Subgroups — C₁₁₃×#20973 #43288993

Order 28928.

2238 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#418×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1895	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1893	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1736	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₁₃	—	2	1	no	—
9	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₁₃	—	2	4	no	—
12	C₂²×M₁₆×C₁₁₃	—	2	8	no	—
13	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	complemented
15	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	complemented
16	C₂×#121×C₁₁₃	—	2	4	no	—
17	C₂×#121×C₁₁₃	—	2	1	no	—
18	C₂×#121×C₁₁₃	—	2	1	no	—
19	C₂×#121×C₁₁₃	C₄	1	8	yes	complemented
20	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
21	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
22	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
25	#418×C₁₁₃	—	2	8	no	—
26	C₂×#102×C₁₁₃	C₂²	1	8	yes	complemented
27	#381×C₁₁₃	—	2	1	no	—
28	#380×C₁₁₃	C₂²	1	2	yes	complemented
29	#380×C₁₁₃	C₂²	1	2	yes	complemented
30	#379×C₁₁₃	—	2	1	no	—
31	C₄×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
32	C₄×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
33	#340×C₁₁₃	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₁₃	—	2	1	no	—
35	C₂⁵×C₁₁₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₁₃	—	2	8	no	—
37	C₂²×D₄×C₁₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₁₃	—	4	8	no	—
44	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
45	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
50	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
54	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₁₃	—	2	32	no	—
58	C₂×M₁₆×C₁₁₃	—	2	4	no	—
59	C₂×M₁₆×C₁₁₃	—	2	4	no	—
60	C₂×M₁₆×C₁₁₃	—	2	4	no	—
61	C₂×M₁₆×C₁₁₃	—	2	8	no	—
62	C₂×M₁₆×C₁₁₃	D₄	1	8	yes	complemented
63	C₂²×C₈×C₁₁₃	—	2	4	no	—
64	C₂²×C₈×C₁₁₃	—	2	8	no	—
65	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
66	#121×C₁₁₃	—	2	8	no	—
67	#121×C₁₁₃	—	2	8	no	—
68	#121×C₁₁₃	—	2	4	no	—
69	#121×C₁₁₃	—	2	4	no	—
70	#121×C₁₁₃	C₂×C₄	1	8	yes	—
71	#121×C₁₁₃	C₂×C₄	1	8	yes	—
72	#117×C₁₁₃	—	2	4	no	—
73	#117×C₁₁₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
85	C₂×C₄²×C₁₁₃	—	2	2	no	—
86	#102×C₁₁₃	—	2	16	no	—
87	#95×C₁₁₃	—	2	2	no	—
88	#95×C₁₁₃	—	2	2	no	—
89	C₂⁴×C₁₁₃	—	2	4	no	—
90	C₂⁴×C₁₁₃	—	2	4	no	—
91	C₂⁴×C₁₁₃	—	2	4	no	—
92	C₂⁴×C₁₁₃	—	2	2	no	—
93	C₂⁴×C₁₁₃	—	4	2	no	—
94	C₂⁴×C₁₁₃	—	4	4	no	—
95	C₂⁴×C₁₁₃	—	4	4	no	—
96	C₂⁴×C₁₁₃	—	4	4	no	—
97	C₂⁴×C₁₁₃	C₂²⋊C₄	1	4	yes	—
98	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₁₁₃	—	2	8	no	—
102	C₂×D₄×C₁₁₃	—	2	8	no	—
103	C₂×D₄×C₁₁₃	—	2	4	no	—
104	C₂×D₄×C₁₁₃	—	2	16	no	—
105	C₂×D₄×C₁₁₃	—	2	4	no	—
106	C₂×D₄×C₁₁₃	—	2	2	no	—
107	C₂×D₄×C₁₁₃	—	2	4	no	—
108	C₂×D₄×C₁₁₃	—	4	32	no	—
109	C₂×D₄×C₁₁₃	—	4	8	no	—
110	C₂×D₄×C₁₁₃	—	4	8	no	—
111	C₂×D₄×C₁₁₃	—	4	4	no	—
112	C₂×D₄×C₁₁₃	—	4	4	no	—
113	C₂×D₄×C₁₁₃	—	4	4	no	—
114	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₁₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₁₃	—	2	16	no	—
117	C₂²×C₄×C₁₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₁₃	—	4	4	no	—
129	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
130	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
131	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
132	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
