Subgroups — C₂×C₈×C₂²⋊C₄×C₁₁₃ #43288400

Order 28928.

2046 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₈×C₂²⋊C₄×C₁₁₃	C₂	1	8	yes	maximal, direct product factor
6	C₂×#336×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₁₃	—	2	8	no	—
9	C₂³×C₈×C₁₁₃	C₄	1	8	yes	complemented
10	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₁₃	C₂²	1	4	yes	—
13	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₁₃	C₄	1	2	yes	—
15	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₁₃	C₄	1	8	yes	complemented
17	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₁₃	—	2	8	no	—
19	C₂×C₄×C₈×C₁₁₃	C₂²	1	8	yes	complemented
20	C₄×C₂²⋊C₄×C₁₁₃	C₄	1	4	yes	—
21	C₄×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
22	C₂×#95×C₁₁₃	C₄	1	2	yes	—
23	#336×C₁₁₃	C₂²	1	8	yes	complemented
24	C₂⁵×C₁₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₁₃	—	2	4	no	—
26	C₂³×C₄×C₁₁₃	—	2	4	no	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
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	4	yes	—
31	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₁₃	—	2	4	no	—
36	C₂²×C₈×C₁₁₃	—	2	4	no	—
37	C₂²×C₈×C₁₁₃	—	2	32	no	—
38	C₂²×C₈×C₁₁₃	—	2	16	no	—
39	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₁₃	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₁₁₃	C₂×C₄	1	16	yes	complemented
43	C₂²×C₈×C₁₁₃	D₄	1	8	yes	—
44	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
46	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₁₃	C₈	1	16	yes	direct product factor
48	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	8	yes	—
49	C₂×C₄²×C₁₁₃	—	2	4	no	—
50	C₂×C₄²×C₁₁₃	—	2	4	no	—
51	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₁₃	C₂³	1	4	yes	—
53	C₂²⋊C₈×C₁₁₃	C₂×C₄	1	16	yes	complemented
54	C₄×C₈×C₁₁₃	—	2	16	no	—
55	#95×C₁₁₃	C₂×C₄	1	8	yes	—
56	C₂⁴×C₁₁₃	—	2	4	no	—
57	C₂⁴×C₁₁₃	—	2	4	no	—
58	C₂⁴×C₁₁₃	C₄²	1	4	yes	—
59	C₂⁴×C₁₁₃	C₂×C₈	1	8	yes	—
60	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
61	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁₃	—	2	8	no	—
63	C₂²×C₄×C₁₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₁₃	—	2	8	no	—
65	C₂²×C₄×C₁₁₃	—	2	8	no	—
66	C₂²×C₄×C₁₁₃	—	2	8	no	—
67	C₂²×C₄×C₁₁₃	—	2	8	no	—
68	C₂²×C₄×C₁₁₃	—	2	16	no	—
69	C₂²×C₄×C₁₁₃	—	2	4	no	—
70	C₂²×C₄×C₁₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₁₃	C₄²	1	4	yes	—
72	C₂²×C₄×C₁₁₃	C₄²	1	8	yes	—
73	C₂²×C₄×C₁₁₃	C₂×C₈	1	16	yes	complemented
74	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
76	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₁₁₃	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
82	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
83	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
84	C₂×C₈×C₁₁₃	—	2	8	no	—
85	C₂×C₈×C₁₁₃	—	2	16	no	—
86	C₂×C₈×C₁₁₃	—	2	4	no	—
87	C₂×C₈×C₁₁₃	—	2	4	no	—
88	C₂×C₈×C₁₁₃	—	2	4	no	—
89	C₂×C₈×C₁₁₃	—	2	32	no	—
90	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	16	yes	direct product factor
91	C₂×C₈×C₁₁₃	C₂²×C₄	1	8	yes	—
92	C₂×C₈×C₁₁₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₁₃	C₂²×C₄	1	4	yes	—
94	C₂×C₈×C₁₁₃	C₂×D₄	1	8	yes	—
95	C₂²⋊C₄×C₁₁₃	C₂×C₈	1	32	yes	direct product factor
96	C₄²×C₁₁₃	—	2	8	no	—
97	C₄²×C₁₁₃	—	2	4	no	—
98	C₄²×C₁₁₃	—	2	4	no	—
99	C₂³×C₁₁₃	—	2	4	no	—
100	C₂³×C₁₁₃	—	2	4	no	—
101	C₂³×C₁₁₃	—	2	8	no	—
102	C₂³×C₁₁₃	—	2	8	no	—
