Finite Group Databasebeta

← C2×#11756341 #14481327

Subgroups — C2×#11756341 #14481327

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×#91836C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic, complemented
4#11756341C2116yesmaximal, direct product factor
5C2×#91785C212yesmaximal, complemented
6C2×#91784C211yesmaximal, characteristic
7C2×#91783C212yesmaximal, complemented
8C2×#91777C211yesmaximal, characteristic, complemented
9C2×#91765C212yesmaximal, complemented
10C2×#91764C212yesmaximal, complemented
11C2×C4×D60C211yesmaximal, characteristic, complemented
12C2×#91761C211yesmaximal, characteristic, complemented
13C2×#65916—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×D60C2211yescharacteristic
16C22×D60C2212yes—
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2212yes—
19C22×Dic30C2212yes—
20C3×C4×C5×Q8C2218yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C42×C5C2212yes—
25#91836C2218yescomplemented
26#91835C2218yescomplemented
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2212yes—
33C2×#6714C2212yes—
34C2×C4⋊Dic15C2211yescharacteristic
35C2×#6712C2212yes—
36C2×#6712C2211yescharacteristic
37C2×#6712C2211yescharacteristic
38C2×#6712C2212yes—
39C2×C4×Dic15C2211yescharacteristic
40#91785C22116yescomplemented
41#91784C2218yes—
42#91783C22116yescomplemented
43#91777C2218yescomplemented
44#91765C22116yescomplemented
45#91764C22116yescomplemented
46C4×D60C2218yescomplemented
47#91761C2218yescomplemented
48C2×#5582—51nomaximal, Hall
49C2×C4×C5×Q8D311yescharacteristic, complemented
50C2×#4093—31no—
51C2×#4092—31no—
52#65916—316no—
53C2×#4042—32no—
54C2×#4041—31no—
55C2×#4040—32no—
56C2×#4034—31no—
57C2×#4022—32no—
58C2×#4021—32no—
59C2×C4×D20—31no—
60C2×#4018—31no—
61C23×D15C2311yescharacteristic
62C23×D15C2312yes—
63C2×C3×C5×Q8—24no—
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2312yes—
74C2×D60—24no—
75C2×D60—44no—
76C2×D60C2314yes—
77C2×D60C2318yes—
78C2×C4×D15—24no—
79C2×C4×D15—44no—
80C2×C4×D15C2314yes—
81C2×C4×D15C2318yes—
82C2×Dic30—44no—
83C2×Dic30C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2318yes—
86C3×C42×C5C2314yes—
87C3×C42×C5C2318yes—
88#6714C2314yes—
89#6714C2314yes—
90#6714C2318yes—
91#6714C2318yes—
92#6714C2318yes—
93#6714C2318yes—
94#6714C2318yes—
95C4⋊Dic15C2314yes—
96#6712C2314yes—
97#6712C2314yes—
98#6712C2318yes—
99#6712C2318yes—
100C4×Dic15C2314yes—
101C2×C3×C4×Q8D511yescharacteristic, complemented
102C2×#947—51no—
103C2×#946—51no—
104#5582—516no—
105C2×#896—52no—
106C2×#895—51no—
107C2×#894—52no—
108C2×#888—51no—
109C2×#876—52no—
110C2×#875—52no—
111C2×C4×D12—51no—
112C2×#872—51no—
113C22×C5×Q8C2×D311yescharacteristic
114C22×D20—31no—
115C22×D20—32no—
116C22×C4×D5—31no—
117C22×C4×D5—32no—
118C22×Dic10—32no—
119C4×C5×Q8C2×D318yescomplemented
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D312yes—
122C2×C42×C5C2×D311yescharacteristic
123C2×C42×C5C2×D312yes—
124#4093—38no—
125#4092—38no—
126C2×#685—31no—
127C2×#685—31no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×#685—32no—
133C2×C4⋊Dic5—31no—
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—31no—
139#4042—316no—
140#4041—38no—
141#4040—316no—
142#4034—38no—
143#4022—316no—
