Subgroups — C₁₁₃×#22431 #43290451

Order 28928.

1530 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#436×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	D₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#1894	C₂	1	2	yes	maximal, complemented
8	C₁₁₃×#1872	C₂	1	2	yes	maximal, complemented
9	C₁₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁₃×#1788	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₁₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
14	#547×C₁₁₃	—	2	4	no	—
15	#547×C₁₁₃	C₄	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×#123×C₁₁₃	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
19	C₂×#121×C₁₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
21	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₁₃	—	2	1	no	—
24	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
25	#436×C₁₁₃	—	2	4	no	—
26	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
27	#417×C₁₁₃	—	2	8	no	—
28	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
30	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
31	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
32	C₂×#102×C₁₁₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
34	C₂×#102×C₁₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
37	#389×C₁₁₃	—	2	1	no	—
38	#385×C₁₁₃	—	2	2	no	—
39	#384×C₁₁₃	C₂²	1	1	yes	characteristic
40	#380×C₁₁₃	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
42	#340×C₁₁₃	C₂²	1	2	yes	—
43	#340×C₁₁₃	C₂²	1	1	yes	characteristic
44	#340×C₁₁₃	C₂²	1	1	yes	characteristic
45	C₂×#41×C₁₁₃	—	2	4	no	—
46	C₂×#41×C₁₁₃	—	2	4	no	—
47	C₂×#41×C₁₁₃	—	2	4	no	—
48	C₂×#41×C₁₁₃	—	4	2	no	—
49	C₂×#41×C₁₁₃	—	4	2	no	—
50	C₂×#41×C₁₁₃	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₁₃	—	2	4	no	—
60	C₂×M₁₆×C₁₁₃	—	2	4	no	—
61	C₂×M₁₆×C₁₁₃	—	4	2	no	—
62	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
66	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
67	#123×C₁₁₃	—	2	16	no	—
68	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
69	C₂²⋊Q₈×C₁₁₃	C₂×C₄	1	8	yes	complemented
70	#121×C₁₁₃	—	2	8	no	—
71	C₄×D₄×C₁₁₃	—	2	2	no	—
72	C₄×D₄×C₁₁₃	—	4	4	no	—
73	C₄×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
75	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
80	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₁₃	—	4	2	no	—
85	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
94	C₂×C₄²×C₁₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₁₁₃	—	2	2	no	—
97	#103×C₁₁₃	—	2	4	no	—
98	#103×C₁₁₃	—	2	4	no	—
99	#103×C₁₁₃	—	4	2	no	—
100	#103×C₁₁₃	—	4	2	no	—
101	#102×C₁₁₃	—	2	4	no	—
102	#102×C₁₁₃	—	2	2	no	—
103	#102×C₁₁₃	D₄	1	4	yes	complemented
104	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
105	C₄×C₈×C₁₁₃	—	2	2	no	—
106	#95×C₁₁₃	—	2	1	no	—
107	#95×C₁₁₃	—	2	2	no	—
108	C₂⁴×C₁₁₃	—	2	1	no	—
109	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
110	#41×C₁₁₃	—	2	16	no	—
111	#41×C₁₁₃	—	4	8	no	—
112	#41×C₁₁₃	—	4	8	no	—
113	#41×C₁₁₃	—	4	8	no	—
114	C₂×Q₈×C₁₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₁₃	C₂²×C₄	1	4	yes	—
