Subgroups — C₄×#11718146 #15768124

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718146	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₁₃	C₄	1	2	yes	—
9	C₂²×#6099	C₂²	1	2	yes	—
10	C₄×C₁₃×M₁₆	—	2	2	no	—
11	C₄×C₁₃×M₁₆	C₄	1	4	yes	complemented
12	C₂×C₁₃×#97	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	—	2	1	no	—
14	C₂×#88071	C₄	1	2	yes	—
15	C₄×C₄⋊Dic₁₃	—	2	1	no	—
16	C₄×C₄⋊Dic₁₃	—	2	1	no	—
17	C₄×C₄⋊Dic₁₃	—	2	1	no	—
18	C₄×C₄⋊Dic₁₃	—	2	1	no	—
19	C₄×#6099	—	2	2	no	—
20	C₄×#6099	C₄	1	4	yes	complemented
21	C₂×#88043	—	2	1	no	—
22	C₂×C₄×#1055	—	2	1	no	—
23	#11718146	C₄	1	16	yes	direct product factor
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂³×Dic₁₃	C₂×C₄	1	4	yes	—
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	—	2	4	no	—
30	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃	—	2	2	no	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	D₄	1	2	yes	—
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
41	C₂×C₄⋊Dic₁₃	—	2	2	no	—
42	C₂×C₄⋊Dic₁₃	—	2	2	no	—
43	C₂×C₄⋊Dic₁₃	—	2	4	no	—
44	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	—
45	C₂×C₄×Dic₁₃	—	2	2	no	—
46	C₂×C₄×Dic₁₃	—	2	2	no	—
47	C₂×C₄×Dic₁₃	—	4	4	no	—
48	C₂×#6099	—	2	2	no	—
49	C₂×#6099	—	2	4	no	—
50	C₂×#6099	C₂×C₄	1	8	yes	—
51	C₂×#6099	C₂×C₄	1	4	yes	—
52	C₂²×#1055	—	2	2	no	—
53	C₁₃×#97	—	2	4	no	—
54	C₄×C₈×C₁₃	—	2	4	no	—
55	#88071	—	2	2	no	—
56	#88071	—	2	2	no	—
57	#88043	—	2	4	no	—
58	C₄×#1055	—	2	4	no	—
59	C₄×#343	—	13	1	no	maximal, Sylow
60	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	#41	1	4	yes	—
80	C₂²×Dic₁₃	—	2	4	no	—
81	C₂²×Dic₁₃	—	2	4	no	—
82	C₂²×Dic₁₃	—	4	4	no	—
83	C₂²×Dic₁₃	—	4	4	no	—
84	C₂²×Dic₁₃	C₄²	1	8	yes	—
85	C₁₃×M₁₆	—	2	4	no	—
86	C₁₃×M₁₆	—	2	8	no	—
87	C₁₃×M₁₆	C₄²	1	8	yes	complemented
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	8	no	—
90	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
91	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
92	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
95	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
98	C₄⋊Dic₁₃	—	2	8	no	—
99	C₄⋊Dic₁₃	—	2	8	no	—
100	C₄×Dic₁₃	—	4	4	no	—
101	C₄×Dic₁₃	—	4	4	no	—
102	#6099	—	2	4	no	—
103	#6099	—	2	8	no	—
104	#6099	C₄²	1	8	yes	complemented
105	C₂×#1055	—	2	4	no	—
106	C₂×#1055	—	2	8	no	—
107	C₂×C₄×M₁₆	—	13	1	no	—
108	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
109	C₂×C₄×C₄⋊C₄	—	13	1	no	—
110	C₂×#343	—	13	4	no	—
111	C₂³×C₁₃	—	2	1	no	—
112	C₂³×C₁₃	—	2	1	no	—
113	C₂³×C₁₃	—	2	2	no	—
114	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
115	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
116	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₁₃	#117	1	2	yes	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	2	no	—
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	—	2	4	no	—
124	C₂×C₄×C₁₃	—	2	4	no	—
125	C₂×C₄×C₁₃	—	4	2	no	—
126	C₂×C₄×C₁₃	—	4	2	no	—
127	C₂×C₄×C₁₃	#95	1	2	yes	—
128	C₂×C₄×C₁₃	#95	1	2	yes	—
129	C₂×C₄×C₁₃	#95	1	2	yes	—
130	C₂×C₄×C₁₃	#95	1	2	yes	—
131	C₂×C₄×C₁₃	#100	1	2	yes	—
132	C₂×C₄×C₁₃	#101	1	2	yes	—
133	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#117	1	2	yes	—
140	C₂×C₄×C₁₃	#117	1	2	yes	—
141	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
144	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
145	C₂×Dic₁₃	—	2	8	no	—
146	C₂×Dic₁₃	—	4	8	no	—
147	C₂×Dic₁₃	—	4	4	no	—
