Subgroups — C₂×C₁₁₃×#1884 #43288966

Order 28928.

1794 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#421×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×#410×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1884	C₂	1	8	yes	maximal, direct product factor
6	C₂×#339×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	#568×C₁₁₃	—	2	2	no	—
10	#568×C₁₁₃	—	2	4	no	—
11	#568×C₁₁₃	C₂²	1	4	yes	complemented
12	C₂×#131×C₁₁₃	—	2	4	no	—
13	C₂²×M₁₆×C₁₁₃	—	2	2	no	—
14	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
15	#532×C₁₁₃	—	2	2	no	—
16	#532×C₁₁₃	—	2	2	no	—
17	#532×C₁₁₃	C₄	1	4	yes	complemented
18	#532×C₁₁₃	C₂²	1	4	yes	—
19	C₂×C₄⋊Q₈×C₁₁₃	C₄	1	1	yes	characteristic, complemented
20	C₂×#127×C₁₁₃	C₄	1	1	yes	characteristic, complemented
21	C₂×#124×C₁₁₃	C₄	1	1	yes	characteristic, complemented
22	C₂×#124×C₁₁₃	C₄	1	1	yes	characteristic, complemented
23	C₂×#121×C₁₁₃	—	2	2	no	—
24	C₂×C₄×D₄×C₁₁₃	—	2	2	no	—
25	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
27	#421×C₁₁₃	—	2	4	no	—
28	#421×C₁₁₃	C₂²	1	8	yes	complemented
29	C₂×#104×C₁₁₃	—	2	4	no	—
30	#410×C₁₁₃	—	2	2	no	—
31	#410×C₁₁₃	C₂²	1	4	yes	complemented
32	C₂×#99×C₁₁₃	—	2	2	no	—
33	#339×C₁₁₃	C₂²	1	8	yes	complemented
34	C₂×#41×C₁₁₃	—	2	2	no	—
35	C₂×#41×C₁₁₃	—	2	2	no	—
36	C₂×#41×C₁₁₃	—	2	1	no	—
37	C₂×#41×C₁₁₃	—	2	1	no	—
38	C₂×#41×C₁₁₃	—	2	2	no	—
39	C₂×#41×C₁₁₃	—	2	2	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂×#41×C₁₁₃	—	2	2	no	—
42	C₂×#41×C₁₁₃	—	2	2	no	—
43	C₂×#41×C₁₁₃	—	2	2	no	—
44	C₂×#41×C₁₁₃	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₁₃	C₂×C₄	1	2	yes	—
46	C₂×#41×C₁₁₃	D₄	1	2	yes	—
47	C₂×#41×C₁₁₃	D₄	1	2	yes	—
48	C₂×#41×C₁₁₃	C₂³	1	2	yes	—
49	C₂×#41×C₁₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₁₃	D₄	1	2	yes	—
57	C₂³×C₄×C₁₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₁₃	—	2	1	no	—
59	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
60	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
61	#131×C₁₁₃	—	2	16	no	—
62	#131×C₁₁₃	—	2	16	no	—
63	C₂×M₁₆×C₁₁₃	—	2	4	no	—
64	C₂×M₁₆×C₁₁₃	—	2	8	no	—
65	C₂×M₁₆×C₁₁₃	—	2	2	no	—
66	C₂×M₁₆×C₁₁₃	—	2	8	no	—
67	C₂×M₁₆×C₁₁₃	—	2	2	no	—
68	C₂×M₁₆×C₁₁₃	—	2	2	no	—
69	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	complemented
70	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	complemented
71	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₁₃	—	2	4	no	—
73	C₂²×C₈×C₁₁₃	—	2	2	no	—
74	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
75	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
76	#127×C₁₁₃	—	2	2	no	—
77	#127×C₁₁₃	C₂×C₄	1	4	yes	complemented
78	#124×C₁₁₃	—	2	2	no	—
79	#124×C₁₁₃	—	2	2	no	—
80	#124×C₁₁₃	C₂×C₄	1	4	yes	complemented
81	#124×C₁₁₃	C₂×C₄	1	4	yes	complemented
82	#121×C₁₁₃	—	2	8	no	—
83	#121×C₁₁₃	—	2	8	no	—
84	C₄×D₄×C₁₁₃	—	2	8	no	—
85	C₄×D₄×C₁₁₃	—	2	8	no	—
86	#117×C₁₁₃	—	2	2	no	—
87	#117×C₁₁₃	—	2	2	no	—
88	#117×C₁₁₃	—	2	2	no	—
89	#117×C₁₁₃	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₁₃	—	2	2	no	—
99	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
102	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
103	#104×C₁₁₃	—	2	16	no	—
104	#99×C₁₁₃	—	2	8	no	—
105	C₂⁴×C₁₁₃	—	2	1	no	—
106	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
108	#41×C₁₁₃	—	2	4	no	—
109	#41×C₁₁₃	—	2	4	no	—
