Subgroups — D₄×#88038 #16016127

Order 3328.

734 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	C₂²×#88038	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13116669	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116667	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116661	C₂	1	2	yes	maximal, complemented
6	#13116658	C₂	1	2	yes	maximal, complemented
7	D₄×#6090	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116590	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116445	C₂	1	2	yes	maximal, complemented
10	C₄×#88038	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
13	C₄×D₄×D₁₃	C₄	1	1	yes	characteristic
14	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
15	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
17	C₂²×#6090	C₂²	1	2	yes	complemented
18	D₄×#1055	C₄	1	1	yes	characteristic
19	C₂×#88038	—	2	8	no	—
20	C₂×#88038	C₂²	1	1	yes	characteristic
21	C₂×#88038	C₂²	1	2	yes	—
22	C₂×#88038	C₂²	1	1	yes	characteristic
23	C₂×#88038	C₂²	1	2	yes	complemented
24	C₂×#88038	C₂²	1	2	yes	complemented
25	#11718495	C₄	1	1	yes	characteristic
26	D₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
27	#11718386	C₄	1	2	yes	—
28	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
29	C₈×D₅₂	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²⋊#6090	C₂²	1	2	yes	complemented
35	#11718099	C₂²	1	2	yes	complemented
36	#11718099	C₂²	1	2	yes	complemented
37	#11718094	C₂²	1	1	yes	characteristic, complemented
38	#11718094	C₂²	1	1	yes	characteristic, complemented
39	#11718093	C₂²	1	2	yes	complemented
40	C₄⋊#6090	C₂²	1	1	yes	characteristic, complemented
41	C₄×#6090	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₃	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	D₄×Dic₁₃	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
48	C₂²×#1055	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₁₃	—	2	4	no	—
50	C₂×C₈×D₁₃	—	2	4	no	—
51	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂³	1	2	yes	—
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	#88147	C₈	1	1	yes	characteristic
57	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
58	#88135	C₈	1	2	yes	—
59	C₂²⋊C₄×D₁₃	C₈	1	2	yes	—
60	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₁₆	—	2	4	no	—
63	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²⋊#1055	C₂×C₄	1	2	yes	—
70	#88060	C₂×C₄	1	2	yes	—
71	#88060	C₂×C₄	1	2	yes	—
72	#88054	C₂×C₄	1	2	yes	—
73	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
75	C₂×#6090	—	2	4	no	—
76	C₂×#6090	C₂³	1	2	yes	—
77	C₂×#6090	C₂³	1	1	yes	characteristic
78	C₂×#6090	C₂³	1	1	yes	characteristic
79	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
80	C₄×#1055	C₂×C₄	1	1	yes	characteristic
81	#88038	—	2	4	no	—
82	#88038	—	2	2	no	—
83	#88038	—	2	4	no	—
84	#88038	—	2	4	no	—
85	#88038	D₄	1	4	yes	direct product factor
86	D₄×M₃₂	—	13	1	no	maximal, Sylow
87	C₂³×D₁₃	C₂×C₈	1	2	yes	—
88	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
91	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
92	D₄×D₁₃	—	2	4	no	—
