Subgroups — C₄×#407×C₁₁₃ #43288396

Order 28928.

2246 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#1749	C₂	1	4	yes	maximal, complemented
5	C₄×C₂²⋊C₈×C₁₁₃	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1728	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₁₃	C₄	1	2	yes	—
8	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₁₃	C₂²	1	4	yes	—
10	C₂²×C₄²×C₁₁₃	—	2	8	no	—
11	C₂²×C₄²×C₁₁₃	C₄	1	2	yes	—
12	C₂²×C₄²×C₁₁₃	C₄	1	4	yes	—
13	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
17	#407×C₁₁₃	C₄	1	16	yes	direct product factor
18	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	8	yes	—
19	C₄×M₁₆×C₁₁₃	—	2	8	no	—
20	C₂×#97×C₁₁₃	C₂²	1	4	yes	complemented
21	C₂×C₄×C₈×C₁₁₃	C₂²	1	4	yes	complemented
22	#336×C₁₁₃	C₂²	1	8	yes	complemented
23	C₂⁵×C₁₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁₃	—	2	8	no	—
25	C₂³×C₄×C₁₁₃	—	2	16	no	—
26	C₂³×C₄×C₁₁₃	—	2	4	no	—
27	C₂³×C₄×C₁₁₃	—	2	4	no	—
28	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₁₃	C₂×C₄	1	8	yes	—
33	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₁₃	—	2	8	no	—
38	C₂×M₁₆×C₁₁₃	—	2	8	no	—
39	C₂×M₁₆×C₁₁₃	C₂×C₄	1	16	yes	complemented
40	C₂²×C₈×C₁₁₃	C₂³	1	8	yes	—
41	C₂×C₄²×C₁₁₃	—	2	8	no	—
42	C₂×C₄²×C₁₁₃	—	2	4	no	—
43	C₂×C₄²×C₁₁₃	—	2	16	no	—
44	C₂×C₄²×C₁₁₃	—	2	8	no	—
45	C₂×C₄²×C₁₁₃	—	2	8	no	—
46	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₁₃	D₄	1	8	yes	—
51	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
54	C₂²⋊C₈×C₁₁₃	C₂×C₄	1	32	yes	complemented
55	#97×C₁₁₃	—	2	8	no	—
56	C₄×C₈×C₁₁₃	—	2	8	no	—
57	C₂⁴×C₁₁₃	—	2	2	no	—
58	C₂⁴×C₁₁₃	—	2	2	no	—
59	C₂⁴×C₁₁₃	—	2	8	no	—
60	C₂⁴×C₁₁₃	C₄²	1	4	yes	—
61	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
63	C₂²×C₄×C₁₁₃	—	2	64	no	—
64	C₂²×C₄×C₁₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₁₃	—	2	8	no	—
68	C₂²×C₄×C₁₁₃	—	2	8	no	—
69	C₂²×C₄×C₁₁₃	—	2	4	no	—
70	C₂²×C₄×C₁₁₃	—	2	8	no	—
71	C₂²×C₄×C₁₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₁₃	—	2	32	no	—
73	C₂²×C₄×C₁₁₃	—	2	8	no	—
74	C₂²×C₄×C₁₁₃	—	2	8	no	—
75	C₂²×C₄×C₁₁₃	—	2	8	no	—
76	C₂²×C₄×C₁₁₃	—	2	8	no	—
77	C₂²×C₄×C₁₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	C₄²	1	4	yes	—
80	C₂²×C₄×C₁₁₃	C₄²	1	8	yes	—
81	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
82	C₂²×C₄×C₁₁₃	M₁₆	1	16	yes	complemented
83	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₁₃	C₂²×C₄	1	8	yes	—
85	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
92	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
93	M₁₆×C₁₁₃	—	2	32	no	—
94	C₂×C₈×C₁₁₃	—	2	8	no	—
95	C₂×C₈×C₁₁₃	—	2	8	no	—
96	C₂×C₈×C₁₁₃	C₂²×C₄	1	16	yes	complemented
97	C₄²×C₁₁₃	—	2	8	no	—
98	C₄²×C₁₁₃	—	2	4	no	—
99	C₄²×C₁₁₃	—	2	8	no	—
100	C₄²×C₁₁₃	—	2	4	no	—
101	C₄²×C₁₁₃	C₂²⋊C₄	1	8	yes	—
102	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
