Subgroups — C₁₁₃×#1436 #28386232

Order 14464.

612 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄²×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#95×C₁₁₃	C₂	1	2	yes	maximal
4	C₂×#95×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#95×C₁₁₃	C₂	1	2	yes	maximal
6	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₁₁₃	C₂²	1	2	yes	—
8	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₁₁₃	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
12	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
13	C₂×C₄⋊C₄×C₁₁₃	C₄	1	4	yes	complemented
14	C₂×C₄²×C₁₁₃	—	2	2	no	—
15	C₂×C₄²×C₁₁₃	—	2	4	no	—
16	#95×C₁₁₃	—	2	2	no	—
17	#95×C₁₁₃	—	2	4	no	—
18	#95×C₁₁₃	C₄	1	8	yes	complemented
19	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₁₃	—	2	2	no	—
21	C₂²×C₄×C₁₁₃	—	2	2	no	—
22	C₂²×C₄×C₁₁₃	—	2	2	no	—
23	C₂²×C₄×C₁₁₃	—	2	1	no	—
24	C₂²×C₄×C₁₁₃	—	2	1	no	—
25	C₂²×C₄×C₁₁₃	—	2	2	no	—
26	C₂²×C₄×C₁₁₃	—	2	2	no	—
27	C₂²×C₄×C₁₁₃	—	2	2	no	—
28	C₂²×C₄×C₁₁₃	—	2	2	no	—
29	C₂²×C₄×C₁₁₃	—	2	2	no	—
30	C₂²×C₄×C₁₁₃	—	2	2	no	—
31	C₂²×C₄×C₁₁₃	—	2	2	no	—
32	C₂²×C₄×C₁₁₃	—	2	1	no	—
33	C₂²×C₄×C₁₁₃	—	2	1	no	—
34	C₂²×C₄×C₁₁₃	—	2	2	no	—
35	C₂²×C₄×C₁₁₃	—	2	2	no	—
36	C₂²×C₄×C₁₁₃	—	2	2	no	—
37	C₂²×C₄×C₁₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₁₃	—	2	2	no	—
39	C₂²×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
40	C₂²×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
41	C₂²×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
42	C₂²×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
43	C₂²×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
44	C₂²×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
45	C₂²×C₄×C₁₁₃	D₄	1	2	yes	—
46	C₂²×C₄×C₁₁₃	D₄	1	2	yes	—
47	C₂²×C₄×C₁₁₃	D₄	1	4	yes	—
48	C₂²×C₄×C₁₁₃	Q₈	1	4	yes	—
49	C₄⋊C₄×C₁₁₃	—	2	8	no	—
50	C₄²×C₁₁₃	—	2	8	no	—
51	C₂³×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂³×C₁₁₃	C₂²×C₄	1	2	yes	—
53	C₂³×C₁₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂³×C₁₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂³×C₁₁₃	C₂×D₄	1	2	yes	—
56	C₂³×C₁₁₃	C₂×Q₈	1	2	yes	—
57	C₂³×C₁₁₃	#41	1	2	yes	—
58	C₂³×C₁₁₃	#41	1	2	yes	—
59	C₂³×C₁₁₃	#41	1	2	yes	—
60	C₂×C₄×C₁₁₃	—	2	2	no	—
61	C₂×C₄×C₁₁₃	—	2	2	no	—
62	C₂×C₄×C₁₁₃	—	2	4	no	—
63	C₂×C₄×C₁₁₃	—	2	4	no	—
64	C₂×C₄×C₁₁₃	—	2	4	no	—
65	C₂×C₄×C₁₁₃	—	2	4	no	—
66	C₂×C₄×C₁₁₃	—	2	4	no	—
67	C₂×C₄×C₁₁₃	—	2	4	no	—
68	C₂×C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₄×C₁₁₃	—	2	4	no	—
70	C₂×C₄×C₁₁₃	—	2	4	no	—
71	C₂×C₄×C₁₁₃	—	2	4	no	—
72	C₂×C₄×C₁₁₃	—	2	4	no	—
73	C₂×C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₄×C₁₁₃	—	2	2	no	—
75	C₂×C₄×C₁₁₃	—	2	4	no	—
