Subgroups — C₁₁₃×#8310 #43276330

Order 28928.

1520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂²⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊C₈×C₁₁₃	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₁₁₃	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₁₃	—	2	1	no	—
7	C₂×C₄×D₄×C₁₁₃	—	2	8	no	—
8	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
9	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
10	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₁₃	C₄	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
14	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	complemented
16	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
17	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
18	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	complemented
19	#336×C₁₁₃	—	2	1	no	—
20	#336×C₁₁₃	—	2	1	no	—
21	D₄⋊C₈×C₁₁₃	—	2	8	no	—
22	C₂⁵×C₁₁₃	—	2	1	no	—
23	C₂²×D₄×C₁₁₃	—	2	4	no	—
24	C₂²×D₄×C₁₁₃	—	2	4	no	—
25	C₂²×D₄×C₁₁₃	—	2	1	no	—
26	C₂²×D₄×C₁₁₃	—	2	2	no	—
27	C₂²×D₄×C₁₁₃	C₈	1	4	yes	complemented
28	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₁₃	—	2	8	no	—
30	C₂³×C₄×C₁₁₃	—	2	1	no	—
31	C₂³×C₄×C₁₁₃	—	2	2	no	—
32	C₂³×C₄×C₁₁₃	—	2	2	no	—
33	C₂³×C₄×C₁₁₃	—	4	4	no	—
34	C₂³×C₄×C₁₁₃	—	4	2	no	—
35	C₂³×C₄×C₁₁₃	—	4	2	no	—
36	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁₃	—	2	2	no	—
40	C₂²×C₈×C₁₁₃	—	2	2	no	—
41	C₄×D₄×C₁₁₃	—	2	8	no	—
42	C₄×D₄×C₁₁₃	—	2	8	no	—
43	C₄×D₄×C₁₁₃	—	2	4	no	—
44	C₄×D₄×C₁₁₃	—	2	4	no	—
45	C₄×D₄×C₁₁₃	—	2	4	no	—
46	C₄×D₄×C₁₁₃	D₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
53	C₂×C₄²×C₁₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₁₁₃	—	2	4	no	—
59	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
60	C₂²⋊C₈×C₁₁₃	—	4	2	no	—
61	C₄×C₈×C₁₁₃	—	2	4	no	—
62	C₂⁴×C₁₁₃	—	2	4	no	—
63	C₂⁴×C₁₁₃	—	2	4	no	—
64	C₂⁴×C₁₁₃	—	2	4	no	—
65	C₂⁴×C₁₁₃	—	2	2	no	—
66	C₂⁴×C₁₁₃	—	4	2	no	—
67	C₂⁴×C₁₁₃	—	4	2	no	—
68	C₂⁴×C₁₁₃	—	4	2	no	—
69	C₂⁴×C₁₁₃	—	4	2	no	—
70	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×D₄×C₁₁₃	—	2	4	no	—
72	C₂×D₄×C₁₁₃	—	2	4	no	—
73	C₂×D₄×C₁₁₃	—	2	16	no	—
74	C₂×D₄×C₁₁₃	—	2	16	no	—
75	C₂×D₄×C₁₁₃	—	2	4	no	—
76	C₂×D₄×C₁₁₃	—	2	2	no	—
77	C₂×D₄×C₁₁₃	—	2	2	no	—
78	C₂×D₄×C₁₁₃	—	2	2	no	—
79	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
80	C₂×D₄×C₁₁₃	C₂×C₈	1	4	yes	—
81	C₂×D₄×C₁₁₃	M₁₆	1	4	yes	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₁₃	—	4	16	no	—
95	C₂²×C₄×C₁₁₃	—	4	16	no	—
96	C₂²×C₄×C₁₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₁₃	—	4	4	no	—
99	C₂²×C₄×C₁₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₁₃	—	4	4	no	—
102	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁₃	C₂×C₈	1	2	yes	—
106	C₂²×C₄×C₁₁₃	M₁₆	1	2	yes	—
