Finite Group Databasebeta

← C2×#11749268 #14423327

Subgroups — C2×#11749268 #14423327

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic, complemented
2C22×#6717C211yesmaximal, characteristic, complemented
3C2×#91450C211yesmaximal, characteristic
4C22×#6658C211yesmaximal, characteristic, complemented
5C2×C5×#835C211yesmaximal, characteristic, complemented
6#11749268C218yesmaximal, direct product factor
7C2×#90970C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65095—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×D60C2211yescharacteristic
12C2×C3×Q8×D5—24no—
13C2×C3×Q8×D5—22no—
14C2×C3×Q8×D5—24no—
15C2×C3×Q8×D5C2214yescomplemented
16C22×C3×C4×D5—21no—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×Dic10—21no—
19C22×C3×Dic10C2211yescharacteristic
20C22×#1202—21no—
21C2×#6717—24no—
22C2×#6717C2214yescomplemented
23C22×C3⋊#168C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic
26C2×#6667—21no—
27#91450—22no—
28#91450C2214yes—
29C2×#6658—24no—
30C2×#6658C2214yescomplemented
31C5×#835C2214yescomplemented
32#90970C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5227—51nomaximal, Hall
35C22×Q8×D5D311yescharacteristic, complemented
36C22×#688—31no—
37C22×#677—31no—
38C2×#4041—31no—
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65095—38no—
43C23×D15—21no—
44C23×C3×D5D411yescharacteristic
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8D414yescomplemented
48C2×C3×C5×Q8C2312yes—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×D60—22no—
52C2×D60—22no—
53C2×D60—21no—
54C2×D60C2312yes—
55C22×C5×Dic3—21no—
56C22×C3×Dic5—21no—
57C22×C3×Dic5D411yescharacteristic
58C3×Q8×D5—216no—
59C3×Q8×D5—28no—
60C3×Q8×D5—28no—
61C2×C3×C4×D5—28no—
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5D412yes—
66C2×C3×C4×D5C2312yes—
67C2×C3×Dic10—28no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10—24no—
71C2×C3×Dic10D414yescomplemented
72C2×C3×Dic10C2312yes—
73C2×#1202—24no—
74C2×#1202—44no—
75#6717—28no—
76C2×C3⋊#168—22no—
77C2×C3⋊#168C2312yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2312yes—
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yes—
82#6667—24no—
83#6658—28no—
84C23×C3×Q8—51no—
85C22×#215—51no—
86C22×#215—51no—
87C2×#930—51no—
88#5227—58no—
89C2×#835—51no—
90C2×#835D511yescharacteristic, complemented
91C2×#830—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—24no—
94C2×Q8×D5—22no—
95C2×Q8×D5—24no—
96C2×Q8×D5C2×D314yescomplemented
97C22×D20—31no—
98C22×D20—61no—
99C22×C4×D5—21no—
100C22×C4×D5C2×D311yescharacteristic
101C22×Dic10—21no—
102C22×Dic10C2×D311yescharacteristic
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×#688—34no—
106C2×#688—64no—
107C2×#685—61no—
108C22×#168—31no—
109C2×#677—34no—
110C2×#677—64no—
111#4041—34no—
112#4041—62no—
113C5×#103—34no—
114#3952—34no—
115#3942—34no—
116C2×#448—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—42no—
120C22×D15—42no—
121C22×D15—42no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5SD1614yescomplemented
125C22×C3×D5C2×D412yes—
126C3×C5×Q8—24no—
127C3×C5×Q8—22no—
128C3×C5×Q8C2×D414yescomplemented
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2411yescharacteristic
135D60—22no—
136D60—22no—