110	#41×C₁₁₃	—	2	4	no	—
111	#41×C₁₁₃	—	2	4	no	—
112	#41×C₁₁₃	—	2	4	no	—
113	#41×C₁₁₃	—	2	4	no	—
114	#41×C₁₁₃	—	2	4	no	—
115	#41×C₁₁₃	—	2	4	no	—
116	#41×C₁₁₃	—	2	4	no	—
117	#41×C₁₁₃	—	2	4	no	—
118	#41×C₁₁₃	—	2	4	no	—
119	#41×C₁₁₃	—	2	4	no	—
120	#41×C₁₁₃	—	4	2	no	—
121	#41×C₁₁₃	—	4	2	no	—
122	#41×C₁₁₃	—	4	2	no	—
123	#41×C₁₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
130	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₁₁₃	—	2	4	no	—
133	C₂×D₄×C₁₁₃	—	2	4	no	—
134	C₂×D₄×C₁₁₃	—	2	8	no	—
135	C₂×D₄×C₁₁₃	—	2	2	no	—
136	C₂×D₄×C₁₁₃	—	2	2	no	—
137	C₂×D₄×C₁₁₃	—	2	1	no	—
138	C₂×D₄×C₁₁₃	—	2	2	no	—
139	C₂×D₄×C₁₁₃	—	2	2	no	—
140	C₂×D₄×C₁₁₃	—	2	2	no	—
141	C₂×D₄×C₁₁₃	—	2	2	no	—
142	C₂×D₄×C₁₁₃	—	4	8	no	—
143	C₂×D₄×C₁₁₃	—	4	2	no	—
144	C₂×D₄×C₁₁₃	—	4	2	no	—
145	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
146	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₁₃	—	4	4	no	—
162	C₂²×C₄×C₁₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
169	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
178	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
179	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
180	M₁₆×C₁₁₃	—	2	16	no	—
181	M₁₆×C₁₁₃	—	2	4	no	—
182	M₁₆×C₁₁₃	—	2	4	no	—
183	M₁₆×C₁₁₃	—	2	4	no	—
184	M₁₆×C₁₁₃	C₂×D₄	1	8	yes	complemented
185	C₂×C₈×C₁₁₃	—	2	16	no	—
186	C₂×C₈×C₁₁₃	—	2	4	no	—
187	C₂×C₈×C₁₁₃	—	2	4	no	—
188	C₂×C₈×C₁₁₃	—	2	4	no	—
189	C₄⋊C₄×C₁₁₃	—	2	8	no	—
190	C₄⋊C₄×C₁₁₃	—	2	4	no	—
191	C₄⋊C₄×C₁₁₃	—	4	2	no	—
192	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
193	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
194	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
195	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
196	C₄²×C₁₁₃	—	2	2	no	—
197	C₄²×C₁₁₃	—	2	1	no	—
198	C₄²×C₁₁₃	—	2	1	no	—
199	C₄²×C₁₁₃	—	2	2	no	—
200	C₄²×C₁₁₃	—	2	4	no	—
201	C₄²×C₁₁₃	—	4	2	no	—
202	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
203	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
204	C₂³×C₁₁₃	—	2	2	no	—
205	C₂³×C₁₁₃	—	2	2	no	—
206	C₂³×C₁₁₃	—	2	2	no	—
207	C₂³×C₁₁₃	—	4	2	no	—
208	C₂³×C₁₁₃	—	4	4	no	—
209	C₂³×C₁₁₃	—	4	4	no	—
210	C₂³×C₁₁₃	—	4	1	no	—
211	C₂³×C₁₁₃	—	4	1	no	—
212	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
214	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₁₁₃	#121	1	2	yes	—
216	C₂³×C₁₁₃	#121	1	2	yes	—
217	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₁₃	—	2	4	no	—
219	Q₈×C₁₁₃	—	2	4	no	—
220	Q₈×C₁₁₃	—	2	4	no	—
221	Q₈×C₁₁₃	—	4	2	no	—
222	D₄×C₁₁₃	—	2	8	no	—
223	D₄×C₁₁₃	—	2	8	no	—
224	D₄×C₁₁₃	—	2	4	no	—
225	D₄×C₁₁₃	—	2	4	no	—
226	D₄×C₁₁₃	—	2	4	no	—
227	D₄×C₁₁₃	—	4	16	no	—
228	D₄×C₁₁₃	—	4	4	no	—
229	D₄×C₁₁₃	—	4	4	no	—
230	D₄×C₁₁₃	—	4	2	no	—
231	C₂×C₄×C₁₁₃	—	2	4	no	—
232	C₂×C₄×C₁₁₃	—	2	2	no	—
233	C₂×C₄×C₁₁₃	—	2	2	no	—
234	C₂×C₄×C₁₁₃	—	2	2	no	—
235	C₂×C₄×C₁₁₃	—	2	4	no	—
236	C₂×C₄×C₁₁₃	—	2	4	no	—
237	C₂×C₄×C₁₁₃	—	2	4	no	—
238	C₂×C₄×C₁₁₃	—	2	4	no	—
239	C₂×C₄×C₁₁₃	—	2	2	no	—
240	C₂×C₄×C₁₁₃	—	2	2	no	—
241	C₂×C₄×C₁₁₃	—	4	4	no	—
242	C₂×C₄×C₁₁₃	—	4	4	no	—
243	C₂×C₄×C₁₁₃	—	4	2	no	—
244	C₂×C₄×C₁₁₃	—	4	1	no	—
245	C₂×C₄×C₁₁₃	—	4	1	no	—
246	C₂×C₄×C₁₁₃	—	4	2	no	—
247	C₂×C₄×C₁₁₃	—	4	2	no	—
248	C₂×C₄×C₁₁₃	—	4	2	no	—
249	C₂×C₄×C₁₁₃	—	4	2	no	—
250	C₂×C₄×C₁₁₃	—	4	4	no	—
251	C₂×C₄×C₁₁₃	—	8	4	no	—
