Subgroups — C₁₁₃×#21922 #43289942

Order 28928.

798 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	C₄×#117×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#1923	C₂	1	4	yes	maximal
3	C₁₁₃×#1916	C₂	1	4	yes	maximal, complemented
4	C₁₁₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#1797	C₂	1	2	yes	maximal
7	C₄×C₄⋊C₈×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	C₂×#117×C₁₁₃	C₄	1	1	yes	characteristic
9	C₂×#117×C₁₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	4	yes	—
14	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₁₁₃	C₂²	1	4	yes	—
16	C₄×C₄⋊C₄×C₁₁₃	C₄	1	2	yes	—
17	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
18	C₄×C₂²⋊C₄×C₁₁₃	C₄	1	2	yes	—
19	C₄×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
20	#376×C₁₁₃	C₄	1	1	yes	characteristic
21	#376×C₁₁₃	C₄	1	1	yes	characteristic
22	C₄³×C₁₁₃	C₂²	1	1	yes	characteristic
23	C₄³×C₁₁₃	C₂²	1	1	yes	characteristic
24	#336×C₁₁₃	C₂²	1	4	yes	—
25	#336×C₁₁₃	C₂²	1	4	yes	—
26	#336×C₁₁₃	C₂²	1	4	yes	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
31	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
32	#117×C₁₁₃	—	2	4	no	—
33	#117×C₁₁₃	C₈	1	8	yes	complemented
34	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₁₃	—	2	2	no	—
39	C₂×C₄²×C₁₁₃	—	2	2	no	—
40	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₁₁₃	—	2	4	no	—
53	C₄⋊C₈×C₁₁₃	—	2	4	no	—
54	C₄⋊C₈×C₁₁₃	—	4	4	no	—
55	C₂²⋊C₈×C₁₁₃	—	4	4	no	—
56	C₄×C₈×C₁₁₃	—	4	4	no	—
57	#95×C₁₁₃	C₂×C₄	1	2	yes	—
58	#95×C₁₁₃	C₂×C₄	1	2	yes	—
59	#95×C₁₁₃	C₂×C₄	1	2	yes	—
60	#95×C₁₁₃	C₂×C₄	1	2	yes	—
61	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₁₃	—	2	2	no	—
65	C₂²×C₄×C₁₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₁₃	C₂×C₈	1	4	yes	—
71	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₁₁₃	—	2	4	no	—
82	C₂×C₈×C₁₁₃	—	2	4	no	—
83	C₂×C₈×C₁₁₃	—	2	4	no	—
84	C₂×C₈×C₁₁₃	—	2	4	no	—
85	C₂×C₈×C₁₁₃	—	2	4	no	—
86	C₂×C₈×C₁₁₃	—	2	4	no	—
87	C₄⋊C₄×C₁₁₃	—	2	4	no	—
88	C₄⋊C₄×C₁₁₃	C₂×C₈	1	8	yes	—
89	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
90	C₂²⋊C₄×C₁₁₃	C₂×C₈	1	8	yes	—
91	C₄²×C₁₁₃	—	2	2	no	—
92	C₄²×C₁₁₃	—	2	2	no	—
93	C₄²×C₁₁₃	—	2	2	no	—
94	C₄²×C₁₁₃	—	2	1	no	—
95	C₄²×C₁₁₃	—	2	1	no	—
96	C₄²×C₁₁₃	—	2	2	no	—
97	C₄²×C₁₁₃	—	2	2	no	—
98	C₄²×C₁₁₃	—	2	2	no	—
99	C₄²×C₁₁₃	—	2	2	no	—
100	C₄²×C₁₁₃	—	4	2	no	—
101	C₄²×C₁₁₃	—	4	2	no	—
102	C₄²×C₁₁₃	C₂×C₈	1	4	yes	—
103	C₄²×C₁₁₃	C₂×C₈	1	4	yes	—
104	C₄²×C₁₁₃	M₁₆	1	4	yes	—
105	C₄²×C₁₁₃	#41	1	2	yes	—
106	C₄²×C₁₁₃	#41	1	2	yes	—
107	C₂³×C₁₁₃	—	2	1	no	—
108	C₂³×C₁₁₃	—	2	2	no	—
109	C₂³×C₁₁₃	—	2	1	no	—
110	C₂³×C₁₁₃	—	2	2	no	—
111	C₂³×C₁₁₃	C₂²×C₈	1	2	yes	—
112	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁₃	—	2	1	no	—
114	C₂×C₄×C₁₁₃	—	2	2	no	—
115	C₂×C₄×C₁₁₃	—	2	2	no	—
116	C₂×C₄×C₁₁₃	—	2	2	no	—
117	C₂×C₄×C₁₁₃	—	2	1	no	—
118	C₂×C₄×C₁₁₃	—	2	2	no	—
119	C₂×C₄×C₁₁₃	—	2	2	no	—
120	C₂×C₄×C₁₁₃	—	2	2	no	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	8	no	—
