Subgroups — C₁₁₃×#21052 #43289072

Order 28928.

1150 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#408×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#408×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#405×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2297	C₂	1	1	yes	maximal, characteristic
6	C₁₁₃×#1924	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1923	C₂	1	4	yes	maximal, complemented
8	C₁₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₁₃	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
20	#408×C₁₁₃	—	2	4	no	—
21	#408×C₁₁₃	—	2	4	no	—
22	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
25	#405×C₁₁₃	—	2	4	no	—
26	C₂×#97×C₁₁₃	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
28	#391×C₁₁₃	C₄	1	2	yes	—
29	#390×C₁₁₃	C₄	1	2	yes	—
30	#386×C₁₁₃	C₄	1	2	yes	—
31	#386×C₁₁₃	C₄	1	2	yes	—
32	C₄×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
33	#336×C₁₁₃	C₂²	1	4	yes	—
34	#336×C₁₁₃	C₂²	1	4	yes	—
35	C₂×#41×C₁₁₃	—	2	2	no	—
36	C₂×#41×C₁₁₃	—	2	2	no	—
37	C₂×#41×C₁₁₃	—	2	2	no	—
38	C₂×#41×C₁₁₃	—	2	2	no	—
39	C₂×#41×C₁₁₃	—	2	2	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₁₁₃	—	2	2	no	—
49	C₂×M₁₆×C₁₁₃	—	2	2	no	—
50	C₂×M₁₆×C₁₁₃	—	2	2	no	—
51	C₂×M₁₆×C₁₁₃	—	2	2	no	—
52	C₂×M₁₆×C₁₁₃	—	2	2	no	—
53	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	—
54	C₂²×C₈×C₁₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₁₃	D₄	1	4	yes	—
60	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
65	#117×C₁₁₃	—	2	2	no	—
66	#117×C₁₁₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
70	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
71	C₂×C₄²×C₁₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
76	C₄⋊C₈×C₁₁₃	—	2	4	no	—
77	C₄⋊C₈×C₁₁₃	—	2	4	no	—
78	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
79	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
80	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
81	#97×C₁₁₃	—	2	4	no	—
82	C₄×C₈×C₁₁₃	—	2	4	no	—
83	#95×C₁₁₃	C₂×C₄	1	4	yes	—
84	#95×C₁₁₃	C₂×C₄	1	4	yes	—
85	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
86	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
87	#41×C₁₁₃	—	4	4	no	—
88	#41×C₁₁₃	—	4	4	no	—
89	#41×C₁₁₃	—	4	4	no	—
90	#41×C₁₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₁₃	—	2	2	no	—
94	C₂×D₄×C₁₁₃	—	2	4	no	—
95	C₂×D₄×C₁₁₃	—	2	4	no	—
96	C₂×D₄×C₁₁₃	—	2	4	no	—
97	C₂×D₄×C₁₁₃	—	2	2	no	—
98	C₂×D₄×C₁₁₃	—	2	2	no	—
99	C₂×D₄×C₁₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
118	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₁₁₃	—	2	8	no	—
123	M₁₆×C₁₁₃	—	4	4	no	—
124	C₂×C₈×C₁₁₃	—	2	8	no	—
125	C₂×C₈×C₁₁₃	—	2	1	no	—
126	C₂×C₈×C₁₁₃	—	2	1	no	—
127	C₂×C₈×C₁₁₃	—	2	1	no	—
128	C₂×C₈×C₁₁₃	—	2	1	no	—
129	C₂×C₈×C₁₁₃	—	2	2	no	—
130	C₂×C₈×C₁₁₃	—	2	2	no	—
131	C₂×C₈×C₁₁₃	—	2	2	no	—
132	C₂×C₈×C₁₁₃	—	2	2	no	—
133	C₂×C₈×C₁₁₃	—	2	2	no	—
134	C₂×C₈×C₁₁₃	—	2	2	no	—
135	C₂×C₈×C₁₁₃	—	2	2	no	—
136	C₂×C₈×C₁₁₃	—	2	2	no	—
137	C₂×C₈×C₁₁₃	—	4	4	no	—
138	C₂×C₈×C₁₁₃	C₂×D₄	1	4	yes	—
139	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	—	2	4	no	—
142	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
143	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
144	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
145	C₄²×C₁₁₃	—	2	4	no	—
146	C₄²×C₁₁₃	—	2	2	no	—
147	C₄²×C₁₁₃	—	2	2	no	—
