Subgroups — C₁₁₃×#21145 #43289165

Order 28928.

1010 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#424×C₁₁₃	C₂	1	2	yes	maximal
2	C₂²×C₄⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#2285	C₂	1	1	yes	maximal, characteristic
5	C₁₁₃×#1940	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1939	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1729	C₂	1	2	yes	maximal
8	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
11	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
13	#424×C₁₁₃	—	2	8	no	—
14	C₂×C₄⋊C₈×C₁₁₃	—	2	4	no	—
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	8	yes	—
18	C₄×M₁₆×C₁₁₃	—	2	4	no	—
19	C₂×#97×C₁₁₃	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
21	#384×C₁₁₃	C₄	1	2	yes	—
22	#382×C₁₁₃	C₄	1	2	yes	—
23	#380×C₁₁₃	C₄	1	2	yes	—
24	#380×C₁₁₃	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
27	#336×C₁₁₃	C₂²	1	8	yes	—
28	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
31	C₂×M₁₆×C₁₁₃	—	2	2	no	—
32	C₂×M₁₆×C₁₁₃	—	2	2	no	—
33	C₂×M₁₆×C₁₁₃	—	2	2	no	—
34	C₂×M₁₆×C₁₁₃	—	2	2	no	—
35	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	—
36	C₂×M₁₆×C₁₁₃	Q₈	1	4	yes	—
37	C₂²×C₈×C₁₁₃	—	2	4	no	—
38	C₂²×C₈×C₁₁₃	—	2	4	no	—
39	C₂²×C₈×C₁₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
41	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
43	#117×C₁₁₃	—	2	4	no	—
44	#117×C₁₁₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
52	C₂×C₄²×C₁₁₃	Q₈	1	4	yes	—
53	C₂×C₄²×C₁₁₃	C₂³	1	4	yes	—
54	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₁₁₃	—	2	16	no	—
57	C₄⋊C₈×C₁₁₃	—	2	4	no	—
58	C₄⋊C₈×C₁₁₃	—	2	4	no	—
59	#97×C₁₁₃	—	2	4	no	—
60	C₄×C₈×C₁₁₃	—	2	4	no	—
61	#95×C₁₁₃	C₂×C₄	1	4	yes	—
62	#95×C₁₁₃	C₂×C₄	1	4	yes	—
63	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
68	C₂²×C₄×C₁₁₃	C₂²×C₄	1	8	yes	—
69	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
74	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
79	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
80	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
81	M₁₆×C₁₁₃	—	2	8	no	—
82	M₁₆×C₁₁₃	—	2	8	no	—
83	C₂×C₈×C₁₁₃	—	2	2	no	—
84	C₂×C₈×C₁₁₃	—	2	2	no	—
85	C₂×C₈×C₁₁₃	—	2	2	no	—
86	C₂×C₈×C₁₁₃	—	2	2	no	—
87	C₂×C₈×C₁₁₃	—	2	4	no	—
88	C₂×C₈×C₁₁₃	—	2	4	no	—
89	C₂×C₈×C₁₁₃	—	2	4	no	—
90	C₂×C₈×C₁₁₃	—	4	8	no	—
91	C₂×C₈×C₁₁₃	C₂×D₄	1	4	yes	—
92	C₂×C₈×C₁₁₃	C₂×Q₈	1	4	yes	—
93	C₄⋊C₄×C₁₁₃	—	2	8	no	—
94	C₄⋊C₄×C₁₁₃	—	2	8	no	—
95	C₄⋊C₄×C₁₁₃	—	4	4	no	—
96	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
97	C₄²×C₁₁₃	—	2	4	no	—
98	C₄²×C₁₁₃	—	2	4	no	—
99	C₄²×C₁₁₃	C₄⋊C₄	1	4	yes	—
100	C₄²×C₁₁₃	C₄⋊C₄	1	4	yes	—
101	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
102	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
103	C₄²×C₁₁₃	C₂×Q₈	1	2	yes	—
104	C₄²×C₁₁₃	C₂×Q₈	1	2	yes	—
105	C₂³×C₁₁₃	—	2	2	no	—
106	C₂³×C₁₁₃	—	2	2	no	—
107	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
108	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
109	C₂³×C₁₁₃	C₄×Q₈	1	2	yes	—
110	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁₃	—	2	2	no	—
112	C₂×C₄×C₁₁₃	—	2	2	no	—
113	C₂×C₄×C₁₁₃	—	2	2	no	—
114	C₂×C₄×C₁₁₃	—	2	8	no	—
115	C₂×C₄×C₁₁₃	—	2	8	no	—
116	C₂×C₄×C₁₁₃	—	2	8	no	—
117	C₂×C₄×C₁₁₃	—	2	8	no	—
118	C₂×C₄×C₁₁₃	—	4	4	no	—
119	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₁₁₃	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₁₁₃	#121	1	4	yes	—
127	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