252	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
253	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₁₁₃	#120	1	2	yes	—
260	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₁₃	#121	1	2	yes	—
263	C₂×C₄×C₁₁₃	#121	1	2	yes	—
264	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
266	C₂×C₄×C₁₁₃	#123	1	2	yes	—
267	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
271	C₈×C₁₁₃	—	2	8	no	—
272	C₂²×C₁₁₃	—	2	2	no	—
273	C₂²×C₁₁₃	—	2	4	no	—
274	C₂²×C₁₁₃	—	2	4	no	—
275	C₂²×C₁₁₃	—	4	1	no	—
276	C₂²×C₁₁₃	—	4	1	no	—
277	C₂²×C₁₁₃	—	4	2	no	—
278	C₂²×C₁₁₃	—	4	4	no	—
279	C₂²×C₁₁₃	—	4	4	no	—
280	C₂²×C₁₁₃	—	4	4	no	—
281	C₂²×C₁₁₃	—	4	2	no	—
282	C₂²×C₁₁₃	—	8	2	no	—
283	C₂²×C₁₁₃	—	8	2	no	—
284	C₂²×C₁₁₃	—	8	2	no	—
285	C₂²×C₁₁₃	#386	1	1	yes	characteristic
286	C₂²×C₁₁₃	#386	1	2	yes	—
287	C₂²×C₁₁₃	#386	1	1	yes	characteristic
288	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
290	C₄×C₁₁₃	—	2	4	no	—
291	C₄×C₁₁₃	—	2	4	no	—
292	C₄×C₁₁₃	—	4	2	no	—
293	C₄×C₁₁₃	—	4	2	no	—
294	C₄×C₁₁₃	—	8	4	no	—
295	C₄×C₁₁₃	#386	1	1	yes	characteristic
296	C₄×C₁₁₃	#386	1	1	yes	characteristic
297	C₄×C₁₁₃	#386	1	2	yes	—
298	C₄×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
299	C₄×C₁₁₃	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
301	C₂×#1884	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂×C₁₁₃	—	2	1	no	—
303	C₂×C₁₁₃	—	2	2	no	—
304	C₂×C₁₁₃	—	2	1	no	—
305	C₂×C₁₁₃	—	2	2	no	—
306	C₂×C₁₁₃	—	4	4	no	—
307	C₂×C₁₁₃	—	8	2	no	—
308	C₂×C₁₁₃	#1884	1	2	yes	direct product factor
309	C₂×C₁₁₃	C₂×#386	1	1	yes	characteristic
310	C₂×#568	C₂×C₁₁₃	1	1	yes	characteristic, complemented
311	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic
312	C₂×#421	C₂×C₁₁₃	1	2	yes	complemented
313	C₂×#410	C₂×C₁₁₃	1	1	yes	characteristic, complemented
314	#1884	C₂×C₁₁₃	1	8	yes	direct product factor
315	C₂×#339	C₂×C₁₁₃	1	2	yes	complemented
316	C₁₁₃	C₂×#1884	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
318	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
319	#568	—	2	2	no	—
320	#568	—	2	4	no	—
321	#568	C₂²×C₁₁₃	1	4	yes	complemented
322	C₂×#131	—	2	4	no	—
323	C₂²×M₁₆	—	2	2	no	—
324	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
325	#532	—	2	2	no	—
326	#532	—	2	2	no	—
327	#532	C₄×C₁₁₃	1	4	yes	complemented
328	#532	C₂²×C₁₁₃	1	4	yes	—
329	C₂×C₄⋊Q₈	C₄×C₁₁₃	1	1	yes	characteristic, complemented
330	C₂×#127	C₄×C₁₁₃	1	1	yes	characteristic, complemented
331	C₂×#124	C₄×C₁₁₃	1	1	yes	characteristic, complemented
332	C₂×#124	C₄×C₁₁₃	1	1	yes	characteristic, complemented
333	C₂×#121	—	2	2	no	—
334	C₂×C₄×D₄	—	2	2	no	—
335	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
336	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
337	#421	—	2	4	no	—
338	#421	C₂²×C₁₁₃	1	8	yes	complemented
339	C₂×#104	—	2	4	no	—
340	#410	—	2	2	no	—
341	#410	C₂²×C₁₁₃	1	4	yes	complemented
342	C₂×#99	—	2	2	no	—
343	#339	C₂²×C₁₁₃	1	8	yes	complemented
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	C₂×C₄×C₁₁₃	1	2	yes	—
355	C₂×#41	C₂×C₄×C₁₁₃	1	2	yes	—
356	C₂×#41	D₄×C₁₁₃	1	2	yes	—
357	C₂×#41	D₄×C₁₁₃	1	2	yes	—
358	C₂×#41	C₂³×C₁₁₃	1	2	yes	—
359	C₂×#41	C₂³×C₁₁₃	1	2	yes	—
360	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
361	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
365	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
