Subgroups — C₂×D₄×#6131 #16769883

Order 3328.

12314 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6131	C₂	1	2	yes	maximal, complemented
2	D₄×#6131	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719282	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719522	C₂	1	2	yes	maximal, complemented
5	C₂×#11719431	C₂	1	3	yes	maximal, complemented
6	C₂×#11719335	C₂	1	6	yes	maximal, complemented
7	C₂×D₄×D₅₂	C₂	1	3	yes	maximal, complemented
8	C₂×#11719430	C₂	1	3	yes	maximal, complemented
9	C₂×#11719332	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#6131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×D₁₃	C₂	1	3	yes	maximal, complemented
12	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
14	C₂²×#6131	—	2	32	no	—
15	C₂²×#6131	C₂²	1	1	yes	characteristic
16	C₂²×#6131	C₂²	1	6	yes	complemented
17	C₂²×#6131	C₂²	1	2	yes	complemented
18	C₂²×#6131	C₂²	1	6	yes	complemented
19	C₂²×#6131	C₂²	1	32	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	3	yes	—
21	C₂³×D₅₂	C₂²	1	6	yes	complemented
22	C₂³×C₄×D₁₃	C₂²	1	6	yes	complemented
23	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
28	#11719522	C₂²	1	32	yes	complemented
29	C₂×#88201	C₂²	1	6	yes	complemented
30	C₂×#88200	C₂²	1	6	yes	complemented
31	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₄×Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂×#88184	C₂²	1	6	yes	complemented
34	C₂×C₄×C₂²⋊D₁₃	C₂²	1	6	yes	complemented
35	#11719431	C₂²	1	48	yes	complemented
36	#11719430	C₂²	1	48	yes	complemented
37	#11719335	C₂²	1	96	yes	complemented
38	#11719332	C₂²	1	96	yes	complemented
39	#11719282	C₂²	1	16	yes	complemented
40	C₄×#6131	C₂²	1	16	yes	complemented
41	D₄×D₅₂	C₂²	1	48	yes	complemented
42	C₄×D₄×D₁₃	C₂²	1	48	yes	complemented
43	C₂×#88149	C₂²	1	6	yes	complemented
44	C₂×#88149	C₂²	1	6	yes	complemented
45	C₂×#88149	C₂²	1	6	yes	complemented
46	C₂×#88148	C₂²	1	12	yes	complemented
47	C₂×#88147	C₂²	1	3	yes	complemented
48	C₂×#88147	C₂²	1	3	yes	complemented
49	C₂×#88147	C₂²	1	6	yes	complemented
50	C₂×#88146	C₂²	1	3	yes	complemented
51	C₂×C₄⋊C₄×D₁₃	C₂²	1	3	yes	complemented
52	C₂×#88136	C₂²	1	12	yes	complemented
53	C₂×#88135	C₂²	1	6	yes	complemented
54	C₂×C₂²⋊C₄×D₁₃	C₂²	1	6	yes	complemented
55	C₂×#88128	C₂²	1	3	yes	complemented
56	C₂×C₄×D₅₂	C₂²	1	3	yes	complemented
57	C₂×C₄×D₅₂	C₂²	1	3	yes	complemented
58	C₂×C₄²×D₁₃	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₃	C₂³	1	6	yes	—
60	C₂²×Q₈×C₁₃	—	2	16	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
66	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
67	C₂³×Dic₁₃	C₂³	1	2	yes	—
68	C₂×#6131	—	2	16	no	—
69	C₂×#6131	—	2	256	no	—
70	C₂×#6131	—	2	48	no	—
71	C₂×#6131	—	2	48	no	—
72	C₂×#6131	D₄	1	16	yes	direct product factor
73	C₂×#6131	C₂³	1	8	yes	—
74	C₂×#6131	C₂³	1	48	yes	complemented
