Finite Group Databasebeta

← #30594931

Subgroups — #30594931

Order 15616.

284 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460746C211yesmaximal, characteristic, complemented
2#21460722C211yesmaximal, characteristic, complemented
3#21446951C211yesmaximal, characteristic
4#16840732—21no—
5#16840605—21no—
6#16840324C411yescharacteristic
7C2×#14519761—21no—
8C2×#14519691—21no—
9#16839623C2211yescharacteristic
10C61×#342C411yescharacteristic
11C2×#11758217—41no—
12C22⋊#92420—22no—
13C22⋊#92420—41no—
14C22⋊#92420—41no—
15C22×C22⋊D61—21no—
16C23×Dic61D411yescharacteristic
17#14519761—42no—
18#14519761—41no—
19#14519761—41no—
20#14519761—41no—
21#14519751—41no—
22#14519747—41no—
23C2×C4⋊Dic61—41no—
24C2×C22⋊Dic61D411yescharacteristic
25C2×#11758198—41no—
26#14519691—42no—
27#14519684—41no—
28C2×C22⋊C4×C61—21no—
29C2×C22⋊C4×C61C2×C411yescharacteristic
30C24×C61C22⋊C411yescharacteristic
31C23×D61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—41no—
34C2×C22⋊D61—41no—
35C2×C22⋊D61—41no—
36C2×C22⋊D61—41no—
37C2×C22⋊D61—41no—
38C2×C22⋊D61—41no—
39C2×C22⋊D61—41no—
40C22×Dic61—21no—
41C22×Dic61—21no—
42C22×Dic61—21no—
43C22×Dic61—21no—
44C22×Dic61—41no—
45C22×Dic61—41no—
46C22×Dic61D811yescharacteristic
47C22×Dic61SD1611yescharacteristic
48C2×D244—41no—
49#11758217—81no—
50#11758217—81no—
51C2×#92420—42no—
52C2×#92420—81no—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—41no—
55C22⋊C4×C61—41no—
56C22⋊Dic61—41no—
57#11758198—42no—
58#11758198—42no—
59#11758198—42no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—41no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—81no—
66C23×C61#9911yescharacteristic
67C23×C61#10211yescharacteristic
68C23×C61#10411yescharacteristic
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—82no—
73C2×C4×C61—42no—
74C2×C4×C61—41no—
75C2×C4×C61—82no—
76C2×C4×C61—81no—
77C22⋊D61—81no—
78C22⋊D61—81no—
79C22⋊D61—81no—
80C22⋊D61—81no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—81no—
92C2×Dic61—81no—
93D244—161no—
94#92420—82no—
95#92420—161no—
96#7395—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61—81no—
104C22×C61#32711yescharacteristic
105C22×C61AΣL(1,𝔽16)11yescharacteristic
106C22×C61#35311yescharacteristic
107C2×D61—82no—
108C2×D61—82no—
109C2×D61—81no—
110C2×D61—161no—
111C4×C61—81no—
112C4×C61—82no—
113Dic61—41no—
114Dic61—41no—
115Dic61—81no—
116Dic61—81no—
117#2022—611no—
118#1317—611no—
119#1306—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—41no—
124C2×C61—41no—
125C2×C61#134311yescharacteristic
126D61—161no—
127#534—611no—
128C2×#123—1221no—
129C2×#99—1221no—
130#407—1221no—
131#381—611no—
132#342#692311yescharacteristic
133#323—1221no—
134C61#739511yescharacteristic, complemented, Sylow
135C22×D4—1221no—
136C23×C4—611no—
137C2×M16—2441no—
138#123—2442no—
139#123—2441no—
140#123—2441no—
141#123—2441no—
142#121—2441no—
143#120—2441no—
144C2×C4⋊C4—2441no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—611no—
147C2×C22⋊C4—2441no—
148C2×C22⋊C4C2×#692311yescharacteristic
149#99—2442no—
150C22⋊C8—1222no—
151C22⋊C8—2441no—
152C22⋊C8—2441no—
153#95—2441no—
154C24—1221no—
155C24C22⋊#692311yescharacteristic
156C2×D4—2441no—
157C2×D4—2441no—
158C2×D4—2441no—
159C2×D4—2441no—
160C2×D4—2441no—
161C2×D4—2441no—
162C2×D4—2441no—
163C22×C4—21no—
164C22×C4—41no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—2441no—
172C22×C4—2441no—
173M16—4881no—
174M16—4881no—
175C2×C8—4881no—
176C2×C8—2442no—
177C4⋊C4—2441no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C22⋊C4—22no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—2442no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2441no—
187C23—21no—
188C23—21no—
189C23—81no—
190C23—4882no—
191C23—2441no—
192C23—2441no—
193C23—2441no—
194C23#1451983611yescharacteristic
195C23#1451983911yescharacteristic
196C23#1451984211yescharacteristic
197D4—9761no—
198D4—4881no—
199D4—4881no—
200D4—4881no—
201D4—4881no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—82no—
205C2×C4—81no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4881no—
209C2×C4—4881no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C8—9761no—
219C8—4882no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—9761no—
228C22—4882no—
229C22—4882no—
230C22—4881no—
231C22#1684061411yescharacteristic
232C22#1684066311yescharacteristic
233C22#1684066711yescharacteristic
234C4—81no—
235C4—82no—
236C4—4881no—
237C4—4881no—
238C4—2441no—
239C4—2441no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—9761no—
246C2#2146079811yescharacteristic
subgroupG/H
centerC2#21460798
commutatorC2×C22⋊C4×C61C2×C4
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#342C4
socleC2×C61#1343
prime radical#16840324C4
cosocle#16839623C22
hypercenter#342#6923
hypocenterC61#7395
LCSG ▷ C2×C22⋊C4×C61 ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #21460746C2semidirect
2. #21460722C2semidirect
134. C61#7395semidirect

Maximal subgroups

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

subgroupindex
#214607462
#214607222
#214469512
#739561