Subgroups — C₄×D₄×#1057 #16797336

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#1057	C₂	1	2	yes	maximal
2	C₂²×C₄×#1057	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×#1057	C₂	1	2	yes	maximal, complemented
4	C₄×C₄⋊#1057	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊C₄×#1057	C₂	1	4	yes	maximal, complemented
6	C₄×C₂²⋊#1057	C₂	1	2	yes	maximal, complemented
7	C₄²×#1057	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×#1057	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂×D₄×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂×D₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₂²⋊#1057	C₂²	1	4	yes	—
15	D₄×#1057	C₄	1	16	yes	direct product factor
16	C₂×C₄⋊#1057	C₂²	1	2	yes	—
17	C₂×C₄×#1057	—	2	8	no	—
18	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
19	C₂×C₄×#1057	C₂²	1	2	yes	—
20	C₂×C₄×#1057	C₂²	1	2	yes	—
21	C₂×C₄×#1057	C₂²	1	4	yes	—
22	C₂×C₄×#1057	C₂²	1	2	yes	—
23	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊Dic₁₃	C₄	1	2	yes	—
25	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
26	C₄⋊C₄×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂²⋊C₄×Dic₁₃	C₄	1	2	yes	—
28	C₂²⋊C₄×Dic₁₃	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
30	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
31	#11718290	C₂²	1	4	yes	—
32	#11718290	C₂²	1	2	yes	—
33	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
36	C₂³×Dic₁₃	C₂³	1	2	yes	—
37	C₂²×#1057	—	2	8	no	—
38	C₂²×#1057	—	2	8	no	—
39	C₂²×#1057	C₂×C₄	1	16	yes	complemented
40	C₂²×#1057	C₂³	1	2	yes	—
41	C₂²×#1057	C₂³	1	4	yes	—
42	C₂²×#1057	C₂³	1	2	yes	—
43	C₄×D₄×C₁₃	C₈	1	8	yes	complemented
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
49	D₄×Dic₁₃	C₈	1	8	yes	complemented
50	D₄×Dic₁₃	C₂×C₄	1	8	yes	—
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	—	2	4	no	—
54	C₂×C₄×Dic₁₃	—	2	4	no	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
61	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
64	C₂²⋊#1057	C₂×C₄	1	16	yes	complemented
65	C₄⋊#1057	C₂×C₄	1	8	yes	complemented
66	C₄×#1057	—	2	8	no	—
67	C₄×#1057	—	2	4	no	—
68	C₄×#1057	—	2	4	no	—
69	C₄×#1057	—	2	2	no	—
70	C₄×#1057	C₂×C₄	1	8	yes	complemented
71	C₄×#1057	D₄	1	4	yes	direct product factor
72	#88071	C₂×C₄	1	2	yes	—
73	#88071	C₂×C₄	1	2	yes	—
74	#88071	C₂×C₄	1	2	yes	—
75	C₄×C₈×D₄	—	13	1	no	maximal, Sylow
76	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂×D₄×C₁₃	C₄²	1	4	yes	—
78	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
79	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
80	C₂²×C₄×C₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	C₂×C₈	1	8	yes	complemented
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	—	2	4	no	—
88	C₂²×Dic₁₃	—	2	4	no	—
89	C₂²×Dic₁₃	—	2	2	no	—
90	C₂²×Dic₁₃	—	2	2	no	—
91	C₂²×Dic₁₃	—	2	4	no	—
92	C₂²×Dic₁₃	C₂×C₈	1	8	yes	complemented
93	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
100	C₂×#1057	—	2	4	no	—
101	C₂×#1057	—	2	2	no	—
102	C₂×#1057	—	2	2	no	—
103	C₂×#1057	—	2	4	no	—
104	C₂×#1057	—	2	32	no	—
105	C₂×#1057	C₂²×C₄	1	4	yes	—
106	C₂×#1057	C₂²×C₄	1	8	yes	—
107	C₂×#1057	C₂²×C₄	1	4	yes	—
108	C₂×#1057	C₂×D₄	1	4	yes	—
109	C₂×#1057	#41	1	4	yes	—
110	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
111	C₁₃×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