144#4021—316no—
145C4×D20—38no—
146#4018—38no—
147C2×#542—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—22no—
150C22×D15—24no—
151C22×D15—24no—
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—24no—
155C22×D15C2412yes—
156C22×D15C2414yes—
157C3×C5×Q8—28no—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5—24no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5#4114yes—
163C2×C3×C4×C5C2412yes—
164C2×C3×C4×C5C2414yes—
165C2×C3×C4×C5C2414yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168C2×Dic15—22no—
169C2×Dic15—22no—
170C2×Dic15—24no—
171C2×Dic15—22no—
172C2×Dic15C2412yes—
173C2×Dic15C2412yes—
174C2×Dic15C2412yes—
175C2×Dic15C2414yes—
176D60—28no—
177D60—48no—
178C4×D15—28no—
179C4×D15—48no—
180Dic30—48no—
181C22×C3×Q8C2×D511yescharacteristic
182C22×D12—51no—
183C22×D12—52no—
184C22×C4×D3—51no—
185C22×C4×D3—52no—
186C22×Dic6—52no—
187C3×C4×Q8C2×D518yescomplemented
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C4⋊C4C2×D512yes—
190C2×C3×C42C2×D511yescharacteristic
191C2×C3×C42C2×D512yes—
192#947—58no—
193#946—58no—
194C2×(C2×D3)⋊C4—51no—
195C2×(C2×D3)⋊C4—51no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—51no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4—51no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—51no—
207#896—516no—
208#895—58no—
209#894—516no—
210#888—58no—
211#876—516no—
212#875—516no—
213C4×D12—58no—
214#872—58no—
215C23×D5—31no—
216C23×D5—32no—
217C2×C5×Q8—24no—
218C2×C5×Q8C22×D314yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D312yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—31no—
225C22×Dic5—32no—
226C22×Dic5—31no—
227C22×Dic5—31no—
228C2×D20—34no—
229C2×D20—38no—
230C2×D20—64no—
231C2×D20—124no—
232C2×C4×D5—34no—
233C2×C4×D5—38no—
234C2×C4×D5—64no—
235C2×C4×D5—124no—
236C2×Dic10—38no—
237C2×Dic10—124no—
238C5×C4⋊C4C22×D314yes—
239C5×C4⋊C4C22×D318yes—
240C42×C5C22×D314yes—
241C42×C5C22×D318yes—
242#685—34no—
243#685—34no—
244#685—38no—
245#685—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249C4⋊Dic5—34no—
250#683—34no—
251#683—34no—
252#683—38no—
253#683—38no—
254C4×Dic5—34no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—151no—
259C2×#124—152no—
260C2×#123—152no—
261C2×C22⋊Q8—151no—
262C2×C22⋊Q8—152no—
263C2×#121—151no—
264C2×C4×Q8D1511yescharacteristic, complemented
265C2×C4×D4—151no—
266C2×#117—151no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5H(5,𝔽2)12yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×D15—22no—
272C2×D15—24no—
273C2×D15—24no—
274C2×D15—22no—
275C2×D15—22no—
276C2×D15—24no—
277C2×D15—44no—
278C2×D15—48no—
279C3×C4×C5—24no—
280C3×C4×C5—24no—
281C3×C4×C5—22no—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284Dic15—22no—
285Dic15—22no—
286Dic15—24no—
287Dic15—22no—
288C23×D3—51no—
289C23×D3—52no—
290C2×C3×Q8—24no—
291C2×C3×Q8C22×D514yes—
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D512yes—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—52no—
301C2×D12—54no—
302C2×D12—58no—
303C2×D12—104no—
304C2×D12—204no—
305C2×C4×D3—54no—
306C2×C4×D3—58no—
307C2×C4×D3—104no—
308C2×C4×D3—204no—
309C2×Dic6—58no—
310C2×Dic6—204no—
311C3×C4⋊C4C22×D514yes—
312C3×C4⋊C4C22×D518yes—
313C3×C42C22×D514yes—