366	C₂²×D₄	D₄×C₁₁₃	1	2	yes	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
370	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
371	#131	—	2	16	no	—
372	#131	—	2	16	no	—
373	C₂×M₁₆	—	2	4	no	—
374	C₂×M₁₆	—	2	8	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	8	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	complemented
380	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	complemented
381	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
382	C₂²×C₈	—	2	4	no	—
383	C₂²×C₈	—	2	2	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	complemented
386	#127	—	2	2	no	—
387	#127	C₂×C₄×C₁₁₃	1	4	yes	complemented
388	#124	—	2	2	no	—
389	#124	—	2	2	no	—
390	#124	C₂×C₄×C₁₁₃	1	4	yes	complemented
391	#124	C₂×C₄×C₁₁₃	1	4	yes	complemented
392	#121	—	2	8	no	—
393	#121	—	2	8	no	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	8	no	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	C₂³×C₁₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	2	no	—
409	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
412	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
413	#104	—	2	16	no	—
414	#99	—	2	8	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
417	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
418	#41	—	2	4	no	—
419	#41	—	2	4	no	—
420	#41	—	2	4	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	2	4	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
440	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
441	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
456	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
457	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
458	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
459	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
478	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
479	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
482	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
486	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
487	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
488	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
490	M₁₆	—	2	16	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	—	2	4	no	—
493	M₁₆	—	2	4	no	—
494	M₁₆	C₂×D₄×C₁₁₃	1	8	yes	complemented
495	C₂×C₈	—	2	16	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	4	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	4	2	no	—
512	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
513	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
523	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
524	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
525	C₂³	#121×C₁₁₃	1	2	yes	—
526	C₂³	#121×C₁₁₃	1	2	yes	—
527	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	Q₈	—	4	2	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	4	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	16	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
563	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
565	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
566	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
567	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
568	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