120	C₂×D₄×C₁₁₃	—	2	8	no	—
121	C₂×D₄×C₁₁₃	—	2	2	no	—
122	C₂×D₄×C₁₁₃	—	2	2	no	—
123	C₂×D₄×C₁₁₃	—	2	1	no	—
124	C₂×D₄×C₁₁₃	—	2	1	no	—
125	C₂×D₄×C₁₁₃	—	2	1	no	—
126	C₂×D₄×C₁₁₃	—	4	4	no	—
127	C₂×D₄×C₁₁₃	—	4	4	no	—
128	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
129	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₁₁₃	#41	1	2	yes	—
132	C₂²×C₄×C₁₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₁₃	—	2	8	no	—
141	C₂²×C₄×C₁₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₁₃	—	8	2	no	—
150	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₁₁₃	—	4	8	no	—
157	C₂×C₈×C₁₁₃	—	2	1	no	—
158	C₂×C₈×C₁₁₃	—	2	1	no	—
159	C₂×C₈×C₁₁₃	—	2	1	no	—
160	C₂×C₈×C₁₁₃	—	2	2	no	—
161	C₂×C₈×C₁₁₃	—	2	2	no	—
162	C₂×C₈×C₁₁₃	—	2	1	no	—
163	C₂×C₈×C₁₁₃	—	2	1	no	—
164	C₂×C₈×C₁₁₃	—	2	2	no	—
165	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₁₁₃	—	2	4	no	—
167	C₄⋊C₄×C₁₁₃	—	2	8	no	—
168	C₄⋊C₄×C₁₁₃	—	2	4	no	—
169	C₄⋊C₄×C₁₁₃	—	2	1	no	—
170	C₄⋊C₄×C₁₁₃	—	2	1	no	—
171	C₄⋊C₄×C₁₁₃	—	2	2	no	—
172	C₄⋊C₄×C₁₁₃	—	2	1	no	—
173	C₄⋊C₄×C₁₁₃	—	2	1	no	—
174	C₄⋊C₄×C₁₁₃	—	2	2	no	—
175	C₄⋊C₄×C₁₁₃	—	4	4	no	—
176	C₄⋊C₄×C₁₁₃	—	4	2	no	—
177	C₄⋊C₄×C₁₁₃	—	8	1	no	—
178	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
179	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
182	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
183	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
184	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
185	C₄²×C₁₁₃	—	4	2	no	—
186	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
187	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
188	C₂³×C₁₁₃	—	2	2	no	—
189	C₂³×C₁₁₃	—	2	2	no	—
190	C₂³×C₁₁₃	—	2	2	no	—
191	C₂³×C₁₁₃	—	2	2	no	—
192	C₂³×C₁₁₃	—	2	2	no	—
193	C₂³×C₁₁₃	—	2	2	no	—
194	C₂³×C₁₁₃	—	2	2	no	—
195	C₂³×C₁₁₃	—	2	2	no	—
196	C₂³×C₁₁₃	—	2	2	no	—
197	C₂³×C₁₁₃	—	4	1	no	—
198	C₂³×C₁₁₃	—	4	1	no	—
199	C₂³×C₁₁₃	—	4	1	no	—
200	C₂³×C₁₁₃	—	4	1	no	—
201	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
202	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₁₃	—	2	4	no	—
204	Q₈×C₁₁₃	—	2	4	no	—
205	Q₈×C₁₁₃	—	4	2	no	—
206	Q₈×C₁₁₃	—	4	2	no	—
207	D₄×C₁₁₃	—	2	2	no	—
208	D₄×C₁₁₃	—	2	2	no	—
209	D₄×C₁₁₃	—	2	2	no	—
210	D₄×C₁₁₃	—	2	8	no	—
211	D₄×C₁₁₃	—	4	16	no	—
212	D₄×C₁₁₃	C₄×D₄	1	4	yes	complemented
213	C₂×C₄×C₁₁₃	—	2	2	no	—
214	C₂×C₄×C₁₁₃	—	2	2	no	—
215	C₂×C₄×C₁₁₃	—	2	1	no	—
216	C₂×C₄×C₁₁₃	—	2	1	no	—
217	C₂×C₄×C₁₁₃	—	2	4	no	—
218	C₂×C₄×C₁₁₃	—	2	4	no	—
219	C₂×C₄×C₁₁₃	—	2	4	no	—
220	C₂×C₄×C₁₁₃	—	2	4	no	—
221	C₂×C₄×C₁₁₃	—	2	2	no	—
222	C₂×C₄×C₁₁₃	—	2	4	no	—
223	C₂×C₄×C₁₁₃	—	2	2	no	—
224	C₂×C₄×C₁₁₃	—	4	16	no	—
225	C₂×C₄×C₁₁₃	—	4	2	no	—
226	C₂×C₄×C₁₁₃	—	4	2	no	—
227	C₂×C₄×C₁₁₃	—	4	1	no	—
228	C₂×C₄×C₁₁₃	—	4	1	no	—
229	C₂×C₄×C₁₁₃	—	4	1	no	—
230	C₂×C₄×C₁₁₃	—	4	1	no	—
231	C₂×C₄×C₁₁₃	—	4	8	no	—
232	C₂×C₄×C₁₁₃	—	4	2	no	—
233	C₂×C₄×C₁₁₃	—	4	1	no	—
234	C₂×C₄×C₁₁₃	—	4	1	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	4	2	no	—
237	C₂×C₄×C₁₁₃	—	4	1	no	—
238	C₂×C₄×C₁₁₃	—	8	8	no	—
239	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
