Finite Group Databasebeta

← #30594652

Subgroups — #30594652

Order 15616.

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

normal subgroups only

This group has 402 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
1C4×#14519836C212yesmaximal
2#21446617C211yesmaximal, characteristic
3C2×#14519836—22no—
4C4×C22⋊#6923—22no—
5#16840640C414yescomplemented
6C2×C4×D244C2211yescharacteristic
7C2×C4⋊#92418C411yescharacteristic, complemented
8C2×#14519689—22no—
9C2×#97×C61C411yescharacteristic, complemented
10C2×C22⋊#6923—24no—
11C2×C4×#6923—42no—
12#14519836—28no—
13(C2×#6923)⋊C4—42no—
14C22×D244D411yescharacteristic
15C22×C4×D61D412yes—
16C22×#92418—21no—
17C4×D244—41no—
18C4×D244—41no—
19C2×C4⋊Dic61Q811yescharacteristic
20C2×#11758198C2×C412yes—
21C4⋊#92418—41no—
22#14519689—44no—
23C22×C8×C61—21no—
24C2×C42×C61C2×C411yescharacteristic
25#97×C61—41no—
26C23×D61C22⋊C412yes—
27C22×#6923—44no—
28C22×C4×C61C4211yescharacteristic
29C22×C4×C61C22⋊C411yescharacteristic
30C22×C4×C61C4⋊C411yescharacteristic
31C22×Dic61C4⋊C412yes—
32C2×D244—24no—
33C2×D244—41no—
34C2×C4×D61—22no—
35C2×C4×D61—22no—
36C2×C4×D61—42no—
37C2×C4×D61—42no—
38C22⋊#6923—28no—
39C22⋊#6923—44no—
40C4×#6923—82no—
41C4×#6923—82no—
42C2×C8×C61—22no—
43C2×C8×C61—41no—
44C2×C8×C61—41no—
45C42×C61—21no—
46C42×C61—21no—
47#11758198—42no—
48C4⋊Dic61—41no—
49C2×#92418—42no—
50C2×#92418—41no—
51C23×C61#9511yescharacteristic
52C22×D61—22no—
53C22×D61—22no—
54C22×D61—42no—
55C22×D61—42no—
56C22×D61#10414yes—
57C2×#6923—48no—
58C2×#6923—84no—
59C2×#6923—84no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61#9911yescharacteristic
67C2×C4×C61#9911yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—42no—
70D244—44no—
71C4×D61—42no—
72C4×D61—42no—
73C4×D61—82no—
74C8×C61—42no—
75#92418—81no—
76#7283—611nomaximal, Sylow
77C22×C61—21no—
78C22×C61—21no—
79C22×C61#33912yes—
80C22×C61#34211yescharacteristic
81C2×D61—24no—
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—44no—
85C2×D61—82no—
86#6923—88no—
87C4×C61—21no—
88C4×C61—41no—
89C4×C61—41no—
90C4×C61#35311yescharacteristic
91C4×C61#35411yescharacteristic
92Dic61—42no—
93#1955—611no—
94C4×#99—612no—
95C2×C61—22no—
96C2×C61#129711yescharacteristic
97C2×C61#139111yescharacteristic
98C2×C61#139311yescharacteristic
99D61—44no—
100C2×C4×D4—611no—
101C2×C4⋊C8—611no—
102C2×#99—1222no—
103C2×C22⋊C8—1222no—
104C2×#97#692311yescharacteristic, complemented
105C4×C22⋊C4—1222no—
106#342—614no—
107C61#728311yescharacteristic, complemented, Sylow
108C22×D4—611no—
109C23×C4—612no—
110C22×C8—21no—
111C22×C8—1221no—
112C4×D4—2441no—
113C4×D4—2441no—
114C2×C4⋊C4—611no—
115C2×C22⋊C4—612no—
116C2×C22⋊C4—1224no—
117C2×C42—2442no—
118C2×C42C2×#692311yescharacteristic
119C4⋊C8—2441no—
120#99—1228no—
121C22⋊C8—2444no—
122#97—41no—
123#95—2442no—
124C24—612no—
125C2×D4—1224no—
126C2×D4—2441no—
127C22×C4—612no—
128C22×C4—1222no—
129C22×C4—1222no—
130C22×C4—2442no—
131C22×C4—2442no—
132C22×C4—2444no—
133C22×C4C4×#692311yescharacteristic
134C22×C4C4⋊#692311yescharacteristic
135C22×C4C22⋊#692311yescharacteristic
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—2442no—
140C2×C8—2441no—
141C4⋊C4—2441no—
142C22⋊C4—1228no—
143C22⋊C4—2442no—
144C22⋊C4—2444no—
145C42—21no—
146C42—21no—
147C42—4882no—
148C42—4882no—
149C23—614no—
150C23—1222no—
151C23—1222no—
152C23—2442no—
153C23—2442no—
154C23(C2×#6923)⋊C411yescharacteristic
155D4—2444no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—1222no—
163C2×C4—4882no—
164C2×C4—4884no—
165C2×C4—4884no—
166C2×C4—2448no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4#1451983511yescharacteristic
171C2×C4#1451983611yescharacteristic
172C8—42no—
173C8—4881no—
174C22—21no—
175C22—21no—
176C22—1224no—
177C22—4882no—
178C22—2444no—
179C22—2442no—
180C22—2442no—
181C22#1684063412yes—
182C22#1684064011yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—4888no—
187C4—2442no—
188C4#1684066711yescharacteristic
189C4#1684066911yescharacteristic
190C2—22no—
191C2—2444no—
192C2#2146069911yescharacteristic
193C2#2146090811yescharacteristic
194C2#2146091311yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC22×C61#342
prime radicalC22×D244D4
cosocleC2×C4×D244C22
hypercenterC2×#97#6923
hypocenterC61#7283
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
5. #16840640C4semidirect
7. C2×C4⋊#92418C4semidirect
9. C2×#97×C61C4semidirect
104. C2×#97#6923semidirect
107. C61#7283semidirect

Maximal subgroups

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

subgroupindex
C4×#145198362
#214466172
#728361