Subgroups — C₁₁₃×#3510 #28388306

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#559×C₁₁₃	C₂	1	4	yes	maximal, complemented
2	#556×C₁₁₃	C₂	1	4	yes	maximal, complemented
3	#551×C₁₁₃	C₂	1	8	yes	maximal, complemented
4	#542×C₁₁₃	C₂	1	4	yes	maximal, complemented
5	#536×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#535×C₁₁₃	C₂	1	1	yes	maximal, characteristic
7	#533×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#529×C₁₁₃	C₂	1	4	yes	maximal, complemented
9	C₂×#124×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#519×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#518×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
17	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
18	#127×C₁₁₃	C₂²	1	2	yes	—
19	#126×C₁₁₃	C₂²	1	8	yes	complemented
20	#126×C₁₁₃	C₂²	1	8	yes	complemented
21	#125×C₁₁₃	C₂²	1	2	yes	complemented
22	#124×C₁₁₃	C₂²	1	2	yes	—
23	#124×C₁₁₃	C₂²	1	2	yes	—
24	#124×C₁₁₃	C₂²	1	4	yes	—
25	#124×C₁₁₃	C₂²	1	2	yes	—
26	#124×C₁₁₃	C₂²	1	2	yes	complemented
27	#124×C₁₁₃	C₂²	1	8	yes	complemented
28	#123×C₁₁₃	C₂²	1	4	yes	—
29	#123×C₁₁₃	C₂²	1	8	yes	complemented
30	#123×C₁₁₃	C₂²	1	8	yes	complemented
31	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
32	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
33	C₂²⋊Q₈×C₁₁₃	C₂²	1	8	yes	complemented
34	#121×C₁₁₃	C₂²	1	4	yes	—
35	#120×C₁₁₃	C₂²	1	4	yes	—
36	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
37	C₄×Q₈×C₁₁₃	C₂²	1	4	yes	complemented
38	C₄×Q₈×C₁₁₃	C₂²	1	4	yes	complemented
39	C₄×Q₈×C₁₁₃	C₂²	1	4	yes	complemented
40	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
41	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
42	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
43	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
44	C₄×D₄×C₁₁₃	C₂²	1	8	yes	complemented
45	#117×C₁₁₃	C₂²	1	1	yes	characteristic
46	#117×C₁₁₃	C₂²	1	1	yes	characteristic
47	#117×C₁₁₃	C₂²	1	1	yes	characteristic
48	#117×C₁₁₃	C₂²	1	4	yes	—
49	#117×C₁₁₃	C₂²	1	2	yes	complemented
50	#117×C₁₁₃	C₂²	1	8	yes	complemented
51	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
52	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
53	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	complemented
55	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
56	#41×C₁₁₃	—	2	4	no	—
57	C₂×Q₈×C₁₁₃	—	2	4	no	—
58	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
59	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
60	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
61	C₂×Q₈×C₁₁₃	C₂³	1	4	yes	—
62	C₂×D₄×C₁₁₃	—	2	4	no	—
63	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
64	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
65	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
66	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₁₃	C₂³	1	8	yes	—
68	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
69	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
71	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
72	C₂²×C₄×C₁₁₃	C₂³	1	8	yes	—
73	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
75	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
76	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
77	C₄⋊C₄×C₁₁₃	C₂³	1	8	yes	—
78	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
79	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
80	C₄⋊C₄×C₁₁₃	C₂³	1	8	yes	—
81	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
82	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
83	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
84	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
85	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