143	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₁₁₃	—	2	16	no	—
145	M₁₆×C₁₁₃	—	2	16	no	—
146	C₂×C₈×C₁₁₃	—	2	16	no	—
147	C₂×C₈×C₁₁₃	—	2	4	no	—
148	C₂×C₈×C₁₁₃	—	2	4	no	—
149	C₂×C₈×C₁₁₃	C₂×D₄	1	8	yes	complemented
150	C₄⋊C₄×C₁₁₃	—	2	4	no	—
151	C₄⋊C₄×C₁₁₃	—	2	2	no	—
152	C₄⋊C₄×C₁₁₃	—	2	4	no	—
153	C₄⋊C₄×C₁₁₃	—	2	4	no	—
154	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
155	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
156	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
157	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
158	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
159	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
160	C₄²×C₁₁₃	—	4	4	no	—
161	C₂³×C₁₁₃	—	2	2	no	—
162	C₂³×C₁₁₃	—	2	2	no	—
163	C₂³×C₁₁₃	—	2	2	no	—
164	C₂³×C₁₁₃	—	2	2	no	—
165	C₂³×C₁₁₃	—	2	2	no	—
166	C₂³×C₁₁₃	—	2	2	no	—
167	C₂³×C₁₁₃	—	2	2	no	—
168	C₂³×C₁₁₃	—	2	8	no	—
169	C₂³×C₁₁₃	—	2	8	no	—
170	C₂³×C₁₁₃	—	2	4	no	—
171	C₂³×C₁₁₃	—	4	4	no	—
172	C₂³×C₁₁₃	—	4	16	no	—
173	C₂³×C₁₁₃	—	4	8	no	—
174	C₂³×C₁₁₃	—	4	8	no	—
175	C₂³×C₁₁₃	—	4	4	no	—
176	C₂³×C₁₁₃	—	4	4	no	—
177	C₂³×C₁₁₃	—	4	4	no	—
178	C₂³×C₁₁₃	—	4	8	no	—
179	C₂³×C₁₁₃	—	8	16	no	—
180	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₁₁₃	#121	1	4	yes	—
184	C₂³×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
185	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
186	D₄×C₁₁₃	—	2	8	no	—
187	D₄×C₁₁₃	—	4	16	no	—
188	D₄×C₁₁₃	—	4	16	no	—
189	D₄×C₁₁₃	—	4	2	no	—
190	D₄×C₁₁₃	—	4	2	no	—
191	D₄×C₁₁₃	—	4	8	no	—
192	C₂×C₄×C₁₁₃	—	2	2	no	—
193	C₂×C₄×C₁₁₃	—	2	2	no	—
194	C₂×C₄×C₁₁₃	—	2	8	no	—
195	C₂×C₄×C₁₁₃	—	2	4	no	—
196	C₂×C₄×C₁₁₃	—	2	4	no	—
197	C₂×C₄×C₁₁₃	—	2	2	no	—
198	C₂×C₄×C₁₁₃	—	2	2	no	—
199	C₂×C₄×C₁₁₃	—	2	2	no	—
200	C₂×C₄×C₁₁₃	—	2	2	no	—
201	C₂×C₄×C₁₁₃	—	2	8	no	—
202	C₂×C₄×C₁₁₃	—	2	8	no	—
203	C₂×C₄×C₁₁₃	—	2	4	no	—
204	C₂×C₄×C₁₁₃	—	4	8	no	—
205	C₂×C₄×C₁₁₃	—	4	4	no	—
206	C₂×C₄×C₁₁₃	—	4	4	no	—
207	C₂×C₄×C₁₁₃	—	4	4	no	—
208	C₂×C₄×C₁₁₃	—	4	4	no	—
209	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₁₁₃	C₄×D₄	1	8	yes	—
213	C₂×C₄×C₁₁₃	#120	1	4	yes	—
214	C₂×C₄×C₁₁₃	#121	1	4	yes	—
215	C₂×C₄×C₁₁₃	#123	1	4	yes	—
216	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
220	C₈×C₁₁₃	—	2	8	no	—
221	C₂²×C₁₁₃	—	2	2	no	—
222	C₂²×C₁₁₃	—	2	2	no	—
223	C₂²×C₁₁₃	—	2	2	no	—
224	C₂²×C₁₁₃	—	2	2	no	—
225	C₂²×C₁₁₃	—	2	8	no	—
226	C₂²×C₁₁₃	—	2	8	no	—
227	C₂²×C₁₁₃	—	2	2	no	—
228	C₂²×C₁₁₃	—	2	2	no	—
229	C₂²×C₁₁₃	—	2	2	no	—
230	C₂²×C₁₁₃	—	4	16	no	—
231	C₂²×C₁₁₃	—	4	4	no	—
232	C₂²×C₁₁₃	—	4	4	no	—
233	C₂²×C₁₁₃	—	4	4	no	—
234	C₂²×C₁₁₃	—	4	4	no	—
235	C₂²×C₁₁₃	—	8	16	no	—
236	C₂²×C₁₁₃	—	8	8	no	—
237	C₂²×C₁₁₃	#386	1	4	yes	—
238	C₂²×C₁₁₃	#418	1	4	yes	complemented
239	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
241	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
242	C₂²×C₁₁₃	#575	1	2	yes	—
243	C₄×C₁₁₃	—	2	2	no	—
244	C₄×C₁₁₃	—	2	2	no	—
245	C₄×C₁₁₃	—	4	4	no	—
246	C₄×C₁₁₃	—	8	4	no	—
247	C₄×C₁₁₃	#386	1	4	yes	—
248	C₄×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
249	C₄×C₁₁₃	C₂×#120	1	1	yes	characteristic
250	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
251	#20973	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂×C₁₁₃	—	2	4	no	—
253	C₂×C₁₁₃	—	2	4	no	—
254	C₂×C₁₁₃	—	4	2	no	—
255	C₂×C₁₁₃	—	8	4	no	—
256	C₂×C₁₁₃	C₂×#386	1	1	yes	characteristic
257	C₂×C₁₁₃	C₂×#418	1	1	yes	characteristic
