Finite Group Databasebeta

← #29584176

Subgroups — #29584176

Order 15616.

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

normal subgroups only

This group has 342 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#21445993C211yesmaximal, characteristic
3#21444550C212yesmaximal
4#21444435C212yesmaximal
5C61×#1307C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10C2×#14519712—22no—
11#16839786C2211yescharacteristic
12C2×#14519688C2211yescharacteristic
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#14519712—44no—
30#14519709—22no—
31C4⋊#92418—22no—
32#14519702—24no—
33#14519688—21no—
34#14519688D412yes—
35C2×M16×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—22no—
38C4⋊C8×C61—22no—
39C22⋊C8×C61—22no—
40#97×C61—22no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4112yes—
43C2×Dic122—22no—
44C2×Dic122—22no—
45M16×C61—42no—
46C2×C8×C61—22no—
47C2×C8×C61—42no—
48C42×C61C2×D412yes—
49C42×C61C2×D411yescharacteristic
50C42×C61#4111yescharacteristic
51C22⋊Dic61—42no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56#11758196—42no—
57#11758196—42no—
58C4×Dic61—42no—
59#11758194—42no—
60C2×#92418—22no—
61C2×#92418—22no—
62C2×#92418—22no—
63C2×#92418—41no—
64Dic244—82no—
65C23×C61#12411yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—42no—
69C2×C4×C61#12011yescharacteristic
70C2×C4×C61#12112yes—
71C2×C4×C61#12111yescharacteristic
72C2×C4×C61#12312yes—
73C2×Dic61—42no—
74C2×Dic61—42no—
75Dic122—42no—
76Dic122—42no—
77Dic122—82no—
78C8×C61—42no—
79C8×C61—82no—
80#92418—24no—
81#92418—81no—
82#10528—611nomaximal, Sylow
83C22×C61—22no—
84C22×C61—21no—
85C22×C61#39411yescharacteristic
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—21no—
89C4×C61#45311yescharacteristic
90C4×C61#45611yescharacteristic
91Dic61—82no—
92Dic61—82no—
93#3255—611no—
94#1849—611no—
95#1559—612no—
96#1531—612no—
97#1307D6111yescharacteristic
98C2×C61—41no—
99C2×C61#203911yescharacteristic
100C2×C61#204912yes—
101#533—612no—
102#475—1222no—
103#470—1222no—
104#462—1222no—
105#432C2×D6112yes—
106C2×#108—1222no—
107#423—611no—
108#423C2×D6111yescharacteristic
109C2×#97—611no—
110#333—1222no—
111#332—1222no—
112#330—1224no—
113C61#1052811yescharacteristic, complemented, Sylow
114C2×Q16—1222no—
115C2×M16—1221no—
116C2×M16D24412yes—
117C22×C8—1221no—
118C4⋊Q8—612no—
119C4⋊Q8—612no—
120#125—1222no—
121C22⋊Q8—1222no—
122C22⋊Q8—1222no—
123C4×Q8—1222no—
124C4×Q8—1222no—
125#117—1222no—
126C2×C42C22×D6111yescharacteristic
127#108—2444no—
128#106—1222no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—1222no—
132#103—1224no—
133C22⋊C8—22no—
134#97—22no—
135#97—612no—
136#97—1221no—
137C2×Q8—1222no—
138C2×Q8—1222no—
139C22×C4C2×D24411yescharacteristic
140C22×C4#1175822212yes—
141Q16—4882no—
142M16—42no—
143M16—2442no—
144C2×C8—22no—
145C2×C8—42no—
146C2×C8—1222no—
147C2×C8—1222no—
148C2×C8—1222no—
149C2×C8—2441no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—2442no—
155C4⋊C4—2442no—
156C22⋊C4—2442no—
157C42—2442no—
158C42D4×D6112yes—
159C42D4×D6111yescharacteristic
160C42#1175822611yescharacteristic
161C23#1451976511yescharacteristic
162Q8—4882no—
163Q8—2442no—
164Q8—2442no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4#1451974711yescharacteristic
171C2×C4#1451975012yes—
172C2×C4#1451975211yescharacteristic
173C2×C4#1451976212yes—
174C8—42no—
175C8—82no—
176C8—1224no—
177C8—4881no—
178C22—21no—
179C22—22no—
180C22#1683968011yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—4882no—
185C4—4882no—
186C4#1683993211yescharacteristic
187C4#1683994711yescharacteristic
188C2—41no—
189C2#2144704411yescharacteristic
190C2#2144710212yes—
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1307C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1307D61
hypocenterC61#10528
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
113. C61#10528semidirect

Maximal subgroups

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

subgroupindex
#214572132
#214459932
#214445502
#214444352
C61×#13072
#1052861