103	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
104	C₂³×C₁₁₃	—	2	16	no	—
105	C₂³×C₁₁₃	—	2	16	no	—
106	C₂³×C₁₁₃	—	2	2	no	—
107	C₂³×C₁₁₃	—	2	2	no	—
108	C₂³×C₁₁₃	—	2	4	no	—
109	C₂³×C₁₁₃	—	2	4	no	—
110	C₂³×C₁₁₃	—	2	8	no	—
111	C₂³×C₁₁₃	—	2	16	no	—
112	C₂³×C₁₁₃	C₂×C₄²	1	2	yes	—
113	C₂³×C₁₁₃	C₂×C₄²	1	4	yes	—
114	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂³×C₁₁₃	#117	1	2	yes	—
116	C₂³×C₁₁₃	C₂×M₁₆	1	8	yes	—
117	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁₃	—	2	32	no	—
119	C₂×C₄×C₁₁₃	—	2	16	no	—
120	C₂×C₄×C₁₁₃	—	2	4	no	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	2	no	—
123	C₂×C₄×C₁₁₃	—	2	4	no	—
124	C₂×C₄×C₁₁₃	—	2	4	no	—
125	C₂×C₄×C₁₁₃	—	2	8	no	—
126	C₂×C₄×C₁₁₃	—	2	16	no	—
127	C₂×C₄×C₁₁₃	—	2	16	no	—
128	C₂×C₄×C₁₁₃	—	2	16	no	—
129	C₂×C₄×C₁₁₃	—	2	32	no	—
130	C₂×C₄×C₁₁₃	C₂×C₄²	1	4	yes	—
131	C₂×C₄×C₁₁₃	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
133	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₁₁₃	#117	1	2	yes	—
136	C₂×C₄×C₁₁₃	C₄×D₄	1	16	yes	—
137	C₂×C₄×C₁₁₃	C₂×M₁₆	1	8	yes	—
138	C₂×C₄×C₁₁₃	C₂×M₁₆	1	8	yes	—
139	C₂×C₄×C₁₁₃	C₂³×C₄	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
142	C₈×C₁₁₃	—	2	16	no	—
143	C₂²×C₁₁₃	—	2	32	no	—
144	C₂²×C₁₁₃	—	2	4	no	—
145	C₂²×C₁₁₃	—	2	4	no	—
146	C₂²×C₁₁₃	—	2	4	no	—
147	C₂²×C₁₁₃	—	2	8	no	—
148	C₂²×C₁₁₃	—	2	4	no	—
149	C₂²×C₁₁₃	—	2	8	no	—
150	C₂²×C₁₁₃	—	2	4	no	—
151	C₂²×C₁₁₃	C₄×C₂²⋊C₄	1	4	yes	—
152	C₂²×C₁₁₃	C₄×M₁₆	1	8	yes	complemented
153	C₂²×C₁₁₃	C₂²×C₄²	1	1	yes	characteristic
154	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
156	C₂²×C₁₁₃	C₂²×M₁₆	1	4	yes	—
157	C₄×C₁₁₃	—	2	4	no	—
158	C₄×C₁₁₃	—	2	8	no	—
159	C₄×C₁₁₃	—	2	4	no	—
160	C₄×C₁₁₃	C₄×C₂²⋊C₄	1	4	yes	—
161	C₄×C₁₁₃	#407	1	8	yes	direct product factor
162	C₄×C₁₁₃	C₂×C₄×D₄	1	4	yes	—
163	C₄×#407	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂×C₁₁₃	—	2	4	no	—
165	C₂×C₁₁₃	—	2	8	no	—
166	C₂×C₁₁₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₁₁₃	C₂×C₄×M₁₆	1	2	yes	—
168	C₂×C₁₁₃	C₂×#407	1	2	yes	—
169	C₂×C₁₁₃	#2920	1	2	yes	—
170	C₂³×C₄²	C₂×C₁₁₃	1	1	yes	characteristic
171	C₂×#407	C₂×C₁₁₃	1	2	yes	—
172	C₂×C₄×M₁₆	C₂×C₁₁₃	1	2	yes	complemented
173	#1749	C₂×C₁₁₃	1	4	yes	complemented
174	C₄×C₂²⋊C₈	C₂×C₁₁₃	1	4	yes	complemented
175	#1728	C₂×C₁₁₃	1	2	yes	complemented
176	C₁₁₃	C₄×#407	1	1	yes	characteristic, direct product factor, Sylow
177	C₂⁴×C₄	C₄×C₁₁₃	1	2	yes	—
178	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
179	C₂²×M₁₆	C₂²×C₁₁₃	1	4	yes	—
180	C₂²×C₄²	—	2	8	no	—
181	C₂²×C₄²	C₄×C₁₁₃	1	2	yes	—
182	C₂²×C₄²	C₄×C₁₁₃	1	4	yes	—
183	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
184	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
185	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
186	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
187	#407	C₄×C₁₁₃	1	16	yes	direct product factor