258	C₂×C₁₁₃	#2896	1	1	yes	characteristic
259	C₂×C₁₁₃	#3055	1	4	yes	—
260	C₂³×M₁₆	C₂×C₁₁₃	1	1	yes	characteristic, complemented
261	C₂²×#121	C₂×C₁₁₃	1	1	yes	characteristic
262	C₂×#418	C₂×C₁₁₃	1	2	yes	complemented
263	#2280	C₂×C₁₁₃	1	1	yes	characteristic, complemented
264	#1895	C₂×C₁₁₃	1	4	yes	complemented
265	#1893	C₂×C₁₁₃	1	4	yes	complemented
266	#1736	C₂×C₁₁₃	1	2	yes	complemented
267	C₁₁₃	#20973	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³×D₄	—	2	1	no	—
269	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
271	C₂²×M₁₆	—	2	4	no	—
272	C₂²×M₁₆	—	2	8	no	—
273	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
274	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	complemented
275	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	complemented
276	C₂×#121	—	2	4	no	—
277	C₂×#121	—	2	1	no	—
278	C₂×#121	—	2	1	no	—
279	C₂×#121	C₄×C₁₁₃	1	8	yes	complemented
280	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
281	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
282	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	—	2	1	no	—
285	#418	—	2	8	no	—
286	C₂×#102	C₂²×C₁₁₃	1	8	yes	complemented
287	#381	—	2	1	no	—
288	#380	C₂²×C₁₁₃	1	2	yes	complemented
289	#380	C₂²×C₁₁₃	1	2	yes	complemented
290	#379	—	2	1	no	—
291	C₄×C₂²⋊C₄	—	2	1	no	—
292	C₄×C₂²⋊C₄	—	2	1	no	—
293	#340	C₂²×C₁₁₃	1	8	yes	complemented
294	C₂⁵	—	2	1	no	—
295	C₂⁵	D₄×C₁₁₃	1	1	yes	characteristic
296	C₂²×D₄	—	2	8	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	—	4	8	no	—
304	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
305	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
306	C₂³×C₄	—	2	4	no	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
310	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
311	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
314	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
317	C₂×M₁₆	—	2	32	no	—
318	C₂×M₁₆	—	2	4	no	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	—	2	8	no	—
322	C₂×M₁₆	D₄×C₁₁₃	1	8	yes	complemented
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	8	no	—
325	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
326	#121	—	2	8	no	—
327	#121	—	2	8	no	—
328	#121	—	2	4	no	—
329	#121	—	2	4	no	—
330	#121	C₂×C₄×C₁₁₃	1	8	yes	—
331	#121	C₂×C₄×C₁₁₃	1	8	yes	—
332	#117	—	2	4	no	—
333	#117	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	#102	—	2	16	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	4	4	no	—
355	C₂⁴	—	4	4	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	C₂²⋊C₄×C₁₁₃	1	4	yes	—
358	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
359	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
360	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	32	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	16	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
390	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
391	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
392	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
394	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
402	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
404	M₁₆	—	2	16	no	—
405	M₁₆	—	2	16	no	—
406	C₂×C₈	—	2	16	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	C₂×D₄×C₁₁₃	1	8	yes	complemented
