Finite Group Databasebeta

← #29592768

Subgroups — #29592768

Order 15616.

404 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 59 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#21452749C211yesmaximal, characteristic
2#21444827C212yesmaximal, complemented
3#21443824C212yesmaximal, complemented
4#21443751C211yesmaximal, characteristic
5C61×#2027C211yesmaximal, characteristic
6C2×#14519758—21no—
7#16840090—22no—
8#16839692C2212yes—
9#16839687—22no—
10#16839660—21no—
11#16839637—22no—
12#16839499—22no—
13#16839488C2212yes—
14C61×#544C2211yescharacteristic
15C61×#418—21no—
16C61×#390C2211yescharacteristic
17C61×#343C2211yescharacteristic
18C61×#339—21no—
19C23×Dic61—21no—
20#14519758—42no—
21#14519758—42no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61D412yes—
25C2×#11758196—22no—
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—22no—
28#14519708—42no—
29#14519701—42no—
30C22⋊#92418—22no—
31#14519684—22no—
32#14519684—22no—
33#14519684D412yes—
34C22×D4×C61D411yescharacteristic
35C2×M16×C61—21no—
36C4⋊Q8×C61—41no—
37#125×C61—41no—
38C22⋊Q8×C61—22no—
39#117×C61—21no—
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C22⋊C4×C61—22no—
42C2×C42×C61D411yescharacteristic
43#102×C61—41no—
44#102×C61—41no—
45C24×C61—21no—
46C2×Q8×C61—22no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×D4×C61SD1612yes—
51C22×C4×C61—21no—
52C22×C4×C61C2×D411yescharacteristic
53C22×C4×C61C2×D412yes—
54C22×Dic61—22no—
55C22×Dic61—22no—
56C22×Dic61—42no—
57C22×Dic61—81no—
58C22×Dic61—81no—
59M16×C61—41no—
60M16×C61—41no—
61C2×C8×C61—41no—
62C4⋊C4×C61—21no—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—42no—
67C22⋊C4×C61—44no—
68C22⋊C4×C61—41no—
69C42×C61—41no—
70C42×C61—41no—
71C22⋊Dic61—42no—
72C22⋊Dic61—44no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4⋊Dic61—81no—
76#11758196—42no—
77#11758196—42no—
78C2×#92418—42no—
79C23×C61—22no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61#12011yescharacteristic
85Q8×C61—82no—
86D4×C61—42no—
87D4×C61—81no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61C2×SD1611yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—84no—
106C8×C61—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—81no—
124C4×C61—81no—
125Dic61—82no—
126Dic61—82no—
127#2724—611no—
128#2027D6111yescharacteristic
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#544C2×D6111yescharacteristic
139C2×#123—1221no—
140#483—1222no—
141#418—21no—
142#398—612no—
143#397—1222no—
144#390C2×D6111yescharacteristic
145#389—1221no—
146#385—1222no—
147#343C2×D6111yescharacteristic
148#339—21no—
149#328—1222no—
150#324—612no—
151C61#1220911yescharacteristic, complemented, Sylow
152C22×D4C22⋊D6111yescharacteristic
153C23×C4—1221no—
154C2×M16—21no—
155C4⋊Q8—41no—
156#125—41no—
157#123—2442no—
158#123—2442no—
159C22⋊Q8—22no—
160#117—21no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4C22×D6111yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—1222no—
168C2×C22⋊C4—1221no—
169C2×C42C22⋊D6111yescharacteristic
170#106—2442no—
171#103—2442no—
172#102—41no—
173#102—41no—
174C22⋊C8—1222no—
175#95—612no—
176#95—1222no—
177#95—1222no—
178C24—21no—
179C2×Q8—22no—
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4#1175820112yes—
184C22×C4—21no—
185C22×C4—1222no—
186C22×C4—1222no—
187C22×C4—4881no—
188C22×C4—4881no—
189C22×C4—2442no—
190C22×C4D4×D6112yes—
191C22×C4C2×C22⋊D6111yescharacteristic
192M16—41no—
193M16—41no—
194C2×C8—41no—
195C2×C8—2442no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—4881no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2442no—
206C22⋊C4—44no—
207C22⋊C4—41no—
208C22⋊C4—2442no—
209C22⋊C4—2444no—
210C42—41no—
211C42—41no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23—41no—
216C23—41no—
217C23#1451974511yescharacteristic
218Q8—82no—
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—41no—
229C2×C4—41no—
230C2×C4—4884no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4C2×#1175820111yescharacteristic
238C2×C4#1451980211yescharacteristic
239C8—81no—
240C8—4882no—
241C22—21no—
242C22—21no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1683991211yescharacteristic
249C22#1683993911yescharacteristic
250C22#1683994811yescharacteristic
251C4—21no—
252C4—21no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C4—4882no—
258C4—4882no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#2144477011yescharacteristic
263C2#2144781411yescharacteristic
264C2#2144783911yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2027C2
socleC22×C61B(4,𝔽2)
prime radicalC22×D4×C61D4
hypercenter#2027D61
hypocenterC61#12209
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2027

Complements

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

NH ≅ G/Ntype
2. #21444827C2semidirect
3. #21443824C2semidirect
151. C61#12209semidirect

Maximal subgroups

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

subgroupindex
#214527492
#214448272
#214438242
#214437512
C61×#20272
#1220961