Finite Group Databasebeta

← #30594586

Subgroups — #30594586

Order 15616.

320 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D61⋊(C22⋊C16)C211yesmaximal, characteristic
2#21461699C211yesmaximal, characteristic
3#341×D61C211yesmaximal, characteristic
4C2×D61⋊C16—21no—
5C2×#14519848C412yes—
6#16840733—21no—
7#16840657C412yes—
8C22⋊#11758187—21no—
9#16840638—21no—
10C2×M16×D61—21no—
11C22×C8×D61C2211yescharacteristic
12#16839527C411yescharacteristic
13#16839526—21no—
14C61×#341C411yescharacteristic
15C2×#11758213—22no—
16D61⋊C16—42no—
17C2×#11758187—22no—
18#14519848—42no—
19#14519834—41no—
20C22⋊#92420—41no—
21C22×C4×D61D411yescharacteristic
22C2×#11758194—21no—
23C2×#11758189—41no—
24M16×D61—24no—
25M16×D61—42no—
26C22×#92418D411yescharacteristic
27C2×C8×D61—42no—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61Q811yescharacteristic
33C2×M16×C61—21no—
34C22×C8×C61C2×C411yescharacteristic
35C23×D61Q1611yescharacteristic
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61SD1611yescharacteristic
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61C22⋊C411yescharacteristic
41C2×C4×D61C4⋊C411yescharacteristic
42C2×C4×D61D811yescharacteristic
43C2×C4×D61SD1611yescharacteristic
44C2×#92420—42no—
45#11758213—42no—
46#11758213—42no—
47M16×C61—22no—
48M16×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C4211yescharacteristic
52C2×C8×C61C4⋊C411yescharacteristic
53#11758194—22no—
54#11758194—41no—
55C2×#92418—41no—
56C2×#92418—41no—
57C2×#92418C22⋊C411yescharacteristic
58C2×#92418C4⋊C411yescharacteristic
59#11758189—44no—
60C8×D61—22no—
61C8×D61—22no—
62C8×D61—41no—
63C8×D61—41no—
64C8×D61—44no—
65#11758187—42no—
66C23×C61#10311yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—41no—
70C22×D61#10311yescharacteristic
71C22×D61#10711yescharacteristic
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61#9511yescharacteristic
75C2×C4×C61#10211yescharacteristic
76C2×Dic61—22no—
77C2×Dic61#10211yescharacteristic
78C2×Dic61#10611yescharacteristic
79C4×D61—22no—
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—22no—
83C4×D61#9912yes—
84C4×D61#10412yes—
85#92420—82no—
86C8×C61—21no—
87C8×C61—21no—
88C8×C61—42no—
89#92418—21no—
90#92418—21no—
91#92418—42no—
92#7261—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61#34011yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—44no—
102C2×D61#32812yes—
103C2×D61#36812yes—
104C4×C61—21no—
105C4×C61#33911yescharacteristic
106C4×C61#34211yescharacteristic
107Dic61—21no—
108Dic61#32712yes—
109C2×C22⋊C16—611no—
110#1810—611no—
111C2×#341—611no—
112C2×C61—41no—
113C2×C61#129411yescharacteristic
114C2×C61#138111yescharacteristic
115C2×C61#138811yescharacteristic
116D61—22no—
117D61—22no—
118C22×M16—1221no—
119C23×C8—611no—
120C22×C16—1221no—
121C2×#108—612no—
122#407—1221no—
123C22⋊C16—612no—
124C22⋊C16—1221no—
125#341—611no—
126#341—1221no—
127#341—1221no—
128#341#692311yescharacteristic
129C61#726111yescharacteristic, complemented, Sylow
130C23×C4—611no—
131C2×M16—21no—
132C2×M16—1224no—
133C2×M16—1221no—
134C2×M16—1222no—
135C2×M16—2441no—
136C2×M16—2442no—
137C22×C8—611no—
138C22×C8—611no—
139C22×C8—611no—
140C22×C8—611no—
141C22×C8—611no—
142C22×C8—2442no—
143C22×C8—2441no—
144C22×C8C2×#692311yescharacteristic
145C2×C16—1222no—
146C2×C16—2442no—
147#108—2442no—
148C22⋊C8—2441no—
149C22⋊C8—2441no—
150C24—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—1222no—
157C22×C4—1222no—
158C22×C4C22⋊#692311yescharacteristic
159M16—22no—
160M16—41no—
161M16—1222no—
162M16—2444no—
163M16—2442no—
164M16—2442no—
165M16—2441no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—1222no—
171C2×C8—1222no—
172C2×C8—2441no—
173C2×C8—2441no—
174C2×C8—2444no—
175C2×C8—2441no—
176C2×C8—2442no—
177C2×C8—2441no—
178C2×C8C4×#692311yescharacteristic
179C2×C8C4⋊#692311yescharacteristic
180C16—2442no—
181C23—611no—
182C23—611no—
183C23—1222no—
184C23—1222no—
185C23—2441no—
186C23#1451984011yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—611no—
190C2×C4—612no—
191C2×C4—612no—
192C2×C4—611no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4(C2×#6923)⋊C411yescharacteristic
199C2×C4#1451983911yescharacteristic
200C8—21no—
201C8—21no—
202C8—42no—
203C8—1221no—
204C8—1221no—
205C8—4882no—
206C8—2442no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—612no—
211C22—612no—
212C22—1221no—
213C22—1221no—
214C22—1221no—
215C22—1221no—
216C22—2444no—
217C22#1684063511yescharacteristic
218C4—21no—
219C4—612no—
220C4—1221no—
221C4#1684063311yescharacteristic
222C4#1684063911yescharacteristic
223C2—41no—
224C2—1222no—
225C2—1222no—
226C2#2146069311yescharacteristic
227C2#2146087811yescharacteristic
228C2#2146089811yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61Q16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7261
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
129. C61#7261semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616992
#341×D612
#726161