Subgroups — C₁₁₃×#11257 #43279277

Order 28928.

814 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#106×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#340×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×#340×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#336×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₁₃×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂×#106×C₁₁₃	—	2	2	no	—
12	C₂×#106×C₁₁₃	—	2	4	no	—
13	C₂×#95×C₁₁₃	—	2	2	no	—
14	C₂×#95×C₁₁₃	—	2	2	no	—
15	#340×C₁₁₃	—	2	4	no	—
16	#340×C₁₁₃	C₄	1	4	yes	complemented
17	#336×C₁₁₃	—	2	2	no	—
18	C₂³×C₄×C₁₁₃	—	2	2	no	—
19	C₂³×C₄×C₁₁₃	—	2	2	no	—
20	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
21	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₈×C₁₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₁₃	—	2	2	no	—
24	C₂²×C₈×C₁₁₃	—	2	1	no	—
25	C₂²×C₈×C₁₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₁₃	—	2	1	no	—
28	C₂²×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₁₃	D₄	1	2	yes	—
30	C₂²×C₈×C₁₁₃	Q₈	1	2	yes	—
31	C₂²×C₈×C₁₁₃	Q₈	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₁₃	D₄	1	4	yes	—
44	C₂×C₄²×C₁₁₃	—	2	1	no	—
45	C₂×C₄²×C₁₁₃	—	2	2	no	—
46	C₂×C₄²×C₁₁₃	—	2	2	no	—
47	C₂×C₄²×C₁₁₃	—	2	1	no	—
48	#106×C₁₁₃	—	2	8	no	—
49	#95×C₁₁₃	—	4	4	no	—
50	#95×C₁₁₃	—	4	4	no	—
51	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₁₃	—	4	2	no	—
61	C₂²×C₄×C₁₁₃	—	4	2	no	—
62	C₂²×C₄×C₁₁₃	—	4	2	no	—
63	C₂²×C₄×C₁₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₁₃	—	4	2	no	—
65	C₂²×C₄×C₁₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₁₃	—	4	2	no	—
68	C₂²×C₄×C₁₁₃	—	4	2	no	—
69	C₂²×C₄×C₁₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₁₃	SD₁₆	1	4	yes	—
73	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
79	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
80	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
81	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
83	C₂×C₈×C₁₁₃	—	2	4	no	—
84	C₂×C₈×C₁₁₃	—	2	2	no	—
85	C₂×C₈×C₁₁₃	—	2	4	no	—
86	C₂×C₈×C₁₁₃	—	2	2	no	—
87	C₂×C₈×C₁₁₃	—	2	4	no	—
88	C₂×C₈×C₁₁₃	—	2	2	no	—
89	C₂×C₈×C₁₁₃	—	4	1	no	—
90	C₂×C₈×C₁₁₃	—	4	1	no	—
91	C₂×C₈×C₁₁₃	—	4	2	no	—
92	C₂×C₈×C₁₁₃	C₄⋊C₄	1	4	yes	—
93	C₄⋊C₄×C₁₁₃	—	2	4	no	—
94	C₄⋊C₄×C₁₁₃	—	2	4	no	—
95	C₄⋊C₄×C₁₁₃	—	2	4	no	—
96	C₄⋊C₄×C₁₁₃	—	2	4	no	—
97	C₄⋊C₄×C₁₁₃	—	4	2	no	—
98	C₄⋊C₄×C₁₁₃	—	4	2	no	—
99	C₄⋊C₄×C₁₁₃	—	4	2	no	—
100	C₄⋊C₄×C₁₁₃	—	4	2	no	—
101	C₄²×C₁₁₃	—	4	1	no	—
102	C₄²×C₁₁₃	—	4	1	no	—
103	C₄²×C₁₁₃	—	4	2	no	—
104	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
105	C₂³×C₁₁₃	#121	1	2	yes	—
106	C₂³×C₁₁₃	#121	1	1	yes	characteristic
107	C₂³×C₁₁₃	#123	1	2	yes	—
108	C₂³×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
109	C₂³×C₁₁₃	C₂×SD₁₆	1	2	yes	—
110	C₂³×C₁₁₃	#135	1	2	yes	—
111	C₂³×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
112	C₂³×C₁₁₃	#137	1	2	yes	—
113	C₂×C₄×C₁₁₃	—	2	4	no	—
114	C₂×C₄×C₁₁₃	—	2	4	no	—
115	C₂×C₄×C₁₁₃	—	2	4	no	—
116	C₂×C₄×C₁₁₃	—	4	2	no	—
117	C₂×C₄×C₁₁₃	—	4	2	no	—
118	C₂×C₄×C₁₁₃	—	4	2	no	—
119	C₂×C₄×C₁₁₃	—	4	2	no	—
120	C₂×C₄×C₁₁₃	—	4	4	no	—
121	C₂×C₄×C₁₁₃	—	4	4	no	—
122	C₂×C₄×C₁₁₃	—	4	4	no	—
123	C₂×C₄×C₁₁₃	—	4	4	no	—
124	C₂×C₄×C₁₁₃	—	4	4	no	—
125	C₂×C₄×C₁₁₃	—	4	4	no	—
126	C₂×C₄×C₁₁₃	—	8	2	no	—
