Finite Group Databasebeta

← C61×#21827 #29525260

Subgroups — C61×#21827 #29525260

Order 15616.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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
1C2×C61×#543C211yesmaximal, characteristic
2C61×#2312C212yesmaximal
3C61×#1996C218yesmaximal, complemented
4C61×#1819C214yesmaximal
5C61×#543—28no—
6C2×C22⋊Q8×C61C418yescomplemented
7C2×C22⋊Q8×C61C2214yes—
8C22×C22⋊C4×C61C2212yes—
9C22×C22⋊C4×C61C2211yescharacteristic
10C61×#388—28no—
11C61×#380C2214yes—
12C61×#379C2214yes—
13C4×C22⋊C4×C61C2214yes—
14C61×#342C22116yes—
15C25×C61C2311yescharacteristic
16C22×Q8×C61C2×C414yes—
17C23×C4×C61C2×C414yes—
18C23×C4×C61C2312yes—
19C22⋊Q8×C61—28no—
20C22⋊Q8×C61—28no—
21C22⋊Q8×C61—232no—
22C2×C4⋊C4×C61—24no—
23C2×C4⋊C4×C61C2×C4112yes—
24C2×C22⋊C4×C61—28no—
25C2×C22⋊C4×C61—24no—
26C2×C22⋊C4×C61—24no—
27C2×C22⋊C4×C61C2×C414yes—
28C2×C22⋊C4×C61C2×C414yes—
29C2×C22⋊C4×C61D418yes—
30C2×C22⋊C4×C61C2318yes—
31C2×C22⋊C4×C61C2314yes—
32C2×C42×C61—24no—
33#95×C61—24no—
34#95×C61—24no—
35C24×C61—24no—
36C24×C61—82no—
37C24×C61C22×C412yes—
38C24×C61C2×D414yes—
39C24×C61C2411yescharacteristic
40C2×Q8×C61—28no—
41C2×Q8×C61—84no—
42C22×C4×C61—28no—
43C22×C4×C61—28no—
44C22×C4×C61—82no—
45C22×C4×C61—84no—
46C22×C4×C61C22×C418yes—
47C22×C4×C61C22×C414yes—
48C22×C4×C61C2×D414yes—
49C22×C4×C61C2×D414yes—
50C4⋊C4×C61—224no—
51C4⋊C4×C61—84no—
52C22⋊C4×C61—28no—
53C22⋊C4×C61—28no—
54C22⋊C4×C61—216no—
55C22⋊C4×C61—84no—
56C22⋊C4×C61—84no—
57C22⋊C4×C61C22⋊C4116yes—
58C42×C61—84no—
59C23×C61—24no—
60C23×C61—28no—
61C23×C61—44no—
62C23×C61—42no—
63C23×C61—44no—
64C23×C61—44no—
65C23×C61—88no—
66C23×C61C2×C22⋊C414yes—
67C23×C61C23×C411yescharacteristic
68C23×C61C22×D412yes—
69C23×C612−1+414yes—
70Q8×C61—88no—
71C2×C4×C61—28no—
72C2×C4×C61—44no—
73C2×C4×C61—44no—
74C2×C4×C61—44no—
75C2×C4×C61—48no—
76C2×C4×C61—48no—
77C2×C4×C61—48no—
78C2×C4×C61—48no—
79C2×C4×C61—88no—
80C2×C4×C61C2×C22⋊C418yes—
81#21827C6111yesmaximal, characteristic, direct product factor, Sylow
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—22no—
85C22×C61—24no—
86C22×C61—28no—
87C22×C61—44no—
88C22×C61—48no—
89C22×C61—88no—
90C22×C61C22×C22⋊C411yescharacteristic
91C22×C61#51912yes—
92C22×C61#53614yes—
93C4×C61—28no—
94C4×C61—48no—
95C4×C61—88no—
96C2×#543C2×C6111yescharacteristic
97#2312C2×C6112yes—
98#1996C2×C6118yescomplemented
99#1819C2×C6114yes—
100C2×C61—24no—
101C2×C61—22no—
102C2×C61—44no—
103C2×C61#231011yescharacteristic
104C2×C61#288312yes—
105#543—28no—
106C2×C22⋊Q8C4×C6118yescomplemented
107C2×C22⋊Q8C22×C6114yes—
108C22×C22⋊C4C22×C6112yes—
109C22×C22⋊C4C22×C6111yescharacteristic
110#388—28no—
111#380C22×C6114yes—
112#379C22×C6114yes—
113C4×C22⋊C4C22×C6114yes—
114#342C22×C61116yes—
115C61#2182711yescharacteristic, direct product factor, Sylow
116C25C23×C6111yescharacteristic
117C22×Q8C2×C4×C6114yes—
118C23×C4C2×C4×C6114yes—
119C23×C4C23×C6112yes—
120C22⋊Q8—28no—
121C22⋊Q8—28no—
122C22⋊Q8—232no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4C2×C4×C61112yes—
125C2×C22⋊C4—28no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4—24no—
128C2×C22⋊C4C2×C4×C6114yes—
129C2×C22⋊C4C2×C4×C6114yes—
130C2×C22⋊C4D4×C6118yes—
131C2×C22⋊C4C23×C6118yes—
132C2×C22⋊C4C23×C6114yes—
133C2×C42—24no—
134#95—24no—
135#95—24no—
136C24—24no—
137C24—82no—
138C24C22×C4×C6112yes—
139C24C2×D4×C6114yes—
140C24C24×C6111yescharacteristic
141C2×Q8—28no—
142C2×Q8—84no—
143C22×C4—28no—
144C22×C4—28no—
145C22×C4—82no—
146C22×C4—84no—
147C22×C4C22×C4×C6118yes—
148C22×C4C22×C4×C6114yes—
149C22×C4C2×D4×C6114yes—
150C22×C4C2×D4×C6114yes—
151C4⋊C4—224no—
152C4⋊C4—84no—
153C22⋊C4—28no—
154C22⋊C4—28no—
155C22⋊C4—216no—
156C22⋊C4—84no—
157C22⋊C4—84no—
158C22⋊C4C22⋊C4×C61116yes—
159C42—84no—
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊C4×C6114yes—
168C23C23×C4×C6111yescharacteristic
169C23C22×D4×C6112yes—
170C232−1+4×C6114yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—88no—
181C2×C4C2×C22⋊C4×C6118yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—24no—
186C22—28no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C22⋊C4×C6111yescharacteristic
191C22C61×#51912yes—
192C22C61×#53614yes—
193C4—28no—
194C4—48no—
195C4—88no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2C61×#231011yescharacteristic
200C2C61×#288312yes—
subgroupG/H
center, socleC22×C61C22×C22⋊C4
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1996C2semidirect
6. C2×C22⋊Q8×C61C4semidirect
81. #21827C61direct (N × H)
98. #1996C2×C61semidirect
106. C2×C22⋊Q8C4×C61semidirect
115. C61#21827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5432
C61×#23122
C61×#19962
C61×#18192
#2182761