93	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	2	4	no	—
96	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
99	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
111	#6103	C₂×C₈	1	2	yes	—
112	#6103	C₂×C₈	1	2	yes	—
113	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
114	#6101	C₂×C₈	1	2	yes	—
115	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×#1055	—	2	4	no	—
119	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
120	C₂×#1055	C₂²×C₄	1	2	yes	—
121	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₁₃	—	2	4	no	—
123	C₈×D₁₃	—	2	2	no	—
124	C₈×D₁₃	—	2	2	no	—
125	C₈×D₁₃	—	2	2	no	—
126	C₈×D₁₃	—	2	4	no	—
127	C₈×D₁₃	C₂×D₄	1	2	yes	—
128	C₈×D₁₃	#41	1	2	yes	—
129	C₁₃×C₁₆	—	2	2	no	—
130	C₁₃×C₁₆	—	2	1	no	—
131	C₁₃×C₁₆	C₂×D₄	1	2	yes	complemented
132	#6090	—	2	2	no	—
133	#6090	—	2	1	no	—
134	#6090	C₂×D₄	1	2	yes	complemented
135	C₂²×M₃₂	—	13	2	no	—
136	C₂×C₈×D₄	—	13	1	no	—
137	#2169	—	13	1	no	—
138	#2169	—	13	1	no	—
139	#2168	—	13	2	no	—
140	#2168	—	13	2	no	—
141	D₄×C₁₆	—	13	1	no	—
142	D₄×C₁₆	D₁₃	1	1	yes	characteristic, complemented
143	#2150	—	13	1	no	—
144	#2112	—	13	2	no	—
145	C₄×M₃₂	—	13	1	no	—
146	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
147	C₂²×D₁₃	—	2	4	no	—
148	C₂²×D₁₃	—	2	4	no	—
149	C₂²×D₁₃	—	4	2	no	—
150	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
151	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
152	D₄×C₁₃	M₃₂	1	4	yes	complemented
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂²⋊D₁₃	—	2	4	no	—
160	C₂×Dic₁₃	—	2	4	no	—
161	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
164	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
165	D₅₂	—	2	2	no	—
166	C₄×D₁₃	—	2	4	no	—
167	C₄×D₁₃	—	2	2	no	—
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	4	no	—
171	C₄×D₁₃	—	4	1	no	—
172	C₄×D₁₃	C₄×D₄	1	2	yes	—
173	C₄×D₁₃	#131	1	2	yes	—
174	C₈×C₁₃	—	2	2	no	—
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
178	#1055	—	2	2	no	—
179	#1055	—	2	1	no	—
180	#1055	C₄×D₄	1	2	yes	—
181	C₂³×C₈	—	13	2	no	—
182	C₂×C₄×D₄	—	13	1	no	—
183	C₂×M₃₂	—	13	1	no	—
184	C₂×M₃₂	—	13	1	no	—
185	C₂×M₃₂	—	13	2	no	—
186	C₂×M₃₂	—	13	2	no	—
187	C₂×M₃₂	—	13	2	no	—
188	C₂×M₃₂	—	26	8	no	—
189	C₂²×C₁₆	—	13	2	no	—
190	C₂²×C₁₆	C₂×D₁₃	1	2	yes	complemented
191	C₈×D₄	—	13	2	no	—
192	C₈×D₄	—	13	1	no	—
193	C₈×D₄	—	13	1	no	—
194	C₈×D₄	—	13	2	no	—
195	C₈×D₄	—	13	1	no	—
196	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
197	C₂×C₄⋊C₈	—	13	1	no	—
198	C₂×C₂²⋊C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	1	no	—
200	C₄⋊C₁₆	—	13	2	no	—
201	C₄⋊C₁₆	—	13	1	no	—
202	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
203	C₂²⋊C₁₆	—	13	2	no	—
204	C₂²⋊C₁₆	—	13	2	no	—
205	C₂²⋊C₁₆	—	13	2	no	—
206	C₂²⋊C₁₆	C₂×D₁₃	1	2	yes	complemented
207	#346	—	13	1	no	—
208	#346	—	13	1	no	—
209	C₄×C₁₆	—	13	1	no	—
210	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	C₂×M₃₂	1	4	yes	complemented
214	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
215	C₂×D₁₃	—	2	1	no	—