76	C₂×C₄×C₁₁₃	—	2	4	no	—
77	C₂×C₄×C₁₁₃	—	2	4	no	—
78	C₂×C₄×C₁₁₃	—	2	4	no	—
79	C₂×C₄×C₁₁₃	—	4	1	no	—
80	C₂×C₄×C₁₁₃	—	4	2	no	—
81	C₂×C₄×C₁₁₃	—	4	2	no	—
82	C₂×C₄×C₁₁₃	—	4	1	no	—
83	C₂×C₄×C₁₁₃	—	4	2	no	—
84	C₂×C₄×C₁₁₃	—	4	2	no	—
85	C₂×C₄×C₁₁₃	—	4	2	no	—
86	C₂×C₄×C₁₁₃	C₄²	1	4	yes	complemented
87	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
88	C₂×C₄×C₁₁₃	C₄⋊C₄	1	8	yes	complemented
89	C₂²×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
90	C₂²×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
92	C₂²×C₁₁₃	#117	1	1	yes	characteristic
93	C₂²×C₁₁₃	#117	1	2	yes	—
94	C₂²×C₁₁₃	C₄×D₄	1	2	yes	—
95	C₂²×C₁₁₃	C₄×D₄	1	2	yes	—
96	C₂²×C₁₁₃	C₄×D₄	1	2	yes	—
97	C₂²×C₁₁₃	C₄×D₄	1	2	yes	—
98	C₂²×C₁₁₃	C₄×Q₈	1	2	yes	—
99	C₂²×C₁₁₃	C₄×Q₈	1	2	yes	—
100	C₂²×C₁₁₃	#120	1	1	yes	characteristic
101	C₂²×C₁₁₃	#121	1	2	yes	—
102	C₂²×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
103	C₂²×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
104	C₂²×C₁₁₃	#123	1	2	yes	—
105	C₂²×C₁₁₃	#123	1	1	yes	characteristic
106	C₂²×C₁₁₃	#124	1	1	yes	characteristic
107	C₂²×C₁₁₃	#125	1	2	yes	—
108	C₂²×C₁₁₃	#126	1	2	yes	—
109	C₂²×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
110	C₄×C₁₁₃	—	2	4	no	—
111	C₄×C₁₁₃	—	2	8	no	—
112	C₄×C₁₁₃	—	2	4	no	—
113	C₄×C₁₁₃	—	4	2	no	—
114	C₄×C₁₁₃	—	4	4	no	—
115	C₂×C₁₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₁₁₃	C₄×C₄⋊C₄	1	2	yes	—
117	C₂×C₁₁₃	#385	1	2	yes	—
118	C₂×C₁₁₃	#386	1	1	yes	characteristic
119	C₂×C₁₁₃	#387	1	2	yes	—
120	C₂×C₁₁₃	#387	1	2	yes	—
121	C₂×C₁₁₃	#388	1	2	yes	—
122	C₂×C₁₁₃	#389	1	2	yes	—
123	C₂×C₁₁₃	#391	1	1	yes	characteristic
124	#1436	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₁₃	#1436	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
127	C₂²×C₄²	C₂×C₁₁₃	1	1	yes	characteristic
128	C₂×#95	C₂×C₁₁₃	1	2	yes	—
129	C₂×#95	C₂×C₁₁₃	1	1	yes	characteristic
130	C₂×#95	C₂×C₁₁₃	1	2	yes	—
131	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
132	C₂³×C₄	C₂²×C₁₁₃	1	2	yes	—
133	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
134	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
135	C₂³×C₄	C₂²×C₁₁₃	1	2	yes	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	C₄×C₁₁₃	1	4	yes	complemented
139	C₂×C₄²	—	2	2	no	—
140	C₂×C₄²	—	2	4	no	—
141	#95	—	2	2	no	—
142	#95	—	2	4	no	—
143	#95	C₄×C₁₁₃	1	8	yes	complemented
144	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	2	1	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
165	C₂²×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
166	C₂²×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
167	C₂²×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
