Finite Group Databasebeta

← #30594509

Subgroups — #30594509

Order 15616.

376 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461680C212yesmaximal
2#21446613C211yesmaximal, characteristic
3C2×#14519836—22no—
4#16840704—22no—
5#16840640C414yescomplemented
6C2×C4×D244C2211yescharacteristic
7C2×C4⋊#92418C411yescharacteristic, complemented
8C2×#14519689—22no—
9C2×C4×C8×C61C411yescharacteristic, complemented
10C2×C4⋊#6923—42no—
11C2×C22⋊#6923—24no—
12#14519836—42no—
13#14519836—42no—
14(C2×#6923)⋊C4—42no—
15C22×D244D411yescharacteristic
16C22×C4×D61D412yes—
17C22×#92418—21no—
18C4×D244—41no—
19C4×D244—41no—
20C2×C4⋊Dic61Q811yescharacteristic
21C2×#11758198C2×C412yes—
22C4⋊#92418—41no—
23#14519689—44no—
24C22×C8×C61—21no—
25C2×C42×C61C2×C411yescharacteristic
26C4×C8×C61—41no—
27C23×D61C22⋊C412yes—
28C22×#6923—44no—
29C22×C4×C61C4211yescharacteristic
30C22×C4×C61C22⋊C411yescharacteristic
31C22×C4×C61C4⋊C411yescharacteristic
32C22×Dic61C4⋊C412yes—
33C2×D244—41no—
34C2×D244—41no—
35C2×D244D811yescharacteristic
36C2×D244SD1612yes—
37C2×D244Q1611yescharacteristic
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61—42no—
41C2×C4×D61—42no—
42C22⋊#6923—44no—
43C22⋊#6923—44no—
44C4⋊#6923—82no—
45C4⋊#6923—82no—
46C2×C8×C61—22no—
47C2×C8×C61—41no—
48C2×C8×C61—41no—
49C42×C61—21no—
50C42×C61—21no—
51#11758198—42no—
52C4⋊Dic61—41no—
53C2×#92418—42no—
54C2×#92418—41no—
55C23×C61#9511yescharacteristic
56C22×D61—22no—
57C22×D61—22no—
58C22×D61—42no—
59C22×D61—42no—
60C22×D61#10212yes—
61C22×D61#10312yes—
62C2×#6923—84no—
63C2×#6923—84no—
64C2×#6923—84no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61#9911yescharacteristic
72C2×C4×C61#9911yescharacteristic
73C2×C4×C61#10611yescharacteristic
74C2×C4×C61#10711yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—42no—
77D244—41no—
78D244—42no—
79D244—41no—
80C4×D61—42no—
81C4×D61—42no—
82C4×D61—82no—
83C8×C61—42no—
84#92418—81no—
85#7237—611nomaximal, Sylow
86C22×C61—21no—
87C22×C61—21no—
88C22×C61H(3,ℤ/4)11yescharacteristic
89C22×C61#34011yescharacteristic
90C22×C61#34211yescharacteristic
91C2×D61—22no—
92C2×D61—22no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—82no—
98#6923—164no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61#35311yescharacteristic
104C4×C61#35411yescharacteristic
105Dic61—42no—
106#1954—611no—
107#1799—612no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#128911yescharacteristic
111C2×C61#139111yescharacteristic
112C2×C61#139311yescharacteristic
113D61—42no—
114D61—42no—
115C2×C4×D4—611no—
116C2×C4⋊C8—611no—
117C2×#99—1222no—
118C2×C22⋊C8—1222no—
119C2×C4×C8#692311yescharacteristic, complemented
120#380—1222no—
121#342—614no—
122C61#723711yescharacteristic, complemented, Sylow
123C22×D4—611no—
124C23×C4—612no—
125C22×C8—21no—
126C22×C8—1221no—
127C4×D4—2441no—
128C4×D4—2441no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4—2442no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4—1224no—
133C2×C42C2×#692311yescharacteristic
134C4⋊C8—2441no—
135#99—2442no—
136#99—2442no—
137C22⋊C8—2444no—
138C4×C8—41no—
139#95—2442no—
140C24—612no—
141C2×D4—612no—
142C2×D4—611no—
143C2×D4—611no—
144C2×D4—2441no—
145C2×D4—2441no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4—1222no—
149C22×C4—2442no—
150C22×C4—2442no—
151C22×C4—2444no—
152C22×C4C4×#692311yescharacteristic
153C22×C4C4⋊#692311yescharacteristic
154C22×C4C22⋊#692311yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—2442no—
159C2×C8—2441no—
160C4⋊C4—4882no—
161C4⋊C4—4882no—
162C4⋊C4—2441no—
163C22⋊C4—2442no—
164C22⋊C4—2444no—
165C22⋊C4—2444no—
166C42—21no—
167C42—21no—
168C23—612no—
169C23—612no—
170C23—1222no—
171C23—1222no—
172C23—2442no—
173C23—2442no—
174C23(C2×#6923)⋊C411yescharacteristic
175D4—2442no—
176D4—2441no—
177D4—2441no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—1222no—
185C2×C4—4882no—
186C2×C4—4884no—
187C2×C4—4884no—
188C2×C4—4884no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4#1451983511yescharacteristic
193C2×C4#1451983611yescharacteristic
194C2×C4#1451984511yescharacteristic
195C2×C4#1451984611yescharacteristic
196C8—42no—
197C8—4881no—
198C22—21no—
199C22—21no—
200C22—1222no—
201C22—1222no—
202C22—4882no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22—2442no—
207C22#1684063011yescharacteristic
208C22#1684063611yescharacteristic
209C22#1684064011yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—9764no—
215C4—2442no—
216C4#1684066711yescharacteristic
217C4#1684066911yescharacteristic
218C2—21no—
219C2—21no—
220C2—2442no—
221C2—2442no—
222C2#2146068211yescharacteristic
223C2#2146090711yescharacteristic
224C2#2146091311yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#342
prime radicalC22×D244D4
cosocleC2×C4×D244C22
hypercenterC2×C4×C8#6923
hypocenterC61#7237
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
5. #16840640C4semidirect
7. C2×C4⋊#92418C4semidirect
9. C2×C4×C8×C61C4semidirect
119. C2×C4×C8#6923semidirect
122. C61#7237semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214466132
#723761