75	C₂×#6131	C₂³	1	48	yes	complemented
76	C₂×#6131	C₂³	1	16	yes	complemented
77	C₂×D₄×D₁₃	—	2	24	no	—
78	C₂×D₄×D₁₃	C₂³	1	24	yes	—
79	C₂²×D₅₂	—	2	48	no	—
80	C₂²×D₅₂	C₂³	1	3	yes	—
81	C₂²×D₅₂	C₂³	1	6	yes	—
82	C₂²×D₅₂	C₂³	1	12	yes	—
83	C₂²×D₅₂	C₂³	1	6	yes	—
84	C₂²×D₅₂	C₂³	1	3	yes	—
85	C₂²×D₅₂	C₂³	1	48	yes	complemented
86	C₂²×C₄×D₁₃	—	2	48	no	—
87	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
88	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
89	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
90	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
91	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
92	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
93	C₂²×C₄×D₁₃	C₂³	1	48	yes	complemented
94	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
95	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
96	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
97	C₄×D₄×C₁₃	C₂³	1	24	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
103	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
104	#88201	C₂³	1	48	yes	complemented
105	#88200	C₂³	1	48	yes	complemented
106	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
107	D₄×Dic₁₃	C₂³	1	8	yes	—
108	#88184	C₂³	1	48	yes	complemented
109	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
110	C₂×#6103	C₂³	1	6	yes	—
111	C₂×#6103	C₂³	1	6	yes	—
112	C₂×#6103	C₂³	1	6	yes	—
113	C₂×#6103	C₂³	1	12	yes	—
114	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
116	C₂×#6101	C₂³	1	6	yes	—
117	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
119	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
120	#88149	C₂³	1	48	yes	complemented
121	#88149	C₂³	1	48	yes	complemented
122	#88149	C₂³	1	48	yes	complemented
123	#88148	C₂³	1	96	yes	complemented
124	#88147	C₂³	1	24	yes	complemented
125	#88147	C₂³	1	48	yes	complemented
126	#88147	C₂³	1	24	yes	complemented
127	#88146	C₂³	1	24	yes	complemented
128	C₄⋊C₄×D₁₃	C₂³	1	24	yes	complemented
129	#88136	C₂³	1	96	yes	complemented
130	#88135	C₂³	1	48	yes	complemented
131	C₂²⋊C₄×D₁₃	C₂³	1	48	yes	complemented
132	#88128	C₂³	1	24	yes	complemented
133	C₄×D₅₂	C₂³	1	24	yes	complemented
134	C₄×D₅₂	C₂³	1	24	yes	complemented
135	C₄²×D₁₃	C₂³	1	24	yes	complemented
136	C₂×D₄×#41	—	13	1	no	maximal, Sylow
137	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
138	C₂³×D₁₃	—	2	24	no	—
139	C₂³×D₁₃	—	2	24	no	—
140	C₂³×D₁₃	—	4	12	no	—
141	C₂³×D₁₃	C₂⁴	1	6	yes	—
142	C₂³×D₁₃	C₂⁴	1	24	yes	—
143	C₂³×D₁₃	C₂⁴	1	3	yes	—
144	C₂×Q₈×C₁₃	—	2	64	no	—
145	C₂×Q₈×C₁₃	—	2	24	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
147	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	#41	1	8	yes	complemented
150	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	—	2	24	no	—
