Finite Group Databasebeta

← #30594955

Subgroups — #30594955

Order 15616.

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

normal subgroups only

This group has 240 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#21460911C211yesmaximal, characteristic, complemented
2#21460742C211yesmaximal, characteristic, complemented
3#21446924C211yesmaximal, characteristic
4#16840748—21no—
5C22⋊#11758187—21no—
6#16840562—21no—
7#16840562C411yescharacteristic
8#16839730—21no—
9#16839730C2211yescharacteristic
10C61×#338C411yescharacteristic
11D61⋊M16—41no—
12C2×#11758187—41no—
13#14519838—41no—
14#14519837—22no—
15C2×#11758222—21no—
16C2×#11758222D411yescharacteristic
17#14519810—41no—
18#14519810—41no—
19#14519810—41no—
20#14519805—41no—
21#14519805—41no—
22#14519805—41no—
23#14519799—41no—
24#14519799—42no—
25C22×#92418D411yescharacteristic
26#14519689—41no—
27#14519689—42no—
28C2×M16×C61—21no—
29C2×M16×C61C2×C411yescharacteristic
30C22×C4×C61C22⋊C411yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—41no—
33#11758222—41no—
34#11758222—41no—
35#11758222—41no—
36#11758222—41no—
37#11758222—41no—
38#11758222—41no—
39C2×D244—21no—
40C2×D244SD1611yescharacteristic
41C2×C4×D61—21no—
42C2×C4×D61—41no—
43C2×Dic122—21no—
44C2×Dic122D811yescharacteristic
45#11758217—42no—
46#11758213—81no—
47D61⋊C8—81no—
48M16×C61—41no—
49M16×C61—41no—
50M16×C61—41no—
51C2×C8×C61—22no—
52C2×C8×C61—21no—
53C2×#92418—21no—
54C2×#92418—41no—
55Dic244—42no—
56Dic244—41no—
57D488—42no—
58D488—41no—
59#11758190—42no—
60#11758190—42no—
61#11758190—42no—
62#11758187—81no—
63C23×C61#10411yescharacteristic
64C22×D61—21no—
65C22×D61—41no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61#9911yescharacteristic
69C2×C4×C61#10211yescharacteristic
70C22⋊D61—81no—
71C22⋊D61—81no—
72C22⋊D61—81no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75D244—41no—
76D244—41no—
77D244—41no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—81no—
81C4×D61—81no—
82Dic122—41no—
83Dic122—41no—
84Dic122—41no—
85#92420—82no—
86C8×C61—42no—
87C8×C61—41no—
88#92418—41no—
89#7407—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—41no—
92C22×C61#32711yescharacteristic
93C2×D61—41no—
94C2×D61—81no—
95C2×D61—82no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61AΣL(1,𝔽16)11yescharacteristic
99C4×C61#35311yescharacteristic
100Dic61—41no—
101Dic61—81no—
102#2017—611no—
103#1392—611no—
104#1315—611no—
105C2×C61—21no—
106C2×C61—41no—
107C2×C61#134311yescharacteristic
108D61—81no—
109D61—161no—
110#575—611no—
111#575—1221no—
112#413—1221no—
113#408—611no—
114#408—1221no—
115C22⋊C16—1221no—
116#338#692311yescharacteristic
117C61#740711yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C2×#41—1221no—
120#137—2441no—
121#137—2441no—
122#137—2441no—
123AGL(1,ℤ/8)—2441no—
124AGL(1,ℤ/8)—2441no—
125AGL(1,ℤ/8)—2441no—
126#135—2441no—
127#135—2442no—
128C2×M16—21no—
129C2×M16—2441no—
130C2×M16C2×#692311yescharacteristic
131C22×C8—611no—
132C2×C16—2441no—
133#101—2441no—
134#100—1222no—
135C22⋊C8—2441no—
136C22⋊C8—2442no—
137#41—2441no—
138#41—2441no—
139#41—2441no—
140#41—2441no—
141#41—2441no—
142#41—2441no—
143C2×Q8—611no—
144C2×Q8—1221no—
145C2×D4—611no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—2441no—
149C22×C4—1221no—
150C22×C4—2441no—
151C22×C4C22⋊#692311yescharacteristic
152Q16—2441no—
153Q16—2442no—
154SD16—2442no—
155SD16—2442no—
156SD16—2442no—
157D8—2441no—
158D8—2442no—
159M16—41no—
160M16—41no—
161M16—41no—
162M16—4881no—
163M16—2442no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—1221no—
167C2×C8—4881no—
168C2×C8—2441no—
169C16—4881no—
170C23—1221no—
171C23—2441no—
172C23#1451984211yescharacteristic
173Q8—2441no—
174Q8—2441no—
175Q8—2441no—
176D4—4881no—
177D4—4881no—
178D4—4881no—
179D4—2441no—
180D4—2441no—
181D4—2441no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—1221no—
185C2×C4—4881no—
186C2×C4—4881no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4#1451983611yescharacteristic
191C2×C4#1451983911yescharacteristic
192C8—42no—
193C8—41no—
194C8—4882no—
195C8—2441no—
196C22—21no—
197C22—41no—
198C22—4881no—
199C22—4882no—
200C22—4881no—
201C22—2441no—
202C22#1684061411yescharacteristic
203C4—21no—
204C4—4881no—
205C4—2441no—
206C4#1684066311yescharacteristic
207C4#1684066711yescharacteristic
208C2—21no—
209C2—41no—
210C2—9761no—
211C2—4881no—
212C2#2146079811yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1343
prime radical#21446924C2
cosocle#16839730C22
hypercenter#338#6923
hypocenterC61#7407
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
1. #21460911C2semidirect
2. #21460742C2semidirect
117. C61#7407semidirect

Maximal subgroups

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

subgroupindex
#214609112
#214607422
#214469242
#740761