Finite Group Databasebeta

← #29584792

Subgroups — #29584792

Order 15616.

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

normal subgroups only

This group has 310 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#21446651C211yesmaximal, characteristic
2#21444469C212yesmaximal
3#21443716C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#1832C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9C2×#14519705—22no—
10#16839509—22no—
11#16839505—22no—
12C2×C4⋊C8×C61C2212yes—
13C61×#376C2211yescharacteristic
14C61×#336—22no—
15C2×#11758222—21no—
16C2×#11758194—21no—
17#14519777D411yescharacteristic
18#14519774D411yescharacteristic
19#14519765—21no—
20#14519751—22no—
21C4×D244—22no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24#14519705—44no—
25C22⋊#92418—22no—
26C4×#92418—22no—
27C22×C8×C61—22no—
28C2×C42×C61D412yes—
29C2×C42×C61C2311yescharacteristic
30C4⋊C8×C61—22no—
31C4⋊C8×C61—22no—
32#95×C61—22no—
33C22×C4×C61—22no—
34C22×C4×C61C2×D411yescharacteristic
35C22×C4×C61#4112yes—
36C2×C22⋊D61—41no—
37#11758222—42no—
38#11758222—42no—
39C2×D244—21no—
40C2×D244—22no—
41C2×C4×D61—41no—
42C2×Dic122—21no—
43C2×C8×C61—42no—
44C2×C8×C61—42no—
45C2×C8×C61—42no—
46C42×C61—22no—
47C42×C61—22no—
48C42×C61C2×D411yescharacteristic
49C42×C61#4111yescharacteristic
50C42×C61#4112yes—
51#11758198—42no—
52C4⋊Dic61—22no—
53#11758194—42no—
54C2×#92418—42no—
55C2×#92418—41no—
56C23×C61#12311yescharacteristic
57C22×D61—41no—
58C2×C4×C61—42no—
59C2×C4×C61—44no—
60C2×C4×C61—42no—
61C2×C4×C61#12111yescharacteristic
62C2×C4×C61#12312yes—
63C2×C4×C61#12411yescharacteristic
64C2×C4×C61#12612yes—
65C2×C4×C61#13512yes—
66C2×C4×C61AGL(1,ℤ/8)12yes—
67C22⋊D61—82no—
68C2×Dic61—41no—
69D244—42no—
70D244—82no—
71C4×D61—81no—
72C4×D61—81no—
73Dic122—42no—
74C8×C61—82no—
75#92418—82no—
76#92418—81no—
77#10629—611nomaximal, Sylow
78C22×C61—22no—
79C22×C61#39711yescharacteristic
80C22×C61#48212yes—
81C2×D61—81no—
82C2×D61—82no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—82no—
86C4×C61#46312yes—
87C4×C61#48811yescharacteristic
88C4×C61#49011yescharacteristic
89Dic61—81no—
90#1963—611no—
91#1832D6111yescharacteristic, complemented
92#1540—612no—
93#1301—612no—
94#1274—611no—
95C2×C61—22no—
96C2×C61#207311yescharacteristic
97C2×C61#208012yes—
98D61—161no—
99#532—611no—
100#431—612no—
101#423—611no—
102C2×C4⋊C8C2×D6112yes—
103C2×#104—1222no—
104#376C2×D6111yescharacteristic
105#336—22no—
106#332—1222no—
107#331—1222no—
108C61#1062911yescharacteristic, complemented, Sylow
109C2×#41—1221no—
110C2×M16—1221no—
111C22×C8—22no—
112C4⋊Q8—611no—
113#127—611no—
114#124—1221no—
115#121—1222no—
116C4×D4—1222no—
117C2×C42C22⋊D6112yes—
118C2×C42C22×D6111yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—1222no—
122C4⋊C8—1222no—
123#104—2444no—
124C22⋊C8—1222no—
125C4×C8—1222no—
126#95—22no—
127#41—2442no—
128#41—2442no—
129C2×Q8—1221no—
130C2×D4—1221no—
131C2×D4—1222no—
132C2×D4—2441no—
133C22×C4—22no—
134C22×C4—2441no—
135C22×C4#1175822212yes—
136C22×C4C2×C22⋊D6111yescharacteristic
137M16—2442no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8—2442no—
142C2×C8—2441no—
143C4⋊C4—1222no—
144C22⋊C4—2442no—
145C42—22no—
146C42—22no—
147C42D4×D6111yescharacteristic
148C42#1175822411yescharacteristic
149C42#1175822612yes—
150C23—2441no—
151C23#1451976011yescharacteristic
152Q8—2442no—
153D4—4882no—
154D4—4882no—
155D4—2442no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—4881no—
160C2×C4—4881no—
161C2×C4—2441no—
162C2×C4#1451974811yescharacteristic
163C2×C4#1451976212yes—
164C2×C4#1451976611yescharacteristic
165C2×C4#1451977212yes—
166C2×C4#1451979712yes—
167C2×C4#1451980212yes—
168C8—82no—
169C8—4882no—
170C8—4881no—
171C22—22no—
172C22—4881no—
173C22—4882no—
174C22#1683968811yescharacteristic
175C22#1684008612yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—4881no—
180C4#1683997412yes—
181C4#1684011911yescharacteristic
182C4#1684012811yescharacteristic
183C2—22no—
184C2—9761no—
185C2#2144723311yescharacteristic
186C2#2144727012yes—
subgroupG/H
centerC2×C4#14519766
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1832C2
socleC22×C61#397
prime radical#16840312C22
hypercenter#1832D61
hypocenterC61#10629
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #21443716C2semidirect
4. #21443648C2semidirect
5. C61×#1832C2semidirect
91. #1832D61semidirect
108. C61#10629semidirect

Maximal subgroups

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

subgroupindex
#214466512
#214444692
#214437162
#214436482
C61×#18322
#1062961