Subgroups — C₁₁₃×#22302 #43290322

Order 28928.

598 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#2402	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#1940	C₂	1	2	yes	maximal
3	C₁₁₃×#1940	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1940	C₂	1	1	yes	maximal, characteristic
5	C₁₁₃×#1939	C₂	1	2	yes	maximal
6	C₁₁₃×#1917	C₂	1	2	yes	maximal
7	C₁₁₃×#1916	C₂	1	2	yes	maximal
8	C₁₁₃×#1843	C₂	1	1	yes	maximal, characteristic
9	C₁₁₃×#1770	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
11	C₁₁₃×#1746	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
18	C₂×#97×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂×#97×C₁₁₃	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
22	#400×C₁₁₃	C₄	1	2	yes	—
23	#400×C₁₁₃	C₄	1	2	yes	—
24	#398×C₁₁₃	C₄	1	2	yes	—
25	#398×C₁₁₃	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
30	#376×C₁₁₃	C₂²	1	1	yes	characteristic
31	#336×C₁₁₃	C₂²	1	2	yes	—
32	#336×C₁₁₃	C₂²	1	2	yes	—
33	#336×C₁₁₃	C₂²	1	1	yes	characteristic
34	#336×C₁₁₃	C₂²	1	2	yes	—
35	#336×C₁₁₃	C₂²	1	2	yes	—
36	#336×C₁₁₃	C₂²	1	1	yes	characteristic
37	#336×C₁₁₃	C₂²	1	1	yes	characteristic
38	#336×C₁₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₁₁₃	—	2	2	no	—
57	C₄⋊C₈×C₁₁₃	—	2	2	no	—
58	C₄⋊C₈×C₁₁₃	—	4	2	no	—
59	C₄⋊C₈×C₁₁₃	—	4	2	no	—
60	C₄⋊C₈×C₁₁₃	—	4	2	no	—
61	C₄⋊C₈×C₁₁₃	—	4	2	no	—
62	#97×C₁₁₃	—	2	2	no	—
63	#97×C₁₁₃	—	4	2	no	—
64	C₄×C₈×C₁₁₃	—	4	2	no	—
65	C₄×C₈×C₁₁₃	Q₈	1	4	yes	—
66	#95×C₁₁₃	C₂×C₄	1	2	yes	—
67	#95×C₁₁₃	C₂×C₄	1	2	yes	—
68	#95×C₁₁₃	C₂×C₄	1	1	yes	characteristic
69	#95×C₁₁₃	C₂×C₄	1	1	yes	characteristic
70	#95×C₁₁₃	C₂×C₄	1	2	yes	—
71	#95×C₁₁₃	C₂×C₄	1	2	yes	—
72	#95×C₁₁₃	C₂×C₄	1	2	yes	—
73	#95×C₁₁₃	C₂×C₄	1	2	yes	—
74	#95×C₁₁₃	C₂×C₄	1	1	yes	characteristic
75	#95×C₁₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₁₃	—	2	1	no	—
86	C₂×C₈×C₁₁₃	—	2	1	no	—
87	C₂×C₈×C₁₁₃	—	2	1	no	—
88	C₂×C₈×C₁₁₃	—	2	1	no	—
89	C₂×C₈×C₁₁₃	—	2	1	no	—
90	C₂×C₈×C₁₁₃	—	2	1	no	—
91	C₂×C₈×C₁₁₃	—	2	2	no	—
92	C₂×C₈×C₁₁₃	—	2	2	no	—
93	C₂×C₈×C₁₁₃	—	2	2	no	—
94	C₂×C₈×C₁₁₃	—	2	2	no	—
95	C₂×C₈×C₁₁₃	—	2	2	no	—
96	C₂×C₈×C₁₁₃	—	2	1	no	—
97	C₂×C₈×C₁₁₃	—	2	1	no	—
98	C₂×C₈×C₁₁₃	—	2	2	no	—
99	C₂×C₈×C₁₁₃	—	2	1	no	—
100	C₂×C₈×C₁₁₃	—	2	1	no	—
101	C₂×C₈×C₁₁₃	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₁₁₃	C₂×Q₈	1	2	yes	—
103	C₄⋊C₄×C₁₁₃	—	2	4	no	—
104	C₄⋊C₄×C₁₁₃	—	2	4	no	—
105	C₄⋊C₄×C₁₁₃	—	2	4	no	—
106	C₄⋊C₄×C₁₁₃	—	4	2	no	—
107	C₄⋊C₄×C₁₁₃	—	4	2	no	—
108	C₄⋊C₄×C₁₁₃	—	4	2	no	—
109	C₄²×C₁₁₃	—	2	2	no	—
110	C₄²×C₁₁₃	—	2	2	no	—
111	C₄²×C₁₁₃	—	2	1	no	—
112	C₄²×C₁₁₃	—	2	1	no	—
113	C₄²×C₁₁₃	—	2	2	no	—
114	C₄²×C₁₁₃	—	2	1	no	—
115	C₄²×C₁₁₃	—	2	1	no	—
116	C₄²×C₁₁₃	—	2	2	no	—
117	C₄²×C₁₁₃	C₂×Q₈	1	2	yes	—
118	C₄²×C₁₁₃	#41	1	2	yes	—
