Subgroups — C₁₁₃×#17689 #43285709

Order 28928.

876 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3504	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2970	C₂	1	2	yes	maximal
3	C₁₁₃×#1537	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1534	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1531	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1528	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#330×C₁₁₃	C₂	1	2	yes	maximal, complemented
9	#557×C₁₁₃	—	2	2	no	—
10	#554×C₁₁₃	—	2	2	no	—
11	#554×C₁₁₃	—	2	4	no	—
12	#544×C₁₁₃	C₄	1	4	yes	—
13	#544×C₁₁₃	C₄	1	2	yes	—
14	#533×C₁₁₃	C₂²	1	1	yes	characteristic
15	#533×C₁₁₃	C₂²	1	2	yes	—
16	C₂×#125×C₁₁₃	C₂²	1	2	yes	—
17	C₂×#125×C₁₁₃	C₂²	1	1	yes	characteristic
18	#520×C₁₁₃	C₄	1	2	yes	—
19	C₄×#41×C₁₁₃	C₂²	1	1	yes	characteristic
20	#446×C₁₁₃	—	2	2	no	—
21	#435×C₁₁₃	—	2	4	no	—
22	C₈×D₄×C₁₁₃	—	2	2	no	—
23	#432×C₁₁₃	C₂²	1	2	yes	—
24	#432×C₁₁₃	C₂²	1	4	yes	—
25	C₄×M₁₆×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#97×C₁₁₃	C₂²	1	4	yes	—
27	#330×C₁₁₃	C₂²	1	1	yes	characteristic
28	#330×C₁₁₃	C₂²	1	4	yes	—
29	#330×C₁₁₃	C₂²	1	2	yes	—
30	#330×C₁₁₃	C₂²	1	2	yes	—
31	#330×C₁₁₃	C₂²	1	1	yes	characteristic
32	#330×C₁₁₃	C₂²	1	4	yes	—
33	#330×C₁₁₃	C₂²	1	2	yes	—
34	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×M₁₆×C₁₁₃	—	2	2	no	—
36	C₂²×C₈×C₁₁₃	—	2	4	no	—
37	C₄⋊Q₈×C₁₁₃	—	2	4	no	—
38	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
39	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
41	#125×C₁₁₃	—	2	4	no	—
42	#125×C₁₁₃	—	2	2	no	—
43	#125×C₁₁₃	—	2	2	no	—
44	#125×C₁₁₃	—	2	4	no	—
45	#125×C₁₁₃	C₂×C₄	1	4	yes	—
46	#125×C₁₁₃	C₂×C₄	1	2	yes	—
47	#125×C₁₁₃	C₂³	1	1	yes	characteristic
48	#125×C₁₁₃	C₂³	1	2	yes	—
49	#125×C₁₁₃	C₂³	1	1	yes	characteristic
50	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
51	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
52	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
53	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
54	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₁₃	D₄	1	2	yes	—
59	C₄×D₄×C₁₁₃	—	2	4	no	—
60	C₄×D₄×C₁₁₃	—	2	2	no	—
61	C₄×D₄×C₁₁₃	D₄	1	2	yes	—
62	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
63	#117×C₁₁₃	C₂×C₄	1	2	yes	—
64	#117×C₁₁₃	C₂×C₄	1	4	yes	—
65	#117×C₁₁₃	C₂×C₄	1	1	yes	characteristic
66	#117×C₁₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₁₃	—	2	2	no	—
74	C₄⋊C₈×C₁₁₃	—	2	4	no	—
75	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
76	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
77	#97×C₁₁₃	—	2	4	no	—
78	#97×C₁₁₃	C₂³	1	2	yes	—
79	#97×C₁₁₃	C₂³	1	4	yes	—
80	#97×C₁₁₃	C₂³	1	2	yes	—
81	C₄×C₈×C₁₁₃	—	2	2	no	—
82	#41×C₁₁₃	—	2	4	no	—
83	C₂×Q₈×C₁₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
87	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
94	M₁₆×C₁₁₃	—	4	4	no	—
95	C₂×C₈×C₁₁₃	—	2	2	no	—
96	C₂×C₈×C₁₁₃	—	2	2	no	—
97	C₂×C₈×C₁₁₃	—	2	4	no	—
98	C₂×C₈×C₁₁₃	—	4	8	no	—
99	C₄⋊C₄×C₁₁₃	—	2	4	no	—
100	C₄⋊C₄×C₁₁₃	—	2	4	no	—
101	C₄⋊C₄×C₁₁₃	—	2	4	no	—
102	C₄⋊C₄×C₁₁₃	—	2	4	no	—
103	C₄⋊C₄×C₁₁₃	—	2	2	no	—
104	C₄⋊C₄×C₁₁₃	—	2	2	no	—
105	C₄⋊C₄×C₁₁₃	—	2	4	no	—
106	C₄⋊C₄×C₁₁₃	—	2	2	no	—
107	C₄⋊C₄×C₁₁₃	—	2	4	no	—
108	C₄⋊C₄×C₁₁₃	—	2	2	no	—
109	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
110	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
112	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
113	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
