Finite Group Databasebeta

← #30609364

Subgroups — #30609364

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840711C214yesmaximal
2#21461008C214yesmaximal
3#21461004C212yesmaximal
4#21460998C212yesmaximal
5#21460995C212yesmaximal
6#384×D61C211yesmaximal, characteristic
7C22×C4⋊#6923C2212yes—
8C22×C4×#6923C2212yes—
9#16840711—216no—
10C2×(C2×#6923)⋊C4C2214yes—
11C2×(C2×#6923)⋊C4C2212yes—
12C2×(C2×#6923)⋊C4C2214yes—
13C2×(C2×#6923)⋊C4C2214yes—
14C2×(C2×#6923)⋊C4C2214yes—
15C2×(C2×#6923)⋊C4C2212yes—
16C2×(C2×#6923)⋊C4C2212yes—
17C2×(C2×#6923)⋊C4C2212yes—
18C2×C4⋊C4×D61C2214yes—
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C42×D61C2211yescharacteristic
22#16839632C411yescharacteristic, complemented
23#16839631C414yescomplemented
24#16839631C411yescharacteristic, complemented
25#16839631C411yescharacteristic, complemented
26C61×#384C411yescharacteristic, complemented
27C23×#6923C2314yes—
28C23×#6923C2314yes—
29C2×C4⋊#6923—28no—
30C2×C4⋊#6923—42no—
31C2×C4×#6923—28no—
32C2×C4×#6923—42no—
33(C2×#6923)⋊C4—28no—
34(C2×#6923)⋊C4—28no—
35(C2×#6923)⋊C4—28no—
36(C2×#6923)⋊C4—28no—
37(C2×#6923)⋊C4—24no—
38(C2×#6923)⋊C4—42no—
39(C2×#6923)⋊C4—42no—
40(C2×#6923)⋊C4D418yes—
41C22×C4×D61C2312yes—
42C22×C4×D61C2312yes—
43C22×C4×D61C2312yes—
44C22×C4×D61C2311yescharacteristic
45C2×C4⋊Dic61C2×C414yes—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196C2×C414yes—
49C2×#11758196C2×C414yes—
50C2×#11758196C2×C412yes—
51C2×#11758196C2×C412yes—
52C4⋊C4×D61—28no—
53C4⋊C4×D61—28no—
54C4⋊C4×D61—41no—
55C4⋊C4×D61—41no—
56C4⋊C4×D61—41no—
57C4⋊C4×D61—41no—
58C2×C4×Dic61C2×C411yescharacteristic
59C2×C4×Dic61C2×C412yes—
60C42×D61—24no—
61C2×C4⋊C4×C61C2×C414yes—
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C42×C61C2×C411yescharacteristic
65C23×D61C2411yescharacteristic
66C22×#6923—24no—
67C22×#6923—24no—
68C22×#6923—24no—
69C22×#6923—24no—
70C22×#6923—24no—
71C22×#6923—24no—
72C22×#6923—24no—
73C22×#6923—24no—
74C22×#6923—24no—
75C22×#6923—24no—
76C22×#6923—24no—
77C22×#6923—24no—
78C22×#6923—24no—
79C22×#6923C2×D418yes—
80C22×C4×C61C22×C412yes—
81C22×C4×C61C22×C412yes—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C22×C412yes—
84C22×Dic61C22×C412yes—
85C22×Dic61C22×C412yes—
86C22×Dic61C22×C411yescharacteristic
87C22×Dic61C22×C412yes—
88C2×C4×D61—24no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—22no—
92C2×C4×D61—24no—
93C2×C4×D61—24no—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—24no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61C2×D414yes—
102C2×C4×D61#4114yes—
103C2×C4×D61#4114yes—
104C4⋊#6923—48no—
105C4×#6923—48no—
106C4⋊C4×C61—28no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C42×C61—22no—
110C4⋊Dic61—28no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113#11758196—28no—
114#11758196—28no—
115#11758196—42no—
116#11758196—42no—
117C4×Dic61—22no—
118C4×Dic61—24no—
119C23×C61C23×C411yescharacteristic
120C22×D61C22×D412yes—
