Finite Group Databasebeta

← #29590626

Subgroups — #29590626

Order 15616.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#14519692C211yesmaximal, characteristic
2#21444160C211yesmaximal, characteristic
3#21443843C214yesmaximal, complemented
4C61×#2487C211yesmaximal, characteristic
5#16839819—21no—
6C2×#14519692—21no—
7C4×C22⋊Dic61—21no—
8#16839529C2212yes—
9#16839486—21no—
10#16839486C2212yes—
11C2×C4×D4×C61C2211yescharacteristic
12C22×C4⋊C4×C61C411yescharacteristic, complemented
13C61×#400C412yescomplemented
14C61×#399C2212yes—
15C61×#389—21no—
16C61×#386—21no—
17C61×#385—21no—
18C61×#380—21no—
19C61×#380C411yescharacteristic, complemented
20C2×C22⋊Dic61—22no—
21C2×C4×Dic61—41no—
22C4⋊#92418—41no—
23#14519692—24no—
24C22⋊#92418—22no—
25#14519688—41no—
26#14519684—41no—
27C22×D4×C61D411yescharacteristic
28C23×C4×C61—21no—
29C23×C4×C61C2×C411yescharacteristic
30C23×C4×C61D411yescharacteristic
31C4×D4×C61—41no—
32C4×D4×C61—41no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—22no—
36C2×C4⋊C4×C61—41no—
37C2×C4⋊C4×C61—41no—
38C2×C4⋊C4×C61C2×C412yes—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—22no—
42C2×C22⋊C4×C61D411yescharacteristic
43C2×C22⋊C4×C61C2311yescharacteristic
44C2×C42×C61D411yescharacteristic
45#95×C61—22no—
46#95×C61—22no—
47#95×C61C2×C412yes—
48C24×C61C22⋊C411yescharacteristic
49C24×C61C2×D411yescharacteristic
50C2×D4×C61—22no—
51C2×D4×C61—22no—
52C2×D4×C61—41no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—82no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—42no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—82no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—82no—
79C42×C61—21no—
80C42×C61—21no—
81C22⋊Dic61—24no—
82C22⋊Dic61—42no—
83C4×Dic61—82no—
84C2×#92418—42no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—41no—
90C23×C61—41no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61#10412yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61#13712yes—
96D4×C61—44no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—81no—
117C2×C4×C61—84no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#9911yescharacteristic
120C2×Dic61—44no—
121C2×Dic61—82no—
122C2×Dic61—82no—
123#92418—82no—
124#11786—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61C2×#9911yescharacteristic
138C22×C61#41911yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—82no—
146C4×C61—82no—
147C4×C61#35212yes—
148Dic61—84no—
149#2487D6111yescharacteristic
150C4×#99—611no—
151#1466—611no—
152#1352—614no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61—42no—
156C2×C61—42no—
157C2×C61#150811yescharacteristic
158C2×C61C2×#35211yescharacteristic
159C2×C61#212811yescharacteristic
160C2×C4×D4C2×D6111yescharacteristic
161C22×C4⋊C4Dic6111yescharacteristic, complemented
162#432—1221no—
163C2×#99—1221no—
164#400Dic6112yescomplemented
165#399C2×D6112yes—
166#389—21no—
167#386—21no—
168#385—21no—
169#380—21no—
170#380Dic6111yescharacteristic, complemented
171C4×C22⋊C4—1221no—
172#342—612no—
173#323—612no—
174#323—1221no—
175C61#1178611yescharacteristic, complemented, Sylow
176C22×D4C22⋊D6111yescharacteristic
177C23×C4—21no—
178C23×C4C2×Dic6111yescharacteristic
179C23×C4C22⋊D6111yescharacteristic
180C4×D4—41no—
181C4×D4—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4C2×Dic6112yes—
188C2×C4⋊C4C2×Dic6111yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—1222no—
192C2×C22⋊C4C22⋊D6111yescharacteristic
193C2×C22⋊C4C22×D6111yescharacteristic
194C2×C42—2441no—
195C2×C42C22⋊D6111yescharacteristic
196C4⋊C8—2441no—
197#99—1224no—
198C22⋊C8—1222no—
199#97—2441no—
200#95—22no—
201#95—22no—
202#95—2441no—
203#95C2×Dic6112yes—
204C24C22⋊Dic6111yescharacteristic
205C24C2×C22⋊D6111yescharacteristic
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—82no—
219C22×C4—2442no—
220C22×C4C22⋊Dic6111yescharacteristic
221C22×C4C22⋊Dic6111yescharacteristic
222C22×C4C22⋊Dic6111yescharacteristic
223C22×C4C22×Dic6111yescharacteristic
224C22×C4C2×C22⋊D6111yescharacteristic
225C2×C8—2442no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—82no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—42no—
235C22⋊C4—82no—
236C22⋊C4—1224no—
237C22⋊C4—2442no—
238C42—21no—
239C42—21no—
240C42—4882no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23#1451970412yes—
250C23C2×C22⋊Dic6111yescharacteristic
251C23#1451980812yes—
252D4—44no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—81no—
273C2×C4—84no—
274C2×C4—4882no—
275C2×C4—4882no—
276C2×C4—2444no—
277C2×C4#1451969211yescharacteristic
278C2×C4#1451969211yescharacteristic
279C8—4882no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22C2×#1451969211yescharacteristic
293C22#1683977111yescharacteristic
294C22C2×#1451970411yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—82no—
301C4—82no—
302C4—4884no—
303C4#1683955212yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#2144433911yescharacteristic
309C2C2×#1683955211yescharacteristic
310C2#2144749111yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2487C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#2487D61
hypocenterC61#11786
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #21443843C2semidirect
12. C22×C4⋊C4×C61C4semidirect
13. C61×#400C4semidirect
19. C61×#380C4semidirect
161. C22×C4⋊C4Dic61semidirect
164. #400Dic61semidirect
170. #380Dic61semidirect
175. C61#11786semidirect

Maximal subgroups

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

subgroupindex
C4×#145196922
#214441602
#214438432
C61×#24872
#1178661