Finite Group Databasebeta

← C2×#11749404 #14423530

Subgroups — C2×#11749404 #14423530

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6766C211yesmaximal, characteristic
2C2×#91835C211yesmaximal, characteristic, complemented
3C22×C5×#216C211yesmaximal, characteristic, complemented
4C22×C3×#688C211yesmaximal, characteristic, complemented
5#11749404C218yesmaximal, direct product factor
6C2×#90973C211yesmaximal, characteristic, complemented
7C2×#90965C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65476—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C4×D15C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×#1202—21no—
15C22×D5×Dic3—21no—
16C2×#6766—22no—
17C2×#6766—24no—
18C2×#6766—24no—
19C2×#6766C2214yes—
20#91835—22no—
21#91835C2214yescomplemented
22C2×#6714—21no—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712—21no—
25C2×C5×#216—24no—
26C2×C5×#216C2214yescomplemented
27C22×C5×C3⋊C8C2211yescharacteristic
28C2×C3×#688—24no—
29C2×C3×#688C2214yescomplemented
30C22×C3×#168C2211yescharacteristic
31#90973C2214yescomplemented
32#90965C2214yescomplemented
33#90957C2214yescomplemented
34C2×#5173—51nomaximal, Hall
35C22×#713—31no—
36C22×C5×Q16—31no—
37C2×#4092—31no—
38C22×#688D311yescharacteristic, complemented
39C2×#3967—31no—
40#65476—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C23×D15D411yescharacteristic
44C23×C3×D5—21no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8C2312yes—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C22×Dic15D411yescharacteristic
53C2×C4×D15—22no—
54C2×C4×D15—22no—
55C2×C4×D15D412yes—
56C2×C4×D15C2312yes—
57C22×C5×Dic3—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—22no—
60C2×C5×Dic6D414yes—
61C2×C5×Dic6C2312yes—
62C2×C3×D20—21no—
63C2×C3×D20—22no—
64C2×C3×D20D414yes—
65C2×C3×D20C2312yes—
66C2×#1202—28no—
67C2×#1202—24no—
68C2×D5×Dic3—28no—
69C2×D5×Dic3—24no—
70#6766—216no—
71#6766—28no—
72#6766—28no—
73#6714—24no—
74C4⋊Dic15—21no—
75C4⋊Dic15C2312yes—
76#6712—24no—
77C5×#216—28no—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2312yes—
80C3×#688—28no—
81C2×C3×#168—22no—
82C2×C3×#168C2312yes—
83C22×#237—51no—
84C22×C3×SD16—51no—
85C2×#946—51no—
86C22×#216D511yescharacteristic, complemented
87C2×#832—51no—
88#5173—58no—
89C2×(C2×D3)⋊C8—51no—
90C2×#816—51no—
91C22×C5×Q8—31no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×#713—34no—
94C2×#713—62no—
95C2×#713—64no—
96C2×#713—64no—
97C22×D20—61no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—31no—
100C22×C4×D5—61no—
101C2×C5×Q16—34no—
102C2×C5×Q16—64no—
103C22×C5×C8—31no—
104#4092—34no—
105#4092—62no—
106C2×#688—24no—
107C2×#688C2×D314yescomplemented
108C2×#685—61no—
109C2×C4⋊Dic5—31no—
110C2×#683—61no—
111C22×#168C2×D311yescharacteristic
112#3967—34no—
113#3953—34no—
114#3952—34no—
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15C2×D412yes—
121C22×C3×D5—24no—
122C22×C3×D5—22no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C3×C5×Q8—22no—
126C3×C5×Q8—22no—
127C3×C5×Q8—42no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—42no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—42no—
137C2×Dic15C2×D412yes—
138C4×D15—24no—
139C4×D15—22no—
140C4×D15—22no—
141C2×C5×Dic3—24no—
142C2×C5×Dic3—22no—
143C5×Dic6—24no—
144C5×Dic6—22no—
145C5×Dic6C2×D414yes—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20C2×D414yes—
149#1202—216no—
150D5×Dic3—216no—
151C3×#168—22no—
152C5×C3⋊C8—22no—
153C22×C3×Q8C2×D511yescharacteristic
154C22×C3×D4—51no—
155C22×#67—101no—
156C23×Dic3—101no—
157C2×#237—54no—
158C2×#237—102no—
159C2×#237—104no—
160C2×#237—104no—
161C22×C4×D3—51no—
162C22×Dic6C2×D511yescharacteristic
163C2×C3×SD16—54no—
164C2×C3×SD16—104no—
165C22×C3×C8—51no—
166#946—54no—
167#946—102no—
168C2×#216—24no—
169C2×#216C2×D514yescomplemented
170C2×(C2×D3)⋊C4—101no—
171C2×C4⋊Dic3—51no—
172C2×Dic3⋊C4—101no—
