Finite Group Databasebeta

← #14424134

Subgroups — #14424134

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic
2C3×D5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#91515C212yesmaximal, complemented
4#11751147C211yesmaximal, characteristic, complemented
5C5×#5050C211yesmaximal, characteristic, complemented
6#11749406C212yesmaximal, complemented
7#11748559C211yesmaximal, characteristic, complemented
8#11748551C211yesmaximal, characteristic, complemented
9#11748499C211yesmaximal, characteristic, complemented
10#11747513C212yesmaximal, complemented
11#11747500C212yesmaximal, complemented
12#10611915—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×Q8×D5C2211yescharacteristic, complemented
16C22×C3×C4×D5C2211yescharacteristic
17C22×#1202—21no—
18C22×#1200—21no—
19C2×#6773—21no—
20C2×#6773—21no—
21C2×#6773—28no—
22C2×#6773C2212yes—
23C2×#6773C2212yes—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C2×#6717C2212yescomplemented
26C2×C5×#216C2212yescomplemented
27C3×#4092C2211yescharacteristic, complemented
28C3×#4070C2211yescharacteristic
29C3×#4043C2211yescharacteristic, complemented
30C3×#4042—21no—
31C3×D5×C4⋊C4—21no—
32C3×D5×C4⋊C4C2211yescharacteristic, complemented
33C3×D5×C22⋊C4—21no—
34C3×#4024—21no—
35#91515—28no—
36C2×#6661C2212yescomplemented
37C2×#6658C2212yescomplemented
38C2×#6649C2212yescomplemented
39#91114C2211yescharacteristic
40#91093C2212yescomplemented
41C5×#830C2211yescharacteristic
42C5×#810C2212yescomplemented
43#90972C2212yescomplemented
44#90968C2212yescomplemented
45#90955C2212yescomplemented
46#82735—51nomaximal, Hall
47C22×#713—31no—
48C2×#4064—32no—
49D5×C22⋊Q8D311yescharacteristic, complemented
50C5×#451—31no—
51#65517—31no—
52#65476—32no—
53#65335—31no—
54#65099—32no—
55#65092—32no—
56#65020—31no—
57#65015—31no—
58C23×D15—21no—
59C23×C3×D5D411yescharacteristic
60C2×C3×C5×Q8C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C2×D60—21no—
63C2×D60—24no—
64C2×D60C2312yes—
65C22×C5×Dic3—21no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6—24no—
68C2×C5×Dic6C2312yes—
69C22×C3×Dic5D411yescharacteristic
70C3×Q8×D5—24no—
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5D411yescharacteristic
75C2×C3×C4×D5D411yescharacteristic
76C2×C3×C4×D5C2311yescharacteristic
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×Dic10—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—28no—
81C2×#1202—22no—
82C2×#1202—22no—
83C2×#1200—28no—
84C2×#1200—22no—
85C2×#1200—22no—
86#6773—28no—
87#6773—28no—
88#6773—24no—
89#6773—24no—
90#6773—24no—
91#6773D418yes—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95#6717—24no—
96C2×C3⋊#168C2312yes—
97C5×#216—24no—
98C2×C5×C3⋊C8C2312yes—
99C3×C22⋊Dic5—21no—
100C3×#685—21no—
101C3×#685—21no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5C2311yescharacteristic
104C3×#683—21no—
105C3×#683—21no—
106C3×#683—21no—
107#6661—24no—
108#6658—24no—
109#6649—24no—
110C22×#235—51no—
111C2×C3×C22⋊Q8—51no—
112C2×#942—52no—
113#5207—51no—
114#5050—51no—
