Finite Group Databasebeta

← C2×#11751287 #14423348

Subgroups — C2×#11751287 #14423348

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic
2C22×C3×C5×Q16C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic
4C22×#6718C211yesmaximal, characteristic, complemented
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751287C218yesmaximal, direct product factor
7C2×#91104C211yesmaximal, characteristic
8C2×#91100C211yesmaximal, characteristic, complemented
9C2×#65475—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×Q8C2211yescharacteristic
12C2×Q8×D15—24no—
13C2×Q8×D15—22no—
14C2×Q8×D15—24no—
15C2×Q8×D15C2214yes—
16C22×C4×D15—21no—
17C22×C4×D15C2211yescharacteristic
18C22×Dic30—21no—
19C22×Dic30C2211yescharacteristic
20C2×C3×C5×Q16—24no—
21C2×C3×C5×Q16C2214yescomplemented
22C22×C3×C5×C8C2211yescharacteristic
23#91835—22no—
24#91835C2214yes—
25C2×#6718—24no—
26C2×#6718C2214yescomplemented
27C2×#6714—21no—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712—21no—
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91104C2214yes—
33#91100C2214yescomplemented
34C2×#5186—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×C5×Q16D311yescharacteristic, complemented
37C2×#4092—31no—
38C22×#689—31no—
39C2×#3967—31no—
40#65475—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C23×D15D411yescharacteristic
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8—22no—
49C2×C3×C5×Q8D414yes—
50C2×C3×C5×Q8C2312yes—
51C2×C3×C5×Q8C2312yes—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—21no—
56C22×Dic15—21no—
57C22×Dic15D411yescharacteristic
58Q8×D15—216no—
59Q8×D15—28no—
60Q8×D15—28no—
61C2×C4×D15—28no—
62C2×C4×D15—24no—
63C2×C4×D15—22no—
64C2×C4×D15—22no—
65C2×C4×D15D412yes—
66C2×C4×D15C2312yes—
67C2×Dic30—28no—
68C2×Dic30—21no—
69C2×Dic30—22no—
70C2×Dic30—24no—
71C2×Dic30D414yes—
72C2×Dic30C2312yes—
73C3×C5×Q16—28no—
74C2×C3×C5×C8—22no—
75C2×C3×C5×C8C2312yes—
76#6718—28no—
77#6714—24no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80#6712—24no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83C22×D3×Q8—51no—
84C22×C3×Q16D511yescharacteristic, complemented
85C2×#946—51no—
86C22×#216—51no—
87C2×#835—51no—
88#5186—58no—
89C2×(C2×D3)⋊C8—51no—
90C2×#816—51no—
91C22×C5×Q8C2×D311yescharacteristic
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—34no—
94C2×Q8×D5—64no—
95C2×Q8×D5—62no—
96C2×Q8×D5—64no—
97C22×C4×D5—31no—
98C22×C4×D5—61no—
99C22×Dic10—31no—
100C22×Dic10—61no—
101C2×C5×Q16—24no—
102C2×C5×Q16C2×D314yescomplemented
103C22×C5×C8C2×D311yescharacteristic
104#4092—34no—
105#4092—62no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—61no—
109C2×C4⋊Dic5—31no—
110C2×#683—61no—
111C22×#168—31no—
112#3967—34no—
113#3952—34no—
114#3948—34no—
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15Q1614yescomplemented
120C22×D15C2×D412yes—
121C3×C5×Q8—24no—
122C3×C5×Q8—22no—
123C3×C5×Q8—22no—
124C3×C5×Q8—22no—
125C3×C5×Q8—42no—