152	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₃	—	2	24	no	—
158	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
159	C₂²×Dic₁₃	—	2	8	no	—
160	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
161	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
162	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
163	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
164	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
165	#6131	—	2	64	no	—
166	#6131	—	2	192	no	—
167	#6131	—	2	192	no	—
168	#6131	C₂×D₄	1	64	yes	direct product factor
169	D₄×D₁₃	—	2	96	no	—
170	C₂×D₅₂	—	2	48	no	—
171	C₂×D₅₂	—	2	24	no	—
172	C₂×D₅₂	—	2	12	no	—
173	C₂×D₅₂	—	2	192	no	—
174	C₂×D₅₂	—	4	12	no	—
175	C₂×D₅₂	C₂×D₄	1	24	yes	complemented
176	C₂×D₅₂	C₂⁴	1	12	yes	—
177	C₂×D₅₂	C₂⁴	1	24	yes	—
178	C₂×D₅₂	C₂⁴	1	48	yes	—
179	C₂×D₅₂	C₂⁴	1	24	yes	—
180	C₂×D₅₂	C₂⁴	1	12	yes	—
181	C₂×C₄×D₁₃	—	2	24	no	—
182	C₂×C₄×D₁₃	—	2	24	no	—
183	C₂×C₄×D₁₃	—	2	12	no	—
184	C₂×C₄×D₁₃	—	2	24	no	—
185	C₂×C₄×D₁₃	—	2	192	no	—
186	C₂×C₄×D₁₃	—	4	6	no	—
187	C₂×C₄×D₁₃	C₂×D₄	1	24	yes	complemented
188	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
189	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
190	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
191	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
192	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
193	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
197	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
198	C₄²×C₁₃	C₂⁴	1	12	yes	—
199	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
200	#6103	C₂⁴	1	24	yes	—
201	#6103	C₂⁴	1	24	yes	—
202	#6103	C₂⁴	1	24	yes	—
203	#6103	C₂⁴	1	48	yes	—
204	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
205	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
206	#6101	C₂⁴	1	24	yes	—
207	C₄×Dic₁₃	C₂⁴	1	4	yes	—
208	C₄×Dic₁₃	C₂⁴	1	12	yes	—
209	C₄×Dic₁₃	C₂⁴	1	12	yes	—
210	C₂³×#41	—	13	2	no	—
211	D₄×#41	—	13	32	no	—
212	C₂×#550	—	13	1	no	—
213	C₂×D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
214	C₂×#548	—	13	2	no	—
215	C₂×#547	—	13	3	no	—
216	C₂×#546	—	13	6	no	—
217	C₂×D₄²	—	13	3	no	—
218	C₂×#532	—	13	3	no	—
219	C₂×#525	—	13	6	no	—
220	C₂×C₄×#41	—	13	1	no	—
221	C₂²×C₄×D₄	—	13	3	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	C₂×#41	1	8	yes	complemented
225	C₂³×C₁₃	C₂⁵	1	4	yes	—
226	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₂²×D₁₃	—	2	6	no	—
228	C₂²×D₁₃	—	2	6	no	—
229	C₂²×D₁₃	—	2	12	no	—
230	C₂²×D₁₃	—	2	12	no	—
231	C₂²×D₁₃	—	2	48	no	—
232	C₂²×D₁₃	—	2	12	no	—
233	C₂²×D₁₃	—	2	48	no	—
234	C₂²×D₁₃	—	4	24	no	—
235	C₂²×D₁₃	—	4	96	no	—
236	C₂²×D₁₃	C₂²×D₄	1	12	yes	—
237	C₂²×D₁₃	C₂⁵	1	12	yes	—
238	C₂²×D₁₃	C₂⁵	1	6	yes	—
239	Q₈×C₁₃	—	2	48	no	—
240	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
241	D₄×C₁₃	C₂×#41	1	16	yes	complemented