103	C₂³×C₁₁₃	—	2	32	no	—
104	C₂³×C₁₁₃	C₄×C₈	1	16	yes	complemented
105	C₂³×C₁₁₃	C₂×C₄²	1	4	yes	—
106	C₂³×C₁₁₃	C₂×C₄²	1	2	yes	—
107	C₂³×C₁₁₃	C₄×D₄	1	4	yes	—
108	C₂³×C₁₁₃	C₂²×C₈	1	8	yes	—
109	C₂³×C₁₁₃	C₂²×C₈	1	4	yes	—
110	C₂³×C₁₁₃	#131	1	4	yes	—
111	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁₃	—	2	8	no	—
113	C₂×C₄×C₁₁₃	—	2	4	no	—
114	C₂×C₄×C₁₁₃	—	2	8	no	—
115	C₂×C₄×C₁₁₃	—	2	8	no	—
116	C₂×C₄×C₁₁₃	—	2	32	no	—
117	C₂×C₄×C₁₁₃	—	2	4	no	—
118	C₂×C₄×C₁₁₃	—	2	4	no	—
119	C₂×C₄×C₁₁₃	—	2	8	no	—
120	C₂×C₄×C₁₁₃	—	2	16	no	—
121	C₂×C₄×C₁₁₃	C₂×C₄²	1	4	yes	—
122	C₂×C₄×C₁₁₃	C₂×C₄²	1	2	yes	—
123	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
124	C₂×C₄×C₁₁₃	#117	1	4	yes	—
125	C₂×C₄×C₁₁₃	C₄×D₄	1	8	yes	—
126	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
127	C₂×C₄×C₁₁₃	C₂²×C₈	1	16	yes	complemented
128	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
131	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
132	C₈×C₁₁₃	—	2	4	no	—
133	C₈×C₁₁₃	—	2	8	no	—
134	C₈×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	direct product factor
135	C₂²×C₁₁₃	—	2	4	no	—
136	C₂²×C₁₁₃	—	2	16	no	—
137	C₂²×C₁₁₃	—	2	32	no	—
138	C₂²×C₁₁₃	—	2	4	no	—
139	C₂²×C₁₁₃	C₄×C₂²⋊C₄	1	4	yes	—
140	C₂²×C₁₁₃	C₂×C₄×C₈	1	4	yes	—
141	C₂²×C₁₁₃	C₂×C₄×C₈	1	8	yes	complemented
142	C₂²×C₁₁₃	#405	1	4	yes	—
143	C₂²×C₁₁₃	C₈×D₄	1	16	yes	—
144	C₂²×C₁₁₃	C₂²×C₄²	1	1	yes	characteristic
145	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
146	C₂²×C₁₁₃	C₂³×C₈	1	2	yes	—
147	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
148	C₄×C₁₁₃	—	2	16	no	—
149	C₄×C₁₁₃	—	2	4	no	—
150	C₄×C₁₁₃	C₄×C₂²⋊C₄	1	4	yes	—
151	C₄×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
152	C₄×C₁₁₃	C₂×#117	1	1	yes	characteristic
153	C₄×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
154	C₂×C₈×C₂²⋊C₄	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂×C₁₁₃	—	2	8	no	—
156	C₂×C₁₁₃	C₈×C₂²⋊C₄	1	8	yes	direct product factor
157	C₂×C₁₁₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₁₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
159	C₂×C₁₁₃	C₂×#405	1	1	yes	characteristic
160	C₂×C₁₁₃	C₂×C₈×D₄	1	4	yes	—
161	C₂⁴×C₈	C₂×C₁₁₃	1	1	yes	characteristic
162	C₂²×C₂²⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic
163	C₂²×C₄×C₈	C₂×C₁₁₃	1	2	yes	complemented
164	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
165	C₈×C₂²⋊C₄	C₂×C₁₁₃	1	8	yes	direct product factor
166	C₂×#336	C₂×C₁₁₃	1	2	yes	complemented
167	C₁₁₃	C₂×C₈×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
168	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
169	C₂³×C₈	—	2	8	no	—
170	C₂³×C₈	C₄×C₁₁₃	1	8	yes	complemented
171	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
172	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₁₁₃	1	4	yes	—
174	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
175	C₂²×C₂²⋊C₄	C₄×C₁₁₃	1	2	yes	—
176	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
177	C₂×C₂²⋊C₈	C₄×C₁₁₃	1	8	yes	complemented
178	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
179	C₂×C₄×C₈	—	2	8	no	—
180	C₂×C₄×C₈	C₂²×C₁₁₃	1	8	yes	complemented
181	C₄×C₂²⋊C₄	C₄×C₁₁₃	1	4	yes	—
182	C₄×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
183	C₂×#95	C₄×C₁₁₃	1	2	yes	—
184	#336	C₂²×C₁₁₃	1	8	yes	complemented
185	C₂⁵	C₂×C₄×C₁₁₃	1	1	yes	characteristic
