Finite Group Databasebeta

← C61×#17301 #29520734

Subgroups — C61×#17301 #29520734

Order 15616.

926 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#1443C215yesmaximal
2C61×#1442C215yesmaximal
3C61×#1441C215yesmaximal
4C22×C4⋊C4×C61C2215yes—
5C2×#95×C61C2215yes—
6C2×#95×C61C2215yes—
7C2×#95×C61C2215yes—
8C2×#95×C61C2215yes—
9C2×#95×C61C2215yes—
10C2×#95×C61C2215yes—
11C23×C4×C61C2315yes—
12C23×C4×C61C2315yes—
13C23×C4×C61C2315yes—
14C2×C4⋊C4×C61—210no—
15C2×C4⋊C4×C61—45no—
16C2×C4⋊C4×C61—45no—
17#95×C61—210no—
18#95×C61—210no—
19#95×C61—45no—
20#95×C61—45no—
21#95×C61—45no—
22#95×C61—45no—
23C24×C61C2411yescharacteristic
24C22×C4×C61—25no—
25C22×C4×C61—25no—
26C22×C4×C61—25no—
27C22×C4×C61—25no—
28C22×C4×C61—25no—
29C22×C4×C61—25no—
30C22×C4×C61—25no—
31C22×C4×C61—25no—
32C22×C4×C61—25no—
33C22×C4×C61—25no—
34C22×C4×C61—25no—
35C22×C4×C61—25no—
36C22×C4×C61—25no—
37C22×C4×C61—25no—
38C22×C4×C61—25no—
39C22×C4×C61—25no—
40C22×C4×C61—25no—
41C22×C4×C61—25no—
42C22×C4×C61—25no—
43C22×C4×C61—25no—
44C22×C4×C61#41110yes—
45C4⋊C4×C61—420no—
46C23×C61C2×#4115yes—
47C23×C61H(5,𝔽2)15yes—
48C23×C612−1+415yes—
49C2×C4×C61—210no—
50C2×C4×C61—210no—
51C2×C4×C61—210no—
52C2×C4×C61—45no—
53C2×C4×C61—45no—
54C2×C4×C61—45no—
55C2×C4×C61—45no—
56C2×C4×C61—45no—
57C2×C4×C61—45no—
58C2×C4×C61—45no—
59C2×C4×C61—45no—
60C2×C4×C61—45no—
61C2×C4×C61—45no—
62C2×C4×C61—45no—
63C2×C4×C61—45no—
64C2×C4×C61—45no—
65C2×C4×C61—45no—
66C2×C4×C61—45no—
67C2×C4×C61—45no—
68C2×C4×C61—45no—
69C2×C4×C61—45no—
70#17301C6111yesmaximal, characteristic, direct product factor, Sylow
71C22×C61#53815yes—
72C22×C61#54115yes—
73C22×C61#54215yes—
74C22×C61#55215yes—
75C22×C61#55315yes—
76C22×C61#56215yes—
77C22×C61#56315yes—
78C4×C61—410no—
79C4×C61—85no—
80C4×C61—85no—
81#1443C2×C6115yes—
82#1442C2×C6115yes—
83#1441C2×C6115yes—
84C2×C61#276615yes—
85C2×C61#277915yes—
86C2×C61#283115yes—
87C22×C4⋊C4C22×C6115yes—
88C2×#95C22×C6115yes—
89C2×#95C22×C6115yes—
90C2×#95C22×C6115yes—
91C2×#95C22×C6115yes—
92C2×#95C22×C6115yes—
93C2×#95C22×C6115yes—
94C61#1730111yescharacteristic, direct product factor, Sylow
95C23×C4C23×C6115yes—
96C23×C4C23×C6115yes—
97C23×C4C23×C6115yes—
98C2×C4⋊C4—210no—
99C2×C4⋊C4—45no—
100C2×C4⋊C4—45no—
101#95—210no—
102#95—210no—
103#95—45no—
104#95—45no—
105#95—45no—
106#95—45no—
107C24C24×C6111yescharacteristic
108C22×C4—25no—
109C22×C4—25no—
110C22×C4—25no—
111C22×C4—25no—
112C22×C4—25no—
113C22×C4—25no—
114C22×C4—25no—
115C22×C4—25no—
116C22×C4—25no—
117C22×C4—25no—
118C22×C4—25no—
119C22×C4—25no—
120C22×C4—25no—
121C22×C4—25no—
122C22×C4—25no—
123C22×C4—25no—
124C22×C4—25no—
125C22×C4—25no—
126C22×C4—25no—
127C22×C4—25no—
128C22×C4#41×C61110yes—
129C4⋊C4—420no—
130C23C2×#41×C6115yes—
131C23H(5,𝔽2)×C6115yes—
132C232−1+4×C6115yes—
133C2×C4—210no—
134C2×C4—210no—
135C2×C4—210no—
136C2×C4—45no—
137C2×C4—45no—
138C2×C4—45no—
139C2×C4—45no—
140C2×C4—45no—
141C2×C4—45no—
142C2×C4—45no—
143C2×C4—45no—
144C2×C4—45no—
145C2×C4—45no—
146C2×C4—45no—
147C2×C4—45no—
148C2×C4—45no—
149C2×C4—45no—
150C2×C4—45no—
151C2×C4—45no—
152C2×C4—45no—
153C2×C4—45no—
154C22C61×#53815yes—
155C22C61×#54115yes—
156C22C61×#54215yes—
157C22C61×#55215yes—
158C22C61×#55315yes—
159C22C61×#56215yes—
160C22C61×#56315yes—
161C4—410no—
162C4—85no—
163C4—85no—
164C2C61×#276615yes—
165C2C61×#277915yes—
166C2C61×#283115yes—
subgroupG/H
center, socle, prime radicalC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
70. #17301C61direct (N × H)
94. C61#17301direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#14432
C61×#14422
C61×#14412
#1730161