Subgroups — C₄×#11718767 #15860969

Order 3328.

1182 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×#11718767	C₂	1	2	yes	maximal
2	C₄×#88180	C₂	1	2	yes	maximal
3	C₄×#88058	C₂	1	4	yes	maximal, complemented
4	C₄×#88057	C₂	1	4	yes	maximal, complemented
5	#13114553	C₂	1	2	yes	maximal
6	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88180	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₄	1	8	yes	complemented
12	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
14	C₄×C₂²⋊Dic₁₃	—	2	4	no	—
15	#11718767	C₄	1	16	yes	direct product factor
16	C₂×#88058	C₂²	1	4	yes	—
17	C₂×#88057	C₂²	1	4	yes	—
18	C₄×C₄⋊Dic₁₃	C₂²	1	8	yes	—
19	#11718593	—	2	2	no	—
20	C₄²×Dic₁₃	—	2	2	no	—
21	#11718143	C₂²	1	8	yes	—
22	C₂³×C₄×C₁₃	D₄	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	—	2	4	no	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
36	C₂×C₂²⋊Dic₁₃	—	2	4	no	—
37	#88180	—	2	8	no	—
38	#88180	C₂×C₄	1	16	yes	—
39	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
40	C₂×C₄×Dic₁₃	—	2	4	no	—
41	C₂×C₄×Dic₁₃	—	2	8	no	—
42	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
43	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
44	#88071	—	2	8	no	—
45	#88058	C₂×C₄	1	16	yes	complemented
46	#88057	C₂×C₄	1	16	yes	complemented
47	C₄×#427	—	13	1	no	maximal, Sylow
48	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	—	2	8	no	—
50	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
57	C₂²×C₄×C₁₃	#41	1	4	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
59	C₂²×Dic₁₃	—	2	8	no	—
60	C₂×C₈×C₁₃	—	2	8	no	—
61	C₂×C₈×C₁₃	—	2	4	no	—
62	C₂×C₈×C₁₃	C₄²	1	16	yes	complemented
63	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
64	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
69	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
70	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
71	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
72	C₂²⋊Dic₁₃	—	2	16	no	—
73	C₄⋊Dic₁₃	—	2	8	no	—
74	C₄⋊Dic₁₃	C₂²×C₄	1	16	yes	—
75	C₄×Dic₁₃	—	2	16	no	—
76	C₄×Dic₁₃	—	4	16	no	—
77	C₂×#427	—	13	2	no	—
78	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
79	C₄×#117	—	13	2	no	—
80	C₄×#107	—	13	4	no	—
81	C₄×#106	—	13	4	no	—
82	#1735	—	13	2	no	—
83	C₂³×C₁₃	—	2	4	no	—
84	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
85	C₂³×C₁₃	C₄×D₄	1	4	yes	—
86	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	—	2	4	no	—
88	C₂×C₄×C₁₃	—	2	16	no	—
89	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
93	C₂×C₄×C₁₃	#117	1	4	yes	—
94	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
95	C₂×C₄×C₁₃	C₄×Q₈	1	8	yes	—
96	C₂×C₄×C₁₃	#135	1	8	yes	—
97	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
99	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
101	C₂×Dic₁₃	—	2	16	no	—
102	C₂×Dic₁₃	—	4	16	no	—
103	C₈×C₁₃	—	2	4	no	—
104	C₈×C₁₃	C₂×C₄²	1	4	yes	—
105	C₈×C₁₃	C₂×C₄²	1	4	yes	—
106	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
107	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
108	C₂×#117	—	13	4	no	—
109	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
110	#427	—	13	16	no	—
111	C₂×#107	—	13	4	no	—
112	C₂×#106	—	13	4	no	—
113	C₂×C₄×C₈	Dic₁₃	1	8	yes	complemented
114	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
115	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
116	C₄×C₄⋊C₄	—	13	8	no	—
117	C₄×C₂²⋊C₄	—	26	4	no	—
118	#376	—	26	2	no	—
119	C₄³	—	26	2	no	—
120	#340	—	13	8	no	—
121	C₂²×C₁₃	—	2	4	no	—
122	C₂²×C₁₃	—	2	8	no	—
123	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
124	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
126	C₂²×C₁₃	C₂×#135	1	4	yes	—
127	C₄×C₁₃	—	2	4	no	—
128	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
129	C₄×C₁₃	#427	1	8	yes	complemented
130	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
131	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
132	C₄×C₁₃	C₂×C₄×Q₈	1	2	yes	—
133	Dic₁₃	—	4	16	no	—
134	C₂³×C₄	D₅₂	1	2	yes	—
135	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
136	C₂²×C₈	—	2	4	no	—
137	C₂²×C₈	C₄×D₁₃	1	8	yes	—
138	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
139	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
