Finite Group Databasebeta

← C61×#8306 #29511739

Subgroups — C61×#8306 #29511739

Order 15616.

810 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 182 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
1C22×#125×C61C211yesmaximal, characteristic
2C61×#1817C212yesmaximal
3C2×C61×#324C214yesmaximal
4C2×#125×C61—28no—
5C2×#125×C61—24no—
6C22×C4⋊C4×C61C411yescharacteristic
7C22×C4⋊C4×C61C412yes—
8C22×C4⋊C4×C61C411yescharacteristic
9C22×C4⋊C4×C61C2212yes—
10C22×C42×C61C2211yescharacteristic
11C2×C22⋊C8×C61C2214yes—
12C61×#336—24no—
13C61×#324—28no—
14C23×C4×C61C2×C411yescharacteristic
15C23×C4×C61C2×C411yescharacteristic
16C23×C4×C61C2×C412yes—
17C23×C4×C61C2×C412yes—
18C23×C4×C61C2311yescharacteristic
19C22×C8×C61—24no—
20#125×C61—232no—
21C2×C4⋊C4×C61—24no—
22C2×C4⋊C4×C61—24no—
23C2×C4⋊C4×C61—24no—
24C2×C4⋊C4×C61—24no—
25C2×C4⋊C4×C61—24no—
26C2×C4⋊C4×C61—22no—
27C2×C4⋊C4×C61—22no—
28C2×C4⋊C4×C61—24no—
29C2×C4⋊C4×C61—24no—
30C2×C4⋊C4×C61D418yes—
31C2×C42×C61—24no—
32C2×C42×C61D414yes—
33C22⋊C8×C61—28no—
34C24×C61C22×C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—24no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—24no—
43C22×C4×C61—28no—
44C22×C4×C61—42no—
45C22×C4×C61—44no—
46C22×C4×C61C22⋊C414yes—
47C22×C4×C61C22⋊C412yes—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22⋊C414yes—
50C22×C4×C61C2×D412yes—
51C22×C4×C61C2×D414yes—
52C2×C8×C61—48no—
53C2×C8×C61—44no—
54C4⋊C4×C61—28no—
55C4⋊C4×C61—28no—
56C4⋊C4×C61—216no—
57C4⋊C4×C61—216no—
58C42×C61—28no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61C2×C22⋊C412yes—
62C23×C61C2×C22⋊C411yescharacteristic
63C23×C61#13114yes—
64C2×C4×C61—28no—
65C2×C4×C61—22no—
66C2×C4×C61—24no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—24no—
70C2×C4×C61—24no—
71C2×C4×C61—28no—
72C2×C4×C61—24no—
73C2×C4×C61—44no—
74C2×C4×C61—44no—
75C2×C4×C61—44no—
76C2×C4×C61—44no—
77C2×C4×C61—44no—
78C2×C4×C61—44no—
79C2×C4×C61—44no—
80C2×C4×C61#10114yes—
81C2×C4×C61#12014yes—
82C8×C61—84no—
83#8306C6111yesmaximal, characteristic, direct product factor, Sylow
84C22×C61—28no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61#37911yescharacteristic
88C22×C61#40814yes—
89C22×C61#40812yes—
90C22×C61#41012yes—
91C22×C61C2×#10112yes—
92C4×C61—24no—
93C4×C61—24no—
94C4×C61—42no—
95C4×C61—44no—
96C4×C61—44no—
97C22×#125C2×C6111yescharacteristic
98#1817C2×C6112yes—
99C2×#324C2×C6114yes—
100C2×C61—24no—
101C2×C61#147014yes—
102C2×C61#178011yescharacteristic
103C2×C61#178211yescharacteristic
104C2×C61#178411yescharacteristic
105C2×#125—28no—
106C2×#125—24no—
107C22×C4⋊C4C4×C6111yescharacteristic
108C22×C4⋊C4C4×C6112yes—
109C22×C4⋊C4C4×C6111yescharacteristic
110C22×C4⋊C4C22×C6112yes—
111C22×C42C22×C6111yescharacteristic
112C2×C22⋊C8C22×C6114yes—
113#336—24no—
114#324—28no—
115C61#830611yescharacteristic, direct product factor, Sylow
116C23×C4C2×C4×C6112yes—
117C23×C4C2×C4×C6111yescharacteristic
118C23×C4C2×C4×C6111yescharacteristic
119C23×C4C2×C4×C6112yes—
120C23×C4C23×C6111yescharacteristic
121C22×C8—24no—
122#125—232no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—24no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4D4×C6118yes—
133C2×C42—24no—
134C2×C42D4×C6114yes—
135C22⋊C8—28no—
136C24C22×C4×C6111yescharacteristic
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—28no—
145C22×C4—24no—
146C22×C4—42no—
147C22×C4—44no—
148C22×C4C22⋊C4×C6112yes—
149C22×C4C22⋊C4×C6114yes—
150C22×C4C22⋊C4×C6112yes—
151C22×C4C22⋊C4×C6114yes—
152C22×C4C2×D4×C6112yes—
153C22×C4C2×D4×C6114yes—
154C2×C8—48no—
155C2×C8—44no—
156C4⋊C4—28no—
157C4⋊C4—28no—
158C4⋊C4—216no—
159C4⋊C4—216no—
160C42—28no—
161C23—22no—
162C23—22no—
163C23C2×C22⋊C4×C6112yes—
164C23C2×C22⋊C4×C6111yescharacteristic
165C23#131×C6114yes—
166C2×C4—28no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4—44no—
181C2×C4—44no—
182C2×C4#101×C6114yes—
183C2×C4#120×C6114yes—
184C8—84no—
185C22—22no—
186C22—22no—
187C22—28no—
188C22C61×#37911yescharacteristic
189C22C61×#40814yes—
190C22C61×#40812yes—
191C22C61×#41012yes—
192C22C2×#101×C6112yes—
193C4—24no—
194C4—24no—
195C4—42no—
196C4—44no—
197C4—44no—
198C2—24no—
199C2C61×#147014yes—
200C2C61×#178011yescharacteristic
201C2C61×#178211yescharacteristic
202C2C61×#178411yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC24C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC24×C61C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
83. #8306C61direct (N × H)
115. C61#8306direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C612
C61×#18172
C2×C61×#3242
#830661