Finite Group Databasebeta

← #30594580

Subgroups — #30594580

Order 15616.

342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461696C211yesmaximal, characteristic
3#341×D61C211yesmaximal, characteristic
4C2×D61⋊C16—21no—
5C2×#14519846C412yes—
6#16840704—21no—
7#16840657C412yescomplemented
8C22⋊#11758187—21no—
9#16840636—21no—
10C2×M16×D61—21no—
11C22×C8×D61C2211yescharacteristic
12#16839527C411yescharacteristic, complemented
13#16839526—21no—
14C61×#341C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17D61⋊C16—42no—
18C2×#11758187—22no—
19#14519846—42no—
20(C2×#6923)⋊C4—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×D61SD1611yescharacteristic
36C22×#6923—42no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61Q1611yescharacteristic
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61C22⋊C411yescharacteristic
42C2×C4×D61C4⋊C411yescharacteristic
43C2×C4×D61D811yescharacteristic
44C2×C4×D61SD1611yescharacteristic
45C22⋊#6923—82no—
46C4⋊#6923—42no—
47C4⋊#6923—42no—
48M16×C61—22no—
49M16×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C4211yescharacteristic
53C2×C8×C61C4⋊C411yescharacteristic
54#11758194—22no—
55#11758194—41no—
56C2×#92418—41no—
57C2×#92418—41no—
58C2×#92418C22⋊C411yescharacteristic
59C2×#92418C4⋊C411yescharacteristic
60#11758189—44no—
61C8×D61—22no—
62C8×D61—22no—
63C8×D61—41no—
64C8×D61—41no—
65C8×D61—44no—
66#11758187—42no—
67C23×C61#10311yescharacteristic
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—21no—
71C22×D61—21no—
72C22×D61#10211yescharacteristic
73C22×D61#10611yescharacteristic
74C2×#6923—82no—
75C2×#6923—82no—
76C2×#6923—82no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61#9511yescharacteristic
80C2×C4×C61#10211yescharacteristic
81C2×Dic61—22no—
82C2×Dic61#10311yescharacteristic
83C2×Dic61#10711yescharacteristic
84C4×D61—22no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—22no—
88C4×D61#9912yes—
89C4×D61#10412yes—
90C8×C61—21no—
91C8×C61—21no—
92C8×C61—42no—
93#92418—21no—
94#92418—21no—
95#92418—42no—
96#7259—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61#34011yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61#32712yes—
107C2×D61#35912yes—
108C2×D61#36111yescharacteristic
109C2×D61#36211yescharacteristic
110#6923—162no—
111C4×C61—21no—
112C4×C61#33911yescharacteristic
113C4×C61#34211yescharacteristic
114Dic61—21no—
115Dic61#32812yes—
116C2×C22⋊C16—611no—
117#1808—611no—
118C2×#341—611no—
119C2×C61—41no—
120C2×C61#129411yescharacteristic
121C2×C61#138211yescharacteristic
122C2×C61#138711yescharacteristic
123D61—41no—
124D61#134912yes—
125D61#135012yes—
126C22×M16—1221no—
127C23×C8—611no—
128C22×C16—1221no—
129C2×#107—612no—
130#380—1221no—
131C22⋊C16—612no—
132C22⋊C16—1221no—
133#341—611no—
134#341—1221no—
135#341#692311yescharacteristic, complemented
136#340—1221no—
137C61#725911yescharacteristic, complemented, Sylow
138C23×C4—611no—
139C2×M16—21no—
140C2×M16—1224no—
141C2×M16—1221no—
142C2×M16—2441no—
143C2×M16—2442no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—611no—
147C22×C8—611no—
148C22×C8—611no—
149C22×C8—2442no—
150C22×C8—2441no—
151C22×C8C2×#692311yescharacteristic
152C2×C4⋊C4—1222no—
153C2×C22⋊C4—2441no—
154C2×C16—1222no—
155C2×C16—2442no—
156#107—2442no—
157#95—2441no—
158C24—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—1222no—
165C22×C4—1222no—
166C22×C4—2442no—
167C22×C4C22⋊#692311yescharacteristic
168M16—22no—
169M16—41no—
170M16—1222no—
171M16—2444no—
172M16—2441no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—611no—
176C2×C8—611no—
177C2×C8—1222no—
178C2×C8—1222no—
179C2×C8—2441no—
180C2×C8—2441no—
181C2×C8—2444no—
182C2×C8—2441no—
183C2×C8—2441no—
184C2×C8C4×#692311yescharacteristic
185C2×C8C4⋊#692311yescharacteristic
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C22⋊C4—4882no—
189C16—2442no—
190C23—611no—
191C23—611no—
192C23—1221no—
193C23—1222no—
194C23—1222no—
195C23—1221no—
196C23#1451984011yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—611no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—611no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4882no—
209C2×C4—4882no—
210C2×C4—4882no—
211C2×C4(C2×#6923)⋊C411yescharacteristic
212C2×C4#1451983911yescharacteristic
213C8—21no—
214C8—21no—
215C8—42no—
216C8—1221no—
217C8—1221no—
218C8—2442no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—612no—
223C22—611no—
224C22—611no—
225C22—612no—
226C22—1221no—
227C22—1221no—
228C22—1221no—
229C22—2442no—
230C22—2442no—
231C22#1684063511yescharacteristic
232C4—21no—
233C4—612no—
234C4—1221no—
235C4—9762no—
236C4#1684063311yescharacteristic
237C4#1684063911yescharacteristic
238C2—41no—
239C2—612no—
240C2—612no—
241C2—2441no—
242C2#2146069311yescharacteristic
243C2#2146088211yescharacteristic
244C2#2146089511yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7259
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
7. #16840657C4semidirect
12. #16839527C4semidirect
14. C61×#341C4semidirect
135. #341#6923semidirect
137. C61#7259semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616962
#341×D612
#725961