243	C₂×C₄×C₁₁₃	#137	1	2	yes	—
244	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
250	C₈×C₁₁₃	—	2	2	no	—
251	C₈×C₁₁₃	—	4	2	no	—
252	C₈×C₁₁₃	—	4	1	no	—
253	C₂²×C₁₁₃	—	2	4	no	—
254	C₂²×C₁₁₃	—	2	4	no	—
255	C₂²×C₁₁₃	—	2	4	no	—
256	C₂²×C₁₁₃	—	2	4	no	—
257	C₂²×C₁₁₃	—	4	2	no	—
258	C₂²×C₁₁₃	—	4	2	no	—
259	C₂²×C₁₁₃	—	4	2	no	—
260	C₂²×C₁₁₃	—	4	2	no	—
261	C₂²×C₁₁₃	—	4	2	no	—
262	C₂²×C₁₁₃	—	4	2	no	—
263	C₂²×C₁₁₃	—	4	2	no	—
264	C₂²×C₁₁₃	—	4	2	no	—
265	C₂²×C₁₁₃	—	4	2	no	—
266	C₂²×C₁₁₃	—	4	2	no	—
267	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₁₁₃	D₄²	1	1	yes	characteristic
269	C₂²×C₁₁₃	#546	1	1	yes	characteristic
270	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂²×C₁₁₃	C₂×#137	1	1	yes	characteristic
272	C₂²×C₁₁₃	#577	1	1	yes	characteristic
273	C₂²×C₁₁₃	#578	1	1	yes	characteristic
274	C₄×C₁₁₃	—	2	4	no	—
275	C₄×C₁₁₃	—	2	2	no	—
276	C₄×C₁₁₃	—	4	4	no	—
277	C₄×C₁₁₃	—	4	2	no	—
278	C₄×C₁₁₃	—	4	2	no	—
279	C₄×C₁₁₃	—	8	1	no	—
280	C₄×C₁₁₃	—	8	2	no	—
281	C₄×C₁₁₃	#417	1	4	yes	complemented
282	C₄×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₁₁₃	#518	1	1	yes	characteristic
284	C₄×C₁₁₃	D₄²	1	1	yes	characteristic
285	C₄×C₁₁₃	#546	1	1	yes	characteristic
286	#22431	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₁₁₃	—	4	4	no	—
288	C₂×C₁₁₃	—	4	4	no	—
289	C₂×C₁₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₁₁₃	C₂×#417	1	1	yes	characteristic
291	C₂×C₁₁₃	#2898	1	1	yes	characteristic
292	C₂×C₁₁₃	#3272	1	1	yes	characteristic
293	C₂×C₁₁₃	#3276	1	1	yes	characteristic
294	C₂×C₁₁₃	#3330	1	1	yes	characteristic
295	C₂×C₁₁₃	#3331	1	1	yes	characteristic
296	C₂×#547	C₂×C₁₁₃	1	1	yes	characteristic
297	C₂×#436	C₂×C₁₁₃	1	1	yes	characteristic, complemented
298	C₂×#417	C₂×C₁₁₃	1	2	yes	complemented
299	D₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
300	#1981	C₂×C₁₁₃	1	1	yes	characteristic, complemented
301	#1956	C₂×C₁₁₃	1	1	yes	characteristic, complemented
302	#1894	C₂×C₁₁₃	1	2	yes	complemented
303	#1872	C₂×C₁₁₃	1	2	yes	complemented
304	#1802	C₂×C₁₁₃	1	1	yes	characteristic, complemented
305	#1788	C₂×C₁₁₃	1	2	yes	complemented
306	C₄×#102	C₂×C₁₁₃	1	1	yes	characteristic, complemented
307	C₁₁₃	#22431	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×#41	C₂²×C₁₁₃	1	2	yes	—
309	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
310	#547	—	2	4	no	—
311	#547	C₄×C₁₁₃	1	8	yes	complemented
312	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
313	C₂×#123	—	2	2	no	—
314	C₂×C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	—
315	C₂×#121	—	2	1	no	—
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	—	2	1	no	—
320	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
321	#436	—	2	4	no	—
322	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
323	#417	—	2	8	no	—
324	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
325	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
326	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
327	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