86	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
87	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
88	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
89	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
90	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
91	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
92	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
93	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
94	C₄²×C₁₁₃	C₂³	1	2	yes	—
95	C₄²×C₁₁₃	C₂³	1	2	yes	—
96	C₄²×C₁₁₃	C₂³	1	4	yes	—
97	C₄²×C₁₁₃	C₂³	1	8	yes	—
98	C₄²×C₁₁₃	C₂³	1	2	yes	—
99	C₄²×C₁₁₃	C₂³	1	2	yes	—
100	C₂³×C₁₁₃	—	2	4	no	—
101	C₂³×C₁₁₃	—	4	4	no	—
102	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
103	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
104	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
105	Q₈×C₁₁₃	—	2	4	no	—
106	Q₈×C₁₁₃	—	2	4	no	—
107	Q₈×C₁₁₃	—	2	2	no	—
108	Q₈×C₁₁₃	—	4	4	no	—
109	D₄×C₁₁₃	—	2	4	no	—
110	D₄×C₁₁₃	—	2	4	no	—
111	D₄×C₁₁₃	—	2	4	no	—
112	D₄×C₁₁₃	—	2	2	no	—
113	D₄×C₁₁₃	—	4	8	no	—
114	C₂×C₄×C₁₁₃	—	2	4	no	—
115	C₂×C₄×C₁₁₃	—	2	4	no	—
116	C₂×C₄×C₁₁₃	—	4	4	no	—
117	C₂×C₄×C₁₁₃	—	4	8	no	—
118	C₂×C₄×C₁₁₃	—	4	2	no	—
119	C₂×C₄×C₁₁₃	#41	1	4	yes	—
120	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
121	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
122	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
123	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
124	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
125	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
126	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²×C₁₁₃	—	2	2	no	—
130	C₂²×C₁₁₃	—	2	2	no	—
131	C₂²×C₁₁₃	—	2	4	no	—
132	C₂²×C₁₁₃	—	2	4	no	—
133	C₂²×C₁₁₃	—	2	8	no	—
134	C₂²×C₁₁₃	—	8	4	no	—
135	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
136	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
137	C₄×C₁₁₃	—	2	2	no	—
138	C₄×C₁₁₃	—	2	4	no	—
139	C₄×C₁₁₃	—	2	2	no	—
140	C₄×C₁₁₃	—	2	4	no	—
141	C₄×C₁₁₃	—	2	4	no	—
142	C₄×C₁₁₃	—	2	2	no	—
143	C₄×C₁₁₃	—	2	4	no	—
144	C₄×C₁₁₃	C₂×#41	1	2	yes	—
145	C₄×C₁₁₃	C₂×#41	1	2	yes	—
146	C₂×C₁₁₃	—	2	2	no	—
147	C₂×C₁₁₃	—	4	2	no	—
148	C₂×C₁₁₃	—	4	4	no	—
149	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
150	C₂×C₁₁₃	#585	1	2	yes	—
151	#3510	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₁₁₃	#3510	1	1	yes	characteristic, direct product factor, Sylow
153	#559	C₂×C₁₁₃	1	4	yes	complemented
154	#556	C₂×C₁₁₃	1	4	yes	complemented
155	#551	C₂×C₁₁₃	1	8	yes	complemented
156	#542	C₂×C₁₁₃	1	4	yes	complemented
157	#536	C₂×C₁₁₃	1	1	yes	characteristic, complemented
158	#535	C₂×C₁₁₃	1	1	yes	characteristic
159	#533	C₂×C₁₁₃	1	1	yes	characteristic, complemented
160	#529	C₂×C₁₁₃	1	4	yes	complemented
161	C₂×#124	C₂×C₁₁₃	1	1	yes	characteristic, complemented
162	#519	C₂×C₁₁₃	1	1	yes	characteristic, complemented
163	#518	C₂×C₁₁₃	1	1	yes	characteristic, complemented
164	C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic, complemented
165	C₂×#41	C₂²×C₁₁₃	1	1	yes	characteristic
166	C₂²×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
167	C₂²×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
168	C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
169	C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
170	#127	C₂²×C₁₁₃	1	2	yes	—
171	#126	C₂²×C₁₁₃	1	8	yes	complemented
172	#126	C₂²×C₁₁₃	1	8	yes	complemented
173	#125	C₂²×C₁₁₃	1	2	yes	complemented
174	#124	C₂²×C₁₁₃	1	2	yes	—
175	#124	C₂²×C₁₁₃	1	2	yes	—
176	#124	C₂²×C₁₁₃	1	4	yes	—
177	#124	C₂²×C₁₁₃	1	2	yes	—
178	#124	C₂²×C₁₁₃	1	2	yes	complemented
179	#124	C₂²×C₁₁₃	1	8	yes	complemented