188	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	8	yes	—
189	C₄×M₁₆	—	2	8	no	—
190	C₂×#97	C₂²×C₁₁₃	1	4	yes	complemented
191	C₂×C₄×C₈	C₂²×C₁₁₃	1	4	yes	complemented
192	#336	C₂²×C₁₁₃	1	8	yes	complemented
193	C₂⁵	C₂×C₄×C₁₁₃	1	1	yes	characteristic
194	C₂³×C₄	—	2	8	no	—
195	C₂³×C₄	—	2	16	no	—
196	C₂³×C₄	—	2	4	no	—
197	C₂³×C₄	—	2	4	no	—
198	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
199	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
200	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
201	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
202	C₂³×C₄	C₂×C₄×C₁₁₃	1	8	yes	—
203	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
204	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
207	C₂×M₁₆	—	2	8	no	—
208	C₂×M₁₆	—	2	8	no	—
209	C₂×M₁₆	C₂×C₄×C₁₁₃	1	16	yes	complemented
210	C₂²×C₈	C₂³×C₁₁₃	1	8	yes	—
211	C₂×C₄²	—	2	8	no	—
212	C₂×C₄²	—	2	4	no	—
213	C₂×C₄²	—	2	16	no	—
214	C₂×C₄²	—	2	8	no	—
215	C₂×C₄²	—	2	8	no	—
216	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
217	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
218	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
220	C₂×C₄²	D₄×C₁₁₃	1	8	yes	—
221	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
222	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
224	C₂²⋊C₈	C₂×C₄×C₁₁₃	1	32	yes	complemented
225	#97	—	2	8	no	—
226	C₄×C₈	—	2	8	no	—
227	C₂⁴	—	2	2	no	—
228	C₂⁴	—	2	2	no	—
229	C₂⁴	—	2	8	no	—
230	C₂⁴	C₄²×C₁₁₃	1	4	yes	—
231	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
232	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
233	C₂²×C₄	—	2	64	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	32	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	C₄²×C₁₁₃	1	4	yes	—
250	C₂²×C₄	C₄²×C₁₁₃	1	8	yes	—
251	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
252	C₂²×C₄	M₁₆×C₁₁₃	1	16	yes	complemented
253	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₁₃	1	8	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
261	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
262	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
263	M₁₆	—	2	32	no	—
264	C₂×C₈	—	2	8	no	—
265	C₂×C₈	—	2	8	no	—
266	C₂×C₈	C₂²×C₄×C₁₁₃	1	16	yes	complemented
267	C₄²	—	2	8	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	8	no	—
270	C₄²	—	2	4	no	—
271	C₄²	C₂²⋊C₄×C₁₁₃	1	8	yes	—
272	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
273	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
274	C₂³	—	2	16	no	—
275	C₂³	—	2	16	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	16	no	—
282	C₂³	C₂×C₄²×C₁₁₃	1	2	yes	—
283	C₂³	C₂×C₄²×C₁₁₃	1	4	yes	—
284	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
285	C₂³	#117×C₁₁₃	1	2	yes	—
286	C₂³	C₂×M₁₆×C₁₁₃	1	8	yes	—
287	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