127	C₂×C₄×C₁₁₃	—	8	2	no	—
128	C₂×C₄×C₁₁₃	—	8	2	no	—
129	C₂×C₄×C₁₁₃	—	8	2	no	—
130	C₂×C₄×C₁₁₃	—	8	2	no	—
131	C₂×C₄×C₁₁₃	—	8	2	no	—
132	C₂×C₄×C₁₁₃	—	8	2	no	—
133	C₂×C₄×C₁₁₃	—	8	2	no	—
134	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₁₃	#117	1	2	yes	—
136	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
139	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	#123	1	2	yes	—
144	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
145	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
146	C₂×C₄×C₁₁₃	#124	1	2	yes	—
147	C₂×C₄×C₁₁₃	#125	1	2	yes	—
148	C₂×C₄×C₁₁₃	#125	1	2	yes	—
149	C₂×C₄×C₁₁₃	#125	1	1	yes	characteristic
150	C₂×C₄×C₁₁₃	#126	1	2	yes	—
151	C₂×C₄×C₁₁₃	#126	1	2	yes	—
152	C₈×C₁₁₃	—	2	4	no	—
153	C₈×C₁₁₃	—	4	2	no	—
154	C₂²×C₁₁₃	#388	1	2	yes	—
155	C₂²×C₁₁₃	#389	1	1	yes	characteristic
156	C₂²×C₁₁₃	#394	1	1	yes	characteristic
157	C₂²×C₁₁₃	#397	1	1	yes	characteristic
158	C₂²×C₁₁₃	#398	1	2	yes	—
159	C₂²×C₁₁₃	C₄×SD₁₆	1	2	yes	—
160	C₂²×C₁₁₃	#441	1	1	yes	characteristic
161	C₂²×C₁₁₃	#442	1	1	yes	characteristic
162	C₂²×C₁₁₃	#460	1	2	yes	—
163	C₂²×C₁₁₃	#461	1	2	yes	—
164	C₂²×C₁₁₃	#463	1	2	yes	—
165	C₂²×C₁₁₃	#464	1	2	yes	—
166	C₂²×C₁₁₃	#465	1	2	yes	—
167	C₂²×C₁₁₃	#468	1	2	yes	—
168	C₂²×C₁₁₃	#481	1	2	yes	—
169	C₂²×C₁₁₃	#482	1	2	yes	—
170	C₂²×C₁₁₃	#483	1	2	yes	—
171	C₂²×C₁₁₃	#485	1	2	yes	—
172	C₂²×C₁₁₃	#498	1	1	yes	characteristic
173	C₂²×C₁₁₃	#499	1	1	yes	characteristic
174	C₂²×C₁₁₃	#501	1	2	yes	—
175	C₄×C₁₁₃	—	4	4	no	—
176	C₄×C₁₁₃	—	8	4	no	—
177	C₄×C₁₁₃	—	8	4	no	—
178	C₄×C₁₁₃	#382	1	1	yes	characteristic
179	C₄×C₁₁₃	#385	1	1	yes	characteristic
180	C₄×C₁₁₃	#387	1	2	yes	—
181	C₄×C₁₁₃	#393	1	1	yes	characteristic
182	C₄×C₁₁₃	#400	1	2	yes	—
183	C₄×C₁₁₃	#400	1	1	yes	characteristic
184	#11257	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₁₁₃	#1442	1	1	yes	characteristic
186	C₂×C₁₁₃	#1926	1	2	yes	—
187	C₂×C₁₁₃	#1927	1	2	yes	—
188	C₂×C₁₁₃	#1941	1	1	yes	characteristic
189	C₂×C₁₁₃	#1943	1	1	yes	characteristic
190	C₂×C₁₁₃	#2055	1	2	yes	—
191	C₂×C₁₁₃	#2077	1	2	yes	—
192	C₂×C₁₁₃	#2084	1	2	yes	—
193	C₂×C₁₁₃	#2085	1	2	yes	—
194	C₂²×#106	C₂×C₁₁₃	1	1	yes	characteristic
195	C₂×#340	C₂×C₁₁₃	1	2	yes	—
196	C₂×#340	C₂×C₁₁₃	1	1	yes	characteristic
197	C₂×#336	C₂×C₁₁₃	1	1	yes	characteristic
198	C₄⋊#95	C₂×C₁₁₃	1	2	yes	—
199	C₁₁₃	#11257	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
204	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
205	C₂×#106	—	2	2	no	—
206	C₂×#106	—	2	4	no	—
207	C₂×#95	—	2	2	no	—
208	C₂×#95	—	2	2	no	—
209	#340	—	2	4	no	—
210	#340	C₄×C₁₁₃	1	4	yes	complemented
211	#336	—	2	2	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	C₂×C₄×C₁₁₃	1	2	yes	—
223	C₂²×C₈	D₄×C₁₁₃	1	2	yes	—
224	C₂²×C₈	Q₈×C₁₁₃	1	2	yes	—
225	C₂²×C₈	Q₈×C₁₁₃	1	2	yes	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
237	C₂×C₄⋊C₄	D₄×C₁₁₃	1	4	yes	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	1	no	—
242	#106	—	2	8	no	—
243	#95	—	4	4	no	—
244	#95	—	4	4	no	—
245	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	SD₁₆×C₁₁₃	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
272	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
273	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
274	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
