Finite Group Databasebeta

← #30595645

Subgroups — #30595645

Order 15616.

468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461747C212yesmaximal, complemented
2#21460640C212yesmaximal, complemented
3#21460635C212yesmaximal
4C4×#14519764C211yesmaximal, characteristic
5#16840628—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×#14519764C411yescharacteristic
9C2×C4×Dic122C411yescharacteristic
10#16839667C2211yescharacteristic
11#16839665C2211yescharacteristic
12#16839656—22no—
13#16839627C411yescharacteristic
14C4×C22⋊Dic61—22no—
15C42×Dic61C2211yescharacteristic
16C2×C4×D4×C61C411yescharacteristic
17C22×#92420—24no—
18C22×Dic122C2×C411yescharacteristic
19#14519764—22no—
20#14519764—22no—
21C4×Dic122—42no—
22C2×C4⋊Dic61C2×C411yescharacteristic
23C2×#11758196—21no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26C2×C4×Dic61—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D412yes—
29C2×C4×Dic61D412yes—
30C2×C4×Dic61C2311yescharacteristic
31#14519684—22no—
32#14519684—22no—
33C22×D4×C61C2×C411yescharacteristic
34C23×C4×C61—21no—
35C4×D4×C61—42no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C2×C22⋊C4×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C24×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61—41no—
42C2×D4×C61—41no—
43C2×D4×C61M1612yes—
44C22×C4×C61—21no—
45C22×C4×C61—44no—
46C22×C4×C61—42no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61C22⋊C412yes—
53C22×Dic61C2×D412yes—
54C2×Dic122—21no—
55C2×Dic122—41no—
56C2×Dic122—41no—
57C2×Dic122M1612yes—
58C2×#92420—44no—
59C2×#92420—44no—
60C2×#92420—44no—
61C4⋊C4×C61—41no—
62C22⋊C4×C61—42no—
63C42×C61—22no—
64C22⋊Dic61—28no—
65C22⋊Dic61—44no—
66C4⋊Dic61—41no—
67#11758196—42no—
68C4×Dic61—21no—
69C4×Dic61—21no—
70C4×Dic61—24no—
71C4×Dic61—42no—
72C4×Dic61—41no—
73C4×Dic61—42no—
74C23×C61—22no—
75C23×C61—41no—
76C23×C61—41no—
77C23×C61—42no—
78C23×C61—42no—
79C23×C61C2×C22⋊C411yescharacteristic
80D4×C61—42no—
81D4×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61—84no—
90C2×C4×C61#10012yes—
91C2×C4×C61C2×M1611yescharacteristic
92C2×C4×C61C2×M1611yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61#13514yes—
104Dic122—42no—
105Dic122—42no—
106#92420—84no—
107#7649—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—44no—
110C22×C61—81no—
111C22×C61—82no—
112C22×C61—81no—
113C22×C61#40711yescharacteristic
114C22×C61#41011yescharacteristic
115C22×C61C2×#10011yescharacteristic
116C22×C61#41612yes—
117C22×C61#42112yes—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—41no—
122C4×C61—81no—
123Dic61—24no—
124Dic61—42no—
125Dic61—42no—
126Dic61—81no—
127C4×#124—611no—
128#1839—612no—
129#1272—612no—
130#1270—612no—
131C2×C61—82no—
132C2×C61#146611yescharacteristic
133C2×C61#148812yes—
134C2×C61#152112yes—
135C2×C61#153311yescharacteristic
136C2×C61#154311yescharacteristic
137C2×#124—611no—
138C2×C4×Q8—611no—
139C2×C4×D4#692311yescharacteristic
140#391—611no—
141#390—611no—
142#388—1222no—
143#382—611no—
144C4×C22⋊C4—1222no—
145C43—611no—
146#336—614no—
147#336—1222no—
148#336—1222no—
149C61#764911yescharacteristic, complemented, Sylow
150C22×Q8—611no—
151C22×D4C2×#692311yescharacteristic
152C23×C4—21no—
153C22×C8—1224no—
154#124—1222no—
155#124—1222no—
156C4×Q8—2442no—
157C4×D4—42no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4C2×#692311yescharacteristic
161C2×C22⋊C4—21no—
162C2×C22⋊C4—1222no—
163C2×C22⋊C4—1222no—
164C2×C42—612no—
165C2×C42—611no—
166C2×C42—612no—
167C2×C42—611no—
168C2×C42—1221no—
169C2×C42C2×#692311yescharacteristic
170#95—1222no—
171#95—1222no—
172C24—21no—
173C2×Q8—612no—
174C2×Q8—1221no—
175C2×Q8—2441no—
176C2×Q8—2441no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#1175821312yes—
181C22×C4—21no—
182C22×C4—44no—
183C22×C4—42no—
184C22×C4—612no—
185C22×C4—612no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4C22⋊#692311yescharacteristic
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22×#692311yescharacteristic
191C2×C8—2444no—
192C2×C8—2444no—
193C2×C8—2444no—
194C4⋊C4—41no—
195C4⋊C4—2441no—
196C4⋊C4—2442no—
197C22⋊C4—42no—
198C22⋊C4—1228no—
199C22⋊C4—2444no—
200C42—22no—
201C42—1224no—
202C42—1221no—
203C42—1221no—
204C42—2441no—
205C42—2442no—
206C42—2442no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—42no—
211C23—42no—
212C23C2×C22⋊#692311yescharacteristic
213Q8—2442no—
214Q8—2442no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—84no—
225C2×C4—614no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—2441no—
233C2×C4—2442no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4#1451983712yes—
237C2×C4D61⋊M1611yescharacteristic
238C2×C4C2×#1175821311yescharacteristic
239C8—4884no—
240C22—42no—
241C22—44no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22#1684073311yescharacteristic
246C22#1684074111yescharacteristic
247C22C2×#1451983711yescharacteristic
248C22#1684075212yes—
249C22#1684076012yes—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—41no—
254C4—81no—
255C4—1224no—
256C4—4881no—
257C4—2442no—
258C4—2442no—
259C2—82no—
260C2#2146107811yescharacteristic
261C2#2146115112yes—
262C2#2146126112yes—
263C2#2146129811yescharacteristic
264C2#2146132211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7649
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21460640C2semidirect
149. C61#7649semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606402
#214606352
C4×#145197642
#764961