121C22×D61C2×#4112yes—
122C22×D61C2×#4112yes—
123C22×D61H(5,𝔽2)11yescharacteristic
124C22×D61H(5,𝔽2)11yescharacteristic
125C22×D612−1+412yes—
126C22×D612−1+414yes—
127C2×#6923—28no—
128C2×#6923—28no—
129C2×#6923—28no—
130C2×#6923—44no—
131C2×#6923—44no—
132C2×#6923—44no—
133C2×#6923—44no—
134C2×#6923—44no—
135C2×#6923—44no—
136C2×#6923—44no—
137C2×#6923—44no—
138C2×#6923—44no—
139C2×#6923—44no—
140C2×#6923—44no—
141C2×C4×C61—22no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—24no—
146C2×C4×C61—24no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61#11712yes—
150C2×C4×C61C4×D414yes—
151C2×Dic61—22no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—22no—
155C2×Dic61—24no—
156C2×Dic61—24no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61#11712yes—
160C2×Dic61C4×D414yes—
161C4×D61—24no—
162C4×D61—24no—
163C4×D61—28no—
164C4×D61—28no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—44no—
168C4×D61—44no—
169C4×D61—42no—
170C4×D61—42no—
171#14424—611nomaximal, Sylow
172C22×C61C2×#11711yescharacteristic
173C22×C61C2×C4×D412yes—
174C22×C61#51811yescharacteristic
175C22×C61#51911yescharacteristic
176C22×C61#51912yes—
177C2×D61#53614yes—
178C2×D61#53912yes—
179C2×D61#53912yes—
180C2×D61#54114yes—
181C2×D61D4211yescharacteristic
182C2×D61#54714yes—
183C2×D61#55012yes—
184C2×D61#55214yes—
185C2×D61#55911yescharacteristic
186C2×D61#56312yes—
187C2×D61#56312yes—
188#6923—48no—
189#6923—84no—
190C4×C61—22no—
191C4×C61—24no—
192C4×C61—42no—
193C4×C61—42no—
194Dic61—22no—
195Dic61—24no—
196Dic61—42no—
197Dic61—42no—
198C2×#387—614no—
199C2×#384—611no—
200#1445—614no—
201#1441—612no—
202#1436—612no—
203#1434—612no—
204C2×C61#231311yescharacteristic
205C2×C61#232712yes—
206C2×C61#234412yes—
207C2×C61#236611yescharacteristic
208C2×C61#238111yescharacteristic
209D61#268012yes—
210D61#272114yes—
211D61#279412yes—
212C22×C4⋊C4—614no—
213C22×C4⋊C4—611no—
214C22×C4⋊C4—611no—
215C22×C4⋊C4—612no—
216C22×C42—611no—
217C22×C42—612no—
218#387—12216no—
219#384—611no—
220#384—611no—
221#384—614no—
222#384—611no—
223#384#692311yescharacteristic, complemented
224C2×#95—612no—
225C2×#95—614no—
226C2×#95—612no—
227C2×#95—614no—
228C2×#95—614no—
229C2×#95—614no—
230C2×#95—612no—
231C2×#95—612no—
232C61#1442411yescharacteristic, complemented, Sylow
233C23×C4—611no—
234C23×C4—612no—
235C23×C4—614no—
236C23×C4—612no—
237C23×C4—612no—
238C23×C4—614no—
239C2×C4⋊C4—614no—
240C2×C4⋊C4—614no—
241C2×C4⋊C4—614no—
242C2×C4⋊C4—612no—
243C2×C4⋊C4—612no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—1228no—
247C2×C4⋊C4—1228no—
248C2×C4⋊C4—1228no—
249C2×C4⋊C4—2441no—
250C2×C4⋊C4—2441no—
251C2×C4⋊C4—2441no—
252C2×C4⋊C4—2441no—
253C2×C4⋊C4—2442no—
254C2×C4⋊C4C2×#692314yes—
255C2×C4⋊C4C2×#692311yescharacteristic
256C2×C4⋊C4C2×#692311yescharacteristic
257C2×C42—612no—
258C2×C42—611no—
259C2×C42—1224no—
260C2×C42—1228no—
261C2×C42—2442no—
262C2×C42C2×#692311yescharacteristic
263#95—618no—
264#95—1228no—