242	C₂×C₄×C₁₃	—	2	12	no	—
243	C₂×C₄×C₁₃	—	2	6	no	—
244	C₂×C₄×C₁₃	—	2	48	no	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
246	C₂×C₄×C₁₃	C₂×#41	1	4	yes	complemented
247	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
248	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
250	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
251	C₂²⋊D₁₃	—	2	48	no	—
252	C₂×Dic₁₃	—	2	4	no	—
253	C₂×Dic₁₃	—	2	6	no	—
254	C₂×Dic₁₃	—	2	2	no	—
255	C₂×Dic₁₃	—	2	16	no	—
256	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
257	C₂×Dic₁₃	C₂⁵	1	2	yes	—
258	C₂×Dic₁₃	C₂⁵	1	6	yes	—
259	C₂×Dic₁₃	C₂⁵	1	4	yes	—
260	C₂×Dic₁₃	C₂⁵	1	2	yes	—
261	D₅₂	—	2	96	no	—
262	D₅₂	—	2	48	no	—
263	D₅₂	—	2	24	no	—
264	D₅₂	—	4	24	no	—
265	D₅₂	C₂²×D₄	1	48	yes	complemented
266	C₄×D₁₃	—	2	48	no	—
267	C₄×D₁₃	—	2	48	no	—
268	C₄×D₁₃	—	2	24	no	—
269	C₄×D₁₃	—	2	48	no	—
270	C₄×D₁₃	—	4	12	no	—
271	C₄×D₁₃	C₂²×D₄	1	48	yes	complemented
272	C₂²×#41	—	13	1	no	—
273	C₂²×#41	—	13	6	no	—
274	C₂²×#41	—	13	6	no	—
275	C₂²×#41	—	13	2	no	—
276	C₂²×#41	—	13	32	no	—
277	C₂²×#41	—	26	32	no	—
278	C₂³×Q₈	C₂×D₁₃	1	2	yes	complemented
279	C₂³×D₄	—	13	3	no	—
280	C₂³×D₄	—	13	6	no	—
281	C₂⁴×C₄	—	13	6	no	—
282	#550	—	13	16	no	—
283	D₄×Q₈	C₂×D₁₃	1	16	yes	complemented
284	#548	—	13	32	no	—
285	#547	—	13	48	no	—
286	#546	—	13	96	no	—
287	D₄²	—	13	48	no	—
288	#532	—	13	48	no	—
289	C₂×C₄⋊Q₈	C₂×D₁₃	1	3	yes	complemented
290	C₂×#127	—	13	3	no	—
291	C₂×#124	—	13	6	no	—
292	#525	—	13	96	no	—
293	C₂×#123	—	13	12	no	—
294	C₂×C₂²⋊Q₈	—	13	6	no	—
295	C₂×C₂²⋊Q₈	C₂×D₁₃	1	6	yes	complemented
296	C₂×#121	—	13	6	no	—
297	C₂×#121	—	13	6	no	—
298	C₂×#121	—	13	6	no	—
299	C₂×#121	—	13	6	no	—
300	C₂×#120	—	13	12	no	—
301	C₄×#41	—	13	16	no	—
302	C₂×C₄×Q₈	—	13	1	no	—
303	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
304	C₂×C₄×D₄	—	13	1	no	—
305	C₂×C₄×D₄	—	13	6	no	—
306	C₂×C₄×D₄	—	13	48	no	—
307	C₂×C₄×D₄	—	13	3	no	—
308	C₂×C₄×D₄	—	13	3	no	—
309	C₂×C₄×D₄	—	13	6	no	—
310	C₂×C₄×D₄	—	13	6	no	—
311	C₂×C₄×D₄	—	13	3	no	—
312	C₂×C₄×D₄	—	13	3	no	—
313	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	—
314	C₂×#117	—	13	3	no	—
315	C₂²×C₄⋊C₄	—	13	3	no	—
316	C₂²×C₂²⋊C₄	—	13	6	no	—
317	C₂²×C₄²	—	13	3	no	—
318	C₂²×C₁₃	—	2	4	no	—
319	C₂²×C₁₃	—	2	4	no	—
320	C₂²×C₁₃	—	2	16	no	—
321	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
322	C₂²×C₁₃	C₂²×#41	1	2	yes	—
323	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
324	C₂²×C₁₃	#585	1	2	yes	—
325	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
326	C₂×D₁₃	—	2	6	no	—
327	C₂×D₁₃	—	2	6	no	—
328	C₂×D₁₃	—	2	24	no	—
329	C₂×D₁₃	—	2	12	no	—
330	C₂×D₁₃	—	2	12	no	—
331	C₂×D₁₃	—	2	12	no	—
332	C₂×D₁₃	—	4	96	no	—
333	C₂×D₁₃	—	4	24	no	—
334	C₂×D₁₃	C₂³×D₄	1	12	yes	—
335	C₄×C₁₃	—	2	12	no	—
336	C₄×C₁₃	—	2	6	no	—
337	C₄×C₁₃	C₂³×D₄	1	12	yes	—