123	C₂×C₄×C₁₁₃	—	2	1	no	—
124	C₂×C₄×C₁₁₃	—	2	1	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	—	4	4	no	—
131	C₂×C₄×C₁₁₃	—	4	1	no	—
132	C₂×C₄×C₁₁₃	—	4	1	no	—
133	C₂×C₄×C₁₁₃	—	4	2	no	—
134	C₂×C₄×C₁₁₃	#117	1	2	yes	—
135	C₂×C₄×C₁₁₃	#117	1	2	yes	—
136	C₂×C₄×C₁₁₃	C₂²×C₈	1	4	yes	—
137	C₂×C₄×C₁₁₃	C₂²×C₈	1	4	yes	—
138	C₂×C₄×C₁₁₃	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₁₁₃	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₁₁₃	C₂×M₁₆	1	2	yes	—
142	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
145	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
146	C₈×C₁₁₃	—	4	4	no	—
147	C₈×C₁₁₃	—	4	4	no	—
148	C₂²×C₁₁₃	—	2	2	no	—
149	C₂²×C₁₁₃	—	2	4	no	—
150	C₂²×C₁₁₃	—	4	1	no	—
151	C₂²×C₁₁₃	—	4	1	no	—
152	C₂²×C₁₁₃	—	4	2	no	—
153	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
154	C₂²×C₁₁₃	#520	1	2	yes	—
155	C₂²×C₁₁₃	C₂³×C₈	1	1	yes	characteristic
156	C₂²×C₁₁₃	C₂²×M₁₆	1	1	yes	characteristic
157	C₂²×C₁₁₃	#568	1	2	yes	—
158	C₄×C₁₁₃	—	2	2	no	—
159	C₄×C₁₁₃	—	2	2	no	—
160	C₄×C₁₁₃	—	2	4	no	—
161	C₄×C₁₁₃	—	2	4	no	—
162	C₄×C₁₁₃	—	2	4	no	—
163	C₄×C₁₁₃	—	4	1	no	—
164	C₄×C₁₁₃	—	4	1	no	—
165	C₄×C₁₁₃	—	4	2	no	—
166	C₄×C₁₁₃	#431	1	4	yes	—
167	C₄×C₁₁₃	#540	1	1	yes	characteristic
168	C₄×C₁₁₃	#541	1	1	yes	characteristic
169	C₄×C₁₁₃	#542	1	2	yes	—
170	#21922	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂×C₁₁₃	—	4	2	no	—
172	C₂×C₁₁₃	#2314	1	1	yes	characteristic
173	C₂×C₁₁₃	C₂×#431	1	1	yes	characteristic
174	C₂×C₁₁₃	#2921	1	1	yes	characteristic
175	C₂×C₁₁₃	#2988	1	2	yes	—
176	C₂×C₁₁₃	#2989	1	2	yes	—
177	C₄×#117	C₂×C₁₁₃	1	1	yes	characteristic
178	#1923	C₂×C₁₁₃	1	4	yes	—
179	#1916	C₂×C₁₁₃	1	4	yes	complemented
180	#1842	C₂×C₁₁₃	1	1	yes	characteristic, complemented
181	#1831	C₂×C₁₁₃	1	1	yes	characteristic, complemented
182	#1797	C₂×C₁₁₃	1	2	yes	—
183	C₄×C₄⋊C₈	C₂×C₁₁₃	1	2	yes	complemented
184	C₁₁₃	#21922	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×#117	C₄×C₁₁₃	1	1	yes	characteristic
186	C₂×#117	C₄×C₁₁₃	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
190	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	4	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
192	C₂×C₄×C₈	C₂²×C₁₁₃	1	4	yes	—
193	C₄×C₄⋊C₄	C₄×C₁₁₃	1	2	yes	—
194	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
195	C₄×C₂²⋊C₄	C₄×C₁₁₃	1	2	yes	—
196	C₄×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
197	#376	C₄×C₁₁₃	1	1	yes	characteristic
198	#376	C₄×C₁₁₃	1	1	yes	characteristic
199	C₄³	C₂²×C₁₁₃	1	1	yes	characteristic
200	C₄³	C₂²×C₁₁₃	1	1	yes	characteristic
201	#336	C₂²×C₁₁₃	1	4	yes	—
202	#336	C₂²×C₁₁₃	1	4	yes	—
203	#336	C₂²×C₁₁₃	1	4	yes	—
204	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
209	#117	—	2	4	no	—
210	#117	C₈×C₁₁₃	1	8	yes	complemented
211	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	—	2	2	no	—
217	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
221	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
