Finite Group Databasebeta

← #30595477

Subgroups — #30595477

Order 15616.

492 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461735C212yesmaximal, complemented
2#21460640C212yesmaximal, complemented
3#21460635C212yesmaximal
4C4×#14519764C211yesmaximal, characteristic
5C2×#14519844—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—
18#14519844—44no—
19C22×Dic122C2×C411yescharacteristic
20#14519764—22no—
21#14519764C814yescomplemented
22C4×Dic122—42no—
23C2×C4⋊Dic61C2×C411yescharacteristic
24C2×#11758196—21no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61—22no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—22no—
33#14519684—22no—
34C22×D4×C61C2×C411yescharacteristic
35C23×C4×C61—21no—
36C4×D4×C61—42no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C22⋊C4×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40C24×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61—41no—
43C2×D4×C61—41no—
44C2×D4×C61C2×C812yes—
45C22×C4×C61—21no—
46C22×C4×C61—44no—
47C22×C4×C61—42no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C412yes—
54C22×Dic61C2×D412yes—
55C2×Dic122—21no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122C2×C812yes—
59C2×#92420—44no—
60C2×#92420—44no—
61C2×#92420—44no—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—42no—
64C42×C61—22no—
65C22⋊Dic61—28no—
66C22⋊Dic61—42no—
67C22⋊Dic61—42no—
68C4⋊Dic61—41no—
69#11758196—42no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—42no—
73C4×Dic61—41no—
74C4×Dic61—42no—
75C4×Dic61C2×C812yes—
76C4×Dic61M1612yes—
77C23×C61—22no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83D4×C61—42no—
84D4×C61—42no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—84no—
93C2×C4×C61#10012yes—
94C2×C4×C61C22×C811yescharacteristic
95C2×C4×C61C2×M1611yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105C2×Dic61C22⋊C814yes—
106C2×Dic61AGL(1,ℤ/8)12yes—
107C2×Dic61#13712yes—
108Dic122—42no—
109Dic122—42no—
110#92420—84no—
111#7601—611nomaximal, Sylow
112C22×C61—42no—
113C22×C61—44no—
114C22×C61—81no—
115C22×C61—82no—
116C22×C61—81no—
117C22×C61C2×C22⋊C811yescharacteristic
118C22×C61#41011yescharacteristic
119C22×C61C2×#10011yescharacteristic
120C22×C61#41712yes—
121C22×C61#42112yes—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—41no—
126C4×C61—81no—
127Dic61—24no—
128Dic61—22no—
129Dic61—22no—
130Dic61—42no—
131Dic61—81no—
132C4×#124—611no—
133#1831—612no—
134#1272—612no—
135#1270—612no—
136C2×C61—82no—
137C2×C61#146011yescharacteristic
138C2×C61#147712yes—
139C2×C61#151212yes—
140C2×C61#153311yescharacteristic
141C2×C61#156011yescharacteristic
142C2×#124—611no—
143C2×C4×Q8—611no—
144C2×C4×D4#692311yescharacteristic
145C2×C4⋊C8—1222no—
146#391—611no—
147#390—611no—
148#388—1222no—
149#382—611no—
150C4×C22⋊C4—1222no—
151C43—611no—
152#336—614no—
153#336—1222no—
154C61#760111yescharacteristic, complemented, Sylow
155C22×Q8—611no—
156C22×D4C2×#692311yescharacteristic
157C23×C4—21no—
158C22×C8—1224no—
159#124—614no—
160#124—1222no—
161C4×Q8—2442no—
162C4×D4—42no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4C2×#692311yescharacteristic
166C2×C22⋊C4—21no—
167C2×C22⋊C4—1222no—
168C2×C22⋊C4—1222no—
169C2×C42—611no—
170C2×C42—612no—
171C2×C42—612no—
172C2×C42—611no—
173C2×C42—1221no—
174C2×C42C2×#692311yescharacteristic
175C4⋊C8—2444no—
176#95—1222no—
177#95—1222no—
178C24—21no—
179C2×Q8—612no—
180C2×Q8—1221no—
181C2×Q8—2441no—
182C2×Q8—2441no—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4D61⋊C812yes—
187C22×C4—21no—
188C22×C4—44no—
189C22×C4—42no—
190C22×C4—612no—
191C22×C4—612no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4C22⋊#692311yescharacteristic
195C22×C4C22⋊#692311yescharacteristic
196C22×C4C22×#692311yescharacteristic
197C2×C8—2444no—
198C2×C8—2444no—
199C2×C8—2444no—
200C4⋊C4—41no—
201C4⋊C4—2441no—
202C4⋊C4—2442no—
203C22⋊C4—42no—
204C22⋊C4—1228no—
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C42—22no—
208C42—612no—
209C42—612no—
210C42—1222no—
211C42—1222no—
212C42—2441no—
213C42—2442no—
214C42—2442no—
215C23—22no—
216C23—41no—
217C23—41no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊#692311yescharacteristic
221Q8—2442no—
222Q8—2442no—
223D4—42no—
224D4—42no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—84no—
233C2×C4—614no—
234C2×C4—612no—
235C2×C4—612no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—2441no—
242C2×C4—2442no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983712yes—
246C2×C4C2×D61⋊C811yescharacteristic
247C2×C4D61⋊M1611yescharacteristic
248C8—4884no—
249C22—42no—
250C22—44no—
251C22—81no—
252C22—81no—
253C22—82no—
254C22D61⋊(C22⋊C8)11yescharacteristic
255C22#1684074111yescharacteristic
256C22C2×#1451983711yescharacteristic
257C22#1684075312yes—
258C22#1684076012yes—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—41no—
263C4—81no—
264C4—1224no—
265C4—1222no—
266C4—1222no—
267C4—4881no—
268C4—2442no—
269C2—82no—
270C2#2146105811yescharacteristic
271C2#2146111512yes—
272C2#2146123012yes—
273C2#2146129811yescharacteristic
274C2#2146135611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7601
LCSG ▷ C2×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. #21461735C2semidirect
2. #21460640C2semidirect
21. #14519764C8semidirect
154. C61#7601semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606402
#214606352
C4×#145197642
#760161