338	C₄×C₁₃	C₂²×#41	1	4	yes	complemented
339	Dic₁₃	—	2	4	no	—
340	Dic₁₃	—	2	6	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	C₂³×D₄	1	4	yes	—
343	C₂⁵	—	13	6	no	—
344	C₂×#41	—	13	16	no	—
345	C₂×#41	—	13	8	no	—
346	C₂×#41	—	13	48	no	—
347	C₂×#41	—	13	48	no	—
348	C₂×#41	—	13	16	no	—
349	C₂×#41	—	26	48	no	—
350	C₂×#41	—	26	48	no	—
351	C₂×#41	—	26	256	no	—
352	C₂×#41	—	26	16	no	—
353	C₂²×Q₈	—	2	16	no	—
354	C₂²×Q₈	C₂²×D₁₃	1	6	yes	—
355	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₂²×Q₈	C₂²×D₁₃	1	16	yes	complemented
357	C₂²×D₄	—	13	6	no	—
358	C₂²×D₄	—	13	24	no	—
359	C₂²×D₄	—	13	3	no	—
360	C₂²×D₄	—	13	3	no	—
361	C₂²×D₄	—	13	12	no	—
362	C₂²×D₄	—	13	6	no	—
363	C₂²×D₄	—	13	48	no	—
364	C₂²×D₄	—	13	6	no	—
365	C₂²×D₄	—	26	48	no	—
366	C₂²×D₄	—	26	24	no	—
367	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
368	C₂³×C₄	—	13	3	no	—
369	C₂³×C₄	—	13	2	no	—
370	C₂³×C₄	—	13	6	no	—
371	C₂³×C₄	—	13	3	no	—
372	C₂³×C₄	—	13	6	no	—
373	C₂³×C₄	—	13	6	no	—
374	C₂³×C₄	—	13	48	no	—
375	C₂³×C₄	—	13	3	no	—
376	C₂³×C₄	—	26	48	no	—
377	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
378	C₄⋊Q₈	C₂²×D₁₃	1	24	yes	complemented
379	#127	—	13	24	no	—
380	#124	—	13	48	no	—
381	#123	—	13	96	no	—
382	C₂²⋊Q₈	—	13	48	no	—
383	C₂²⋊Q₈	C₂²×D₁₃	1	48	yes	complemented
384	#121	—	13	48	no	—
385	#121	—	13	48	no	—
386	#121	—	13	48	no	—
387	#121	—	13	48	no	—
388	#120	—	13	96	no	—
389	C₄×Q₈	—	13	8	no	—
390	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
391	C₄×D₄	—	13	8	no	—
392	C₄×D₄	—	13	48	no	—
393	C₄×D₄	—	13	24	no	—
394	C₄×D₄	—	13	24	no	—
395	C₄×D₄	—	13	48	no	—
396	C₄×D₄	—	13	48	no	—
397	C₄×D₄	—	13	24	no	—
398	C₄×D₄	—	13	24	no	—
399	C₄×D₄	C₂²×D₁₃	1	24	yes	—
400	#117	—	13	24	no	—
401	C₂×C₄⋊C₄	—	13	1	no	—
402	C₂×C₄⋊C₄	—	13	6	no	—
403	C₂×C₄⋊C₄	—	13	3	no	—
404	C₂×C₄⋊C₄	—	13	24	no	—
405	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
406	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
407	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	—
408	C₂×C₂²⋊C₄	—	13	2	no	—
409	C₂×C₂²⋊C₄	—	13	6	no	—
410	C₂×C₂²⋊C₄	—	13	6	no	—
411	C₂×C₂²⋊C₄	—	13	6	no	—
412	C₂×C₂²⋊C₄	—	13	12	no	—
413	C₂×C₂²⋊C₄	—	13	48	no	—
414	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
415	C₂×C₄²	—	13	3	no	—
416	C₂×C₄²	—	13	1	no	—
417	C₂×C₄²	—	13	3	no	—
418	C₂×C₄²	—	13	24	no	—
419	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
420	C₂×C₁₃	—	2	8	no	—
421	C₂×C₁₃	D₄×#41	1	4	yes	complemented
422	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
423	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
424	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
425	D₁₃	—	2	12	no	—
426	D₁₃	—	4	12	no	—
427	C₂⁴	—	13	3	no	—
428	C₂⁴	—	13	6	no	—
429	C₂⁴	—	13	24	no	—
430	C₂⁴	—	26	24	no	—
431	C₂⁴	—	26	24	no	—
432	C₂⁴	—	52	12	no	—