115#5050D511yescharacteristic, complemented
116#5047—52no—
117#5047—52no—
118#5046—51no—
119#5046—51no—
120#4966—52no—
121C22×C5×Q8—31no—
122C2×#713—32no—
123C2×#713—32no—
124C2×#713—68no—
125C2×#713—61no—
126C2×#713—61no—
127C2×Q8×D5C2×D311yescharacteristic, complemented
128C22×D20—31no—
129C22×D20—61no—
130C22×C4×D5—61no—
131C22×C4×D5C2×D311yescharacteristic
132C2×C5×Q16—32no—
133C5×C22⋊Q8C2×D311yescharacteristic
134#4092C2×D311yescharacteristic, complemented
135C2×#689—32no—
136C2×#688—32no—
137#4070C2×D311yescharacteristic
138#4064—68no—
139C2×#677—32no—
140C2×#676—32no—
141#4043C2×D311yescharacteristic, complemented
142#4042—21no—
143D5×C4⋊C4—21no—
144D5×C4⋊C4C2×D311yescharacteristic, complemented
145D5×C22⋊C4—21no—
146#4024—21no—
147C5×#103—32no—
148C5×C22⋊C8—31no—
149#3967—32no—
150C22⋊#168—31no—
151#3953—32no—
152#3952—32no—
153#3941—32no—
154#3007—151noSylow
155C23×C3×C5C2×D411yescharacteristic
156C22×D15—24no—
157C22×D15—22no—
158C22×D15—42no—
159C22×D15—42no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—41no—
163C22×C3×D5C2×D411yescharacteristic
164C22×C3×D5C2×D411yescharacteristic
165C3×C5×Q8—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2411yescharacteristic
171D60—24no—
172D60—22no—
173D60C2×D414yes—
174C2×C5×Dic3—24no—
175C2×C5×Dic3—22no—
176C5×Dic6—24no—
177C5×Dic6—22no—
178C5×Dic6C2×D414yes—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5—21no—
182C2×C3×Dic5C2×D411yescharacteristic
183C2×C3×Dic5C2×D411yescharacteristic
184C3×C4×D5—22no—
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×C4×D5—42no—
188C3×C4×D5—42no—
189C3×C4×D5C2×D414yes—
190C3×Dic10—22no—
191C3×Dic10—42no—
192#1202—28no—
193#1202—28no—
194#1200—28no—
195#1200—28no—
196C3⋊#168—22no—
197C5×C3⋊C8—22no—
198C22×C3×Q8—51no—
199C23×C3×C4—51no—
200C22×#67—101no—
201C2×#235—52no—
202C2×#235—52no—
203C2×#235—108no—
204C2×#235—101no—
205C2×#235—101no—
206C22×D12—51no—
207C22×C4×D3—101no—
208C22×Dic6C2×D511yescharacteristic
209C3×C22⋊Q8—51no—
210C3×C22⋊Q8—51no—
211C3×C22⋊Q8—51no—
212C3×C22⋊Q8—101no—
213C3×C22⋊Q8—101no—
214C3×C22⋊Q8C2×D511yescharacteristic
215C2×C3×C4⋊C4—51no—
216C2×C3×C4⋊C4—101no—
217C2×C3×C22⋊C4—101no—
218C2×#216—52no—
219C2×#216C2×D512yescomplemented
220#942—108no—
221C2×#215—52no—
222C2×#215—52no—
223C2×#208—52no—
224#830—51no—
225#830—52no—
226#830C2×D511yescharacteristic
227#810—52no—
228#810C2×D512yescomplemented
229#809—52no—
230#809—52no—
231C23×D5—61no—
232C23×D5#6711yescharacteristic
233C2×C5×Q8—32no—
234C2×C5×Q8—64no—
235C2×C5×Q8—61no—
236C2×C5×Q8C22×D311yescharacteristic
237C22×C4×C5—61no—
238C22×C4×C5C22×D311yescharacteristic
239C22×Dic5#6711yescharacteristic
240#713—38no—
241#713—64no—
242#713—64no—
243#713—68no—
244#713—68no—
245#713—64no—
246Q8×D5—24no—
247C2×D20—32no—
248C2×D20—64no—
249C2×D20—68no—
250C2×D20—62no—
251C2×D20—62no—
252C2×D20—61no—
253C2×C4×D5—24no—
254C2×C4×D5—21no—
255C2×C4×D5—21no—
256C2×C4×D5—68no—
257C2×C4×D5—62no—
258C2×C4×D5—62no—
259C2×C4×D5#6711yescharacteristic
260C2×C4×D5#6711yescharacteristic
261C2×C4×D5C22×D311yescharacteristic
