Subgroups — C₄×#10622130 #14668985

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622130	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#13066707	C₂	1	2	yes	maximal
5	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₄	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₂₂	—	2	1	no	—
8	C₂×C₁₁×#107	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
11	C₂×#66882	C₂²	1	1	yes	characteristic
12	C₂×#66880	—	2	1	no	—
13	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
14	C₄×Dic₄₄	—	2	2	no	—
15	C₄×Dic₄₄	C₄	1	4	yes	complemented
16	C₁₁×#340	—	2	1	no	—
17	#10622130	C₄	1	8	yes	direct product factor
18	C₄×C₁₁⋊C₁₆	—	2	2	no	—
19	C₂²×Dic₂₂	—	2	1	no	—
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄²×C₁₁	—	4	1	no	—
24	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₁	—	2	1	no	—
26	C₂×Dic₁₁⋊C₄	—	4	1	no	—
27	C₂×C₄×Dic₁₁	—	4	1	no	—
28	C₂×Dic₄₄	—	2	1	no	—
29	C₂×Dic₄₄	—	2	2	no	—
30	C₂×Dic₄₄	C₂×C₄	1	2	yes	—
31	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
32	C₄×Dic₂₂	—	2	4	no	—
33	C₄×Dic₂₂	—	4	2	no	—
34	C₁₁×#107	—	2	2	no	—
35	C₁₁×#107	C₂×C₄	1	4	yes	—
36	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₁	D₄	1	2	yes	—
38	C₁₁×#95	—	4	1	no	—
39	#66882	—	2	1	no	—
40	#66882	C₂×C₄	1	2	yes	—
41	#66880	—	2	4	no	—
42	C₂×C₁₁⋊C₁₆	—	2	2	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
45	C₄×#358	—	11	1	no	maximal, Sylow
46	C₂²×C₄×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₁	—	4	1	no	—
51	C₂²×Dic₁₁	—	4	1	no	—
52	C₂×Dic₂₂	—	2	2	no	—
53	C₂×Dic₂₂	—	2	4	no	—
54	C₂×Dic₂₂	—	4	1	no	—
55	C₂×Dic₂₂	—	4	2	no	—
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	#41	1	2	yes	—
62	C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₄²×C₁₁	—	8	2	no	—
65	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₁₁	SD₁₆	1	2	yes	—
67	C₄⋊Dic₁₁	—	2	2	no	—
68	C₄⋊Dic₁₁	—	4	1	no	—
69	Dic₁₁⋊C₄	—	4	4	no	—
70	C₄×Dic₁₁	—	4	4	no	—
71	Dic₄₄	—	2	2	no	—
72	Dic₄₄	—	2	4	no	—
73	Dic₄₄	C₄²	1	4	yes	complemented
74	C₁₁⋊C₁₆	—	2	4	no	—
75	C₂×C₄×Q₁₆	—	11	1	no	—
76	C₂×#358	—	11	2	no	—
77	C₂×C₄×C₁₆	—	11	1	no	—
78	C₄×#107	D₁₁	1	1	yes	characteristic
79	#1380	—	11	2	no	—
80	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	4	4	no	—
83	C₂×C₄×C₁₁	—	8	2	no	—
84	C₂×C₄×C₁₁	—	8	2	no	—
85	C₂×C₄×C₁₁	#102	1	2	yes	—
86	C₂×C₄×C₁₁	#102	1	2	yes	—
87	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
88	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
89	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#135	1	2	yes	—
93	C₂×Dic₁₁	—	4	2	no	—
94	C₂×Dic₁₁	—	4	4	no	—
95	C₂×Dic₁₁	—	4	2	no	—
96	C₂×Dic₁₁	—	8	2	no	—
97	Dic₂₂	—	2	4	no	—
98	Dic₂₂	—	4	2	no	—
99	Dic₂₂	—	4	4	no	—
100	C₈×C₁₁	—	2	2	no	—
101	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
102	C₈×C₁₁	#117	1	1	yes	characteristic
103	C₈×C₁₁	C₄×D₄	1	2	yes	—
104	C₂²×Q₁₆	—	11	1	no	—
105	C₂×C₄×Q₈	—	22	1	no	—
106	C₂²×C₁₆	—	11	2	no	—
107	C₄×Q₁₆	—	11	4	no	—
108	C₄×Q₁₆	—	22	2	no	—
109	C₂×#107	—	11	1	no	—
110	C₂×#107	C₂×D₁₁	1	2	yes	—
111	C₂×#103	—	22	1	no	—
112	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
113	C₄×C₄⋊C₄	—	2	1	no	—
114	#358	—	11	8	no	—
115	C₄×C₁₆	—	22	2	no	—
116	#340	—	2	1	no	—
117	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
118	C₂²×C₁₁	C₄×D₈	1	2	yes	—
119	C₂²×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
120	C₂²×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
121	C₂²×C₁₁	#508	1	2	yes	—
122	C₄×C₁₁	—	2	2	no	—
123	C₄×C₁₁	—	8	4	no	—
124	C₄×C₁₁	#358	1	4	yes	complemented
125	C₄×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
126	C₄×C₁₁	#416	1	1	yes	characteristic
127	C₄×C₁₁	C₄×SD₁₆	1	2	yes	—
128	Dic₁₁	—	4	4	no	—
129	Dic₁₁	—	8	2	no	—
130	C₂²×Q₈	—	22	1	no	—
131	C₂×Q₁₆	—	11	4	no	—
132	C₂×Q₁₆	—	11	2	no	—
