Subgroups — C₁₁₃×#20992 #43289012

Order 28928.

1738 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#537×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#413×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1901	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1900	C₂	1	4	yes	maximal, complemented
7	C₂×#343×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
10	#568×C₁₁₃	—	2	8	no	—
11	C₂×#131×C₁₁₃	—	2	4	no	—
12	C₂²×M₁₆×C₁₁₃	C₂²	1	4	yes	—
13	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
15	#537×C₁₁₃	—	2	4	no	—
16	#537×C₁₁₃	—	2	4	no	—
17	C₂×C₂²⋊Q₈×C₁₁₃	C₄	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
19	C₂×#121×C₁₁₃	C₄	1	2	yes	—
20	C₂×#121×C₁₁₃	C₄	1	4	yes	—
21	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
23	#413×C₁₁₃	—	2	8	no	—
24	C₂×#101×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#100×C₁₁₃	C₂²	1	4	yes	—
26	#408×C₁₁₃	—	2	4	no	—
27	#407×C₁₁₃	C₂²	1	4	yes	—
28	#343×C₁₁₃	C₂²	1	8	yes	—
29	C₂×#41×C₁₁₃	—	2	4	no	—
30	C₂×#41×C₁₁₃	—	2	2	no	—
31	C₂×#41×C₁₁₃	—	2	2	no	—
32	C₂×#41×C₁₁₃	—	2	4	no	—
33	C₂×#41×C₁₁₃	—	2	4	no	—
34	C₂×#41×C₁₁₃	—	2	4	no	—
35	C₂×#41×C₁₁₃	D₄	1	4	yes	—
36	C₂×#41×C₁₁₃	D₄	1	4	yes	—
37	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
43	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
48	#131×C₁₁₃	—	2	32	no	—
49	C₂×M₁₆×C₁₁₃	—	2	4	no	—
50	C₂×M₁₆×C₁₁₃	—	2	2	no	—
51	C₂×M₁₆×C₁₁₃	—	2	4	no	—
52	C₂×M₁₆×C₁₁₃	—	2	16	no	—
53	C₂×M₁₆×C₁₁₃	—	2	2	no	—
54	C₂×M₁₆×C₁₁₃	—	2	4	no	—
55	C₂×M₁₆×C₁₁₃	—	2	4	no	—
56	C₂×M₁₆×C₁₁₃	D₄	1	8	yes	complemented
57	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
58	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₁₃	—	2	4	no	—
60	C₂²×C₈×C₁₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₁₃	—	2	2	no	—
62	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
63	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
64	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
65	#121×C₁₁₃	—	2	8	no	—
66	#121×C₁₁₃	—	2	16	no	—
67	#121×C₁₁₃	—	2	4	no	—
68	#121×C₁₁₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
76	#101×C₁₁₃	—	2	8	no	—
77	#100×C₁₁₃	—	2	8	no	—
78	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
79	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
81	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
82	#41×C₁₁₃	—	2	8	no	—
83	#41×C₁₁₃	—	2	8	no	—
84	#41×C₁₁₃	—	2	8	no	—
85	#41×C₁₁₃	—	2	8	no	—
86	#41×C₁₁₃	—	4	4	no	—
87	#41×C₁₁₃	—	4	4	no	—
88	#41×C₁₁₃	—	4	4	no	—
89	#41×C₁₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	4	yes	—
96	C₂×D₄×C₁₁₃	—	2	8	no	—
97	C₂×D₄×C₁₁₃	—	2	4	no	—
98	C₂×D₄×C₁₁₃	—	2	8	no	—
99	C₂×D₄×C₁₁₃	—	2	8	no	—
100	C₂×D₄×C₁₁₃	—	2	4	no	—
101	C₂×D₄×C₁₁₃	—	2	2	no	—
102	C₂×D₄×C₁₁₃	—	2	1	no	—
103	C₂×D₄×C₁₁₃	—	2	1	no	—
104	C₂×D₄×C₁₁₃	—	2	2	no	—
105	C₂×D₄×C₁₁₃	—	8	4	no	—
106	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
107	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₁₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
124	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₁₁₃	—	2	16	no	—
126	M₁₆×C₁₁₃	—	2	8	no	—
127	M₁₆×C₁₁₃	—	2	4	no	—
128	M₁₆×C₁₁₃	—	2	4	no	—
129	M₁₆×C₁₁₃	—	2	4	no	—
130	M₁₆×C₁₁₃	—	4	4	no	—
131	M₁₆×C₁₁₃	C₂×D₄	1	8	yes	—
132	C₂×C₈×C₁₁₃	—	2	16	no	—
133	C₂×C₈×C₁₁₃	—	2	8	no	—
134	C₂×C₈×C₁₁₃	—	2	4	no	—
135	C₂×C₈×C₁₁₃	—	2	4	no	—
136	C₂×C₈×C₁₁₃	—	4	4	no	—
137	C₄⋊C₄×C₁₁₃	—	2	4	no	—
138	C₄⋊C₄×C₁₁₃	—	2	8	no	—
139	C₄⋊C₄×C₁₁₃	—	2	2	no	—
140	C₄⋊C₄×C₁₁₃	—	2	2	no	—
141	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
142	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
143	C₂³×C₁₁₃	—	2	4	no	—
144	C₂³×C₁₁₃	—	2	2	no	—
145	C₂³×C₁₁₃	—	2	4	no	—
146	C₂³×C₁₁₃	—	4	1	no	—
147	C₂³×C₁₁₃	—	4	1	no	—
148	C₂³×C₁₁₃	—	4	2	no	—
149	C₂³×C₁₁₃	—	4	2	no	—