262C2×C4×D5C22×D311yescharacteristic
263C2×Dic10—21no—
264C2×Dic10C22×D311yescharacteristic
265C5×Q16—64no—
266C2×C5×C8—32no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4C22×D311yescharacteristic
269C5×C22⋊C4—21no—
270C22⋊Dic5—21no—
271#689—64no—
272#688—64no—
273#685—21no—
274#685—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5C22×D311yescharacteristic
277#683—21no—
278#683—21no—
279#683—21no—
280C2×#168—32no—
281#677—64no—
282#676—64no—
283C22×#41—151no—
284C2×#137—152no—
285C2×C22⋊Q8—51no—
286#452—152no—
287#452—152no—
288#451—31no—
289#451—151no—
290#450—151no—
291#450—151no—
292#417—152no—
293#407—151no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5#13712yescomplemented
297C22×C3×C5C22×D411yescharacteristic
298C2×D15—24no—
299C2×D15—48no—
300C2×D15—42no—
301C2×D15—42no—
302C2×C3×D5—21no—
303C2×C3×D5—21no—
304C2×C3×D5—21no—
305C2×C3×D5—21no—
306C2×C3×D5—21no—
307C2×C3×D5—44no—
308C2×C3×D5#12012yes—
309C3×C4×C5—21no—
310C3×C4×C5—41no—
311C3×C4×C5—41no—
312C3×C4×C5C22×D412yes—
313C3×Dic5—21no—
314C3×Dic5—41no—
315C3×Dic5—41no—
316C3×Dic5#12012yes—
317C5×Dic3—24no—
318C24×C3—51no—
319C23×D3—101no—
320C2×C3×Q8—51no—
321C2×C3×Q8—101no—
322C2×C3×Q8—104no—
323C2×C3×Q8C22×D511yescharacteristic
324C22×C3×C4—51no—
325C22×C3×C4—51no—
326C22×C3×C4—51no—
327C22×C3×C4—51no—
328C22×C3×C4—51no—
329C22×C3×C4—104no—
330C22×C3×C4—101no—
331C22×C3×C4—101no—
332C22×C3×C4C22×D511yescharacteristic
333C2×#67—102no—
334C2×#67—102no—
335C2×#67—108no—
336C22×Dic3—21no—
337#235—58no—
338#235—104no—
339#235—104no—
340#235—108no—
341#235—108no—
342#235—104no—
343C2×D12—52no—
344C2×D12—104no—
345C2×D12—101no—
346C2×C4×D3—102no—
347C2×C4×D3—102no—
348C2×C4×D3—108no—
349C2×Dic6—21no—
350C2×Dic6—24no—
351C2×Dic6C22×D512yes—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4—101no—
358C3×C4⋊C4C22×D511yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—101no—
361C3×C22⋊C4—101no—
362C3×C22⋊C4—101no—
363#216—24no—
364#216—104no—
365#215—104no—
366#215—104no—
367#208—104no—
368C2×C3⋊C8—52no—
369C2×C3⋊C8C22×D512yes—
370C23×C5C2×#6711yescharacteristic
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—41no—
374C22×D5—64no—
375C22×D5—62no—
376C22×D5—122no—
377C22×D5—122no—
378C22×D5C2×#6711yescharacteristic
379C22×D5C2×#6711yescharacteristic
380C5×Q8—22no—
381C5×Q8—34no—
382C5×Q8—64no—
383C5×Q8—62no—
384C2×C4×C5—22no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—64no—
388C2×C4×C5—62no—
389C2×C4×C5C2×#6711yescharacteristic
390C2×C4×C5C23×D311yescharacteristic
391C2×Dic5—22no—
392C2×Dic5—21no—
393C2×Dic5—21no—
394C2×Dic5C2×#6711yescharacteristic
395C2×Dic5C2×#6711yescharacteristic
396D20—34no—
397D20—64no—
398D20—68no—
399D20—68no—
400D20—62no—
401C4×D5—22no—
402C4×D5—22no—
403C4×D5—22no—
404C4×D5—42no—
405C4×D5—42no—
406C4×D5—68no—
407C4×D5—68no—
408C4×D5D3×D414yes—
409Dic10—22no—
410Dic10—42no—
411C5×C8—62no—
412#168—62no—
413C2×#41—152no—
414C2×#41—152no—
415C2×#41—301no—
416C2×#41—301no—
417C2×#41—308no—
418C22×Q8—31no—
419C22×Q8—51no—
