Finite Group Databasebeta

← C61×#8759 #29512192

Subgroups — C61×#8759 #29512192

Order 15616.

474 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2312C211yesmaximal, characteristic
2C61×#1462C212yesmaximal
3C61×#1305C214yesmaximal, complemented
4C22×C22⋊C4×C61C2211yescharacteristic
5C61×#407C2214yes—
6C61×#388—24no—
7C61×#380C2212yes—
8C61×#379C412yes—
9C4×C22⋊C4×C61C412yes—
10C61×#323—24no—
11C25×C61C2×C411yescharacteristic
12C23×C4×C61C2×C411yescharacteristic
13C23×C4×C61C2311yescharacteristic
14C2×M16×C61—24no—
15C2×C4⋊C4×C61—22no—
16C2×C22⋊C4×C61—24no—
17C2×C22⋊C4×C61—22no—
18C2×C22⋊C4×C61—22no—
19C2×C22⋊C4×C61C2×C414yes—
20C2×C22⋊C4×C61D414yes—
21C2×C42×C61—22no—
22C22⋊C8×C61—24no—
23C22⋊C8×C61—24no—
24#95×C61—22no—
25#95×C61—22no—
26C24×C61—22no—
27C24×C61—42no—
28C24×C61—81no—
29C24×C61—81no—
30C24×C61C22⋊C412yes—
31C24×C61C22×C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61—24no—
34C22×C4×C61—81no—
35C22×C4×C61—81no—
36C22×C4×C61C22⋊C412yes—
37C22×C4×C61C2×D412yes—
38C22×C4×C61#4114yes—
39M16×C61—84no—
40C2×C8×C61—44no—
41C4⋊C4×C61—82no—
42C22⋊C4×C61—28no—
43C22⋊C4×C61—44no—
44C22⋊C4×C61—82no—
45C22⋊C4×C61—82no—
46C42×C61—82no—
47C23×C61—22no—
48C23×C61—22no—
49C23×C61—24no—
50C23×C61—41no—
51C23×C61—41no—
52C23×C61—44no—
53C23×C61—42no—
54C23×C61—42no—
55C23×C61—82no—
56C23×C61—82no—
57C23×C61—88no—
58C23×C61C2×C22⋊C411yescharacteristic
59C23×C61#11712yes—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C2×C4×C61—44no—
63C2×C4×C61—42no—
64C2×C4×C61—44no—
65C2×C4×C61—44no—
66C2×C4×C61—44no—
67C2×C4×C61—82no—
68C2×C4×C61#12314yes—
69C8×C61—84no—
70#8759C6111yesmaximal, characteristic, direct product factor, Sylow
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—22no—
74C22×C61—22no—
75C22×C61—22no—
76C22×C61—44no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—84no—
81C22×C61—88no—
82C22×C61#38111yescharacteristic
83C22×C61#41312yes—
84C4×C61—24no—
85C4×C61—42no—
86C4×C61—84no—
87#2312C2×C6111yescharacteristic
88#1462C2×C6112yes—
89#1305C2×C6114yescomplemented
90C2×C61—22no—
91C2×C61—42no—
92C2×C61—82no—
93C2×C61#182211yescharacteristic
94C2×C61#182811yescharacteristic
95C2×C61#182911yescharacteristic
96C22×C22⋊C4C22×C6111yescharacteristic
97#407C22×C6114yes—
98#388—24no—
99#380C22×C6112yes—
100#379C4×C6112yes—
101C4×C22⋊C4C4×C6112yes—
102#323—24no—
103C61#875911yescharacteristic, direct product factor, Sylow
104C25C2×C4×C6111yescharacteristic
105C23×C4C2×C4×C6111yescharacteristic
106C23×C4C23×C6111yescharacteristic
107C2×M16—24no—
108C2×C4⋊C4—22no—
109C2×C22⋊C4—24no—
110C2×C22⋊C4—22no—
111C2×C22⋊C4—22no—
112C2×C22⋊C4C2×C4×C6114yes—
113C2×C22⋊C4D4×C6114yes—
114C2×C42—22no—
115C22⋊C8—24no—
116C22⋊C8—24no—
117#95—22no—
118#95—22no—
119C24—22no—
120C24—42no—
121C24—81no—
122C24—81no—
123C24C22⋊C4×C6112yes—
124C24C22×C4×C6111yescharacteristic
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4C22⋊C4×C6112yes—
130C22×C4C2×D4×C6112yes—
131C22×C4#41×C6114yes—
132M16—84no—
133C2×C8—44no—
134C4⋊C4—82no—
135C22⋊C4—28no—
136C22⋊C4—44no—
137C22⋊C4—82no—
138C22⋊C4—82no—
139C42—82no—
140C23—22no—
141C23—22no—
142C23—24no—
143C23—41no—
144C23—41no—
145C23—44no—
146C23—42no—
147C23—42no—
148C23—82no—
149C23—82no—
150C23—88no—
151C23C2×C22⋊C4×C6111yescharacteristic
152C23#117×C6112yes—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—82no—
161C2×C4#123×C6114yes—
162C8—84no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—84no—
173C22—88no—
174C22C61×#38111yescharacteristic
175C22C61×#41312yes—
176C4—24no—
177C4—42no—
178C4—84no—
179C2—22no—
180C2—42no—
181C2—82no—
182C2C61×#182211yescharacteristic
183C2C61×#182811yescharacteristic
184C2C61×#182911yescharacteristic
subgroupG/H
center, socleC22×C61#381
commutatorC24C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC25×C61C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1305C2semidirect
70. #8759C61direct (N × H)
89. #1305C2×C61semidirect
103. C61#8759direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#23122
C61×#14622
C61×#13052
#875961