133	C₂×Q₁₆	—	22	1	no	—
134	C₂×Q₁₆	—	22	2	no	—
135	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
136	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
137	C₄×Q₈	—	22	4	no	—
138	C₄×Q₈	—	44	2	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	22	1	no	—
141	C₂×C₄⋊C₄	—	44	1	no	—
142	C₂×C₄²	—	4	1	no	—
143	C₂×C₄²	—	44	1	no	—
144	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
145	C₂×C₁₆	—	11	4	no	—
146	C₂×C₁₆	—	22	2	no	—
147	C₂×C₁₆	—	22	2	no	—
148	#107	—	2	2	no	—
149	#107	—	11	2	no	—
150	#107	—	22	1	no	—
151	#107	C₄×D₁₁	1	4	yes	—
152	#103	—	22	4	no	—
153	C₄×C₈	C₄×D₁₁	1	2	yes	—
154	C₄×C₈	D₄₄	1	2	yes	—
155	#95	—	4	1	no	—
156	C₂×C₁₁	C₄×#102	1	1	yes	characteristic
157	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
158	C₂×C₁₁	#2138	1	1	yes	characteristic
159	C₂×C₁₁	C₄×SD₃₂	1	2	yes	—
160	C₂×C₁₁	C₄×Q₃₂	1	2	yes	—
161	C₂×Q₈	—	22	2	no	—
162	C₂×Q₈	—	22	4	no	—
163	C₂×Q₈	—	44	1	no	—
164	C₂×Q₈	—	44	2	no	—
165	C₂²×C₄	—	4	2	no	—
166	C₂²×C₄	—	44	1	no	—
167	C₂²×C₄	—	44	1	no	—
168	C₂²×C₄	#4323	1	1	yes	characteristic
169	C₂²×C₄	#4323	1	1	yes	characteristic
170	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
171	Q₁₆	—	11	4	no	—
172	Q₁₆	—	22	2	no	—
173	Q₁₆	—	22	4	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
176	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
177	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
178	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
179	C₂×C₈	#4339	1	2	yes	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	22	2	no	—
183	C₄⋊C₄	—	44	4	no	—
184	C₄⋊C₄	—	44	1	no	—
185	C₄²	—	8	2	no	—
186	C₄²	—	44	4	no	—
187	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
188	C₄²	#4325	1	2	yes	—
189	C₁₆	—	22	4	no	—
190	C₁₁	C₄×#358	1	1	yes	characteristic, complemented, Sylow
191	C₂³	C₂×#4323	1	1	yes	characteristic
192	Q₈	—	22	4	no	—
193	Q₈	—	44	2	no	—
194	Q₈	—	44	4	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	44	2	no	—
200	C₂×C₄	—	44	4	no	—
201	C₂×C₄	—	44	2	no	—
202	C₂×C₄	—	88	2	no	—
203	C₂×C₄	#66873	1	2	yes	—
204	C₂×C₄	#66873	1	2	yes	—
205	C₂×C₄	#66891	1	2	yes	—
206	C₂×C₄	#66893	1	2	yes	—
207	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
208	C₂×C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
209	C₂×C₄	C₂×#4325	1	1	yes	characteristic
210	C₂×C₄	#67003	1	2	yes	—
211	C₈	—	2	2	no	—
212	C₈	C₄²×D₁₁	1	1	yes	characteristic
213	C₈	#66925	1	1	yes	characteristic
214	C₈	C₄×D₄₄	1	2	yes	—
215	C₂²	C₂×#66873	1	1	yes	characteristic
216	C₂²	C₄×#4323	1	2	yes	—
217	C₂²	C₂×#66891	1	1	yes	characteristic
218	C₂²	C₂×#66893	1	1	yes	characteristic
219	C₂²	#10622807	1	2	yes	—
220	C₄	—	2	2	no	—
221	C₄	—	8	4	no	—
222	C₄	—	44	4	no	—
223	C₄	—	88	2	no	—
224	C₄	#10622130	1	4	yes	direct product factor
225	C₄	C₄×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
226	C₄	#10622615	1	1	yes	characteristic
227	C₄	C₄×#4325	1	2	yes	—
228	C₂	C₄×#66873	1	1	yes	characteristic
229	C₂	C₂×#10622130	1	1	yes	characteristic
230	C₂	#13070321	1	1	yes	characteristic
231	C₂	C₄×#66891	1	2	yes	—
232	C₂	C₄×#66893	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#4323
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×#107	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄×#107	D₁₁
hypocenter	C₁₁	C₄×#358
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
15. C₄×Dic₄₄	C₄	semidirect
17. #10622130	C₄	direct (N × H)
73. Dic₄₄	C₄²	semidirect
124. C₄×C₁₁	#358	semidirect
190. C₁₁	C₄×#358	semidirect
224. C₄	#10622130	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×C₄×Dic₄₄	2
C₂×#10622130	2
C₂×C₄×C₁₁⋊C₁₆	2
#13066707	2
C₄×C₁₁×#107	2
C₄×#358	11

Subgroups — C4×#10622130 #14668985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10622130 #14668985