328	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
329	C₂×#102	C₂²×C₁₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
332	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
333	#389	—	2	1	no	—
334	#385	—	2	2	no	—
335	#384	C₂²×C₁₁₃	1	1	yes	characteristic
336	#380	C₂²×C₁₁₃	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
338	#340	C₂²×C₁₁₃	1	2	yes	—
339	#340	C₂²×C₁₁₃	1	1	yes	characteristic
340	#340	C₂²×C₁₁₃	1	1	yes	characteristic
341	C₂×#41	—	2	4	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	4	no	—
344	C₂×#41	—	4	2	no	—
345	C₂×#41	—	4	2	no	—
346	C₂×#41	C₂×C₄×C₁₁₃	1	8	yes	complemented
347	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	2	2	no	—
353	C₂³×C₄	—	2	2	no	—
354	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
355	C₂×M₁₆	—	2	4	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	4	2	no	—
358	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
359	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	complemented
363	#123	—	2	16	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	C₂×C₄×C₁₁₃	1	8	yes	complemented
366	#121	—	2	8	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	4	4	no	—
369	C₄×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
370	C₄×D₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
371	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	8	no	—
376	C₂×C₄⋊C₄	—	2	4	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	4	2	no	—
381	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
392	C₄⋊C₈	—	2	2	no	—
393	#103	—	2	4	no	—
394	#103	—	2	4	no	—
395	#103	—	4	2	no	—
396	#103	—	4	2	no	—
397	#102	—	2	4	no	—
398	#102	—	2	2	no	—
399	#102	D₄×C₁₁₃	1	4	yes	complemented
400	C₂²⋊C₈	—	2	4	no	—
401	C₄×C₈	—	2	2	no	—
402	#95	—	2	1	no	—
403	#95	—	2	2	no	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
406	#41	—	2	16	no	—
407	#41	—	4	8	no	—
408	#41	—	4	8	no	—
409	#41	—	4	8	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂²×C₄×C₁₁₃	1	4	yes	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
425	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
427	C₂×D₄	#41×C₁₁₃	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	8	2	no	—
446	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
452	M₁₆	—	4	8	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	4	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	8	1	no	—
474	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
475	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
481	C₄²	—	4	2	no	—
482	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
483	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
498	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
499	Q₈	—	2	4	no	—
500	Q₈	—	2	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	8	no	—
507	D₄	—	4	16	no	—
508	D₄	C₄×D₄×C₁₁₃	1	4	yes	complemented
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	16	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	8	no	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
536	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
