Finite Group Databasebeta

← #14484532

Subgroups — #14484532

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D15C211yesmaximal, characteristic
2C5×#5569C211yesmaximal, characteristic, complemented
3C3×#65903C211yesmaximal, characteristic, complemented
4#11755268C211yesmaximal, characteristic, complemented
5#11755267C211yesmaximal, characteristic, complemented
6Q8×#1200C211yesmaximal, characteristic
7Q8×#1200C211yesmaximal, characteristic
8#11753620C213yesmaximal
9#11753425C213yesmaximal
10#11753318C213yesmaximal, complemented
11#11753313C213yesmaximal, complemented
12#11752631C213yesmaximal
13C4×D15⋊Q8C213yesmaximal
14#11752467C213yesmaximal, complemented
15#11752463C213yesmaximal, complemented
16D5×#557—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×D15⋊Q8C2213yes—
19C3×C4×C5×Q8C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21C4⋊C4×D15C2213yes—
22#91776C2213yes—
23C42×D15C2213yes—
24C4×Dic30C2213yes—
25C5×Q8×Dic3C2211yescharacteristic
26C5×Q8×Dic3C2211yescharacteristic
27C5×#890C2213yes—
28C5×#888C2213yes—
29C5×#870C2213yes—
30C4×C5×Dic6C2213yes—
31C3×Q8×Dic5C2211yescharacteristic
32C3×Q8×Dic5C2211yescharacteristic
33C3×#4036C2213yes—
34C3×#4034C2213yes—
35C3×#4016C2213yes—
36C3×C4×Dic10C2213yes—
37#91469C2213yes—
38#91468C2213yes—
39C4×#1204C2213yes—
40C4×#1204C2213yes—
41#91437C2213yes—
42#91437C2213yes—
43#91437C2213yes—
44#91404C2211yescharacteristic
45#91404C2213yes—
46#91404C2216yes—
47C4×#1200C2213yes—
48C4×#1200C2213yes—
49#91388C2213yes—
50#91384C2213yes—
51#91384C2213yes—
52#91382C2216yes—
53#91382C2216yes—
54#91381C2213yes—
55#91344C2213yes—
56#91340C2213yes—
57#91340C2213yes—
58#91339C2216yes—
59#91336C2216yes—
60#91333C2213yes—
61#91333C2213yes—
62#91331C2213yes—
63#91329C2216yes—
64#91327C2216yes—
65#91325C2213yes—
66#91325C2213yes—
67D3×#557—51nomaximal, Hall
68C5×#557—31no—
69D5×C4⋊Q8—33no—
70#66055—33no—
71D5×#125—33no—
72D5×#125—33no—
73#66019—33no—
74#66019—33no—
75C4×Q8×D5—31no—
76C4×Q8×D5—31no—
77C4×Q8×D5—33no—
78C4×Q8×D5—31no—
79#65904—31no—
80#65903—31no—
81#65903D311yescharacteristic, complemented
82#65901—33no—
83C2×C3×C5×Q8C2311yescharacteristic
84Q8×D15Q818yescomplemented
85C2×C4×D15C2311yescharacteristic
86C2×C4×D15C2313yes—
87C2×C4×D15C2313yes—
88C2×Dic30C2313yes—
89C2×C5×Dic6C2313yes—
90C2×C3×Dic10C2313yes—
91C2×#1204C2313yes—
92C2×#1204C2313yes—
93C2×#1200C2311yescharacteristic