112	C₄²×C₁₃	C₂×C₈	1	4	yes	complemented
113	C₂²⋊Dic₁₃	C₄²	1	8	yes	—
114	C₂²⋊Dic₁₃	C₂×C₈	1	8	yes	complemented
115	C₄⋊Dic₁₃	C₄²	1	4	yes	—
116	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	complemented
117	C₄×Dic₁₃	—	2	4	no	—
118	C₄×Dic₁₃	—	2	2	no	—
119	C₄×Dic₁₃	—	2	4	no	—
120	C₄×Dic₁₃	—	2	2	no	—
121	C₄×Dic₁₃	—	2	2	no	—
122	C₄×Dic₁₃	—	2	2	no	—
123	C₄×Dic₁₃	—	2	2	no	—
124	C₄×Dic₁₃	C₂×C₈	1	4	yes	complemented
125	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
126	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
127	C₄×Dic₁₃	#41	1	2	yes	—
128	C₂×C₈×D₄	—	13	2	no	—
129	C₂²×C₄×C₈	—	13	2	no	—
130	C₄²×D₄	—	13	1	no	—
131	C₈×C₄⋊C₄	—	13	2	no	—
132	C₄×C₄⋊C₈	—	13	1	no	—
133	C₈×C₂²⋊C₄	—	13	4	no	—
134	C₄×C₂²⋊C₈	—	13	2	no	—
135	C₄²×C₈	—	13	1	no	—
136	C₂³×C₁₃	—	2	2	no	—
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	2	2	no	—
140	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
141	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
142	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
143	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₁₃	C₄×C₈	1	16	yes	complemented
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	16	no	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
154	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₁₃	#131	1	2	yes	—
158	C₂×Dic₁₃	—	2	2	no	—
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	—	2	1	no	—
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	1	no	—
163	C₂×Dic₁₃	—	2	1	no	—
164	C₂×Dic₁₃	—	2	1	no	—
165	C₂×Dic₁₃	—	2	2	no	—
166	C₂×Dic₁₃	—	2	8	no	—
167	C₂×Dic₁₃	—	2	8	no	—
168	C₂×Dic₁₃	—	2	16	no	—
169	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
170	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
171	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
172	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
173	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
174	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
175	C₂×Dic₁₃	#131	1	2	yes	—
176	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
177	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×#41	1	2	yes	—
179	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
180	#1057	—	2	8	no	—
181	#1057	—	2	4	no	—
182	#1057	C₄×D₄	1	8	yes	direct product factor
183	C₂³×C₈	—	13	4	no	—
184	C₂×C₄×D₄	—	13	1	no	—
185	C₂×C₄×D₄	—	13	1	no	—
186	C₂×C₄×D₄	#261	1	1	yes	characteristic
187	C₂²×C₄²	—	13	2	no	—
188	C₈×D₄	—	13	16	no	—
189	C₂×C₄⋊C₈	—	13	2	no	—
190	C₂×C₂²⋊C₈	—	13	4	no	—
191	C₂×C₄×C₈	—	13	1	no	—
192	C₂×C₄×C₈	—	13	2	no	—
193	C₂×C₄×C₈	—	13	2	no	—
194	C₂×C₄×C₈	—	13	4	no	—
195	C₂×C₄×C₈	—	13	1	no	—
196	C₂×C₄×C₈	—	13	2	no	—
197	C₂×C₄×C₈	—	26	8	no	—
198	C₄×C₄⋊C₄	—	13	1	no	—
199	C₄×C₄⋊C₄	—	13	1	no	—
200	C₄×C₄⋊C₄	—	13	1	no	—
201	C₄×C₂²⋊C₄	—	13	2	no	—
202	C₄×C₂²⋊C₄	—	13	2	no	—
203	C₄×C₂²⋊C₄	—	13	2	no	—
204	C₄³	—	13	1	no	—
205	#336	—	13	4	no	—
206	#336	—	13	2	no	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	2	4	no	—
209	C₂²×C₁₃	—	2	4	no	—
210	C₂²×C₁₃	—	2	4	no	—
211	C₂²×C₁₃	—	2	4	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	C₂×C₄×C₈	1	8	yes	complemented
214	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
217	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
218	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	complemented
224	C₄×C₁₃	C₈×D₄	1	4	yes	complemented