126C3×C5×Q8C2×D414yes—
127C2×C3×C4×C5—24no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—42no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—24no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—42no—
140C2×Dic15C2×D412yes—
141C4×D15—216no—
142C4×D15—24no—
143C4×D15—22no—
144C4×D15—22no—
145Dic30—216no—
146Dic30—24no—
147Dic30—22no—
148Dic30C2×D414yes—
149C3×C5×C8—22no—
150C3⋊#168—22no—
151C22×C3×Q8C2×D511yescharacteristic
152C22×C3×Q8C2×D511yescharacteristic
153C2×D3×Q8—54no—
154C2×D3×Q8—104no—
155C2×D3×Q8—102no—
156C2×D3×Q8—104no—
157C22×C4×D3—51no—
158C22×C4×D3—101no—
159C22×Dic6—51no—
160C22×Dic6—101no—
161C2×C3×Q16—24no—
162C2×C3×Q16C2×D514yescomplemented
163C22×C3×C8C2×D511yescharacteristic
164#946—54no—
165#946—102no—
166C2×#216—54no—
167C2×#216—104no—
168C2×(C2×D3)⋊C4—101no—
169C2×C4⋊Dic3—51no—
170C2×Dic3⋊C4—101no—
171C22×C3⋊C8—51no—
172#835—54no—
173(C2×D3)⋊C8—54no—
174#816—54no—
175C23×D5—31no—
176C2×C5×Q8—22no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—22no—
180C2×C5×Q8—22no—
181C2×C5×Q8#6714yes—
182C2×C5×Q8C22×D312yes—
183C2×C5×Q8C22×D312yes—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5C22×D311yescharacteristic
187C22×Dic5—31no—
188C22×Dic5—61no—
189C22×Dic5—61no—
190Q8×D5—68no—
191Q8×D5—616no—
192Q8×D5—68no—
193C2×C4×D5—32no—
194C2×C4×D5—32no—
195C2×C4×D5—64no—
196C2×C4×D5—68no—
197C2×C4×D5—62no—
198C2×C4×D5—62no—
199C2×Dic10—34no—
200C2×Dic10—32no—
201C2×Dic10—64no—
202C2×Dic10—68no—
203C2×Dic10—61no—
204C2×Dic10—62no—
205C5×Q16—28no—
206C2×C5×C8—22no—
207C2×C5×C8C22×D312yes—
208#689—68no—
209#685—64no—
210C4⋊Dic5—32no—
211C4⋊Dic5—61no—
212#683—64no—
213C2×#168—32no—
214C2×#168—62no—
215C23×Q8—151no—
216C22×Q16—151no—
217C22×Q16D1511yescharacteristic, complemented
218C2×C22⋊Q8—151no—
219#451—158no—
220C2×#103—151no—
221C2×#103—151no—
222C2×C22⋊C8—151no—
223C22×C3×C5#12012yes—
224C22×C3×C5C2×Q1612yes—
225C22×C3×C5#13712yes—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—22no—
229C2×D15—28no—
230C2×D15C2×Q1614yescomplemented
231C3×C4×C5—24no—
232C3×C4×C5—42no—
233C3×C4×C5#12012yes—
234C3×C4×C5C22×D411yescharacteristic
235C3×C4×C5C22×D411yescharacteristic
236Dic15—22no—
237Dic15—24no—
238Dic15—42no—
239C23×D3—51no—
240C2×C3×Q8—21no—
241C2×C3×Q8—22no—
242C2×C3×Q8—21no—
243C2×C3×Q8—22no—
244C2×C3×Q8—22no—
245C2×C3×Q8C22⋊D514yes—
246C2×C3×Q8C22×D512yes—
247C2×C3×Q8C22×D512yes—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4C22×D511yescharacteristic
251C22×Dic3—51no—
252C22×Dic3—101no—
253C22×Dic3—101no—
254D3×Q8—108no—
255D3×Q8—1016no—
256D3×Q8—108no—
257C2×C4×D3—52no—
258C2×C4×D3—52no—
259C2×C4×D3—104no—
260C2×C4×D3—108no—
261C2×C4×D3—102no—
262C2×C4×D3—102no—
263C2×Dic6—54no—
264C2×Dic6—52no—
265C2×Dic6—104no—
266C2×Dic6—108no—
267C2×Dic6—101no—
268C2×Dic6—102no—
269C3×Q16—28no—
270C2×C3×C8—22no—
271C2×C3×C8C22×D512yes—
272#216—108no—
273(C2×D3)⋊C4—104no—
274C4⋊Dic3—52no—