168	C₂²×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
169	C₂²×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
170	C₂²×C₄	D₄×C₁₁₃	1	2	yes	—
171	C₂²×C₄	D₄×C₁₁₃	1	2	yes	—
172	C₂²×C₄	D₄×C₁₁₃	1	4	yes	—
173	C₂²×C₄	Q₈×C₁₁₃	1	4	yes	—
174	C₄⋊C₄	—	2	8	no	—
175	C₄²	—	2	8	no	—
176	C₂³	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
177	C₂³	C₂²×C₄×C₁₁₃	1	2	yes	—
178	C₂³	C₂×D₄×C₁₁₃	1	1	yes	characteristic
179	C₂³	C₂×D₄×C₁₁₃	1	1	yes	characteristic
180	C₂³	C₂×D₄×C₁₁₃	1	2	yes	—
181	C₂³	C₂×Q₈×C₁₁₃	1	2	yes	—
182	C₂³	#41×C₁₁₃	1	2	yes	—
183	C₂³	#41×C₁₁₃	1	2	yes	—
184	C₂³	#41×C₁₁₃	1	2	yes	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₄²×C₁₁₃	1	4	yes	complemented
212	C₂×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
213	C₂×C₄	C₄⋊C₄×C₁₁₃	1	8	yes	complemented
214	C₂²	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
215	C₂²	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
216	C₂²	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
217	C₂²	#117×C₁₁₃	1	1	yes	characteristic
218	C₂²	#117×C₁₁₃	1	2	yes	—
219	C₂²	C₄×D₄×C₁₁₃	1	2	yes	—
220	C₂²	C₄×D₄×C₁₁₃	1	2	yes	—
221	C₂²	C₄×D₄×C₁₁₃	1	2	yes	—
222	C₂²	C₄×D₄×C₁₁₃	1	2	yes	—
223	C₂²	C₄×Q₈×C₁₁₃	1	2	yes	—
224	C₂²	C₄×Q₈×C₁₁₃	1	2	yes	—
225	C₂²	#120×C₁₁₃	1	1	yes	characteristic
226	C₂²	#121×C₁₁₃	1	2	yes	—
227	C₂²	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
228	C₂²	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
229	C₂²	#123×C₁₁₃	1	2	yes	—
230	C₂²	#123×C₁₁₃	1	1	yes	characteristic
231	C₂²	#124×C₁₁₃	1	1	yes	characteristic
232	C₂²	#125×C₁₁₃	1	2	yes	—
233	C₂²	#126×C₁₁₃	1	2	yes	—
234	C₂²	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
235	C₄	—	2	4	no	—
236	C₄	—	2	8	no	—
237	C₄	—	2	4	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	4	no	—
240	C₂	C₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
241	C₂	C₄×C₄⋊C₄×C₁₁₃	1	2	yes	—
242	C₂	#385×C₁₁₃	1	2	yes	—
243	C₂	#386×C₁₁₃	1	1	yes	characteristic
244	C₂	#387×C₁₁₃	1	2	yes	—
245	C₂	#387×C₁₁₃	1	2	yes	—
246	C₂	#388×C₁₁₃	1	2	yes	—
247	C₂	#389×C₁₁₃	1	2	yes	—
248	C₂	#391×C₁₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₂×C₄⋊C₄×C₁₁₃	C₄	semidirect
18. #95×C₁₁₃	C₄	semidirect
86. C₂×C₄×C₁₁₃	C₄²	semidirect
88. C₂×C₄×C₁₁₃	C₄⋊C₄	semidirect
124. #1436	C₁₁₃	direct (N × H)
125. C₁₁₃	#1436	direct (N × H)
138. C₂×C₄⋊C₄	C₄×C₁₁₃	semidirect
143. #95	C₄×C₁₁₃	semidirect
211. C₂×C₄	C₄²×C₁₁₃	semidirect
213. C₂×C₄	C₄⋊C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₄×C₁₁₃	2
C₂²×C₄²×C₁₁₃	2
C₂×#95×C₁₁₃	2
#1436	113

Subgroups — C113×#1436 #28386232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#1436 #28386232