Finite Group Databasebeta

← #29594419

Subgroups — #29594419

Order 15616.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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#21448062C211yesmaximal, characteristic, complemented
2#21447992C211yesmaximal, characteristic, complemented
3#21447896C211yesmaximal, characteristic
4#21447660C211yesmaximal, characteristic, complemented
5#21443886C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#1366C211yesmaximal, characteristic, complemented
8#16840200—21no—
9#16840180—21no—
10#16840139C2211yescharacteristic
11#16839880C2211yescharacteristic
12#16839584—21no—
13#16839583C2211yescharacteristic
14#16839576—21no—
15#16839571—21no—
16#16839562—21no—
17#16839562—21no—
18#16839547—21no—
19#16839538C2211yescharacteristic
20C61×#499C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#364C2211yescharacteristic
23#14519799D411yescharacteristic
24C2×D488—21no—
25C2×D488—21no—
26#14519783—21no—
27#14519774—21no—
28#14519722—41no—
29D976—41no—
30#14519717—21no—
31#14519716—41no—
32C2×#11758185D411yescharacteristic
33C2×#11758185D411yescharacteristic
34C16×D61—41no—
35#14519713D411yescharacteristic
36#14519705—21no—
37#125×C61—21no—
38M32×C61—21no—
39M32×C61—21no—
40#107×C61—21no—
41#106×C61—21no—
42C4×C8×C61C2311yescharacteristic
43#11758222—21no—
44C2×D244—41no—
45C2×D244—81no—
46C2×C8×C61C2×D411yescharacteristic
47C2×C8×C61C2×D411yescharacteristic
48C4⋊C4×C61—41no—
49C4⋊C4×C61—81no—
50C42×C61#4111yescharacteristic
51#11758194—21no—
52Dic244SD1611yescharacteristic
53D488—41no—
54D488—41no—
55D488—41no—
56D488—41no—
57D488SD1611yescharacteristic
58#11758190—21no—
59#11758189—41no—
60C8×D61—41no—
61C16×C61—41no—
62C16×C61—41no—
63#11758185—21no—
64#11758185—21no—
65#11758185—41no—
66C22×D61—81no—
67C2×C4×C61—21no—
68C2×C4×C61—81no—
69C2×C4×C61#12111yescharacteristic
70C22⋊D61—41no—
71D244—21no—
72D244—81no—
73D244—81no—
74D244—162no—
75C4×D61—41no—
76Dic122—21no—
77C8×C61C2×SD1611yescharacteristic
78C8×C61#13511yescharacteristic
79C8×C61#13511yescharacteristic
80C8×C61AGL(1,ℤ/8)11yescharacteristic
81#92418—41no—
82#12465—611nomaximal, Sylow
83C22×C61#47211yescharacteristic
84C2×D61—41no—
85C2×D61—162no—
86C2×D61—161no—
87C4×C61—41no—
88C4×C61—161no—
89C4×C61#46311yescharacteristic
90C4×C61#46511yescharacteristic
91Dic61—41no—
92#2244—611no—
93#2231—611no—
94#2213—611no—
95#2171—611no—
96#1369—611no—
97#1366D6111yescharacteristic, complemented
98#1357—611no—
99C2×C61—21no—
100C2×C61#167711yescharacteristic
101D61—81no—
102D61—321no—
103#509—1221no—
104#504—1221no—
105#499C2×D6111yescharacteristic
106#493—611no—
107#443—611no—
108#365—1221no—
109#364—611no—
110#364C2×D6111yescharacteristic
111#364C2×D6111yescharacteristic
112#361—1221no—
113#360—1221no—
114#357—1221no—
115#357—1221no—
116#350—1221no—
117#346—611no—
118C61#1246511yescharacteristic, complemented, Sylow
119#135—611no—
120C2×D8—1221no—
121C2×D8—1221no—
122#131—1221no—
123#127—1221no—
124#125—21no—
125SD32—2441no—
126D16—2441no—
127M32—21no—
128M32—21no—
129M32—1221no—
130M32—2441no—
131C2×C16—611no—
132C2×C16—611no—
133C2×C16—2441no—
134#108—611no—
135#107—21no—
136#106—21no—
137#104—1221no—
138C4×C8C22×D6111yescharacteristic
139#41—1221no—
140C2×D4—4881no—
141C2×D4—2441no—
142Q16—611no—
143SD16—1221no—
144D8—611no—
145D8—2441no—
146D8—2441no—
147D8—2441no—
148D8—2441no—
149M16—1221no—
150M16—2441no—
151C2×C8—2441no—
152C2×C8D4×D6111yescharacteristic
153C2×C8D4×D6111yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1175822211yescharacteristic
157C16—41no—
158C16—41no—
159C16—1221no—
160C16—1221no—
161C16—2441no—
162C23—4881no—
163Q8—1221no—
164D4—1221no—
165D4—9762no—
166D4—4881no—
167D4—4881no—
168D4—2441no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—2441no—
172C2×C4#1451975011yescharacteristic
173C8—2441no—
174C8SD16×D6111yescharacteristic
175C8#1451980011yescharacteristic
176C8#1451980011yescharacteristic
177C8#1451980411yescharacteristic
178C22—9762no—
179C22—9761no—
180C22—2441no—
181C22#1684003111yescharacteristic
182C4—41no—
183C4—161no—
184C4—2441no—
185C4#1683998011yescharacteristic
186C4#1683999411yescharacteristic
187C2—21no—
188C2—19521no—
189C2—4881no—
190C2#2144523111yescharacteristic
subgroupG/H
centerC2#21445231
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1366C2
socleC2×C61#1677
prime radical#21447896C2
hypercenter#1366D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #21448062C2semidirect
2. #21447992C2semidirect
4. #21447660C2semidirect
5. #21443886C2semidirect
6. #21443855C2semidirect
7. C61×#1366C2semidirect
97. #1366D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214480622
#214479922
#214478962
#214476602
#214438862
#214438552
C61×#13662
#1246561