420C22×D4—151no—
421C22×D4—301no—
422C23×C4—51no—
423C23×C4—301no—
424#137—308no—
425C2×Q16—32no—
426C2×Q16—152no—
427C2×SD16—152no—
428C2×SD16—152no—
429C2×M16—152no—
430C22⋊Q8—51no—
431C22⋊Q8—51no—
432C22⋊Q8—51no—
433C22⋊Q8—101no—
434C22⋊Q8—101no—
435C22⋊Q8D3×D511yescharacteristic
436C2×C4⋊C4—51no—
437C2×C4⋊C4—101no—
438C2×C22⋊C4—101no—
439#103—32no—
440#103—152no—
441#102—152no—
442#102—152no—
443C22⋊C8—31no—
444C22⋊C8—152no—
445C22⋊C8—151no—
446C2×C3×C5—22no—
447C2×C3×C5C2×#12011yescharacteristic
448C2×C3×C5C2×#13711yescharacteristic
449C2×C3×C5#57511yescharacteristic
450D15—44no—
451C3×D5—22no—
452C3×D5—41no—
453C23×C3—51no—
454C23×C3—51no—
455C23×C3—102no—
456C23×C3—102no—
457C23×C3—201no—
458C23×C3D4×D511yescharacteristic
459C22×D3—104no—
460C22×D3—102no—
461C22×D3—202no—
462C22×D3—202no—
463C3×Q8—22no—
464C3×Q8—102no—
465C3×Q8—202no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—51no—
470C2×C3×C4—54no—
471C2×C3×C4—51no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—101no—
477C2×C3×C4—101no—
478C2×C3×C4—202no—
479C2×C3×C4—202no—
480C2×C3×C4D4×D511yescharacteristic
481C2×C3×C4C23×D511yescharacteristic
482#67—108no—
483#67—108no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486D12—54no—
487D12—104no—
488D12—102no—
489C4×D3—108no—
490C4×D3—108no—
491Dic6—24no—
492Dic6—22no—
493Dic6D4×D514yes—
494C3⋊C8—22no—
495C3⋊C8—102no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5#94212yescomplemented
499C22×C5C22×#6711yescharacteristic
500C2×D5—21no—
501C2×D5—21no—
502C2×D5—21no—
503C2×D5—21no—
504C2×D5—21no—
505C2×D5—44no—
506C2×D5—64no—
507C2×D5—128no—
508C2×D5—122no—
509C2×D5—122no—
510C2×D5#93712yes—
511C4×C5—21no—
512C4×C5—41no—
513C4×C5—41no—
514C4×C5—64no—
515C4×C5C2×D3×D412yes—
516Dic5—21no—
517Dic5—41no—
518Dic5—41no—
519Dic5#93712yes—
520C24—51no—
521C24—301no—
522#41—158no—
523#41—304no—
524#41—304no—
525#41—304no—
526#41—308no—
527#41—308no—
528C2×Q8—32no—
529C2×Q8—51no—
530C2×Q8—64no—
531C2×Q8—61no—
532C2×Q8—101no—
533C2×Q8—104no—
534C2×Q8C2×D3×D511yescharacteristic
535C2×D4—152no—
536C2×D4—304no—
537C2×D4—302no—
538C2×D4—302no—
539C2×D4—308no—
540C2×D4—301no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—61no—
547C22×C4—104no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—302no—
551C22×C4—302no—
552C22×C4—308no—
553C22×C4C2×D3×D511yescharacteristic
554Q16—64no—
555Q16—304no—
556SD16—304no—
557SD16—304no—
558M16—304no—
559C2×C8—32no—
560C2×C8—152no—
561C4⋊C4—21no—
562C4⋊C4—51no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4C2×D3×D511yescharacteristic
568C22⋊C4—21no—
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4—101no—
572C3×C5#300711yescharacteristic, complemented, Hall
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—52no—
576C22×C3—101no—
577C22×C3—101no—
578C22×C3—101no—
579C22×C3—101no—
580C22×C3—101no—
581C22×C3—204no—
582C22×C3#406412yescomplemented
583C22×C3C2×D4×D511yescharacteristic
584C2×D3—104no—
585C2×D3—208no—
586C2×D3—202no—
587C2×D3—202no—