569	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
570	C₂×C₄	#120×C₁₁₃	1	2	yes	—
571	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
572	C₂×C₄	#121×C₁₁₃	1	2	yes	—
573	C₂×C₄	#121×C₁₁₃	1	2	yes	—
574	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
575	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
576	C₂×C₄	#123×C₁₁₃	1	2	yes	—
577	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
581	C₈	—	2	8	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	4	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	2	no	—
595	C₂²	#386×C₁₁₃	1	1	yes	characteristic
596	C₂²	#386×C₁₁₃	1	2	yes	—
597	C₂²	#386×C₁₁₃	1	1	yes	characteristic
598	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
599	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
600	C₄	—	2	4	no	—
601	C₄	—	2	4	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	8	4	no	—
605	C₄	#386×C₁₁₃	1	1	yes	characteristic
606	C₄	#386×C₁₁₃	1	1	yes	characteristic
607	C₄	#386×C₁₁₃	1	2	yes	—
608	C₄	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
609	C₄	C₂×#120×C₁₁₃	1	1	yes	characteristic
610	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	2	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	2	no	—
615	C₂	—	4	4	no	—
616	C₂	—	8	2	no	—
617	C₂	C₁₁₃×#1884	1	2	yes	direct product factor
618	C₂	C₂×#386×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁₃	#120
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	#386
prime radical	C₂×#532×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂³×C₄×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×#421×C₁₁₃	C₂	semidirect
4. C₂×#410×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1884	C₂	direct (N × H)
6. C₂×#339×C₁₁₃	C₂	semidirect
11. #568×C₁₁₃	C₂²	semidirect
17. #532×C₁₁₃	C₄	semidirect
19. C₂×C₄⋊Q₈×C₁₁₃	C₄	semidirect
20. C₂×#127×C₁₁₃	C₄	semidirect
21. C₂×#124×C₁₁₃	C₄	semidirect
22. C₂×#124×C₁₁₃	C₄	semidirect
28. #421×C₁₁₃	C₂²	semidirect
31. #410×C₁₁₃	C₂²	semidirect
33. #339×C₁₁₃	C₂²	semidirect
69. C₂×M₁₆×C₁₁₃	D₄	semidirect
70. C₂×M₁₆×C₁₁₃	D₄	semidirect
75. C₄⋊Q₈×C₁₁₃	C₂×C₄	semidirect
77. #127×C₁₁₃	C₂×C₄	semidirect
80. #124×C₁₁₃	C₂×C₄	semidirect
81. #124×C₁₁₃	C₂×C₄	semidirect
184. M₁₆×C₁₁₃	C₂×D₄	semidirect
301. C₂×#1884	C₁₁₃	direct (N × H)
308. C₂×C₁₁₃	#1884	direct (N × H)
310. C₂×#568	C₂×C₁₁₃	semidirect
312. C₂×#421	C₂×C₁₁₃	semidirect
313. C₂×#410	C₂×C₁₁₃	semidirect
314. #1884	C₂×C₁₁₃	direct (N × H)
315. C₂×#339	C₂×C₁₁₃	semidirect
316. C₁₁₃	C₂×#1884	direct (N × H)
321. #568	C₂²×C₁₁₃	semidirect
327. #532	C₄×C₁₁₃	semidirect
329. C₂×C₄⋊Q₈	C₄×C₁₁₃	semidirect
330. C₂×#127	C₄×C₁₁₃	semidirect
331. C₂×#124	C₄×C₁₁₃	semidirect
332. C₂×#124	C₄×C₁₁₃	semidirect
338. #421	C₂²×C₁₁₃	semidirect
341. #410	C₂²×C₁₁₃	semidirect
343. #339	C₂²×C₁₁₃	semidirect
379. C₂×M₁₆	D₄×C₁₁₃	semidirect
380. C₂×M₁₆	D₄×C₁₁₃	semidirect
385. C₄⋊Q₈	C₂×C₄×C₁₁₃	semidirect
387. #127	C₂×C₄×C₁₁₃	semidirect
390. #124	C₂×C₄×C₁₁₃	semidirect
391. #124	C₂×C₄×C₁₁₃	semidirect
494. M₁₆	C₂×D₄×C₁₁₃	semidirect
617. C₂	C₁₁₃×#1884	direct (N × H)

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×#532×C₁₁₃	2
C₂×#421×C₁₁₃	2
C₂×#410×C₁₁₃	2
C₁₁₃×#1884	2
C₂×#339×C₁₁₃	2
C₂×#1884	113

Subgroups — C2×C113×#1884 #43288966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1884 #43288966