137D60—42no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—42no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—24no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C3×C4×D5—216no—
145C3×C4×D5—24no—
146C3×C4×D5—22no—
147C3×C4×D5—22no—
148C3×Dic10—216no—
149C3×Dic10—24no—
150C3×Dic10—22no—
151C3×Dic10C2×D414yescomplemented
152#1202—48no—
153C3⋊#168—22no—
154C5×C3⋊C8—22no—
155C22×C3×Q8—54no—
156C22×C3×Q8—51no—
157C22×C3×Q8—101no—
158C22×C3×Q8—102no—
159C22×C3×Q8—104no—
160C22×C3×Q8—104no—
161C22×C3×Q8C2×D511yescharacteristic
162C23×C3×C4—51no—
163C23×C3×C4—101no—
164C22×#67—101no—
165C22×D12—51no—
166C2×#215—54no—
167C2×#215—54no—
168C2×#215—104no—
169C2×#215—104no—
170#930—54no—
171#930—102no—
172C2×(C2×D3)⋊C4—101no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C22×C3⋊C8—51no—
175C22×C3⋊C8C2×D511yescharacteristic
176#835—54no—
177#835C2×D514yescomplemented
178#830—54no—
179C23×D5—61no—
180C23×D5#6711yescharacteristic
181C2×C5×Q8—22no—
182C2×C5×Q8—21no—
183C2×C5×Q8#6714yescomplemented
184C2×C5×Q8C22×D312yes—
185C22×C4×C5—21no—
186C22×C4×C5—61no—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—21no—
189C22×Dic5#6711yescharacteristic
190Q8×D5—216no—
191Q8×D5—28no—
192Q8×D5—28no—
193C2×D20—32no—
194C2×D20—62no—
195C2×D20—62no—
196C2×D20—64no—
197C2×D20—61no—
198C2×D20—124no—
199C2×C4×D5—28no—
200C2×C4×D5—24no—
201C2×C4×D5—22no—
202C2×C4×D5—22no—
203C2×C4×D5#6712yes—
204C2×C4×D5C22×D312yes—
205C2×Dic10—28no—
206C2×Dic10—22no—
207C2×Dic10—21no—
208C2×Dic10—24no—
209C2×Dic10#6714yescomplemented
210C2×Dic10C22×D312yes—
211C2×C5×C8—32no—
212C2×C5×C8—62no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215#688—68no—
216#685—64no—
217C2×#168—32no—
218C2×#168—62no—
219#677—68no—
220C23×Q8—51no—
221C22×SD16—151no—
222C22×SD16—151no—
223C2×#121—151no—
224#448—158no—
225C2×#103—31no—
226C2×#103—151no—
227C2×C22⋊C8—151no—
228C22×C3×C5#12012yes—
229C22×C3×C5C2×SD1612yes—
230C22×C3×C5#13712yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×D15—42no—
233C2×D15—42no—
234C2×D15—42no—
235C2×D15—84no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5—28no—
239C2×C3×D5C2×SD1614yescomplemented
240C3×C4×C5—24no—
241C3×C4×C5#12012yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244C3×Dic5—22no—
245C3×Dic5—24no—
246C5×Dic3—42no—
247C24×C3—51no—
248C23×D3—101no—
249C2×C3×Q8—21no—
250C2×C3×Q8—22no—
251C2×C3×Q8—54no—
252C2×C3×Q8—52no—
253C2×C3×Q8—104no—
254C2×C3×Q8—108no—
255C2×C3×Q8—108no—
256C2×C3×Q8—1016no—
257C2×C3×Q8—108no—
258C2×C3×Q8—102no—
259C2×C3×Q8—101no—
260C2×C3×Q8D2014yescomplemented
261C2×C3×Q8C22×D512yes—
262C22×C3×C4—21no—
263C22×C3×C4—51no—
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4—104no—
267C22×C3×C4—108no—
268C22×C3×C4—101no—
269C22×C3×C4—102no—
270C22×C3×C4—102no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—104no—
273C2×#67—204no—
274C22×Dic3—21no—
275C2×D12—52no—
276C2×D12—102no—
277C2×D12—102no—
278C2×D12—101no—
279#215—108no—
280#215—108no—
281(C2×D3)⋊C4—104no—
282C4⋊Dic3—21no—
283C4⋊Dic3C22×D512yes—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—52no—
286C2×C3⋊C8—102no—
287C2×C3⋊C8C22×D512yes—
288C23×C5C2×#6711yescharacteristic
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—62no—
292C22×D5—122no—
293C22×D5—122no—
294C22×D5—122no—
295C22×D5#21514yescomplemented