186	C₂³×C₄	—	2	4	no	—
187	C₂³×C₄	—	2	4	no	—
188	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
189	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
190	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
191	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
192	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
193	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
194	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
195	C₂²×C₈	—	2	4	no	—
196	C₂²×C₈	—	2	4	no	—
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	—	2	32	no	—
199	C₂²×C₈	—	2	16	no	—
200	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
201	C₂²×C₈	C₂×C₄×C₁₁₃	1	8	yes	—
202	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
203	C₂²×C₈	C₂×C₄×C₁₁₃	1	16	yes	complemented
204	C₂²×C₈	D₄×C₁₁₃	1	8	yes	—
205	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
206	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
207	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
208	C₂×C₂²⋊C₄	C₈×C₁₁₃	1	16	yes	direct product factor
209	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	8	yes	—
210	C₂×C₄²	—	2	4	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
213	C₂×C₄²	C₂³×C₁₁₃	1	4	yes	—
214	C₂²⋊C₈	C₂×C₄×C₁₁₃	1	16	yes	complemented
215	C₄×C₈	—	2	16	no	—
216	#95	C₂×C₄×C₁₁₃	1	8	yes	—
217	C₂⁴	—	2	4	no	—
218	C₂⁴	—	2	4	no	—
219	C₂⁴	C₄²×C₁₁₃	1	4	yes	—
220	C₂⁴	C₂×C₈×C₁₁₃	1	8	yes	—
221	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
222	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
223	C₂²×C₄	—	2	8	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	8	no	—
226	C₂²×C₄	—	2	8	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	2	8	no	—
229	C₂²×C₄	—	2	16	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	C₄²×C₁₁₃	1	4	yes	—
233	C₂²×C₄	C₄²×C₁₁₃	1	8	yes	—
234	C₂²×C₄	C₂×C₈×C₁₁₃	1	16	yes	complemented
235	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₁₁₃	1	8	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
242	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
243	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
244	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
245	C₂×C₈	—	2	8	no	—
246	C₂×C₈	—	2	16	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	32	no	—
251	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	16	yes	direct product factor
252	C₂×C₈	C₂²×C₄×C₁₁₃	1	8	yes	—
253	C₂×C₈	C₂²×C₄×C₁₁₃	1	4	yes	—
254	C₂×C₈	C₂²×C₄×C₁₁₃	1	4	yes	—
255	C₂×C₈	C₂×D₄×C₁₁₃	1	8	yes	—
256	C₂²⋊C₄	C₂×C₈×C₁₁₃	1	32	yes	direct product factor
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	4	no	—
260	C₂³	—	2	4	no	—
261	C₂³	—	2	4	no	—
262	C₂³	—	2	8	no	—
263	C₂³	—	2	8	no	—
264	C₂³	—	2	32	no	—
265	C₂³	C₄×C₈×C₁₁₃	1	16	yes	complemented
266	C₂³	C₂×C₄²×C₁₁₃	1	4	yes	—
267	C₂³	C₂×C₄²×C₁₁₃	1	2	yes	—
268	C₂³	C₄×D₄×C₁₁₃	1	4	yes	—
269	C₂³	C₂²×C₈×C₁₁₃	1	8	yes	—
270	C₂³	C₂²×C₈×C₁₁₃	1	4	yes	—
271	C₂³	#131×C₁₁₃	1	4	yes	—
272	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
273	C₂×C₄	—	2	8	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	8	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	32	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	16	no	—
282	C₂×C₄	C₂×C₄²×C₁₁₃	1	4	yes	—
283	C₂×C₄	C₂×C₄²×C₁₁₃	1	2	yes	—
284	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