94C2×#1200C2313yes—
95C2×#1200C2313yes—
96C2×#1200C2311yescharacteristic
97D15⋊Q8—212no—
98C3×C5×C4⋊C4C2313yes—
99C3×C42×C5C2313yes—
100C4⋊Dic15C2313yes—
101#6712C2316yes—
102C4×Dic15C2313yes—
103C4×Dic15C2313yes—
104C4×Dic15C2313yes—
105C5×C4⋊Dic3C2313yes—
106C5×C4⋊Dic3C2313yes—
107C5×C4⋊Dic3C2313yes—
108C5×Dic3⋊C4C2311yescharacteristic
109C5×Dic3⋊C4C2313yes—
110C5×Dic3⋊C4C2316yes—
111C4×C5×Dic3C2313yes—
112C4×C5×Dic3C2313yes—
113C3×C4⋊Dic5C2313yes—
114C3×C4⋊Dic5C2313yes—
115C3×C4⋊Dic5C2313yes—
116C3×#683C2311yescharacteristic
117C3×#683C2313yes—
118C3×#683C2316yes—
119C3×C4×Dic5C2313yes—
120C3×C4×Dic5C2313yes—
121Dic3⋊Dic5C2311yescharacteristic
122Dic3⋊Dic5C2313yes—
123Dic3⋊Dic5C2316yes—
124#6669C2313yes—
125#6669C2313yes—
126#6669C2316yes—
127#6669C2316yes—
128#6668C2311yescharacteristic
129#6668C2313yes—
130#6668C2316yes—
131Dic3×Dic5C2313yes—
132Dic3×Dic5C2313yes—
133Dic3×Dic5C2313yes—
134Dic3×Dic5C2313yes—
135C3×#557—51no—
136D3×C4⋊Q8—53no—
137#5721—53no—
138D3×#125—53no—
139D3×#125—53no—
140#5685—53no—
141#5685—53no—
142C4×D3×Q8—51no—
143C4×D3×Q8—51no—
144C4×D3×Q8—51no—
145C4×D3×Q8—53no—
146#5570—51no—
147#5569—51no—
148#5569D511yescharacteristic, complemented
149#5567—53no—
150C2×Q8×D5—31no—
151C2×Q8×D5—33no—
152C5×C4⋊Q8—33no—
153C5×#125—33no—
154C5×#125—33no—
155C4×C5×Q8—31no—
156C4×C5×Q8—31no—
157C4×C5×Q8—33no—
158C4×C5×Q8C2×D311yescharacteristic
159Q8×Dic5—31no—
160Q8×Dic5—33no—
161Q8×Dic5C2×D311yescharacteristic
162Q8×Dic5C2×D311yescharacteristic
163#4090—36no—
164D5×C4⋊C4—33no—
165D5×C4⋊C4—33no—
166D5×C4⋊C4—33no—
167D5×C4⋊C4—33no—
168D5×C4⋊C4—36no—
169D5×C4⋊C4—31no—
170D5×C4⋊C4—33no—
171#4036—33no—
172#4036—33no—
173#4036—33no—
174#4036C2×D313yes—
175#4035—36no—
176#4035—36no—
177#4035—36no—
178#4035—36no—
179#4034—36no—
180#4034—33no—
181#4034C2×D313yes—
182#4033—33no—
183#4033—33no—
184#4033—33no—
185#4033—33no—
186#4033—33no—
187#4033—33no—
188C42×D5—33no—
189C42×D5—33no—
190C42×D5—33no—
191#4016—33no—
192#4016C2×D313yes—
193#4015—33no—
194C4×Dic10—33no—
195C4×Dic10—33no—
196C4×Dic10—33no—
197C4×Dic10—33no—
198C4×Dic10—33no—
199C4×Dic10C2×D313yes—
200C2×#557—151noSylow
201C22×D15C2411yescharacteristic
202C3×C5×Q8C2×Q814yescomplemented
203C2×C3×C4×C5C2411yescharacteristic
204C2×C3×C4×C5C2413yes—
205C2×C3×C4×C5C2413yes—
206C2×Dic15C2411yescharacteristic
207C2×Dic15C2413yes—
208C2×Dic15C2413yes—
209C4×D15—26no—
210C4×D15—22no—