225	Dic₁₃	—	2	2	no	—
226	Dic₁₃	—	2	4	no	—
227	Dic₁₃	—	2	2	no	—
228	Dic₁₃	—	2	4	no	—
229	Dic₁₃	C₈×D₄	1	4	yes	complemented
230	Dic₁₃	C₂×C₄×D₄	1	2	yes	—
231	Dic₁₃	C₄×#41	1	2	yes	—
232	C₂²×D₄	C₂×#261	1	1	yes	characteristic
233	C₂³×C₄	—	13	2	no	—
234	C₂³×C₄	—	13	2	no	—
235	C₂³×C₄	C₂×#261	1	2	yes	—
236	C₂²×C₈	—	13	2	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂²×C₈	—	13	16	no	—
239	C₂²×C₈	—	13	2	no	—
240	C₂²×C₈	—	26	8	no	—
241	C₂²×C₈	—	26	8	no	—
242	C₄×D₄	—	13	8	no	—
243	C₄×D₄	—	13	8	no	—
244	C₄×D₄	#1057	1	8	yes	direct product factor
245	C₂×C₄⋊C₄	—	13	1	no	—
246	C₂×C₄⋊C₄	—	13	1	no	—
247	C₂×C₄⋊C₄	C₂×#261	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	13	2	no	—
249	C₂×C₂²⋊C₄	—	13	2	no	—
250	C₂×C₂²⋊C₄	C₂×#261	1	2	yes	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	2	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	2	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	2	no	—
260	C₂×C₄²	—	26	4	no	—
261	C₂×C₄²	—	26	4	no	—
262	C₂×C₄²	C₂×#261	1	1	yes	characteristic
263	C₄⋊C₈	—	13	8	no	—
264	C₂²⋊C₈	—	13	16	no	—
265	C₄×C₈	—	13	8	no	—
266	C₄×C₈	—	13	4	no	—
267	C₄×C₈	—	26	2	no	—
268	C₄×C₈	—	26	4	no	—
269	C₄×C₈	—	26	4	no	—
270	C₄×C₈	—	26	8	no	—
271	#95	—	13	2	no	—
272	#95	—	13	2	no	—
273	#95	—	13	2	no	—
274	C₂×C₁₃	—	2	8	no	—
275	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
276	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
277	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
278	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
279	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
280	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
281	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
282	C₂⁴	C₂²×#261	1	2	yes	—
283	C₂×D₄	D₁₃⋊C₈	1	4	yes	—
284	C₂×D₄	C₄×#261	1	4	yes	—
285	C₂×D₄	C₂×#1057	1	4	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	8	no	—
291	C₂²×C₄	—	13	8	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	2	no	—
295	C₂²×C₄	—	13	2	no	—
296	C₂²×C₄	—	26	2	no	—
297	C₂²×C₄	—	26	2	no	—
298	C₂²×C₄	—	26	4	no	—
299	C₂²×C₄	—	26	4	no	—
300	C₂²×C₄	—	26	4	no	—
301	C₂²×C₄	C₂×#1057	1	8	yes	complemented
302	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
303	C₂²×C₄	C₂²×#261	1	2	yes	—
304	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
305	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
306	C₂×C₈	—	13	4	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	13	4	no	—
309	C₂×C₈	—	13	4	no	—
310	C₂×C₈	—	13	8	no	—
311	C₂×C₈	—	26	32	no	—
312	C₂×C₈	—	26	4	no	—
313	C₂×C₈	—	26	2	no	—
314	C₂×C₈	—	26	2	no	—
315	C₂×C₈	—	26	4	no	—
316	C₄⋊C₄	—	13	4	no	—
317	C₄⋊C₄	—	13	4	no	—
318	C₄⋊C₄	C₂×#1057	1	4	yes	complemented
319	C₂²⋊C₄	—	13	8	no	—
320	C₂²⋊C₄	—	13	8	no	—
321	C₂²⋊C₄	C₂×#1057	1	8	yes	complemented
322	C₄²	—	13	4	no	—
323	C₄²	—	13	4	no	—
324	C₄²	—	13	2	no	—
325	C₄²	—	13	2	no	—
326	C₄²	—	26	2	no	—
327	C₄²	—	26	2	no	—
328	C₄²	—	26	2	no	—
329	C₄²	—	26	4	no	—
330	C₄²	—	26	2	no	—
331	C₄²	—	26	2	no	—
332	C₄²	—	26	4	no	—
333	C₄²	C₂×#1057	1	4	yes	complemented
334	C₁₃	C₄×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	C₂×D₁₃⋊C₈	1	4	yes	—
340	C₂³	C₂×C₄×#261	1	4	yes	—
341	C₂³	C₂²×#1057	1	4	yes	—
342	C₂³	C₂³×#261	1	1	yes	characteristic
343	D₄	C₄×#1057	1	16	yes	direct product factor
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	16	no	—