314C3×C42C22×D518yes—
315(C2×D3)⋊C4—54no—
316(C2×D3)⋊C4—54no—
317(C2×D3)⋊C4—58no—
318(C2×D3)⋊C4—58no—
319(C2×D3)⋊C4—58no—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322C4⋊Dic3—54no—
323Dic3⋊C4—54no—
324Dic3⋊C4—54no—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327C4×Dic3—54no—
328C23×C5C23×D311yescharacteristic
329C22×D5—32no—
330C22×D5—34no—
331C22×D5—62no—
332C22×D5—64no—
333C22×D5—62no—
334C22×D5—64no—
335C22×D5—64no—
336C22×D5—62no—
337C5×Q8—28no—
338C2×C4×C5—24no—
339C2×C4×C5—22no—
340C2×C4×C5—24no—
341C2×C4×C5—22no—
342C2×C4×C5#23514yes—
343C2×C4×C5C23×D312yes—
344C2×C4×C5C23×D314yes—
345C2×C4×C5C23×D314yes—
346C2×C4×C5C23×D312yes—
347C2×C4×C5C23×D312yes—
348C2×Dic5—32no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—34no—
352C2×Dic5—62no—
353C2×Dic5—62no—
354C2×Dic5—62no—
355C2×Dic5—64no—
356D20—68no—
357D20—128no—
358C4×D5—68no—
359C4×D5—128no—
360Dic10—128no—
361C22×Q8—152no—
362C22×Q8C2×D1511yescharacteristic
363C22×D4—151no—
364C22×D4—152no—
365C23×C4—151no—
366C23×C4—152no—
367C4⋊Q8—158no—
368#126—1516no—
369#124—158no—
370#124—1516no—
371#123—1516no—
372C22⋊Q8—158no—
373C22⋊Q8—1516no—
374#121—158no—
375C4×Q8C2×D1518yescomplemented
376C4×D4—158no—
377#117—158no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4C2×D1511yescharacteristic
384C2×C4⋊C4C2×D1512yes—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C42—151no—
393C2×C42C2×D1511yescharacteristic
394C2×C42C2×D1512yes—
395C2×C3×C5#54214yescomplemented
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
398C2×C3×C5C2×2−1+411yescharacteristic
399D15—42no—
400D15—44no—
401C23×C3C23×D511yescharacteristic
402C22×D3—52no—
403C22×D3—54no—
404C22×D3—102no—
405C22×D3—104no—
406C22×D3—102no—
407C22×D3—104no—
408C22×D3—104no—
409C22×D3—102no—
410C3×Q8—28no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4#70914yes—
416C2×C3×C4C23×D512yes—
417C2×C3×C4C23×D514yes—
418C2×C3×C4C23×D514yes—
419C2×C3×C4C23×D512yes—
420C2×C3×C4C23×D512yes—
421C2×Dic3—52no—
422C2×Dic3—52no—
423C2×Dic3—52no—
424C2×Dic3—54no—
425C2×Dic3—102no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—104no—
429D12—108no—
430D12—208no—
431C4×D3—108no—
432C4×D3—208no—
433Dic6—208no—
434C22×C5C2×#23512yes—
435C22×C5#100712yes—
436C22×C5#100912yes—
437C22×C5C24×D311yescharacteristic
438C2×D5—62no—
439C2×D5—64no—
440C2×D5—62no—
441C2×D5—64no—
442C2×D5—64no—
443C2×D5—62no—
444C2×D5—124no—
445C2×D5—128no—
446C4×C5—24no—
447C4×C5—22no—
448C4×C5—24no—
449C4×C5—22no—
450C4×C5C2×#23514yes—
451Dic5—62no—
452Dic5—62no—
453Dic5—62no—
454Dic5—64no—
455C24—151no—
456C24—152no—
457C2×Q8—24no—
458C2×Q8—158no—
459C2×Q8—604no—
460C2×Q8C22×D1514yes—
461C2×D4—154no—
462C2×D4—158no—
463C2×D4—304no—
464C2×D4—604no—
465C22×C4—151no—
466C22×C4—151no—
467C22×C4—151no—
468C22×C4—152no—
469C22×C4—154no—
470C22×C4—158no—
471C22×C4—304no—
472C22×C4—604no—
473C22×C4C22×D1511yescharacteristic
474C22×C4C22×D1512yes—
475C22×C4C22×D1511yescharacteristic
476C22×C4C22×D1512yes—
477C22×C4C22×D1511yescharacteristic
478C4⋊C4—154no—
479C4⋊C4—154no—
480C4⋊C4—154no—
481C4⋊C4—158no—
482C4⋊C4—158no—
483C4⋊C4C22×D1514yes—
484C4⋊C4C22×D1518yes—
485C22⋊C4—154no—
486C22⋊C4—154no—