180	#123	C₂²×C₁₁₃	1	4	yes	—
181	#123	C₂²×C₁₁₃	1	8	yes	complemented
182	#123	C₂²×C₁₁₃	1	8	yes	complemented
183	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	—
184	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	complemented
185	C₂²⋊Q₈	C₂²×C₁₁₃	1	8	yes	complemented
186	#121	C₂²×C₁₁₃	1	4	yes	—
187	#120	C₂²×C₁₁₃	1	4	yes	—
188	C₄×Q₈	C₂²×C₁₁₃	1	2	yes	complemented
189	C₄×Q₈	C₂²×C₁₁₃	1	4	yes	complemented
190	C₄×Q₈	C₂²×C₁₁₃	1	4	yes	complemented
191	C₄×Q₈	C₂²×C₁₁₃	1	4	yes	complemented
192	C₄×D₄	C₂²×C₁₁₃	1	4	yes	—
193	C₄×D₄	C₂²×C₁₁₃	1	4	yes	—
194	C₄×D₄	C₂²×C₁₁₃	1	4	yes	—
195	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
196	C₄×D₄	C₂²×C₁₁₃	1	8	yes	complemented
197	#117	C₂²×C₁₁₃	1	1	yes	characteristic
198	#117	C₂²×C₁₁₃	1	1	yes	characteristic
199	#117	C₂²×C₁₁₃	1	1	yes	characteristic
200	#117	C₂²×C₁₁₃	1	4	yes	—
201	#117	C₂²×C₁₁₃	1	2	yes	complemented
202	#117	C₂²×C₁₁₃	1	8	yes	complemented
203	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
205	C₂×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
206	C₂×C₄²	C₂²×C₁₁₃	1	2	yes	complemented
207	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
208	#41	—	2	4	no	—
209	C₂×Q₈	—	2	4	no	—
210	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
211	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
212	C₂×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
213	C₂×Q₈	C₂³×C₁₁₃	1	4	yes	—
214	C₂×D₄	—	2	4	no	—
215	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
216	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
217	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
218	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
219	C₂×D₄	C₂³×C₁₁₃	1	8	yes	—
220	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
221	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
222	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
223	C₂²×C₄	C₂³×C₁₁₃	1	4	yes	—
224	C₂²×C₄	C₂³×C₁₁₃	1	8	yes	—
225	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
226	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
227	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
228	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
229	C₄⋊C₄	C₂³×C₁₁₃	1	8	yes	—
230	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
231	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
232	C₄⋊C₄	C₂³×C₁₁₃	1	8	yes	—
233	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
234	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
235	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
236	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
237	C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
238	C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
239	C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
240	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
241	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
242	C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
243	C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
244	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
245	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
246	C₄²	C₂³×C₁₁₃	1	2	yes	—
247	C₄²	C₂³×C₁₁₃	1	2	yes	—
248	C₄²	C₂³×C₁₁₃	1	4	yes	—
249	C₄²	C₂³×C₁₁₃	1	8	yes	—
250	C₄²	C₂³×C₁₁₃	1	2	yes	—
251	C₄²	C₂³×C₁₁₃	1	2	yes	—
252	C₂³	—	2	4	no	—
253	C₂³	—	4	4	no	—
254	C₂³	C₂⁴×C₁₁₃	1	4	yes	—
255	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
256	C₂³	C₂⁴×C₁₁₃	1	1	yes	characteristic
257	Q₈	—	2	4	no	—
258	Q₈	—	2	4	no	—
259	Q₈	—	2	2	no	—
260	Q₈	—	4	4	no	—
261	D₄	—	2	4	no	—
262	D₄	—	2	4	no	—
263	D₄	—	2	4	no	—
264	D₄	—	2	2	no	—
265	D₄	—	4	8	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	8	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	#41×C₁₁₃	1	4	yes	—