433	C₂⁴	C₂³×D₁₃	1	2	yes	—
434	#41	—	13	64	no	—
435	#41	—	26	192	no	—
436	#41	—	26	192	no	—
437	#41	—	26	64	no	—
438	C₂×Q₈	—	2	64	no	—
439	C₂×Q₈	—	2	24	no	—
440	C₂×Q₈	D₄×D₁₃	1	8	yes	complemented
441	C₂×Q₈	C₂³×D₁₃	1	24	yes	—
442	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
443	C₂×D₄	—	13	24	no	—
444	C₂×D₄	—	13	24	no	—
445	C₂×D₄	—	13	12	no	—
446	C₂×D₄	—	13	12	no	—
447	C₂×D₄	—	13	48	no	—
448	C₂×D₄	—	13	24	no	—
449	C₂×D₄	—	13	24	no	—
450	C₂×D₄	—	26	192	no	—
451	C₂×D₄	—	26	48	no	—
452	C₂×D₄	—	26	24	no	—
453	C₂×D₄	—	26	96	no	—
454	C₂×D₄	—	26	24	no	—
455	C₂×D₄	—	26	12	no	—
456	C₂×D₄	—	52	12	no	—
457	C₂×D₄	#6131	1	8	yes	direct product factor
458	C₂×D₄	C₂³×D₁₃	1	4	yes	—
459	C₂²×C₄	—	2	24	no	—
460	C₂²×C₄	—	13	1	no	—
461	C₂²×C₄	—	13	24	no	—
462	C₂²×C₄	—	13	12	no	—
463	C₂²×C₄	—	13	8	no	—
464	C₂²×C₄	—	13	1	no	—
465	C₂²×C₄	—	13	3	no	—
466	C₂²×C₄	—	13	2	no	—
467	C₂²×C₄	—	13	12	no	—
468	C₂²×C₄	—	13	24	no	—
469	C₂²×C₄	—	13	24	no	—
470	C₂²×C₄	—	13	24	no	—
471	C₂²×C₄	—	13	12	no	—
472	C₂²×C₄	—	26	24	no	—
473	C₂²×C₄	—	26	192	no	—
474	C₂²×C₄	—	26	24	no	—
475	C₂²×C₄	—	26	8	no	—
476	C₂²×C₄	—	26	24	no	—
477	C₂²×C₄	—	26	12	no	—
478	C₂²×C₄	—	52	6	no	—
479	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
480	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
481	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
482	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
483	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
484	C₄⋊C₄	—	13	4	no	—
485	C₄⋊C₄	—	13	24	no	—
486	C₄⋊C₄	—	13	12	no	—
487	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
488	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
489	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
490	C₂²⋊C₄	—	13	8	no	—
491	C₂²⋊C₄	—	13	24	no	—
492	C₂²⋊C₄	—	13	24	no	—
493	C₂²⋊C₄	—	13	24	no	—
494	C₂²⋊C₄	—	13	48	no	—
495	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
496	C₄²	—	13	4	no	—
497	C₄²	—	13	12	no	—
498	C₄²	—	13	12	no	—
499	C₄²	C₂³×D₁₃	1	12	yes	—
500	C₁₃	C₂×D₄×#41	1	1	yes	characteristic, complemented, Sylow
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	13	12	no	—
504	C₂³	—	13	6	no	—
505	C₂³	—	13	12	no	—
506	C₂³	—	26	48	no	—
507	C₂³	—	26	6	no	—
508	C₂³	—	26	6	no	—
509	C₂³	—	26	12	no	—
510	C₂³	—	26	12	no	—
511	C₂³	—	26	48	no	—
512	C₂³	—	26	12	no	—
513	C₂³	—	52	24	no	—
514	C₂³	—	52	96	no	—
515	C₂³	C₂×#6131	1	8	yes	complemented
516	C₂³	C₂⁴×D₁₃	1	4	yes	—
517	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
518	Q₈	—	2	48	no	—
519	Q₈	C₂×D₄×D₁₃	1	16	yes	complemented
520	D₄	—	13	48	no	—
521	D₄	—	26	96	no	—
522	D₄	—	26	48	no	—
523	D₄	—	26	48	no	—
524	D₄	—	26	24	no	—
525	D₄	—	52	24	no	—
526	D₄	C₂×#6131	1	16	yes	direct product factor
527	C₂×C₄	—	2	12	no	—
528	C₂×C₄	—	2	6	no	—
529	C₂×C₄	—	2	48	no	—
530	C₂×C₄	—	13	4	no	—
531	C₂×C₄	—	13	2	no	—