275C4⋊Dic3—101no—
276Dic3⋊C4—104no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—102no—
279C23×C5D3×D411yescharacteristic
280C22×D5—34no—
281C22×D5—32no—
282C22×D5—62no—
283C22×D5—62no—
284C5×Q8—24no—
285C5×Q8—22no—
286C5×Q8—22no—
287C5×Q8—22no—
288C5×Q8—42no—
289C5×Q8C2×#6714yes—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—42no—
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×D412yes—
296C2×C4×C5C2×#6712yes—
297C2×C4×C5C23×D311yescharacteristic
298C2×Dic5—32no—
299C2×Dic5—64no—
300C2×Dic5—62no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5—122no—
304C4×D5—616no—
305C4×D5—64no—
306C4×D5—62no—
307C4×D5—62no—
308Dic10—34no—
309Dic10—616no—
310Dic10—64no—
311Dic10—62no—
312C5×C8—22no—
313#168—62no—
314C22×Q8—154no—
315C22×Q8—151no—
316C22×Q8—301no—
317C22×Q8—302no—
318C22×Q8—304no—
319C22×Q8—304no—
320C22×Q8C2×D1511yescharacteristic
321C22×Q8C2×D1511yescharacteristic
322C23×C4—151no—
323C23×C4—301no—
324C2×Q16—24no—
325C2×Q16—154no—
326C2×Q16—304no—
327C2×Q16C2×D1514yescomplemented
328C22×C8—151no—
329C22×C8C2×D1511yescharacteristic
330C22⋊Q8—154no—
331C22⋊Q8—302no—
332C2×C4⋊C4—151no—
333C2×C4⋊C4—301no—
334C2×C22⋊C4—301no—
335#103—154no—
336#103—154no—
337C22⋊C8—154no—
338C2×C3×C5#45114yescomplemented
339C2×C3×C5C2×#12011yescharacteristic
340C2×C3×C5C22×Q1611yescharacteristic
341C2×C3×C5C2×#13711yescharacteristic
342D15—24no—
343C23×C3D4×D511yescharacteristic
344C22×D3—52no—
345C22×D3—54no—
346C22×D3—102no—
347C22×D3—102no—
348C3×Q8—22no—
349C3×Q8—24no—
350C3×Q8—22no—
351C3×Q8—22no—
352C3×Q8—42no—
353C3×Q8C2×C22⋊D514yes—
354C2×C3×C4—22no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—42no—
358C2×C3×C4D4×D512yes—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4C2×C22⋊D512yes—
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—52no—
363C2×Dic3—102no—
364C2×Dic3—104no—
365C2×Dic3—102no—
366C2×Dic3—102no—
367C2×Dic3—202no—
368C4×D3—1016no—
369C4×D3—102no—
370C4×D3—102no—
371C4×D3—104no—
372Dic6—54no—
373Dic6—1016no—
374Dic6—102no—
375Dic6—104no—
376C3×C8—22no—
377C3⋊C8—102no—
378C22×C5D3×Q1612yes—
379C22×C5#91812yes—
380C22×C5#93712yes—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—34no—
383C2×D5—68no—
384C2×D5—62no—
385C2×D5—62no—
386C4×C5—24no—
387C4×C5—42no—
388C4×C5#93712yes—
389C4×C5C2×D3×D411yescharacteristic
390C4×C5C22×#6711yescharacteristic
391Dic5—64no—
392Dic5—62no—
393Dic5—122no—
394C24—151no—
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—154no—
401C2×Q8—152no—
402C2×Q8—304no—
403C2×Q8—308no—
404C2×Q8—308no—
405C2×Q8—3016no—
406C2×Q8—308no—
407C2×Q8—301no—
408C2×Q8—302no—
409C2×Q8#122014yes—
410C2×Q8C22×D1512yes—
411C2×Q8C22×D1512yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—151no—
415C22×C4—152no—
416C22×C4—152no—
417C22×C4—304no—
418C22×C4—308no—
419C22×C4—301no—
420C22×C4—302no—
421C22×C4—302no—
422C22×C4—301no—
423C22×C4C22×D1511yescharacteristic
424Q16—28no—
425Q16—308no—
