Finite Group Databasebeta

← C2×#11756383 #14479795

Subgroups — C2×#11756383 #14479795

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#91836C211yesmaximal, characteristic, complemented
3C2×Q8×Dic15C211yesmaximal, characteristic, complemented
4C2×#91819C211yesmaximal, characteristic
5C22×C4×Dic15C211yesmaximal, characteristic, complemented
6#11756383C2116yesmaximal, direct product factor
7C2×#91787C212yesmaximal, complemented
8C2×#91782C211yesmaximal, characteristic, complemented
9C2×#91781C212yesmaximal, complemented
10C2×#91779C211yesmaximal, characteristic, complemented
11C2×#91775C212yesmaximal, complemented
12C2×#91770C212yesmaximal, complemented
13C2×#65958—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×#1220C2212yes—
17C23×Dic15C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2212yes—
21C3×C5×C22⋊Q8C2218yescomplemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25#91836C2218yescomplemented
26Q8×Dic15C2218yescomplemented
27#91819C2218yes—
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×#6714C2212yes—
31C2×#6714C2212yes—
32C2×C4⋊Dic15C2211yescharacteristic
33C2×C4⋊Dic15C2212yes—
34C2×C4⋊Dic15C2212yes—
35C2×#6712C2212yes—
36C2×C4×Dic15C2212yes—
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2218yescomplemented
42#91787C22116yescomplemented
43#91782C2218yescomplemented
44#91781C22116yescomplemented
45#91779C2218yescomplemented
46#91775C22116yescomplemented
47#91770C22116yescomplemented
48C2×#5624—51nomaximal, Hall
49C2×C5×C22⋊Q8D311yescharacteristic, complemented
50C2×#4093—31no—
51C2×Q8×Dic5—31no—
52C2×#4076—31no—
53C22×C4×Dic5—31no—
54#65958—316no—
55C2×#4044—32no—
56C2×#4039—31no—
57C2×#4038—32no—
58C2×#4036—31no—
59C2×#4032—32no—
60C2×#4027—32no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C2×C3×C5×Q8—24no—
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5—24no—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2314yes—
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2311yescharacteristic
71C2×#1220—28no—
72C2×#1220C2318yes—
73C22×Dic15—24no—
74C22×Dic15—24no—
75C22×Dic15C2314yes—
76C22×Dic15C2314yes—
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2312yes—
81C22×Dic15C2311yescharacteristic
82C2×D60—24no—
83C2×D60C2314yes—
84C2×C4×D15—28no—
85C2×C4×D15C2318yes—
86C3×C5×C4⋊C4C2314yes—
87C3×C5×C4⋊C4C2318yes—
88C3×C5×C22⋊C4C2318yes—
89#6714C2318yes—
90#6714C2318yes—
91#6714C2318yes—
92#6714C2318yes—
93C4⋊Dic15C2318yes—
94C4⋊Dic15C2318yes—
95C4⋊Dic15C2314yes—
96#6712C2318yes—
97C4×Dic15C2318yes—
98C4×Dic15C2314yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C4×Dic15C2314yes—
102C2×C3×C22⋊Q8D511yescharacteristic, complemented
103C2×#947—51no—
104C2×Q8×Dic3—51no—
105C2×#930—51no—
106C22×C4×Dic3—51no—
107#5624—516no—
108C2×#898—52no—
109C2×#893—51no—
110C2×#892—52no—
111C2×#890—51no—
112C2×#886—52no—
113C2×#67⋊C4—52no—
114C22×C5×Q8C2×D311yescharacteristic
115C23×C4×C5C2×D311yescharacteristic
116C22×C22⋊D5—32no—
117C23×Dic5—31no—
118C23×Dic5—31no—
119C22×D20—31no—
120C22×C4×D5—32no—
121C5×C22⋊Q8C2×D318yescomplemented
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C5×C4⋊C4C2×D312yes—
124C2×C5×C22⋊C4C2×D312yes—
125#4093—38no—
126Q8×Dic5—38no—
127#4076—38no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5—32no—
134C2×C4⋊Dic5—31no—