285	C₂×C₄	#117×C₁₁₃	1	4	yes	—
286	C₂×C₄	C₄×D₄×C₁₁₃	1	8	yes	—
287	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
288	C₂×C₄	C₂²×C₈×C₁₁₃	1	16	yes	complemented
289	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
290	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
291	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
292	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
293	C₈	—	2	4	no	—
294	C₈	—	2	8	no	—
295	C₈	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	direct product factor
296	C₂²	—	2	4	no	—
297	C₂²	—	2	16	no	—
298	C₂²	—	2	32	no	—
299	C₂²	—	2	4	no	—
300	C₂²	C₄×C₂²⋊C₄×C₁₁₃	1	4	yes	—
301	C₂²	C₂×C₄×C₈×C₁₁₃	1	4	yes	—
302	C₂²	C₂×C₄×C₈×C₁₁₃	1	8	yes	complemented
303	C₂²	#405×C₁₁₃	1	4	yes	—
304	C₂²	C₈×D₄×C₁₁₃	1	16	yes	—
305	C₂²	C₂²×C₄²×C₁₁₃	1	1	yes	characteristic
306	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
307	C₂²	C₂³×C₈×C₁₁₃	1	2	yes	—
308	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
309	C₄	—	2	16	no	—
310	C₄	—	2	4	no	—
311	C₄	C₄×C₂²⋊C₄×C₁₁₃	1	4	yes	—
312	C₄	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
313	C₄	C₂×#117×C₁₁₃	1	1	yes	characteristic
314	C₄	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
315	C₂	—	2	8	no	—
316	C₂	C₈×C₂²⋊C₄×C₁₁₃	1	8	yes	direct product factor
317	C₂	C₂×C₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
318	C₂	C₂²×C₄×C₈×C₁₁₃	1	1	yes	characteristic
319	C₂	C₂×#405×C₁₁₃	1	1	yes	characteristic
320	C₂	C₂×C₈×D₄×C₁₁₃	1	4	yes	—

	subgroup	G/H
center	C₂³×C₈×C₁₁₃	C₂²
commutator	C₂	C₂²×C₄×C₈×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂⁴×C₁₁₃	C₂²×C₄
prime radical	C₂⁵×C₁₁₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₈×C₁₁₃	C₂	semidirect
5. C₈×C₂²⋊C₄×C₁₁₃	C₂	direct (N × H)
6. C₂×#336×C₁₁₃	C₂	semidirect
9. C₂³×C₈×C₁₁₃	C₄	semidirect
16. C₂×C₂²⋊C₈×C₁₁₃	C₄	semidirect
19. C₂×C₄×C₈×C₁₁₃	C₂²	semidirect
23. #336×C₁₁₃	C₂²	semidirect
42. C₂²×C₈×C₁₁₃	C₂×C₄	semidirect
47. C₂×C₂²⋊C₄×C₁₁₃	C₈	direct (N × H)
53. C₂²⋊C₈×C₁₁₃	C₂×C₄	semidirect
73. C₂²×C₄×C₁₁₃	C₂×C₈	semidirect
90. C₂×C₈×C₁₁₃	C₂²⋊C₄	direct (N × H)
95. C₂²⋊C₄×C₁₁₃	C₂×C₈	direct (N × H)
104. C₂³×C₁₁₃	C₄×C₈	semidirect
127. C₂×C₄×C₁₁₃	C₂²×C₈	semidirect
134. C₈×C₁₁₃	C₂×C₂²⋊C₄	direct (N × H)
141. C₂²×C₁₁₃	C₂×C₄×C₈	semidirect
154. C₂×C₈×C₂²⋊C₄	C₁₁₃	direct (N × H)
156. C₂×C₁₁₃	C₈×C₂²⋊C₄	direct (N × H)
163. C₂²×C₄×C₈	C₂×C₁₁₃	semidirect
165. C₈×C₂²⋊C₄	C₂×C₁₁₃	direct (N × H)
166. C₂×#336	C₂×C₁₁₃	semidirect
167. C₁₁₃	C₂×C₈×C₂²⋊C₄	direct (N × H)
170. C₂³×C₈	C₄×C₁₁₃	semidirect
177. C₂×C₂²⋊C₈	C₄×C₁₁₃	semidirect
180. C₂×C₄×C₈	C₂²×C₁₁₃	semidirect
184. #336	C₂²×C₁₁₃	semidirect
203. C₂²×C₈	C₂×C₄×C₁₁₃	semidirect
208. C₂×C₂²⋊C₄	C₈×C₁₁₃	direct (N × H)
214. C₂²⋊C₈	C₂×C₄×C₁₁₃	semidirect
234. C₂²×C₄	C₂×C₈×C₁₁₃	semidirect
251. C₂×C₈	C₂²⋊C₄×C₁₁₃	direct (N × H)
256. C₂²⋊C₄	C₂×C₈×C₁₁₃	direct (N × H)
265. C₂³	C₄×C₈×C₁₁₃	semidirect
288. C₂×C₄	C₂²×C₈×C₁₁₃	semidirect
295. C₈	C₂×C₂²⋊C₄×C₁₁₃	direct (N × H)
302. C₂²	C₂×C₄×C₈×C₁₁₃	semidirect
316. C₂	C₈×C₂²⋊C₄×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
C₂⁴×C₈×C₁₁₃	2
C₂²×C₂²⋊C₈×C₁₁₃	2
C₂²×C₄×C₈×C₁₁₃	2
C₂×C₄×C₂²⋊C₄×C₁₁₃	2
C₈×C₂²⋊C₄×C₁₁₃	2
C₂×#336×C₁₁₃	2
C₂×C₈×C₂²⋊C₄	113

Subgroups — C2×C8×C22⋊C4×C113 #43288400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₂²⋊C₄×C₁₁₃ #43288400