Finite Group Databasebeta

← #30595484

Subgroups — #30595484

Order 15616.

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

normal subgroups only

This group has 608 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#21461747C212yesmaximal, complemented
2#21460636C212yesmaximal, complemented
3#21460635C212yesmaximal, complemented
4C4×#14519773C211yesmaximal, characteristic
5#16840628—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×#14519773C411yescharacteristic
9C2×C4×D244C411yescharacteristic
10C2×C4×C22⋊D61—22no—
11#16839665C2211yescharacteristic
12#16839663C2211yescharacteristic
13#16839662—22no—
14#16839631C411yescharacteristic
15C42×Dic61C2211yescharacteristic
16C2×C4×D4×C61C411yescharacteristic
17C22×#92420—24no—
18C22×D244C2×C411yescharacteristic
19C22×C22⋊D61—22no—
20C22×C4×D61—21no—
21#14519773—22no—
22#14519773C814yescomplemented
23C4×D244—42no—
24C4×C22⋊D61—48no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—22no—
27C2×C22⋊Dic61—22no—
28C2×#11758198—21no—
29C2×#11758198—22no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D412yes—
32C2×C4×Dic61D412yes—
33C2×C4×Dic61C2311yescharacteristic
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—
41C23×D61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—41no—
44C2×D4×C61—41no—
45C2×D4×C61C2×C812yes—
46C22×C4×C61—21no—
47C22×C4×C61—44no—
48C22×C4×C61—42no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22×C411yescharacteristic
52C2×C22⋊D61—28no—
53C2×C22⋊D61—44no—
54C2×C22⋊D61—44no—
55C22×Dic61—21no—
56C22×Dic61C22⋊C412yes—
57C22×Dic61C2×D412yes—
58C2×D244—21no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244C2×C812yes—
62C2×C4×D61—44no—
63C2×C4×D61—42no—
64C2×#92420—44no—
65C2×#92420—44no—
66C2×#92420—44no—
67C4⋊C4×C61—41no—
68C22⋊C4×C61—42no—
69C42×C61—22no—
70C22⋊Dic61—44no—
71#11758198—42no—
72#11758198—44no—
73C4⋊Dic61—41no—
74#11758196—44no—
75C4×Dic61—24no—
76C4×Dic61—42no—
77C4×Dic61—41no—
78C4×Dic61C2×C812yes—
79C4×Dic61M1612yes—
80C23×C61—22no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86C22×D61—22no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61—42no—
90C22×D61—42no—
91D4×C61—42no—
92D4×C61—42no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—84no—
101C2×C4×C61#10012yes—
102C2×C4×C61C22×C811yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C22⋊D61—416no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—41no—
110C2×Dic61—42no—
111C2×Dic61C22⋊C814yes—
112C2×Dic61AGL(1,ℤ/8)14yes—
113D244—42no—
114D244—42no—
115C4×D61—84no—
116#92420—84no—
117#7603—611nomaximal, Sylow
118C22×C61—42no—
119C22×C61—44no—
120C22×C61—81no—
121C22×C61—81no—
122C22×C61—82no—
123C22×C61C2×C22⋊C811yescharacteristic
124C22×C61#41011yescharacteristic
125C22×C61C2×#10011yescharacteristic
126C22×C61#41812yes—
127C22×C61#42112yes—
128C2×D61—42no—
129C2×D61—44no—
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—82no—
133C4×C61—22no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—81no—
138Dic61—24no—
139Dic61—24no—
140Dic61—81no—
141C4×#127—611no—
142#1839—612no—
143#1270—612no—
144#1270—612no—
145C2×C61—82no—
146C2×C61#146011yescharacteristic
147C2×C61#147812yes—
148C2×C61#151412yes—
149C2×C61#153611yescharacteristic
150C2×C61#155511yescharacteristic
151D61—82no—
152C2×#127—611no—
153C2×C4×D4—611no—
154C2×C4×D4—1222no—
155C2×C4×D4#692311yescharacteristic
156#390—611no—
157#390—611no—
158#390—1222no—
159#384—611no—
160C43—611no—
161#336—614no—
162#336—1222no—
163#336—1222no—
164C61#760311yescharacteristic, complemented, Sylow
165C22×D4—611no—
166C22×D4—1222no—
167C22×D4C2×#692311yescharacteristic
168C23×C4—21no—
169C23×C4—1221no—
170C22×C8—1224no—
171#127—614no—
172#127—1222no—
173C4×D4—42no—
174C4×D4—2442no—
175C4×D4—2448no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—1222no—
178C2×C4⋊C4C2×#692311yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—1222no—
181C2×C22⋊C4—1222no—
182C2×C22⋊C4—1221no—
183C2×C42—611no—
184C2×C42—612no—
185C2×C42—612no—
186C2×C42—611no—
187C2×C42C2×#692311yescharacteristic
188C24—21no—
189C24—1221no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—612no—
194C2×D4—1228no—
195C2×D4—1221no—
196C2×D4—2441no—
197C2×D4—2441no—
198C2×D4—2444no—
199C2×D4—2444no—
200C2×D4D61⋊C812yes—
201C22×C4—21no—
202C22×C4—44no—
203C22×C4—42no—
204C22×C4—612no—
205C22×C4—612no—
206C22×C4—1221no—
207C22×C4—2444no—
208C22×C4—2442no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212C2×C8—2444no—
213C2×C8—2444no—
214C2×C8—2444no—
215C4⋊C4—41no—
216C4⋊C4—2441no—
217C4⋊C4—2444no—
218C22⋊C4—42no—
219C22⋊C4—2442no—
220C22⋊C4—2444no—
221C22⋊C4—2444no—
222C42—22no—
223C42—612no—
224C42—612no—
225C42—1224no—
226C42—2441no—
227C42—2442no—
228C23—22no—
229C23—41no—
230C23—41no—
231C23—42no—
232C23—42no—
233C23—1222no—
234C23—2441no—
235C23—2441no—
236C23—2442no—
237C23—2442no—
238C23C2×C22⋊#692311yescharacteristic
239D4—42no—
240D4—42no—
241D4—2442no—
242D4—2442no—
243D4—24416no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—614no—
253C2×C4—614no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—4884no—
259C2×C4—2441no—
260C2×C4—2442no—
261C2×C4#1451983712yes—
262C2×C4C2×D61⋊C811yescharacteristic
263C2×C4D61⋊M1611yescharacteristic
264C8—4884no—
265C22—42no—
266C22—44no—
267C22—81no—
268C22—81no—
269C22—82no—
270C22—4881no—
271C22—4881no—
272C22—4882no—
273C22—2442no—
274C22—2444no—
275C22D61⋊(C22⋊C8)11yescharacteristic
276C22#1684074111yescharacteristic
277C22C2×#1451983711yescharacteristic
278C22#1684075412yes—
279C22#1684075912yes—
280C4—21no—
281C4—21no—
282C4—22no—
283C4—41no—
284C4—81no—
285C4—1224no—
286C4—1224no—
287C4—4881no—
288C2—82no—
289C2—4882no—
290C2#2146105811yescharacteristic
291C2#2146111912yes—
292C2#2146123812yes—
293C2#2146130711yescharacteristic
294C2#2146134611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7603
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. #21461747C2semidirect
2. #21460636C2semidirect
3. #21460635C2semidirect
22. #14519773C8semidirect
164. C61#7603semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606362
#214606352
C4×#145197732
#760361