Finite Group Databasebeta

← C2×#21460907 #30606275

Subgroups — C2×#21460907 #30606275

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840741C212yesmaximal
2#21460907C214yesmaximal, direct product factor
3C2×#16839728C211yesmaximal, characteristic
4C2×#14519856—22no—
5#16840741—22no—
6#16840741—22no—
7#16840741C414yescomplemented
8#16840741C2214yes—
9C2×#14519836—22no—
10C2×#14519835C414yescomplemented
11C22×#11758222C2211yescharacteristic
12C22×#11758194C411yescharacteristic, complemented
13#16839728—22no—
14#16839728C412yescomplemented
15#16839728C2212yes—
16C2×#14519689—22no—
17C23×C8×C61C411yescharacteristic, complemented
18#14519856—24no—
19#14519856—24no—
20#14519856—42no—
21#14519856—42no—
22C2×C4⋊#6923—42no—
23C2×C22⋊#6923—24no—
24C2×C4×#6923—42no—
25#14519836—24no—
26#14519836—24no—
27#14519835—24no—
28#14519835C2×C418yescomplemented
29C2×#11758222—41no—
30C2×#11758222—41no—
31C2×#11758222—41no—
32C2×#11758222—41no—
33C2×#11758222C2×C411yescharacteristic
34C2×#11758222C2×C412yes—
35C2×#11758222D411yescharacteristic
36C2×#11758222D412yes—
37C2×#11758222Q811yescharacteristic
38C2×#11758222C2311yescharacteristic
39C22×Dic122Q811yescharacteristic
40C22×D244D411yescharacteristic
41C22×C22⋊D61C2×C412yes—
42C22×C4×D61D412yes—
43C2×#11758194—21no—
44C2×#11758194—41no—
45C2×#11758194—41no—
46C2×#11758194C2×C412yescomplemented
47C22×#92418—21no—
48#14519689—24no—
49#14519689—24no—
50C23×C4×C61C2×C411yescharacteristic
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C22×C8×C61—41no—
54C22×C8×C61—41no—
55C22×C8×C61C2×C412yescomplemented
56C24×C61C4211yescharacteristic
57C23×D61C22⋊C412yes—
58C22×#6923—44no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C4211yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C4⋊C411yescharacteristic
67C22×C4×C61C4⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61C4212yes—
72C2×C22⋊D61C22⋊C412yes—
73C2×C22⋊D61C4⋊C412yes—
74C2×C22⋊D61C22×C412yes—
75C22×Dic61C4⋊C412yes—
76#11758222—42no—
77#11758222—42no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82#11758222—42no—
83#11758222—42no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244C22⋊C412yes—
91C2×D244C4⋊C411yescharacteristic
92C2×D244C2×D411yescharacteristic
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61C22⋊C412yes—
98C2×C4×D61C22⋊C412yes—
99C2×C4×D61C4⋊C412yes—
100C2×C4×D61C2×D412yes—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×Dic122C4⋊C411yescharacteristic
104C2×Dic122C4⋊C412yes—
105C2×Dic122C2×Q811yescharacteristic
106C22⋊#6923—28no—
107C22⋊#6923—44no—
108C4⋊#6923—44no—
109C4⋊#6923—44no—
110C4×#6923—44no—
111C4×#6923—44no—
112C2×C8×C61—22no—
113C2×C8×C61—42no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—42no—
117#11758194—42no—
118#11758194—42no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—42no—
125C23×C61#9511yescharacteristic
126C23×C61#9511yescharacteristic
127C23×C61C2×C4211yescharacteristic
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—44no—
131C22×D61#9512yes—
132C22×D61C2×C22⋊C412yes—
133C2×#6923—48no—
134C2×#6923—88no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61#9511yescharacteristic
146C2×C4×C61#9511yescharacteristic
147C2×C4×C61#9911yescharacteristic
148C2×C4×C61#9911yescharacteristic
149C2×C4×C61#9911yescharacteristic
150C2×C4×C61#9911yescharacteristic
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C2×C4×C61C2×C4⋊C411yescharacteristic
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—42no—
156C22⋊D61—42no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61#9512yes—
160C2×Dic61C2×C4⋊C412yes—
161D244—42no—
162D244—41no—
163D244—41no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—22no—
167C4×D61—22no—
168C4×D61—22no—
169C4×D61—22no—
170C4×D61—22no—
171C4×D61—22no—
172Dic122—41no—
173Dic122—42no—
174Dic122—41no—
175C8×C61—42no—
176#92418—42no—
177C2×#1391—611nomaximal, Sylow
178C22×C61—22no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—42no—
184C22×C61—42no—
185C22×C61#34211yescharacteristic
186C22×C61#34211yescharacteristic
187C22×C61C2×#9511yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—44no—
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—82no—
194#6923—88no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61#34211yescharacteristic
198C4×C61#34211yescharacteristic
199C4×C61C2×#9911yescharacteristic
200C4×C61C2×#9911yescharacteristic
201Dic61—22no—
202Dic61—22no—
203C2×#410—612no—
204C2×#408—611no—