216	C₂×D₁₃	—	2	1	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	—	4	8	no	—
221	C₂×D₁₃	C₈×D₄	1	2	yes	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	C₂×M₃₂	1	2	yes	complemented
225	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
227	Dic₁₃	—	2	1	no	—
228	Dic₁₃	—	2	1	no	—
229	Dic₁₃	—	2	2	no	—
230	Dic₁₃	C₈×D₄	1	2	yes	—
231	C₂²×D₄	—	13	1	no	—
232	C₂³×C₄	—	13	2	no	—
233	C₂²×C₈	—	13	1	no	—
234	C₂²×C₈	—	13	2	no	—
235	C₂²×C₈	—	13	2	no	—
236	C₂²×C₈	—	13	2	no	—
237	C₂²×C₈	—	13	1	no	—
238	C₂²×C₈	—	13	2	no	—
239	C₂²×C₈	—	26	4	no	—
240	C₂²×C₈	—	26	4	no	—
241	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
242	C₄×D₄	—	13	1	no	—
243	C₄×D₄	—	13	2	no	—
244	C₄×D₄	—	13	1	no	—
245	C₄×D₄	—	13	2	no	—
246	C₄×D₄	—	13	1	no	—
247	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	13	1	no	—
249	C₂×C₂²⋊C₄	—	13	2	no	—
250	C₂×C₄²	—	13	1	no	—
251	M₃₂	—	13	4	no	—
252	M₃₂	—	26	4	no	—
253	M₃₂	—	26	2	no	—
254	M₃₂	—	26	4	no	—
255	M₃₂	—	26	4	no	—
256	C₂×C₁₆	—	2	4	no	—
257	C₂×C₁₆	—	13	1	no	—
258	C₂×C₁₆	—	13	1	no	—
259	C₂×C₁₆	—	13	2	no	—
260	C₂×C₁₆	—	26	4	no	—
261	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
263	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
264	C₄⋊C₈	—	13	2	no	—
265	C₄⋊C₈	—	13	1	no	—
266	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
267	C₂²⋊C₈	—	13	2	no	—
268	C₂²⋊C₈	—	13	2	no	—
269	C₂²⋊C₈	—	13	2	no	—
270	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
271	C₄×C₈	—	13	1	no	—
272	C₄×C₈	—	13	1	no	—
273	C₄×C₈	—	13	1	no	—
274	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
275	C₂×C₁₃	—	2	4	no	—
276	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
277	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
278	C₂×C₁₃	#3407	1	1	yes	characteristic
279	D₁₃	—	2	2	no	—
280	D₁₃	—	4	2	no	—
281	C₂⁴	—	13	2	no	—
282	C₂×D₄	—	13	2	no	—
283	C₂×D₄	—	13	1	no	—
284	C₂×D₄	—	26	4	no	—
285	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	2	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	2	no	—
290	C₂²×C₄	—	13	2	no	—
291	C₂²×C₄	—	13	2	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	26	4	no	—
294	C₂²×C₄	—	26	4	no	—
295	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	13	1	no	—
299	C₂×C₈	—	13	2	no	—
300	C₂×C₈	—	13	2	no	—
301	C₂×C₈	—	13	1	no	—
302	C₂×C₈	—	13	2	no	—
303	C₂×C₈	—	26	4	no	—
304	C₂×C₈	—	26	4	no	—
305	C₂×C₈	—	26	2	no	—
306	C₂×C₈	—	26	4	no	—
307	C₂×C₈	—	26	2	no	—
308	C₂×C₈	—	26	2	no	—
309	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
311	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
312	C₄⋊C₄	—	13	2	no	—
313	C₄⋊C₄	—	13	1	no	—
314	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
315	C₂²⋊C₄	—	13	2	no	—
316	C₂²⋊C₄	—	13	2	no	—
317	C₂²⋊C₄	—	13	2	no	—
318	C₂²⋊C₄	C₈×D₁₃	1	2	yes	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
323	C₁₆	—	2	2	no	—
324	C₁₆	—	2	1	no	—
325	C₁₆	—	13	2	no	—
326	C₁₆	—	26	2	no	—
327	C₁₆	—	26	1	no	—
328	C₁₆	D₄×D₁₃	1	2	yes	complemented
329	C₁₃	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	13	1	no	—
331	C₂³	—	13	2	no	—
332	C₂³	—	26	4	no	—
333	C₂³	—	26	4	no	—