211C4×D15C2×Q8112yes—
212Dic30C2×Q8112yescomplemented
213C2×C5×Dic3C2411yescharacteristic
214C2×C5×Dic3C2413yes—
215C2×C5×Dic3C2413yes—
216C2×C5×Dic3C2411yescharacteristic
217C5×Dic6—26no—
218C2×C3×Dic5C2411yescharacteristic
219C2×C3×Dic5C2413yes—
220C2×C3×Dic5C2413yes—
221C2×C3×Dic5C2411yescharacteristic
222C3×Dic10—26no—
223#1204—26no—
224#1204—26no—
225#1200—26no—
226#1200—22no—
227#1200—26no—
228#1200#4114yes—
229C2×D3×Q8—51no—
230C2×D3×Q8—53no—
231C3×C4⋊Q8—53no—
232C3×#125—53no—
233C3×#125—53no—
234C3×C4×Q8—51no—
235C3×C4×Q8—51no—
236C3×C4×Q8—53no—
237C3×C4×Q8C2×D511yescharacteristic
238Q8×Dic3—51no—
239Q8×Dic3—53no—
240Q8×Dic3C2×D511yescharacteristic
241Q8×Dic3C2×D511yescharacteristic
242#944—56no—
243D3×C4⋊C4—53no—
244D3×C4⋊C4—53no—
245D3×C4⋊C4—53no—
246D3×C4⋊C4—53no—
247D3×C4⋊C4—56no—
248D3×C4⋊C4—53no—
249D3×C4⋊C4—51no—
250#890—53no—
251#890—53no—
252#890—53no—
253#890C2×D513yes—
254#889—56no—
255#889—56no—
256#889—56no—
257#889—56no—
258#888—56no—
259#888—53no—
260#888C2×D513yes—
261#887—53no—
262#887—53no—
263#887—53no—
264#887—53no—
265#887—53no—
266#887—53no—
267C42×D3—53no—
268C42×D3—53no—
269C42×D3—53no—
270#870—53no—
271#870C2×D513yes—
272#869—53no—
273C4×Dic6—53no—
274C4×Dic6—53no—
275C4×Dic6—53no—
276C4×Dic6—53no—
277C4×Dic6—53no—
278C4×Dic6C2×D513yes—
279C2×C5×Q8—33no—
280C2×C5×Q8C22×D311yescharacteristic
281Q8×D5—38no—
282Q8×D5—612no—
283C2×C4×D5—33no—
284C2×C4×D5—31no—
285C2×C4×D5—33no—
286C2×C4×D5—31no—
287C2×C4×D5—33no—
288C2×C4×D5—31no—
289C2×C4×D5—33no—
290C2×Dic10—33no—
291C2×Dic10—33no—
292C2×Dic10—33no—
293C2×Dic10C22×D313yes—
294C5×C4⋊C4—31no—
295C5×C4⋊C4—33no—
296C5×C4⋊C4—33no—
297C5×C4⋊C4—33no—
298C5×C4⋊C4—33no—
299C5×C4⋊C4—36no—
300C5×C4⋊C4C22×D313yes—
301C42×C5—33no—
302C42×C5—33no—
303C42×C5C22×D313yes—
304C4⋊Dic5—33no—
305C4⋊Dic5—31no—
306C4⋊Dic5—33no—
307C4⋊Dic5—36no—
308C4⋊Dic5C22×D313yes—
309C4⋊Dic5C22×D313yes—
310C4⋊Dic5C22×D313yes—
311#683—36no—
312#683—31no—
313#683—33no—
314#683—36no—
315#683—33no—
316#683—36no—
317#683—36no—
318#683—33no—
319#683C22×D311yescharacteristic
320#683C22×D313yes—
321#683C22×D316yes—
322C4×Dic5—33no—
323C4×Dic5—33no—
324C4×Dic5—33no—
325C4×Dic5—33no—
326C4×Dic5—33no—
327C4×Dic5—33no—
328C4×Dic5—33no—
329C4×Dic5C22×D313yes—
330C4×Dic5C22×D313yes—
331#557—31no—
332#557—51no—
333#557—151no—
334#557—151no—
335#557—153no—
336#557—153no—
337#557—153no—
338#557—153no—
