Finite Group Databasebeta

← #30594746

Subgroups — #30594746

Order 15616.

456 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461655C211yesmaximal, characteristic
2#21461648C211yesmaximal, characteristic
3#21445745C211yesmaximal, characteristic
4C2×#14519838—21no—
5C2×#14519837—21no—
6C2×#14519836—21no—
7C2×#14519835—21no—
8#16840734C412yescomplemented
9#16840705C412yes—
10C22×#11758222C2211yescharacteristic
11C2×#14519695—21no—
12C2×#14519693—21no—
13#16839726C411yescharacteristic, complemented
14C61×#407C411yescharacteristic, complemented
15C2×#11758217—22no—
16C2×C22⋊#6923—22no—
17#14519838—41no—
18#14519838—41no—
19#14519837—42no—
20#14519836—41no—
21#14519836—41no—
22#14519835—42no—
23#14519834—42no—
24(C2×#6923)⋊C4—42no—
25C2×#11758222—42no—
26C2×#11758222—41no—
27C2×#11758222—41no—
28C2×#11758222—42no—
29C22×Dic122D411yescharacteristic
30C22×D244D411yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C22×C22⋊D61Q811yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61C2×C411yescharacteristic
35C2×#11758194—21no—
36#14519695—42no—
37#14519693—42no—
38C22⋊#92418—41no—
39C23×C4×C61C2×C411yescharacteristic
40C2×M16×C61—21no—
41C22⋊C8×C61—41no—
42C24×C61C4⋊C411yescharacteristic
43C23×D61C22⋊C411yescharacteristic
44C23×D61C4⋊C411yescharacteristic
45C22×#6923—42no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61C4211yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—41no—
55C2×C22⋊D61—41no—
56C2×C22⋊D61—41no—
57C2×C22⋊D61—41no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C4⋊C411yescharacteristic
60#11758222—48no—
61#11758222—48no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244—41no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—22no—
75C2×Dic122—41no—
76C22⋊#6923—42no—
77C22⋊#6923—42no—
78#11758217—42no—
79#11758217—42no—
80C2×#92420—42no—
81M16×C61—41no—
82M16×C61—41no—
83C2×C8×C61—41no—
84#11758194—41no—
85#11758194—41no—
86C2×#92418—41no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—81no—
91C23×C61#9511yescharacteristic
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—81no—
98C22×D61—81no—
99C22×D61#9912yes—
100C2×#6923—82no—
101C2×#6923—84no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61#9911yescharacteristic
111C22⋊D61—44no—
112C22⋊D61—44no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61#9912yes—
119D244—42no—
120D244—42no—
121C4×D61—44no—
122C4×D61—44no—
123Dic122—42no—
124Dic122—42no—
125#92420—82no—
126C8×C61—81no—
127#92418—81no—
128#7319—611nomaximal, Sylow
129C22×C61—41no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61#34211yescharacteristic
135C22×C61#34211yescharacteristic
136C22×C61#34211yescharacteristic
137C2×D61—22no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—41no—
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—81no—
145#6923—162no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149Dic61—22no—
150Dic61—41no—
151#1785—611no—
152#1785—611no—
153#1782—611no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61—81no—
158C2×C61#130411yescharacteristic
159D61—42no—
160D61—81no—
161C22×#41—611no—
162C2×#101—1221no—
163C2×#101—1221no—
164C2×#100—1221no—
165C2×#100—1221no—
166C2×#99—1221no—
167C2×#99—1221no—
168#407—612no—
169#407—611no—
170#407#692311yescharacteristic, complemented
171#381—612no—
172C61#731911yescharacteristic, complemented, Sylow
173C2×#41—2441no—
174C2×#41—2441no—
175C2×#41—2442no—
176C2×#41—2442no—
177C22×Q8—611no—
178C22×D4—611no—
179C22×D4—611no—
180C22×D4—611no—
181C23×C4—611no—
182C23×C4—611no—
183C23×C4C2×#692311yescharacteristic
184C2×M16—21no—
185C2×M16—1222no—
186C2×M16—1221no—
187C2×C22⋊C4—1222no—
188#101—2442no—
189#101—2441no—
190#101—2441no—
191#100—2442no—
192#100—2442no—
193#99—2442no—
194#99—2441no—
195#99—2441no—
196C22⋊C8—41no—
197C22⋊C8—2441no—
198C22⋊C8—2442no—
199#95—2442no—
200C24—611no—
201C24—611no—
202C24C4⋊#692311yescharacteristic
203#41—2448no—
204#41—2448no—
205C2×Q8—1222no—
206C2×Q8—1221no—
207C2×Q8—1221no—
208C2×Q8—2441no—
209C2×D4—1222no—
210C2×D4—1222no—
211C2×D4—1222no—
212C2×D4—1221no—
213C2×D4—1221no—
214C2×D4—2441no—
215C2×D4—2441no—
216C2×D4—2441no—
217C2×D4—2441no—
218C2×D4—2441no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—1222no—
226C22×C4—1222no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4—2442no—
232C22×C4C4×#692311yescharacteristic
233C22×C4C22⋊#692311yescharacteristic
234M16—41no—
235M16—41no—
236M16—2441no—
237M16—2441no—
238M16—2442no—
239M16—2442no—
240C2×C8—41no—
241C2×C8—2442no—
242C2×C8—2441no—
243C22⋊C4—2442no—
244C22⋊C4—2442no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—81no—
249C23—612no—
250C23—1221no—
251C23—1221no—
252C23—1221no—
253C23—1221no—
254C23—1221no—
255C23—4881no—
256C23—4881no—
257C23(C2×#6923)⋊C411yescharacteristic
258Q8—2442no—
259Q8—2442no—
260D4—2442no—
261D4—2442no—
262D4—2444no—
263D4—2444no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—612no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—4882no—
278C2×C4—4884no—
279C2×C4—2444no—
280C2×C4—2444no—
281C2×C4#1451983511yescharacteristic
282C2×C4#1451983611yescharacteristic
283C8—81no—
284C8—4881no—
285C8—4882no—
286C22—41no—
287C22—42no—
288C22—41no—
289C22—81no—
290C22—81no—
291C22—1222no—
292C22—4881no—
293C22—4881no—
294C22—4881no—
295C22—4881no—
296C22—2442no—
297C22—2442no—
298C22—2441no—
299C22#1684063911yescharacteristic
300C22#1684063911yescharacteristic
301C22#1684064011yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—1222no—
306C4—9762no—
307C4—2441no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—4881no—
313C2—2442no—
314C2#2146071811yescharacteristic
subgroupG/H
centerC2#21460718
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC61×#407C4
socleC2×C61#1304
prime radical, cosocleC22×#11758222C22
hypercenter#407#6923
hypocenterC61#7319
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
8. #16840734C4semidirect
13. #16839726C4semidirect
14. C61×#407C4semidirect
170. #407#6923semidirect
172. C61#7319semidirect

Maximal subgroups

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

subgroupindex
#214616552
#214616482
#214457452
#731961