Finite Group Databasebeta

← #30594573

Subgroups — #30594573

Order 15616.

302 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 62 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⋊#349C211yesmaximal, characteristic
2#21461700C211yesmaximal, characteristic
3#338×D61C211yesmaximal, characteristic
4D61⋊M32—21no—
5C2×#14519848C411yescharacteristic
6C2×#14519847C411yescharacteristic
7#16840733—21no—
8#16840659C412yes—
9#16840658—21no—
10#16840638—21no—
11C2×M16×D61—21no—
12C2×M16×D61C2211yescharacteristic
13#16839520—21no—
14#16839520C411yescharacteristic
15C61×#338C411yescharacteristic
16C2×#11758213—21no—
17C2×#11758213—21no—
18#14519852—41no—
19#14519851—22no—
20D61⋊C16—41no—
21#14519848—41no—
22#14519847—41no—
23#14519834—41no—
24C22⋊#92420—41no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194—21no—
27C2×#11758194D411yescharacteristic
28C2×#11758189—22no—
29C2×#11758189C2×C411yescharacteristic
30C2×#11758189Q811yescharacteristic
31M16×D61—41no—
32M16×D61—41no—
33M16×D61—41no—
34M16×D61—41no—
35M16×D61—41no—
36M16×D61—41no—
37C2×C8×D61—22no—
38C2×C8×D61C2×C411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×M16×C61—21no—
41C2×M16×C61C2×C411yescharacteristic
42C23×D61Q1611yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×Dic61SD1611yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61C22⋊C411yescharacteristic
50C2×C4×D61C4⋊C411yescharacteristic
51C2×C4×D61D811yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53C2×#92420—41no—
54C2×#92420—41no—
55#11758213—41no—
56#11758213—41no—
57#11758213—41no—
58#11758213—41no—
59M16×C61—41no—
60M16×C61—41no—
61M16×C61—41no—
62C2×C8×C61—22no—
63C2×C8×C61C4211yescharacteristic
64C2×C8×C61C4⋊C411yescharacteristic
65#11758194—41no—
66#11758194—41no—
67#11758194—41no—
68C2×#92418—22no—
69C2×#92418C22⋊C411yescharacteristic
70C2×#92418C4⋊C411yescharacteristic
71#11758189—41no—
72#11758189—41no—
73#11758189—42no—
74#11758189—42no—
75C8×D61—21no—
76C8×D61—21no—
77C8×D61—21no—
78C8×D61—21no—
79C8×D61—42no—
80C8×D61—42no—
81#11758187—42no—
82C23×C61#10311yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—81no—
86C22×D61#10311yescharacteristic
87C22×D61#10711yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61#9511yescharacteristic
91C2×C4×C61#10211yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61#10211yescharacteristic
95C2×Dic61#10611yescharacteristic
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61#9911yescharacteristic
103C4×D61#9911yescharacteristic
104C4×D61#10411yescharacteristic
105C4×D61#10411yescharacteristic
106#92420—81no—
107#92420—81no—
108C8×C61—21no—
109C8×C61—21no—
110C8×C61—42no—
111#92418—21no—
112#92418—21no—
113#92418—42no—
114#7257—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—41no—
117C22×C61#34011yescharacteristic
118C2×D61—21no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—41no—
122C2×D61—81no—
123C2×D61#32811yescharacteristic
124C2×D61#32811yescharacteristic
125C4×C61—21no—
126C4×C61#33911yescharacteristic
127C4×C61#34211yescharacteristic
128Dic61—21no—
129Dic61#32711yescharacteristic
130Dic61#32711yescharacteristic
131C2×#349—611no—
132#1811—611no—
133C2×#338—611no—
134C2×C61—21no—
135C2×C61—41no—
136C2×C61#129411yescharacteristic
137D61—21no—
138D61—21no—
139D61—41no—
140C22×M16—611no—
141C22×M16—1221no—
142C2×M32—1221no—
143C2×#108—611no—
144C2×#108—611no—
145#407—1221no—
146#349—612no—
147#349—1221no—
148#341—1221no—
149#338—611no—
150#338—1221no—
151#338#692311yescharacteristic
152C61#725711yescharacteristic, complemented, Sylow
153C23×C4—611no—
154C2×M16—21no—
155C2×M16—611no—
156C2×M16—611no—
157C2×M16—611no—
158C2×M16—1222no—
159C2×M16—1221no—
160C2×M16—1221no—
161C2×M16—1221no—
162C2×M16—2441no—
163C2×M16—2441no—
164C2×M16—2441no—
165C2×M16—2441no—
166C2×M16—2441no—
167C2×M16—2441no—
168C2×M16C2×#692311yescharacteristic
169C22×C8—611no—
170C22×C8—611no—
171C22×C8—1222no—
172M32—1222no—
173M32—2441no—
174C2×C16—2441no—
175#108—2441no—
176#108—2441no—
177C22⋊C8—2441no—
178C22⋊C8—2441no—
179C24—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4C22⋊#692311yescharacteristic
190M16—41no—
191M16—41no—
192M16—41no—
193M16—2441no—
194M16—2441no—
195M16—2442no—
196M16—2442no—
197M16—2441no—
198M16—2441no—
199M16—2441no—
200M16—2441no—
201M16—2441no—
202M16—2441no—
203M16—2441no—
204C2×C8—22no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—1221no—
208C2×C8—1221no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8—1222no—
212C2×C8—2442no—
213C2×C8—2442no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8C4×#692311yescharacteristic
217C2×C8C4⋊#692311yescharacteristic
218C16—2442no—
219C23—611no—
220C23—611no—
221C23—1221no—
222C23—1221no—
223C23—4881no—
224C23#1451984011yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4(C2×#6923)⋊C411yescharacteristic
242C2×C4#1451983911yescharacteristic
243C8—21no—
244C8—21no—
245C8—42no—
246C8—1221no—
247C8—1221no—
248C8—4881no—
249C8—4881no—
250C8—2442no—
251C22—21no—
252C22—41no—
253C22—611no—
254C22—611no—
255C22—1221no—
256C22—4881no—
257C22—2441no—
258C22—2441no—
259C22—2442no—
260C22#1684063511yescharacteristic
261C4—21no—
262C4—611no—
263C4—611no—
264C4—1221no—
265C4#1684063311yescharacteristic
266C4#1684063911yescharacteristic
267C2—21no—
268C2—41no—
269C2—1221no—
270C2—1221no—
271C2—2441no—
272C2#2146069311yescharacteristic
subgroupG/H
centerC2#21460693
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1294
prime radicalC23×D61Q16
cosocleC2×M16×D61C22
hypercenter#338#6923
hypocenterC61#7257
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
152. C61#7257semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214617002
#338×D612
#725761