Finite Group Databasebeta

← C₂×#16840619 #21461267

Subgroups — C₂×#16840619 #21461267

Order 7808.

232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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	C₂×#14519832	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519832	C₂	1	1	yes	maximal, characteristic
3	#16840619	C₂	1	4	yes	maximal, direct product factor
4	C₂×#14519768	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92420	—	2	1	no	—
6	C₂²×#92420	—	2	1	no	—
7	#14519832	—	2	1	no	—
8	#14519832	—	2	1	no	—
9	#14519832	C₂²	1	2	yes	—
10	#14519832	C₂²	1	2	yes	—
11	#14519768	—	2	1	no	—
12	#14519768	—	2	1	no	—
13	#14519768	C₄	1	2	yes	—
14	#14519768	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₆₁	—	2	1	no	—
16	C₂×C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
17	C₂×#11758196	—	2	1	no	—
18	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
20	C₂²×C₄×C₆₁	—	2	1	no	—
21	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×Dic₆₁	—	2	1	no	—
23	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
24	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
25	C₂×#92420	—	2	4	no	—
26	C₂×#92420	—	2	4	no	—
27	C₂×#92420	—	2	2	no	—
28	C₂×#92420	—	2	2	no	—
29	C₄⋊C₄×C₆₁	—	2	1	no	—
30	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
31	C₄⋊Dic₆₁	—	2	1	no	—
32	C₄⋊Dic₆₁	—	2	2	no	—
33	C₄⋊Dic₆₁	—	2	2	no	—
34	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
35	#11758196	—	2	2	no	—
36	#11758196	—	2	2	no	—
37	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
38	C₄×Dic₆₁	D₄	1	1	yes	characteristic
39	C₄×Dic₆₁	D₄	1	1	yes	characteristic
40	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
41	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	—	2	2	no	—
43	C₂×C₄×C₆₁	—	2	2	no	—
44	C₂×C₄×C₆₁	—	4	2	no	—
45	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₆₁	—	2	2	no	—
48	C₂×Dic₆₁	—	2	2	no	—
49	C₂×Dic₆₁	—	2	2	no	—
50	C₂×Dic₆₁	—	4	2	no	—
51	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
55	#92420	—	2	4	no	—
56	#92420	—	2	4	no	—
57	C₂²×C₆₁	#101	1	2	yes	—
58	C₂²×C₆₁	#104	1	2	yes	—
59	C₂²×C₆₁	#104	1	2	yes	—
60	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄×C₆₁	—	2	1	no	—
62	C₄×C₆₁	—	2	1	no	—
63	C₄×C₆₁	—	4	2	no	—
64	Dic₆₁	—	2	1	no	—
65	Dic₆₁	—	2	1	no	—
66	Dic₆₁	—	2	1	no	—
67	Dic₆₁	—	2	1	no	—
68	Dic₆₁	—	4	2	no	—
69	C₂×#330	—	61	1	no	maximal, Sylow
70	C₂×C₆₁	#330	1	4	yes	complemented
71	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
72	C₂×C₆₁	C₂×#104	1	1	yes	characteristic
73	C₂×C₆₁	C₂×#104	1	1	yes	characteristic
74	C₂×#125	—	61	1	no	—
75	C₂×#97	—	61	1	no	—
76	C₂×#97	—	61	1	no	—
77	#330	—	61	4	no	—
78	C₆₁	C₂×#330	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₈	—	122	1	no	—
80	C₂²×C₈	—	122	1	no	—
81	#125	—	61	2	no	—
82	#125	—	61	2	no	—
83	#125	—	122	1	no	—
84	#125	—	122	1	no	—
85	C₂×C₄⋊C₄	—	61	1	no	—
86	C₂×C₄⋊C₄	—	122	1	no	—
87	C₂×C₄⋊C₄	—	122	1	no	—
88	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
89	C₂×C₄²	—	61	1	no	—
90	#97	—	61	2	no	—
91	#97	—	61	2	no	—
92	#97	—	122	1	no	—
93	#97	—	122	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	61	1	no	—
96	C₂²×C₄	—	61	1	no	—
97	C₂²×C₄	—	122	1	no	—
98	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
99	C₂×C₈	—	122	2	no	—
100	C₂×C₈	—	122	2	no	—
101	C₂×C₈	—	122	4	no	—
102	C₂×C₈	—	122	4	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	61	2	no	—
105	C₄⋊C₄	—	122	2	no	—
106	C₄⋊C₄	—	122	2	no	—
107	C₄⋊C₄	—	122	2	no	—
108	C₄⋊C₄	—	122	2	no	—
109	C₄⋊C₄	—	122	1	no	—
110	C₄⋊C₄	C₂×#6923	1	2	yes	—
111	C₄²	—	61	1	no	—
112	C₄²	—	61	1	no	—
113	C₄²	—	61	1	no	—
114	C₄²	—	61	1	no	—
115	C₂³	C₂²⋊#6923	1	1	yes	characteristic
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	61	1	no	—
121	C₂×C₄	—	61	1	no	—
122	C₂×C₄	—	61	1	no	—
123	C₂×C₄	—	122	2	no	—
124	C₂×C₄	—	122	2	no	—
125	C₂×C₄	—	122	2	no	—
126	C₂×C₄	—	244	2	no	—
127	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
128	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
129	C₈	—	122	4	no	—
130	C₈	—	122	4	no	—
131	C₂²	#14519838	1	2	yes	—
132	C₂²	#14519841	1	2	yes	—
133	C₂²	#14519842	1	2	yes	—
134	C₂²	C₂×C₂²⋊#6923	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	2	1	no	—
137	C₄	—	4	2	no	—
138	C₄	—	122	1	no	—
139	C₄	—	122	1	no	—
140	C₄	—	122	1	no	—
141	C₄	—	122	1	no	—
142	C₄	—	244	2	no	—
143	C₂	#16840619	1	4	yes	direct product factor
144	C₂	C₂×#14519838	1	1	yes	characteristic
145	C₂	C₂×#14519841	1	1	yes	characteristic
146	C₂	C₂×#14519842	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	C₂×#330
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #16840619	C₂	direct (N × H)
70. C₂×C₆₁	#330	semidirect
78. C₆₁	C₂×#330	semidirect
143. C₂	#16840619	direct (N × H)