205#1391—614no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—41no—
209C2×C61—41no—
210C2×C61#139112yescomplemented
211C2×C61C2×#34211yescharacteristic
212D61—42no—
213D61—42no—
214C22×#41—611no—
215C22×M16—611no—
216C23×C8#692311yescharacteristic, complemented
217C2×#117—1222no—
218#410—614no—
219#410—614no—
220#410—1222no—
221#410—1222no—
222C2×#99—614no—
223C2×#99—1222no—
224#408—612no—
225#408—612no—
226#408—1222no—
227C2×C22⋊C8—1222no—
228C61C2×#139111yescharacteristic, complemented, Sylow
229C2×#41—612no—
230C2×#41—611no—
231C2×#41—611no—
232C2×#41—612no—
233C2×#41—611no—
234C2×#41—611no—
235C2×#41—2441no—
236C2×#41—2441no—
237C2×#41—2441no—
238C2×#41—2441no—
239C22×Q8—611no—
240C22×D4—612no—
241C22×D4—611no—
242C23×C4—612no—
243C23×C4C2×#692311yescharacteristic
244C2×M16—612no—
245C2×M16—1221no—
246C2×M16—2441no—
247C2×M16—2441no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—41no—
251C22×C8—41no—
252C22×C8—1221no—
253C22×C8C2×#692312yescomplemented
254#117—1224no—
255#117—1224no—
256#117—2442no—
257#117—2442no—
258C2×C4⋊C4—2442no—
259C2×C22⋊C4—1224no—
260C2×C42—2442no—
261#99—618no—
262#99—1224no—
263#99—1224no—
264#99—1224no—
265C22⋊C8—1224no—
266C22⋊C8—1224no—
267C24—612no—
268C24C4×#692311yescharacteristic
269#41—2442no—
270#41—2441no—
271#41—2441no—
272#41—2442no—
273#41—2441no—
274#41—2441no—
275#41—2442no—
276#41—2442no—
277#41—2441no—
278#41—2441no—
279#41—2441no—
280#41—2441no—
281C2×Q8—612no—
282C2×Q8—611no—
283C2×Q8—611no—
284C2×Q8—2441no—
285C2×Q8—2441no—
286C2×D4—612no—
287C2×D4—612no—
288C2×D4—612no—
289C2×D4—612no—
290C2×D4—612no—
291C2×D4—611no—
292C2×D4—611no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2442no—
296C2×D4—2442no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—612no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4—2444no—
311C22×C4C4×#692311yescharacteristic
312C22×C4C4⋊#692311yescharacteristic
313C22×C4C4⋊#692311yescharacteristic
314C22×C4C22⋊#692311yescharacteristic
315C22×C4C22⋊#692311yescharacteristic
316C22×C4C22×#692311yescharacteristic
317M16—2442no—
318M16—2442no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—42no—
324C2×C8—1222no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—2444no—
328C4⋊C4—2444no—
329C22⋊C4—1228no—
330C22⋊C4—2444no—
331C42—2444no—
332C42—2444no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—612no—
337C23—612no—
338C23—1222no—
339C23—1222no—
340C23—2444no—
341C23(C2×#6923)⋊C411yescharacteristic
342C23(C2×#6923)⋊C411yescharacteristic
343C23C2×C4×#692311yescharacteristic
344Q8—2442no—
345Q8—2441no—
346Q8—2441no—
347D4—2442no—
348D4—2441no—
349D4—2441no—
350D4—2442no—
351D4—2442no—
352D4—2442no—
353D4—2442no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—4888no—
377C2×C4—2448no—
378C2×C4(C2×#6923)⋊C411yescharacteristic
379C2×C4(C2×#6923)⋊C411yescharacteristic
380C2×C4#1451983511yescharacteristic
381C2×C4#1451983511yescharacteristic
382C2×C4#1451983611yescharacteristic
383C2×C4#1451983611yescharacteristic
384C2×C4C2×C22⋊#692311yescharacteristic
385C2×C4C2×C4⋊#692311yescharacteristic
386C8—42no—
387C8—2442no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—42no—
394C22—42no—
395C22—1222no—
396C22—1222no—
397C22—4882no—
398C22—2442no—
399C22—2442no—
400C22—2444no—
401C22#1684064011yescharacteristic
402C22#1684064011yescharacteristic
403C22C2×(C2×#6923)⋊C411yescharacteristic
404C4—21no—
405C4—21no—
406C4—1222no—
407C4—1222no—
408C4—4888no—
409C4#1684064011yescharacteristic
410C4#1684064011yescharacteristic
411C4C2×#1451983511yescharacteristic
412C4C2×#1451983611yescharacteristic
413C2—21no—
414C2—21no—
415C2—41no—
416C2—41no—
417C2—2442no—
418C2—2442no—
419C2#2146090712yesdirect product factor
420C2C2×#1684064011yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC22×C61#342
prime radicalC22×#11758222C22
cosocleC2×#11758222C23
hypercenterC23×C8#6923
hypocenterC61C2×#1391
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #21460907C2direct (N × H)
7. #16840741C4semidirect
10. C2×#14519835C4semidirect
12. C22×#11758194C4semidirect
14. #16839728C4semidirect
17. C23×C8×C61C4semidirect
28. #14519835C2×C4semidirect
46. C2×#11758194C2×C4semidirect
55. C22×C8×C61C2×C4semidirect
210. C2×C61#1391semidirect
216. C23×C8#6923semidirect
228. C61C2×#1391semidirect
253. C22×C8C2×#6923semidirect
419. C2#21460907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407412
#214609072
C2×#168397282
C2×#139161