135C2×#683—32no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—38no—
142#4044—316no—
143#4039—38no—
144#4038—316no—
145#4036—38no—
146#4032—316no—
147#4027—316no—
148C2×#529—151noSylow
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5#4114yes—
152C23×C3×C5C2412yes—
153C23×C3×C5C2411yescharacteristic
154C22×D15—24no—
155C22×D15—24no—
156C22×D15—24no—
157C22×D15C2414yes—
158C3×C5×Q8—28no—
159C2×C3×C4×C5—24no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—24no—
162C2×C3×C4×C5—28no—
163C2×C3×C4×C5#4114yes—
164C2×C3×C4×C5C2412yes—
165C2×C3×C4×C5C2414yes—
166C2×C3×C4×C5C2414yes—
167C2×C3×C4×C5C2412yes—
168#1220—216no—
169C2×Dic15—28no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15—24no—
174C2×Dic15—28no—
175C2×Dic15#4114yes—
176C2×Dic15C2412yes—
177C2×Dic15C2412yes—
178C2×Dic15C2412yes—
179C2×Dic15C2414yes—
180C2×Dic15C2412yes—
181D60—28no—
182C4×D15—216no—
183C22×C3×Q8C2×D511yescharacteristic
184C23×C3×C4C2×D511yescharacteristic
185C22×#67—52no—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C22×D12—51no—
189C22×C4×D3—52no—
190C3×C22⋊Q8C2×D518yescomplemented
191C2×C3×C4⋊C4C2×D511yescharacteristic
192C2×C3×C4⋊C4C2×D512yes—
193C2×C3×C22⋊C4C2×D512yes—
194#947—58no—
195Q8×Dic3—58no—
196#930—58no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—52no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3—51no—
204C2×Dic3⋊C4—52no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3—51no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—58no—
211#898—516no—
212#893—58no—
213#892—516no—
214#890—58no—
215#886—516no—
216#67⋊C4—516no—
217C24×C5C22×D311yescharacteristic
218C23×D5—32no—
219C2×C5×Q8—24no—
220C2×C5×Q8C22×D314yes—
221C22×C4×C5—24no—
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D312yes—
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D314yes—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—38no—
228C2×C22⋊D5—68no—
229C22×Dic5—31no—
230C22×Dic5—34no—
231C22×Dic5—34no—
232C22×Dic5—31no—
233C22×Dic5—31no—
234C22×Dic5—31no—
235C22×Dic5—32no—
236C22×Dic5—64no—
237C22×Dic5—64no—
238C2×D20—34no—
239C2×D20—64no—
240C2×C4×D5—38no—
241C2×C4×D5—68no—
242C5×C4⋊C4C22×D314yes—
243C5×C4⋊C4C22×D318yes—
244C5×C22⋊C4C22×D318yes—
245#685—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249C4⋊Dic5—38no—
250C4⋊Dic5—38no—
251C4⋊Dic5—34no—
252#683—38no—
253C4×Dic5—38no—
254C4×Dic5—34no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5—34no—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8D1511yescharacteristic, complemented
264C2×#121—151no—
265C2×C4×Q8—151no—
266C2×C4×D4—151no—
267C2×C4×D4—152no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5—28no—
271C22×C3×C5—22no—
272C22×C3×C5—22no—
273C22×C3×C5C2×#4112yes—
274C22×C3×C5C2×#4114yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5C2511yescharacteristic
278C2×D15—24no—
279C2×D15—24no—
280C2×D15—24no—
281C2×D15—48no—
282C3×C4×C5—24no—
283C3×C4×C5—22no—
284C3×C4×C5—24no—
285C3×C4×C5C2×#4114yes—
286Dic15—22no—
287Dic15—22no—
288Dic15—22no—
289Dic15—24no—
290Dic15C2×#4114yes—
291C24×C3C22×D511yescharacteristic
292C23×D3—52no—
293C2×C3×Q8—24no—
294C2×C3×Q8C22×D514yes—
295C22×C3×C4—24no—
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D514yes—
298C22×C3×C4C22×D512yes—
299C22×C3×C4C22×D512yes—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—58no—
