Finite Group Databasebeta

← #29594416

Subgroups — #29594416

Order 15616.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448061C211yesmaximal, characteristic, complemented
2#21447995C211yesmaximal, characteristic, complemented
3#21447895C211yesmaximal, characteristic
4#21443887C211yesmaximal, characteristic, complemented
5#21443881C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#2171C211yesmaximal, characteristic, complemented
8#16840197—21no—
9#16840164C2211yescharacteristic
10#16840139C2211yescharacteristic
11#16839586—21no—
12#16839583C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839574—21no—
15#16839572—21no—
16#16839564—21no—
17#16839564—21no—
18C61×#504—21no—
19C61×#443C2211yescharacteristic
20C61×#364C2211yescharacteristic
21C61×#350—21no—
22C61×#346C2211yescharacteristic
23C2×D488—21no—
24C2×D488—21no—
25#14519774—21no—
26#14519769—21no—
27#14519720—41no—
28#14519718—41no—
29#14519717—21no—
30#14519717—21no—
31#14519711—21no—
32#14519709—21no—
33#135×C61D411yescharacteristic
34#131×C61—21no—
35M32×C61—21no—
36M32×C61—41no—
37C2×C16×C61—41no—
38C2×C16×C61D411yescharacteristic
39C2×C16×C61D411yescharacteristic
40#108×C61D411yescharacteristic
41#104×C61—21no—
42C4×C8×C61C2311yescharacteristic
43#41×C61—21no—
44C2×D244—41no—
45C2×D244—81no—
46Q16×C61SD1611yescharacteristic
47SD16×C61—21no—
48D8×C61SD1611yescharacteristic
49M16×C61—21no—
50M16×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61C2×D411yescharacteristic
54C42×C61#4111yescharacteristic
55C4⋊Dic61—41no—
56#11758196—81no—
57D488—41no—
58D488—41no—
59D488—41no—
60D488—41no—
61C16×C61—21no—
62C16×C61—21no—
63C16×C61—41no—
64#11758185—41no—
65#11758185—41no—
66C22×D61—81no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—41no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61#12111yescharacteristic
73C2×Dic61—81no—
74D244—81no—
75D244—81no—
76D244—162no—
77C8×C61—41no—
78C8×C61C2×SD1611yescharacteristic
79C8×C61#13511yescharacteristic
80C8×C61#13511yescharacteristic
81C8×C61AGL(1,ℤ/8)11yescharacteristic
82#12465—611nomaximal, Sylow
83C22×C61—41no—
84C22×C61#47211yescharacteristic
85C2×D61—162no—
86C2×D61—161no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61#46311yescharacteristic
90C4×C61#46511yescharacteristic
91Dic61—161no—
92#2244—611no—
93#2231—611no—
94#2213—611no—
95#2171D6111yescharacteristic, complemented
96#1369—611no—
97#1366—611no—
98#1357—611no—
99C2×C61—21no—
100C2×C61—81no—
101C2×C61#167711yescharacteristic
102D61—321no—
103#509—1221no—
104#504—21no—
105#499—611no—
106#493—611no—
107#443C2×D6111yescharacteristic
108#365—1221no—
109#364—611no—
110#364—611no—
111#364C2×D6111yescharacteristic
112#361—1221no—
113#360—1221no—
114#357—1221no—
115#357—1221no—
116#350—21no—
117#346C2×D6111yescharacteristic
118C61#1246511yescharacteristic, complemented, Sylow
119#135D24411yescharacteristic
120C2×D8—1221no—
121C2×D8—1221no—
122#131—21no—
123#127—1221no—
124#125—1221no—
125SD32—2441no—
126D16—2441no—
127M32—21no—
128M32—41no—
129M32—1221no—
130M32—1221no—
131C2×C16—41no—
132C2×C16C22⋊D6111yescharacteristic
133C2×C16C22⋊D6111yescharacteristic
134#108D24411yescharacteristic
135#107—1221no—
136#106—1221no—
137#104—21no—
138C4×C8C22×D6111yescharacteristic
139#41—21no—
140C2×D4—4881no—
141C2×D4—2441no—
142Q16#1175819011yescharacteristic
143SD16—21no—
144D8—2441no—
145D8—2441no—
146D8—2441no—
147D8—2441no—
148D8#1175819011yescharacteristic
149M16—21no—
150M16—41no—
151C2×C8—41no—
152C2×C8C2×D24411yescharacteristic
153C2×C8C2×C22⋊D6111yescharacteristic
154C4⋊C4—4881no—
155C4⋊C4—2441no—
156C42#1175822211yescharacteristic
157C16—21no—
158C16—21no—
159C16—41no—
160C16—2441no—
161C16—2441no—
162C23—4881no—
163Q8—21no—
164D4—21no—
165D4—41no—
166D4—9762no—
167D4—4881no—
168D4—4881no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—4881no—
172C2×C4#1451975111yescharacteristic
173C8—41no—
174C8C2×#1175819011yescharacteristic
175C8#1451979711yescharacteristic
176C8#1451979911yescharacteristic
177C8#1451980311yescharacteristic
178C22—41no—
179C22—9762no—
180C22—9761no—
181C22#1684003211yescharacteristic
182C4—41no—
183C4—41no—
184C4—9761no—
185C4#1683997711yescharacteristic
186C4#1683999111yescharacteristic
187C2—21no—
188C2—81no—
189C2—19521no—
190C2#2144522811yescharacteristic
subgroupG/H
centerC2#21445228
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2171C2
socleC2×C61#1677
prime radical#21447895C2
hypercenter#2171D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2171

Complements

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

NH ≅ G/Ntype
1. #21448061C2semidirect
2. #21447995C2semidirect
4. #21443887C2semidirect
5. #21443881C2semidirect
6. #21443855C2semidirect
7. C61×#2171C2semidirect
95. #2171D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214480612
#214479952
#214478952
#214438872
#214438812
#214438552
C61×#21712
#1246561