Finite Group Databasebeta

← #29584181

Subgroups — #29584181

Order 15616.

326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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#21457213C211yesmaximal, characteristic
2#21445959C211yesmaximal, characteristic
3#21444550C212yesmaximal
4#21444435C212yesmaximal
5C61×#1307C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10#16839786C2211yescharacteristic
11C2×#14519688C2211yescharacteristic
12#16839526—22no—
13#16839510—22no—
14#16839507—22no—
15#16839503—24no—
16C61×#432C2212yes—
17C61×#423C2211yescharacteristic
18C2×Dic244—22no—
19C2×#11758194—21no—
20C22×#92418—21no—
21#14519777D412yes—
22#14519777D412yes—
23#14519769—22no—
24#14519756—22no—
25#14519756—22no—
26C4×Dic122—22no—
27C4×Dic122—22no—
28#14519736—22no—
29#14519709—22no—
30C4⋊#92418—22no—
31#14519702—24no—
32#14519688—21no—
33#14519688D412yes—
34C2×M16×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38C22⋊C8×C61—22no—
39#97×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61#4112yes—
42C2×Dic122—22no—
43C2×Dic122—22no—
44M16×C61—42no—
45C2×C8×C61—22no—
46C2×C8×C61—42no—
47C42×C61C2×D412yes—
48C42×C61C2×D411yescharacteristic
49C42×C61#4111yescharacteristic
50C22⋊Dic61—42no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55#11758196—42no—
56#11758196—42no—
57C4×Dic61—42no—
58#11758194—42no—
59C2×#92418—22no—
60C2×#92418—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63Dic244—82no—
64C23×C61#12411yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—42no—
68C2×C4×C61#12011yescharacteristic
69C2×C4×C61#12112yes—
70C2×C4×C61#12111yescharacteristic
71C2×C4×C61#12312yes—
72C2×Dic61—42no—
73C2×Dic61—42no—
74Dic122—42no—
75Dic122—42no—
76Dic122—82no—
77C8×C61—42no—
78C8×C61—82no—
79#92418—42no—
80#92418—81no—
81#10529—611nomaximal, Sylow
82C22×C61—22no—
83C22×C61—21no—
84C22×C61#39411yescharacteristic
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—21no—
88C4×C61#45411yescharacteristic
89C4×C61#45511yescharacteristic
90Dic61—82no—
91Dic61—82no—
92#3255—611no—
93#1838—611no—
94#1559—612no—
95#1531—612no—
96#1307D6111yescharacteristic
97C2×C61—41no—
98C2×C61#204011yescharacteristic
99C2×C61#204912yes—
100#533—612no—
101#475—1222no—
102#470—1222no—
103#462—1222no—
104#432C2×D6112yes—
105#423—611no—
106#423C2×D6111yescharacteristic
107C2×#97—611no—
108#341—1222no—
109#333—1222no—
110#332—1222no—
111#330—1224no—
112C61#1052911yescharacteristic, complemented, Sylow
113C2×Q16—1222no—
114C2×M16—1221no—
115C2×M16D24412yes—
116C22×C8—1221no—
117C4⋊Q8—612no—
118C4⋊Q8—612no—
119#125—1222no—
120C22⋊Q8—1222no—
121C22⋊Q8—1222no—
122C4×Q8—1222no—
123C4×Q8—1222no—
124#117—1222no—
125C2×C42C22×D6111yescharacteristic
126#106—1222no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—1222no—
130#103—1224no—
131C22⋊C8—22no—
132#97—22no—
133#97—612no—
134#97—1221no—
135C2×Q8—1222no—
136C2×Q8—1222no—
137C22×C4C2×D24411yescharacteristic
138C22×C4#1175822212yes—
139Q16—4882no—
140M16—42no—
141M16—2442no—
142C2×C8—22no—
143C2×C8—42no—
144C2×C8—1222no—
145C2×C8—2441no—
146C2×C8—2441no—
147C2×C8—2441no—
148C4⋊C4—1222no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—2442no—
153C4⋊C4—2442no—
154C22⋊C4—2442no—
155C42—2442no—
156C42D4×D6112yes—
157C42D4×D6111yescharacteristic
158C42#1175822611yescharacteristic
159C23#1451976511yescharacteristic
160Q8—4882no—
161Q8—2442no—
162Q8—2442no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4#1451974711yescharacteristic
169C2×C4#1451975012yes—
170C2×C4#1451975211yescharacteristic
171C2×C4#1451976212yes—
172C8—42no—
173C8—82no—
174C8—4881no—
175C8—2442no—
176C22—21no—
177C22—22no—
178C22#1683968011yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—4882no—
183C4—4882no—
184C4#1683993711yescharacteristic
185C4#1683994211yescharacteristic
186C2—41no—
187C2#2144704911yescharacteristic
188C2#2144710212yes—
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1307C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1307D61
hypocenterC61#10529
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
112. C61#10529semidirect

Maximal subgroups

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

subgroupindex
#214572132
#214459592
#214445502
#214444352
C61×#13072
#1052961