Finite Group Databasebeta

← #29573423

Subgroups — #29573423

Order 15616.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#21445581C212yesmaximal
2#21443700C214yesmaximal, complemented
3C61×#2285C211yesmaximal, characteristic
4C2×C22⋊#92418—22no—
5C2×#14519688C2214yes—
6#16839517—22no—
7C2×#117×C61C412yes—
8C22×C42×C61C2211yescharacteristic
9C61×#384C411yescharacteristic
10C61×#384C411yescharacteristic
11C61×#382C2212yes—
12C61×#380—22no—
13C4×C4⋊C4×C61—22no—
14C22×#92418—24no—
15C22⋊#92418—28no—
16#14519688—28no—
17C23×C4×C61C2×C411yescharacteristic
18C23×C4×C61D412yes—
19#117×C61—44no—
20C2×C4⋊C4×C61—22no—
21C2×C4⋊C4×C61—22no—
22C2×C4⋊C4×C61C2×C412yes—
23C2×C4⋊C4×C61C2×C412yes—
24C2×C22⋊C4×C61—22no—
25C2×C42×C61—24no—
26C2×C42×C61—22no—
27C2×C42×C61C2×C411yescharacteristic
28C2×C42×C61D412yes—
29C2×C42×C61C2311yescharacteristic
30#95×C61—24no—
31C24×C61C22⋊C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61—22no—
34C22×C4×C61—22no—
35C22×C4×C61—24no—
36C22×C4×C61—24no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—42no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22⋊C412yes—
42C22×C4×C61C22×C411yescharacteristic
43C22×C4×C61C2×D412yes—
44C4⋊C4×C61—44no—
45C4⋊C4×C61—42no—
46C4⋊C4×C61—42no—
47C4⋊C4×C61—44no—
48C22⋊C4×C61—44no—
49C42×C61—22no—
50C42×C61—24no—
51C42×C61—44no—
52C42×C61#4114yes—
53C2×#92418—28no—
54C2×#92418—44no—
55C2×#92418—44no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61#10112yes—
61C23×C61C2×C22⋊C411yescharacteristic
62C2×C4×C61—28no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—48no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—44no—
75C2×C4×C61—44no—
76C2×C4×C61#10012yes—
77C2×C4×C61#10414yes—
78C2×C4×C61#11712yes—
79C2×C4×C61#12314yes—
80#92418—48no—
81#8721—611nomaximal, Sylow
82C22×C61—22no—
83C22×C61—24no—
84C22×C61—41no—
85C22×C61—42no—
86C22×C61—41no—
87C22×C61#38111yescharacteristic
88C22×C61C2×#10011yescharacteristic
89C22×C61C2×#10111yescharacteristic
90C22×C61C2×#10412yes—
91C22×C61#42112yes—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—24no—
95C4×C61—24no—
96C4×C61—82no—
97C4×C61—82no—
98#2285D6111yescharacteristic
99#1749—612no—
100#1295—614no—
101C2×C61—42no—
102C2×C61#152511yescharacteristic
103C2×C61#153112yes—
104C2×C61#153611yescharacteristic
105C2×C61#182111yescharacteristic
106C2×C61#182612yes—
107C2×#117Dic6112yes—
108C22×C42C2×D6111yescharacteristic
109C2×C22⋊C8—1222no—
110C2×#97—614no—
111#384Dic6111yescharacteristic
112#384Dic6111yescharacteristic
113#382C2×D6112yes—
114#380—22no—
115C4×C4⋊C4—22no—
116#336—1222no—
117C61#872111yescharacteristic, complemented, Sylow
118C23×C4C2×Dic6111yescharacteristic
119C23×C4C22⋊D6112yes—
120C22×C8—1224no—
121#117—44no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4C2×Dic6112yes—
125C2×C4⋊C4C2×Dic6112yes—
126C2×C22⋊C4—22no—
127C2×C42—24no—
128C2×C42—22no—
129C2×C42C2×Dic6111yescharacteristic
130C2×C42C22⋊D6112yes—
131C2×C42C22×D6111yescharacteristic
132C22⋊C8—1228no—
133#97—1228no—
134#95—24no—
135C24C22⋊Dic6111yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4C22⋊Dic6111yescharacteristic
145C22×C4C22⋊Dic6112yes—
146C22×C4C22×Dic6111yescharacteristic
147C22×C4C2×C22⋊D6112yes—
148C2×C8—1228no—
149C2×C8—2444no—
150C2×C8—2444no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C22⋊C4—44no—
156C42—22no—
157C42—24no—
158C42—44no—
159C42#1175822214yes—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23#1451969612yes—
165C23C2×C22⋊Dic6111yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4#1451969412yes—
181C2×C4#1451970414yes—
182C2×C4#1451973612yes—
183C2×C4#1451976014yes—
184C8—2448no—
185C22—22no—
186C22—24no—
187C22—42no—
188C22—41no—
189C22—41no—
190C22#1683962511yescharacteristic
191C22C2×#1451969411yescharacteristic
192C22C2×#1451969611yescharacteristic
193C22C2×#1451970412yes—
194C22#1683977912yes—
195C4—22no—
196C4—22no—
197C4—24no—
198C4—24no—
199C4—82no—
200C4—82no—
201C2—42no—
202C2#2144441111yescharacteristic
203C2#2144443412yes—
204C2#2144445411yescharacteristic
205C2#2144589911yescharacteristic
206C2#2144591812yes—
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2285C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2285D61
hypocenterC61#8721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #21443700C2semidirect
117. C61#8721semidirect

Maximal subgroups

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

subgroupindex
#214455812
#214437002
C61×#22852
#872161