Finite Group Databasebeta

← #29567555

Subgroups — #29567555

Order 15616.

198 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 37 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#21447106C211yesmaximal, characteristic
2#21443770C211yesmaximal, characteristic, complemented
3C61×#1309C211yesmaximal, characteristic, complemented
4#16840562C411yescharacteristic
5C2×#14519705—21no—
6#16839744—21no—
7#16839544—21no—
8#16839520C411yescharacteristic
9C61×#423—21no—
10C61×#423C2211yescharacteristic
11C2×#11758222—21no—
12#14519810—41no—
13#14519805—41no—
14#14519799—41no—
15C2×#11758194—21no—
16#14519717—41no—
17#14519705—41no—
18#14519705—41no—
19#14519695—41no—
20#14519693—41no—
21C2×M16×C61—22no—
22C2×M16×C61C2×C411yescharacteristic
23C2×M16×C61D411yescharacteristic
24C2×C42×C61D411yescharacteristic
25C4⋊C8×C61—41no—
26C4⋊C8×C61—41no—
27C4⋊C8×C61—41no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×C22⋊D61—41no—
31#11758222—41no—
32#11758222—41no—
33#11758222—41no—
34#11758222—41no—
35C2×D244—21no—
36C2×C4×D61—41no—
37C2×Dic122—21no—
38M16×C61—41no—
39M16×C61—41no—
40M16×C61—82no—
41C2×C8×C61—21no—
42C2×C8×C61—21no—
43C2×C8×C61—42no—
44C42×C61—21no—
45C42×C61D811yescharacteristic
46C42×C61SD1611yescharacteristic
47#11758194—41no—
48#11758194—41no—
49C2×#92418—41no—
50Dic244—41no—
51D488—41no—
52#11758190—42no—
53#11758185—81no—
54C23×C61#10411yescharacteristic
55C22×D61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61#9911yescharacteristic
63C2×C4×C61#10211yescharacteristic
64C22⋊D61—81no—
65C22⋊D61—81no—
66C2×Dic61—41no—
67D244—41no—
68D244—41no—
69C4×D61—81no—
70C4×D61—81no—
71Dic122—41no—
72Dic122—41no—
73C8×C61—41no—
74C8×C61—41no—
75C8×C61—82no—
76#92418—81no—
77#7414—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—41no—
80C22×C61#32711yescharacteristic
81C2×D61—81no—
82C2×D61—161no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61AΣL(1,𝔽16)11yescharacteristic
88C4×C61#35511yescharacteristic
89Dic61—81no—
90#2050—611no—
91#1327—611no—
92#1309D6111yescharacteristic, complemented
93C2×C61—21no—
94C2×C61—41no—
95C2×C61#134511yescharacteristic
96D61—161no—
97#575—611no—
98#423—21no—
99#423C2×D6111yescharacteristic
100C2×#104—1221no—
101#413—1221no—
102#349—1221no—
103#338—611no—
104C61#741411yescharacteristic, complemented, Sylow
105C2×#41—1221no—
106#137—2441no—
107AGL(1,ℤ/8)—2441no—
108#135—2441no—
109C2×M16—22no—
110C2×M16—1221no—
111C2×M16C4×D6111yescharacteristic
112C2×M16D24411yescharacteristic
113C2×C42C22⋊D6111yescharacteristic
114M32—2441no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118#104—2441no—
119#104—2441no—
120#101—2441no—
121#100—2441no—
122#41—2441no—
123#41—2441no—
124#41—2441no—
125#41—2441no—
126C2×Q8—1221no—
127C2×D4—1221no—
128C2×D4—2441no—
129C22×C4—21no—
130C22×C4—2441no—
131C22×C4#1175819811yescharacteristic
132Q16—2441no—
133SD16—2442no—
134D8—2441no—
135M16—41no—
136M16—41no—
137M16—82no—
138M16—2441no—
139M16—2441no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—42no—
143C2×C8—2441no—
144C42—21no—
145C42#1175819911yescharacteristic
146C42#1175820111yescharacteristic
147C16—4881no—
148C23—2441no—
149C23#1451970511yescharacteristic
150Q8—2441no—
151Q8—2441no—
152D4—4881no—
153D4—4881no—
154D4—2441no—
155D4—2441no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—4881no—
163C2×C4—4881no—
164C2×C4—2441no—
165C2×C4#1451969111yescharacteristic
166C2×C4#1451969711yescharacteristic
167C8—41no—
168C8—41no—
169C8—82no—
170C8—4881no—
171C22—21no—
172C22—41no—
173C22—9761no—
174C22—4881no—
175C22#1683949511yescharacteristic
176C4—21no—
177C4—21no—
178C4—21no—
179C4—41no—
180C4—4881no—
181C4#1683955011yescharacteristic
182C4#1683955811yescharacteristic
183C2—21no—
184C2—41no—
185C2—9761no—
186C2#2144382111yescharacteristic
subgroupG/H
centerC2#21443821
commutatorC2×M16×C61C2×C4
Frattini#423C2×D61
FittingC61×#1309C2
socleC2×C61#1345
prime radical#16840562C4
cosocleC61×#423C22
hypercenter#1309D61
hypocenterC61#7414
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #21443770C2semidirect
3. C61×#1309C2semidirect
92. #1309D61semidirect
104. C61#7414semidirect

Maximal subgroups

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

subgroupindex
#214471062
#214437702
C61×#13092
#741461