Subgroups — C₁₁₃×#21863 #43289883

Order 28928.

1386 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1990	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1957	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1875	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1804	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	—	2	1	no	—
9	#532×C₁₁₃	—	2	4	no	—
10	#532×C₁₁₃	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₁₃	—	2	1	no	—
14	C₂×#121×C₁₁₃	—	2	1	no	—
15	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	#431×C₁₁₃	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
22	C₂×#102×C₁₁₃	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
25	#384×C₁₁₃	C₂²	1	2	yes	—
26	#382×C₁₁₃	C₂²	1	2	yes	—
27	#380×C₁₁₃	—	2	1	no	—
28	#380×C₁₁₃	—	2	1	no	—
29	C₄×C₄⋊C₄×C₁₁₃	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₁₃	—	2	1	no	—
31	#340×C₁₁₃	C₂²	1	8	yes	—
32	C₂×#41×C₁₁₃	—	2	8	no	—
33	C₂×#41×C₁₁₃	—	4	8	no	—
34	C₂²×Q₈×C₁₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₁₃	—	2	2	no	—
40	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
44	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
45	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
46	#127×C₁₁₃	—	2	2	no	—
47	#127×C₁₁₃	C₂×C₄	1	4	yes	—
48	#124×C₁₁₃	—	2	8	no	—
49	#121×C₁₁₃	—	2	8	no	—
50	#121×C₁₁₃	—	2	4	no	—
51	#121×C₁₁₃	C₂×C₄	1	8	yes	—
52	C₄×D₄×C₁₁₃	—	2	8	no	—
53	C₄×D₄×C₁₁₃	—	2	4	no	—
54	C₄×D₄×C₁₁₃	C₂×C₄	1	8	yes	—
55	#117×C₁₁₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
69	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₁₃	—	2	4	no	—
72	#102×C₁₁₃	—	4	8	no	—
73	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
74	C₄×C₈×C₁₁₃	—	2	4	no	—
75	#95×C₁₁₃	—	2	2	no	—
76	#95×C₁₁₃	—	2	2	no	—
77	C₂⁴×C₁₁₃	—	2	2	no	—
78	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₁₃	—	4	32	no	—
80	C₂×Q₈×C₁₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₁₃	—	4	4	no	—
82	C₂×D₄×C₁₁₃	—	2	8	no	—
83	C₂×D₄×C₁₁₃	—	2	4	no	—
84	C₂×D₄×C₁₁₃	—	2	4	no	—
85	C₂×D₄×C₁₁₃	—	2	2	no	—
86	C₂×D₄×C₁₁₃	—	2	4	no	—
87	C₂×D₄×C₁₁₃	—	2	4	no	—
88	C₂×D₄×C₁₁₃	—	4	8	no	—
89	C₂×D₄×C₁₁₃	—	4	4	no	—
90	C₂×D₄×C₁₁₃	—	4	4	no	—
91	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₁₃	—	2	8	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	4	8	no	—
100	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₁₃	—	2	4	no	—
111	C₂×C₈×C₁₁₃	—	2	4	no	—
112	C₂×C₈×C₁₁₃	—	2	4	no	—
113	C₄⋊C₄×C₁₁₃	—	2	4	no	—
114	C₄⋊C₄×C₁₁₃	—	2	2	no	—
115	C₄⋊C₄×C₁₁₃	—	2	8	no	—
116	C₄⋊C₄×C₁₁₃	—	4	4	no	—
117	C₄⋊C₄×C₁₁₃	—	4	4	no	—
118	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
120	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
121	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
122	C₄²×C₁₁₃	—	4	4	no	—
123	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
128	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
129	C₂³×C₁₁₃	—	2	1	no	—
130	C₂³×C₁₁₃	—	2	1	no	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	2	4	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	—	4	4	no	—
137	C₂³×C₁₁₃	—	4	4	no	—
138	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₁₃	—	4	8	no	—
141	D₄×C₁₁₃	—	2	8	no	—
142	D₄×C₁₁₃	—	4	16	no	—
143	D₄×C₁₁₃	—	4	4	no	—
144	D₄×C₁₁₃	—	4	8	no	—
145	D₄×C₁₁₃	—	4	8	no	—
146	C₂×C₄×C₁₁₃	—	2	1	no	—
147	C₂×C₄×C₁₁₃	—	2	1	no	—
148	C₂×C₄×C₁₁₃	—	2	2	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	4	no	—
151	C₂×C₄×C₁₁₃	—	2	4	no	—
152	C₂×C₄×C₁₁₃	—	2	8	no	—
153	C₂×C₄×C₁₁₃	—	2	8	no	—
154	C₂×C₄×C₁₁₃	—	2	4	no	—
155	C₂×C₄×C₁₁₃	—	4	16	no	—
156	C₂×C₄×C₁₁₃	—	4	4	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	—	4	4	no	—
159	C₂×C₄×C₁₁₃	—	4	4	no	—
160	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₁₃	#135	1	4	yes	—
166	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
167	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
171	C₈×C₁₁₃	—	4	4	no	—
172	C₂²×C₁₁₃	—	2	2	no	—
173	C₂²×C₁₁₃	—	2	2	no	—
174	C₂²×C₁₁₃	—	2	2	no	—
175	C₂²×C₁₁₃	—	4	2	no	—
176	C₂²×C₁₁₃	—	4	2	no	—
177	C₂²×C₁₁₃	—	4	4	no	—
178	C₂²×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	4	4	no	—
180	C₂²×C₁₁₃	—	8	4	no	—
181	C₂²×C₁₁₃	—	8	4	no	—
182	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₁₃	#535	1	1	yes	characteristic
184	C₂²×C₁₁₃	#536	1	1	yes	characteristic
185	C₂²×C₁₁₃	C₂×#135	1	2	yes	—
186	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
187	C₄×C₁₁₃	—	2	2	no	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	4	4	no	—
191	C₄×C₁₁₃	—	8	4	no	—
192	C₄×C₁₁₃	#416	1	4	yes	—