114	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
115	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
116	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
117	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₁₁₃	—	2	4	no	—
119	C₄²×C₁₁₃	—	2	2	no	—
120	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
123	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
124	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
125	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
127	Q₈×C₁₁₃	—	2	2	no	—
128	Q₈×C₁₁₃	—	8	4	no	—
129	Q₈×C₁₁₃	—	8	2	no	—
130	D₄×C₁₁₃	—	2	4	no	—
131	D₄×C₁₁₃	#101	1	4	yes	—
132	C₂×C₄×C₁₁₃	—	2	4	no	—
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	2	no	—
135	C₂×C₄×C₁₁₃	—	2	4	no	—
136	C₂×C₄×C₁₁₃	—	2	2	no	—
137	C₂×C₄×C₁₁₃	—	4	4	no	—
138	C₂×C₄×C₁₁₃	—	4	2	no	—
139	C₂×C₄×C₁₁₃	—	8	4	no	—
140	C₂×C₄×C₁₁₃	—	8	2	no	—
141	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
147	C₈×C₁₁₃	—	2	4	no	—
148	C₈×C₁₁₃	—	4	4	no	—
149	C₈×C₁₁₃	—	4	2	no	—
150	C₂²×C₁₁₃	—	2	4	no	—
151	C₂²×C₁₁₃	—	2	1	no	—
152	C₂²×C₁₁₃	—	2	2	no	—
153	C₂²×C₁₁₃	C₂×#101	1	4	yes	—
154	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₄×C₁₁₃	—	2	1	no	—
156	C₄×C₁₁₃	—	2	2	no	—
157	C₄×C₁₁₃	—	2	2	no	—
158	C₄×C₁₁₃	—	2	4	no	—
159	C₄×C₁₁₃	—	2	2	no	—
160	C₄×C₁₁₃	—	4	2	no	—
161	C₄×C₁₁₃	—	4	4	no	—
162	C₄×C₁₁₃	—	4	2	no	—
163	C₄×C₁₁₃	C₂×#101	1	2	yes	—
164	#17689	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₁₁₃	—	2	4	no	—
166	C₂×C₁₁₃	—	4	1	no	—
167	C₂×C₁₁₃	C₂²×#101	1	1	yes	characteristic
168	C₂×C₁₁₃	#2901	1	2	yes	—
169	#3504	C₂×C₁₁₃	1	1	yes	characteristic
170	#2970	C₂×C₁₁₃	1	2	yes	—
171	#1537	C₂×C₁₁₃	1	1	yes	characteristic, complemented
172	#1534	C₂×C₁₁₃	1	2	yes	complemented
173	#1531	C₂×C₁₁₃	1	4	yes	complemented
174	#1528	C₂×C₁₁₃	1	2	yes	complemented
175	#1526	C₂×C₁₁₃	1	1	yes	characteristic, complemented
176	C₂×#330	C₂×C₁₁₃	1	2	yes	complemented
177	C₁₁₃	#17689	1	1	yes	characteristic, direct product factor, Sylow
178	#557	—	2	2	no	—
179	#554	—	2	2	no	—
180	#554	—	2	4	no	—
181	#544	C₄×C₁₁₃	1	4	yes	—
182	#544	C₄×C₁₁₃	1	2	yes	—
183	#533	C₂²×C₁₁₃	1	1	yes	characteristic
184	#533	C₂²×C₁₁₃	1	2	yes	—
185	C₂×#125	C₂²×C₁₁₃	1	2	yes	—
186	C₂×#125	C₂²×C₁₁₃	1	1	yes	characteristic
187	#520	C₄×C₁₁₃	1	2	yes	—
188	C₄×#41	C₂²×C₁₁₃	1	1	yes	characteristic
189	#446	—	2	2	no	—
190	#435	—	2	4	no	—
191	C₈×D₄	—	2	2	no	—
192	#432	C₂²×C₁₁₃	1	2	yes	—
193	#432	C₂²×C₁₁₃	1	4	yes	—
194	C₄×M₁₆	C₂²×C₁₁₃	1	2	yes	—
195	C₂×#97	C₂²×C₁₁₃	1	4	yes	—
196	#330	C₂²×C₁₁₃	1	2	yes	—
197	#330	C₂²×C₁₁₃	1	2	yes	—
198	#330	C₂²×C₁₁₃	1	1	yes	characteristic
199	#330	C₂²×C₁₁₃	1	4	yes	—
200	#330	C₂²×C₁₁₃	1	2	yes	—
201	#330	C₂²×C₁₁₃	1	1	yes	characteristic
202	#330	C₂²×C₁₁₃	1	4	yes	—
203	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
204	C₂×M₁₆	—	2	2	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₄⋊Q₈	—	2	4	no	—
207	C₄⋊Q₈	—	2	2	no	—
208	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
209	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
210	#125	—	2	4	no	—
211	#125	—	2	2	no	—
212	#125	—	2	2	no	—
213	#125	—	2	4	no	—
214	#125	C₂×C₄×C₁₁₃	1	4	yes	—
215	#125	C₂×C₄×C₁₁₃	1	2	yes	—
216	#125	C₂³×C₁₁₃	1	1	yes	characteristic
217	#125	C₂³×C₁₁₃	1	2	yes	—
218	#125	C₂³×C₁₁₃	1	1	yes	characteristic
219	C₂²⋊Q₈	—	2	4	no	—
220	C₂²⋊Q₈	—	2	2	no	—
221	C₂²⋊Q₈	—	2	4	no	—
222	C₂²⋊Q₈	—	2	4	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	C₄×Q₈	—	2	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₄×Q₈	D₄×C₁₁₃	1	2	yes	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	D₄×C₁₁₃	1	2	yes	—