150	C₂³×C₁₁₃	—	4	2	no	—
151	C₂³×C₁₁₃	—	4	2	no	—
152	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₁₁₃	C₄×D₄	1	4	yes	—
155	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
156	Q₈×C₁₁₃	—	2	8	no	—
157	Q₈×C₁₁₃	—	4	1	no	—
158	Q₈×C₁₁₃	—	4	2	no	—
159	Q₈×C₁₁₃	—	4	1	no	—
160	D₄×C₁₁₃	—	2	16	no	—
161	D₄×C₁₁₃	—	2	8	no	—
162	D₄×C₁₁₃	—	4	8	no	—
163	D₄×C₁₁₃	—	4	1	no	—
164	D₄×C₁₁₃	—	4	2	no	—
165	D₄×C₁₁₃	—	4	1	no	—
166	D₄×C₁₁₃	—	8	8	no	—
167	C₂×C₄×C₁₁₃	—	2	4	no	—
168	C₂×C₄×C₁₁₃	—	2	4	no	—
169	C₂×C₄×C₁₁₃	—	2	8	no	—
170	C₂×C₄×C₁₁₃	—	2	4	no	—
171	C₂×C₄×C₁₁₃	—	2	4	no	—
172	C₂×C₄×C₁₁₃	—	2	2	no	—
173	C₂×C₄×C₁₁₃	—	2	4	no	—
174	C₂×C₄×C₁₁₃	—	4	8	no	—
175	C₂×C₄×C₁₁₃	—	4	4	no	—
176	C₂×C₄×C₁₁₃	—	8	4	no	—
177	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₁₁₃	#120	1	4	yes	—
181	C₂×C₄×C₁₁₃	#121	1	4	yes	—
182	C₂×C₄×C₁₁₃	#121	1	4	yes	—
183	C₂×C₄×C₁₁₃	#123	1	4	yes	—
184	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
188	C₈×C₁₁₃	—	2	8	no	—
189	C₈×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	2	1	no	—
191	C₂²×C₁₁₃	—	2	2	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	—	2	2	no	—
194	C₂²×C₁₁₃	—	2	4	no	—
195	C₂²×C₁₁₃	—	2	4	no	—
196	C₂²×C₁₁₃	—	2	4	no	—
197	C₂²×C₁₁₃	—	4	4	no	—
198	C₂²×C₁₁₃	—	4	2	no	—
199	C₂²×C₁₁₃	—	4	2	no	—
200	C₂²×C₁₁₃	—	4	2	no	—
201	C₂²×C₁₁₃	—	8	4	no	—
202	C₂²×C₁₁₃	—	8	4	no	—
203	C₂²×C₁₁₃	#386	1	4	yes	—
204	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
206	C₄×C₁₁₃	—	2	4	no	—
207	C₄×C₁₁₃	—	4	4	no	—
208	C₄×C₁₁₃	—	4	2	no	—
209	C₄×C₁₁₃	#386	1	4	yes	—
210	C₄×C₁₁₃	C₂×#120	1	1	yes	characteristic
211	C₄×C₁₁₃	C₂×#121	1	2	yes	—
212	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
213	#20992	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₁₃	—	2	2	no	—
215	C₂×C₁₁₃	—	2	4	no	—
216	C₂×C₁₁₃	—	4	4	no	—
217	C₂×C₁₁₃	—	8	2	no	—
218	C₂×C₁₁₃	C₂×#386	1	1	yes	characteristic
219	C₂×C₁₁₃	#2888	1	1	yes	characteristic
220	C₂×C₁₁₃	#2889	1	1	yes	characteristic
221	C₂×#568	C₂×C₁₁₃	1	1	yes	characteristic, complemented
222	C₂×#537	C₂×C₁₁₃	1	1	yes	characteristic
223	C₂×#413	C₂×C₁₁₃	1	2	yes	complemented
224	#2879	C₂×C₁₁₃	1	1	yes	characteristic, complemented
225	#1901	C₂×C₁₁₃	1	4	yes	complemented
226	#1900	C₂×C₁₁₃	1	4	yes	complemented
227	C₂×#343	C₂×C₁₁₃	1	2	yes	complemented
228	C₁₁₃	#20992	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
230	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
231	#568	—	2	8	no	—
232	C₂×#131	—	2	4	no	—
233	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
234	C₂²×M₁₆	C₂²×C₁₁₃	1	4	yes	—
235	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
236	#537	—	2	4	no	—
237	#537	—	2	4	no	—
238	C₂×C₂²⋊Q₈	C₄×C₁₁₃	1	2	yes	—
239	C₂×C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	—
240	C₂×#121	C₄×C₁₁₃	1	2	yes	—
241	C₂×#121	C₄×C₁₁₃	1	4	yes	—
242	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
244	#413	—	2	8	no	—
245	C₂×#101	C₂²×C₁₁₃	1	4	yes	—
246	C₂×#100	C₂²×C₁₁₃	1	4	yes	—
247	#408	—	2	4	no	—
248	#407	C₂²×C₁₁₃	1	4	yes	—
249	#343	C₂²×C₁₁₃	1	8	yes	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	D₄×C₁₁₃	1	4	yes	—
257	C₂×#41	D₄×C₁₁₃	1	4	yes	—
258	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
259	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
260	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
261	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
262	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
263	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
264	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
265	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
266	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
269	#131	—	2	32	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	2	16	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	4	no	—