302C2×#67—108no—
303C22×Dic3—51no—
304C22×Dic3—54no—
305C22×Dic3—54no—
306C22×Dic3—51no—
307C22×Dic3—51no—
308C22×Dic3—51no—
309C22×Dic3—52no—
310C22×Dic3—104no—
311C22×Dic3—104no—
312C2×D12—54no—
313C2×D12—104no—
314C2×C4×D3—58no—
315C2×C4×D3—108no—
316C3×C4⋊C4C22×D514yes—
317C3×C4⋊C4C22×D518yes—
318C3×C22⋊C4C22×D518yes—
319(C2×D3)⋊C4—58no—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—58no—
324C4⋊Dic3—58no—
325C4⋊Dic3—54no—
326Dic3⋊C4—58no—
327C4×Dic3—58no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5#23914yes—
335C23×C5C23×D312yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—34no—
338C22×D5—64no—
339C22×D5—64no—
340C22×D5—64no—
341C5×Q8—28no—
342C2×C4×C5—22no—
343C2×C4×C5—24no—
344C2×C4×C5—24no—
345C2×C4×C5—28no—
346C2×C4×C5#23714yes—
347C2×C4×C5C23×D312yes—
348C2×C4×C5C23×D314yes—
349C2×C4×C5C23×D314yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5—616no—
352C2×Dic5—34no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—32no—
356C2×Dic5—32no—
357C2×Dic5—34no—
358C2×Dic5—68no—
359C2×Dic5—68no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5—64no—
363C2×Dic5—62no—
364D20—68no—
365C4×D5—616no—
366C22×Q8C2×D1511yescharacteristic
367C22×D4—152no—
368C22×D4—151no—
369C23×C4—151no—
370C23×C4—151no—
371C23×C4—152no—
372C23×C4C2×D1511yescharacteristic
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8C2×D1518yescomplemented
378#121—158no—
379C4×Q8—158no—
380C4×D4—158no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—151no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4C2×D1512yes—
388C2×C4⋊C4C2×D1511yescharacteristic
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4C2×D1512yes—
394C2×C42—151no—
395C2×C42—152no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—151no—
399C2×C42—158no—
400C2×C3×C5—24no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405D15—44no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3#71314yes—
409C23×C3C23×D512yes—
410C23×C3C23×D511yescharacteristic
411C22×D3—54no—
412C22×D3—104no—
413C22×D3—104no—
414C22×D3—104no—
415C3×Q8—28no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—28no—
420C2×C3×C4#71114yes—
421C2×C3×C4C23×D512yes—
422C2×C3×C4C23×D514yes—
423C2×C3×C4C23×D514yes—
424C2×C3×C4C23×D512yes—
425#67—1016no—
426C2×Dic3—54no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—52no—
431C2×Dic3—54no—
432C2×Dic3—108no—
433C2×Dic3—108no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—104no—
437C2×Dic3—102no—
438D12—108no—
439C4×D3—1016no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—28no—
443C22×C5C2×#23712yes—
444C22×C5C2×#23914yes—
445C22×C5C2×#23912yes—
446C22×C5D3×#4112yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—64no—
449C2×D5—64no—
450C2×D5—64no—
451C2×D5—128no—
452C4×C5—22no—
453C4×C5—24no—
454C4×C5—24no—
455C4×C5C2×#23714yes—
456Dic5—34no—
457Dic5—62no—
458Dic5—62no—
459Dic5—64no—
460Dic5—62no—
461C24—152no—
462C24C22×D1511yescharacteristic
463C2×Q8—24no—
464C2×Q8C22×D1514yes—
465C2×D4—158no—
466C2×D4—154no—
467C2×D4—308no—
468C2×D4—304no—
469C22×C4—24no—
470C22×C4—151no—
471C22×C4—154no—
472C22×C4—154no—
473C22×C4—151no—
474C22×C4—151no—
475C22×C4—151no—
476C22×C4—152no—
477C22×C4—158no—
478C22×C4—308no—
479C22×C4—304no—
480C22×C4—304no—
481C22×C4C22×D1514yes—
482C22×C4C22×D1511yescharacteristic
483C22×C4C22×D1512yes—