119	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁₃	—	2	2	no	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	2	no	—
123	C₂×C₄×C₁₁₃	—	2	2	no	—
124	C₂×C₄×C₁₁₃	—	2	2	no	—
125	C₂×C₄×C₁₁₃	—	2	2	no	—
126	C₂×C₄×C₁₁₃	—	2	2	no	—
127	C₂×C₄×C₁₁₃	—	2	2	no	—
128	C₂×C₄×C₁₁₃	—	2	2	no	—
129	C₂×C₄×C₁₁₃	—	2	2	no	—
130	C₂×C₄×C₁₁₃	—	2	2	no	—
131	C₂×C₄×C₁₁₃	—	2	2	no	—
132	C₂×C₄×C₁₁₃	—	2	2	no	—
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	2	no	—
135	C₂×C₄×C₁₁₃	—	2	2	no	—
136	C₂×C₄×C₁₁₃	—	2	2	no	—
137	C₂×C₄×C₁₁₃	—	2	2	no	—
138	C₂×C₄×C₁₁₃	—	2	2	no	—
139	C₂×C₄×C₁₁₃	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₁₁₃	#131	1	4	yes	—
142	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
146	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
147	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
148	C₈×C₁₁₃	—	2	2	no	—
149	C₈×C₁₁₃	—	2	2	no	—
150	C₈×C₁₁₃	—	4	1	no	—
151	C₈×C₁₁₃	—	4	2	no	—
152	C₈×C₁₁₃	—	4	2	no	—
153	C₈×C₁₁₃	—	4	1	no	—
154	C₂²×C₁₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
155	C₂²×C₁₁₃	#520	1	1	yes	characteristic
156	C₂²×C₁₁₃	#520	1	1	yes	characteristic
157	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
158	C₂²×C₁₁₃	#568	1	2	yes	—
159	C₄×C₁₁₃	—	2	2	no	—
160	C₄×C₁₁₃	—	2	2	no	—
161	C₄×C₁₁₃	—	2	4	no	—
162	C₄×C₁₁₃	—	4	2	no	—
163	C₄×C₁₁₃	—	4	2	no	—
164	C₄×C₁₁₃	—	4	2	no	—
165	C₄×C₁₁₃	—	4	2	no	—
166	C₄×C₁₁₃	—	4	2	no	—
167	C₄×C₁₁₃	#540	1	1	yes	characteristic
168	C₄×C₁₁₃	#541	1	1	yes	characteristic
169	C₄×C₁₁₃	#544	1	1	yes	characteristic
170	C₄×C₁₁₃	#544	1	1	yes	characteristic
171	#22302	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₁₁₃	#2330	1	1	yes	characteristic
173	C₂×C₁₁₃	#2960	1	1	yes	characteristic
174	C₂×C₁₁₃	#2961	1	1	yes	characteristic
175	C₂×C₁₁₃	#2992	1	2	yes	—
176	C₂×C₁₁₃	#2993	1	2	yes	—
177	#2402	C₂×C₁₁₃	1	1	yes	characteristic
178	#1940	C₂×C₁₁₃	1	1	yes	characteristic
179	#1940	C₂×C₁₁₃	1	1	yes	characteristic
180	#1940	C₂×C₁₁₃	1	2	yes	—
181	#1939	C₂×C₁₁₃	1	2	yes	—
182	#1917	C₂×C₁₁₃	1	2	yes	—
183	#1916	C₂×C₁₁₃	1	2	yes	—
184	#1843	C₂×C₁₁₃	1	1	yes	characteristic
185	#1770	C₂×C₁₁₃	1	1	yes	characteristic
186	C₈×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
187	#1746	C₂×C₁₁₃	1	1	yes	characteristic
188	C₁₁₃	#22302	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
195	C₂×#97	C₂²×C₁₁₃	1	1	yes	characteristic
196	C₂×#97	C₂²×C₁₁₃	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
199	#400	C₄×C₁₁₃	1	2	yes	—
200	#400	C₄×C₁₁₃	1	2	yes	—
201	#398	C₄×C₁₁₃	1	2	yes	—
202	#398	C₄×C₁₁₃	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
207	#376	C₂²×C₁₁₃	1	1	yes	characteristic
208	#336	C₂²×C₁₁₃	1	1	yes	characteristic
209	#336	C₂²×C₁₁₃	1	2	yes	—
210	#336	C₂²×C₁₁₃	1	2	yes	—
211	#336	C₂²×C₁₁₃	1	2	yes	—
212	#336	C₂²×C₁₁₃	1	1	yes	characteristic
213	#336	C₂²×C₁₁₃	1	2	yes	—