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	D₄×C₁₁₃	1	8	yes	complemented
278	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
279	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	8	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	#121	—	2	8	no	—
287	#121	—	2	16	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
297	#101	—	2	8	no	—
298	#100	—	2	8	no	—
299	C₂²⋊C₈	—	2	8	no	—
300	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
301	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
302	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
303	#41	—	2	8	no	—
304	#41	—	2	8	no	—
305	#41	—	2	8	no	—
306	#41	—	2	8	no	—
307	#41	—	4	4	no	—
308	#41	—	4	4	no	—
309	#41	—	4	4	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	4	yes	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	8	4	no	—
327	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
328	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
340	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
341	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
344	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
346	M₁₆	—	2	16	no	—
347	M₁₆	—	2	8	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	4	4	no	—
352	M₁₆	C₂×D₄×C₁₁₃	1	8	yes	—
353	C₂×C₈	—	2	16	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	4	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
374	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
375	C₂³	C₄×D₄×C₁₁₃	1	4	yes	—
376	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
377	Q₈	—	2	8	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	16	no	—
382	D₄	—	2	8	no	—
383	D₄	—	4	8	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	1	no	—
387	D₄	—	8	8	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	8	4	no	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
399	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
400	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
401	C₂×C₄	#120×C₁₁₃	1	4	yes	—
402	C₂×C₄	#121×C₁₁₃	1	4	yes	—
403	C₂×C₄	#121×C₁₁₃	1	4	yes	—
404	C₂×C₄	#123×C₁₁₃	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
409	C₈	—	2	8	no	—
410	C₈	—	4	4	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	4	no	—
424	C₂²	#386×C₁₁₃	1	4	yes	—
425	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
426	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
427	C₄	—	2	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	#386×C₁₁₃	1	4	yes	—
431	C₄	C₂×#120×C₁₁₃	1	1	yes	characteristic
432	C₄	C₂×#121×C₁₁₃	1	2	yes	—
433	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
434	C₂	—	2	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	4	4	no	—
437	C₂	—	8	2	no	—
438	C₂	C₂×#386×C₁₁₃	1	1	yes	characteristic
439	C₂	C₁₁₃×#2888	1	1	yes	characteristic
440	C₂	C₁₁₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#537×C₁₁₃	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂²×#41×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#568×C₁₁₃	C₂	semidirect
3. C₂×#413×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2879	C₂	semidirect
5. C₁₁₃×#1901	C₂	semidirect
6. C₁₁₃×#1900	C₂	semidirect
7. C₂×#343×C₁₁₃	C₂	semidirect
56. C₂×M₁₆×C₁₁₃	D₄	semidirect
213. #20992	C₁₁₃	direct (N × H)
221. C₂×#568	C₂×C₁₁₃	semidirect
223. C₂×#413	C₂×C₁₁₃	semidirect
224. #2879	C₂×C₁₁₃	semidirect
225. #1901	C₂×C₁₁₃	semidirect
226. #1900	C₂×C₁₁₃	semidirect
227. C₂×#343	C₂×C₁₁₃	semidirect
228. C₁₁₃	#20992	direct (N × H)
277. C₂×M₁₆	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#568×C₁₁₃	2
C₂×#537×C₁₁₃	2
C₂×#413×C₁₁₃	2
C₁₁₃×#2879	2
C₁₁₃×#1901	2
C₁₁₃×#1900	2
C₂×#343×C₁₁₃	2
#20992	113

Subgroups — C113×#20992 #43289012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20992 #43289012