107	C₂²×C₄×C₁₁₃	D₈	1	2	yes	—
108	C₂²×C₄×C₁₁₃	SD₁₆	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁₃	—	2	4	no	—
113	C₂×C₈×C₁₁₃	—	4	2	no	—
114	C₂×C₈×C₁₁₃	—	4	2	no	—
115	C₂×C₈×C₁₁₃	—	4	2	no	—
116	C₂×C₈×C₁₁₃	—	4	2	no	—
117	C₂×C₈×C₁₁₃	—	4	2	no	—
118	C₄⋊C₄×C₁₁₃	—	2	4	no	—
119	C₄⋊C₄×C₁₁₃	—	2	2	no	—
120	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
122	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
123	C₄²×C₁₁₃	—	2	2	no	—
124	C₄²×C₁₁₃	—	2	2	no	—
125	C₄²×C₁₁₃	—	2	2	no	—
126	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
127	C₂³×C₁₁₃	—	2	1	no	—
128	C₂³×C₁₁₃	—	2	1	no	—
129	C₂³×C₁₁₃	—	2	1	no	—
130	C₂³×C₁₁₃	—	2	1	no	—
131	C₂³×C₁₁₃	—	2	16	no	—
132	C₂³×C₁₁₃	—	2	4	no	—
133	C₂³×C₁₁₃	—	2	4	no	—
134	C₂³×C₁₁₃	—	2	4	no	—
135	C₂³×C₁₁₃	—	4	8	no	—
136	C₂³×C₁₁₃	—	4	8	no	—
137	C₂³×C₁₁₃	—	4	8	no	—
138	C₂³×C₁₁₃	—	4	8	no	—
139	C₂³×C₁₁₃	—	4	8	no	—
140	C₂³×C₁₁₃	—	4	8	no	—
141	C₂³×C₁₁₃	—	4	2	no	—
142	C₂³×C₁₁₃	—	4	2	no	—
143	C₂³×C₁₁₃	—	4	2	no	—
144	C₂³×C₁₁₃	—	4	2	no	—
145	C₂³×C₁₁₃	C₂²⋊C₈	1	2	yes	—
146	C₂³×C₁₁₃	#102	1	2	yes	—
147	C₂³×C₁₁₃	#104	1	2	yes	—
148	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	D₄×C₁₁₃	—	2	16	no	—
150	D₄×C₁₁₃	—	2	4	no	—
151	D₄×C₁₁₃	—	2	4	no	—
152	D₄×C₁₁₃	—	2	4	no	—
153	D₄×C₁₁₃	C₂²⋊C₈	1	8	yes	complemented
154	C₂×C₄×C₁₁₃	—	2	1	no	—
155	C₂×C₄×C₁₁₃	—	2	1	no	—
156	C₂×C₄×C₁₁₃	—	2	1	no	—
157	C₂×C₄×C₁₁₃	—	2	1	no	—
158	C₂×C₄×C₁₁₃	—	2	1	no	—
159	C₂×C₄×C₁₁₃	—	2	1	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	2	1	no	—
165	C₂×C₄×C₁₁₃	—	2	4	no	—
166	C₂×C₄×C₁₁₃	—	2	1	no	—
167	C₂×C₄×C₁₁₃	—	2	1	no	—
168	C₂×C₄×C₁₁₃	—	4	4	no	—
169	C₂×C₄×C₁₁₃	—	4	16	no	—
170	C₂×C₄×C₁₁₃	—	4	8	no	—
171	C₂×C₄×C₁₁₃	—	4	2	no	—
172	C₂×C₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	4	8	no	—
174	C₂×C₄×C₁₁₃	—	4	8	no	—
175	C₂×C₄×C₁₁₃	C₂²⋊C₈	1	2	yes	—
176	C₂×C₄×C₁₁₃	#102	1	2	yes	—
177	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₁₃	#120	1	2	yes	—
180	C₂×C₄×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₁₃	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
183	C₂×C₄×C₁₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
186	C₈×C₁₁₃	—	4	4	no	—
187	C₈×C₁₁₃	—	8	2	no	—
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	2	2	no	—
190	C₂²×C₁₁₃	—	2	2	no	—
191	C₂²×C₁₁₃	—	2	2	no	—
192	C₂²×C₁₁₃	—	2	2	no	—
193	C₂²×C₁₁₃	—	2	2	no	—
194	C₂²×C₁₁₃	—	2	8	no	—
195	C₂²×C₁₁₃	—	4	32	no	—
196	C₂²×C₁₁₃	—	4	4	no	—
197	C₂²×C₁₁₃	—	4	4	no	—
198	C₂²×C₁₁₃	—	4	4	no	—
199	C₂²×C₁₁₃	—	4	4	no	—
200	C₂²×C₁₁₃	—	4	4	no	—
201	C₂²×C₁₁₃	—	4	4	no	—
202	C₂²×C₁₁₃	D₄⋊C₈	1	4	yes	complemented
203	C₂²×C₁₁₃	#379	1	1	yes	characteristic
204	C₂²×C₁₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
205	C₂²×C₁₁₃	#407	1	1	yes	characteristic