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₄²	—	4	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	16	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	4	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	8	16	no	—
440	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
441	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
442	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
443	C₂³	#121×C₁₁₃	1	4	yes	—
444	C₂³	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
445	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
446	D₄	—	2	8	no	—
447	D₄	—	4	16	no	—
448	D₄	—	4	16	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	8	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
471	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
472	C₂×C₄	C₄×D₄×C₁₁₃	1	8	yes	—
473	C₂×C₄	#120×C₁₁₃	1	4	yes	—
474	C₂×C₄	#121×C₁₁₃	1	4	yes	—
475	C₂×C₄	#123×C₁₁₃	1	4	yes	—
476	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
480	C₈	—	2	8	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	8	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	4	16	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	16	no	—
496	C₂²	—	8	8	no	—
497	C₂²	#386×C₁₁₃	1	4	yes	—
498	C₂²	#418×C₁₁₃	1	4	yes	complemented
499	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
500	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
501	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
502	C₂²	#575×C₁₁₃	1	2	yes	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	8	4	no	—
507	C₄	#386×C₁₁₃	1	4	yes	—
508	C₄	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
509	C₄	C₂×#120×C₁₁₃	1	1	yes	characteristic
510	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
511	C₂	—	2	4	no	—
512	C₂	—	2	4	no	—
513	C₂	—	4	2	no	—
514	C₂	—	8	4	no	—
515	C₂	C₂×#386×C₁₁₃	1	1	yes	characteristic
516	C₂	C₂×#418×C₁₁₃	1	1	yes	characteristic
517	C₂	C₁₁₃×#2896	1	1	yes	characteristic
518	C₂	C₁₁₃×#3055	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×#121×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂⁴×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₁₁₃	C₂	semidirect
3. C₂×#418×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2280	C₂	semidirect
5. C₁₁₃×#1895	C₂	semidirect
6. C₁₁₃×#1893	C₂	semidirect
7. C₁₁₃×#1736	C₂	semidirect
14. C₂²×M₁₆×C₁₁₃	C₂²	semidirect
15. C₂³×C₈×C₁₁₃	C₂²	semidirect
19. C₂×#121×C₁₁₃	C₄	semidirect
26. C₂×#102×C₁₁₃	C₂²	semidirect
28. #380×C₁₁₃	C₂²	semidirect
29. #380×C₁₁₃	C₂²	semidirect
33. #340×C₁₁₃	C₂²	semidirect
62. C₂×M₁₆×C₁₁₃	D₄	semidirect
149. C₂×C₈×C₁₁₃	C₂×D₄	semidirect
238. C₂²×C₁₁₃	#418	semidirect
251. #20973	C₁₁₃	direct (N × H)
260. C₂³×M₁₆	C₂×C₁₁₃	semidirect
262. C₂×#418	C₂×C₁₁₃	semidirect
263. #2280	C₂×C₁₁₃	semidirect
264. #1895	C₂×C₁₁₃	semidirect
265. #1893	C₂×C₁₁₃	semidirect
266. #1736	C₂×C₁₁₃	semidirect
267. C₁₁₃	#20973	direct (N × H)
274. C₂²×M₁₆	C₂²×C₁₁₃	semidirect
275. C₂³×C₈	C₂²×C₁₁₃	semidirect
279. C₂×#121	C₄×C₁₁₃	semidirect
286. C₂×#102	C₂²×C₁₁₃	semidirect
288. #380	C₂²×C₁₁₃	semidirect
289. #380	C₂²×C₁₁₃	semidirect
293. #340	C₂²×C₁₁₃	semidirect
322. C₂×M₁₆	D₄×C₁₁₃	semidirect
409. C₂×C₈	C₂×D₄×C₁₁₃	semidirect
498. C₂²	#418×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₁₃	2
C₂²×#121×C₁₁₃	2
C₂×#418×C₁₁₃	2
C₁₁₃×#2280	2
C₁₁₃×#1895	2
C₁₁₃×#1893	2
C₁₁₃×#1736	2
#20973	113

Subgroups — C113×#20973 #43288993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20973 #43288993