128	C₂×C₄×C₁₁₃	#125	1	4	yes	—
129	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	—
130	C₂×C₄×C₁₁₃	#131	1	4	yes	—
131	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
134	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
137	C₈×C₁₁₃	—	2	4	no	—
138	C₈×C₁₁₃	—	2	4	no	—
139	C₈×C₁₁₃	—	4	4	no	—
140	C₂²×C₁₁₃	—	2	2	no	—
141	C₂²×C₁₁₃	—	2	2	no	—
142	C₂²×C₁₁₃	—	2	4	no	—
143	C₂²×C₁₁₃	—	2	4	no	—
144	C₂²×C₁₁₃	#389	1	4	yes	—
145	C₂²×C₁₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
147	C₂²×C₁₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
149	C₂²×C₁₁₃	#568	1	2	yes	—
150	C₄×C₁₁₃	—	2	2	no	—
151	C₄×C₁₁₃	—	2	2	no	—
152	C₄×C₁₁₃	—	2	2	no	—
153	C₄×C₁₁₃	—	4	8	no	—
154	C₄×C₁₁₃	#389	1	4	yes	—
155	C₄×C₁₁₃	#424	1	4	yes	complemented
156	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
157	C₄×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
158	C₄×C₁₁₃	C₂×#125	1	1	yes	characteristic
159	C₄×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
160	#21145	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₁₁₃	—	2	4	no	—
162	C₂×C₁₁₃	C₂×#389	1	1	yes	characteristic
163	C₂×C₁₁₃	C₂×#424	1	1	yes	characteristic
164	C₂×C₁₁₃	#2905	1	1	yes	characteristic
165	C₂×C₁₁₃	#2935	1	2	yes	—
166	C₂×C₁₁₃	#2962	1	2	yes	—
167	C₂×#424	C₂×C₁₁₃	1	2	yes	—
168	C₂²×C₄⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic
169	C₂×C₄×M₁₆	C₂×C₁₁₃	1	1	yes	characteristic
170	#2285	C₂×C₁₁₃	1	1	yes	characteristic
171	#1940	C₂×C₁₁₃	1	4	yes	complemented
172	#1939	C₂×C₁₁₃	1	4	yes	complemented
173	#1729	C₂×C₁₁₃	1	2	yes	—
174	C₁₁₃	#21145	1	1	yes	characteristic, direct product factor, Sylow
175	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
176	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
178	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
179	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
180	#424	—	2	8	no	—
181	C₂×C₄⋊C₈	—	2	4	no	—
182	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	8	yes	—
185	C₄×M₁₆	—	2	4	no	—
186	C₂×#97	C₂²×C₁₁₃	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
188	#384	C₄×C₁₁₃	1	2	yes	—
189	#382	C₄×C₁₁₃	1	2	yes	—
190	#380	C₄×C₁₁₃	1	2	yes	—
191	#380	C₄×C₁₁₃	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
194	#336	C₂²×C₁₁₃	1	8	yes	—
195	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
196	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	—
203	C₂×M₁₆	Q₈×C₁₁₃	1	4	yes	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
209	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
210	#117	—	2	4	no	—
211	#117	—	2	4	no	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
215	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
216	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
218	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
219	C₂×C₄²	Q₈×C₁₁₃	1	4	yes	—
220	C₂×C₄²	C₂³×C₁₁₃	1	4	yes	—
221	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
223	C₄⋊C₈	—	2	16	no	—
224	C₄⋊C₈	—	2	4	no	—
225	C₄⋊C₈	—	2	4	no	—
226	#97	—	2	4	no	—
227	C₄×C₈	—	2	4	no	—
228	#95	C₂×C₄×C₁₁₃	1	4	yes	—
229	#95	C₂×C₄×C₁₁₃	1	4	yes	—
230	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	4	2	no	—
233	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
234	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₁₃	1	8	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
242	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
243	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
