Finite Group Databasebeta

← #30594481

Subgroups — #30594481

Order 15616.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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#21461703C211yesmaximal, characteristic
2#21461701C211yesmaximal, characteristic
3#21447432C211yesmaximal, characteristic
4D61⋊#108—21no—
5#16840772—21no—
6#16840748—21no—
7#16840741—21no—
8#16840631C412yescomplemented
9#16840630C412yes—
10C2×#14519783C2211yescharacteristic
11C2×#14519717C411yescharacteristic, complemented
12#16839541—21no—
13#16839541—21no—
14C22×C16×C61C411yescharacteristic, complemented
15D61⋊M16—22no—
16#14519856—22no—
17#14519848—41no—
18#14519847—41no—
19#14519846—41no—
20#14519845—41no—
21#14519838—41no—
22#14519837—41no—
23#14519836—41no—
24#14519835—41no—
25C2×#11758222D411yescharacteristic
26#14519783—41no—
27#14519783—41no—
28C2×#11758194Q811yescharacteristic
29C2×#11758189C2×C411yescharacteristic
30C2×#11758189C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519717—41no—
34C2×#11758185—21no—
35C22×C8×C61C2×C411yescharacteristic
36C2×C16×C61—21no—
37C2×C16×C61—41no—
38C22×C4×C61C4⋊C411yescharacteristic
39C2×C22⋊D61D811yescharacteristic
40C2×C22⋊D61Q1611yescharacteristic
41#11758222—41no—
42#11758222—41no—
43C2×D244SD1611yescharacteristic
44C2×C4×D61C22⋊C411yescharacteristic
45C2×C4×D61C22⋊C411yescharacteristic
46C2×Dic122SD1611yescharacteristic
47C22⋊#6923—42no—
48#11758217—42no—
49C4⋊#6923—42no—
50C4×#6923—42no—
51#11758213—42no—
52D61⋊C8—42no—
53C2×C8×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61C4211yescharacteristic
56C2×C8×C61C22⋊C411yescharacteristic
57#11758194—41no—
58C2×#92418C4⋊C411yescharacteristic
59C2×#92418C4⋊C411yescharacteristic
60#11758189—41no—
61#11758189—41no—
62C8×D61—21no—
63C8×D61—21no—
64C8×D61—21no—
65C8×D61—21no—
66C16×C61—41no—
67#11758185—41no—
68C23×C61#10711yescharacteristic
69C22×D61#10211yescharacteristic
70C22×D61#10311yescharacteristic
71C2×#6923—82no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61#9511yescharacteristic
75C2×C4×C61#10611yescharacteristic
76C22⋊D61—41no—
77C22⋊D61—41no—
78C2×Dic61#10211yescharacteristic
79C2×Dic61#10311yescharacteristic
80D244—41no—
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—21no—
84C4×D61—21no—
85Dic122—41no—
86#92420—82no—
87C8×C61—21no—
88C8×C61#9911yescharacteristic
89C8×C61#9911yescharacteristic
90#92418—21no—
91#92418—21no—
92#7227—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—41no—
95C22×C61#34011yescharacteristic
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—41no—
99C2×D61—41no—
100#6923—162no—
101C4×C61—21no—
102C4×C61H(3,ℤ/4)11yescharacteristic
103C4×C61#34211yescharacteristic
104Dic61—21no—
105Dic61—21no—
106#2113—611no—
107#1813—611no—
108#1812—611no—
109C2×C61—21no—
110C2×C61—41no—
111C2×C61#128911yescharacteristic
112D61—41no—
113D61—41no—
114C2×#131—611no—
115C2×M32—611no—
116C22×C16#692311yescharacteristic, complemented
117C2×#108—1221no—
118#427—1221no—
119#413—1221no—
120#410—1221no—
121C22⋊C16—1221no—
122C22⋊C16—1221no—
123#338—612no—
124H(3,ℤ/4)—612no—
125C61#722711yescharacteristic, complemented, Sylow
126C2×#41—611no—
127#131—2441no—
128#131—2441no—
129C2×M16—611no—
130C2×M16—611no—
131C2×M16—611no—
132C2×M16—1222no—
133C22×C8—611no—
134C22×C8—611no—
135C22×C8C2×#692311yescharacteristic
136#117—1222no—
137M32—2441no—
138C2×C16—21no—
139C2×C16—41no—
140C2×C16—1221no—
141#108—2441no—
142#108—2441no—
143#107—2441no—
144#106—2441no—
145#101—2441no—
146#100—2441no—
147#99—2441no—
148#99—2441no—
149#41—2441no—
150#41—2441no—
151C2×Q8—611no—
152C2×D4—611no—
153C2×D4—611no—
154C2×D4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4C4⋊#692311yescharacteristic
158M16—2441no—
159M16—2441no—
160M16—2441no—
161M16—2442no—
162M16—2442no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8—1221no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8—2442no—
172C2×C8C4×#692311yescharacteristic
173C2×C8C22⋊#692311yescharacteristic
174C4⋊C4—2442no—
175C22⋊C4—2442no—
176C42—2442no—
177C16—41no—
178C16—2441no—
179C23—611no—
180C23—611no—
181C23#1451984611yescharacteristic
182Q8—2441no—
183D4—2441no—
184D4—2441no—
185D4—2441no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—4882no—
195C2×C4(C2×#6923)⋊C411yescharacteristic
196C2×C4#1451984511yescharacteristic
197C8—21no—
198C8—1221no—
199C8—1221no—
200C8—4882no—
201C8#1451983511yescharacteristic
202C8#1451983611yescharacteristic
203C22—21no—
204C22—41no—
205C22—1221no—
206C22—1221no—
207C22—2441no—
208C22—2441no—
209C22#1684063611yescharacteristic
210C4—21no—
211C4—1221no—
212C4—1221no—
213C4—9762no—
214C4#1684063011yescharacteristic
215C4#1684064011yescharacteristic
216C2—21no—
217C2—41no—
218C2—2441no—
219C2—2441no—
220C2#2146068211yescharacteristic
subgroupG/H
centerC4#16840630
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC22×C16×C61C4
socleC2×C61#1289
prime radicalC2×#11758222D4
cosocleC2×#14519783C22
hypercenterC22×C16#6923
hypocenterC61#7227
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
8. #16840631C4semidirect
11. C2×#14519717C4semidirect
14. C22×C16×C61C4semidirect
116. C22×C16#6923semidirect
125. C61#7227semidirect

Maximal subgroups

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

subgroupindex
#214617032
#214617012
#214474322
#722761