Subgroups — #15774514

Order 3328.

220 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	1	yes	maximal, characteristic
2	C₄×#88052	C₂	1	1	yes	maximal, characteristic
3	#13112911	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	—	2	1	no	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88052	—	2	1	no	—
8	C₂×#88052	C₄	1	1	yes	characteristic
9	C₂×#88052	C₄	1	1	yes	characteristic
10	C₁₃×#364	—	2	1	no	—
11	C₁₃×#364	C₂²	1	2	yes	—
12	#11718055	—	2	1	no	—
13	#11718055	C₂²	1	2	yes	—
14	#11718053	C₄	1	2	yes	—
15	C₄×#6090	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
19	C₁₃×M₃₂	—	2	2	no	—
20	C₁₃×M₃₂	—	4	1	no	—
21	C₂×C₁₃×C₁₆	—	4	1	no	—
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	#88052	—	2	1	no	—
27	#88052	—	2	1	no	—
28	#88052	—	2	2	no	—
29	#88052	—	4	1	no	—
30	#88052	C₈	1	2	yes	—
31	#88052	C₈	1	2	yes	—
32	C₂×#6090	—	4	1	no	—
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	C₂×#6090	C₂×C₄	1	2	yes	—
35	#12011	—	13	1	no	maximal, Sylow
36	C₂²×C₄×C₁₃	—	2	1	no	—
37	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
45	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₃	—	2	1	no	—
51	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₁₃×C₁₆	—	4	2	no	—
54	#6090	—	2	2	no	—
55	#6090	—	4	2	no	—
56	#6090	C₂×C₈	1	4	yes	—
57	C₂×#364	—	13	1	no	—
58	C₂×#364	D₁₃	1	1	yes	characteristic
59	C₄×M₃₂	—	13	1	no	—
60	#1373	—	13	4	no	—
61	C₂³×C₁₃	#108	1	1	yes	characteristic
62	C₂×C₄×C₁₃	—	2	1	no	—
63	C₂×C₄×C₁₃	—	2	1	no	—
64	C₂×C₄×C₁₃	—	4	2	no	—
65	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#108	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
72	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
73	C₈×C₁₃	#107	1	1	yes	characteristic
74	C₈×C₁₃	#107	1	1	yes	characteristic
75	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
76	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
78	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
79	C₂×M₃₂	—	2	1	no	—
80	C₂×M₃₂	—	13	1	no	—
81	C₂×M₃₂	—	13	1	no	—
82	C₂×M₃₂	—	26	1	no	—
83	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
84	#364	—	2	1	no	—
85	#364	—	13	2	no	—
86	#364	—	26	1	no	—
87	#364	C₂×D₁₃	1	2	yes	—
88	#346	—	13	2	no	—
89	C₄×C₁₆	—	13	2	no	—
90	C₂²×C₁₃	—	4	1	no	—
91	C₂²×C₁₃	#335	1	1	yes	characteristic
92	C₂²×C₁₃	#335	1	1	yes	characteristic
93	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
94	C₄×C₁₃	—	2	2	no	—
95	C₄×C₁₃	—	4	1	no	—
96	C₄×C₁₃	#335	1	1	yes	characteristic
97	C₄×C₁₃	#335	1	1	yes	characteristic
98	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
99	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
100	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
101	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
102	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
103	M₃₂	—	2	2	no	—
104	M₃₂	—	4	1	no	—
105	M₃₂	—	13	2	no	—
106	M₃₂	—	13	2	no	—
107	M₃₂	—	26	1	no	—
108	M₃₂	—	26	1	no	—
109	M₃₂	—	26	2	no	—
110	M₃₂	—	52	1	no	—
111	C₂×C₁₆	—	4	1	no	—
112	C₂×C₁₆	—	13	2	no	—
113	C₂×C₁₆	—	13	2	no	—
114	C₂×C₁₆	—	52	1	no	—
115	C₄×C₈	Dic₂₆	1	1	yes	characteristic
116	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
117	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
118	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
119	C₂×C₁₃	—	2	1	no	—
120	C₂×C₁₃	—	2	1	no	—
121	C₂×C₁₃	—	2	1	no	—
122	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	#6101	1	1	yes	characteristic
125	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
126	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
127	C₂×C₈	#6094	1	1	yes	characteristic
128	C₂×C₈	#6094	1	1	yes	characteristic
129	C₂×C₈	#6101	1	1	yes	characteristic
130	C₂×C₈	#6101	1	1	yes	characteristic
131	C₂×C₈	#6104	1	1	yes	characteristic
132	C₂×C₈	#6104	1	1	yes	characteristic
133	C₂×C₈	#6107	1	1	yes	characteristic
134	C₂×C₈	#6107	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
136	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
137	C₄²	—	2	1	no	—
138	C₄²	#6101	1	1	yes	characteristic
139	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
140	C₁₆	—	4	2	no	—
141	C₁₆	—	13	4	no	—
142	C₁₆	—	26	2	no	—
143	C₁₆	—	52	2	no	—
144	C₁₃	#12011	1	1	yes	characteristic, complemented, Sylow
145	C₂³	#88062	1	1	yes	characteristic
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	#88047	1	1	yes	characteristic
150	C₂×C₄	#88047	1	1	yes	characteristic
151	C₂×C₄	#88054	1	1	yes	characteristic
152	C₂×C₄	#88054	1	1	yes	characteristic
153	C₂×C₄	#88062	1	1	yes	characteristic
154	C₂×C₄	C₂×#6101	1	1	yes	characteristic
155	C₈	#88047	1	1	yes	characteristic
156	C₈	#88047	1	1	yes	characteristic
157	C₈	#88054	1	1	yes	characteristic
158	C₈	#88054	1	1	yes	characteristic
159	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
160	C₈	C₂×#6094	1	1	yes	characteristic
161	C₈	C₂×#6104	1	1	yes	characteristic
162	C₈	C₂×#6107	1	1	yes	characteristic
163	C₂²	—	4	1	no	—
164	C₂²	#11718071	1	1	yes	characteristic
165	C₂²	#11718071	1	1	yes	characteristic
166	C₂²	C₂×#88062	1	1	yes	characteristic
167	C₄	—	2	2	no	—
168	C₄	—	4	1	no	—
169	C₄	#11718071	1	1	yes	characteristic
170	C₄	#11718071	1	1	yes	characteristic
171	C₄	C₂×#88047	1	1	yes	characteristic
172	C₄	C₂×#88054	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	—	2	1	no	—
176	C₂	C₂×#11718071	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#6104
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂×C₁₃	C₂×#335
prime radical	C₂³×C₁₃	#108
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	#12011
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
3. #13112911	C₂	semidirect
144. C₁₃	#12011	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
C₄×#88052	2
#13112911	2
C₂×C₁₃×#364	2
#12011	13