Finite Group Databasebeta

← #30594944

Subgroups — #30594944

Order 15616.

334 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460913C211yesmaximal, characteristic, complemented
2#21460748C211yesmaximal, characteristic, complemented
3#21446890C211yesmaximal, characteristic
4C2×#14519836—21no—
5#16840607—21no—
6C22×#11758199—21no—
7C2×#14519698—21no—
8#16839664C2211yescharacteristic
9#16839517C411yescharacteristic, complemented
10C2×#127×C61C411yescharacteristic, complemented
11C2×C22⋊#6923—41no—
12#14519836—22no—
13#14519836—41no—
14C22⋊#92420—41no—
15C22×D244D411yescharacteristic
16C2×#11758199—42no—
17C2×#11758199—42no—
18C2×#11758199—41no—
19C2×#11758199—41no—
20C22×#92418—21no—
21C2×C4⋊Dic61D411yescharacteristic
22C2×#11758198—41no—
23#14519698—42no—
24C22×D4×C61—21no—
25C22×D4×C61—41no—
26#127×C61—42no—
27C2×C42×C61C2×C411yescharacteristic
28C24×C61—41no—
29C23×D61—21no—
30C22×#6923—81no—
31C2×D4×C61—22no—
32C2×D4×C61—41no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C2×D4×C61—42no—
36C2×D4×C61—42no—
37C2×D4×C61—41no—
38C2×D4×C61—41no—
39C2×D4×C61—82no—
40C2×D4×C61—82no—
41C22×C4×C61—21no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—21no—
44C2×D244—21no—
45C2×D244—41no—
46C2×D244—41no—
47C2×D244D811yescharacteristic
48C2×D244SD1611yescharacteristic
49C22⋊#6923—42no—
50C22⋊#6923—81no—
51C2×#92420—81no—
52C42×C61—41no—
53#11758199—44no—
54#11758199—44no—
55#11758198—82no—
56C4⋊Dic61—41no—
57C2×#92418—22no—
58C2×#92418—41no—
59C2×#92418—41no—
60C23×C61—42no—
61C23×C61—82no—
62C23×C61—82no—
63C23×C61—81no—
64C23×C61—81no—
65C23×C61#9911yescharacteristic
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—41no—
69C22×D61—41no—
70C22×D61—81no—
71C22×D61—81no—
72C2×#6923—82no—
73C2×#6923—161no—
74C2×#6923—161no—
75D4×C61—42no—
76D4×C61—42no—
77D4×C61—81no—
78D4×C61—81no—
79D4×C61—84no—
80D4×C61—84no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61#10411yescharacteristic
88C2×Dic61—41no—
89C2×Dic61—81no—
90D244—41no—
91D244—41no—
92D244—81no—
93#92420—161no—
94#92418—42no—
95#7402—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—84no—
99C22×C61—82no—
100C22×C61—162no—
101C22×C61—161no—
102C22×C61—161no—
103C22×C61#32711yescharacteristic
104C22×C61AΣL(1,𝔽16)11yescharacteristic
105C22×C61#35311yescharacteristic
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—81no—
109C2×D61—81no—
110C2×D61—81no—
111C2×D61—81no—
112C2×D61—161no—
113#6923—162no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—42no—
117Dic61—81no—
118#2011—611no—
119#1393—611no—
120#1318—611no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—162no—
124C2×C61#134311yescharacteristic
125C2×C61#140611yescharacteristic
126C2×C61#140811yescharacteristic
127D61—81no—
128D61—81no—
129C22×D8—1221no—
130C2×#127#692311yescharacteristic, complemented
131C2×#102—1221no—
132C2×#99—1221no—
133#390—611no—
134#336—611no—
135#324—1221no—
136C61#740211yescharacteristic, complemented, Sylow
137C22×D4—21no—
138C22×D4—41no—
139C22×D4—611no—
140C2×D8—2442no—
141C2×D8—2442no—
142C2×D8—2441no—
143C2×D8—2441no—
144C22×C8—1221no—
145#127—42no—
146C2×C4⋊C4—611no—
147C2×C22⋊C4—2441no—
148C2×C22⋊C4—2441no—
149C2×C42C2×#692311yescharacteristic
150#102—2442no—
151#99—1222no—
152#99—2441no—
153C22⋊C8—2441no—
154C24—41no—
155C24—1221no—
156C2×D4—22no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—42no—
161C2×D4—42no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—82no—
165C2×D4—82no—
166C2×D4—611no—
167C2×D4—611no—
168C2×D4—1221no—
169C2×D4—2441no—
170C2×D4—2441no—
171C22×C4—21no—
172C22×C4—1221no—
173C22×C4—4881no—
174C22×C4C22⋊#692311yescharacteristic
175D8—2444no—
176D8—2444no—
177C2×C8—1222no—
178C2×C8—4881no—
179C2×C8—2441no—
180C2×C8—2441no—
181C4⋊C4—2441no—
182C22⋊C4—4882no—
183C22⋊C4—4881no—
184C22⋊C4—2442no—
185C42—41no—
186C23—42no—
187C23—82no—
188C23—82no—
189C23—81no—
190C23—81no—
191C23—1221no—
192C23—1221no—
193C23—4881no—
194C23—4881no—
195C23—2441no—
196C23—2441no—
197C23#1451983511yescharacteristic
198D4—42no—
199D4—42no—
200D4—81no—
201D4—81no—
202D4—84no—
203D4—84no—
204D4—4881no—
205D4—2441no—
206D4—2441no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—9761no—
213C2×C4—9761no—
214C2×C4—4882no—
215C2×C4—4881no—
216C2×C4—2441no—
217C2×C4#1451983911yescharacteristic
218C2×C4#1451984111yescharacteristic
219C8—9761no—
220C8—2442no—
221C22—21no—
222C22—21no—
223C22—84no—
224C22—82no—
225C22—162no—
226C22—161no—
227C22—161no—
228C22—9761no—
229C22—4881no—
230C22—4881no—
231C22—4881no—
232C22—4881no—
233C22—2441no—
234C22—2441no—
235C22#1684061311yescharacteristic
236C22#1684066211yescharacteristic
237C22#1684066611yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—9762no—
242C4—4881no—
243C2—21no—
244C2—21no—
245C2—162no—
246C2—4881no—
247C2—4881no—
248C2#2146079711yescharacteristic
249C2#2146094611yescharacteristic
250C2#2146095011yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC2×#127×C61C4
socleC22×C61#353
prime radical#21446890C2
cosocle#16839664C22
hypercenterC2×#127#6923
hypocenterC61#7402
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21460913C2semidirect
2. #21460748C2semidirect
9. #16839517C4semidirect
10. C2×#127×C61C4semidirect
130. C2×#127#6923semidirect
136. C61#7402semidirect

Maximal subgroups

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

subgroupindex
#214609132
#214607482
#214468902
#740261