214	#336	C₂²×C₁₁₃	1	1	yes	characteristic
215	#336	C₂²×C₁₁₃	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
228	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
231	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
232	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	4	2	no	—
236	C₄⋊C₈	—	4	2	no	—
237	C₄⋊C₈	—	4	2	no	—
238	C₄⋊C₈	—	4	2	no	—
239	#97	—	2	2	no	—
240	#97	—	4	2	no	—
241	C₄×C₈	—	4	2	no	—
242	C₄×C₈	Q₈×C₁₁₃	1	4	yes	—
243	#95	C₂×C₄×C₁₁₃	1	2	yes	—
244	#95	C₂×C₄×C₁₁₃	1	2	yes	—
245	#95	C₂×C₄×C₁₁₃	1	1	yes	characteristic
246	#95	C₂×C₄×C₁₁₃	1	1	yes	characteristic
247	#95	C₂×C₄×C₁₁₃	1	2	yes	—
248	#95	C₂×C₄×C₁₁₃	1	2	yes	—
249	#95	C₂×C₄×C₁₁₃	1	2	yes	—
250	#95	C₂×C₄×C₁₁₃	1	2	yes	—
251	#95	C₂×C₄×C₁₁₃	1	1	yes	characteristic
252	#95	C₂×C₄×C₁₁₃	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
261	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	C₂×Q₈×C₁₁₃	1	2	yes	—
279	C₂×C₈	C₂×Q₈×C₁₁₃	1	2	yes	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	2	no	—
294	C₄²	C₂×Q₈×C₁₁₃	1	2	yes	—
295	C₄²	#41×C₁₁₃	1	2	yes	—
296	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	C₄×Q₈×C₁₁₃	1	2	yes	—
317	C₂×C₄	C₄×Q₈×C₁₁₃	1	2	yes	—
318	C₂×C₄	#131×C₁₁₃	1	4	yes	—
319	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
321	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
322	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
323	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
324	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
325	C₈	—	2	2	no	—
326	C₈	—	2	2	no	—
327	C₈	—	4	1	no	—
328	C₈	—	4	2	no	—
329	C₈	—	4	2	no	—
330	C₈	—	4	1	no	—
331	C₂²	C₂×C₄×Q₈×C₁₁₃	1	1	yes	characteristic
332	C₂²	#520×C₁₁₃	1	1	yes	characteristic
333	C₂²	#520×C₁₁₃	1	1	yes	characteristic
334	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
335	C₂²	#568×C₁₁₃	1	2	yes	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	4	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	2	no	—
341	C₄	—	4	2	no	—
342	C₄	—	4	2	no	—
343	C₄	—	4	2	no	—
344	C₄	#540×C₁₁₃	1	1	yes	characteristic
345	C₄	#541×C₁₁₃	1	1	yes	characteristic
346	C₄	#544×C₁₁₃	1	1	yes	characteristic
347	C₄	#544×C₁₁₃	1	1	yes	characteristic
348	C₂	C₁₁₃×#2330	1	1	yes	characteristic
349	C₂	C₁₁₃×#2960	1	1	yes	characteristic
350	C₂	C₁₁₃×#2961	1	1	yes	characteristic
351	C₂	C₁₁₃×#2992	1	2	yes	—
352	C₂	C₁₁₃×#2993	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
171. #22302	C₁₁₃	direct (N × H)
188. C₁₁₃	#22302	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁₃×#2402	2
C₁₁₃×#1940	2
C₁₁₃×#1939	2
C₁₁₃×#1917	2
C₁₁₃×#1916	2
C₁₁₃×#1843	2
C₁₁₃×#1770	2
C₈×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1746	2
#22302	113

Subgroups — C113×#22302 #43290322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#22302 #43290322