Finite Group Databasebeta

Subgroups — #21461393

Order 7808.

160 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840784	C₂	1	1	yes	maximal, characteristic
2	D₆₁⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#16840626	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840625	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840624	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840623	C₂	1	1	yes	maximal, characteristic, complemented
7	#16839814	C₂	1	1	yes	maximal, characteristic
8	C₂×D₆₁⋊C₈	—	2	1	no	—
9	#14519844	—	2	1	no	—
10	C₄⋊#92420	C₂²	1	1	yes	characteristic
11	C₄⋊#92420	C₂²	1	1	yes	characteristic
12	C₄⋊#92420	C₂²	1	1	yes	characteristic
13	C₄⋊#92420	C₂²	1	1	yes	characteristic
14	#14519834	—	2	1	no	—
15	#14519832	—	2	1	no	—
16	C₄²×D₆₁	C₂²	1	1	yes	characteristic
17	C₄⋊#92418	C₄	1	1	yes	characteristic
18	#14519689	C₄	1	1	yes	characteristic
19	#14519689	C₄	1	1	yes	characteristic
20	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
21	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
23	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
25	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
26	C₂×#92420	—	2	1	no	—
27	C₂×#92420	—	2	1	no	—
28	C₂×#92420	—	2	1	no	—
29	C₂×#92420	—	2	1	no	—
30	D₆₁⋊C₈	—	4	2	no	—
31	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₆₁	D₄	1	1	yes	characteristic
35	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
36	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
37	C₂×#92418	C₂×C₄	1	1	yes	characteristic
38	C₂×#92418	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₆₁	—	2	2	no	—
47	C₄×D₆₁	—	2	1	no	—
48	C₄×D₆₁	—	2	1	no	—
49	C₄×D₆₁	—	2	1	no	—
50	C₄×D₆₁	—	2	1	no	—
51	#92420	—	4	1	no	—
52	#92420	—	4	1	no	—
53	#92420	—	4	1	no	—
54	#92420	—	4	1	no	—
55	C₈×C₆₁	—	2	1	no	—
56	C₈×C₆₁	—	2	1	no	—
57	#92418	—	2	1	no	—
58	#92418	—	2	1	no	—
59	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂×D₆₁	—	2	1	no	—
61	C₂×D₆₁	—	2	1	no	—
62	C₂×D₆₁	#108	1	2	yes	—
63	C₄×C₆₁	—	2	1	no	—
64	C₄×C₆₁	—	2	1	no	—
65	C₄×C₆₁	#131	1	1	yes	characteristic
66	C₄×C₆₁	#131	1	1	yes	characteristic
67	Dic₆₁	—	2	1	no	—
68	Dic₆₁	—	2	1	no	—
69	Dic₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
70	Dic₆₁	#137	1	1	yes	characteristic
71	#1573	—	61	1	no	maximal, Sylow
72	C₂×C₆₁	#424	1	1	yes	characteristic
73	C₂×C₆₁	#428	1	1	yes	characteristic
74	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
75	D₆₁	—	2	2	no	—
76	#432	—	61	1	no	—
77	#431	—	61	1	no	—
78	C₂×C₄⋊C₈	—	61	1	no	—
79	#335	—	61	1	no	—
80	#335	—	61	1	no	—
81	#334	—	61	1	no	—
82	#334	—	61	1	no	—
83	C₆₁	#1573	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₈	—	122	1	no	—
85	C₂×C₄²	—	61	1	no	—
86	C₄⋊C₈	—	61	1	no	—
87	C₄⋊C₈	—	61	1	no	—
88	C₄⋊C₈	—	61	1	no	—
89	C₄⋊C₈	—	61	1	no	—
90	C₄⋊C₈	—	61	1	no	—
91	C₄⋊C₈	—	122	1	no	—
92	C₄⋊C₈	#6923	1	1	yes	characteristic
93	C₂²⋊C₈	—	61	1	no	—
94	C₂²⋊C₈	—	61	1	no	—
95	C₂²⋊C₈	—	122	1	no	—
96	#97	—	122	1	no	—
97	C₄×C₈	—	61	1	no	—
98	C₄×C₈	—	61	1	no	—
99	C₂²×C₄	—	61	1	no	—
100	C₂²×C₄	—	61	1	no	—
101	C₂²×C₄	—	61	1	no	—
102	C₂×C₈	—	61	1	no	—
103	C₂×C₈	—	61	1	no	—
104	C₂×C₈	—	122	1	no	—
105	C₂×C₈	—	122	1	no	—
106	C₂×C₈	—	122	1	no	—
107	C₂×C₈	—	122	1	no	—
108	C₂×C₈	—	244	2	no	—
109	C₂×C₈	C₂×#6923	1	1	yes	characteristic
110	C₂×C₈	C₂×#6923	1	1	yes	characteristic
111	C₄²	—	61	1	no	—
112	C₄²	—	61	1	no	—
113	C₄²	—	61	1	no	—
114	C₄²	C₂×#6923	1	1	yes	characteristic
115	C₂³	—	61	1	no	—
116	C₂×C₄	—	61	1	no	—
117	C₂×C₄	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	122	1	no	—
120	C₂×C₄	—	122	1	no	—
121	C₂×C₄	—	122	2	no	—
122	C₂×C₄	—	122	1	no	—
123	C₂×C₄	—	122	1	no	—
124	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
125	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
126	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
127	C₈	—	2	1	no	—
128	C₈	—	2	1	no	—
129	C₈	—	122	1	no	—
130	C₈	—	122	1	no	—
131	C₈	—	244	1	no	—
132	C₈	—	244	1	no	—
133	C₈	—	244	1	no	—
134	C₈	—	244	1	no	—
135	C₂²	—	61	2	no	—
136	C₂²	—	122	1	no	—
137	C₂²	—	122	1	no	—
138	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	2	1	no	—
141	C₄	—	61	1	no	—
142	C₄	—	61	1	no	—
143	C₄	—	122	1	no	—
144	C₄	—	122	1	no	—
145	C₄	#14519864	1	1	yes	characteristic
146	C₄	#14519865	1	1	yes	characteristic
147	C₂	—	122	2	no	—
148	C₂	#16840769	1	1	yes	characteristic
149	C₂	#16840773	1	1	yes	characteristic
150	C₂	D₆₁⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1573
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #16840626	C₂	semidirect
4. #16840625	C₂	semidirect
5. #16840624	C₂	semidirect
6. #16840623	C₂	semidirect
83. C₆₁	#1573	semidirect