532	C₂×C₄	—	13	48	no	—
533	C₂×C₄	—	13	2	no	—
534	C₂×C₄	—	13	6	no	—
535	C₂×C₄	—	13	4	no	—
536	C₂×C₄	—	26	48	no	—
537	C₂×C₄	—	26	48	no	—
538	C₂×C₄	—	26	16	no	—
539	C₂×C₄	—	26	4	no	—
540	C₂×C₄	—	26	6	no	—
541	C₂×C₄	—	26	2	no	—
542	C₂×C₄	—	26	48	no	—
543	C₂×C₄	—	26	24	no	—
544	C₂×C₄	—	52	12	no	—
545	C₂×C₄	C₂×D₄×D₁₃	1	12	yes	—
546	C₂×C₄	C₂×#6131	1	4	yes	complemented
547	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
548	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
549	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
550	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
551	C₂²	—	2	16	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	13	12	no	—
555	C₂²	—	26	24	no	—
556	C₂²	—	26	6	no	—
557	C₂²	—	26	6	no	—
558	C₂²	—	26	12	no	—
559	C₂²	—	26	12	no	—
560	C₂²	—	26	12	no	—
561	C₂²	—	52	96	no	—
562	C₂²	—	52	24	no	—
563	C₂²	C₂²×D₄×D₁₃	1	2	yes	—
564	C₂²	C₂²×#6131	1	2	yes	—
565	C₂²	C₂²×#6131	1	8	yes	complemented
566	C₂²	#11719652	1	2	yes	—
567	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
568	C₄	—	2	12	no	—
569	C₄	—	2	6	no	—
570	C₄	—	13	4	no	—
571	C₄	—	26	4	no	—
572	C₄	—	26	6	no	—
573	C₄	—	26	2	no	—
574	C₄	C₂²×D₄×D₁₃	1	12	yes	—
575	C₄	C₂²×#6131	1	4	yes	complemented
576	C₂	—	2	8	no	—
577	C₂	—	26	12	no	—
578	C₂	—	52	12	no	—
579	C₂	D₄×#6131	1	4	yes	direct product factor
580	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
581	C₂	C₂³×#6131	1	1	yes	characteristic
582	C₂	C₂×#11719652	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×D₄×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×D₄×Q₈	D₁₃
hypocenter	C₁₃	C₂×D₄×#41
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×#6131	C₂	semidirect
2. D₄×#6131	C₂	direct (N × H)
3. C₂×#11719282	C₂	semidirect
4. C₂×#11719522	C₂	semidirect
5. C₂×#11719431	C₂	semidirect
6. C₂×#11719335	C₂	semidirect
7. C₂×D₄×D₅₂	C₂	semidirect
8. C₂×#11719430	C₂	semidirect
9. C₂×#11719332	C₂	semidirect
10. C₂×C₄×#6131	C₂	semidirect
11. C₂×C₄×D₄×D₁₃	C₂	semidirect
12. C₂×D₄×Q₈×C₁₃	C₂	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
16. C₂²×#6131	C₂²	semidirect
17. C₂²×#6131	C₂²	semidirect
18. C₂²×#6131	C₂²	semidirect
19. C₂²×#6131	C₂²	semidirect
21. C₂³×D₅₂	C₂²	semidirect
22. C₂³×C₄×D₁₃	C₂²	semidirect
23. D₄×Q₈×C₁₃	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. #11719522	C₂²	semidirect
29. C₂×#88201	C₂²	semidirect
30. C₂×#88200	C₂²	semidirect
31. C₂×Q₈×Dic₁₃	C₂²	semidirect
33. C₂×#88184	C₂²	semidirect
34. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
35. #11719431	C₂²	semidirect
36. #11719430	C₂²	semidirect
37. #11719335	C₂²	semidirect
38. #11719332	C₂²	semidirect
39. #11719282	C₂²	semidirect
40. C₄×#6131	C₂²	semidirect
41. D₄×D₅₂	C₂²	semidirect
42. C₄×D₄×D₁₃	C₂²	semidirect
43. C₂×#88149	C₂²	semidirect
