Finite Group Databasebeta

← #30604178

Subgroups — #30604178

Order 15616.

596 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461076C212yesmaximal, complemented
2#21460761C212yesmaximal, complemented
3#21460748C212yesmaximal, complemented
4C4×#14519774C211yesmaximal, characteristic
5#16840733—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519774C411yescharacteristic
9C2×C4×D244—22no—
10C2×C4×D244C411yescharacteristic
11C2×C4×D244C2211yescharacteristic
12#16839664—22no—
13#16839664C411yescharacteristic
14#16839664C2211yescharacteristic
15#16839632C2211yescharacteristic
16C43×C61C411yescharacteristic
17C2×#11758213—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C22×D244—22no—
21C22×D244C2×C411yescharacteristic
22C22×D244C2×C411yescharacteristic
23C22×C4×D61—21no—
24C22×C4×D61D412yes—
25#14519774—22no—
26#14519774—22no—
27C4×D244—41no—
28C4×D244—41no—
29C4×D244—48no—
30C4×D244—41no—
31C4×D244—41no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2311yescharacteristic
35C2×#11758198—22no—
36C2×#11758198—21no—
37C2×#11758198—22no—
38C2×#11758198D412yes—
39C2×C42×C61—21no—
40C2×C42×C61—21no—
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C23×D61—21no—
45C23×D61C22⋊C412yes—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61C2×D412yes—
53C2×D244—28no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244—21no—
57C2×D244—41no—
58C2×D244—41no—
59C2×D244—44no—
60C2×D244—44no—
61C2×D244—41no—
62C2×D244—41no—
63C2×D244M1612yescomplemented
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—44no—
67C2×C4×D61—44no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×#92420—44no—
71#11758213—84no—
72C42×C61—24no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—42no—
77C42×C61—41no—
78C42×C61M1612yescomplemented
79#11758198—42no—
80#11758198—44no—
81#11758198—44no—
82#11758198—42no—
83C4⋊Dic61—41no—
84C4⋊Dic61—44no—
85C4⋊Dic61—41no—
86C23×C61C2×C22⋊C411yescharacteristic
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—41no—
96C22×D61—41no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#9911yescharacteristic
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×C4×C61C2×M1611yescharacteristic
112C2×Dic61—22no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116D244—42no—
117D244—416no—
118D244—42no—
119D244—42no—
120D244—42no—
121C4×D61—44no—
122C4×D61—82no—
123C4×D61—82no—
124C4×D61—82no—
125#92420—84no—
126#11529—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61#40711yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C22×C61#41311yescharacteristic
132C2×D61—44no—
133C2×D61—44no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—82no—
139C2×D61—81no—
140C2×D61—81no—
141C2×D61—82no—
142C4×C61—24no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61#35312yes—
149Dic61—42no—
150Dic61—81no—
151C4×#127—611no—
152#1465—612no—
153#1325—612no—
154#1318—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61#146511yescharacteristic
158C2×C61C2×#35311yescharacteristic
159C2×C61#213211yescharacteristic
160D61—82no—
161D61—82no—
162C2×#127—611no—
163C2×C4×D4—611no—
164C2×C4×D4—611no—
165C2×C4×D4—1222no—
166#407—1222no—
167#390—611no—
168#390—611no—
169#390—1222no—
170#384—611no—
171C43#692311yescharacteristic
172#324—614no—
173#323—1222no—
174C61#1152911yescharacteristic, complemented, Sylow
175C22×D4—611no—
176C22×D4—611no—
177C22×D4—1222no—
178C23×C4—612no—
179C23×C4—1221no—
180C2×M16—2442no—
181#127—1222no—
182#127—1222no—
183C4×D4—2441no—
184C4×D4—2441no—
185C4×D4—2448no—
186C4×D4—2441no—
187C4×D4—2441no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1222no—
191C2×C22⋊C4—612no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1221no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42C2×#692311yescharacteristic
198C2×C42C2×#692311yescharacteristic
199C2×C42C2×#692311yescharacteristic
200C22⋊C8—1224no—
201C22⋊C8—2442no—
202C24—612no—
203C24—1221no—
204C2×D4—612no—
205C2×D4—1228no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4—2441no—
210C2×D4—2441no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2444no—
214C2×D4—2444no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—612no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4—1221no—
221C22×C4—2444no—
222C22×C4—2444no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228M16—4884no—
229C2×C8—2444no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2444no—
233C22⋊C4—2442no—
234C22⋊C4—2444no—
235C22⋊C4—2444no—
236C22⋊C4—2442no—
237C42—24no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—41no—
242C42—42no—
243C42#1175821312yescomplemented
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23—1222no—
248C23—2442no—
249C23—2442no—
250C23—2442no—
251C23—2442no—
252C23—2441no—
253C23—2441no—
254C23C2×C22⋊#692311yescharacteristic
255D4—2442no—
256D4—24416no—
257D4—2442no—
258D4—2442no—
259D4—2442no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—1222no—
272C2×C4—4882no—
273C2×C4—4882no—
274C2×C4—4882no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4—2444no—
278C2×C4—2442no—
279C2×C4#1451983611yescharacteristic
280C2×C4#1451983611yescharacteristic
281C2×C4D61⋊M1611yescharacteristic
282C2×C4C2×#1175821311yescharacteristic
283C8—4884no—
284C22—21no—
285C22—21no—
286C22—4882no—
287C22—4882no—
288C22—4881no—
289C22—4881no—
290C22—2444no—
291C22—2444no—
292C22—2442no—
293C22—2442no—
294C22—2442no—
295C22—2442no—
296C22#1684073311yescharacteristic
297C22C2×#1451983611yescharacteristic
298C22#1684074811yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—4881no—
306C4—2442no—
307C4#1684066712yes—
308C2—21no—
309C2—21no—
310C2—4882no—
311C2—4882no—
312C2#2146107611yescharacteristic
313C2C2×#1684066711yescharacteristic
314C2#2146211211yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC43×C61C4
socleC22×C61C2×#99
prime radicalC2×#14519774C4
cosocleC2×C4⋊Dic61C23
hypercenterC43#6923
hypocenterC61#11529
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
1. #21461076C2semidirect
2. #21460761C2semidirect
3. #21460748C2semidirect
63. C2×D244M16semidirect
78. C42×C61M16semidirect
174. C61#11529semidirect
243. C42#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214607612
#214607482
C4×#145197742
#1152961