244	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
245	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
246	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
247	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
248	M₁₆	—	2	8	no	—
249	M₁₆	—	2	8	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	4	8	no	—
258	C₂×C₈	C₂×D₄×C₁₁₃	1	4	yes	—
259	C₂×C₈	C₂×Q₈×C₁₁₃	1	4	yes	—
260	C₄⋊C₄	—	2	8	no	—
261	C₄⋊C₄	—	2	8	no	—
262	C₄⋊C₄	—	4	4	no	—
263	C₂²⋊C₄	—	2	8	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₄²	C₄⋊C₄×C₁₁₃	1	4	yes	—
267	C₄²	C₄⋊C₄×C₁₁₃	1	4	yes	—
268	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
269	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
270	C₄²	C₂×Q₈×C₁₁₃	1	2	yes	—
271	C₄²	C₂×Q₈×C₁₁₃	1	2	yes	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	2	no	—
274	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
275	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
276	C₂³	C₄×Q₈×C₁₁₃	1	2	yes	—
277	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
287	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
288	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
289	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
290	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
291	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
292	C₂×C₄	C₄×Q₈×C₁₁₃	1	2	yes	—
293	C₂×C₄	#121×C₁₁₃	1	4	yes	—
294	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
295	C₂×C₄	#125×C₁₁₃	1	4	yes	—
296	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	—
297	C₂×C₄	#131×C₁₁₃	1	4	yes	—
298	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
299	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
300	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
302	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
303	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
304	C₈	—	2	4	no	—
305	C₈	—	2	4	no	—
306	C₈	—	4	4	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	2	4	no	—
311	C₂²	#389×C₁₁₃	1	4	yes	—
312	C₂²	C₂²×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
313	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
314	C₂²	C₂×C₄×Q₈×C₁₁₃	1	1	yes	characteristic
315	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
316	C₂²	#568×C₁₁₃	1	2	yes	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	4	8	no	—
321	C₄	#389×C₁₁₃	1	4	yes	—
322	C₄	#424×C₁₁₃	1	4	yes	complemented
323	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
324	C₄	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
325	C₄	C₂×#125×C₁₁₃	1	1	yes	characteristic
326	C₄	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
327	C₂	—	2	4	no	—
328	C₂	C₂×#389×C₁₁₃	1	1	yes	characteristic
329	C₂	C₂×#424×C₁₁₃	1	1	yes	characteristic
330	C₂	C₁₁₃×#2905	1	1	yes	characteristic
331	C₂	C₁₁₃×#2935	1	2	yes	—
332	C₂	C₁₁₃×#2962	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₁₃	C₂²×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
5. C₁₁₃×#1940	C₂	semidirect
6. C₁₁₃×#1939	C₂	semidirect
155. C₄×C₁₁₃	#424	semidirect
160. #21145	C₁₁₃	direct (N × H)
171. #1940	C₂×C₁₁₃	semidirect
172. #1939	C₂×C₁₁₃	semidirect
174. C₁₁₃	#21145	direct (N × H)
322. C₄	#424×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#424×C₁₁₃	2
C₂²×C₄⋊C₈×C₁₁₃	2
C₂×C₄×M₁₆×C₁₁₃	2
C₁₁₃×#2285	2
C₁₁₃×#1940	2
C₁₁₃×#1939	2
C₁₁₃×#1729	2
#21145	113

Subgroups — C113×#21145 #43289165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21145 #43289165