Finite Group Databasebeta

← #29567499

Subgroups — #29567499

Order 15616.

284 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 39 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#21443749C211yesmaximal, characteristic, complemented
2#21443727C211yesmaximal, characteristic, complemented
3C61×#2022C211yesmaximal, characteristic
4#16839726—21no—
5#16839486—21no—
6C61×#534C411yescharacteristic
7C2×#123×C61—21no—
8C2×#99×C61—21no—
9C61×#381C2211yescharacteristic
10C61×#342C411yescharacteristic
11C2×#11758194—41no—
12C22⋊#92418—22no—
13C22⋊#92418—41no—
14C22⋊#92418—41no—
15C22×D4×C61—21no—
16C23×C4×C61D411yescharacteristic
17#123×C61—42no—
18#123×C61—41no—
19#123×C61—41no—
20#123×C61—41no—
21#121×C61—41no—
22#120×C61—41no—
23C2×C4⋊C4×C61—41no—
24C2×C22⋊C4×C61—21no—
25C2×C22⋊C4×C61—41no—
26C2×C22⋊C4×C61C2×C411yescharacteristic
27C2×C22⋊C4×C61D411yescharacteristic
28#99×C61—42no—
29#95×C61—41no—
30C24×C61—21no—
31C24×C61C22⋊C411yescharacteristic
32C2×D4×C61—41no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C2×D4×C61—41no—
36C2×D4×C61—41no—
37C2×D4×C61—41no—
38C2×D4×C61—41no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—41no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61D811yescharacteristic
48C22×C4×C61SD1611yescharacteristic
49C4⋊C4×C61—42no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—41no—
52C22⋊C4×C61—22no—
53C22⋊C4×C61—42no—
54C22⋊C4×C61—42no—
55C22⋊C4×C61—42no—
56C22⋊C4×C61—41no—
57C22⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59#11758194—81no—
60#11758194—81no—
61C2×#92418—42no—
62C2×#92418—81no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—81no—
69C23×C61—82no—
70C23×C61#9911yescharacteristic
71C23×C61#10211yescharacteristic
72C23×C61#10411yescharacteristic
73D4×C61—81no—
74D4×C61—81no—
75D4×C61—81no—
76D4×C61—81no—
77D4×C61—161no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61—82no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94#92418—82no—
95#92418—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—82no—
105C22×C61—82no—
106C22×C61—81no—
107C22×C61—161no—
108C22×C61#32711yescharacteristic
109C22×C61AΣL(1,𝔽16)11yescharacteristic
110C22×C61#35311yescharacteristic
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—81no—
114C4×C61—81no—
115C4×C61—82no—
116C4×C61—81no—
117#2022D6111yescharacteristic
118#1317—611no—
119#1306—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—41no—
124C2×C61—41no—
125C2×C61—161no—
126C2×C61#134311yescharacteristic
127#534Dic6111yescharacteristic
128C2×#123—21no—
129C2×#99—21no—
130#407—1221no—
131#381C2×D6111yescharacteristic
132#342Dic6111yescharacteristic
133#323—1221no—
134C61#739511yescharacteristic, complemented, Sylow
135C22×D4—21no—
136C23×C4C22⋊D6111yescharacteristic
137C2×M16—2441no—
138#123—42no—
139#123—41no—
140#123—41no—
141#123—41no—
142#121—41no—
143#120—41no—
144C2×C4⋊C4—41no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4C2×Dic6111yescharacteristic
148C2×C22⋊C4C22⋊D6111yescharacteristic
149#99—42no—
150C22⋊C8—1222no—
151C22⋊C8—2441no—
152C22⋊C8—2441no—
153#95—41no—
154C24—21no—
155C24C22⋊Dic6111yescharacteristic
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#1175819911yescharacteristic
172C22×C4#1175820011yescharacteristic
173M16—4881no—
174M16—4881no—
175C2×C8—4881no—
176C2×C8—2442no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—22no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C23—21no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—82no—
194C23#1451969211yescharacteristic
195C23#1451969811yescharacteristic
196C23#1451970411yescharacteristic
197D4—81no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—161no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C8—9761no—
219C8—4882no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—82no—
228C22—82no—
229C22—81no—
230C22—161no—
231C22#1683949611yescharacteristic
232C22#1683954911yescharacteristic
233C22#1683955511yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—82no—
239C4—81no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—161no—
246C2#2144381611yescharacteristic
subgroupG/H
centerC2#21443816
commutatorC2×C22⋊C4×C61C2×C4
Frattini#381C2×D61
FittingC61×#2022C2
socleC2×C61#1343
prime radicalC61×#534C4
cosocleC61×#381C22
hypercenter#2022D61
hypocenterC61#7395
LCSG ▷ C2×C22⋊C4×C61 ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #21443749C2semidirect
2. #21443727C2semidirect
134. C61#7395semidirect

Maximal subgroups

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

subgroupindex
#214437492
#214437272
C61×#20222
#739561