Finite Group Databasebeta

← #29594418

Subgroups — #29594418

Order 15616.

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

normal subgroups only

This group has 196 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#21448062C211yesmaximal, characteristic, complemented
2#21447895C211yesmaximal, characteristic
3#21447661C211yesmaximal, characteristic, complemented
4#21443886C211yesmaximal, characteristic, complemented
5#21443880C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#2231C211yesmaximal, characteristic, complemented
8#16840197—21no—
9#16840179—21no—
10#16840139C2211yescharacteristic
11#16839583C2211yescharacteristic
12#16839583C2211yescharacteristic
13#16839574—21no—
14#16839562—21no—
15#16839562—21no—
16#16839546—21no—
17#16839538C2211yescharacteristic
18C61×#499C2211yescharacteristic
19C61×#443C2211yescharacteristic
20C61×#365—21no—
21C61×#364C2211yescharacteristic
22C61×#360—21no—
23C2×D488—21no—
24C2×D488—21no—
25#14519774—21no—
26#14519720—41no—
27#14519718—41no—
28#14519717—21no—
29#14519717—21no—
30#14519717—41no—
31C2×#11758185—41no—
32C2×#11758185D411yescharacteristic
33C2×#11758185D411yescharacteristic
34#135×C61D411yescharacteristic
35#131×C61—21no—
36#125×C61—21no—
37M32×C61—21no—
38#108×C61D411yescharacteristic
39#107×C61—21no—
40#106×C61—21no—
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
54C4⋊C4×C61—41no—
55C4⋊C4×C61—81no—
56C42×C61#4111yescharacteristic
57D488—41no—
58D488—41no—
59D488—41no—
60D488—41no—
61C16×C61—41no—
62#11758185—21no—
63#11758185—21no—
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—81no—
73C2×C4×C61#12111yescharacteristic
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—161no—
90C4×C61#46311yescharacteristic
91C4×C61#46511yescharacteristic
92#2244—611no—
93#2231D6111yescharacteristic, complemented
94#2213—611no—
95#2171—611no—
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—1221no—
105#499C2×D6111yescharacteristic
106#493—611no—
107#443C2×D6111yescharacteristic
108#365—21no—
109#364—611no—
110#364—611no—
111#364C2×D6111yescharacteristic
112#361—1221no—
113#360—21no—
114#357—1221no—
115#357—1221no—
116#350—1221no—
117#346—611no—
118C61#1246511yescharacteristic, complemented, Sylow
119#135C22⋊D6111yescharacteristic
120C2×D8—1221no—
121C2×D8—1221no—
122#131—21no—
123#127—1221no—
124#125—21no—
125SD32—2441no—
126D16—2441no—
127M32—21no—
128M32—1221no—
129M32—1221no—
130M32—2441no—
131C2×C16—611no—
132C2×C16—611no—
133C2×C16—2441no—
134#108C22⋊D6111yescharacteristic
135#107—21no—
136#106—21no—
137#104—21no—
138C4×C8C22×D6111yescharacteristic
139#41—21no—
140C2×D4—4881no—
141C2×D4—2441no—
142Q16#1175820111yescharacteristic
143SD16—21no—
144D8—2441no—
145D8—2441no—
146D8—2441no—
147D8—2441no—
148D8#1175820111yescharacteristic
149M16—21no—
150M16—41no—
151C2×C8—41no—
152C2×C8D4×D6111yescharacteristic
153C2×C8C2×C22⋊D6111yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1175822411yescharacteristic
157C16—41no—
158C16—1221no—
159C16—1221no—
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—81no—
172C2×C4#1451974911yescharacteristic
173C8—41no—
174C8C2×#1175820111yescharacteristic
175C8#1451979711yescharacteristic
176C8#1451979811yescharacteristic
177C8#1451980411yescharacteristic
178C22—41no—
179C22—9762no—
180C22—9761no—
181C22#1684003011yescharacteristic
182C4—41no—
183C4—41no—
184C4—161no—
185C4#1683997911yescharacteristic
186C4#1683999311yescharacteristic
187C2—21no—
188C2—81no—
189C2—19521no—
190C2#2144523011yescharacteristic
subgroupG/H
centerC2#21445230
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2231C2
socleC2×C61#1677
prime radical#21447895C2
hypercenter#2231D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

Complements

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

NH ≅ G/Ntype
1. #21448062C2semidirect
3. #21447661C2semidirect
4. #21443886C2semidirect
5. #21443880C2semidirect
6. #21443855C2semidirect
7. C61×#2231C2semidirect
93. #2231D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214480622
#214478952
#214476612
#214438862
#214438802
#214438552
C61×#22312
#1246561