Finite Group Databasebeta

← #29567498

Subgroups — #29567498

Order 15616.

284 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 37 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#21446950C211yesmaximal, characteristic
2#21443749C211yesmaximal, characteristic, complemented
3C61×#1306C211yesmaximal, characteristic, complemented
4#16840324C411yescharacteristic
5C2×#14519760—21no—
6C2×#14519691—21no—
7#16839529C411yescharacteristic
8#16839486—21no—
9C61×#407—21no—
10C61×#381C2211yescharacteristic
11C22×C22⋊D61—21no—
12#14519761—41no—
13#14519760—42no—
14#14519760—41no—
15#14519760—41no—
16#14519751—41no—
17#14519747—41no—
18C2×#11758196—41no—
19C2×C22⋊Dic61—21no—
20C2×#11758198—41no—
21#14519691—42no—
22C22⋊#92418—41no—
23C23×C4×C61D411yescharacteristic
24C2×M16×C61—41no—
25C2×C22⋊C4×C61C2×C411yescharacteristic
26C2×C22⋊C4×C61D411yescharacteristic
27C22⋊C8×C61—22no—
28C22⋊C8×C61—41no—
29#95×C61—41no—
30C24×C61C22⋊C411yescharacteristic
31C23×D61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61—21no—
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61D811yescharacteristic
39C22×C4×C61SD1611yescharacteristic
40C2×C22⋊D61—41no—
41C2×C22⋊D61—41no—
42C2×C22⋊D61—41no—
43C2×C22⋊D61—41no—
44C2×C22⋊D61—41no—
45C2×C22⋊D61—41no—
46C22×Dic61—21no—
47C22×Dic61—41no—
48C2×D244—41no—
49M16×C61—81no—
50M16×C61—81no—
51C2×C8×C61—42no—
52C22⋊C4×C61—41no—
53C22⋊C4×C61—41no—
54C22⋊Dic61—22no—
55C22⋊Dic61—41no—
56#11758198—42no—
57#11758198—42no—
58#11758198—42no—
59C4⋊Dic61—41no—
60#11758196—42no—
61#11758196—42no—
62C2×#92418—81no—
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—21no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—81no—
82C2×C4×C61—81no—
83C2×C4×C61—81no—
84C22⋊D61—81no—
85C22⋊D61—81no—
86C22⋊D61—81no—
87C22⋊D61—81no—
88C2×Dic61—41no—
89C2×Dic61—42no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—82no—
93D244—161no—
94C8×C61—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#32711yescharacteristic
105C22×C61AΣL(1,𝔽16)11yescharacteristic
106C22×C61#35311yescharacteristic
107C2×D61—82no—
108C2×D61—82no—
109C2×D61—81no—
110C2×D61—161no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—81no—
114C4×C61—81no—
115Dic61—82no—
116Dic61—81no—
117#2022—611no—
118#1317—611no—
119#1306D6111yescharacteristic, complemented
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—21no—
131#381C2×D6111yescharacteristic
132#342—611no—
133#323—1221no—
134C61#739511yescharacteristic, complemented, Sylow
135C22×D4—1221no—
136C23×C4C22⋊D6111yescharacteristic
137C2×M16—41no—
138#123—2441no—
139#123—2442no—
140#123—2441no—
141#123—2441no—
142#121—2441no—
143#120—2441no—
144C2×C4⋊C4—2441no—
145C2×C22⋊C4—1221no—
146C2×C22⋊C4—2441no—
147C2×C22⋊C4C4×D6111yescharacteristic
148C2×C22⋊C4D24411yescharacteristic
149#99—2442no—
150C22⋊C8—22no—
151C22⋊C8—41no—
152C22⋊C8—2441no—
153#95—41no—
154C24—1221no—
155C24#1175819811yescharacteristic
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—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—1221no—
170C22×C4—2441no—
171C22×C4#1175819911yescharacteristic
172C22×C4#1175820111yescharacteristic
173M16—81no—
174M16—81no—
175C2×C8—42no—
176C2×C8—4881no—
177C4⋊C4—2441no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—1222no—
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#1451969111yescharacteristic
195C23#1451969711yescharacteristic
196C23#1451970511yescharacteristic
197D4—9761no—
198D4—4881no—
199D4—4881no—
200D4—4881no—
201D4—4881no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—4882no—
214C2×C4—2442no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C8—82no—
219C8—9761no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—9761no—
228C22—4882no—
229C22—4882no—
230C22—4881no—
231C22#1683949511yescharacteristic
232C22#1683954811yescharacteristic
233C22#1683955411yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—4882no—
239C4—4881no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—9761no—
246C2#2144381511yescharacteristic
subgroupG/H
centerC2#21443815
commutatorC2×C22⋊C4×C61C2×C4
Frattini#381C2×D61
FittingC61×#1306C2
socleC2×C61#1343
prime radical#16840324C4
cosocleC61×#381C22
hypercenter#1306D61
hypocenterC61#7395
LCSG ▷ C2×C22⋊C4×C61 ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
2. #21443749C2semidirect
3. C61×#1306C2semidirect
119. #1306D61semidirect
134. C61#7395semidirect

Maximal subgroups

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

subgroupindex
#214469502
#214437492
C61×#13062
#739561