173C22×C3⋊C8C2×D511yescharacteristic
174#832—54no—
175(C2×D3)⋊C8—54no—
176#816—54no—
177C23×D5—21no—
178C23×D5—31no—
179C2×C5×Q8—21no—
180C2×C5×Q8—22no—
181C2×C5×Q8—22no—
182C2×C5×Q8—34no—
183C2×C5×Q8—32no—
184C2×C5×Q8—61no—
185C2×C5×Q8—62no—
186C2×C5×Q8C22×D312yes—
187C22×C4×C5—21no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C22×Dic5—31no—
191C22×Dic5—61no—
192#713—68no—
193#713—616no—
194#713—68no—
195C2×D20—22no—
196C2×D20—21no—
197C2×D20—64no—
198C2×D20—68no—
199C2×D20#6714yes—
200C2×D20C22×D312yes—
201C2×C4×D5—32no—
202C2×C4×D5—32no—
203C2×C4×D5—64no—
204C2×C4×D5—68no—
205C2×C4×D5—62no—
206C2×C4×D5—62no—
207C5×Q16—68no—
208C2×C5×C8—32no—
209C2×C5×C8—62no—
210#688—28no—
211#685—64no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214#683—64no—
215C2×#168—22no—
216C2×#168C22×D312yes—
217C22×#41—151no—
218C22×Q16—31no—
219C22×SD16—51no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×D15—22no—
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—44no—
233C2×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—48no—
237C3×C4×C5—42no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241Dic15—22no—
242Dic15—42no—
243C5×Dic3—24no—
244C24×C3—101no—
245C23×D3—51no—
246C2×C3×Q8—21no—
247C2×C3×Q8—22no—
248C2×C3×Q8—22no—
249C2×C3×Q8C22×D512yes—
250C2×C3×D4—54no—
251C2×C3×D4—52no—
252C2×C3×D4—101no—
253C2×C3×D4—102no—
254C22×C3×C4—21no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—104no—
257C2×#67—108no—
258C22×Dic3—21no—
259C22×Dic3—51no—
260C22×Dic3—104no—
261C22×Dic3—108no—
262C22×Dic3—101no—
263#237—108no—
264#237—1016no—
265#237—108no—
266C2×C4×D3—52no—
267C2×C4×D3—52no—
268C2×C4×D3—102no—
269C2×C4×D3—102no—
270C2×Dic6—22no—
271C2×Dic6—21no—
272C2×Dic6C22⋊D514yes—
273C2×Dic6C22×D512yes—
274C3×SD16—108no—
275C2×C3×C8—52no—
276C2×C3×C8—102no—
277#216—28no—
278(C2×D3)⋊C4—104no—
279C4⋊Dic3—52no—
280C4⋊Dic3—101no—
281Dic3⋊C4—104no—
282C2×C3⋊C8—22no—
283C2×C3⋊C8C22×D512yes—
284C23×C5D3×D411yescharacteristic
285C22×D5—24no—
286C22×D5—22no—
287C22×D5—32no—
288C22×D5—42no—
289C22×D5—42no—
290C22×D5—62no—
291C22×D5—62no—
292C22×D5—62no—
293C5×Q8—22no—
294C5×Q8—22no—
295C5×Q8—34no—
296C5×Q8—42no—
297C5×Q8—64no—
298C5×Q8—62no—
299C2×C4×C5—22no—
300C2×C4×C5—42no—
301C2×C4×C5—64no—
302C2×C4×C5—62no—
303C2×C4×C5D3×D412yes—
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5C2×#6712yes—
306C2×C4×C5C23×D311yescharacteristic
307C2×Dic5—32no—
308C2×Dic5—62no—
309C2×Dic5—62no—
310C2×Dic5—122no—
311D20—24no—
312D20—22no—
313D20—616no—
314D20C2×#6714yes—
315C4×D5—616no—
316C4×D5—64no—
317C4×D5—62no—
318C4×D5—62no—
319C5×C8—62no—
320#168—22no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—31no—
326C22×Q8D3×D511yescharacteristic
327C22×D4—51no—
328C22×D4—301no—
329C23×C4—151no—
330C23×C4—301no—
331C2×Q16—34no—
332C2×Q16—64no—
333C2×SD16—54no—
334C2×SD16—104no—
335C22×C8—31no—
336C22×C8—51no—
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—151no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—154no—
343#102—154no—
344C22⋊C8—154no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349D15—42no—
350C3×D5—44no—
351C23×C3—102no—
352C23×C3—104no—
353C23×C3—202no—
354C23×C3—202no—
355C23×C3D4×D511yescharacteristic
356C22×D3—52no—
357C22×D3—102no—
358C22×D3—102no—
359C22×D3—102no—
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—42no—
363C3×D4—54no—
364C3×D4—102no—
365C3×D4—104no—
366C2×C3×C4—22no—
367C2×C3×C4—42no—
368C2×C3×C4D4×D512yes—
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4C2×C22⋊D512yes—
371C2×C3×C4C23×D511yescharacteristic
372#67—1016no—
373C2×Dic3—22no—
374C2×Dic3—24no—
375C2×Dic3—52no—
376C2×Dic3—1016no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—202no—
380C4×D3—102no—
381C4×D3—102no—
382C4×D3—104no—
383Dic6—22no—
384Dic6—24no—
385Dic6C2×C22⋊D514yes—
386C3×C8—102no—
387C3⋊C8—22no—
388C22×C5#91512yes—