426C2×C8—22no—
427C2×C8—152no—
428C2×C8—302no—
429C2×C8C22×D1512yes—
430C4⋊C4—152no—
431C4⋊C4—304no—
432C4⋊C4—301no—
433C22⋊C4—304no—
434C3×C5C2×#45111yescharacteristic, complemented, Hall
435C22×C3D5×Q1612yes—
436C22×C3#406412yes—
437C22×C3#408312yes—
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—54no—
440C2×D3—102no—
441C2×D3—102no—
442C2×D3—108no—
443C3×C4—24no—
444C3×C4—42no—
445C3×C4#408312yes—
446C3×C4C2×D4×D511yescharacteristic
447C3×C4C22×C22⋊D511yescharacteristic
448Dic3—104no—
449Dic3—102no—
450Dic3—202no—
451C2×C5#518614yescomplemented
452C2×C5C2×D3×Q1611yescharacteristic
453C2×C5C2×#91811yescharacteristic
454C2×C5C2×#93711yescharacteristic
455D5—64no—
456C23—154no—
457C23—152no—
458C23—302no—
459C23—302no—
460C23D4×D1511yescharacteristic
461Q8—24no—
462Q8—22no—
463Q8—22no—
464Q8—22no—
465Q8—42no—
466Q8—154no—
467Q8—3016no—
468Q8—304no—
469Q8—302no—
470Q8C2×#122014yes—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—152no—
476C2×C4—3016no—
477C2×C4—302no—
478C2×C4—304no—
479C2×C4—302no—
480C2×C4—304no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—602no—
485C2×C4D4×D1511yescharacteristic
486C2×C4D4×D1512yes—
487C2×C4C2×#122012yes—
488C2×C4C23×D1511yescharacteristic
489C8—22no—
490C8—302no—
491C2×C3#6547514yescomplemented
492C2×C3C2×D5×Q1611yescharacteristic
493C2×C3C2×#406411yescharacteristic
494C2×C3C2×#408311yescharacteristic
495D3—104no—
496C5C2×#518611yescharacteristic, complemented, Sylow
497C22—154no—
498C22—302no—
499C22—308no—
500C22—302no—
501C22Q16×D1512yes—
502C22#9180712yes—
503C22#9182612yes—
504C22C2×D4×D1511yescharacteristic
505C4—24no—
506C4—42no—
507C4—302no—
508C4—304no—
509C4—602no—
510C4#9182612yes—
511C4C2×D4×D1511yescharacteristic
512C4C22×#122011yescharacteristic
513C3C2×#6547511yescharacteristic, complemented, Sylow
514C2—304no—
515C2#1175128714yesdirect product factor
516C2C2×Q16×D1511yescharacteristic
517C2C2×#9180711yescharacteristic
518C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×Q16C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
hypercenterC22×Q16D15
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×Q16C2semidirect
4. C22×#6718C2semidirect
5. C2×#91119C2semidirect
6. #11751287C2direct (N × H)
8. C2×#91100C2semidirect
21. C2×C3×C5×Q16C22semidirect
26. C2×#6718C22semidirect
31. #91119C22semidirect
33. #91100C22semidirect
36. C22×C5×Q16D3semidirect
84. C22×C3×Q16D5semidirect
102. C2×C5×Q16C2×D3semidirect
119. C22×D15Q16semidirect
162. C2×C3×Q16C2×D5semidirect
217. C22×Q16D15semidirect
230. C2×D15C2×Q16semidirect
327. C2×Q16C2×D15semidirect
338. C2×C3×C5#451semidirect
434. C3×C5C2×#451semidirect
451. C2×C5#5186semidirect
491. C2×C3#65475semidirect
496. C5C2×#5186semidirect
513. C3C2×#65475semidirect
515. C2#11751287direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C22×C3×C5×Q162
C2×#918352
C22×#67182
C2×#911192
#117512872
C2×#911042
C2×#911002
C2×#654753
C2×#51865