206	C₂²×C₁₁₃	C₂×#102	1	1	yes	characteristic
207	C₂²×C₁₁₃	#418	1	1	yes	characteristic
208	C₂²×C₁₁₃	C₂×#104	1	1	yes	characteristic
209	C₂²×C₁₁₃	#421	1	1	yes	characteristic
210	C₄×C₁₁₃	—	2	2	no	—
211	C₄×C₁₁₃	—	2	2	no	—
212	C₄×C₁₁₃	—	2	2	no	—
213	C₄×C₁₁₃	—	4	4	no	—
214	C₄×C₁₁₃	—	4	1	no	—
215	C₄×C₁₁₃	C₂×C₂²⋊C₈	1	2	yes	—
216	C₄×C₁₁₃	#407	1	2	yes	—
217	C₄×C₁₁₃	#447	1	2	yes	—
218	C₄×C₁₁₃	#450	1	2	yes	—
219	#8310	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₁₁₃	—	2	4	no	—
221	C₂×C₁₁₃	—	4	8	no	—
222	C₂×C₁₁₃	C₂×D₄⋊C₈	1	1	yes	characteristic
223	C₂×C₁₁₃	#1478	1	1	yes	characteristic
224	C₂×C₁₁₃	#1486	1	1	yes	characteristic
225	C₂×C₁₁₃	#1490	1	1	yes	characteristic
226	C₂×C₁₁₃	#1779	1	1	yes	characteristic
227	C₂×C₁₁₃	#1786	1	1	yes	characteristic
228	C₂×C₁₁₃	#1789	1	1	yes	characteristic
229	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
230	#1797	C₂×C₁₁₃	1	1	yes	characteristic, complemented
231	C₄×C₂²⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
232	C₂×D₄⋊C₈	C₂×C₁₁₃	1	4	yes	complemented
233	C₁₁₃	#8310	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³×D₄	C₄×C₁₁₃	1	1	yes	characteristic
235	C₂⁴×C₄	—	2	1	no	—
236	C₂×C₄×D₄	—	2	8	no	—
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₄×C₁₁₃	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	—	2	1	no	—
243	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	complemented
245	C₂×C₂²⋊C₈	—	2	1	no	—
246	C₂×C₂²⋊C₈	—	2	1	no	—
247	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	complemented
248	#336	—	2	1	no	—
249	#336	—	2	1	no	—
250	D₄⋊C₈	—	2	8	no	—
251	C₂⁵	—	2	1	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	C₈×C₁₁₃	1	4	yes	complemented
257	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
258	C₂³×C₄	—	2	8	no	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	—	4	2	no	—
264	C₂³×C₄	—	4	2	no	—
265	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
267	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	D₄×C₁₁₃	1	8	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
287	C₄⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	C₂²⋊C₈	—	4	2	no	—
290	C₄×C₈	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	4	2	no	—
296	C₂⁴	—	4	2	no	—
297	C₂⁴	—	4	2	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	16	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
309	C₂×D₄	C₂×C₈×C₁₁₃	1	4	yes	—
310	C₂×D₄	M₁₆×C₁₁₃	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	16	no	—
324	C₂²×C₄	—	4	16	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₈×C₁₁₃	1	2	yes	—
335	C₂²×C₄	M₁₆×C₁₁₃	1	2	yes	—
336	C₂²×C₄	D₈×C₁₁₃	1	2	yes	—
337	C₂²×C₄	SD₁₆×C₁₁₃	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	16	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	8	no	—
