Finite Group Databasebeta

← #29592769

Subgroups — #29592769

Order 15616.

404 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 63 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#21446975C211yesmaximal, characteristic
2#21444826C212yesmaximal, complemented
3#21443825C212yesmaximal, complemented
4#21443751C211yesmaximal, characteristic
5C61×#2724C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7#16840092—22no—
8#16839767—21no—
9#16839531C2211yescharacteristic
10#16839522—21no—
11#16839498—22no—
12#16839488C2212yes—
13C2×#123×C61—21no—
14C61×#398C2212yes—
15C61×#397—22no—
16C61×#390C2211yescharacteristic
17C61×#389—21no—
18C61×#385—22no—
19C2×#11758194—21no—
20#14519776—41no—
21#14519768—41no—
22#14519756—22no—
23#14519736—21no—
24#14519708—42no—
25#14519700—42no—
26#14519698—41no—
27#14519698—41no—
28C22⋊#92418—22no—
29C22×D4×C61D411yescharacteristic
30C23×C4×C61—21no—
31#123×C61—42no—
32#123×C61—42no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61D412yes—
37C2×C4⋊C4×C61C2311yescharacteristic
38C2×C22⋊C4×C61—22no—
39C2×C22⋊C4×C61—21no—
40C2×C22⋊C4×C61—22no—
41C2×C42×C61D411yescharacteristic
42#95×C61—22no—
43#95×C61—22no—
44#95×C61D412yes—
45C24×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D4×C61SD1612yes—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—81no—
55C22×C4×C61—81no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C2×Dic122—22no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—81no—
65C22⋊C4×C61—44no—
66C22⋊C4×C61—42no—
67C22⋊C4×C61—44no—
68C42×C61—41no—
69C22⋊Dic61—41no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—22no—
73#11758196—42no—
74C4×Dic61—41no—
75#11758194—41no—
76#11758194—41no—
77C2×#92418—42no—
78C2×#92418—41no—
79C23×C61—22no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61#12011yescharacteristic
85D4×C61—42no—
86D4×C61—81no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—84no—
101C2×C4×C61C2×SD1611yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×Dic61—41no—
104C2×Dic61—41no—
105Dic122—82no—
106#92418—81no—
107#92418—82no—
108#12209—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—44no—
112C22×C61—42no—
113C22×C61—82no—
114C22×C61—81no—
115C22×C61—81no—
116C22×C61#45011yescharacteristic
117C22×C61#45511yescharacteristic
118C22×C61B(4,𝔽2)11yescharacteristic
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—42no—
122C4×C61—42no—
123C4×C61—82no—
124C4×C61—82no—
125Dic61—81no—
126Dic61—81no—
127#2724D6111yescharacteristic
128#2027—611no—
129#1611—612no—
130#1346—612no—
131#1318—611no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—82no—
135C2×C61#160111yescharacteristic
136C2×C61#219811yescharacteristic
137C2×C61#220311yescharacteristic
138#544—611no—
139C2×#123—21no—
140#483—1222no—
141#418—1221no—
142#398C2×D6112yes—
143#397—22no—
144#390C2×D6111yescharacteristic
145#389—21no—
146#385—22no—
147#343—611no—
148#339—1221no—
149#328—1222no—
150#324—612no—
151C61#1220911yescharacteristic, complemented, Sylow
152C22×D4C22⋊D6111yescharacteristic
153C23×C4—21no—
154C2×M16—1221no—
155C4⋊Q8—2441no—
156#125—2441no—
157#123—42no—
158#123—42no—
159C22⋊Q8—1222no—
160#117—1221no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C22⋊D6112yes—
165C2×C4⋊C4C22×D6111yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—22no—
169C2×C42C22⋊D6111yescharacteristic
170#106—2442no—
171#103—2442no—
172#102—2441no—
173#102—2441no—
174C22⋊C8—1222no—
175#95—22no—
176#95—22no—
177#95C22⋊D6112yes—
178C24—21no—
179C2×Q8—1222no—
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4#1175820012yes—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4C2×C22⋊D6111yescharacteristic
191C22×C4C2×C22⋊D6112yes—
192M16—2441no—
193M16—2441no—
194C2×C8—2442no—
195C2×C8—2441no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—81no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1222no—
205C4⋊C4—2442no—
206C22⋊C4—44no—
207C22⋊C4—42no—
208C22⋊C4—44no—
209C22⋊C4—2441no—
210C42—41no—
211C42—2441no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23—41no—
216C23—41no—
217C23#1451974611yescharacteristic
218Q8—4882no—
219D4—42no—
220D4—81no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4C2×#1175820011yescharacteristic
238C2×C4#1451980311yescharacteristic
239C8—4881no—
240C8—4882no—
241C22—21no—
242C22—21no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1683991311yescharacteristic
249C22#1683994011yescharacteristic
250C22#1683994911yescharacteristic
251C4—21no—
252C4—21no—
253C4—42no—
254C4—42no—
255C4—82no—
256C4—82no—
257C4—4881no—
258C4—4881no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#2144477111yescharacteristic
263C2#2144781511yescharacteristic
264C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2724C2
socleC22×C61B(4,𝔽2)
prime radicalC22×D4×C61D4
hypercenter#2724D61
hypocenterC61#12209
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2724

Complements

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

NH ≅ G/Ntype
2. #21444826C2semidirect
3. #21443825C2semidirect
151. C61#12209semidirect

Maximal subgroups

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

subgroupindex
#214469752
#214448262
#214438252
#214437512
C61×#27242
#1220961