265#95—1224no—
266#95—1228no—
267#95—1228no—
268#95—1228no—
269#95—2442no—
270#95—2442no—
271C24—611no—
272C22×C4—611no—
273C22×C4—612no—
274C22×C4—614no—
275C22×C4—614no—
276C22×C4—614no—
277C22×C4—618no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—1224no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1224no—
285C22×C4—1224no—
286C22×C4—1224no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1224no—
291C22×C4—1224no—
292C22×C4—1222no—
293C22×C4—1224no—
294C22×C4—1224no—
295C22×C4—1224no—
296C22×C4—1224no—
297C22×C4—1224no—
298C22×C4—1224no—
299C22×C4—1224no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1224no—
303C22×C4—1224no—
304C22×C4—1224no—
305C22×C4—1224no—
306C22×C4C22×#692312yes—
307C22×C4C22×#692312yes—
308C22×C4C22×#692311yescharacteristic
309C22×C4C22×#692312yes—
310C4⋊C4—28no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—1228no—
314C4⋊C4—1228no—
315C4⋊C4—1228no—
316C4⋊C4—2442no—
317C4⋊C4—2442no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2448no—
321C42—22no—
322C42—1224no—
323C42—1222no—
324C42—2448no—
325C23—612no—
326C23—612no—
327C23—612no—
328C23—611no—
329C23—611no—
330C23—612no—
331C23—614no—
332C23C23×#692311yescharacteristic
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—612no—
342C2×C4—614no—
343C2×C4—1224no—
344C2×C4—1224no—
345C2×C4—1228no—
346C2×C4—1228no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1222no—
351C2×C4—1228no—
352C2×C4—1228no—
353C2×C4—1228no—
354C2×C4—1224no—
355C2×C4—1224no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2444no—
361C2×C4—2444no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2444no—
365C2×C4—2444no—
366C2×C4—2444no—
367C2×C4—2444no—
368C2×C4—2444no—
369C2×C4—2444no—
370C2×C4—2444no—
371C2×C4—2444no—
372C2×C4—2444no—
373C2×C4—2444no—
374C2×C4—2444no—
375C2×C4#1451985612yes—
376C2×C4D4×#692314yes—
377C22—612no—
378C22—612no—
379C22—614no—
380C22—614no—
381C22—614no—
382C22—614no—
383C22—611no—
384C22—612no—
385C22—611no—
386C22—612no—
387C22—612no—
388C22C2×#1451985611yescharacteristic
389C22C2×D4×#692312yes—
390C22#1684082911yescharacteristic
391C22#1684083011yescharacteristic
392C22#1684083012yes—
393C4—22no—
394C4—24no—
395C4—42no—
396C4—42no—
397C4—1222no—
398C4—1224no—
399C4—4884no—
400C4—2448no—
401C4—2442no—
402C4—2442no—
403C2—614no—
404C2—612no—
405C2—612no—
406C2#2146229611yescharacteristic
407C2#2146231012yes—
408C2#2146232712yes—
409C2#2146234911yescharacteristic
410C2#2146236411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#384C4
prime radical, cosocleC23×D61C24
hypercenter#384#6923
hypocenterC61#14424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
22. #16839632C4semidirect
23. #16839631C4semidirect
24. #16839631C4semidirect
25. #16839631C4semidirect
26. C61×#384C4semidirect
223. #384#6923semidirect
232. C61#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
#214610082
#214610042
#214609982
#214609952
#384×D612
#1442461