Subgroups — C₁₁₃×#10715 #43278735

Order 28928.

1534 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#336×C₁₁₃	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₁₃	—	2	2	no	—
7	C₂²×M₁₆×C₁₁₃	—	2	2	no	—
8	C₂²×M₁₆×C₁₁₃	—	2	8	no	—
9	C₂²×M₁₆×C₁₁₃	C₄	1	4	yes	complemented
10	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₁₃	C₄	1	2	yes	—
13	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₈×C₁₁₃	—	2	2	no	—
15	C₂×C₂²⋊C₈×C₁₁₃	—	2	2	no	—
16	C₂×C₂²⋊C₈×C₁₁₃	C₄	1	4	yes	complemented
17	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
19	C₂×#95×C₁₁₃	C₄	1	2	yes	—
20	#336×C₁₁₃	—	2	8	no	—
21	C₂⁵×C₁₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₁₃	—	2	4	no	—
23	C₂³×C₄×C₁₁₃	—	2	4	no	—
24	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
29	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
30	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
31	C₂³×C₄×C₁₁₃	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₁₃	—	2	16	no	—
34	C₂×M₁₆×C₁₁₃	—	2	16	no	—
35	C₂×M₁₆×C₁₁₃	—	2	8	no	—
36	C₂×M₁₆×C₁₁₃	—	2	16	no	—
37	C₂²×C₈×C₁₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₁₃	—	2	4	no	—
41	C₂²×C₈×C₁₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₁₃	D₄	1	8	yes	—
47	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
49	C₂×C₄²×C₁₁₃	—	2	4	no	—
50	C₂×C₄²×C₁₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₁₃	—	2	4	no	—
53	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
54	#95×C₁₁₃	—	2	4	no	—
55	C₂⁴×C₁₁₃	—	2	4	no	—
56	C₂⁴×C₁₁₃	—	2	4	no	—
57	C₂⁴×C₁₁₃	—	2	4	no	—
58	C₂⁴×C₁₁₃	C₄²	1	2	yes	—
59	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₁₁₃	C₄⋊C₄	1	2	yes	—
61	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₁₃	—	2	8	no	—
66	C₂²×C₄×C₁₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₁₃	—	2	8	no	—
69	C₂²×C₄×C₁₁₃	—	2	8	no	—
70	C₂²×C₄×C₁₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₁₃	—	2	8	no	—
74	C₂²×C₄×C₁₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₁₃	—	2	8	no	—
76	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
77	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
79	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
80	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₁₁₃	M₁₆	1	8	yes	complemented
84	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
92	M₁₆×C₁₁₃	—	2	32	no	—
93	C₂×C₈×C₁₁₃	—	2	4	no	—
94	C₂×C₈×C₁₁₃	—	2	4	no	—
95	C₂×C₈×C₁₁₃	—	2	8	no	—
96	C₂×C₈×C₁₁₃	—	2	8	no	—
97	C₂×C₈×C₁₁₃	—	2	4	no	—
98	C₂×C₈×C₁₁₃	—	2	8	no	—
99	C₂×C₈×C₁₁₃	—	4	2	no	—
100	C₂×C₈×C₁₁₃	—	4	4	no	—
101	C₂×C₈×C₁₁₃	—	4	2	no	—
102	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	8	yes	complemented
103	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
104	C₄²×C₁₁₃	—	4	2	no	—
105	C₄²×C₁₁₃	—	4	4	no	—
106	C₄²×C₁₁₃	—	4	2	no	—
107	C₂³×C₁₁₃	—	2	4	no	—
108	C₂³×C₁₁₃	—	2	4	no	—
109	C₂³×C₁₁₃	—	2	4	no	—
110	C₂³×C₁₁₃	—	2	4	no	—
111	C₂³×C₁₁₃	—	2	4	no	—
112	C₂³×C₁₁₃	—	2	4	no	—
113	C₂³×C₁₁₃	—	2	4	no	—
114	C₂³×C₁₁₃	—	2	4	no	—
115	C₂³×C₁₁₃	—	2	4	no	—
116	C₂³×C₁₁₃	—	4	8	no	—
117	C₂³×C₁₁₃	—	4	8	no	—
118	C₂³×C₁₁₃	#95	1	4	yes	—
119	C₂³×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
120	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₁₃	C₄×D₄	1	4	yes	—
123	C₂³×C₁₁₃	C₂×M₁₆	1	4	yes	—
124	C₂³×C₁₁₃	#131	1	4	yes	—
125	C₂×C₄×C₁₁₃	—	2	4	no	—
126	C₂×C₄×C₁₁₃	—	2	4	no	—
127	C₂×C₄×C₁₁₃	—	2	4	no	—
128	C₂×C₄×C₁₁₃	—	2	4	no	—
129	C₂×C₄×C₁₁₃	—	2	8	no	—
