Finite Group Databasebeta

← #30594575

Subgroups — #30594575

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
1#21461700C211yesmaximal, characteristic
2D61⋊#338C211yesmaximal, characteristic
3#349×D61C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5C2×#14519848C411yescharacteristic
6C2×#14519847C411yescharacteristic
7#16840733—21no—
8#16840638—21no—
9#16840631—21no—
10#16840631C412yes—
11C2×M16×D61C2211yescharacteristic
12M32×D61—21no—
13#16839544C411yescharacteristic
14#16839543—21no—
15C61×#349C411yescharacteristic
16C2×#11758213—21no—
17C2×#11758213—21no—
18C2×#11758213—41no—
19D61⋊M16—22no—
20D61⋊M16—22no—
21D61⋊M16—41no—
22D61⋊M16—41no—
23C2×#11758217—41no—
24C2×D61⋊C8—22no—
25#14519848—41no—
26#14519847—41no—
27#14519834—41no—
28C22⋊#92420—41no—
29C22×C4×D61D411yescharacteristic
30C2×#11758194Q811yescharacteristic
31C2×#11758189C2×C411yescharacteristic
32C2×#11758189D411yescharacteristic
33M16×D61—41no—
34M16×D61—41no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519717—21no—
38#14519716—41no—
39C16×D61—41no—
40C2×M16×C61C2×C411yescharacteristic
41M32×C61—21no—
42C23×D61Q1611yescharacteristic
43C22×C4×C61C4⋊C411yescharacteristic
44C22×Dic61D811yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61C22⋊C411yescharacteristic
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C4×D61SD1611yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53#11758217—42no—
54#11758217—42no—
55C2×#92420—42no—
56C2×#92420—41no—
57C2×#92420—41no—
58#11758213—42no—
59#11758213—42no—
60#11758213—41no—
61#11758213—41no—
62#11758213—41no—
63#11758213—41no—
64D61⋊C8—24no—
65D61⋊C8—42no—
66M16×C61—41no—
67C2×C8×C61C4211yescharacteristic
68C2×C8×C61C22⋊C411yescharacteristic
69#11758194—41no—
70C2×#92418C4⋊C411yescharacteristic
71C2×#92418C4⋊C411yescharacteristic
72#11758189—41no—
73#11758189—41no—
74C8×D61—21no—
75C8×D61—21no—
76C8×D61—21no—
77C8×D61—21no—
78C16×C61—41no—
79#11758185—41no—
80C23×C61#10711yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—81no—
84C22×D61#10311yescharacteristic
85C22×D61#10311yescharacteristic
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61#9511yescharacteristic
89C2×C4×C61#10611yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61#10211yescharacteristic
93C2×Dic61#10211yescharacteristic
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61#9911yescharacteristic
101C4×D61#9911yescharacteristic
102C4×D61#10411yescharacteristic
103C4×D61#10411yescharacteristic
104#92420—44no—
105#92420—81no—
106#92420—81no—
107C8×C61—21no—
108C8×C61—21no—
109#92418—21no—
110#92418—21no—
111#7257—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—41no—
114C22×C61#34011yescharacteristic
115C2×D61—21no—
116C2×D61—41no—
117C2×D61—42no—
118C2×D61—41no—
119C2×D61—81no—
120C2×D61#32811yescharacteristic
121C2×D61#32811yescharacteristic
122C4×C61—21no—
123C4×C61#33911yescharacteristic
124C4×C61#34211yescharacteristic
125Dic61—21no—
126Dic61#32711yescharacteristic
127Dic61#32711yescharacteristic
128C2×#349—611no—
129#1811—611no—
130C2×#338—611no—
131C2×C61—21no—
132C2×C61—41no—
133C2×C61#129411yescharacteristic
134D61—21no—
135D61—21no—
136D61—41no—
137C22×M16—611no—
138C22×M16—1221no—
139C2×M32—1221no—
140C2×#108—611no—
141C2×#108—611no—
142#407—1221no—
143#349—611no—
144#349—1221no—
145#349#692311yescharacteristic
146#341—1221no—
147#338—612no—
148#338—1221no—
149C61#725711yescharacteristic, complemented, Sylow
150C23×C4—611no—
151C2×M16—611no—
152C2×M16—611no—
153C2×M16—611no—
154C2×M16—1222no—
155C2×M16—1222no—
156C2×M16—1221no—
157C2×M16—1221no—
158C2×M16—2441no—
159C2×M16—2441no—
160C2×M16—2441no—
161C2×M16—2441no—
162C2×M16—2441no—
163C2×M16—2441no—
164C2×M16C2×#692311yescharacteristic
165C22×C8—611no—
166C22×C8—611no—
167C22×C8—1222no—
168M32—21no—
169M32—1221no—
170M32—2441no—
171C2×C16—2441no—
172#108—2441no—
173#108—2441no—
174C22⋊C8—2441no—
175C22⋊C8—2441no—
176C24—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4C4⋊#692311yescharacteristic
187M16—41no—
188M16—2441no—
189M16—2441no—
190M16—2441no—
191M16—2441no—
192M16—2441no—
193M16—2441no—
194M16—2441no—
195M16—2442no—
196M16—2442no—
197M16—2442no—
198M16—2442no—
199C2×C8—611no—
200C2×C8—611no—
201C2×C8—1221no—
202C2×C8—1221no—
203C2×C8—1221no—
204C2×C8—1221no—
205C2×C8—1224no—
206C2×C8—2441no—
207C2×C8—2441no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8C4×#692311yescharacteristic
211C2×C8C22⋊#692311yescharacteristic
212C16—41no—
213C16—2441no—
214C23—611no—
215C23—611no—
216C23—1221no—
217C23—1221no—
218C23—4881no—
219C23#1451984611yescharacteristic
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4(C2×#6923)⋊C411yescharacteristic
237C2×C4#1451984511yescharacteristic
238C8—21no—
239C8—21no—
240C8—1221no—
241C8—1221no—
242C8—4881no—
243C8—4881no—
244C8—2444no—
245C22—21no—
246C22—41no—
247C22—611no—
248C22—611no—
249C22—1221no—
250C22—4881no—
251C22—2441no—
252C22—2441no—
253C22—2442no—
254C22#1684063611yescharacteristic
255C4—21no—
256C4—611no—
257C4—611no—
258C4—1221no—
259C4#1684063411yescharacteristic
260C4#1684063911yescharacteristic
261C2—21no—
262C2—41no—
263C2—1221no—
264C2—1221no—
265C2—2441no—
266C2#2146069411yescharacteristic
subgroupG/H
centerC2#21460694
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×#349C4
socleC2×C61#1294
prime radicalC23×D61Q16
cosocleC2×M16×D61C22
hypercenter#349#6923
hypocenterC61#7257
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
149. C61#7257semidirect

Maximal subgroups

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

subgroupindex
#214617002
D61⋊#3382
#349×D612
#725761