389C22×C5#91612yes—
390C22×C5#93712yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—24no—
393C2×D5—48no—
394C2×D5—42no—
395C2×D5—42no—
396C2×D5—62no—
397C2×D5—62no—
398C2×D5—62no—
399C2×D5—124no—
400C4×C5—42no—
401C4×C5—64no—
402C4×C5#93712yes—
403C4×C5C2×D3×D411yescharacteristic
404C4×C5C22×#6711yescharacteristic
405Dic5—62no—
406Dic5—122no—
407C24—101no—
408C24—151no—
409#41—308no—
410#41—308no—
411#41—3016no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—34no—
416C2×Q8—32no—
417C2×Q8—62no—
418C2×Q8—61no—
419C2×Q8C2×D3×D512yes—
420C2×D4—54no—
421C2×D4—52no—
422C2×D4—102no—
423C2×D4—101no—
424C2×D4—304no—
425C2×D4—308no—
426C22×C4—21no—
427C22×C4—61no—
428C22×C4—151no—
429C22×C4—152no—
430C22×C4—152no—
431C22×C4—304no—
432C22×C4—308no—
433C22×C4—302no—
434C22×C4—302no—
435C22×C4—301no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—68no—
438SD16—108no—
439C2×C8—32no—
440C2×C8—52no—
441C2×C8—62no—
442C2×C8—102no—
443C4⋊C4—152no—
444C4⋊C4—304no—
445C4⋊C4—301no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—104no—
449C22×C3—202no—
450C22×C3—202no—
451C22×C3—208no—
452C22×C3#406412yes—
453C22×C3#406512yes—
454C22×C3#408312yes—
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—102no—
457C2×D3—102no—
458C2×D3—102no—
459C2×D3—204no—
460C3×C4—42no—
461C3×C4#408312yes—
462C3×C4C2×D4×D511yescharacteristic
463C3×C4C22×C22⋊D511yescharacteristic
464Dic3—24no—
465Dic3—102no—
466Dic3—202no—
467C2×C5#517314yescomplemented
468C2×C5C2×#91511yescharacteristic
469C2×C5C2×#91611yescharacteristic
470C2×C5C2×#93711yescharacteristic
471D5—44no—
472D5—122no—
473C23—102no—
474C23—104no—
475C23—152no—
476C23—202no—
477C23—202no—
478C23—302no—
479C23—302no—
480C23—302no—
481C23#679011yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—34no—
485Q8—42no—
486Q8—62no—
487Q8—64no—
488D4—54no—
489D4—102no—
490D4—104no—
491D4—3016no—
492C2×C4—22no—
493C2×C4—42no—
494C2×C4—62no—
495C2×C4—64no—
496C2×C4—152no—
497C2×C4—3016no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—304no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4D5×#6712yes—
505C2×C4D3×C22⋊D512yes—
506C2×C4#679011yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—102no—
510C2×C3—204no—
511C2×C3#6547614yescomplemented
512C2×C3C2×#406411yescharacteristic
513C2×C3C2×#406511yescharacteristic
514C2×C3C2×#408311yescharacteristic
515D3—202no—
516C5C2×#517311yescharacteristic, complemented, Sylow
517C22—104no—
518C22—208no—
519C22—202no—
520C22—202no—
521C22—302no—
522C22—302no—
523C22—302no—
524C22—604no—
525C22#9152112yes—
526C22#9152212yes—
527C22#9157712yes—
528C22C2×#679011yescharacteristic
529C4—42no—
530C4—64no—
531C4—302no—
532C4—602no—
533C4#9157712yes—
534C4C2×D5×#6711yescharacteristic
535C4C2×D3×C22⋊D511yescharacteristic
536C3C2×#6547611yescharacteristic, complemented, Sylow
537C2—204no—
538C2—602no—
539C2#1174940414yesdirect product factor
540C2C2×#9152111yescharacteristic
541C2C2×#9152211yescharacteristic
542C2C2×#9157711yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6766C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91835C2semidirect
3. C22×C5×#216C2semidirect
4. C22×C3×#688C2semidirect
5. #11749404C2direct (N × H)
6. C2×#90973C2semidirect
7. C2×#90965C2semidirect
8. C2×#90957C2semidirect
21. #91835C22semidirect
26. C2×C5×#216C22semidirect
29. C2×C3×#688C22semidirect
31. #90973C22semidirect
32. #90965C22semidirect
33. #90957C22semidirect
38. C22×#688D3semidirect
86. C22×#216D5semidirect
107. C2×#688C2×D3semidirect
169. C2×#216C2×D5semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
467. C2×C5#5173semidirect
511. C2×C3#65476semidirect
516. C5C2×#5173semidirect
536. C3C2×#65476semidirect
539. C2#11749404direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67662
C2×#918352
C22×C5×#2162
C22×C3×#6882
#117494042
C2×#909732
C2×#909652
C2×#909572
C2×#654763
C2×#51735