367	C₂³	—	4	8	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂²⋊C₈×C₁₁₃	1	2	yes	—
375	C₂³	#102×C₁₁₃	1	2	yes	—
376	C₂³	#104×C₁₁₃	1	2	yes	—
377	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
378	D₄	—	2	16	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	C₂²⋊C₈×C₁₁₃	1	8	yes	complemented
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	C₂²⋊C₈×C₁₁₃	1	2	yes	—
405	C₂×C₄	#102×C₁₁₃	1	2	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
407	C₂×C₄	#120×C₁₁₃	1	2	yes	—
408	C₂×C₄	#120×C₁₁₃	1	2	yes	—
409	C₂×C₄	C₂²×C₈×C₁₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×M₁₆×C₁₁₃	1	2	yes	—
411	C₂×C₄	C₂×M₁₆×C₁₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂×D₈×C₁₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	1	yes	characteristic
414	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
415	C₈	—	4	4	no	—
416	C₈	—	8	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	4	32	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	D₄⋊C₈×C₁₁₃	1	4	yes	complemented
432	C₂²	#379×C₁₁₃	1	1	yes	characteristic
433	C₂²	C₂×C₂²⋊C₈×C₁₁₃	1	1	yes	characteristic
434	C₂²	#407×C₁₁₃	1	1	yes	characteristic
435	C₂²	C₂×#102×C₁₁₃	1	1	yes	characteristic
436	C₂²	#418×C₁₁₃	1	1	yes	characteristic
437	C₂²	C₂×#104×C₁₁₃	1	1	yes	characteristic
438	C₂²	#421×C₁₁₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	1	no	—
444	C₄	C₂×C₂²⋊C₈×C₁₁₃	1	2	yes	—
445	C₄	#407×C₁₁₃	1	2	yes	—
446	C₄	#447×C₁₁₃	1	2	yes	—
447	C₄	#450×C₁₁₃	1	2	yes	—
448	C₂	—	2	4	no	—
449	C₂	—	4	8	no	—
450	C₂	C₂×D₄⋊C₈×C₁₁₃	1	1	yes	characteristic
451	C₂	C₁₁₃×#1478	1	1	yes	characteristic
452	C₂	C₁₁₃×#1486	1	1	yes	characteristic
453	C₂	C₁₁₃×#1490	1	1	yes	characteristic
454	C₂	C₁₁₃×#1779	1	1	yes	characteristic
455	C₂	C₁₁₃×#1786	1	1	yes	characteristic
456	C₂	C₁₁₃×#1789	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁₃
socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₁₁₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#1797	C₂	semidirect
3. C₄×C₂²⋊C₈×C₁₁₃	C₂	semidirect
4. C₂×D₄⋊C₈×C₁₁₃	C₂	semidirect
15. C₂×C₄⋊C₈×C₁₁₃	C₂²	semidirect
18. C₂×C₄×C₈×C₁₁₃	C₂²	semidirect
27. C₂²×D₄×C₁₁₃	C₈	semidirect
153. D₄×C₁₁₃	C₂²⋊C₈	semidirect
202. C₂²×C₁₁₃	D₄⋊C₈	semidirect
219. #8310	C₁₁₃	direct (N × H)
230. #1797	C₂×C₁₁₃	semidirect
231. C₄×C₂²⋊C₈	C₂×C₁₁₃	semidirect
232. C₂×D₄⋊C₈	C₂×C₁₁₃	semidirect
233. C₁₁₃	#8310	direct (N × H)
244. C₂×C₄⋊C₈	C₂²×C₁₁₃	semidirect
247. C₂×C₄×C₈	C₂²×C₁₁₃	semidirect
256. C₂²×D₄	C₈×C₁₁₃	semidirect
382. D₄	C₂²⋊C₈×C₁₁₃	semidirect
431. C₂²	D₄⋊C₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₁₃	2
C₁₁₃×#1797	2
C₄×C₂²⋊C₈×C₁₁₃	2
C₂×D₄⋊C₈×C₁₁₃	2
#8310	113

Subgroups — C113×#8310 #43276330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#8310 #43276330