272	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
273	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
274	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
275	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
276	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
277	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
278	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
279	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
280	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	4	no	—
284	C₂²	—	2	4	no	—
285	C₂²	—	2	8	no	—
286	C₂²	—	8	4	no	—
287	C₂²	C₂×#41×C₁₁₃	1	2	yes	—
288	C₂²	C₂⁵×C₁₁₃	1	1	yes	characteristic
289	C₄	—	2	2	no	—
290	C₄	—	2	4	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	4	no	—
293	C₄	—	2	4	no	—
294	C₄	—	2	2	no	—
295	C₄	—	2	4	no	—
296	C₄	C₂×#41×C₁₁₃	1	2	yes	—
297	C₄	C₂×#41×C₁₁₃	1	2	yes	—
298	C₂	—	2	2	no	—
299	C₂	—	4	4	no	—
300	C₂	—	4	2	no	—
301	C₂	C₂²×#41×C₁₁₃	1	1	yes	characteristic
302	C₂	#585×C₁₁₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁₃
prime radical	#535×C₁₁₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. #559×C₁₁₃	C₂	semidirect
2. #556×C₁₁₃	C₂	semidirect
3. #551×C₁₁₃	C₂	semidirect
4. #542×C₁₁₃	C₂	semidirect
5. #536×C₁₁₃	C₂	semidirect
7. #533×C₁₁₃	C₂	semidirect
8. #529×C₁₁₃	C₂	semidirect
9. C₂×#124×C₁₁₃	C₂	semidirect
10. #519×C₁₁₃	C₂	semidirect
11. #518×C₁₁₃	C₂	semidirect
12. C₄×#41×C₁₁₃	C₂	semidirect
16. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
17. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
19. #126×C₁₁₃	C₂²	semidirect
20. #126×C₁₁₃	C₂²	semidirect
21. #125×C₁₁₃	C₂²	semidirect
26. #124×C₁₁₃	C₂²	semidirect
27. #124×C₁₁₃	C₂²	semidirect
29. #123×C₁₁₃	C₂²	semidirect
30. #123×C₁₁₃	C₂²	semidirect
32. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
33. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
36. C₄×Q₈×C₁₁₃	C₂²	semidirect
37. C₄×Q₈×C₁₁₃	C₂²	semidirect
38. C₄×Q₈×C₁₁₃	C₂²	semidirect
39. C₄×Q₈×C₁₁₃	C₂²	semidirect
43. C₄×D₄×C₁₁₃	C₂²	semidirect
44. C₄×D₄×C₁₁₃	C₂²	semidirect
49. #117×C₁₁₃	C₂²	semidirect
50. #117×C₁₁₃	C₂²	semidirect
54. C₂×C₄²×C₁₁₃	C₂²	semidirect
151. #3510	C₁₁₃	direct (N × H)
152. C₁₁₃	#3510	direct (N × H)
153. #559	C₂×C₁₁₃	semidirect
154. #556	C₂×C₁₁₃	semidirect
155. #551	C₂×C₁₁₃	semidirect
156. #542	C₂×C₁₁₃	semidirect
157. #536	C₂×C₁₁₃	semidirect
159. #533	C₂×C₁₁₃	semidirect
160. #529	C₂×C₁₁₃	semidirect
161. C₂×#124	C₂×C₁₁₃	semidirect
162. #519	C₂×C₁₁₃	semidirect
163. #518	C₂×C₁₁₃	semidirect
164. C₄×#41	C₂×C₁₁₃	semidirect
168. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
169. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
171. #126	C₂²×C₁₁₃	semidirect
172. #126	C₂²×C₁₁₃	semidirect
173. #125	C₂²×C₁₁₃	semidirect
178. #124	C₂²×C₁₁₃	semidirect
179. #124	C₂²×C₁₁₃	semidirect
181. #123	C₂²×C₁₁₃	semidirect
182. #123	C₂²×C₁₁₃	semidirect
184. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
185. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
188. C₄×Q₈	C₂²×C₁₁₃	semidirect
189. C₄×Q₈	C₂²×C₁₁₃	semidirect
190. C₄×Q₈	C₂²×C₁₁₃	semidirect
191. C₄×Q₈	C₂²×C₁₁₃	semidirect
195. C₄×D₄	C₂²×C₁₁₃	semidirect
196. C₄×D₄	C₂²×C₁₁₃	semidirect
201. #117	C₂²×C₁₁₃	semidirect
202. #117	C₂²×C₁₁₃	semidirect
206. C₂×C₄²	C₂²×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#559×C₁₁₃	2
#556×C₁₁₃	2
#551×C₁₁₃	2
#542×C₁₁₃	2
#536×C₁₁₃	2
#535×C₁₁₃	2
#533×C₁₁₃	2
#529×C₁₁₃	2
C₂×#124×C₁₁₃	2
#519×C₁₁₃	2
#518×C₁₁₃	2
C₄×#41×C₁₁₃	2
#3510	113

Subgroups — C113×#3510 #28388306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#3510 #28388306