275	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
276	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	C₄⋊C₄×C₁₁₃	1	4	yes	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	—	4	2	no	—
298	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
299	C₂³	#121×C₁₁₃	1	2	yes	—
300	C₂³	#121×C₁₁₃	1	1	yes	characteristic
301	C₂³	#123×C₁₁₃	1	2	yes	—
302	C₂³	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
303	C₂³	C₂×SD₁₆×C₁₁₃	1	2	yes	—
304	C₂³	#135×C₁₁₃	1	2	yes	—
305	C₂³	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
306	C₂³	#137×C₁₁₃	1	2	yes	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	—	8	2	no	—
322	C₂×C₄	—	8	2	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	2	no	—
325	C₂×C₄	—	8	2	no	—
326	C₂×C₄	—	8	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
329	C₂×C₄	#117×C₁₁₃	1	2	yes	—
330	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
331	C₂×C₄	C₄×Q₈×C₁₁₃	1	1	yes	characteristic
332	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
334	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
335	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
336	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
337	C₂×C₄	#123×C₁₁₃	1	2	yes	—
338	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
339	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
340	C₂×C₄	#124×C₁₁₃	1	2	yes	—
341	C₂×C₄	#125×C₁₁₃	1	2	yes	—
342	C₂×C₄	#125×C₁₁₃	1	2	yes	—
343	C₂×C₄	#125×C₁₁₃	1	1	yes	characteristic
344	C₂×C₄	#126×C₁₁₃	1	2	yes	—
345	C₂×C₄	#126×C₁₁₃	1	2	yes	—
346	C₈	—	2	4	no	—
347	C₈	—	4	2	no	—
348	C₂²	#388×C₁₁₃	1	2	yes	—
349	C₂²	#389×C₁₁₃	1	1	yes	characteristic
350	C₂²	#394×C₁₁₃	1	1	yes	characteristic
351	C₂²	#397×C₁₁₃	1	1	yes	characteristic
352	C₂²	#398×C₁₁₃	1	2	yes	—
353	C₂²	C₄×SD₁₆×C₁₁₃	1	2	yes	—
354	C₂²	#441×C₁₁₃	1	1	yes	characteristic
355	C₂²	#442×C₁₁₃	1	1	yes	characteristic
356	C₂²	#460×C₁₁₃	1	2	yes	—
357	C₂²	#461×C₁₁₃	1	2	yes	—
358	C₂²	#463×C₁₁₃	1	2	yes	—
359	C₂²	#464×C₁₁₃	1	2	yes	—
360	C₂²	#465×C₁₁₃	1	2	yes	—
361	C₂²	#468×C₁₁₃	1	2	yes	—
362	C₂²	#481×C₁₁₃	1	2	yes	—
363	C₂²	#482×C₁₁₃	1	2	yes	—
364	C₂²	#483×C₁₁₃	1	2	yes	—
365	C₂²	#485×C₁₁₃	1	2	yes	—
366	C₂²	#498×C₁₁₃	1	1	yes	characteristic
367	C₂²	#499×C₁₁₃	1	1	yes	characteristic
368	C₂²	#501×C₁₁₃	1	2	yes	—
369	C₄	—	4	4	no	—
370	C₄	—	8	4	no	—
371	C₄	—	8	4	no	—
372	C₄	#382×C₁₁₃	1	1	yes	characteristic
373	C₄	#385×C₁₁₃	1	1	yes	characteristic
374	C₄	#387×C₁₁₃	1	2	yes	—
375	C₄	#393×C₁₁₃	1	1	yes	characteristic
376	C₄	#400×C₁₁₃	1	2	yes	—
377	C₄	#400×C₁₁₃	1	1	yes	characteristic
378	C₂	C₁₁₃×#1442	1	1	yes	characteristic
379	C₂	C₁₁₃×#1926	1	2	yes	—
380	C₂	C₁₁₃×#1927	1	2	yes	—
381	C₂	C₁₁₃×#1941	1	1	yes	characteristic
382	C₂	C₁₁₃×#1943	1	1	yes	characteristic
383	C₂	C₁₁₃×#2055	1	2	yes	—
384	C₂	C₁₁₃×#2077	1	2	yes	—
385	C₂	C₁₁₃×#2084	1	2	yes	—
386	C₂	C₁₁₃×#2085	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
16. #340×C₁₁₃	C₄	semidirect
184. #11257	C₁₁₃	direct (N × H)
199. C₁₁₃	#11257	direct (N × H)
210. #340	C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#106×C₁₁₃	2
C₂×#340×C₁₁₃	2
C₂×#336×C₁₁₃	2
C₁₁₃×C₄⋊#95	2
#11257	113

Subgroups — C113×#11257 #43279277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#11257 #43279277