148	C₄²×C₁₁₃	—	2	2	no	—
149	C₄²×C₁₁₃	—	2	2	no	—
150	C₂³×C₁₁₃	—	2	2	no	—
151	C₂³×C₁₁₃	—	2	2	no	—
152	C₂³×C₁₁₃	—	2	2	no	—
153	C₂³×C₁₁₃	—	2	2	no	—
154	C₂³×C₁₁₃	—	2	2	no	—
155	C₂³×C₁₁₃	—	2	4	no	—
156	C₂³×C₁₁₃	—	2	4	no	—
157	C₂³×C₁₁₃	#117	1	2	yes	—
158	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
159	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
160	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₁₁₃	—	4	4	no	—
162	D₄×C₁₁₃	—	4	8	no	—
163	D₄×C₁₁₃	—	4	4	no	—
164	C₂×C₄×C₁₁₃	—	2	8	no	—
165	C₂×C₄×C₁₁₃	—	2	2	no	—
166	C₂×C₄×C₁₁₃	—	2	2	no	—
167	C₂×C₄×C₁₁₃	—	2	2	no	—
168	C₂×C₄×C₁₁₃	—	2	2	no	—
169	C₂×C₄×C₁₁₃	—	2	4	no	—
170	C₂×C₄×C₁₁₃	—	2	2	no	—
171	C₂×C₄×C₁₁₃	—	2	2	no	—
172	C₂×C₄×C₁₁₃	—	2	4	no	—
173	C₂×C₄×C₁₁₃	—	2	2	no	—
174	C₂×C₄×C₁₁₃	—	2	4	no	—
175	C₂×C₄×C₁₁₃	—	2	2	no	—
176	C₂×C₄×C₁₁₃	—	4	4	no	—
177	C₂×C₄×C₁₁₃	—	4	2	no	—
178	C₂×C₄×C₁₁₃	—	4	2	no	—
179	C₂×C₄×C₁₁₃	—	4	2	no	—
180	C₂×C₄×C₁₁₃	—	4	2	no	—
181	C₂×C₄×C₁₁₃	#117	1	2	yes	—
182	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₁₃	#121	1	4	yes	—
185	C₂×C₄×C₁₁₃	#123	1	4	yes	—
186	C₂×C₄×C₁₁₃	#124	1	4	yes	—
187	C₂×C₄×C₁₁₃	#126	1	4	yes	—
188	C₂×C₄×C₁₁₃	#131	1	4	yes	—
189	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
195	C₈×C₁₁₃	—	2	2	no	—
196	C₈×C₁₁₃	—	2	2	no	—
197	C₈×C₁₁₃	—	2	4	no	—
198	C₈×C₁₁₃	—	4	2	no	—
199	C₈×C₁₁₃	—	4	2	no	—
200	C₂²×C₁₁₃	—	2	4	no	—
201	C₂²×C₁₁₃	—	2	2	no	—
202	C₂²×C₁₁₃	—	2	2	no	—
203	C₂²×C₁₁₃	—	2	4	no	—
204	C₂²×C₁₁₃	—	4	4	no	—
205	C₂²×C₁₁₃	—	4	2	no	—
206	C₂²×C₁₁₃	—	4	2	no	—
207	C₂²×C₁₁₃	—	4	4	no	—
208	C₂²×C₁₁₃	—	4	2	no	—
209	C₂²×C₁₁₃	#388	1	4	yes	—
210	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
211	C₂²×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
214	C₂²×C₁₁₃	#568	1	2	yes	—
215	C₄×C₁₁₃	—	2	4	no	—
216	C₄×C₁₁₃	—	4	2	no	—
217	C₄×C₁₁₃	—	4	4	no	—
218	C₄×C₁₁₃	—	4	2	no	—
219	C₄×C₁₁₃	#388	1	4	yes	—
220	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
221	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
222	C₄×C₁₁₃	C₂×#124	1	1	yes	characteristic
223	C₄×C₁₁₃	C₂×#126	1	1	yes	characteristic
224	#21052	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₁₁₃	—	2	4	no	—
226	C₂×C₁₁₃	—	8	2	no	—
227	C₂×C₁₁₃	C₂×#388	1	1	yes	characteristic
228	C₂×C₁₁₃	#2925	1	2	yes	—
229	C₂×C₁₁₃	#2929	1	1	yes	characteristic
230	C₂×C₁₁₃	#2930	1	1	yes	characteristic
231	C₂×C₁₁₃	#2935	1	2	yes	—
232	C₂²×C₄⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
233	C₂×#408	C₂×C₁₁₃	1	1	yes	characteristic
234	C₂×#408	C₂×C₁₁₃	1	1	yes	characteristic
235	C₂×#405	C₂×C₁₁₃	1	1	yes	characteristic, complemented
236	#2297	C₂×C₁₁₃	1	1	yes	characteristic
237	#1924	C₂×C₁₁₃	1	4	yes	complemented
238	#1923	C₂×C₁₁₃	1	4	yes	complemented
239	#1729	C₂×C₁₁₃	1	1	yes	characteristic, complemented
240	#1728	C₂×C₁₁₃	1	1	yes	characteristic, complemented
241	C₁₁₃	#21052	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
243	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
248	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₈	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
252	#408	—	2	4	no	—
253	#408	—	2	4	no	—
254	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
257	#405	—	2	4	no	—
258	C₂×#97	C₂²×C₁₁₃	1	2	yes	—
259	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
260	#391	C₄×C₁₁₃	1	2	yes	—
261	#390	C₄×C₁₁₃	1	2	yes	—
