Finite Group Databasebeta

← #30594063

Subgroups — #30594063

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#21447243C211yesmaximal, 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—81no—
43#11758198—81no—
44C4⋊Dic61—41no—
45C4⋊Dic61—41no—
46C2×#92418—21no—
47C2×#92418—41no—
48#11758187—81no—
49C23×C61#10211yescharacteristic
50C22×D61—21no—
51C22×D61—21no—
52C22×D61—41no—
53C22×D61—41no—
54C22×D61D1611yescharacteristic
55C22×D61SD3211yescharacteristic
56C2×#6923—82no—
57C2×#6923—82no—
58C2×#6923—82no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—81no—
62C2×C4×C61—81no—
63C2×C4×C61—81no—
64C2×C4×C61#9911yescharacteristic
65C2×C4×C61#10411yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61—81no—
69C2×Dic61—81no—
70C2×Dic61—81no—
71C4×D61—41no—
72C4×D61—41no—
73C4×D61—81no—
74C8×C61—41no—
75#92418—41no—
76#7079—611nomaximal, Sylow
77C22×C61—21no—
78C22×C61—21no—
79C22×C61#32711yescharacteristic
80C22×C61#35711yescharacteristic
81C22×C61#36011yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—81no—
89#6923—162no—
90C4×C61—21no—
91C4×C61—161no—
92C4×C61#35211yescharacteristic
93C4×C61#35411yescharacteristic
94Dic61—41no—
95Dic61—161no—
96#2075—611no—
97#1314—611no—
98#1289—611no—
99C2×C61—21no—
100C2×C61—21no—
101C2×C61#134011yescharacteristic
102C2×C61#134411yescharacteristic
103C2×C61#134711yescharacteristic
104D61—41no—
105D61—41no—
106C2×#107#692311yescharacteristic, complemented
107C2×C22⋊C8—611no—
108#380—1221no—
109#380—1221no—
110C22⋊C16—1221no—
111#340—611no—
112#340—1221no—
113C61#707911yescharacteristic, complemented, Sylow
114C23×C4—611no—
115C22×C8—611no—
116C22×C8C2×#692311yescharacteristic
117C2×C4⋊C4—21no—
118C2×C4⋊C4—1221no—
119C2×C4⋊C4—2441no—
120C2×C22⋊C4—2441no—
121C2×C22⋊C4—2441no—
122C2×C16—2441no—
123#107—41no—
124C22⋊C8—2441no—
125#95—1222no—
126#95—2441no—
127C24—611no—
128C22×C4—41no—
129C22×C4—611no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4—2441no—
133C22×C4—2441no—
134C22×C4—2442no—
135C22×C4—2441no—
136C22×C4C22⋊#692311yescharacteristic
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—1221no—
140C2×C8—2441no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—4881no—
144C4⋊C4—4881no—
145C4⋊C4—2441no—
146C4⋊C4—2441no—
147C22⋊C4—4881no—
148C22⋊C4—4881no—
149C22⋊C4—4881no—
150C22⋊C4—4881no—
151C16—4881no—
152C23—611no—
153C23—611no—
154C23—1221no—
155C23—1221no—
156C23—2441no—
157C23—2441no—
158C23#1451983911yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—1221no—
165C2×C4—4881no—
166C2×C4—4881no—
167C2×C4—4881no—
168C2×C4—4882no—
169C2×C4—4882no—
170C2×C4—4882no—
171C2×C4—4881no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4#1451983511yescharacteristic
176C2×C4#1451984111yescharacteristic
177C8—41no—
178C8—2441no—
179C22—21no—
180C22—21no—
181C22—1221no—
182C22—1221no—
183C22—4881no—
184C22—2441no—
185C22—2441no—
186C22—2441no—
187C22—2441no—
188C22#1684061311yescharacteristic
189C22#1684067411yescharacteristic
190C22#1684067811yescharacteristic
191C4—21no—
192C4—161no—
193C4—9761no—
194C4—9762no—
195C4—2441no—
196C4#1684066411yescharacteristic
197C4#1684066811yescharacteristic
198C2—21no—
199C2—21no—
200C2—2441no—
201C2—2441no—
202C2#2146079111yescharacteristic
203C2#2146079911yescharacteristic
204C2#2146080511yescharacteristic
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#7079
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
106. C2×#107#6923semidirect
113. C61#7079semidirect

Maximal subgroups

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

subgroupindex
#214607402
#214606822
#214472432
#707961