Finite Group Databasebeta

← #30594977

Subgroups — #30594977

Order 15616.

198 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460766C211yesmaximal, characteristic, complemented
2#21460727C211yesmaximal, characteristic, complemented
3#21447107C211yesmaximal, characteristic
4#16840765—21no—
5#16840658—21no—
6#16840562C411yescharacteristic
7#16839785C2211yescharacteristic
8C2×#14519703—21no—
9#16839744—21no—
10C61×#338C411yescharacteristic
11C2×#11758217—22no—
12#14519851—41no—
13#14519844—41no—
14C4⋊#92420—41no—
15C2×#11758222—21no—
16#14519810—41no—
17#14519805—41no—
18#14519799—41no—
19C2×#11758194D411yescharacteristic
20C2×C4×Dic61D411yescharacteristic
21#14519706—41no—
22#14519703—41no—
23#14519703—41no—
24#14519695—41no—
25#14519693—41no—
26C2×M16×C61—21no—
27C2×M16×C61C2×C411yescharacteristic
28C22×C4×C61C22⋊C411yescharacteristic
29C2×C22⋊D61—41no—
30C22×Dic61—21no—
31#11758222—41no—
32#11758222—41no—
33#11758222—41no—
34#11758222—41no—
35C2×D244—21no—
36C2×C4×D61—41no—
37C2×Dic122—21no—
38#11758217—82no—
39C2×#92420—42no—
40M16×C61—41no—
41M16×C61—41no—
42M16×C61—41no—
43C2×C8×C61—21no—
44C2×C8×C61—41no—
45C4×Dic61—21no—
46C4×Dic61D811yescharacteristic
47C4×Dic61SD1611yescharacteristic
48#11758194—41no—
49C2×#92418—21no—
50Dic244—41no—
51D488—41no—
52#11758190—42no—
53#11758187—81no—
54C23×C61#10411yescharacteristic
55C22×D61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61#9911yescharacteristic
59C2×C4×C61#10211yescharacteristic
60C22⋊D61—81no—
61C22⋊D61—81no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67D244—41no—
68D244—41no—
69C4×D61—81no—
70C4×D61—81no—
71Dic122—41no—
72Dic122—41no—
73#92420—82no—
74C8×C61—41no—
75C8×C61—81no—
76#92418—41no—
77#7414—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—41no—
80C22×C61#32711yescharacteristic
81C2×D61—81no—
82C2×D61—161no—
83C4×C61—21no—
84C4×C61AΣL(1,𝔽16)11yescharacteristic
85C4×C61#35511yescharacteristic
86Dic61—21no—
87Dic61—21no—
88Dic61—41no—
89Dic61—81no—
90#2050—611no—
91#1327—611no—
92#1309—611no—
93C2×C61—21no—
94C2×C61—41no—
95C2×C61#134511yescharacteristic
96D61—161no—
97#575—611no—
98#423—611no—
99#423—1221no—
100C2×#104—1221no—
101#413—1221no—
102#349—1221no—
103#338#692311yescharacteristic
104C61#741411yescharacteristic, complemented, Sylow
105C2×#41—1221no—
106#137—2441no—
107AGL(1,ℤ/8)—2441no—
108#135—2441no—
109C2×M16—21no—
110C2×M16—611no—
111C2×M16—1222no—
112C2×M16C2×#692311yescharacteristic
113C2×C42—611no—
114M32—2441no—
115C4⋊C8—2441no—
116C4⋊C8—2441no—
117C4⋊C8—2441no—
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—1221no—
130C22×C4—2441no—
131C22×C4C22⋊#692311yescharacteristic
132Q16—2441no—
133SD16—2442no—
134D8—2441no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—4882no—
139M16—2441no—
140C2×C8—21no—
141C2×C8—41no—
142C2×C8—1221no—
143C2×C8—2442no—
144C42—611no—
145C42—611no—
146C42—1221no—
147C16—4881no—
148C23—2441no—
149C23#1451984211yescharacteristic
150Q8—2441no—
151Q8—2441no—
152D4—4881no—
153D4—4881no—
154D4—2441no—
155D4—2441no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—4881no—
161C2×C4—4881no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4#1451983611yescharacteristic
166C2×C4#1451983911yescharacteristic
167C8—41no—
168C8—81no—
169C8—4882no—
170C8—2441no—
171C22—21no—
172C22—41no—
173C22—9761no—
174C22—4881no—
175C22#1684061411yescharacteristic
176C4—21no—
177C4—1221no—
178C4—1221no—
179C4—4881no—
180C4—2441no—
181C4#1684066311yescharacteristic
182C4#1684067111yescharacteristic
183C2—21no—
184C2—41no—
185C2—9761no—
186C2#2146080211yescharacteristic
subgroupG/H
centerC2#21460802
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1345
prime radical#16840562C4
cosocle#16839785C22
hypercenter#338#6923
hypocenterC61#7414
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
1. #21460766C2semidirect
2. #21460727C2semidirect
104. C61#7414semidirect

Maximal subgroups

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

subgroupindex
#214607662
#214607272
#214471072
#741461