288	C₂×C₄	—	2	32	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	16	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	2	16	no	—
299	C₂×C₄	—	2	32	no	—
300	C₂×C₄	C₂×C₄²×C₁₁₃	1	4	yes	—
301	C₂×C₄	C₂×C₄²×C₁₁₃	1	2	yes	—
302	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
304	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
305	C₂×C₄	#117×C₁₁₃	1	2	yes	—
306	C₂×C₄	C₄×D₄×C₁₁₃	1	16	yes	—
307	C₂×C₄	C₂×M₁₆×C₁₁₃	1	8	yes	—
308	C₂×C₄	C₂×M₁₆×C₁₁₃	1	8	yes	—
309	C₂×C₄	C₂³×C₄×C₁₁₃	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
311	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
312	C₈	—	2	16	no	—
313	C₂²	—	2	32	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	2	4	no	—
321	C₂²	C₄×C₂²⋊C₄×C₁₁₃	1	4	yes	—
322	C₂²	C₄×M₁₆×C₁₁₃	1	8	yes	complemented
323	C₂²	C₂²×C₄²×C₁₁₃	1	1	yes	characteristic
324	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
325	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
326	C₂²	C₂²×M₁₆×C₁₁₃	1	4	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	8	no	—
329	C₄	—	2	4	no	—
330	C₄	C₄×C₂²⋊C₄×C₁₁₃	1	4	yes	—
331	C₄	#407×C₁₁₃	1	8	yes	direct product factor
332	C₄	C₂×C₄×D₄×C₁₁₃	1	4	yes	—
333	C₂	—	2	4	no	—
334	C₂	—	2	8	no	—
335	C₂	C₂×C₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
336	C₂	C₂×C₄×M₁₆×C₁₁₃	1	2	yes	—
337	C₂	C₂×#407×C₁₁₃	1	2	yes	—
338	C₂	C₁₁₃×#2920	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₁₃	C₂³
commutator	C₂²	C₂²×C₄²×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂³×C₄
prime radical	C₂⁵×C₁₁₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×M₁₆×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1749	C₂	semidirect
5. C₄×C₂²⋊C₈×C₁₁₃	C₂	semidirect
6. C₁₁₃×#1728	C₂	semidirect
17. #407×C₁₁₃	C₄	direct (N × H)
20. C₂×#97×C₁₁₃	C₂²	semidirect
21. C₂×C₄×C₈×C₁₁₃	C₂²	semidirect
22. #336×C₁₁₃	C₂²	semidirect
39. C₂×M₁₆×C₁₁₃	C₂×C₄	semidirect
54. C₂²⋊C₈×C₁₁₃	C₂×C₄	semidirect
82. C₂²×C₄×C₁₁₃	M₁₆	semidirect
96. C₂×C₈×C₁₁₃	C₂²×C₄	semidirect
152. C₂²×C₁₁₃	C₄×M₁₆	semidirect
161. C₄×C₁₁₃	#407	direct (N × H)
163. C₄×#407	C₁₁₃	direct (N × H)
172. C₂×C₄×M₁₆	C₂×C₁₁₃	semidirect
173. #1749	C₂×C₁₁₃	semidirect
174. C₄×C₂²⋊C₈	C₂×C₁₁₃	semidirect
175. #1728	C₂×C₁₁₃	semidirect
176. C₁₁₃	C₄×#407	direct (N × H)
187. #407	C₄×C₁₁₃	direct (N × H)
190. C₂×#97	C₂²×C₁₁₃	semidirect
191. C₂×C₄×C₈	C₂²×C₁₁₃	semidirect
192. #336	C₂²×C₁₁₃	semidirect
209. C₂×M₁₆	C₂×C₄×C₁₁₃	semidirect
224. C₂²⋊C₈	C₂×C₄×C₁₁₃	semidirect
252. C₂²×C₄	M₁₆×C₁₁₃	semidirect
266. C₂×C₈	C₂²×C₄×C₁₁₃	semidirect
322. C₂²	C₄×M₁₆×C₁₁₃	semidirect
331. C₄	#407×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₁₃	2
C₂×#407×C₁₁₃	2
C₂×C₄×M₁₆×C₁₁₃	2
C₁₁₃×#1749	2
C₄×C₂²⋊C₈×C₁₁₃	2
C₁₁₃×#1728	2
C₄×#407	113

Subgroups — C4×#407×C113 #43288396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#407×C₁₁₃ #43288396