334	C₂³	—	52	2	no	—
335	C₂³	C₂×C₈×D₁₃	1	2	yes	—
336	D₄	—	26	4	no	—
337	D₄	—	26	2	no	—
338	D₄	#88038	1	4	yes	direct product factor
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	2	no	—
343	C₂×C₄	—	13	2	no	—
344	C₂×C₄	—	13	1	no	—
345	C₂×C₄	—	13	1	no	—
346	C₂×C₄	—	13	2	no	—
347	C₂×C₄	—	26	4	no	—
348	C₂×C₄	—	26	4	no	—
349	C₂×C₄	—	26	4	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	52	1	no	—
354	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	2	no	—
360	C₈	—	13	2	no	—
361	C₈	—	26	1	no	—
362	C₈	—	26	2	no	—
363	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
364	C₈	#41×D₁₃	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	13	2	no	—
368	C₂²	—	26	1	no	—
369	C₂²	—	26	1	no	—
370	C₂²	—	26	2	no	—
371	C₂²	—	26	2	no	—
372	C₂²	—	26	2	no	—
373	C₂²	—	52	8	no	—
374	C₂²	C₂×#88038	1	4	yes	complemented
375	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	13	2	no	—
379	C₄	—	26	1	no	—
380	C₄	—	26	2	no	—
381	C₄	—	26	1	no	—
382	C₄	C₂×#88038	1	2	yes	complemented
383	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
384	C₄	D₁₃×#131	1	1	yes	characteristic
385	C₂	—	2	4	no	—
386	C₂	—	26	2	no	—
387	C₂	—	52	2	no	—
388	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
389	C₂	C₂²×#88038	1	1	yes	characteristic
390	C₂	#13127937	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	D₄×C₁₃×C₁₆	C₂
prime radical	C₂×D₄×D₁₃	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	D₄×C₁₆	D₁₃
hypocenter	C₁₃	D₄×M₃₂
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×#88038	C₂	semidirect
3. #13116669	C₂	semidirect
4. #13116667	C₂	semidirect
5. #13116661	C₂	semidirect
6. #13116658	C₂	semidirect
7. D₄×#6090	C₂	semidirect
8. #13116590	C₂	semidirect
9. #13116445	C₂	semidirect
10. C₄×#88038	C₂	semidirect
11. D₄×C₁₃×C₁₆	C₂	semidirect
14. C₂²×C₁₃×C₁₆	C₂²	semidirect
17. C₂²×#6090	C₂²	semidirect
23. C₂×#88038	C₂²	semidirect
24. C₂×#88038	C₂²	semidirect
31. C₁₃×C₄⋊C₁₆	C₂²	semidirect
32. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
33. C₄×C₁₃×C₁₆	C₂²	semidirect
34. C₂²⋊#6090	C₂²	semidirect
35. #11718099	C₂²	semidirect
36. #11718099	C₂²	semidirect
37. #11718094	C₂²	semidirect
38. #11718094	C₂²	semidirect
39. #11718093	C₂²	semidirect
40. C₄⋊#6090	C₂²	semidirect
41. C₄×#6090	C₂²	semidirect
85. #88038	D₄	direct (N × H)
131. C₁₃×C₁₆	C₂×D₄	semidirect
134. #6090	C₂×D₄	semidirect
142. D₄×C₁₆	D₁₃	semidirect
152. D₄×C₁₃	M₃₂	semidirect
190. C₂²×C₁₆	C₂×D₁₃	semidirect
202. C₄⋊C₁₆	C₂×D₁₃	semidirect
206. C₂²⋊C₁₆	C₂×D₁₃	semidirect
210. C₄×C₁₆	C₂×D₁₃	semidirect
213. C₂²×C₁₃	C₂×M₃₂	semidirect
224. C₄×C₁₃	C₂×M₃₂	semidirect
328. C₁₆	D₄×D₁₃	semidirect
329. C₁₃	D₄×M₃₂	semidirect
338. D₄	#88038	direct (N × H)
374. C₂²	C₂×#88038	semidirect
382. C₄	C₂×#88038	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88038	2
C₈×D₄×D₁₃	2
#13116669	2
#13116667	2
#13116661	2
#13116658	2
D₄×#6090	2
#13116590	2
#13116445	2
C₄×#88038	2
D₄×C₁₃×C₁₆	2
D₄×M₃₂	13

Subgroups — D4×#88038 #16016127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#88038 #16016127