231	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
232	#117	C₂×C₄×C₁₁₃	1	2	yes	—
233	#117	C₂×C₄×C₁₁₃	1	4	yes	—
234	#117	C₂×C₄×C₁₁₃	1	1	yes	characteristic
235	#117	C₂×C₄×C₁₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
241	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	4	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	#97	—	2	4	no	—
247	#97	C₂³×C₁₁₃	1	2	yes	—
248	#97	C₂³×C₁₁₃	1	4	yes	—
249	#97	C₂³×C₁₁₃	1	2	yes	—
250	C₄×C₈	—	2	2	no	—
251	#41	—	2	4	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
255	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
256	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
263	M₁₆	—	4	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	4	8	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
279	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
280	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
281	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
282	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	2	4	no	—
285	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
286	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	2	no	—
289	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
290	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
291	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
292	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
293	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
294	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
295	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
296	Q₈	—	2	2	no	—
297	Q₈	—	8	4	no	—
298	Q₈	—	8	2	no	—
299	D₄	—	2	4	no	—
300	D₄	#101×C₁₁₃	1	4	yes	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	8	4	no	—
309	C₂×C₄	—	8	2	no	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
312	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
313	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
314	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
315	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
316	C₈	—	2	4	no	—
317	C₈	—	4	4	no	—
318	C₈	—	4	2	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	C₂×#101×C₁₁₃	1	4	yes	—
323	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
324	C₄	—	2	1	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	4	no	—
328	C₄	—	2	2	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	4	no	—
331	C₄	—	4	2	no	—
332	C₄	C₂×#101×C₁₁₃	1	2	yes	—
333	C₂	—	2	4	no	—
334	C₂	—	4	1	no	—
335	C₂	C₂²×#101×C₁₁₃	1	1	yes	characteristic
336	C₂	C₁₁₃×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
prime radical	C₂×#41×C₁₁₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄×#41×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁₃×#1537	C₂	semidirect
4. C₁₁₃×#1534	C₂	semidirect
5. C₁₁₃×#1531	C₂	semidirect
6. C₁₁₃×#1528	C₂	semidirect
7. C₁₁₃×#1526	C₂	semidirect
8. C₂×#330×C₁₁₃	C₂	semidirect
164. #17689	C₁₁₃	direct (N × H)
171. #1537	C₂×C₁₁₃	semidirect
172. #1534	C₂×C₁₁₃	semidirect
173. #1531	C₂×C₁₁₃	semidirect
174. #1528	C₂×C₁₁₃	semidirect
175. #1526	C₂×C₁₁₃	semidirect
176. C₂×#330	C₂×C₁₁₃	semidirect
177. C₁₁₃	#17689	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×#3504	2
C₁₁₃×#2970	2
C₁₁₃×#1537	2
C₁₁₃×#1534	2
C₁₁₃×#1531	2
C₁₁₃×#1528	2
C₁₁₃×#1526	2
C₂×#330×C₁₁₃	2
#17689	113

Subgroups — C113×#17689 #43285709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#17689 #43285709