130	C₂×C₄×C₁₁₃	—	2	4	no	—
131	C₂×C₄×C₁₁₃	—	2	8	no	—
132	C₂×C₄×C₁₁₃	—	2	8	no	—
133	C₂×C₄×C₁₁₃	—	2	8	no	—
134	C₂×C₄×C₁₁₃	—	2	16	no	—
135	C₂×C₄×C₁₁₃	—	4	4	no	—
136	C₂×C₄×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	—	4	8	no	—
138	C₂×C₄×C₁₁₃	#95	1	4	yes	—
139	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁₃	#117	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₁₁₃	#120	1	2	yes	—
147	C₂×C₄×C₁₁₃	#120	1	2	yes	—
148	C₂×C₄×C₁₁₃	#121	1	4	yes	—
149	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₁₁₃	#123	1	2	yes	—
151	C₂×C₄×C₁₁₃	#123	1	2	yes	—
152	C₈×C₁₁₃	—	2	8	no	—
153	C₈×C₁₁₃	—	4	4	no	—
154	C₂²×C₁₁₃	—	2	4	no	—
155	C₂²×C₁₁₃	—	2	4	no	—
156	C₂²×C₁₁₃	—	2	4	no	—
157	C₂²×C₁₁₃	—	4	8	no	—
158	C₂²×C₁₁₃	—	4	8	no	—
159	C₂²×C₁₁₃	—	4	8	no	—
160	C₂²×C₁₁₃	C₂×#95	1	1	yes	characteristic
161	C₂²×C₁₁₃	C₄×C₂²⋊C₄	1	2	yes	—
162	C₂²×C₁₁₃	#385	1	2	yes	—
163	C₂²×C₁₁₃	#386	1	2	yes	—
164	C₂²×C₁₁₃	C₄×M₁₆	1	2	yes	—
165	C₂²×C₁₁₃	#405	1	2	yes	—
166	C₂²×C₁₁₃	#407	1	2	yes	—
167	C₂²×C₁₁₃	#408	1	2	yes	—
168	C₂²×C₁₁₃	#423	1	2	yes	—
169	C₂²×C₁₁₃	#424	1	2	yes	—
170	C₂²×C₁₁₃	#435	1	8	yes	—
171	C₂²×C₁₁₃	#436	1	8	yes	—
172	C₄×C₁₁₃	—	2	4	no	—
173	C₄×C₁₁₃	—	4	8	no	—
174	C₄×C₁₁₃	#379	1	1	yes	characteristic
175	C₄×C₁₁₃	#380	1	2	yes	—
176	C₄×C₁₁₃	#381	1	1	yes	characteristic
177	C₄×C₁₁₃	#385	1	2	yes	—
178	C₄×C₁₁₃	#386	1	2	yes	—
179	#10715	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₁₁₃	—	4	4	no	—
181	C₂×C₁₁₃	C₂²⋊#95	1	1	yes	characteristic
182	C₂×C₁₁₃	#1728	1	1	yes	characteristic
183	C₂×C₁₁₃	#1729	1	1	yes	characteristic
184	C₂×C₁₁₃	#1753	1	4	yes	—
185	C₂×C₁₁₃	#1851	1	4	yes	—
186	C₂×C₁₁₃	#1870	1	4	yes	—
187	C₂³×M₁₆	C₂×C₁₁₃	1	1	yes	characteristic
188	C₂²×C₂²⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic
189	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
190	C₂×#336	C₂×C₁₁₃	1	4	yes	complemented
191	C₁₁₃	#10715	1	1	yes	characteristic, direct product factor, Sylow
192	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
193	C₂²×M₁₆	—	2	2	no	—
194	C₂²×M₁₆	—	2	2	no	—
195	C₂²×M₁₆	—	2	8	no	—
196	C₂²×M₁₆	C₄×C₁₁₃	1	4	yes	complemented
197	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
198	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
199	C₂²×C₂²⋊C₄	C₄×C₁₁₃	1	2	yes	—
200	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
201	C₂×C₂²⋊C₈	—	2	2	no	—
202	C₂×C₂²⋊C₈	—	2	2	no	—
203	C₂×C₂²⋊C₈	C₄×C₁₁₃	1	4	yes	complemented
204	C₄×C₂²⋊C₄	—	2	2	no	—
205	C₄×C₂²⋊C₄	—	2	2	no	—
206	C₂×#95	C₄×C₁₁₃	1	2	yes	—
207	#336	—	2	8	no	—
208	C₂⁵	C₂×C₄×C₁₁₃	1	1	yes	characteristic
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	4	no	—
211	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
212	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
214	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
215	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
216	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
217	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
218	C₂³×C₄	Q₈×C₁₁₃	1	2	yes	—
219	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
220	C₂×M₁₆	—	2	16	no	—
221	C₂×M₁₆	—	2	16	no	—
222	C₂×M₁₆	—	2	8	no	—
223	C₂×M₁₆	—	2	16	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
232	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
233	C₂²×C₈	D₄×C₁₁₃	1	8	yes	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	8	no	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	4	no	—