228	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
229	C₄⋊C₈	—	2	4	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	4	4	no	—
232	C₂²⋊C₈	—	4	4	no	—
233	C₄×C₈	—	4	4	no	—
234	#95	C₂×C₄×C₁₁₃	1	2	yes	—
235	#95	C₂×C₄×C₁₁₃	1	2	yes	—
236	#95	C₂×C₄×C₁₁₃	1	2	yes	—
237	#95	C₂×C₄×C₁₁₃	1	2	yes	—
238	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	4	2	no	—
247	C₂²×C₄	C₂×C₈×C₁₁₃	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	C₂×C₈×C₁₁₃	1	8	yes	—
266	C₂²⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	C₂×C₈×C₁₁₃	1	8	yes	—
268	C₄²	—	2	2	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	4	2	no	—
278	C₄²	—	4	2	no	—
279	C₄²	C₂×C₈×C₁₁₃	1	4	yes	—
280	C₄²	C₂×C₈×C₁₁₃	1	4	yes	—
281	C₄²	M₁₆×C₁₁₃	1	4	yes	—
282	C₄²	#41×C₁₁₃	1	2	yes	—
283	C₄²	#41×C₁₁₃	1	2	yes	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	2	no	—
288	C₂³	C₂²×C₈×C₁₁₃	1	2	yes	—
289	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	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	—	4	4	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	#117×C₁₁₃	1	2	yes	—
312	C₂×C₄	#117×C₁₁₃	1	2	yes	—
313	C₂×C₄	C₂²×C₈×C₁₁₃	1	4	yes	—
314	C₂×C₄	C₂²×C₈×C₁₁₃	1	4	yes	—
315	C₂×C₄	C₂²×C₈×C₁₁₃	1	2	yes	—
316	C₂×C₄	C₂²×C₈×C₁₁₃	1	2	yes	—
317	C₂×C₄	C₂×M₁₆×C₁₁₃	1	4	yes	—
318	C₂×C₄	C₂×M₁₆×C₁₁₃	1	2	yes	—
319	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
321	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
322	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
323	C₈	—	4	4	no	—
324	C₈	—	4	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	2	no	—
330	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
331	C₂²	#520×C₁₁₃	1	2	yes	—
332	C₂²	C₂³×C₈×C₁₁₃	1	1	yes	characteristic
333	C₂²	C₂²×M₁₆×C₁₁₃	1	1	yes	characteristic
334	C₂²	#568×C₁₁₃	1	2	yes	—
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	2	4	no	—
339	C₄	—	2	4	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	—	4	2	no	—
343	C₄	#431×C₁₁₃	1	4	yes	—
344	C₄	#540×C₁₁₃	1	1	yes	characteristic
345	C₄	#541×C₁₁₃	1	1	yes	characteristic
346	C₄	#542×C₁₁₃	1	2	yes	—
347	C₂	—	4	2	no	—
348	C₂	C₁₁₃×#2314	1	1	yes	characteristic
349	C₂	C₂×#431×C₁₁₃	1	1	yes	characteristic
350	C₂	C₁₁₃×#2921	1	1	yes	characteristic
351	C₂	C₁₁₃×#2988	1	2	yes	—
352	C₂	C₁₁₃×#2989	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁₃×#1916	C₂	semidirect
4. C₁₁₃×#1842	C₂	semidirect
5. C₁₁₃×#1831	C₂	semidirect
7. C₄×C₄⋊C₈×C₁₁₃	C₂	semidirect
33. #117×C₁₁₃	C₈	semidirect
170. #21922	C₁₁₃	direct (N × H)
179. #1916	C₂×C₁₁₃	semidirect
180. #1842	C₂×C₁₁₃	semidirect
181. #1831	C₂×C₁₁₃	semidirect
183. C₄×C₄⋊C₈	C₂×C₁₁₃	semidirect
184. C₁₁₃	#21922	direct (N × H)
210. #117	C₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×#117×C₁₁₃	2
C₁₁₃×#1923	2
C₁₁₃×#1916	2
C₁₁₃×#1842	2
C₁₁₃×#1831	2
C₁₁₃×#1797	2
C₄×C₄⋊C₈×C₁₁₃	2
#21922	113

Subgroups — C113×#21922 #43289942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21922 #43289942