Subgroups — C₁₁₃×#21893 #43289913

Order 28928.

1410 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#423×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1987	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1895	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1802	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	—	2	1	no	—
9	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
10	#532×C₁₁₃	—	2	4	no	—
11	#532×C₁₁₃	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₁₃	—	2	1	no	—
15	C₂×#121×C₁₁₃	—	2	1	no	—
16	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
18	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
19	C₂×#117×C₁₁₃	—	2	1	no	—
20	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
21	#423×C₁₁₃	—	2	4	no	—
22	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
24	C₂×#102×C₁₁₃	C₂²	1	8	yes	—
25	#384×C₁₁₃	C₂²	1	2	yes	—
26	#382×C₁₁₃	—	2	1	no	—
27	#380×C₁₁₃	—	2	1	no	—
28	#380×C₁₁₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₁₃	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
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	C₂×M₁₆×C₁₁₃	—	2	4	no	—
44	C₂×M₁₆×C₁₁₃	—	4	4	no	—
45	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
47	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
48	#127×C₁₁₃	—	2	2	no	—
49	#127×C₁₁₃	C₂×C₄	1	4	yes	—
50	#124×C₁₁₃	—	2	8	no	—
51	#121×C₁₁₃	—	2	8	no	—
52	#121×C₁₁₃	—	2	4	no	—
53	#121×C₁₁₃	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₁₁₃	—	2	8	no	—
55	C₄×D₄×C₁₁₃	—	2	4	no	—
56	C₄×D₄×C₁₁₃	C₂×C₄	1	8	yes	—
57	#117×C₁₁₃	—	4	4	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₁₃	—	2	4	no	—
74	C₄⋊C₈×C₁₁₃	—	2	4	no	—
75	#102×C₁₁₃	—	4	8	no	—
76	#95×C₁₁₃	—	2	2	no	—
77	#95×C₁₁₃	—	2	2	no	—
78	C₂⁴×C₁₁₃	—	2	2	no	—
79	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
80	#41×C₁₁₃	—	4	32	no	—
81	C₂×Q₈×C₁₁₃	—	2	4	no	—
82	C₂×Q₈×C₁₁₃	—	4	4	no	—
83	C₂×D₄×C₁₁₃	—	2	8	no	—
84	C₂×D₄×C₁₁₃	—	2	4	no	—
85	C₂×D₄×C₁₁₃	—	2	4	no	—
86	C₂×D₄×C₁₁₃	—	2	2	no	—
87	C₂×D₄×C₁₁₃	—	2	4	no	—
88	C₂×D₄×C₁₁₃	—	2	4	no	—
89	C₂×D₄×C₁₁₃	—	4	4	no	—
90	C₂×D₄×C₁₁₃	—	4	8	no	—
91	C₂×D₄×C₁₁₃	—	4	2	no	—
92	C₂×D₄×C₁₁₃	—	4	2	no	—
93	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₁₃	—	4	8	no	—
103	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₁₁₃	—	4	8	no	—
114	C₂×C₈×C₁₁₃	—	2	4	no	—
115	C₂×C₈×C₁₁₃	—	2	8	no	—
116	C₄⋊C₄×C₁₁₃	—	2	4	no	—
117	C₄⋊C₄×C₁₁₃	—	2	2	no	—
118	C₄⋊C₄×C₁₁₃	—	2	4	no	—
119	C₄⋊C₄×C₁₁₃	—	2	4	no	—
120	C₄⋊C₄×C₁₁₃	—	4	4	no	—
121	C₄⋊C₄×C₁₁₃	—	4	4	no	—
122	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
124	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
125	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
126	C₄²×C₁₁₃	—	4	4	no	—
127	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
129	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
132	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
133	C₂³×C₁₁₃	—	2	2	no	—
134	C₂³×C₁₁₃	—	2	1	no	—
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	2	1	no	—
137	C₂³×C₁₁₃	—	2	4	no	—
138	C₂³×C₁₁₃	—	4	4	no	—
139	C₂³×C₁₁₃	—	4	4	no	—
140	C₂³×C₁₁₃	—	4	2	no	—
141	C₂³×C₁₁₃	—	4	2	no	—
142	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₁₃	—	4	8	no	—
145	D₄×C₁₁₃	—	2	8	no	—
146	D₄×C₁₁₃	—	4	8	no	—
147	D₄×C₁₁₃	—	4	16	no	—
148	D₄×C₁₁₃	—	4	2	no	—
149	D₄×C₁₁₃	—	4	2	no	—
150	D₄×C₁₁₃	—	4	8	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	1	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	2	1	no	—
155	C₂×C₄×C₁₁₃	—	2	4	no	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	8	no	—
159	C₂×C₄×C₁₁₃	—	2	8	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	4	4	no	—
162	C₂×C₄×C₁₁₃	—	4	16	no	—
163	C₂×C₄×C₁₁₃	—	4	4	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	4	no	—
166	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
173	C₂×C₄×C₁₁₃	#137	1	2	yes	—
174	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
177	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
178	C₈×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	2	2	no	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	2	no	—
182	C₂²×C₁₁₃	—	4	2	no	—
183	C₂²×C₁₁₃	—	4	2	no	—
184	C₂²×C₁₁₃	—	4	4	no	—
185	C₂²×C₁₁₃	—	4	4	no	—
186	C₂²×C₁₁₃	—	4	4	no	—
187	C₂²×C₁₁₃	—	8	4	no	—
188	C₂²×C₁₁₃	—	8	4	no	—
189	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₁₁₃	#537	1	2	yes	—
191	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
192	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₁₁₃	C₂×#137	1	1	yes	characteristic
194	C₄×C₁₁₃	—	2	2	no	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	2	no	—
197	C₄×C₁₁₃	—	4	4	no	—
198	C₄×C₁₁₃	—	8	4	no	—
199	C₄×C₁₁₃	#417	1	4	yes	—
200	C₄×C₁₁₃	#418	1	4	yes	—
201	C₄×C₁₁₃	#520	1	2	yes	—
202	C₄×C₁₁₃	#535	1	1	yes	characteristic
203	C₄×C₁₁₃	#536	1	1	yes	characteristic
