semidirect
346. C₄	C₂×#3944	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×D₄	2
C₂²×#3944	2
#10602756	2
#10601651	2
#10601650	2
D₄×#672	2
#10600536	2
C₄×#3944	2
D₄×M₃₂	5

Subgroups — D4×#3944 #12252514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#3944 #12252514