44. C₂×#88149	C₂²	semidirect
45. C₂×#88149	C₂²	semidirect
46. C₂×#88148	C₂²	semidirect
47. C₂×#88147	C₂²	semidirect
48. C₂×#88147	C₂²	semidirect
49. C₂×#88147	C₂²	semidirect
50. C₂×#88146	C₂²	semidirect
51. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
52. C₂×#88136	C₂²	semidirect
53. C₂×#88135	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
55. C₂×#88128	C₂²	semidirect
56. C₂×C₄×D₅₂	C₂²	semidirect
57. C₂×C₄×D₅₂	C₂²	semidirect
58. C₂×C₄²×D₁₃	C₂²	semidirect
63. C₂²×Q₈×C₁₃	C₂³	semidirect
72. C₂×#6131	D₄	direct (N × H)
74. C₂×#6131	C₂³	semidirect
75. C₂×#6131	C₂³	semidirect
76. C₂×#6131	C₂³	semidirect
85. C₂²×D₅₂	C₂³	semidirect
93. C₂²×C₄×D₁₃	C₂³	semidirect
94. C₁₃×C₄⋊Q₈	C₂³	semidirect
95. C₁₃×C₂²⋊Q₈	C₂³	semidirect
96. C₄×Q₈×C₁₃	C₂³	semidirect
104. #88201	C₂³	semidirect
105. #88200	C₂³	semidirect
106. Q₈×Dic₁₃	C₂³	semidirect
108. #88184	C₂³	semidirect
109. C₄×C₂²⋊D₁₃	C₂³	semidirect
120. #88149	C₂³	semidirect
121. #88149	C₂³	semidirect
122. #88149	C₂³	semidirect
123. #88148	C₂³	semidirect
124. #88147	C₂³	semidirect
125. #88147	C₂³	semidirect
126. #88147	C₂³	semidirect
127. #88146	C₂³	semidirect
128. C₄⋊C₄×D₁₃	C₂³	semidirect
129. #88136	C₂³	semidirect
130. #88135	C₂³	semidirect
131. C₂²⋊C₄×D₁₃	C₂³	semidirect
132. #88128	C₂³	semidirect
133. C₄×D₅₂	C₂³	semidirect
134. C₄×D₅₂	C₂³	semidirect
135. C₄²×D₁₃	C₂³	semidirect
146. C₂×Q₈×C₁₃	C₂×D₄	semidirect
149. C₂×D₄×C₁₃	#41	semidirect
168. #6131	C₂×D₄	direct (N × H)
175. C₂×D₅₂	C₂×D₄	semidirect
187. C₂×C₄×D₁₃	C₂×D₄	semidirect
213. C₂×D₄×Q₈	D₁₃	semidirect
224. C₂³×C₁₃	C₂×#41	semidirect
240. Q₈×C₁₃	C₂²×D₄	semidirect
241. D₄×C₁₃	C₂×#41	semidirect
246. C₂×C₄×C₁₃	C₂×#41	semidirect
265. D₅₂	C₂²×D₄	semidirect
271. C₄×D₁₃	C₂²×D₄	semidirect
278. C₂³×Q₈	C₂×D₁₃	semidirect
283. D₄×Q₈	C₂×D₁₃	semidirect
289. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
295. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
303. C₂×C₄×Q₈	C₂×D₁₃	semidirect
323. C₂²×C₁₃	C₂²×#41	semidirect
338. C₄×C₁₃	C₂²×#41	semidirect
356. C₂²×Q₈	C₂²×D₁₃	semidirect
378. C₄⋊Q₈	C₂²×D₁₃	semidirect
383. C₂²⋊Q₈	C₂²×D₁₃	semidirect
390. C₄×Q₈	C₂²×D₁₃	semidirect
421. C₂×C₁₃	D₄×#41	semidirect
440. C₂×Q₈	D₄×D₁₃	semidirect
457. C₂×D₄	#6131	direct (N × H)
500. C₁₃	C₂×D₄×#41	semidirect
515. C₂³	C₂×#6131	semidirect
519. Q₈	C₂×D₄×D₁₃	semidirect
526. D₄	C₂×#6131	direct (N × H)
546. C₂×C₄	C₂×#6131	semidirect
565. C₂²	C₂²×#6131	semidirect
575. C₄	C₂²×#6131	semidirect
579. C₂	D₄×#6131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6131	2
D₄×#6131	2
C₂×#11719282	2
C₂×#11719522	2
C₂×#11719431	2
C₂×#11719335	2
C₂×D₄×D₅₂	2
C₂×#11719430	2
C₂×#11719332	2
C₂×C₄×#6131	2
C₂×C₄×D₄×D₁₃	2
C₂×D₄×Q₈×C₁₃	2
C₂×D₄×#41	13

Subgroups — C2×D4×#6131 #16769883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×#6131 #16769883