Finite Group Databasebeta

← #29584820

Subgroups — #29584820

Order 15616.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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#21446643C211yesmaximal, characteristic
2#21445960C211yesmaximal, characteristic, complemented
3#21444486C212yesmaximal
4#21443678C212yesmaximal, complemented
5C61×#1281C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7#16839786C2212yes—
8C2×#14519699—22no—
9#16839628C2211yescharacteristic
10#16839527—22no—
11#16839505—24no—
12C61×#431C2212yes—
13C2×#97×C61C2211yescharacteristic
14C22×D244—21no—
15C22×D244—22no—
16C2×#11758194—22no—
17#14519774—21no—
18#14519774—22no—
19#14519774D412yes—
20C2×C4⋊Dic61—21no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23#14519699—44no—
24#14519684—22no—
25C22×C8×C61D412yes—
26C2×C42×C61C2311yescharacteristic
27C4⋊C8×C61—22no—
28C22⋊C8×C61—22no—
29#97×C61—22no—
30C4×C8×C61—22no—
31C23×D61—41no—
32C22×C4×C61C2×D411yescharacteristic
33C22×C4×C61#4112yes—
34C22×Dic61—41no—
35C2×D244—22no—
36C2×D244—24no—
37C2×D244—42no—
38C2×D244—42no—
39C2×D244—41no—
40C2×D244—42no—
41C2×D244—84no—
42C2×C8×C61—22no—
43C2×C8×C61—22no—
44C2×C8×C61—22no—
45C2×C8×C61—42no—
46C42×C61C2×D411yescharacteristic
47C42×C61#4111yescharacteristic
48C42×C61#4112yes—
49C4⋊Dic61—42no—
50#11758194—42no—
51#11758194—42no—
52C2×#92418—42no—
53C23×C61#12411yescharacteristic
54C22×D61—42no—
55C22×D61—84no—
56C22×D61—81no—
57C22×D61—81no—
58C2×C4×C61—42no—
59C2×C4×C61#12111yescharacteristic
60C2×C4×C61#12312yes—
61C2×C4×C61#12311yescharacteristic
62C2×C4×C61#12612yes—
63C2×C4×C61#13512yes—
64C2×C4×C61AGL(1,ℤ/8)12yes—
65C2×Dic61—82no—
66C2×Dic61—81no—
67D244—44no—
68D244—84no—
69D244—84no—
70D244—82no—
71C8×C61—42no—
72C8×C61—82no—
73#92418—82no—
74#10634—611nomaximal, Sylow
75C22×C61—22no—
76C22×C61#39711yescharacteristic
77C22×C61#48811yescharacteristic
78C22×C61#49011yescharacteristic
79C2×D61—82no—
80C2×D61—84no—
81C2×D61—162no—
82C2×D61—162no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61#46312yes—
86C4×C61#48212yes—
87Dic61—161no—
88#1961—611no—
89#1838—611no—
90#1545—612no—
91#1286—612no—
92#1281D6111yescharacteristic, complemented
93C2×C61—21no—
94C2×C61—21no—
95C2×C61#207311yescharacteristic
96C2×C61#208112yes—
97D61—162no—
98C2×#127—611no—
99#431C2×D6112yes—
100#423—612no—
101C2×#102—1222no—
102C2×#97C2×D6111yescharacteristic
103#382—611no—
104#341—1222no—
105#331—1224no—
106C61#1063411yescharacteristic, complemented, Sylow
107C22×D4—1221no—
108C22×D4—1222no—
109C2×M16—1222no—
110C22×C8D24412yes—
111#127—612no—
112#127—1222no—
113#127—1221no—
114C2×C4⋊C4—1221no—
115C2×C42C22×D6111yescharacteristic
116C4⋊C8—22no—
117C4⋊C8—1222no—
118C4⋊C8—1222no—
119#102—2444no—
120C22⋊C8—22no—
121#97—22no—
122C4×C8—22no—
123#95—1222no—
124C24—2441no—
125C2×D4—1222no—
126C2×D4—1224no—
127C2×D4—4884no—
128C2×D4—2441no—
129C2×D4—2442no—
130C2×D4—2442no—
131C2×D4—2442no—
132C22×C4—2441no—
133C22×C4C2×D24411yescharacteristic
134C22×C4#1175822212yes—
135M16—2442no—
136M16—2442no—
137C2×C8—22no—
138C2×C8—22no—
139C2×C8—22no—
140C2×C8—42no—
141C2×C8—2442no—
142C4⋊C4—2442no—
143C42D4×D6111yescharacteristic
144C42#1175822412yes—
145C42#1175822611yescharacteristic
146C23—4884no—
147C23—4881no—
148C23—4881no—
149C23—2442no—
150C23#1451976511yescharacteristic
151D4—4884no—
152D4—4884no—
153D4—4882no—
154D4—2444no—
155C2×C4—42no—
156C2×C4—4882no—
157C2×C4—4881no—
158C2×C4#1451975211yescharacteristic
159C2×C4#1451975912yes—
160C2×C4#1451976111yescharacteristic
161C2×C4#1451977212yes—
162C2×C4#1451979912yes—
163C2×C4#1451980512yes—
164C8—42no—
165C8—82no—
166C8—4882no—
167C22—22no—
168C22—9762no—
169C22—9762no—
170C22—4882no—
171C22—4884no—
172C22#1683968911yescharacteristic
173C22#1684011711yescharacteristic
174C22#1684012711yescharacteristic
175C4—22no—
176C4—22no—
177C4—9761no—
178C4#1683997812yes—
179C4#1684008712yes—
180C2—21no—
181C2—21no—
182C2—9762no—
183C2#2144723411yescharacteristic
184C2#2144727812yes—
subgroupG/H
centerC22#16839689
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1281C2
socleC22×C61#397
prime radicalC2×#14519774C22
hypercenter#1281D61
hypocenterC61#10634
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
2. #21445960C2semidirect
4. #21443678C2semidirect
5. C61×#1281C2semidirect
92. #1281D61semidirect
106. C61#10634semidirect

Maximal subgroups

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

subgroupindex
#214466432
#214459602
#214444862
#214436782
C61×#12812
#1063461