240	C₂²⋊C₈	—	2	8	no	—
241	#95	—	2	4	no	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	C₄²×C₁₁₃	1	2	yes	—
246	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
247	C₂⁴	C₄⋊C₄×C₁₁₃	1	2	yes	—
248	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	C₄²×C₁₁₃	1	2	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
265	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
266	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
267	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
268	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
269	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
270	C₂²×C₄	M₁₆×C₁₁₃	1	8	yes	complemented
271	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
278	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
279	M₁₆	—	2	32	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
290	C₂²⋊C₄	—	2	16	no	—
291	C₄²	—	4	2	no	—
292	C₄²	—	4	4	no	—
293	C₄²	—	4	2	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	8	no	—
305	C₂³	#95×C₁₁₃	1	4	yes	—
306	C₂³	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
307	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
309	C₂³	C₄×D₄×C₁₁₃	1	4	yes	—
310	C₂³	C₂×M₁₆×C₁₁₃	1	4	yes	—
311	C₂³	#131×C₁₁₃	1	4	yes	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	#95×C₁₁₃	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
331	C₂×C₄	#117×C₁₁₃	1	2	yes	—
332	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
333	C₂×C₄	#120×C₁₁₃	1	2	yes	—
334	C₂×C₄	#120×C₁₁₃	1	2	yes	—
335	C₂×C₄	#121×C₁₁₃	1	4	yes	—
336	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
337	C₂×C₄	#123×C₁₁₃	1	2	yes	—
338	C₂×C₄	#123×C₁₁₃	1	2	yes	—
339	C₈	—	2	8	no	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	4	8	no	—
346	C₂²	—	4	8	no	—
347	C₂²	C₂×#95×C₁₁₃	1	1	yes	characteristic
348	C₂²	C₄×C₂²⋊C₄×C₁₁₃	1	2	yes	—
349	C₂²	#385×C₁₁₃	1	2	yes	—
350	C₂²	#386×C₁₁₃	1	2	yes	—
351	C₂²	C₄×M₁₆×C₁₁₃	1	2	yes	—
352	C₂²	#405×C₁₁₃	1	2	yes	—
353	C₂²	#407×C₁₁₃	1	2	yes	—
354	C₂²	#408×C₁₁₃	1	2	yes	—
355	C₂²	#423×C₁₁₃	1	2	yes	—
356	C₂²	#424×C₁₁₃	1	2	yes	—
357	C₂²	#435×C₁₁₃	1	8	yes	—
358	C₂²	#436×C₁₁₃	1	8	yes	—
359	C₄	—	2	4	no	—
360	C₄	—	4	8	no	—
361	C₄	#379×C₁₁₃	1	1	yes	characteristic
362	C₄	#380×C₁₁₃	1	2	yes	—
363	C₄	#381×C₁₁₃	1	1	yes	characteristic
364	C₄	#385×C₁₁₃	1	2	yes	—
365	C₄	#386×C₁₁₃	1	2	yes	—
366	C₂	—	4	4	no	—
367	C₂	C₁₁₃×C₂²⋊#95	1	1	yes	characteristic
368	C₂	C₁₁₃×#1728	1	1	yes	characteristic
369	C₂	C₁₁₃×#1729	1	1	yes	characteristic
370	C₂	C₁₁₃×#1753	1	4	yes	—
371	C₂	C₁₁₃×#1851	1	4	yes	—
372	C₂	C₁₁₃×#1870	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁₃	C₂³
commutator	C₂³	C₂×C₄²×C₁₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁₃
socle	C₂⁴×C₁₁₃	C₂²×C₄
prime radical	C₂⁵×C₁₁₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#336×C₁₁₃	C₂	semidirect
9. C₂²×M₁₆×C₁₁₃	C₄	semidirect
16. C₂×C₂²⋊C₈×C₁₁₃	C₄	semidirect
83. C₂²×C₄×C₁₁₃	M₁₆	semidirect
102. C₂×C₈×C₁₁₃	C₂²⋊C₄	semidirect
179. #10715	C₁₁₃	direct (N × H)
190. C₂×#336	C₂×C₁₁₃	semidirect
191. C₁₁₃	#10715	direct (N × H)
196. C₂²×M₁₆	C₄×C₁₁₃	semidirect
203. C₂×C₂²⋊C₈	C₄×C₁₁₃	semidirect
270. C₂²×C₄	M₁₆×C₁₁₃	semidirect
289. C₂×C₈	C₂²⋊C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₁₃	2
C₂²×C₂²⋊C₈×C₁₁₃	2
C₂×C₄×C₂²⋊C₄×C₁₁₃	2
C₂×#336×C₁₁₃	2
#10715	113

Subgroups — C113×#10715 #43278735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#10715 #43278735