Finite Group Databasebeta

← #30605522

Subgroups — #30605522

Order 15616.

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

normal subgroups only

This group has 296 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#21462192C211yesmaximal, characteristic, complemented
2#21462040C211yesmaximal, characteristic, complemented
3#21460823C212yesmaximal, complemented
4#21460821C212yesmaximal, complemented
5#21456463C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840685—21no—
8#16840658—21no—
9#16840654—21no—
10#16840654C2212yes—
11#16840654C2212yes—
12#16840367C411yescharacteristic
13#16840161C411yescharacteristic
14#16840138C411yescharacteristic
15#16840128C2211yescharacteristic
16#16840126C2211yescharacteristic
17#16840013—21no—
18#16839996—21no—
19#16839872—21no—
20C4×#11758199—21no—
21#16839718C2211yescharacteristic
22C61×#540C411yescharacteristic
23#14519851—22no—
24#14519851—22no—
25#14519851—22no—
26C2×#11758187—22no—
27C2×#11758199—21no—
28C2×#11758199—21no—
29C2×#11758194D411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519774C2×C411yescharacteristic
32#14519769C2×C411yescharacteristic
33#14519762—41no—
34#14519751—21no—
35#14519750—41no—
36C4×D244—21no—
37#14519710—21no—
38#14519708—21no—
39#14519698—21no—
40#14519698—21no—
41#14519697—21no—
42#14519697—21no—
43#14519688D411yescharacteristic
44#14519688C2311yescharacteristic
45C4×#92418C2×C411yescharacteristic
46C4×#92418D411yescharacteristic
47#127×C61C2×C411yescharacteristic
48#125×C61C2×C411yescharacteristic
49#123×C61—41no—
50#121×C61—21no—
51#121×C61—41no—
52C4×D4×C61—21no—
53#117×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C2×C22⋊D61—41no—
60C2×D244—21no—
61C2×D244—41no—
62C2×C4×D61—41no—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—41no—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—41no—
68C22⋊C4×C61—41no—
69C42×C61C22⋊C411yescharacteristic
70C42×C61C22×C411yescharacteristic
71#11758199—42no—
72#11758199—41no—
73#11758199—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—21no—
77#11758196—41no—
78#11758194—41no—
79C2×#92418—21no—
80C2×#92418—21no—
81C2×#92418C22⋊C411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758187—24no—
86#11758187—42no—
87C23×C61—41no—
88C23×C61#10011yescharacteristic
89C22×D61—41no—
90D4×C61—41no—
91D4×C61—41no—
92D4×C61—161no—
93D4×C61—161no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—161no—
100C2×C4×C61#10011yescharacteristic
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C22⋊D61—161no—
103C2×Dic61—41no—
104D244—41no—
105D244—41no—
106D244—161no—
107C4×D61—161no—
108#92418—21no—
109#92418—21no—
110#92418—21no—
111#92418#10411yescharacteristic
112#92418#10411yescharacteristic
113#11913—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—41no—
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61C2×#10011yescharacteristic
120C2×D61—81no—
121C2×D61—81no—
122C2×D61—81no—
123C4×C61—21no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61—81no—
127C4×C61C2×#10411yescharacteristic
128C4×C61#42111yescharacteristic
129Dic61—81no—
130#3176—611no—
131#2166—611no—
132#2110—611no—
133#1355—612no—
134#1355—612no—
135C2×C61—21no—
136C2×C61—41no—
137C2×C61—161no—
138C2×C61#153011yescharacteristic
139D61—161no—
140#540—611no—
141#540#692311yescharacteristic
142C2×M32—1221no—
143#499—611no—
144#493—611no—
145#490—611no—
146#490—611no—
147#469—1221no—
148#466—1221no—
149#442—1221no—
150C4×D8—1221no—
151#405—611no—
152#364—1221no—
153#349—1221no—
154#347—612no—
155#347—612no—
156#347—1221no—
157C61#1191311yescharacteristic, complemented, Sylow
158C2×D8—1221no—
159C2×D8—1221no—
160C2×M16—611no—
161C22×C8—611no—
162#127—611no—
163#127C2×#692311yescharacteristic
164#125—611no—
165#125C2×#692311yescharacteristic
166#123—41no—
167#123—2441no—
168#121—21no—
169#121—41no—
170#121—1221no—
171#121—2441no—
172C4×D4—21no—
173C4×D4—1221no—
174#117C2×#692311yescharacteristic
175M32—1222no—
176M32—1222no—
177M32—1222no—
178C2×C16—1222no—
179#107—1221no—
180#106—1221no—
181#102—1221no—
182#102—1221no—
183#102—1221no—
184#102—1221no—
185#97—611no—
186#97—611no—
187C4×C8—611no—
188C4×C8—611no—
189C2×D4—21no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—1221no—
193C2×D4—2441no—
194C2×D4—2441no—
195C22×C4—41no—
196C22×C4—2441no—
197C22×C4C22⋊#692311yescharacteristic
198D8—2441no—
199D8—2441no—
200D8—2442no—
201M16—2441no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—611no—
205C2×C8—611no—
206C2×C8—1221no—
207C2×C8—1221no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—1221no—
212C4⋊C4—2441no—
213C22⋊C4—21no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—2441no—
217C22⋊C4—2441no—
218C42C22⋊#692311yescharacteristic
219C42C22×#692311yescharacteristic
220C16—1224no—
221C16—2442no—
222C23—41no—
223C23—2441no—
224C23#1451983711yescharacteristic
225D4—41no—
226D4—41no—
227D4—161no—
228D4—161no—
229D4—9761no—
230D4—9761no—
231D4—2441no—
232D4—2441no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—161no—
239C2×C4—9761no—
240C2×C4—2441no—
241C2×C4#1451983711yescharacteristic
242C2×C4C2×C22⋊#692311yescharacteristic
243C8—611no—
244C8—611no—
245C8—1221no—
246C8—1221no—
247C8—1221no—
248C22—21no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—81no—
253C22—4881no—
254C22—4881no—
255C22—4881no—
256C22C2×#1451983711yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—81no—
261C4—4881no—
262C4D61⋊#10411yescharacteristic
263C4#1684075911yescharacteristic
264C2—21no—
265C2—41no—
266C2—161no—
267C2—9761no—
268C2#2146128811yescharacteristic
subgroupG/H
centerC2#21461288
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#540C4
socleC2×C61#1530
prime radical#21456463C2
cosocle#14519688C23
hypercenter#540#6923
hypocenterC61#11913
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462192C2semidirect
2. #21462040C2semidirect
3. #21460823C2semidirect
4. #21460821C2semidirect
157. C61#11913semidirect

Maximal subgroups

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

subgroupindex
#214621922
#214620402
#214608232
#214608212
#214564632
#1191361