Finite Group Databasebeta

← #29567503

Subgroups — #29567503

Order 15616.

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

normal subgroups only

This group has 296 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#21446886C211yesmaximal, characteristic
2#21443704C211yesmaximal, characteristic, complemented
3C61×#1320C211yesmaximal, characteristic, complemented
4#16840562C411yescharacteristic, complemented
5#16840273—21no—
6#16839778—21no—
7C4×C22⋊Dic61—21no—
8#16839519C411yescharacteristic, complemented
9C61×#407C2211yescharacteristic
10C61×#349—21no—
11C2×#11758222—21no—
12#14519810—41no—
13#14519805—41no—
14#14519799—41no—
15#14519760—41no—
16#14519756—41no—
17#14519751—41no—
18#14519746—41no—
19C4×C22⋊D61—42no—
20#14519736—21no—
21C2×C22⋊Dic61—41no—
22C2×C4×Dic61—41no—
23#14519703—42no—
24#14519684—22no—
25C23×C4×C61D411yescharacteristic
26C2×M16×C61C2×C411yescharacteristic
27C2×M16×C61D411yescharacteristic
28M32×C61—41no—
29C22⋊C8×C61—41no—
30C24×C61D811yescharacteristic
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—41no—
34C22×C4×C61—41no—
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61SD1611yescharacteristic
37C2×C22⋊D61—42no—
38C2×C22⋊D61—41no—
39C22×Dic61—42no—
40#11758222—41no—
41#11758222—41no—
42#11758222—41no—
43#11758222—41no—
44C2×D244—21no—
45C2×C4×D61—41no—
46C2×Dic122—21no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C22⋊Dic61—44no—
52C22⋊Dic61—42no—
53C22⋊Dic61—41no—
54#11758198—42no—
55C4⋊Dic61—41no—
56#11758196—42no—
57C4×Dic61—22no—
58C4×Dic61—81no—
59C4×Dic61—81no—
60Dic244—41no—
61D488—41no—
62#11758190—42no—
63C16×C61—81no—
64C23×C61—21no—
65C23×C61—41no—
66C23×C61—42no—
67C23×C61#10211yescharacteristic
68C22×D61—41no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—81no—
76C2×C4×C61#9911yescharacteristic
77C2×C4×C61#10411yescharacteristic
78C22⋊D61—81no—
79C22⋊D61—84no—
80C22⋊D61—81no—
81C2×Dic61—42no—
82C2×Dic61—41no—
83C2×Dic61—44no—
84C2×Dic61—82no—
85C2×Dic61—82no—
86D244—41no—
87D244—41no—
88C4×D61—81no—
89C4×D61—81no—
90Dic122—41no—
91Dic122—41no—
92C8×C61—41no—
93C8×C61—41no—
94#7396—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—21no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61—41no—
101C22×C61—81no—
102C22×C61#32711yescharacteristic
103C2×D61—82no—
104C2×D61—81no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61AΣL(1,𝔽16)11yescharacteristic
108C4×C61#35311yescharacteristic
109Dic61—84no—
110Dic61—82no—
111Dic61—81no—
112#2010—611no—
113#1320D6111yescharacteristic, complemented
114#1297—611no—
115C2×C61—21no—
116C2×C61—41no—
117C2×C61—42no—
118C2×C61#134311yescharacteristic
119D61—161no—
120#575—611no—
121#525—1221no—
122#421—1221no—
123#407C2×D6111yescharacteristic
124C4×C22⋊C4—1221no—
125#349—21no—
126H(3,ℤ/4)—611no—
127C61#739611yescharacteristic, complemented, Sylow
128C2×#41—1221no—
129C23×C4D24411yescharacteristic
130#137—2441no—
131AGL(1,ℤ/8)—2441no—
132#135—2441no—
133C2×M16C4×D6111yescharacteristic
134C2×M16C22⋊D6111yescharacteristic
135#123—2441no—
136C22⋊Q8—2441no—
137#121—2441no—
138#120—2441no—
139C4×D4—2442no—
140#117—1221no—
141C2×C22⋊C4—2441no—
142C2×C42—2441no—
143M32—41no—
144#104—2442no—
145C22⋊C8—41no—
146#95—1222no—
147C24D48811yescharacteristic
148#41—2441no—
149#41—2441no—
150#41—2441no—
151#41—2441no—
152C2×Q8—1221no—
153C2×D4—1221no—
154C2×D4—2442no—
155C2×D4—2441no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—2441no—
161C22×C4—2442no—
162C22×C4#1175819011yescharacteristic
163C22×C4#1175819811yescharacteristic
164Q16—2441no—
165SD16—2442no—
166D8—2441no—
167M16—41no—
168M16—41no—
169C2×C8—21no—
170C2×C8—21no—
171C4⋊C4—2441no—
172C4⋊C4—2442no—
173C22⋊C4—2442no—
174C22⋊C4—2444no—
175C22⋊C4—2442no—
176C22⋊C4—2441no—
177C42—1222no—
178C42—4881no—
179C42—4881no—
180C16—81no—
181C23—21no—
182C23—41no—
183C23—42no—
184C23—2441no—
185C23#1451969911yescharacteristic
186Q8—2441no—
187Q8—2441no—
188D4—4881no—
189D4—4884no—
190D4—4881no—
191D4—2441no—
192D4—2441no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—81no—
200C2×C4—4881no—
201C2×C4—4882no—
202C2×C4—4882no—
203C2×C4—4881no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4—2444no—
207C2×C4#1451969111yescharacteristic
208C2×C4#1451970311yescharacteristic
209C8—41no—
210C8—41no—
211C22—22no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22—81no—
218C22—4882no—
219C22—4881no—
220C22#1683949711yescharacteristic
221C4—21no—
222C4—41no—
223C4—4884no—
224C4—4882no—
225C4—4881no—
226C4#1683955011yescharacteristic
227C4#1683955411yescharacteristic
228C2—21no—
229C2—41no—
230C2—42no—
231C2—9761no—
232C2#2144381711yescharacteristic
subgroupG/H
centerC4#16839554
commutatorC2×M16×C61C2×C4
Frattini#407C2×D61
FittingC61×#1320C2
socleC2×C61#1343
prime radical#21446886C2
cosocleC61×#407C22
hypercenter#1320D61
hypocenterC61#7396
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #21443704C2semidirect
3. C61×#1320C2semidirect
4. #16840562C4semidirect
8. #16839519C4semidirect
113. #1320D61semidirect
127. C61#7396semidirect

Maximal subgroups

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

subgroupindex
#214468862
#214437042
C61×#13202
#739661