484C22×C4C22×D1512yes—
485C22×C4C22×D1511yescharacteristic
486C4⋊C4—158no—
487C4⋊C4—158no—
488C4⋊C4—154no—
489C4⋊C4—158no—
490C4⋊C4C22×D1518yes—
491C4⋊C4C22×D1514yes—
492C22⋊C4—158no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4C22×D1518yes—
497C42—154no—
498C42—154no—
499C42—154no—
500C42—154no—
501C42—158no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3C2×#71112yes—
507C22×C3C2×#71314yes—
508C22×C3C2×#71312yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—104no—
512C2×D3—104no—
513C2×D3—104no—
514C2×D3—208no—
515C3×C4—22no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4C2×#71114yes—
519Dic3—54no—
520Dic3—102no—
521Dic3—102no—
522Dic3—104no—
523Dic3—102no—
524C2×C5—24no—
525C2×C5#562414yescomplemented
526C2×C5C22×#23711yescharacteristic
527C2×C5C22×#23911yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529D5—124no—
530C23—22no—
531C23—22no—
532C23—154no—
533C23—304no—
534C23—304no—
535C23—304no—
536C23#682114yes—
537C23C23×D1512yes—
538C23C23×D1511yescharacteristic
539Q8—28no—
540D4—3016no—
541D4—308no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—28no—
546C2×C4—154no—
547C2×C4—152no—
548C2×C4—152no—
549C2×C4—152no—
550C2×C4—152no—
551C2×C4—154no—
552C2×C4—3016no—
553C2×C4—308no—
554C2×C4—308no—
555C2×C4—302no—
556C2×C4—302no—
557C2×C4—304no—
558C2×C4—302no—
559C2×C4#681914yes—
560C2×C4C23×D1512yes—
561C2×C4C23×D1514yes—
562C2×C4C23×D1514yes—
563C2×C4C23×D1512yes—
564C2×C3—24no—
565C2×C3#6595814yescomplemented
566C2×C3C22×#71111yescharacteristic
567C2×C3C22×#71311yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—204no—
570C5C2×#562411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—22no—
573C22—28no—
574C22—304no—
575C22—304no—
576C22—304no—
577C22—608no—
578C22C2×#681912yes—
579C22C2×#682114yes—
580C22C2×#682112yes—
581C22#41×D1512yes—
582C22C24×D1511yescharacteristic
583C4—22no—
584C4—24no—
585C4—24no—
586C4—154no—
587C4—302no—
588C4—302no—
589C4—304no—
590C4—302no—
591C4C2×#681914yes—
592C3C2×#6595811yescharacteristic, complemented, Sylow
593C2—24no—
594C2—604no—
595C2#1175638314yesdirect product factor
596C2C22×#681911yescharacteristic
597C2C22×#682111yescharacteristic
598C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C22⋊Q8C2semidirect
2. C2×#91836C2semidirect
3. C2×Q8×Dic15C2semidirect
5. C22×C4×Dic15C2semidirect
6. #11756383C2direct (N × H)
7. C2×#91787C2semidirect
8. C2×#91782C2semidirect
9. C2×#91781C2semidirect
10. C2×#91779C2semidirect
11. C2×#91775C2semidirect
12. C2×#91770C2semidirect
21. C3×C5×C22⋊Q8C22semidirect
25. #91836C22semidirect
26. Q8×Dic15C22semidirect
41. C2×C4×Dic15C22semidirect
42. #91787C22semidirect
43. #91782C22semidirect
44. #91781C22semidirect
45. #91779C22semidirect
46. #91775C22semidirect
47. #91770C22semidirect
49. C2×C5×C22⋊Q8D3semidirect
102. C2×C3×C22⋊Q8D5semidirect
121. C5×C22⋊Q8C2×D3semidirect
190. C3×C22⋊Q8C2×D5semidirect
263. C2×C22⋊Q8D15semidirect
377. C22⋊Q8C2×D15semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5624semidirect
565. C2×C3#65958semidirect
570. C5C2×#5624semidirect
592. C3C2×#65958semidirect
595. C2#11756383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C2×#918362
C2×Q8×Dic152
C2×#918192
C22×C4×Dic152
#117563832
C2×#917872
C2×#917822
C2×#917812
C2×#917792
C2×#917752
C2×#917702
C2×#659583
C2×#56245