148	C₂×Dic₁₃	—	4	4	no	—
149	C₂×Dic₁₃	—	4	8	no	—
150	C₈×C₁₃	—	2	8	no	—
151	#1055	—	2	8	no	—
152	C₂²×M₁₆	—	13	2	no	—
153	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
154	C₂²×C₄⋊C₄	—	13	2	no	—
155	C₂²×C₄²	—	13	2	no	—
156	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
157	C₄×M₁₆	—	2	2	no	—
158	C₄×M₁₆	—	13	4	no	—
159	C₄×M₁₆	—	26	2	no	—
160	C₄×M₁₆	Dic₁₃	1	4	yes	complemented
161	C₂×#97	—	2	1	no	—
162	C₂×#97	—	26	1	no	—
163	C₂×C₄×C₈	—	2	1	no	—
164	C₂×C₄×C₈	—	26	1	no	—
165	C₄×C₄⋊C₄	—	26	1	no	—
166	C₄×C₄⋊C₄	—	26	1	no	—
167	C₄×C₄⋊C₄	—	26	1	no	—
168	C₄×C₄⋊C₄	—	26	1	no	—
169	C₂×#95	—	13	2	no	—
170	#343	—	13	16	no	—
171	C₂²×C₁₃	—	2	1	no	—
172	C₂²×C₁₃	—	2	1	no	—
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	2	1	no	—
175	C₂²×C₁₃	—	2	2	no	—
176	C₂²×C₁₃	—	2	2	no	—
177	C₂²×C₁₃	—	2	2	no	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	C₄³	1	1	yes	characteristic
180	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
181	C₂²×C₁₃	#376	1	1	yes	characteristic
182	C₂²×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
183	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
184	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
185	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
186	C₂²×C₁₃	#413	1	2	yes	—
187	C₄×C₁₃	—	2	2	no	—
188	C₄×C₁₃	—	2	2	no	—
189	C₄×C₁₃	—	2	2	no	—
190	C₄×C₁₃	#343	1	4	yes	complemented
191	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
192	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
193	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
194	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
195	Dic₁₃	—	4	8	no	—
196	C₂³×C₄	—	13	4	no	—
197	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
198	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
199	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
200	C₂×M₁₆	—	2	4	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	13	8	no	—
203	C₂×M₁₆	—	13	4	no	—
204	C₂×M₁₆	—	26	4	no	—
205	C₂×M₁₆	—	26	2	no	—
206	C₂×M₁₆	C₄×D₁₃	1	8	yes	—
207	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	—	26	2	no	—
210	C₂×C₄⋊C₄	—	13	8	no	—
211	C₂×C₄⋊C₄	—	26	2	no	—
212	C₂×C₄⋊C₄	—	26	4	no	—
213	C₂×C₄⋊C₄	—	26	2	no	—
214	C₂×C₄²	—	26	2	no	—
215	C₂×C₄²	—	26	2	no	—
216	C₂×C₄²	—	52	4	no	—
217	C₂×C₄²	Dic₂₆	1	2	yes	—
218	C₂×C₄²	C₄×D₁₃	1	2	yes	—
219	C₂×C₄²	D₅₂	1	1	yes	characteristic
220	C₂×C₄²	D₅₂	1	1	yes	characteristic
221	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
222	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
225	#97	—	2	4	no	—
226	#97	—	26	4	no	—
227	C₄×C₈	—	2	4	no	—
228	C₄×C₈	—	26	4	no	—
229	#95	—	26	2	no	—
230	#95	—	26	2	no	—
231	C₂×C₁₃	—	2	1	no	—
232	C₂×C₁₃	—	2	1	no	—
233	C₂×C₁₃	—	2	2	no	—
234	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
235	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
236	C₂×C₁₃	#1742	1	1	yes	characteristic
237	C₂×C₁₃	C₄×#100	1	2	yes	—
238	C₂×C₁₃	C₄×#101	1	2	yes	—
239	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	—	13	8	no	—
244	C₂²×C₄	—	26	4	no	—
245	C₂²×C₄	—	26	4	no	—
246	C₂²×C₄	—	52	4	no	—
247	C₂²×C₄	—	52	4	no	—
248	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
249	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
250	C₂²×C₄	#6101	1	2	yes	—
251	C₂²×C₄	#6101	1	2	yes	—
252	C₂²×C₄	#6103	1	1	yes	characteristic
253	C₂²×C₄	#6103	1	1	yes	characteristic
254	C₂²×C₄	#6103	1	1	yes	characteristic
