Finite Group Databasebeta

← #30594059

Subgroups — #30594059

Order 15616.

218 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 42 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#21460740C211yesmaximal, characteristic
2#21460682C211yesmaximal, characteristic
3#21447248C211yesmaximal, characteristic
4#16840704—21no—
5C22⋊#11758187—21no—
6C2×#14519689C2211yescharacteristic
7#16839619—21no—
8#16839525C411yescharacteristic, complemented
9#16839524—21no—
10C2×#107×C61C411yescharacteristic, complemented
11C2×C4⋊#6923—41no—
12C2×C22⋊#6923—41no—
13C2×#11758187—41no—
14(C2×#6923)⋊C4—22no—
15C22×C4×D61D411yescharacteristic
16C22×#92418D411yescharacteristic
17C2×C4⋊Dic61—21no—
18C2×#11758198—41no—
19#14519689—41no—
20#14519684—41no—
21C22×C8×C61C2×C411yescharacteristic
22C2×C4⋊C4×C61—21no—
23#107×C61—41no—
24C23×D61D811yescharacteristic
25C22×#6923—42no—
26C22×C4×C61—41no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×Dic61—41no—
29C22×Dic61SD1611yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—41no—
33C2×C4×D61—41no—
34C22⋊#6923—81no—
35C22⋊#6923—81no—
36C4⋊#6923—81no—
37C4⋊#6923—81no—
38C2×C8×C61—21no—
39C2×C8×C61—41no—
40C4⋊C4×C61—41no—
41C4⋊C4×C61—41no—
42#11758198—82no—
43C4⋊Dic61—41no—
44C4⋊Dic61—41no—
45C2×#92418—21no—
46C2×#92418—41no—
47#11758187—81no—
48C23×C61#10211yescharacteristic
49C22×D61—21no—
50C22×D61—21no—
51C22×D61—41no—
52C22×D61—41no—
53C22×D61SD3211yescharacteristic
54C22×D61Q3211yescharacteristic
55C2×#6923—82no—
56C2×#6923—82no—
57C2×#6923—82no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—81no—
61C2×C4×C61—81no—
62C2×C4×C61—81no—
63C2×C4×C61#9911yescharacteristic
64C2×C4×C61#10411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—41no—
67C2×Dic61—81no—
68C2×Dic61—81no—
69C2×Dic61—81no—
70C4×D61—41no—
71C4×D61—41no—
72C4×D61—81no—
73C8×C61—41no—
74#92418—41no—
75#7077—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61#32711yescharacteristic
79C22×C61#35811yescharacteristic
80C22×C61#36011yescharacteristic
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—81no—
88#6923—162no—
89C4×C61—21no—
90C4×C61—161no—
91C4×C61#35211yescharacteristic
92C4×C61#35411yescharacteristic
93Dic61—41no—
94Dic61—161no—
95#2076—611no—
96#1314—611no—
97#1289—611no—
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#133911yescharacteristic
101C2×C61#134411yescharacteristic
102C2×C61#134811yescharacteristic
103D61—41no—
104D61—41no—
105C2×#107#692311yescharacteristic, complemented
106C2×C22⋊C8—611no—
107#380—1221no—
108#380—1221no—
109C22⋊C16—1221no—
110#340—611no—
111#340—1221no—
112C61#707711yescharacteristic, complemented, Sylow
113C23×C4—611no—
114C22×C8—611no—
115C22×C8C2×#692311yescharacteristic
116C2×C4⋊C4—21no—
117C2×C4⋊C4—1221no—
118C2×C4⋊C4—2441no—
119C2×C22⋊C4—2441no—
120C2×C22⋊C4—2441no—
121C2×C16—2441no—
122#107—41no—
123C22⋊C8—2441no—
124#95—1222no—
125#95—2441no—
126C24—611no—
127C22×C4—41no—
128C22×C4—611no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4—2441no—
132C22×C4—2441no—
133C22×C4—2442no—
134C22×C4—2441no—
135C22×C4C22⋊#692311yescharacteristic
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—1221no—
139C2×C8—2441no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—4881no—
143C4⋊C4—4881no—
144C4⋊C4—2441no—
145C4⋊C4—2441no—
146C22⋊C4—4882no—
147C22⋊C4—4881no—
148C22⋊C4—4881no—
149C16—4881no—
150C23—611no—
151C23—611no—
152C23—1221no—
153C23—1221no—
154C23—2441no—
155C23—2441no—
156C23#1451983911yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—1221no—
163C2×C4—4881no—
164C2×C4—4881no—
165C2×C4—4881no—
166C2×C4—4882no—
167C2×C4—4882no—
168C2×C4—4882no—
169C2×C4—4881no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4#1451983511yescharacteristic
174C2×C4#1451984111yescharacteristic
175C8—41no—
176C8—2441no—
177C22—21no—
178C22—21no—
179C22—1221no—
180C22—1221no—
181C22—4881no—
182C22—2441no—
183C22—2441no—
184C22—2441no—
185C22—2441no—
186C22#1684061311yescharacteristic
187C22#1684067511yescharacteristic
188C22#1684067911yescharacteristic
189C4—21no—
190C4—161no—
191C4—9761no—
192C4—9762no—
193C4—2441no—
194C4#1684066411yescharacteristic
195C4#1684066811yescharacteristic
196C2—21no—
197C2—21no—
198C2—2441no—
199C2—2441no—
200C2#2146078911yescharacteristic
201C2#2146079911yescharacteristic
202C2#2146080711yescharacteristic
subgroupG/H
centerC22#16840613
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC2×#107×C61C4
socleC22×C61#327
prime radicalC23×D61D8
cosocleC2×#14519689C22
hypercenterC2×#107#6923
hypocenterC61#7077
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
8. #16839525C4semidirect
10. C2×#107×C61C4semidirect
105. C2×#107#6923semidirect
112. C61#7077semidirect

Maximal subgroups

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

subgroupindex
#214607402
#214606822
#214472482
#707761