296C22×D5C2×#6712yes—
297C5×Q8—24no—
298C5×Q8—22no—
299C5×Q8C2×#6714yescomplemented
300C2×C4×C5—24no—
301C2×C4×C5—22no—
302C2×C4×C5—62no—
303C2×C4×C5—122no—
304C2×C4×C5C2×#6712yes—
305C2×C4×C5C2×#6711yescharacteristic
306C2×C4×C5C2×#6712yes—
307C2×C4×C5C23×D311yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—24no—
310C2×Dic5—22no—
311C2×Dic5C2×#6712yes—
312D20—62no—
313D20—62no—
314D20—128no—
315D20—122no—
316C4×D5—216no—
317C4×D5—24no—
318C4×D5—22no—
319C4×D5—22no—
320Dic10—216no—
321Dic10—24no—
322Dic10—22no—
323Dic10C2×#6714yescomplemented
324C5×C8—62no—
325#168—62no—
326C22×Q8—54no—
327C22×Q8—51no—
328C22×Q8—101no—
329C22×Q8—102no—
330C22×Q8—104no—
331C22×Q8—104no—
332C22×Q8D3×D511yescharacteristic
333C22×D4—151no—
334C22×D4—301no—
335C23×C4—51no—
336C23×C4—101no—
337C2×SD16—154no—
338C2×SD16—154no—
339C2×SD16—304no—
340C2×SD16—304no—
341C22×C8—31no—
342C22×C8—151no—
343#121—154no—
344#121—302no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—301no—
347#103—34no—
348#103—154no—
349C22⋊C8—154no—
350C2×C3×C5#44814yescomplemented
351C2×C3×C5C2×#12011yescharacteristic
352C2×C3×C5C22×SD1611yescharacteristic
353C2×C3×C5C2×#13711yescharacteristic
354D15—82no—
355C3×D5—24no—
356C23×C3—52no—
357C23×C3—54no—
358C23×C3—102no—
359C23×C3—102no—
360C23×C3D4×D511yescharacteristic
361C22×D3—102no—
362C22×D3—202no—
363C22×D3—202no—
364C22×D3—202no—
365C3×Q8—22no—
366C3×Q8—24no—
367C3×Q8—54no—
368C3×Q8—1016no—
369C3×Q8—102no—
370C3×Q8—104no—
371C3×Q8C2×D2014yescomplemented
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4—52no—
375C2×C3×C4—1016no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—104no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4—104no—
382C2×C3×C4C2×D2012yes—
383C2×C3×C4D4×D512yes—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—208no—
387C2×Dic3—22no—
388C2×Dic3—42no—
389D12—102no—
390D12—102no—
391D12—202no—
392C3⋊C8—22no—
393C3⋊C8—102no—
394C22×C5C2×#21512yes—
395C22×C5#94212yes—
396C22×C5#95312yes—
397C22×C5C22×#6711yescharacteristic
398C2×D5—28no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—122no—
402C2×D5—122no—
403C2×D5—122no—
404C2×D5—244no—
405C2×D5C2×#21514yescomplemented
406C4×C5—24no—
407C4×C5—122no—
408C4×C5#95312yes—
409C4×C5C22×#6711yescharacteristic
410C4×C5C22×#6711yescharacteristic
411Dic5—22no—
412Dic5—24no—
413C24—51no—
414C24—301no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—54no—
418C2×Q8—52no—
419C2×Q8—104no—
420C2×Q8—108no—
421C2×Q8—108no—
422C2×Q8—1016no—
423C2×Q8—108no—
424C2×Q8—102no—
425C2×Q8—101no—
426C2×Q8#120214yescomplemented
427C2×Q8C2×D3×D512yes—
428C2×D4—152no—
429C2×D4—304no—
430C2×D4—302no—
431C2×D4—302no—
432C2×D4—301no—
433C2×D4—604no—
434C22×C4—21no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—61no—
439C22×C4—104no—
440C22×C4—108no—
441C22×C4—101no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4C2×D3×D511yescharacteristic
445SD16—308no—
446SD16—308no—
447C2×C8—32no—
448C2×C8—62no—
449C2×C8—152no—
450C2×C8—302no—
451C4⋊C4—32no—
452C4⋊C4—61no—
453C22⋊C4—304no—
454C3×C5C2×#44811yescharacteristic, complemented, Hall
455C22×C3—54no—
456C22×C3—102no—
457C22×C3—102no—
458C22×C3—108no—
459C22×C3#402812yes—
460C22×C3D5×SD1612yes—
461C22×C3#406412yes—