193	C₄×C₁₁₃	#418	1	4	yes	—
194	C₄×C₁₁₃	#520	1	2	yes	—
195	C₄×C₁₁₃	#537	1	2	yes	—
196	#21863	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₁₁₃	—	4	2	no	—
198	C₂×C₁₁₃	—	8	4	no	—
199	C₂×C₁₁₃	#2311	1	1	yes	characteristic
200	C₂×C₁₁₃	C₂×#416	1	1	yes	characteristic
201	C₂×C₁₁₃	C₂×#418	1	1	yes	characteristic
202	C₂×C₁₁₃	#3207	1	2	yes	—
203	C₂×C₁₁₃	#3228	1	2	yes	—
204	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic
205	C₂×#431	C₂×C₁₁₃	1	1	yes	characteristic, complemented
206	#2285	C₂×C₁₁₃	1	1	yes	characteristic, complemented
207	#1990	C₂×C₁₁₃	1	2	yes	complemented
208	#1957	C₂×C₁₁₃	1	2	yes	complemented
209	#1875	C₂×C₁₁₃	1	4	yes	complemented
210	#1804	C₂×C₁₁₃	1	4	yes	complemented
211	C₁₁₃	#21863	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²×#41	—	2	1	no	—
213	#532	—	2	4	no	—
214	#532	C₄×C₁₁₃	1	8	yes	complemented
215	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
217	C₂×#124	—	2	1	no	—
218	C₂×#121	—	2	1	no	—
219	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
222	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
224	#431	—	2	4	no	—
225	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₁₃	1	8	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
229	#384	C₂²×C₁₁₃	1	2	yes	—
230	#382	C₂²×C₁₁₃	1	2	yes	—
231	#380	—	2	1	no	—
232	#380	—	2	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	#340	C₂²×C₁₁₃	1	8	yes	—
236	C₂×#41	—	2	8	no	—
237	C₂×#41	—	4	8	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
250	#127	—	2	2	no	—
251	#127	C₂×C₄×C₁₁₃	1	4	yes	—
252	#124	—	2	8	no	—
253	#121	—	2	8	no	—
254	#121	—	2	4	no	—
255	#121	C₂×C₄×C₁₁₃	1	8	yes	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	C₂×C₄×C₁₁₃	1	8	yes	—
259	#117	—	4	4	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
270	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
273	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	4	no	—
276	#102	—	4	8	no	—
277	C₂²⋊C₈	—	2	4	no	—
278	C₄×C₈	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
283	#41	—	4	32	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	4	8	no	—
304	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₄²	—	4	4	no	—
327	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
328	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
329	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
330	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
331	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
332	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
343	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
344	Q₈	—	4	8	no	—
345	D₄	—	2	8	no	—
346	D₄	—	4	16	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	8	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	16	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
369	C₂×C₄	#135×C₁₁₃	1	4	yes	—
370	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
371	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
373	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
374	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
375	C₈	—	4	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
387	C₂²	#535×C₁₁₃	1	1	yes	characteristic
388	C₂²	#536×C₁₁₃	1	1	yes	characteristic
389	C₂²	C₂×#135×C₁₁₃	1	2	yes	—
390	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	4	no	—
396	C₄	#416×C₁₁₃	1	4	yes	—
397	C₄	#418×C₁₁₃	1	4	yes	—
398	C₄	#520×C₁₁₃	1	2	yes	—
399	C₄	#537×C₁₁₃	1	2	yes	—
400	C₂	—	4	2	no	—
401	C₂	—	8	4	no	—
402	C₂	C₁₁₃×#2311	1	1	yes	characteristic
403	C₂	C₂×#416×C₁₁₃	1	1	yes	characteristic
404	C₂	C₂×#418×C₁₁₃	1	1	yes	characteristic
405	C₂	C₁₁₃×#3207	1	2	yes	—
406	C₂	C₁₁₃×#3228	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#532×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₁₃	C₂	semidirect
3. C₁₁₃×#2285	C₂	semidirect
4. C₁₁₃×#1990	C₂	semidirect
5. C₁₁₃×#1957	C₂	semidirect
6. C₁₁₃×#1875	C₂	semidirect
7. C₁₁₃×#1804	C₂	semidirect
10. #532×C₁₁₃	C₄	semidirect
196. #21863	C₁₁₃	direct (N × H)
205. C₂×#431	C₂×C₁₁₃	semidirect
206. #2285	C₂×C₁₁₃	semidirect
207. #1990	C₂×C₁₁₃	semidirect
208. #1957	C₂×C₁₁₃	semidirect
209. #1875	C₂×C₁₁₃	semidirect
210. #1804	C₂×C₁₁₃	semidirect
211. C₁₁₃	#21863	direct (N × H)
214. #532	C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₁₃	2
C₂×#431×C₁₁₃	2
C₁₁₃×#2285	2
C₁₁₃×#1990	2
C₁₁₃×#1957	2
C₁₁₃×#1875	2
C₁₁₃×#1804	2
#21863	113

Subgroups — C113×#21863 #43289883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21863 #43289883