537	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
538	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
539	C₂×C₄	#137×C₁₁₃	1	2	yes	—
540	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
544	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
545	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	4	2	no	—
548	C₈	—	4	1	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
564	C₂²	D₄²×C₁₁₃	1	1	yes	characteristic
565	C₂²	#546×C₁₁₃	1	1	yes	characteristic
566	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
567	C₂²	C₂×#137×C₁₁₃	1	1	yes	characteristic
568	C₂²	#577×C₁₁₃	1	1	yes	characteristic
569	C₂²	#578×C₁₁₃	1	1	yes	characteristic
570	C₄	—	2	4	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	2	no	—
577	C₄	#417×C₁₁₃	1	4	yes	complemented
578	C₄	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
579	C₄	#518×C₁₁₃	1	1	yes	characteristic
580	C₄	D₄²×C₁₁₃	1	1	yes	characteristic
581	C₄	#546×C₁₁₃	1	1	yes	characteristic
582	C₂	—	4	4	no	—
583	C₂	—	4	4	no	—
584	C₂	D₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
585	C₂	C₂×#417×C₁₁₃	1	1	yes	characteristic
586	C₂	C₁₁₃×#2898	1	1	yes	characteristic
587	C₂	C₁₁₃×#3272	1	1	yes	characteristic
588	C₂	C₁₁₃×#3276	1	1	yes	characteristic
589	C₂	C₁₁₃×#3330	1	1	yes	characteristic
590	C₂	C₁₁₃×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#547×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄×D₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#436×C₁₁₃	C₂	semidirect
3. C₂×#417×C₁₁₃	C₂	semidirect
4. D₄×C₄⋊C₄×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1981	C₂	semidirect
6. C₁₁₃×#1956	C₂	semidirect
7. C₁₁₃×#1894	C₂	semidirect
8. C₁₁₃×#1872	C₂	semidirect
9. C₁₁₃×#1802	C₂	semidirect
10. C₁₁₃×#1788	C₂	semidirect
11. C₄×#102×C₁₁₃	C₂	semidirect
15. #547×C₁₁₃	C₄	semidirect
50. C₂×#41×C₁₁₃	C₂×C₄	semidirect
66. C₄⋊Q₈×C₁₁₃	C₂×C₄	semidirect
69. C₂²⋊Q₈×C₁₁₃	C₂×C₄	semidirect
74. C₄×D₄×C₁₁₃	C₂×C₄	semidirect
103. #102×C₁₁₃	D₄	semidirect
212. D₄×C₁₁₃	C₄×D₄	semidirect
281. C₄×C₁₁₃	#417	semidirect
286. #22431	C₁₁₃	direct (N × H)
297. C₂×#436	C₂×C₁₁₃	semidirect
298. C₂×#417	C₂×C₁₁₃	semidirect
299. D₄×C₄⋊C₄	C₂×C₁₁₃	semidirect
300. #1981	C₂×C₁₁₃	semidirect
301. #1956	C₂×C₁₁₃	semidirect
302. #1894	C₂×C₁₁₃	semidirect
303. #1872	C₂×C₁₁₃	semidirect
304. #1802	C₂×C₁₁₃	semidirect
305. #1788	C₂×C₁₁₃	semidirect
306. C₄×#102	C₂×C₁₁₃	semidirect
307. C₁₁₃	#22431	direct (N × H)
311. #547	C₄×C₁₁₃	semidirect
346. C₂×#41	C₂×C₄×C₁₁₃	semidirect
362. C₄⋊Q₈	C₂×C₄×C₁₁₃	semidirect
365. C₂²⋊Q₈	C₂×C₄×C₁₁₃	semidirect
370. C₄×D₄	C₂×C₄×C₁₁₃	semidirect
399. #102	D₄×C₁₁₃	semidirect
508. D₄	C₄×D₄×C₁₁₃	semidirect
577. C₄	#417×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₁₃	2
C₂×#436×C₁₁₃	2
C₂×#417×C₁₁₃	2
D₄×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1981	2
C₁₁₃×#1956	2
C₁₁₃×#1894	2
C₁₁₃×#1872	2
C₁₁₃×#1802	2
C₁₁₃×#1788	2
C₄×#102×C₁₁₃	2
#22431	113

Subgroups — C113×#22431 #43290451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#22431 #43290451