204	#21893	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₁₁₃	—	4	2	no	—
206	C₂×C₁₁₃	—	8	4	no	—
207	C₂×C₁₁₃	#2311	1	1	yes	characteristic
208	C₂×C₁₁₃	C₂×#418	1	1	yes	characteristic
209	C₂×C₁₁₃	C₂×#417	1	1	yes	characteristic
210	C₂×C₁₁₃	#3253	1	2	yes	—
211	C₂×C₁₁₃	#3254	1	2	yes	—
212	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic
213	C₂×#423	C₂×C₁₁₃	1	1	yes	characteristic, complemented
214	#2285	C₂×C₁₁₃	1	1	yes	characteristic, complemented
215	#1987	C₂×C₁₁₃	1	2	yes	complemented
216	#1982	C₂×C₁₁₃	1	2	yes	complemented
217	#1895	C₂×C₁₁₃	1	4	yes	complemented
218	#1802	C₂×C₁₁₃	1	4	yes	complemented
219	C₁₁₃	#21893	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²×#41	—	2	1	no	—
221	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
222	#532	—	2	4	no	—
223	#532	C₄×C₁₁₃	1	8	yes	complemented
224	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
225	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
226	C₂×#124	—	2	1	no	—
227	C₂×#121	—	2	1	no	—
228	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
231	C₂×#117	—	2	1	no	—
232	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
233	#423	—	2	4	no	—
234	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
236	C₂×#102	C₂²×C₁₁₃	1	8	yes	—
237	#384	C₂²×C₁₁₃	1	2	yes	—
238	#382	—	2	1	no	—
239	#380	—	2	1	no	—
240	#380	C₂²×C₁₁₃	1	2	yes	—
241	C₄×C₄⋊C₄	—	2	1	no	—
242	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
243	#340	C₂²×C₁₁₃	1	8	yes	—
244	C₂×#41	—	2	8	no	—
245	C₂×#41	—	4	8	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
255	C₂×M₁₆	—	2	4	no	—
256	C₂×M₁₆	—	4	4	no	—
257	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
260	#127	—	2	2	no	—
261	#127	C₂×C₄×C₁₁₃	1	4	yes	—
262	#124	—	2	8	no	—
263	#121	—	2	8	no	—
264	#121	—	2	4	no	—
265	#121	C₂×C₄×C₁₁₃	1	8	yes	—
266	C₄×D₄	—	2	8	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	C₂×C₄×C₁₁₃	1	8	yes	—
269	#117	—	4	4	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
280	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
285	C₄⋊C₈	—	2	4	no	—
286	C₄⋊C₈	—	2	4	no	—
287	#102	—	4	8	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
292	#41	—	4	32	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	4	8	no	—
315	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
316	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
325	M₁₆	—	4	8	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	8	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	4	4	no	—
339	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
340	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
341	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
342	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
343	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
344	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
355	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
356	Q₈	—	4	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	4	8	no	—
359	D₄	—	4	16	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
383	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
384	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
385	C₂×C₄	#137×C₁₁₃	1	2	yes	—
386	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
388	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
389	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
390	C₈	—	4	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
402	C₂²	#537×C₁₁₃	1	2	yes	—
403	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
404	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
405	C₂²	C₂×#137×C₁₁₃	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	4	no	—
411	C₄	#417×C₁₁₃	1	4	yes	—
412	C₄	#418×C₁₁₃	1	4	yes	—
413	C₄	#520×C₁₁₃	1	2	yes	—
414	C₄	#535×C₁₁₃	1	1	yes	characteristic
415	C₄	#536×C₁₁₃	1	1	yes	characteristic
416	C₂	—	4	2	no	—
417	C₂	—	8	4	no	—
418	C₂	C₁₁₃×#2311	1	1	yes	characteristic
419	C₂	C₂×#418×C₁₁₃	1	1	yes	characteristic
420	C₂	C₂×#417×C₁₁₃	1	1	yes	characteristic
421	C₂	C₁₁₃×#3253	1	2	yes	—
422	C₂	C₁₁₃×#3254	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×#423×C₁₁₃	C₂	semidirect
3. C₁₁₃×#2285	C₂	semidirect
4. C₁₁₃×#1987	C₂	semidirect
5. C₁₁₃×#1982	C₂	semidirect
6. C₁₁₃×#1895	C₂	semidirect
7. C₁₁₃×#1802	C₂	semidirect
11. #532×C₁₁₃	C₄	semidirect
204. #21893	C₁₁₃	direct (N × H)
213. C₂×#423	C₂×C₁₁₃	semidirect
214. #2285	C₂×C₁₁₃	semidirect
215. #1987	C₂×C₁₁₃	semidirect
216. #1982	C₂×C₁₁₃	semidirect
217. #1895	C₂×C₁₁₃	semidirect
218. #1802	C₂×C₁₁₃	semidirect
219. C₁₁₃	#21893	direct (N × H)
223. #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×#423×C₁₁₃	2
C₁₁₃×#2285	2
C₁₁₃×#1987	2
C₁₁₃×#1982	2
C₁₁₃×#1895	2
C₁₁₃×#1802	2
#21893	113

Subgroups — C113×#21893 #43289913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21893 #43289913