349	C₂×C₄	—	13	2	no	—
350	C₂×C₄	—	13	2	no	—
351	C₂×C₄	—	13	1	no	—
352	C₂×C₄	—	13	1	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	2	no	—
355	C₂×C₄	—	13	2	no	—
356	C₂×C₄	—	13	2	no	—
357	C₂×C₄	—	13	4	no	—
358	C₂×C₄	—	13	2	no	—
359	C₂×C₄	—	13	4	no	—
360	C₂×C₄	—	26	8	no	—
361	C₂×C₄	—	26	8	no	—
362	C₂×C₄	—	26	16	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
372	C₂×C₄	C₂×C₄×#261	1	2	yes	—
373	C₂×C₄	#88238	1	2	yes	—
374	C₂×C₄	D₄×#261	1	2	yes	—
375	C₂×C₄	C₂²×#1057	1	2	yes	—
376	C₂×C₄	C₂²×#1057	1	4	yes	—
377	C₂×C₄	C₂²×#1057	1	2	yes	—
378	C₂×C₄	C₂²×#1057	1	2	yes	—
379	C₈	—	13	8	no	—
380	C₈	—	26	8	no	—
381	C₈	—	26	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	C₂×C₄×#1057	1	8	yes	complemented
389	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
390	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
391	C₂²	C₂×#88238	1	1	yes	characteristic
392	C₂²	C₂×D₄×#261	1	1	yes	characteristic
393	C₂²	D₁₃⋊#131	1	1	yes	characteristic
394	C₂²	#41×#261	1	1	yes	characteristic
395	C₂²	C₂³×#1057	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	2	2	no	—
398	C₄	—	13	2	no	—
399	C₄	—	13	2	no	—
400	C₄	—	13	4	no	—
401	C₄	—	26	4	no	—
402	C₄	—	26	4	no	—
403	C₄	—	26	2	no	—
404	C₄	—	26	2	no	—
405	C₄	C₂×C₄×#1057	1	4	yes	complemented
406	C₄	D₄×#1057	1	4	yes	direct product factor
407	C₂	—	2	8	no	—
408	C₂	C₄×D₄×#261	1	1	yes	characteristic
409	C₂	C₂²×C₄×#1057	1	1	yes	characteristic
410	C₂	C₄×#88238	1	1	yes	characteristic
411	C₂	C₂×D₄×#1057	1	1	yes	characteristic
412	C₂	D₄×D₁₃⋊C₈	1	1	yes	characteristic
413	C₂	#41×#1057	1	1	yes	characteristic
414	C₂	#13131641	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂³	C₂³×#261
Fitting	C₂×C₄×D₄×C₁₃	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×D₄	#261
hypocenter	C₁₃	C₄×C₈×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×#1057	C₂	semidirect
3. C₄⋊C₄×#1057	C₂	semidirect
4. C₄×C₄⋊#1057	C₂	semidirect
5. C₂²⋊C₄×#1057	C₂	semidirect
6. C₄×C₂²⋊#1057	C₂	semidirect
7. C₄²×#1057	C₂	semidirect
15. D₄×#1057	C₄	direct (N × H)
39. C₂²×#1057	C₂×C₄	semidirect
43. C₄×D₄×C₁₃	C₈	semidirect
49. D₄×Dic₁₃	C₈	semidirect
64. C₂²⋊#1057	C₂×C₄	semidirect
65. C₄⋊#1057	C₂×C₄	semidirect
70. C₄×#1057	C₂×C₄	semidirect
71. C₄×#1057	D₄	direct (N × H)
82. C₂²×C₄×C₁₃	C₂×C₈	semidirect
92. C₂²×Dic₁₃	C₂×C₈	semidirect
110. C₁₃×C₄⋊C₄	C₂×C₈	semidirect
111. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
112. C₄²×C₁₃	C₂×C₈	semidirect
114. C₂²⋊Dic₁₃	C₂×C₈	semidirect
116. C₄⋊Dic₁₃	C₂×C₈	semidirect
124. C₄×Dic₁₃	C₂×C₈	semidirect
144. D₄×C₁₃	C₄×C₈	semidirect
182. #1057	C₄×D₄	direct (N × H)
213. C₂²×C₁₃	C₂×C₄×C₈	semidirect
223. C₄×C₁₃	C₂×C₄×C₈	semidirect
224. C₄×C₁₃	C₈×D₄	semidirect
229. Dic₁₃	C₈×D₄	semidirect
244. C₄×D₄	#1057	direct (N × H)
301. C₂²×C₄	C₂×#1057	semidirect
318. C₄⋊C₄	C₂×#1057	semidirect
321. C₂²⋊C₄	C₂×#1057	semidirect
333. C₄²	C₂×#1057	semidirect
334. C₁₃	C₄×C₈×D₄	semidirect
343. D₄	C₄×#1057	direct (N × H)
388. C₂²	C₂×C₄×#1057	semidirect
405. C₄	C₂×C₄×#1057	semidirect
406. C₄	D₄×#1057	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×D₄×#1057	2
C₂²×C₄×#1057	2
C₄⋊C₄×#1057	2
C₄×C₄⋊#1057	2
C₂²⋊C₄×#1057	2
C₄×C₂²⋊#1057	2
C₄²×#1057	2
C₄×D₄×Dic₁₃	2
C₄×C₈×D₄	13

Subgroups — C4×D4×#1057 #16797336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×#1057 #16797336