Finite Group Databasebeta

← #30594079

Subgroups — #30594079

Order 15616.

196 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460691C211yesmaximal, characteristic
3#21447243C211yesmaximal, characteristic
4#16840733—21no—
5C22⋊#11758187—21no—
6C2×#14519689C2211yescharacteristic
7#16839619—21no—
8#16839525C411yescharacteristic
9#16839524—21no—
10C2×#107×C61C411yescharacteristic
11C2×#11758213—41no—
12C2×#11758187—41no—
13#14519834—22no—
14C22⋊#92420—41no—
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×D61SD1611yescharacteristic
25C22×C4×C61—41no—
26C22×C4×C61C22⋊C411yescharacteristic
27C22×Dic61—41no—
28C22×Dic61D811yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—41no—
32C2×C4×D61—41no—
33C2×#92420—42no—
34#11758213—81no—
35#11758213—81no—
36C2×C8×C61—21no—
37C2×C8×C61—41no—
38C4⋊C4×C61—41no—
39C4⋊C4×C61—41no—
40#11758198—82no—
41C4⋊Dic61—41no—
42C4⋊Dic61—41no—
43C2×#92418—21no—
44C2×#92418—41no—
45#11758187—81no—
46C23×C61#10211yescharacteristic
47C22×D61—21no—
48C22×D61—21no—
49C22×D61—21no—
50C22×D61—41no—
51C22×D61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—81no—
55C2×C4×C61—81no—
56C2×C4×C61—81no—
57C2×C4×C61#9911yescharacteristic
58C2×C4×C61#10411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—41no—
61C2×Dic61—81no—
62C2×Dic61—81no—
63C2×Dic61—81no—
64C4×D61—41no—
65C4×D61—41no—
66C4×D61—81no—
67#92420—82no—
68C8×C61—41no—
69#92418—41no—
70#7087—611nomaximal, Sylow
71C22×C61—21no—
72C22×C61—21no—
73C22×C61#32711yescharacteristic
74C22×C61#35911yescharacteristic
75C22×C61#36111yescharacteristic
76C2×D61—42no—
77C2×D61—41no—
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—81no—
81C4×C61—21no—
82C4×C61—161no—
83C4×C61#35211yescharacteristic
84C4×C61#35411yescharacteristic
85Dic61—41no—
86Dic61—161no—
87#2075—611no—
88#1314—611no—
89#1293—611no—
90C2×C61—21no—
91C2×C61—21no—
92C2×C61#134211yescharacteristic
93C2×C61#134411yescharacteristic
94C2×C61#134911yescharacteristic
95D61—81no—
96C2×#107#692311yescharacteristic
97#407—1221no—
98C2×C22⋊C8—611no—
99#380—1221no—
100C22⋊C16—1221no—
101#340—611no—
102#340—1221no—
103C61#708711yescharacteristic, complemented, Sylow
104C23×C4—611no—
105C2×M16—2441no—
106C22×C8—611no—
107C22×C8C2×#692311yescharacteristic
108C2×C4⋊C4—21no—
109C2×C4⋊C4—1221no—
110C2×C22⋊C4—2441no—
111C2×C16—2441no—
112#107—41no—
113C22⋊C8—1222no—
114C22⋊C8—2441no—
115C22⋊C8—2441no—
116#95—2441no—
117C24—611no—
118C22×C4—41no—
119C22×C4—611no—
120C22×C4—1221no—
121C22×C4—1221no—
122C22×C4—2441no—
123C22×C4—2441no—
124C22×C4—2441no—
125C22×C4C22⋊#692311yescharacteristic
126M16—4881no—
127M16—4881no—
128C2×C8—21no—
129C2×C8—41no—
130C2×C8—1221no—
131C2×C8—2442no—
132C2×C8—2441no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—2441no—
136C4⋊C4—2441no—
137C22⋊C4—4882no—
138C16—4881no—
139C23—1221no—
140C23—1221no—
141C23—1221no—
142C23—2441no—
143C23—2441no—
144C23#1451983911yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—1221no—
151C2×C4—4881no—
152C2×C4—4881no—
153C2×C4—4881no—
154C2×C4—4881no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4#1451983511yescharacteristic
159C2×C4#1451984111yescharacteristic
160C8—41no—
161C8—4882no—
162C8—2441no—
163C22—21no—
164C22—21no—
165C22—4881no—
166C22—2442no—
167C22—2441no—
168C22—2441no—
169C22—2441no—
170C22#1684061311yescharacteristic
171C22#1684067611yescharacteristic
172C22#1684068011yescharacteristic
173C4—21no—
174C4—161no—
175C4—9761no—
176C4—2441no—
177C4#1684066411yescharacteristic
178C4#1684066811yescharacteristic
179C2—21no—
180C2—21no—
181C2—4881no—
182C2#2146079511yescharacteristic
183C2#2146079911yescharacteristic
184C2#2146080911yescharacteristic
subgroupG/H
centerC22#16840613
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC2×#107×C61C4
socleC22×C61#327
prime radicalC23×D61SD16
cosocleC2×#14519689C22
hypercenterC2×#107#6923
hypocenterC61#7087
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
103. C61#7087semidirect

Maximal subgroups

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

subgroupindex
#214607402
#214606912
#214472432
#708761