Finite Group Databasebeta

← #29585024

Subgroups — #29585024

Order 15616.

354 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446651C211yesmaximal, characteristic
2#21445973C211yesmaximal, characteristic, complemented
3#21444590C212yesmaximal, complemented
4#21444219C212yesmaximal
5C61×#1274C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839786C2211yescharacteristic
8C2×C4⋊#92418—22no—
9C2×C4⋊#92418C2212yes—
10C2×#14519705—22no—
11#16839513—24no—
12#16839491—24no—
13C61×#431C2212yes—
14C61×#376C2211yescharacteristic
15C2×#11758222—21no—
16C2×#11758194—21no—
17C22×#92418—22no—
18#14519777Q811yescharacteristic
19#14519774Q811yescharacteristic
20#14519765—21no—
21#14519751—22no—
22C4×D244—22no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26C4⋊#92418—44no—
27#14519705—44no—
28C2×C42×C61D412yes—
29C2×C42×C61C2311yescharacteristic
30C4⋊C8×C61—22no—
31C22⋊C8×C61—22no—
32C4×C8×C61D414yes—
33#95×C61—22no—
34C22×C4×C61—22no—
35C22×C4×C61C2×D411yescharacteristic
36C22×C4×C61#4112yes—
37C2×C22⋊D61—41no—
38#11758222—42no—
39#11758222—42no—
40C2×D244—21no—
41C2×D244—22no—
42C2×C4×D61—41no—
43C2×Dic122—21no—
44C2×C8×C61—24no—
45C42×C61—22no—
46C42×C61SD1614yes—
47C42×C61C2×D412yes—
48C42×C61C2×Q811yescharacteristic
49C42×C61#4111yescharacteristic
50#11758198—42no—
51C4⋊Dic61—22no—
52#11758194—42no—
53C2×#92418—42no—
54C2×#92418—41no—
55C2×#92418—44no—
56C23×C61#12311yescharacteristic
57C22×D61—41no—
58C2×C4×C61—24no—
59C2×C4×C61—42no—
60C2×C4×C61—44no—
61C2×C4×C61C22⋊Q812yes—
62C2×C4×C61C22⋊Q811yescharacteristic
63C2×C4×C61#12312yes—
64C2×C4×C61#12711yescharacteristic
65C2×C4×C61C2×SD1612yes—
66C2×C4×C61AGL(1,ℤ/8)12yes—
67C22⋊D61—82no—
68C2×Dic61—41no—
69D244—44no—
70D244—42no—
71C4×D61—81no—
72C4×D61—81no—
73Dic122—42no—
74C8×C61—44no—
75#92418—81no—
76#92418—82no—
77#10666—611nomaximal, Sylow
78C22×C61—22no—
79C22×C61#39911yescharacteristic
80C22×C61#48112yes—
81C2×D61—81no—
82C2×D61—82no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—44no—
86C4×C61#47612yes—
87C4×C61#49211yescharacteristic
88C4×C61#49611yescharacteristic
89Dic61—81no—
90#1963—611no—
91#1843—611no—
92#1570—612no—
93#1480—612no—
94#1274D6111yescharacteristic, complemented
95C2×C61—22no—
96C2×C61#209411yescharacteristic
97C2×C61#209812yes—
98D61—161no—
99#532—611no—
100#431C2×D6112yes—
101#423—611no—
102C2×C4⋊C8—612no—
103C2×C4⋊C8—1222no—
104C2×#104—1222no—
105#376C2×D6111yescharacteristic
106#334—1224no—
107D4⋊C8—1224no—
108C61#1066611yescharacteristic, complemented, Sylow
109C2×#41—1221no—
110C2×M16—1221no—
111C22×C8—1222no—
112C4⋊Q8—611no—
113#127—611no—
114#124—1221no—
115#121—1222no—
116C4×D4—1222no—
117C2×C42D24412yes—
118C2×C42C22×D6111yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—1222no—
121C4⋊C8—1222no—
122C4⋊C8—1222no—
123C4⋊C8—2444no—
124#104—2444no—
125C22⋊C8—22no—
126C4×C8D24414yes—
127#95—22no—
128#41—2442no—
129#41—2442no—
130C2×Q8—1221no—
131C2×D4—1222no—
132C2×D4—1221no—
133C2×D4—2441no—
134C22×C4—22no—
135C22×C4—2441no—
136C22×C4C2×D24411yescharacteristic
137C22×C4#1175822412yes—
138M16—2442no—
139C2×C8—24no—
140C2×C8—2442no—
141C2×C8—2441no—
142C2×C8—2444no—
143C4⋊C4—1222no—
144C22⋊C4—2442no—
145C42—22no—
146C42#1175819014yes—
147C42C2×D24412yes—
148C42#1175822411yescharacteristic
149C42Q8×D6111yescharacteristic
150C23—2441no—
151C23#1451976111yescharacteristic
152Q8—2442no—
153D4—4882no—
154D4—2444no—
155D4—2442no—
156C2×C4—24no—
157C2×C4—42no—
158C2×C4—44no—
159C2×C4—4881no—
160C2×C4—4881no—
161C2×C4—2441no—
162C2×C4#1451975712yes—
163C2×C4#1451975711yescharacteristic
164C2×C4#1451976112yes—
165C2×C4#1451977411yescharacteristic
166C2×C4C2×#1175819012yes—
167C2×C4#1451980512yes—
168C8—44no—
169C8—4881no—
170C8—4882no—
171C22—22no—
172C22—4881no—
173C22—4882no—
174C22#1683969911yescharacteristic
175C22#1684008112yes—
176C4—22no—
177C4—22no—
178C4—44no—
179C4—4881no—
180C4#1684005312yes—
181C4#1684013511yescharacteristic
182C4#1684015111yescharacteristic
183C2—22no—
184C2—9761no—
185C2#2144735111yescharacteristic
186C2#2144737312yes—
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#399
prime radical#16840312C22
hypercenter#1274D61
hypocenterC61#10666
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #21445973C2semidirect
3. #21444590C2semidirect
5. C61×#1274C2semidirect
94. #1274D61semidirect
108. C61#10666semidirect

Maximal subgroups

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

subgroupindex
#214466512
#214459732
#214445902
#214442192
C61×#12742
#1066661