Finite Group Databasebeta

← #29584180

Subgroups — #29584180

Order 15616.

326 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 75 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#21444547C212yesmaximal
3#21444433C212yesmaximal
4#21443730C211yesmaximal, characteristic
5C61×#1838C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10#16839819C2212yes—
11#16839510—22no—
12#16839509—22no—
13#16839503—24no—
14C61×#423C2211yescharacteristic
15C61×#423C2211yescharacteristic
16C2×#97×C61C2211yescharacteristic
17C61×#341—22no—
18C2×Dic244—22no—
19#14519777D412yes—
20#14519777D412yes—
21#14519769—22no—
22#14519756—22no—
23#14519756—22no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26#14519736—22no—
27#14519709—22no—
28C4⋊#92418—22no—
29#14519702—24no—
30C22⋊#92418—22no—
31#14519688—22no—
32C2×M16×C61—21no—
33C2×M16×C61D412yes—
34C22×C8×C61—21no—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38#97×C61—21no—
39#97×C61D412yes—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61#4112yes—
42C2×Dic122—22no—
43C2×Dic122—22no—
44M16×C61—42no—
45M16×C61—42no—
46C2×C8×C61—22no—
47C2×C8×C61—22no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C42×C61C2×D412yes—
52C42×C61C2×D411yescharacteristic
53C42×C61#4111yescharacteristic
54C22⋊Dic61—42no—
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59#11758196—42no—
60#11758196—42no—
61C4×Dic61—42no—
62C2×#92418—42no—
63Dic244—82no—
64C23×C61#12411yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—42no—
68C2×C4×C61#12011yescharacteristic
69C2×C4×C61#12111yescharacteristic
70C2×C4×C61#12112yes—
71C2×C4×C61#12312yes—
72C2×Dic61—42no—
73C2×Dic61—42no—
74Dic122—42no—
75Dic122—42no—
76Dic122—82no—
77C8×C61—42no—
78C8×C61—42no—
79C8×C61—81no—
80#92418—82no—
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#1838D6111yescharacteristic
94#1559—612no—
95#1531—612no—
96#1307—611no—
97C2×C61—41no—
98C2×C61#204011yescharacteristic
99C2×C61#204912yes—
100#533—612no—
101#475—1222no—
102#470—1222no—
103#462—1222no—
104#432—612no—
105#423C2×D6111yescharacteristic
106#423C2×D6111yescharacteristic
107C2×#97C2×D6111yescharacteristic
108#341—22no—
109#333—1222no—
110#332—1222no—
111#330—1224no—
112C61#1052911yescharacteristic, complemented, Sylow
113C2×Q16—1222no—
114C2×M16—21no—
115C2×M16C22⋊D6112yes—
116C22×C8—21no—
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—1222no—
132#97—21no—
133#97—1222no—
134#97D24412yes—
135C2×Q8—1222no—
136C2×Q8—1222no—
137C22×C4#1175822612yes—
138C22×C4C2×C22⋊D6111yescharacteristic
139Q16—4882no—
140M16—42no—
141M16—42no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8—41no—
147C2×C8—2442no—
148C4⋊C4—1222no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—2442no—
153C4⋊C4—2442no—
154C22⋊C4—2442no—
155C42—2442no—
156C42C2×D24411yescharacteristic
157C42#1175822211yescharacteristic
158C42D4×D6112yes—
159C23#1451976611yescharacteristic
160Q8—4882no—
161Q8—2442no—
162Q8—2442no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4#1451974511yescharacteristic
169C2×C4#1451975111yescharacteristic
170C2×C4#1451975212yes—
171C2×C4#1451976212yes—
172C8—42no—
173C8—42no—
174C8—81no—
175C8—4882no—
176C22—21no—
177C22—22no—
178C22#1683967911yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—4882no—
183C4—4882no—
184C4#1683993411yescharacteristic
185C4#1683993911yescharacteristic
186C2—41no—
187C2#2144704811yescharacteristic
188C2#2144710112yes—
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1838C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1838D61
hypocenterC61#10529
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1838

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
#214445472
#214444332
#214437302
C61×#18382
#1052961