339C2×C4⋊Q8—153no—
340C2×#125—153no—
341C2×#125—153no—
342C2×C4×Q8—151no—
343C2×C4×Q8—153no—
344C2×C4×Q8—151no—
345C2×C4×Q8—151no—
346C22×C3×C5C2511yescharacteristic
347C2×D15C22×Q812yes—
348C2×D15C2×#4112yes—
349C2×D152−1+412yes—
350C3×C4×C5—23no—
351C3×C4×C5—21no—
352C3×C4×C5C22×Q816yes—
353Dic15—23no—
354Dic15—21no—
355Dic15C22×Q816yes—
356C3×Dic5—23no—
357C3×Dic5—21no—
358C3×Dic5—23no—
359C3×Dic5C2×#4112yes—
360C5×Dic3—23no—
361C5×Dic3—21no—
362C5×Dic3—23no—
363C5×Dic3C2×#4112yes—
364C2×C3×Q8—53no—
365C2×C3×Q8C22×D511yescharacteristic
366D3×Q8—58no—
367D3×Q8—1012no—
368C2×C4×D3—53no—
369C2×C4×D3—51no—
370C2×C4×D3—51no—
371C2×C4×D3—53no—
372C2×C4×D3—51no—
373C2×C4×D3—53no—
374C2×C4×D3—53no—
375C2×Dic6—53no—
376C2×Dic6—53no—
377C2×Dic6—53no—
378C2×Dic6C22×D513yes—
379C3×C4⋊C4—51no—
380C3×C4⋊C4—53no—
381C3×C4⋊C4—56no—
382C3×C4⋊C4—53no—
383C3×C4⋊C4—53no—
384C3×C4⋊C4—53no—
385C3×C4⋊C4C22×D513yes—
386C3×C42—53no—
387C3×C42—53no—
388C3×C42C22×D513yes—
389C4⋊Dic3—53no—
390C4⋊Dic3—51no—
391C4⋊Dic3—53no—
392C4⋊Dic3—56no—
393C4⋊Dic3C22×D513yes—
394C4⋊Dic3C22×D513yes—
395C4⋊Dic3C22×D513yes—
396Dic3⋊C4—56no—
397Dic3⋊C4—53no—
398Dic3⋊C4—56no—
399Dic3⋊C4—56no—
400Dic3⋊C4—53no—
401Dic3⋊C4—51no—
402Dic3⋊C4—53no—
403Dic3⋊C4—56no—
404Dic3⋊C4C22×D511yescharacteristic
405Dic3⋊C4C22×D513yes—
406Dic3⋊C4C22×D516yes—
407C4×Dic3—53no—
408C4×Dic3—53no—
409C4×Dic3—53no—
410C4×Dic3—53no—
411C4×Dic3—53no—
412C4×Dic3—53no—
413C4×Dic3—53no—
414C4×Dic3C22×D513yes—
415C4×Dic3C22×D513yes—
416C22×D5—31no—
417C5×Q8—66no—
418C5×Q8D3×Q814yescomplemented
419C2×C4×C5—31no—
420C2×C4×C5—31no—
421C2×C4×C5—33no—
422C2×C4×C5—33no—
423C2×C4×C5C23×D311yescharacteristic
424C2×C4×C5C23×D313yes—
425C2×C4×C5C23×D313yes—
426C2×Dic5—33no—
427C2×Dic5—31no—
428C2×Dic5—33no—
429C2×Dic5C23×D311yescharacteristic
430C2×Dic5C23×D313yes—
431C2×Dic5C23×D313yes—
432C2×Dic5C23×D311yescharacteristic
433C4×D5—312no—
434C4×D5—34no—
435C4×D5—62no—
436C4×D5—66no—
437C4×D5—66no—
438C4×D5—62no—
439C4×D5—66no—
440Dic10—26no—
441Dic10—312no—
442Dic10—66no—
443Dic10—66no—
444C22×Q8—153no—
445C22×Q8—151no—
446C4⋊Q8—33no—
447C4⋊Q8—53no—
448C4⋊Q8—153no—
449C4⋊Q8—153no—
450C4⋊Q8—156no—
451C4⋊Q8—156no—
452#125—33no—
453#125—33no—
454#125—53no—
455#125—53no—
456#125—153no—
457#125—153no—
458#125—156no—
459#125—156no—
460#125—156no—
461#125—156no—
462#125—153no—
463#125—153no—
464C4×Q8—31no—
465C4×Q8—31no—
