Finite Group Databasebeta

← #29594421

Subgroups — #29594421

Order 15616.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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#21448064C211yesmaximal, characteristic, complemented
2#21447995C211yesmaximal, characteristic
3#21447661C211yesmaximal, characteristic
4#21443886C211yesmaximal, characteristic, complemented
5#21443879C211yesmaximal, characteristic, complemented
6#21443858C211yesmaximal, characteristic, complemented
7C61×#2214C211yesmaximal, characteristic
8#16840179—21no—
9#16840164C2211yescharacteristic
10#16839586—21no—
11#16839583C2211yescharacteristic
12#16839583C2211yescharacteristic
13#16839572—21no—
14#16839566—21no—
15#16839566—21no—
16#16839546—21no—
17#16839538C2211yescharacteristic
18C61×#510—21no—
19C61×#494C2211yescharacteristic
20C61×#443C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#362—21no—
23#14519769—21no—
24#14519717—21no—
25#14519717—21no—
26#14519717—41no—
27C2×#11758185—41no—
28C2×#11758185D411yescharacteristic
29C2×#11758185D411yescharacteristic
30#14519711—21no—
31#14519709—21no—
32#135×C61D411yescharacteristic
33C2×Q16×C61—21no—
34C2×Q16×C61—21no—
35#131×C61—21no—
36C4⋊Q8×C61—21no—
37Q32×C61—41no—
38SD32×C61—41no—
39M32×C61—21no—
40#108×C61D411yescharacteristic
41#104×C61—21no—
42C4×C8×C61C2311yescharacteristic
43#41×C61—21no—
44C2×Q8×C61—41no—
45Q16×C61—41no—
46Q16×C61—41no—
47Q16×C61—41no—
48Q16×C61—41no—
49Q16×C61SD1611yescharacteristic
50SD16×C61—21no—
51D8×C61SD1611yescharacteristic
52M16×C61—21no—
53M16×C61—41no—
54C2×C8×C61—41no—
55C2×C8×C61C2×D411yescharacteristic
56C2×C8×C61C2×D411yescharacteristic
57C4⋊C4×C61—81no—
58C42×C61#4111yescharacteristic
59C4⋊Dic61—41no—
60#11758196—81no—
61C16×C61—41no—
62#11758185—21no—
63#11758185—21no—
64#11758185—41no—
65#11758185—41no—
66Q8×C61—21no—
67Q8×C61—81no—
68Q8×C61—81no—
69D4×C61—21no—
70D4×C61—41no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—81no—
74C2×C4×C61#12111yescharacteristic
75C2×Dic61—81no—
76C8×C61—41no—
77C8×C61C2×SD1611yescharacteristic
78C8×C61#13511yescharacteristic
79C8×C61#13511yescharacteristic
80C8×C61AGL(1,ℤ/8)11yescharacteristic
81#12466—611nomaximal, Sylow
82C22×C61—41no—
83C22×C61#47211yescharacteristic
84C4×C61—41no—
85C4×C61—41no—
86C4×C61—161no—
87C4×C61#46311yescharacteristic
88C4×C61#46511yescharacteristic
89Dic61—161no—
90#2245—611no—
91#2231—611no—
92#2214D6111yescharacteristic
93#2171—611no—
94#1369—611no—
95#1366—611no—
96#1358—611no—
97C2×C61—21no—
98C2×C61—81no—
99C2×C61#167711yescharacteristic
100#510—21no—
101#504—1221no—
102#499—611no—
103#494C2×D6111yescharacteristic
104#443C2×D6111yescharacteristic
105#365—1221no—
106#364—611no—
107#364—611no—
108#364C2×D6111yescharacteristic
109#362—21no—
110#360—1221no—
111#358—1221no—
112#358—1221no—
113#350—1221no—
114#346—611no—
115C61#1246611yescharacteristic, complemented, Sylow
116#135C22⋊D6111yescharacteristic
117C2×Q16—21no—
118C2×Q16—21no—
119#131—21no—
120C4⋊Q8—21no—
121#125—1221no—
122Q32—41no—
123SD32—41no—
124M32—21no—
125M32—1221no—
126M32—1221no—
127M32—2441no—
128C2×C16—611no—
129C2×C16—611no—
130C2×C16—2441no—
131#108C22⋊D6111yescharacteristic
132#107—1221no—
133#106—1221no—
134#104—21no—
135C4×C8C22×D6111yescharacteristic
136#41—21no—
137C2×Q8—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—41no—
142Q16#1175820011yescharacteristic
143SD16—21no—
144D8#1175820011yescharacteristic
145M16—21no—
146M16—41no—
147C2×C8—41no—
148C2×C8D4×D6111yescharacteristic
149C2×C8C2×C22⋊D6111yescharacteristic
150C4⋊C4—81no—
151C4⋊C4—4881no—
152C4⋊C4—2441no—
153C42#1175822411yescharacteristic
154C16—41no—
155C16—1221no—
156C16—1221no—
157C16—2441no—
158C16—2441no—
159Q8—21no—
160Q8—81no—
161Q8—81no—
162D4—21no—
163D4—41no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—4881no—
168C2×C4#1451974911yescharacteristic
169C8—41no—
170C8C2×#1175820011yescharacteristic
171C8#1451979611yescharacteristic
172C8#1451979711yescharacteristic
173C8#1451980111yescharacteristic
174C22—41no—
175C22#1684003011yescharacteristic
176C4—41no—
177C4—41no—
178C4—161no—
179C4—9761no—
180C4#1683997511yescharacteristic
181C4#1683998911yescharacteristic
182C2—21no—
183C2—81no—
184C2#2144522611yescharacteristic
subgroupG/H
centerC2#21445226
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2214C2
socleC2×C61#1677
prime radical#135×C61D4
hypercenter#2214D61
hypocenterC61#12466
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #21448064C2semidirect
4. #21443886C2semidirect
5. #21443879C2semidirect
6. #21443858C2semidirect
115. C61#12466semidirect

Maximal subgroups

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

subgroupindex
#214480642
#214479952
#214476612
#214438862
#214438792
#214438582
C61×#22142
#1246661