140	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
141	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
143	#117	—	13	16	no	—
144	#117	—	26	8	no	—
145	C₂×C₄⋊C₄	—	13	8	no	—
146	C₂×C₂²⋊C₄	—	26	4	no	—
147	C₂×C₄²	—	26	4	no	—
148	C₂×C₄²	—	26	8	no	—
149	C₂×C₄²	Dic₂₆	1	4	yes	—
150	C₂×C₄²	D₅₂	1	1	yes	characteristic
151	C₂×C₄²	D₅₂	1	1	yes	characteristic
152	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
153	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
154	#107	—	13	16	no	—
155	#106	—	13	16	no	—
156	C₄×C₈	C₂×Dic₁₃	1	8	yes	—
157	C₄×C₈	C₂×Dic₁₃	1	8	yes	—
158	#95	—	26	8	no	—
159	C₂×C₁₃	—	2	4	no	—
160	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₁₃	C₂×#427	1	2	yes	—
162	C₂×C₁₃	C₄×#135	1	4	yes	—
163	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
164	C₂²×C₄	—	2	8	no	—
165	C₂²×C₄	—	26	8	no	—
166	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
167	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
168	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
169	C₂²×C₄	C₂×D₅₂	1	2	yes	—
170	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
171	C₂²×C₄	C₂×D₅₂	1	2	yes	—
172	C₂²×C₄	#6127	1	4	yes	—
173	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
174	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
175	C₂×C₈	—	2	8	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	C₄×Dic₁₃	1	16	yes	complemented
178	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
179	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
180	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
181	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
182	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
183	C₄⋊C₄	—	13	16	no	—
184	C₄⋊C₄	—	26	8	no	—
185	C₂²⋊C₄	—	26	16	no	—
186	C₄²	—	26	16	no	—
187	C₄²	—	52	16	no	—
188	C₄²	C₄⋊Dic₁₃	1	4	yes	—
189	C₄²	C₄⋊Dic₁₃	1	4	yes	—
190	C₄²	C₂×Dic₂₆	1	4	yes	—
191	C₄²	C₂²×Dic₁₃	1	4	yes	—
192	C₁₃	C₄×#427	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	2	4	no	—
194	C₂³	C₄×D₅₂	1	4	yes	—
195	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
196	C₂³	C₂²×D₅₂	1	1	yes	characteristic
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	16	no	—
199	C₂×C₄	—	26	16	no	—
200	C₂×C₄	—	52	16	no	—
201	C₂×C₄	C₄×Dic₂₆	1	8	yes	—
202	C₂×C₄	C₄×D₅₂	1	4	yes	—
203	C₂×C₄	#88158	1	8	yes	—
204	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
205	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
206	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
207	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
208	C₂×C₄	#88180	1	4	yes	—
209	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
211	C₂×C₄	C₂×#6127	1	2	yes	—
212	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
213	C₈	—	2	4	no	—
214	C₈	C₂×C₄×Dic₁₃	1	4	yes	—
215	C₈	C₂×C₄×Dic₁₃	1	4	yes	—
216	C₂²	—	2	8	no	—
217	C₂²	—	2	4	no	—
218	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
219	C₂²	C₂×C₄×D₅₂	1	2	yes	—
220	C₂²	C₂×#88158	1	4	yes	—
221	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
222	C₄	—	2	4	no	—
223	C₄	—	52	16	no	—
224	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
225	C₄	#11718767	1	8	yes	direct product factor
226	C₄	C₂×C₄×Dic₂₆	1	2	yes	—
227	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
228	C₄	C₂×#88180	1	1	yes	characteristic
229	C₂	—	2	4	no	—
230	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
231	C₂	C₂×#11718767	1	2	yes	—
232	C₂	C₄×#88158	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	C₄×#427
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#88058	C₂	semidirect
4. C₄×#88057	C₂	semidirect
11. C₂×C₄×C₈×C₁₃	C₄	semidirect
15. #11718767	C₄	direct (N × H)
45. #88058	C₂×C₄	semidirect
46. #88057	C₂×C₄	semidirect
62. C₂×C₈×C₁₃	C₄²	semidirect
113. C₂×C₄×C₈	Dic₁₃	semidirect
129. C₄×C₁₃	#427	semidirect
177. C₂×C₈	C₄×Dic₁₃	semidirect
192. C₁₃	C₄×#427	semidirect
225. C₄	#11718767	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×#11718767	2
C₄×#88180	2
C₄×#88058	2
C₄×#88057	2
#13114553	2
C₂²×C₄×C₈×C₁₃	2
C₄×#427	13

Subgroups — C4×#11718767 #15860969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718767 #15860969