255	C₂²×C₄	#6103	1	1	yes	characteristic
256	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
258	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
260	C₂²×C₄	#6127	1	4	yes	—
261	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
264	M₁₆	—	2	4	no	—
265	M₁₆	—	2	8	no	—
266	M₁₆	—	13	8	no	—
267	M₁₆	—	26	4	no	—
268	M₁₆	—	26	8	no	—
269	M₁₆	C₄×Dic₁₃	1	8	yes	complemented
270	C₂×C₈	—	2	8	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	26	8	no	—
273	C₂×C₈	—	26	4	no	—
274	C₄⋊C₄	—	26	8	no	—
275	C₄⋊C₄	—	26	8	no	—
276	C₄²	—	52	4	no	—
277	C₄²	—	52	4	no	—
278	C₄²	#6101	1	2	yes	—
279	C₄²	#6101	1	2	yes	—
280	C₄²	C₄⋊Dic₁₃	1	2	yes	—
281	C₄²	C₄⋊Dic₁₃	1	2	yes	—
282	C₄²	#6103	1	2	yes	—
283	C₄²	#6103	1	2	yes	—
284	C₄²	C₂²⋊Dic₁₃	1	2	yes	—
285	C₄²	C₂²⋊Dic₁₃	1	2	yes	—
286	C₁₃	C₄×#343	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	2	1	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	1	no	—
290	C₂³	C₄²×D₁₃	1	2	yes	—
291	C₂³	#88126	1	2	yes	—
292	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
293	C₂³	C₂×#6101	1	1	yes	characteristic
294	C₂³	C₂×#6103	1	1	yes	characteristic
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	26	8	no	—
304	C₂×C₄	—	52	8	no	—
305	C₂×C₄	—	52	4	no	—
306	C₂×C₄	—	52	4	no	—
307	C₂×C₄	—	52	8	no	—
308	C₂×C₄	#88063	1	2	yes	—
309	C₂×C₄	#88064	1	2	yes	—
310	C₂×C₄	#88071	1	2	yes	—
311	C₂×C₄	#88071	1	2	yes	—
312	C₂×C₄	#88071	1	2	yes	—
313	C₂×C₄	#88071	1	2	yes	—
314	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
315	C₂×C₄	C₄²×D₁₃	1	2	yes	—
316	C₂×C₄	#88126	1	2	yes	—
317	C₂×C₄	C₄×D₅₂	1	4	yes	—
318	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
319	C₂×C₄	C₂×#6101	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
321	C₂×C₄	#88180	1	2	yes	—
322	C₂×C₄	C₂×#6103	1	1	yes	characteristic
323	C₂×C₄	C₄×C₂²⋊D₁₃	1	4	yes	—
324	C₂×C₄	C₄×C₂²⋊D₁₃	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
326	C₈	—	2	8	no	—
327	C₈	—	26	8	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
337	C₂²	C₄×#6101	1	2	yes	—
338	C₂²	#11718593	1	1	yes	characteristic
339	C₂²	C₄×#6103	1	2	yes	—
340	C₂²	C₂×#88063	1	1	yes	characteristic
341	C₂²	#11718793	1	2	yes	—
342	C₂²	C₂×#88064	1	1	yes	characteristic
343	C₂²	C₂×#88071	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	52	8	no	—
348	C₄	#11718146	1	4	yes	direct product factor
349	C₄	C₄×#6101	1	2	yes	—
350	C₄	C₄×C₄⋊Dic₁₃	1	2	yes	—
351	C₄	C₄×#6103	1	2	yes	—
352	C₄	C₄×C₂²⋊Dic₁₃	1	2	yes	—
353	C₂	—	2	1	no	—
354	C₂	—	2	2	no	—
355	C₂	—	2	1	no	—
356	C₂	C₄×#88071	1	1	yes	characteristic
357	C₂	C₂×#11718146	1	1	yes	characteristic
358	C₂	#13114574	1	1	yes	characteristic
359	C₂	C₄×#88063	1	2	yes	—
360	C₂	C₄×#88064	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#6103
commutator	C₂²×C₁₃	C₄³
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₄×#343
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
11. C₄×C₁₃×M₁₆	C₄	semidirect
20. C₄×#6099	C₄	semidirect
23. #11718146	C₄	direct (N × H)
87. C₁₃×M₁₆	C₄²	semidirect
104. #6099	C₄²	semidirect
160. C₄×M₁₆	Dic₁₃	semidirect
190. C₄×C₁₃	#343	semidirect
269. M₁₆	C₄×Dic₁₃	semidirect
286. C₁₃	C₄×#343	semidirect
348. C₄	#11718146	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×C₄×#6099	2
C₂×C₄×C₄⋊Dic₁₃	2
C₂×#11718146	2
C₂×C₄×C₁₃×M₁₆	2
C₄×#343	13

Subgroups — C4×#11718146 #15768124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718146 #15768124