487C22⋊C4—158no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4—158no—
492C42—154no—
493C42C22×D1514yes—
494C42C22×D1518yes—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3C2×#70912yes—
497C22×C3#414712yes—
498C22×C3#414912yes—
499C22×C3C24×D511yescharacteristic
500C2×D3—102no—
501C2×D3—104no—
502C2×D3—102no—
503C2×D3—104no—
504C2×D3—104no—
505C2×D3—102no—
506C2×D3—204no—
507C2×D3—208no—
508C3×C4—24no—
509C3×C4—22no—
510C3×C4—24no—
511C3×C4—22no—
512C3×C4C2×#70914yes—
513Dic3—102no—
514Dic3—102no—
515Dic3—102no—
516Dic3—104no—
517C2×C5#558214yescomplemented
518C2×C5C22×#23511yescharacteristic
519C2×C5C2×#100711yescharacteristic
520C2×C5C2×#100911yescharacteristic
521D5—122no—
522D5—124no—
523C23—152no—
524C23—154no—
525C23—302no—
526C23—304no—
527C23—302no—
528C23—304no—
529C23—304no—
530C23—302no—
531C23C23×D1511yescharacteristic
532Q8—28no—
533Q8—608no—
534D4—308no—
535D4—608no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—152no—
541C2×C4—152no—
542C2×C4—152no—
543C2×C4—154no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—304no—
547C2×C4—302no—
548C2×C4—308no—
549C2×C4—608no—
550C2×C4#681714yes—
551C2×C4C23×D1512yes—
552C2×C4C23×D1514yes—
553C2×C4C23×D1512yes—
554C2×C4C23×D1514yes—
555C2×C4C23×D1512yes—
556C2×C3#6591614yescomplemented
557C2×C3C22×#70911yescharacteristic
558C2×C3C2×#414711yescharacteristic
559C2×C3C2×#414911yescharacteristic
560D3—202no—
561D3—204no—
562C5C2×#558211yescharacteristic, complemented, Sylow
563C22—302no—
564C22—304no—
565C22—302no—
566C22—304no—
567C22—304no—
568C22—302no—
569C22—604no—
570C22—608no—
571C22C2×#681712yes—
572C22#9209812yes—
573C22#9210012yes—
574C22C24×D1511yescharacteristic
575C4—24no—
576C4—22no—
577C4—22no—
578C4—24no—
579C4—302no—
580C4—302no—
581C4—304no—
582C4—302no—
583C4C2×#681714yes—
584C3C2×#6591611yescharacteristic, complemented, Sylow
585C2—602no—
586C2—604no—
587C2#1175634114yesdirect product factor
588C2C22×#681711yescharacteristic
589C2C2×#9209811yescharacteristic
590C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
prime radicalC2×#91784C2
hypercenterC2×C4×Q8D15
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
2. C2×#91836C2semidirect
3. C2×#91835C2semidirect
4. #11756341C2direct (N × H)
5. C2×#91785C2semidirect
7. C2×#91783C2semidirect
8. C2×#91777C2semidirect
9. C2×#91765C2semidirect
10. C2×#91764C2semidirect
11. C2×C4×D60C2semidirect
12. C2×#91761C2semidirect
20. C3×C4×C5×Q8C22semidirect
25. #91836C22semidirect
26. #91835C22semidirect
40. #91785C22semidirect
42. #91783C22semidirect
43. #91777C22semidirect
44. #91765C22semidirect
45. #91764C22semidirect
46. C4×D60C22semidirect
47. #91761C22semidirect
49. C2×C4×C5×Q8D3semidirect
101. C2×C3×C4×Q8D5semidirect
119. C4×C5×Q8C2×D3semidirect
187. C3×C4×Q8C2×D5semidirect
264. C2×C4×Q8D15semidirect
375. C4×Q8C2×D15semidirect
395. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
517. C2×C5#5582semidirect
556. C2×C3#65916semidirect
562. C5C2×#5582semidirect
584. C3C2×#65916semidirect
587. C2#11756341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
C2×#918362
C2×#918352
#117563412
C2×#917852
C2×#917842
C2×#917832
C2×#917772
C2×#917652
C2×#917642
C2×C4×D602
C2×#917612
C2×#659163
C2×#55825