466C4×Q8—33no—
467C4×Q8—51no—
468C4×Q8—51no—
469C4×Q8—53no—
470C4×Q8—153no—
471C4×Q8—153no—
472C4×Q8—153no—
473C4×Q8—153no—
474C4×Q8—153no—
475C4×Q8—153no—
476C4×Q8—153no—
477C4×Q8—153no—
478C4×Q8—153no—
479C4×Q8—153no—
480C4×Q8—151no—
481C4×Q8—153no—
482C4×Q8—153no—
483C4×Q8D3×D511yescharacteristic
484C2×C4⋊C4—151no—
485C2×C4⋊C4—153no—
486C2×C4⋊C4—153no—
487C2×C4⋊C4—153no—
488C2×C4⋊C4—153no—
489C2×C4⋊C4—156no—
490C2×C4⋊C4—153no—
491C2×C42—153no—
492C2×C42—153no—
493C2×C42—153no—
494C2×C3×C5C23×Q811yescharacteristic
495C2×C3×C5C22×#4111yescharacteristic
496C2×C3×C5C2×2−1+411yescharacteristic
497D15#55714yescomplemented
498C22×D3—51no—
499C3×Q8—106no—
500C3×Q8Q8×D514yescomplemented
501C2×C3×C4—51no—
502C2×C3×C4—51no—
503C2×C3×C4—53no—
504C2×C3×C4—53no—
505C2×C3×C4C23×D511yescharacteristic
506C2×C3×C4C23×D513yes—
507C2×C3×C4C23×D513yes—
508C2×Dic3—53no—
509C2×Dic3—51no—
510C2×Dic3—53no—
511C2×Dic3C23×D511yescharacteristic
512C2×Dic3C23×D513yes—
513C2×Dic3C23×D513yes—
514C2×Dic3C23×D511yescharacteristic
515C4×D3—512no—
516C4×D3—54no—
517C4×D3—102no—
518C4×D3—106no—
519C4×D3—106no—
520C4×D3—102no—
521C4×D3—106no—
522Dic6—26no—
523Dic6—512no—
524Dic6—106no—
525Dic6—106no—
526C22×C5C24×D311yescharacteristic
527C2×D5—32no—
528C2×D5—32no—
529C2×D5—32no—
530C4×C5—23no—
531C4×C5—21no—
532C4×C5—32no—
533C4×C5—63no—
534C4×C5—61no—
535C4×C5—63no—
536C4×C5C2×D3×Q816yes—
537Dic5—23no—
538Dic5—21no—
539Dic5—23no—
540Dic5—36no—
541Dic5—63no—
542Dic5—61no—
543Dic5D3×#4112yes—
544C2×Q8—33no—
545C2×Q8—53no—
546C2×Q8—153no—
547C2×Q8—153no—
548C2×Q8—158no—
549C2×Q8—153no—
550C2×Q8—3012no—
551C2×Q8C2×D3×D511yescharacteristic
552C22×C4—151no—
553C22×C4—151no—
554C22×C4—153no—
555C22×C4—153no—
556C22×C4—153no—
557C22×C4—151no—
558C22×C4—153no—
559C4⋊C4—31no—
560C4⋊C4—33no—
561C4⋊C4—33no—
562C4⋊C4—33no—
563C4⋊C4—33no—
564C4⋊C4—36no—
565C4⋊C4—51no—
566C4⋊C4—53no—
567C4⋊C4—53no—
568C4⋊C4—53no—
569C4⋊C4—53no—
570C4⋊C4—56no—
571C4⋊C4—151no—
572C4⋊C4—151no—
573C4⋊C4—153no—
574C4⋊C4—153no—
575C4⋊C4—156no—
576C4⋊C4—153no—
577C4⋊C4—153no—
578C4⋊C4—156no—
579C4⋊C4—156no—
580C4⋊C4—156no—
581C4⋊C4—156no—
582C4⋊C4—153no—
583C4⋊C4C2×D3×D513yes—
584C42—33no—
585C42—33no—
586C42—53no—
587C42—53no—
588C42—153no—
589C42—153no—
590C42—153no—
591C42—153no—
592C42—153no—
593C42—153no—
594C42—153no—
595C42C2×D3×D513yes—
596C3×C5C2×#55711yescharacteristic, complemented, Hall