462C22×C3C2×D4×D511yescharacteristic
463C2×D3—202no—
464C2×D3—202no—
465C2×D3—202no—
466C2×D3—404no—
467C3×C4—24no—
468C3×C4—102no—
469C3×C4—104no—
470C3×C4#402812yes—
471C3×C4C22×D2011yescharacteristic
472C3×C4C2×D4×D511yescharacteristic
473Dic3—42no—
474C2×C5#522714yescomplemented
475C2×C5C22×#21511yescharacteristic
476C2×C5C2×#94211yescharacteristic
477C2×C5C2×#95311yescharacteristic
478D5—24no—
479D5—242no—
480C23—54no—
481C23—52no—
482C23—102no—
483C23—102no—
484C23—302no—
485C23—602no—
486C23—602no—
487C23—602no—
488C23D5×#6711yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8—54no—
492Q8—1016no—
493Q8—102no—
494Q8—104no—
495Q8C2×#120214yescomplemented
496D4—302no—
497D4—302no—
498D4—608no—
499D4—602no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—52no—
503C2×C4—62no—
504C2×C4—1016no—
505C2×C4—102no—
506C2×C4—102no—
507C2×C4—104no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—104no—
511C2×C4—122no—
512C2×C4C2×#120212yes—
513C2×C4D5×#6712yes—
514C2×C4D5×#6711yescharacteristic
515C2×C4C22×D3×D511yescharacteristic
516C8—62no—
517C8—302no—
518C2×C3—104no—
519C2×C3#6509514yescomplemented
520C2×C3C2×#402811yescharacteristic
521C2×C3C2×D5×SD1611yescharacteristic
522C2×C3C2×#406411yescharacteristic
523D3—402no—
524C5C2×#522711yescharacteristic, complemented, Sylow
525C22—54no—
526C22—102no—
527C22—108no—
528C22—102no—
529C22—602no—
530C22—602no—
531C22—602no—
532C22—1204no—
533C22D5×#21512yes—
534C22#9151512yes—
535C22#9156412yes—
536C22C2×D5×#6711yescharacteristic
537C4—24no—
538C4—102no—
539C4—104no—
540C4—122no—
541C4#9156412yes—
542C4C22×#120211yescharacteristic
543C4C2×D5×#6711yescharacteristic
544C3C2×#6509511yescharacteristic, complemented, Sylow
545C2—104no—
546C2—1202no—
547C2#1174926814yesdirect product factor
548C2C2×D5×#21511yescharacteristic
549C2C2×#9151511yescharacteristic
550C2C2×#9156411yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC2×#91450C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#448
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
1. C22×C3×Q8×D5C2semidirect
2. C22×#6717C2semidirect
4. C22×#6658C2semidirect
5. C2×C5×#835C2semidirect
6. #11749268C2direct (N × H)
7. C2×#90970C2semidirect
8. C2×#90955C2semidirect
15. C2×C3×Q8×D5C22semidirect
22. C2×#6717C22semidirect
30. C2×#6658C22semidirect
31. C5×#835C22semidirect
32. #90970C22semidirect
33. #90955C22semidirect
35. C22×Q8×D5D3semidirect
47. C2×C3×C5×Q8D4semidirect
71. C2×C3×Dic10D4semidirect
90. C2×#835D5semidirect
96. C2×Q8×D5C2×D3semidirect
124. C22×C3×D5SD16semidirect
128. C3×C5×Q8C2×D4semidirect
151. C3×Dic10C2×D4semidirect
177. #835C2×D5semidirect
183. C2×C5×Q8#67semidirect
209. C2×Dic10#67semidirect
239. C2×C3×D5C2×SD16semidirect
260. C2×C3×Q8D20semidirect
295. C22×D5#215semidirect
299. C5×Q8C2×#67semidirect
323. Dic10C2×#67semidirect
350. C2×C3×C5#448semidirect
371. C3×Q8C2×D20semidirect
405. C2×D5C2×#215semidirect
426. C2×Q8#1202semidirect
454. C3×C5C2×#448semidirect
474. C2×C5#5227semidirect
495. Q8C2×#1202semidirect
519. C2×C3#65095semidirect
524. C5C2×#5227semidirect
544. C3C2×#65095semidirect
547. C2#11749268direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C22×#67172
C2×#914502
C22×#66582
C2×C5×#8352
#117492682
C2×#909702
C2×#909552
C2×#650953
C2×#52275