588C3×C4—21no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—52no—
592C3×C4—101no—
593C3×C4—201no—
594C3×C4—201no—
595C3×C4C2×D4×D512yes—
596Dic3—24no—
597C2×C5—22no—
598C2×C5C2×#93711yescharacteristic
599C2×C5C2×#94211yescharacteristic
600C2×C5#582211yescharacteristic
601D5—22no—
602D5—41no—
603D5—124no—
604C23—51no—
605C23—51no—
606C23—102no—
607C23—102no—
608C23—201no—
609C23—304no—
610C23—302no—
611C23—602no—
612C23—602no—
613C23D5×#6711yescharacteristic
614Q8—22no—
615Q8—34no—
616Q8—64no—
617Q8—62no—
618Q8—102no—
619Q8—202no—
620D4—154no—
621D4—304no—
622D4—308no—
623D4—308no—
624D4—302no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—51no—
629C2×C4—54no—
630C2×C4—51no—
631C2×C4—64no—
632C2×C4—62no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—202no—
640C2×C4—202no—
641C2×C4—308no—
642C2×C4—308no—
643C2×C4D5×#6711yescharacteristic
644C2×C4C22×D3×D511yescharacteristic
645C8—62no—
646C8—302no—
647C2×C3—22no—
648C2×C3—102no—
649C2×C3—201no—
650C2×C3D5×#12011yescharacteristic
651C2×C3C2×#406411yescharacteristic
652C2×C3#6611111yescharacteristic
653D3—204no—
654C5#8273511yescharacteristic, complemented, Sylow
655C22—21no—
656C22—21no—
657C22—52no—
658C22—101no—
659C22—101no—
660C22—101no—
661C22—101no—
662C22—101no—
663C22—204no—
664C22—304no—
665C22—608no—
666C22—602no—
667C22—602no—
668C22#9151512yescomplemented
669C22C2×D5×#6711yescharacteristic
670C4—21no—
671C4—41no—
672C4—41no—
673C4—52no—
674C4—64no—
675C4—101no—
676C4—201no—
677C4—201no—
678C4D3×D4×D512yes—
679C3#1061191511yescharacteristic, complemented, Sylow
680C2—22no—
681C2—102no—
682C2—201no—
683C2—604no—
684C2D5×#93711yescharacteristic
685C2C2×#9151511yescharacteristic
686C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×#6773C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C22⋊Q8C2semidirect
3. C2×#91515C2semidirect
4. #11751147C2semidirect
5. C5×#5050C2semidirect
6. #11749406C2semidirect
7. #11748559C2semidirect
8. #11748551C2semidirect
9. #11748499C2semidirect
10. #11747513C2semidirect
11. #11747500C2semidirect
15. C2×C3×Q8×D5C22semidirect
25. C2×#6717C22semidirect
26. C2×C5×#216C22semidirect
27. C3×#4092C22semidirect
29. C3×#4043C22semidirect
32. C3×D5×C4⋊C4C22semidirect
36. C2×#6661C22semidirect
37. C2×#6658C22semidirect
38. C2×#6649C22semidirect
40. #91093C22semidirect
42. C5×#810C22semidirect
43. #90972C22semidirect
44. #90968C22semidirect
45. #90955C22semidirect
49. D5×C22⋊Q8D3semidirect
115. #5050D5semidirect
127. C2×Q8×D5C2×D3semidirect
134. #4092C2×D3semidirect
141. #4043C2×D3semidirect
144. D5×C4⋊C4C2×D3semidirect
219. C2×#216C2×D5semidirect
228. #810C2×D5semidirect
296. C22×C3×C5#137semidirect
498. C22×C5#942semidirect
572. C3×C5#3007semidirect
582. C22×C3#4064semidirect
654. C5#82735semidirect
668. C22#91515semidirect
679. C3#10611915semidirect

Maximal subgroups

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

subgroupindex
C22×#67732
C3×D5×C22⋊Q82
C2×#915152
#117511472
C5×#50502
#117494062
#117485592
#117485512
#117484992
#117475132
#117475002
#106119153
#827355