597C22×C3C24×D511yescharacteristic
598C2×D3—52no—
599C2×D3—52no—
600C2×D3—52no—
601C3×C4—23no—
602C3×C4—21no—
603C3×C4—52no—
604C3×C4—103no—
605C3×C4—101no—
606C3×C4—103no—
607C3×C4C2×Q8×D516yes—
608Dic3—23no—
609Dic3—21no—
610Dic3—23no—
611Dic3—56no—
612Dic3—103no—
613Dic3—101no—
614Dic3D5×#4112yes—
615C2×C5C22×D3×Q811yescharacteristic
616C2×C5C2×D3×#4111yescharacteristic
617C2×C5D3×2−1+411yescharacteristic
618D5—34no—
619C23—151no—
620Q8—66no—
621Q8—106no—
622Q8—1512no—
623Q8—306no—
624Q8—306no—
625Q8D15⋊Q814yescomplemented
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—33no—
629C2×C4—33no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—53no—
633C2×C4—53no—
634C2×C4—154no—
635C2×C4—153no—
636C2×C4—1512no—
637C2×C4—151no—
638C2×C4—153no—
639C2×C4—306no—
640C2×C4—302no—
641C2×C4—306no—
642C2×C4—302no—
643C2×C4—306no—
644C2×C4C22×D3×D511yescharacteristic
645C2×C4C22×D3×D513yes—
646C2×C4C22×D3×D513yes—
647C2×C3C22×Q8×D511yescharacteristic
648C2×C3C2×D5×#4111yescharacteristic
649C2×C3D5×2−1+411yescharacteristic
650D3—54no—
651C5D3×#55711yescharacteristic, complemented, Sylow
652C22—152no—
653C22—152no—
654C22—152no—
655C22C23×D3×D511yescharacteristic
656C4—21no—
657C4—23no—
658C4—32no—
659C4—52no—
660C4—61no—
661C4—63no—
662C4—63no—
663C4—101no—
664C4—103no—
665C4—103no—
666C4—156no—
667C4—301no—
668C4—303no—
669C4C2×D15⋊Q816yes—
670C3D5×#55711yescharacteristic, complemented, Sylow
671C2—154no—
672C2C22×D15⋊Q811yescharacteristic
673C2#1175704711yescharacteristic
674C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC22×D15C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#557
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5569C2semidirect
3. C3×#65903C2semidirect
4. #11755268C2semidirect
5. #11755267C2semidirect
10. #11753318C2semidirect
11. #11753313C2semidirect
14. #11752467C2semidirect
15. #11752463C2semidirect
81. #65903D3semidirect
84. Q8×D15Q8semidirect
148. #5569D5semidirect
202. C3×C5×Q8C2×Q8semidirect
212. Dic30C2×Q8semidirect
418. C5×Q8D3×Q8semidirect
497. D15#557semidirect
500. C3×Q8Q8×D5semidirect
596. C3×C5C2×#557semidirect
625. Q8D15⋊Q8semidirect
651. C5D3×#557semidirect
670. C3D5×#557semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D152
C5×#55692
C3×#659032
#117552682
#117552672
Q8×#12002
#117536202
#117534252
#117533182
#117533132
#117526312
C4×D15⋊Q82
#117524672
#117524632
D5×#5573
D3×#5575