262	#386	C₄×C₁₁₃	1	2	yes	—
263	#386	C₄×C₁₁₃	1	2	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
265	#336	C₂²×C₁₁₃	1	4	yes	—
266	#336	C₂²×C₁₁₃	1	4	yes	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
275	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	D₄×C₁₁₃	1	4	yes	—
292	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
308	C₄⋊C₈	—	2	4	no	—
309	C₄⋊C₈	—	2	4	no	—
310	C₂²⋊C₈	—	2	8	no	—
311	C₂²⋊C₈	—	2	4	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#97	—	2	4	no	—
314	C₄×C₈	—	2	4	no	—
315	#95	C₂×C₄×C₁₁₃	1	4	yes	—
316	#95	C₂×C₄×C₁₁₃	1	4	yes	—
317	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
318	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
349	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
350	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
351	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
352	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
354	M₁₆	—	2	8	no	—
355	M₁₆	—	4	4	no	—
356	C₂×C₈	—	2	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	4	no	—
370	C₂×C₈	C₂×D₄×C₁₁₃	1	4	yes	—
371	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
373	C₄⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	#117×C₁₁₃	1	2	yes	—
390	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
391	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
392	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
393	Q₈	—	4	4	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	#117×C₁₁₃	1	2	yes	—
414	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
415	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
416	C₂×C₄	#121×C₁₁₃	1	4	yes	—
417	C₂×C₄	#123×C₁₁₃	1	4	yes	—
418	C₂×C₄	#124×C₁₁₃	1	4	yes	—
419	C₂×C₄	#126×C₁₁₃	1	4	yes	—
420	C₂×C₄	#131×C₁₁₃	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	#388×C₁₁₃	1	4	yes	—
442	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
443	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
444	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
445	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
446	C₂²	#568×C₁₁₃	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	4	no	—
451	C₄	#388×C₁₁₃	1	4	yes	—
452	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
453	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
454	C₄	C₂×#124×C₁₁₃	1	1	yes	characteristic
455	C₄	C₂×#126×C₁₁₃	1	1	yes	characteristic
456	C₂	—	2	4	no	—
457	C₂	—	8	2	no	—
458	C₂	C₂×#388×C₁₁₃	1	1	yes	characteristic
459	C₂	C₁₁₃×#2925	1	2	yes	—
460	C₂	C₁₁₃×#2929	1	1	yes	characteristic
461	C₂	C₁₁₃×#2930	1	1	yes	characteristic
462	C₂	C₁₁₃×#2935	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊C₈×C₁₁₃	C₂	semidirect
4. C₂×#405×C₁₁₃	C₂	semidirect
6. C₁₁₃×#1924	C₂	semidirect
7. C₁₁₃×#1923	C₂	semidirect
8. C₁₁₃×#1729	C₂	semidirect
9. C₁₁₃×#1728	C₂	semidirect
224. #21052	C₁₁₃	direct (N × H)
232. C₂²×C₄⋊C₈	C₂×C₁₁₃	semidirect
235. C₂×#405	C₂×C₁₁₃	semidirect
237. #1924	C₂×C₁₁₃	semidirect
238. #1923	C₂×C₁₁₃	semidirect
239. #1729	C₂×C₁₁₃	semidirect
240. #1728	C₂×C₁₁₃	semidirect
241. C₁₁₃	#21052	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₁₁₃	2
C₂×#408×C₁₁₃	2
C₂×#405×C₁₁₃	2
C₁₁₃×#2297	2
C₁₁₃×#1924	2
C₁₁₃×#1923	2
C₁₁₃×#1729	2
C₁₁₃×#1728	2
#21052	113

Subgroups — C113×#21052 #43289072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21052 #43289072